Optimisation of the energy use in a

residential environment

Othman Danoun

Supervisors: Prof. dr. ir. Lieven Vandevelde, dr. ir. Bart Meersman

Counsellor: Dimitar Bozalakov

Master's dissertation submitted in order to obtain the academic degree of Master of Science

in Electromechanical Engineering

Department of Electrical Energy, Systems and Automation

Chair: Prof. dr. ir. Jan Melkebeek

Faculty of Engineering and Architecture

Academic year 2015-2016

Optimisation of the energy use in a

residential environment

Othman Danoun

Supervisors: Prof. dr. ir. Lieven Vandevelde, dr. ir. Bart Meersman

Counsellor: Dimitar Bozalakov

Master's dissertation submitted in order to obtain the academic degree of Master of Science

in Electromechanical Engineering

Department of Electrical Energy, Systems and Automation

Chair: Prof. dr. ir. Jan Melkebeek

Faculty of Engineering and Architecture

Academic year 2015-2016

Preface First of all I want to thank my promoter Bart Meersman for his guidance and good advice during my

master dissertation. His sincere and constructive feedback has been helpful to bring this thesis to a

good end. I also want to thank him for proofreading my dissertation. Secondly, I want to thank

Christof Deckmyn for providing an optimisation example in Matlab. This has helped me a lot in

building my own optimisation model.

Finally, I want to thank my friends and family for the support during my education at the Faculty of

Engineering. I especially want to thank my classmates for the good times inside and outside the

classroom.

Abstract Production and consumption of electricity need to be equal at all times to keep the network

balanced. Conventionally, the production responds to changes in demand but the integration of

renewable energy sources challenges us to think differently. As the integration of renewable sources

grows every day due to the global concern of global warming, the transition towards “generation

drives demand” must be made. A part of the solution is to improve the flexibility of production units

and consumers. Next, storage technology can help to cope with the unbalance between production

and consumption by storing the excess of energy during low consumption and re-use it again during

high consumption and/or low production.

A way to improve the flexibility of consumers is to foresee some kind of control of their consuming

appliances. This can be on a large scale for industrial consumers or on a smaller scale for residential

consumers. This dissertation focuses on residential consumers where the control infrastructure and

logic is located in the residence. So the goal of this work is to optimise the energy use in a residential

environment. We first start with a literature study to obtain a better view of the different

possibilities present. The subject treated here is better known in literature as a Home Energy

Management System (HEMS). As the name says, it manages your energy consumption at home. A

HEMS controls different groups of appliances in a residence. Residential appliances can normally be

divided into four groups, namely the essential appliances, the shiftable appliances, the controllable

appliances and the thermal appliances. Each of these appliances, besides the essential ones because

they provide a necessary value to the members of the house (e.g. lighting), together with a PV –and

storage system form the HEMS.

Secondly an optimisation model for a HEMS is proposed here. An optimisation problem is

characterised by one or more optimisation objectives and need to satisfy a number of constraints.

The optimisation objectives chosen for this dissertation are cost and user’s comfort. There are

several other objectives, like emission and consumption, but the most commonly used ones in

literature is the combination cost and comfort. The constraints are limitations to the operation of the

household appliances that are set due to physical reason or by the residential user. For example the

minimal energy level of the home battery is set to 20% of its capacity such that the anticipated

lifetime is guaranteed.

Finally we end with simulations of three cases and some conclusions drawn from the three case

studies. The last chapter summarises the conclusions and ends with some final remarks based on a

white paper written by the Smart Grid team of Eandis. Eandis is the largest Distribution System

Operator (DSO) of Belgium, so it is interesting to know how they will tackle the problem of a major

change in our energy production and thus distribution.

I

Optimisation of the energy use in a

residential environment Othman Danoun

Supervisors: Prof. dr. ir. Lieven Vandevelde and dr. ir. Bart Meersman

Abstract - Production and consumption of

electricity need to be equal at all times to

keep the network balanced. Conventionally,

the production responds to changes in

demand but the integration of renewable

energy sources challenges us to think

differently. A part of the solution is to

improve the flexibility of residential

consumers. To study the behaviour of

different home appliances and their flexibility

a Home Energy Management System (HEMS)

is proposed in this master dissertation. It

proposes a framework of HEMS including a

grid, PV, a thermal storage tank and a home

energy storage battery. A multi-objective

optimisation algorithm for HEMS is proposed,

which minimizes electricity cost and

maximizes the comfort of the residential user

simultaneously.

Index terms – HEMS, multi-objective

optimisation, optimisation objectives, cost,

user’s comfort, constraints

1. Introduction

Over the past decade renewable energy has

taken a more prominent role in our electrical

energy production. The worldwide concern of

climate change and the limited amount of

primary energy resources left have turned

renewable generation sources such as wind

and solar into an important player on the

energy market. Conventionally, the production

responds to changes in demand but the

integration of renewable energy sources

challenges us to think differently. As the

integration of renewable sources grows every

day, the transition towards “generation drives

demand” must be made.

A way to improve the flexibility of consumers is

to foresee some kind of control of their

consuming appliances. This can be on a large

scale for industrial consumers or on a smaller

scale for residential consumers. This

dissertation focuses on residential consumers

where the control infrastructure and logic is

located in the residence. The subject treated

here is better known in literature as a Home

Energy Management System (HEMS). A HEMS

can consist of four interconnected components

[1]-[4], namely a monitor module, a prediction

module, the control logic unit and the

scheduling module (see Figure 1).

Figure 1: Architecture of a Home Energy

Management System (HEMS).

II

The monitor module monitors the actual

behaviour of the household appliances, the

storage system and the Photovoltaic (PV)

installation. In practice the appliances are

monitored by smart meters that continuously

measure the power consumption over a

certain period. The power production of the PV

is calculated by the prediction module

according to the input data of the monitor

module. These input data are solar radiation

data and environmental variables, such as the

temperature of the PV panels, which can come

from weather forecast or sensors. The

environmental variables are monitored,

because they affect the power output of the PV

panels. The scheduling module contains the

DSM software that computes the optimal

schedule according to the specified

optimisation objectives, e.g. electricity cost and

well-being/comfort, that home owners want to

pursue. After the optimisation procedure, the

control logic unit sends the optimal schedule to

the appliances and directly controls the

shiftable, controllable and thermal appliances.

Dynamic Pricing of electricity is a very

important element in the study of a HEMS. The

variability of electricity generation due to

renewables together with the variable

electricity consumption of households makes it

difficult for the Distribution System Operators

(DSOs) to keep working as before. Of course

this gives uncertainty regarding DSO costs and

revenues. The big challenge in Europe today is

to guarantee the grids stability for any

situation while encouraging the integration of

renewables in a way that is socially and

economically fair. There are several time-based

pricing schemes [5], namely Time of Use (ToU)

scheme, Critical Peak Pricing (CPP) scheme,

Critical Peak Rebate/Peak Time Rebate

(CPR/PTR) scheme, Real Time Pricing (RTP)

scheme and Inclining Block Rate (IBR) scheme.

These pricing schemes are published day

ahead, such that the schedule module can

calculate the optimal schedule for the next

day.

2. System Model

In this section the models for the home

battery, the thermal storage system (Combined

Heat and Power (CHP) unit and thermal

storage tank (TS)), the heat pump (HP) and the

non-interruptible loads, namely the washing

machine (WM), the dishwasher (DW) and the

cloth dryer (CD), will be developed. The

decision vector that is sent by the scheduling

module to the monitor module (see Figure 1) is

written as [4]:

, - (1)

Where

,

- is the power

that is put into or withdrawn from the battery

at every time slot N.

,

- is the

power that is withdrawn or put back into the

grid at every time slot N.

,

- is the working

status of the heat pump at every time slot N.

,

- is the

working status of the combined heat and

power unit at every time slot N.

,

- are the starting

times of the non-interruptible loads, where

WM: Washing machine, DW: Dishwasher, CD:

Cloth dryer.

Note that Pbat and Pgrid are double vectors, SHP

and SCHP are binary vectors, and Tstart is a

discrete vector.

III

2.1 The battery

The HEMS needs to prevent the home energy

storage battery from overcharge and

overdischarge by controlling the State Of

Charge (SOC) within a specified range

[SOCmin,SOCmax], where SOCmin and SOCmax are

the minimum and maximum allowable SOC of

the battery. This constraint is depicted in

equation (2).

The batteries SOC associated with the charge

and discharge of the battery is calculated by

the following equations, respectively [4]:

Where Cbat is the rated battery capacity in kWh,

PBat,tch and PBat,t

disch represent the charging -and

discharging power of the battery at timeslot t,

ηch and ηdisch are the charging -and discharging

efficiency of the battery system.

2.2 The thermal Storage system

As shown in Figure 2 the thermal storage

system consists of the CHP unit and the

thermal storage tank (TS). The CHP unit and

the thermal storage tank will be modeled

together. The HP that satisfies the space

heating demand of the house will be modeled

separately. The natural gas FNG comes in the

ICE of the CHP unit and simultaneously

produces heat QEG and electrical power PCHP.

The heat is recovered in the heat recovery

system and delivered (QCHP) to the thermal

storage tank. This hot water (Qhot water) is then

supplied to the hot water circuit of the

building. The electrical power that the CHP unit

produces is fed to the HP that delivers

Qspace_heating to the building. The excess of

produced electrical power is than supplied to

the grid or battery. If there is less production,

the difference is buffered by the battery, grid

or directly by the PV-system. The user

consumes hot water at approximately 50oC-

60oC. When the temperature of the hot water

exceeds one of these bounds, it gives the

HEMS a signal to start or stop the CHP unit. The

model presented in [4] is used to calculate the

temperature of the hot water inside the

thermal storage tank:

.

/ [

] 0 .

/1

Where and

are the hot water

temperatures (oC) inside the hot water tank in

time slots t and t+1; and

are the

temperatures of the ambient environment and

inlet water in time slot t; C is the equivalent

thermal mass (Wh/K); is the length of a

timeslot in hours; G is the product of the

surface area and thermal resistance of the

thermal storage tank (W/K). , and

are calculated according to the following

equations, respectively:

(W/K)

(K/W)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Figure 2: Schematic diagram of

thermal storage system.

IV

Where is the density of water (1000

kg/m3), is the hot water usage in time slot t

(l/h) and the specific heat capacity of water

(J/kg K). is the rated power of the CHP

unit (kW) and is the status of the CHP

unit in timeslot t (1 = ON, 0 = OFF). and

are the electrical and thermal efficiency of the

CHP unit respectively. In order to ensure the

comfort preference of the user, the CHP unit

should regulate the hot water temperature

within a prespecified range set by the user:

2.3 The Heat Pump (HP)

The model for the space heating/cooling load

developed in [6] is adopted in this dissertation.

In this model, the room temperature is

calculated as

Where and

are the room

temperatures (oC) in time slots t and t+1

respectively; is the length of a time slot;

is the heat gain rate of the house (Wh/h); is

the energy needed to change the temperature

of the air in the room by 1 K (Wh/K); is the

heating capacity of the heat pump unit

(=COP*PHP), PHP is the rated power of the HP

and is the working status of the heat pump

in time slot t (1 = ON, 0 = OFF). Now the room

temperature is expressed as a function of the

working status of the heat pump ( ), the

room temperature can be controlled within a

prespecified range set by the user.

(11)

2.4 The non-interruptible loads

In this dissertation, a washing machine (WM),

dishwasher (DW) and cloth dryer (CD) are

taken as non-interruptible appliances. These

appliances have two statuses, namely ON or

OFF. Once they have turned on, they must

keep working until their task is completed. The

task starting time and the number of time slots

needed for completing the task of each

appliance is set by the user. These appliances

should meet the constraints [4]:

∑

Where * + is the time

slot in which the task of the appliance a is

started; is the number of time slots that

are needed to complete the task of appliance

a.

3. Multi-objective Optimisation of HEMS

3.1 Energy Cost objective.

The overall net energy price over the

scheduling horizon is formulated in equation

(13), which consists of four parts: the first term

represents the overall electricity cost of buying

electricity from the grid, the second term

stands for the overall revenue of selling

electricity to the grid, the third term stands for

the degradation cost of the home energy

storage battery and the last term denotes the

cost of buying natural gas for the CHP unit.

∑ ( )

∑ ( )

∑

∑

(9)

(10)

(12)

(13)

V

(€/kWh) is the electricity price at timeslot

t when the user buys electricity from the grid;

and (€/kWh) is the electricity price at

timeslot t when the user sells electricity to the

grid. Note that ( ) means that

power is withdrawn from the grid and

( ) that power is feed into the

grid. is the battery degradation cost

(€/kWh) and (€/kWh) is the price of

natural gas at timeslot t.

3.2 User’s comfort level objective

In practice a residential user wants to reduce

his energy price without losing comfort. There

are different comfort concerns depending on

the type of home appliance. For example, for

space heating and hot water demand, the user

pays more attention to temperature, however,

for the washing machine (WM), dishwasher

(DW) and cloth dryer (CD), he focuses on when

the tasks of these appliance are completed.

Therefore in [4], a set of comfort level

indicators are proposed based on appliance

type. The comfort cost function is formulated

as

∑

Where A ={HP, TS, WM, DW, CD}; is the

comfort level indicator of appliance a and NA is

the number of controllable appliances in the

HEMS.

3.2.1 The Heat Pump (HP)

To quantify the user’s comfort level under the

operation of the HP, [4] proposes a comfort

level indicator whose definition is based on the

assumption that when the room temperature

is equal to the user setting temperature, the

user is most comfortable. If the room

temperature deviates from the setting value to

a certain extent, the user comfort level will be

decreased. The indicator is calculated as:

∑

Where

*

+

and is determined by

Where is the desired room temperature

set by the user and and

are

the two parameters that are related to the

temperature dead band of the heat pump.

According to the definition of in equation

(15), it is within the range of [0 100], where

zero means the user is most comfortable and

100 the user is least comfortable.

A similar comfort level indicator can be built

for the CHP unit. In this case the hot water

temperature determines the user’s comfort.

3.2.2 The non-interruptible appliances

A user’s comfort level for the non-interruptible

loads (WM, DW, CD) is determined by the

finishing time of these appliances [4].

(

)

(

) (

)

and

specify the valid working

interval for appliance a. If appliance a starts

within the interval ,

-,

where is the delay the user can tolerate

and is the preferred starting time of the

(14)

(15)

VI

user, the user is most satisfied. is the

number of timeslots appliance a need to finish

its task.

3.3 Multi-objective optimisation

In this model, the working status of HP and

CHP in each time slot and the task starting

times of WM, DW and CD are decision

variables. Minimizing the energy cost and

maximizing the user comfort level are the two

objectives of this problem. This model is

transformed into a single objective

optimisation model by the factor α [4]:

( )

( ) ( ) ( ) ( )

Where α is called the user preference factor,

0 ≤ α ≤1, through which the residential user

can take a tradeoff between the energy cost

and the comfort level conveniently.

4. Simulation results

Two cases will be investigated, all based on the

same production -and consumption profile.

The scheduling horizon is 24 hours, and is

divided evenly into 96 timeslots of 15 minutes;

that is Nslot = 96, ∆t = 0.25 h.

In case 0 we want to investigate how the

energy cost changes when we allow some

flexibility of the household appliances. The

results are shown in Table 1.

Case 0 Purchase cost (€)

Battery cost (€)

Sales revenue

(€)

Net cost (€)

No flexibility (case 00)

4.73 2.27 1.84 5.16

Flexibility (case 01)

4.09 2.21 1.57 4.75

From the last column in Table 1 we see that in

the case were we allow some flexibility of the

home appliances the net energy cost is smaller

than the case were there is no or little

operation flexibility of the home appliances

(€ 0.41 difference).

In case 1 the effect of comfort and cost as

objective will be examined. Cost and comfort

are contradictory, which means that the cost

will be larger (smaller) if the comfort level

indicator is lower (higher). Note that a higher

comfort level indicator means that the user’s

comfort is low. The user preference factor α

will be set to 0, 0.5 and 1, where 0.5 means

that cost and comfort are considered equally

important for the user.

From Figure 3 we see that the net energy cost

decreases and the comfort level indicator

increases with increasing α. Important to

remember is that a higher comfort level

indicator indicates that the most comfortable

bounds set by the user are exceeded (within a

reasonable margin) and thus that the user is

less comfortable.

Table 1: Simulation results case 0 (scheduling horizon = 24 h)

Figure 3: The net energy cost and comfort level as a function of the user’s

preference fact or α

VII

5. Conclusions

From case 0 it became clear that allowing

flexibility to the home appliances results in a

lower energy cost. This case is carried out with

a two-level Time ToU pricing scheme that has

an off peak –and standard rate price. The

difference between allowing and not allowing

flexibility resulted in a net energy cost gain

over a day of € 0.41 (see Table 1). This is of the

same magnitude that was obtained in [4].

The user’s preference α is a way for the

residential user to take a tradeoff between

cost and comfort level. The factor α is set to 0,

0.5 and 1, where zero means that only the

comfort level of the user is considered, one

indicates that only the cost objective is

minimized and 0.5 means that cost and

comfort are considered equally. The model is

run for the three values of α. The results

confirm the conclusion given in [4], namely

that the cost –and comfort objective are

contradictory. This means that maximising the

comfort results in a higher cost and vice-versa.

The algorithm behaves pretty much the same

for a three-level ToU -or RTP scheme.

References

[1] Y.Huan, H.Tian,L.Wang., "Demand response for

home energy management system," in Electrical

Power and Energy Systems., 2015, pp. 448-455.

[2] Christos S. Ioakimidis, Luis J.

Oliveira,Konstantinos N. Genikomsakis, Panagiotis

I.Dallas, "Design, architecture and implementation

of a residential energy box management tool in a

smartGrid," Energy, vol. 2013, no. 3 july 2014, pp. 1-

15, 2014.

[3] G. Graditi, M.G.Ippolito, R.Lamedica, A.Piccolo,

A.Ruvio, P.Siano, G.Zizzo, "Innovative control logics

for a rational utilization of electrical loads and air-

conditioning systems in a residential building.,"

Energy and Buildings, vol. 2014, no. 22 May 2015,

pp. 1-17, 2015

[4] Y.Zhang, P.Zeng,S.Li, C.Zang and H.Li., "A Novel

Multiobjective Optimisation Algorithm for Home

Energy Management System in Smart Grid,"

Hindawi, no. 18 January 2015, p. 19, 2015.

[5] Dr. S.C.Breukers, Dr. R.M.Mourik, "The end-

users as starting point for designing dynamic pricing

approaches to change household energy

consumption behaviours," Report for Netbeheer

Nederland, Projectgroep Smart Grids (Pg SG). March

2013.

[6] S. Shao, M. Pipattanasomporn and S. Rahman,

"Development of Physical-Based Demand

Response-Enabled Residential Load Models," vol.

28,no.2, pp. 607–614, 2013.

Table of contents

Chapter 1 ............................................................................................................................................... 1

Introduction ............................................................................................................................................. 1

1.1 Context and Motivation ................................................................................................................ 1

1.2 Outline ......................................................................................................................................... 12

Chapter 2 ............................................................................................................................................. 13

Pricing tariffs ......................................................................................................................................... 13

2.1 Capacity versus Volumetric tariffs ............................................................................................... 13

2.2 Dynamic pricing schemes ............................................................................................................ 17

2.3 Essential components of a dynamic pricing approach ................................................................ 18

2.3.1 Supportive Technology ......................................................................................................... 18

2.3.2 Feedback ............................................................................................................................... 19

2.4 Conclusions .................................................................................................................................. 21

2.5 Research questions...................................................................................................................... 22

Chapter 3 ............................................................................................................................................. 23

Dimensioning ......................................................................................................................................... 23

3.1 The PV-storage system ................................................................................................................ 23

3.1.1 General dimensioning criteria .............................................................................................. 24

3.1.2 Battery types ....................................................................................................................... 26

3.1.3 Sizing the PV-storage system ............................................................................................... 31

3.2 Thermal Storage System .............................................................................................................. 34

3.2.1 Sizing the Thermal Storage and CHP unit ............................................................................. 36

3.2.2 Sizing The Heat Pump ........................................................................................................... 41

Chapter 4 ............................................................................................................................................. 46

Modelling ............................................................................................................................................... 46

4.1 The Battery .................................................................................................................................. 46

4.2 The Thermal Storage System ....................................................................................................... 48

4.2.1 The thermal storage tank and CHP unit ............................................................................... 48

4.2.2 The heat pump ..................................................................................................................... 49

4.3 The non-interruptible loads ........................................................................................................ 50

Chapter 5 ............................................................................................................................................. 51

Optimisation .......................................................................................................................................... 51

5.1 The Cost Objective ....................................................................................................................... 52

5.2 The Comfort Objective ................................................................................................................ 53

5.2.1 Heat Pump (HP) .................................................................................................................... 53

5.2.2 Thermal Storage (TS) ............................................................................................................ 54

5.2.3 The non-interruptible appliances ......................................................................................... 55

5.3 Multi-objective Optimisation Model ........................................................................................... 56

5.3.1 The equality constraints ....................................................................................................... 57

5.3.2 The inequality constraints .................................................................................................... 59

Chapter 6 ............................................................................................................................................. 66

Case studies ........................................................................................................................................... 66

6.1 Case 0 .......................................................................................................................................... 68

6.2 Case 1 .......................................................................................................................................... 73

6.3 Case 2 .......................................................................................................................................... 77

Chapter 7 ............................................................................................................................................. 80

Conclusions ............................................................................................................................................ 80

7.1 Final Remarks .................................................................................................................................. 82

References ............................................................................................................................................. 85

Appendix ................................................................................................................................................ 91

List of Figures

Figure 1: Share in renewable energy in gross electricity consumption (%) of different EU countries

(source: Eurostat 2013). .......................................................................................................................... 1

Figure 2: Architecture of a Home Energy Management System (HEMS). ............................................... 2

Figure 3: Energy distribution in a single-family house of 4 members (source: Eandis). ......................... 4

Figure 4: Wind speed forecast at the residence location [2]. ................................................................. 5

Figure 5: Cost distribution of electricity bill in Belgium (source: Eandis). ............................................... 6

Figure 6: Overview of an external controlled Home Automation Network (HAN) [38]. ......................... 9

Figure 7: Architecture of a Wireless Sensor Network. .......................................................................... 10

Figure 8: Demonstrates the inefficiency of volumetric systems to address capacity [40]. .................. 14

Figure 9: Effect of the switch to capacity tariffs in the Netherlands in 2009 for different Volumes

(source: Liander) [40]. ........................................................................................................................... 16

Figure 10: Impact of automation on peak reduction [42]. .................................................................... 19

Figure 11: Multiple large pricing pilots vs. their percentage reduction in peak load [48]. (w/tech:

pricing scheme used in combination with automated appliances and feedback) ................................ 21

Figure 12: Optimal ratio (production/consumption) as a function of the battery capacity [50]. ......... 24

Figure 13: Optimal storage capacity (top) and Zc, Zs as a function of PV production [50]. ................... 25

Figure 14: Battery capacity versus temperature and charge-rate [50]. ................................................ 26

Figure 15: State Of Charge (SOC) as a function of the Open Circuit Voltage (OCV) for a AGM-battery

[50]. ....................................................................................................................................................... 27

Figure 16: The charging characteristic of a lead-acid (left) -and a Li-ion battery (right) [50]. .............. 28

Figure 17: Calendar lifetime of a Li-ion battery (left) and cycle lifetime for a AGM battery (right) [50].

............................................................................................................................................................... 28

Figure 18: A basic configuration of a micro-CHP unit with thermal storage [58]. ................................ 34

Figure 19: Schematic diagram of CHP-HP system [60]. ......................................................................... 35

Figure 20: Schematic diagram of thermal storage system. ................................................................... 36

Figure 21: Hot water usage profile [61]. ............................................................................................... 38

Figure 22: Temperature of hot water inside thermal storage tank. ..................................................... 39

Figure 23: Thermal power output of CHP unit. ..................................................................................... 40

Figure 24: House floor plan of a single family house [64]. .................................................................... 42

Figure 25: Air Exchange Rates (ACH) for different environments in a single family house [65]. .......... 43

Figure 26: Schematic diagram of a grid-interactive PV-system with DC -coupling [50]. ....................... 47

Figure 27: Schematic diagram that illustrates the three types of children [68]. .................................. 51

Figure 28: Relationship among parameters of HP comfort level indicator [4]. .................................... 54

Figure 29: Relationships among parameters of WM, DW and CD comfort level indicators [4]. .......... 55

Figure 30: Power distribution relationships of the HEMS in smart grid [4]. ......................................... 57

Figure 32: Critical load profile of residential household [72] ................................................................ 66

Figure 31: Forecasted PV power profile [72] ......................................................................................... 66

Figure 33: Electricity pricing schemes [70]- [71] ................................................................................... 67

Figure 34: Forecasted Outdoor temperature [73] ................................................................................ 67

Figure 35: Room temperature band over a day .................................................................................... 68

Figure 36: Simulation results in case of no flexibility of home appliance ............................................. 70

Figure 37: Simulation results in case of flexibility of home appliances ................................................ 70

Figure 38: Simulation results in case of no flexibility of home appliances ........................................... 71

Figure 39: Simulation results in case of flexibility of home appliances ................................................ 72

Figure 40: The net energy cost and comfort level as a function of the user’s preference factor α for

the case with the three-level ToU pricing scheme ................................................................................ 74

Figure 41: Power flow for case with ToU pricing scheme for α = 0.5 ................................................... 75

Figure 42: Power flow for case with RTP scheme for α = 0.5 ................................................................ 75

Figure 43: Power flow for α=0 (ToU-3 level) ......................................................................................... 76

Figure 44: Power flow for α=1 (ToU-3 level) ......................................................................................... 76

Figure 45: Power flow for case without battery degradation cost (ToU-3 level) .................................. 78

Figure 46: Power flow for case with battery degradation cost (ToU-3 level) ....................................... 78

Figure 47: Power flow for case without battery degradation cost (RTP scheme) ................................ 79

Figure 48: Power flow for case with battery degradation cost (RTP scheme) ...................................... 79

Figure 49: Levelized Cost Of Energy (LCOE) for wind turbines [74]. ..................................................... 83

Figure 50: Triangle of efficiency [74]. .................................................................................................... 84

List of Tables

Table 1: Overview of optimisation objectives considered in literature [8]. ............................................ 6

Table 2: Overview of the mathematical optimisation procedures [8]. ................................................... 7

Table 3: Effect of the switch to capacity tariffs in the Netherlands in 2009 (source: Liander) [40]. .... 16

Table 4: Parameter values of some commonly used battery types [50]. ............................................. 29

Table 5: characteristic data of a typical Belgium house [50]. ............................................................... 31

Table 6: Average energy consumption per day for some typical household appliances [50]- [55]. ..... 31

Table 7: Maximum Depth Of Charge (DOD) for different battery types ............................................... 32

Table 8: Correction factor for a specific orientation and roof inclination (source: HESPUL) [56]. ....... 33

Table 9: Summary of the results . .......................................................................................................... 33

Table 10: Commercial available micro-CHP units [58]. ......................................................................... 40

Table 11: The heat transfer coefficients of the different construction items in a house [64]. ............. 41

Table 12: Heating factor for different heat-up times and temperature drops [63]. ............................. 44

Table 13: The calculation of the total heating power for each room of a single family house. ........... 45

Table 14: The dimensioning results of chapter 3. ................................................................................. 45

Table 15: Parameter setting of WM, DW and CD [4] ............................................................................ 68

Table 16: Parameters for a Lithium-iron phosphate (LFP) battery ....................................................... 69

Table 17: Simulation results of case 0 (scheduling horizon = 24 h) ...................................................... 69

Table 18: Simulation results of case 1 (scheduling horizon = 24 h) ...................................................... 73

Table 19: Simulation results of case 2 (scheduling horizon = 24 h) ...................................................... 77

Abbreviations

DSM: Demand Side Management

HEMS: Home Energy Management System

PV: Photovoltaic

HVAC: Heating Ventilation and Air

conditioning

EW: Electrical Water heater

CHP: Combined Heat and Power

TS: Thermal Storage

HP: Heat Pump

WM: Washing machine

DW: Dish Washer

CD: Cloth Dryer

EV: Electrical Vehicle

ADP: Adaptive Dynamic Programming

PSO: Particle Swarm Optimisation

HAN: Home Automation Network

WSN: Wireless Sensor Network

MCU: Micro-Controller Unit

PLC: Power Line Communication

RF: Radio Frequency

DSOs: Distribution System Operators

ToU: Time of Use pricing scheme

CPP: Critical Peak Pricing

CPR/PTR: Critical Peak Rebate/Peak Time

Rebate

RTP: Real Time Pricing

IBR: Inclining Block Rate pricing

IHD: In Home Display

C-Rate: Charge rate of battery

SOC: State Of Charge

DOD: Depth Of Discharge

OCV: Open Circuit Voltage

CCV: Closed Circuit Voltage

FLA: Flooded Lead acid battery

AGM VRLA: Absorbed Glass Mat Valve

Regulated Lead-acid battery

Gel VRLA: Gel Valve Regulated Lead-acid

battery

LFP: Lithium-iron Phosphate battery

NiMH: Nickel- Metal Hydride battery

NiFe: Nickel-iron battery

ICE: Internal Combustion Engine

HRS: Heat Recovery System

MPP: Maximum Power Point

TSO: Transmission System Operator

List of symbols

Zc: Self-consumption

Zs: Self-sufficiency

Wp: Watt peak

Ah: Ampere-hour

A: Ampere

Cap: Useful battery capacity

Cap real: Real battery capacity

CBat: Batteries capacity in kWh

ηch: Charging efficiency of battery

ηdisch: Discharging efficiency of battery

Pmaxch: Max. charging power of battery

Pmaxdisch: Max. discharging power of battery

EPV: Yearly PV production

PPV: Peak power of PV installation

FNG: Fuel energy of Natural Gas

ηe: Electrical efficiency of CHP unit

ηHRS: Thermal efficiency of Heat Recovery

System

ηtot: Overall efficiency of CHP unit

PCHP: Electrical power output of CHP unit

QEG: Heat output of Exhaust Gasses

Qw: Heat loss of Heat Recovery System

Qspace heating: Heat demand for space heating

circuit of building

Qhot water: Heat demand for hot water circuit of

building

Pbat: Power exchange with battery

Pgrid: Power exchange with grid

SHP: Operation status of heat pump

SCHP: Operation status of CHP unit

Tstart: Discrete vector of starting times of non-

interruptible loads

Tambient: Ambient temperature of room where

the thermal storage tank in located

Tin: Cold water inlet heated until the desired

user temperature

U: Heat transfer coefficient

A: Heat-exchanging surface

φT: Transmission losses in a house

φV: Ventilation losses in a house

φRH: Required heating power for a house

Ti: Indoor room temperature

To: Outdoor temperature

HV: Heat transfer coefficient by ventilation

qV: Ventilation flow in a room

ρa: Mass density of air

ca: Specific heat capacity of air

ACH: Air Exchange Rate

Af: Floor area of a room

fRH: Heating factor

COP: Coefficient of performance of the heat

pump

Gt: Heat gain rate of a house

mTS: Mass of water in Thermal Storage tank

C: The equivalent thermal mass

G: Product of the surface area and thermal

resistance of the thermal storage tank

B: Product of hot water mass flow and specific

heat capacity of water ( )

R’: equals

ρwater: The mass density of water

cp: Specific heat capacity of water

τ: Time constant of the thermal storage tank

(R’C)

∆t: Time length of a timeslot in hours

Ft: The hot water flow rate in time slot t

TTSt: Temperature of hot water in thermal

store per timeslot t

TsetTS: User’s set point of hot water

temperature

∆TLTS: Lower temperature limit of thermal

store temperature dead band

∆TUTS: Upper temperature limit of thermal

store temperature dead band

TRoomt: Room temperature per time slot t

TsetRoom: User’s set point of room temperature

∆TLRoom: Lower temperature limit of heat

pump temperature dead band

∆TURoom: Upper temperature limit of heat

pump temperature dead band

PHP: Rated power of heat pump

CHP: Thermal capacity of heat pump (COP*PHP)

Nmina: minimal time slot at which non-

interruptible appliance can start its task

Nstarta: Starting time of non-interruptible

appliance a

Nmaxa: Maximum time slot at which non-

interruptible appliance a finishes its task

Ntaska: Number of time slots needed to finish

task of the non-interruptible appliance a

Pa: Rated power of non-interruptible appliance

a

ctgrid: Purchase cost of electricity at time slot t

ctsell: Selling price of electricity to the grid at

time slot t

cdeg: Degradation cost of the home battery

CC: Capital cost of home battery

LE: Battery life throughput energy in kWh

LN: Theoretical lifetime of battery in number of

cycles

LC: Actual lifetime of battery in number of

cycles

Es: Total energy storage capacity under

reference conditions, namely at 20oC and DOD

of 80%

ηTem: Temperature dependence factor (=LC/LN)

Fcost: Cost function of optimisation problem

Fcomfort: Comfort function of optimisation

problem

Ftotal: Objective function of multi-objective

optimisation problem

NA: Number of controllable appliances in the

optimisation problem

Ia: Comfort level indicator of controllable

appliance a

Nslot: Number of time slots in the scheduling

horizon

tmina: minimal time slot at which non-

interruptible appliance a can start its task

tmaxa: Maximum time slot at which non-

interruptible appliance a finishes its task

tideala: Ideal starting time of non-interruptible

appliance a

tdelaya: Acceptable delay w.r.t. starting time of

the non-interruptible appliance a

tworka: Number of time slots needed to finish

task of the non-interruptible appliance a

α: User’s preference factor (αFcost+(1-α)Fcomfort)

A: Matrix of the inequality constraints (A.x≤b)

b: Column vector of the inequality constraints

Aeq: Matrix of the equality constraints

(Aeq.x=beq)

beq: Column vector of the equality constraints

Ptcl: The consumption of the critical loads in a

house per time slot t

1

Chapter 1

Introduction

1.1 Context and Motivation

Over the past decade renewable energy has taken a more prominent role in our electrical energy

production. The worldwide concern of climate change and the limited amount of primary energy

resources left have turned renewable generation sources such as wind and solar into an important

player on the energy market. Also the 20/20/20 target of the European commission is responsible for

this. The 20/20/20 target stands for 20% of energy production must be renewable, 20% emission

reduction with respect to the emission level of 1990 and 20% increase in energy efficiency. In

Figure 1 you see the share of renewables in different European countries. In the past electricity

always flowed from a centralized power plant to the end users via a transmission and distribution

network. This one-way flow of energy made it possible to maintain the network balance using a

centralized management system. Nowadays the power generation is more decentralized due to the

introduction of renewable energy sources. Today Belgium has over 200 000 electricity generation

systems, scaling from large power plants and large wind turbine parks to small PV installations on the

roof of houses. Only a decade ago Belgium just had a few dozen of electricity generation sites. As a

result, utility companies and network operators will have to change their game plan. Transmission

operators are designing new products for better controlling the grids balance in these changing

market conditions. One of these new products uses cold storage warehouses for flexibility. These

warehouses can be cooled to lower temperatures when there is excess of energy, and turned off for

a couple of hours when there is less energy available without affecting the shelf-life of the stored

products. This gives the transmission operators the flexibility to quickly respond to unbalances in the

grid.

Figure 1: Share in renewable energy in gross electricity consumption (%) of different EU countries (source: Eurostat 2013)

2

To assure the security of supply and deal with the intermittent character of renewables we have to

make our grid smarter and enable an information exchange between users and utility companies.

The main advantage of this information exchange is that we can implement demand side

management (DSM) programs to control the consumption of the users. DSM control can be

advantageous for both users and utility companies. The utility companies will be able to reduce the

peak electricity loads and increase the reliability of their power grid and the users will be rewarded

by a reduction of their electricity bill.

A Home Energy Management System (HEMS) can consist of four interconnected components,

namely a monitor module, a prediction module, the control logic unit and the scheduling module

(see Figure 2). The monitor module monitors the actual behaviour of the household appliances, the

storage system and the Photovoltaic (PV) installation. In practice the appliances are monitored by

smart meters that continuously measure the power consumption over a certain period.

The power production of the PV is calculated by the prediction module according to the input data of

the monitor module. These input data are solar radiation data and environmental variables, such as

the temperature of the PV panels, which can come from weather forecast or sensors. The

environmental variables are monitored, because they affect the power output of the PV panels.

The scheduling module contains the DSM software that computes the optimal schedule according to

the specified optimisation objectives, e.g. electricity cost and well-being/comfort, that home owners

want to pursue. After the optimisation procedure, the control logic unit sends the optimal schedule

to the appliances and directly controls the shiftable, controllable and thermal appliances. These

appliances will be further specified below. Over the past few years HEMS became a very popular

research topic for universities and industries all around the world and therefore we will give a brief

overview of the different approaches in literature.

Figure 2: Architecture of a Home Energy Management System (HEMS)

3

The main idea and approach is for most literature studies the same, but there are some differences

in the used appliances, the optimisation objectives- and procedures. The appliances for HEMS

proposed in literature can be grouped in four categories [1], [2], [3], [4]:

The essential appliances : essential lighting, multimedia,..

The shiftable appliances: dish washer, washing machine, tumble dryer,…

The thermal appliances: Heating Ventilation and Air conditioning (HVAC), electrical water

heater (EW), combined heat and power (CHP) unit, heat pump (HP),…

The battery assisted appliances: electrical vehicle (as buffer and load), electrical battery as

buffer,…

In this dissertation we propose the following loads (see Figure 2):

1) The essential loads: loads that will not be controlled by the HEMS, because they provide a

necessary value to the members of the house

e.g.: essential lighting, television, computer, oven,…

2) The shiftable loads: loads that can be shifted in time, but once it starts its operation it cannot be

interrupted anymore. These appliances can be controlled by the HEMS according to the available

energy and preferential intervals set by the user. The typical loads that can be shifted in time are:

Washing machine (WM)

Dish washer (DW)

Cloth Dryer (CD)

3) The controllable loads: loads that can be controlled within their operation limits according to the

available energy. The two appliances that fit into this description are :

Refrigerator: Temperature control between 4 and 7oC. Above 7oC food items such as meat

,fish and dairy products have a reduced shelf life.

Freezer: The optimal temperature of a freezer is -18oC, because below this temperature the

shelf life of products is not extended. On moments of high production we can reduce the

temperature of the freezer and rely on the thermal inertia of the freezer on moments where

the production is low. When the freezers temperature gets higher than -18oC, this gives us

the input signal to send power to it.

4) The thermal loads: loads that must maintain a certain desired state according to the users set

point. The two thermal loads in a home are :

Space heating/cooling

Water heating

A combined heat and power unit and a heat pump will be used for the heat supply. In literature the

most HEMS use an electrical water heater, but because of the more stringent rules of Europe these

will be probably excluded in the near future. On the 26th of September 2017 the second tier

requirements regarding energy efficiency will come into force. The Energy Labelling scale for

4

water heaters is updated to A+ to F. In 2018 this will again be updated [5]. If we look at the energy

distribution of the different loads in a single-family house (4 members) than the largest consumption

of energy is due to heating (see Figure 3). This means that the control of the thermal appliances in a

home will be the most important ones.

In [1] they use a local battery for storage, whereas in [2] a plugged -in electrical vehicle (EV) is used as

local storage. This subtle difference makes the DSM control a bit more complicated. You have extra

conditions, like preferred battery level of the vehicle and time that the EV is not plugged in, that you

have to take into account. The storage system can be a battery where electrical energy is stored, or a

hot water tank to store thermal energy. This thermal energy can for example be used by a heat pump

for space heating or for hot water usage (e.g. a shower) on moments when the energy production is

low or energy demand is high. Some literature studies also use a micro-wind turbine as power

generation system. In [2] they use this in combination with a PV installation. The prediction of the

power output of a wind turbine is more complicated than for a PV panel, because wind speed data

for a residential location depend on several variables and location characteristics, such as

surrounding buildings and trees, which influences the actual wind energy that the wind turbine can

utilize. This means that relying solely on regional wind data forecast for a region where the residence

is located may result in a wrong prediction of the power output. A method for forecasting the wind

speed at a residential location is given in [6]. In this article they consider a three hour time window

for the forecasted wind speeds and approximate these wind speeds with a discrete probability

function of eight values. These values tell you the wind speed you can expect with a certain

probability of occurrence during a period of three hours. An example of such a wind speed forecast is

given in Figure 4.

There are two optimisation objectives that always come back in literature, namely cost and well-

being/comfort. Cost is sometimes the only objective that is considered [1], but the two objectives are

mostly considered together [2] - [4], [7]. In Table 1 [8] an overview of different objectives

combinations used in literature is given. In some HEMS literature they even consider emissions as an

optimisation objective, but this is less common than the other two.

Figure 3: Energy distribution in a single-family house of 4 members (source: Eandis)

5

The cost objective is described as a function that mostly consists of two terms, namely a term that

describes the electricity that we buy from the grid and a term that describes the electricity that we

sell to the grid [2] - [4]. In [4] they even take the degradation cost of the battery into account. Some

literature studies do not take this into account, but this is a very important parameter, besides the

charging/discharging efficiency, whether or not a profitable situation can be obtained.

Almost all literature studies consider a dynamic pricing for electricity, but in most countries there is

no regulatory framework. According to [9] the introduction of real-time price tariff would create a

flatter demand by ‘’shaving the peaks and filling the valleys’’, which basically means that the peak

loads can be reduced or shifted in time. In chapter 2 a brief overview of different dynamic pricing

tariffs and their potential of reducing peak loads will be given. In [2] they assume that the electricity

has a 5% lower price when supplied to the grid, compared to the buying price in every specific

instance. According to them this ensures two important issues:

1) This allows the utility companies to have a profit margin, allowing them to possibly cover

maintenance cost and unexpected problems of the distribution network .

2) The HEMS creates more value for the installed renewable energy source, by enabling a

higher penetration of renewable energy at the residence. This also reduces the use of the

distribution grid.

When several HEMSs in the grid are synchronized, this might result in undesirable oscillations of the

network frequency and voltage. By desynchronizing the real-time pricing of the HEMSs this

phenomena can be prevented [2]. This is beyond the scope of the present work, because we focus on

the working of a HEMS in a residential environment.

Figure 4: Wind speed forecast at the residence location [2]

6

All HEMS in our literature study assume a limited peak power transfer between grid and home. The

same idea is used in micro grids and the reason for that is:

1) Economical: the user will have a reduced electricity bill, because his cost for distribution and

transportation of electricity will be smaller (see Figure 5 ).

2) The utility companies will have a reduced network operation -and infrastructure cost.

The storage and connection with the grid are the two buffers needed to assure the security of supply

on moments when the energy production is low and/- or the consumption is high. Some literature

studies only assume an electrical buffer (battery), but since heating covers a large piece in our energy

use (see Figure 3) it is a good idea to foresee a thermal buffer where we store hot water.

Objectives References

Cost Well-being Consumption Cost and well-being Cost and consumption pattern Consumption and well-being Cost, consumption, emission Cost, well-being, emission, consumption

[10], [11], [12], [13], [14], [15] [16], [17] [18], [19], [20] [21], [22], [9], [23], [24], [25], [26] [27] [28] [29] [30]

Figure 5: Cost distribution of electricity bill in Belgium (source: Eandis)

Table 1: Overview of optimisation objectives considered in literature [8]

7

Mathematical optimisation References

Linear programming Convex programming Dynamic programming Mixed Integer linear programming Mixed Integer non-linear programming Meta-heuristic search Particle swarm optimisation Tabu search Genetic algorithm Heuristic scheduling Mix of optimisation and heuristics Backtracking-based scheduling State-queuing model Markov decision processes Artificial neural networks

[22], [31] [32] [9], [13] [10], [12], [25], [26], [27], [28] [14] References [21], [33] [23] [20] References [28] [19] [34] [35] [18]

The well-being objective is described in two different ways. In [4], they construct a comfort level

indicator for each controllable device. These indicators are in the range of [0,100], where close to

zero means the device operates within the users preferred limits, and 100 means the device operates

beyond or below the preferred limits of the user, e.g.: heat spacing device, indicator level will be

close to zero if room temperature is around 20oC, and will increase if you deviate from the 20oC.

A very different approach is used in [7] where they use queuing theory to model the well-being

objective. The waiting times of the specified household appliances are modelled according to

queuing theory. Queuing theory mathematically describes a queuing system and tries to relates the

uncertainty in the arrival patterns of its customers (home appliances in our case) to the uncertainty

of how the queuing system performs [36]. It is for everyone clear that the waiting times and the

number of customers in the queuing system depends on how its customers arrive at the queue and

how long they occupy the server (this will depend on the available energy in our case). In literature,

they assume two kind of demands in the model of their queuing system [7]. According to different

delay requirements they categorized it into:

Table 2: Overview of the mathematical optimisation procedures [8]

8

1. Delay-sensitive demands: which are appliances such as a cloth dryer, a washing machine and

a dish washer. These appliances are sensitive to the operation delay, because they directly

affect the users comfort level.

2. Delay-tolerant demands: these are the heating appliances, which are insensitive to the

operation delay due to their thermal inertia.

In [7] they assume that the delay-sensitive demands enter a high-priority queue, while the delay-

tolerant demands are put in a low-priority queue. The high-priority queue gets served first and when

this queue is empty then the low-priority queue is served. The problem they observed with this

approach is that this can cause a significant delay for the delay-tolerant demands. A solution they

proposed is to allow the demands in the low-priority queue to upgrade to the high-priority one with

probability β.

In literature, the problem is formulated as a multi-objective optimisation problem, where the two

optimisation objectives are the boundary conditions that need to be satisfied. Several optimisation

procedures are used in literature, but the two that always come back are the Particle Swarm

Optimisation (PSO) [1], [4] and the Adaptive Dynamic Programming (ADP) algorithm [7].

PSO is a stochastic global optimisation method inspired by the choreography of a bird flock. It

depends on the exchange of information between particles. A particle is a part of the HEMS that we

control, e.g. charging or discharging rates of the battery. In PSO, each particle adjusts its route

towards the positions with their own previous best performance and the best previous performance

of the whole swarm [1]. ADP is an iterative algorithm based on the principle of optimality. It is a very

useful tool for solving optimisation problems. The principle of optimality is, regardless the initial state

and decisions, the remaining decisions must provide an optimal policy [7]. Table 2 [8] gives an

overview of the mathematical optimisation procedures for HEMS scheduling used in literature.

Several projects about HEMSs have been carried out in the last few years. One of them is the

GreenCom project that started in 2012 and ended in 2015. The aim of this project is to balance the

local exchange of energy at the community microgrid level, to avoid affecting the centralized grid

with instability. The GreenCom Energy Management System controls energy consuming devices and

local energy generating and storage devices. The DSM will be based on individual consumer contracts

with attractive tariffs, reward/penalty clauses, etc. GreenCom has conducted its pilot on the island of

FUR, Denmark [37].

9

In the project they implemented a Home Automation Network (HAN) depicted in Figure 6. There are

three options to implement a HAN [38], these are:

Smart Meter Controlled Network

Internal Controller Network

Gateway/External Controlled Network

With the smart meter controlled network the smart meter acts as a central hub for the wireless

network. The data of the appliances will be gathered by the smart meters and sent to the utility

provider via GSM or long distance GSM. The control strategies are then determined by the utility

provider. The internal controlled HANs does not have a connection with the outside world and is

controlled by an internal controller. The control strategies and decisions are implemented in an in

home display (dedicated console/PC) . Within this thesis we will carry out the internal controlled

approach.

The gateway/external controlled network has an connection with the outside world via a dedicated

gateway device, such as an embedded PC/laptop. The data is sent to a backhaul network (web based

service) , which then provides control decisions that can be sent to the HAN via the gateway device.

This approach was carried out in the GreenCom project. For proper monitoring and controlling of the

devices we need a Wireless Sensor Network (WSN) [38]. The power output of the PV installation for

example depends on several factors like irradiation of the sun (W/m2) and temperature of the panels

(affects efficiency). To calculate an accurate power output we need to monitor these factors. The

basic building blocks of a WSN are the sensors, which are the senses of the system, and the

MicroController Unit (MCU) that contains the computational power of the system (see Figure 7).

Other devices where we use sensors for monitoring are the heating system, storage system, etc.

These systems will be further explained in Chapter 3. The antenna is used for wireless

communication with the network. This is one way to communicate with the network and is also

known as RF (Radio Frequency) communication. Another way is PLC (Power Line Communication).

Figure 6: Overview of an external controlled Home Automation Network (HAN) [38]

10

PLC uses the power wiring of the house to transport data from the plugged in devices to the HAN.

The advantage of PLC is that you do not need extra wiring and high speeds can be achieved for data

transfer. PLC is not the best way to transfer data, because the wiring of the house is not designed for

communication. The typical issues are noise on the line, impedance issues leading to attenuation

(weakening of electrical signal), surge protectors ( device that protects against over voltage) blocking

signals, etc. All these issues affect the performance of the network and therefore PLC is not

recommended for communication.

To power a wireless sensor node [38] (see Figure 7) there are three options:

Mains power

The wireless device is continuously powered and allows a greater range and data

throughput. The possibility of this depends on the operational environment. Within the

home environment a part of the network can be powered by mains, but for a ZigBee

network this is essential to ensure a correct operation. ZigBee is a meshed wireless

communication network between devices on a short distance. It is used for sending sensor

data and process monitoring and controlling.

Battery powered

It is the most common method for powering a wireless sensor node and has some pros and

cons. The advantage is that it is flexible in terms of placement and has a life time of 3-5 years

if used properly. The cons are a reduced duty cycle to achieve a long life time, limited to

monitor slow moving events like environmental temperature and of course the maintenance

of the battery.

Energy harvesting

This is a new way of powering a wireless sensor network and is being considered as a way to

permanently power a wireless sensor node. The major advantage is the removal of the

maintenance and battery change. Energy sources for energy scavenging can be light

(indoor/outdoor), temperature differences, vibrations, etc. The source that can be used

Figure 7: Architecture of a Wireless Sensor Network

11

depends on the application and available source. Light is the most energy rich source, and

thus the most frequently used energy source nowadays.

In this thesis, the focus will be on the residential market, because it is the most challenging market to

implement a HEMS in. If we look from the user’s point of view monetary expenses and high comfort

level are the two objectives that they will try to pursue. Due to the DSM program the operation of

certain home appliances will be postponed according to the available energy. Waiting time of the

non-interruptible appliances, the room temperature and the hot water temperature are used to

indicate the user’s comfort level. So if we rephrase, the multi-objective optimisation procedure

simultaneously:

1) minimizes monetary expenses/electricity bill

2) maximizes the comfort level of the residential user

A very important threshold for residential users regarding an implementation of a HEMS, is the

investment cost. The cost of smart appliances, such as a smart washing machine or a smart boiler, is

very high nowadays. Questions that a home owner will ask are:

1) What is the total investment cost?

2) When is the return of investment?

In [3] they implemented a HEMS in a 140 m2 house in Italy. They worked with a fixed electricity cost,

and the yearly saving was budgeted at €193,45. With question 1 and 2 in mind, we need to wonder if

it is necessary to use everything we proposed in the architecture of a HEMS in Figure 2. In Figure 3,

the energy distribution of a single-family home (4 members), we see that the heat consumption is

almost 80% of the total consumption. Washing and drying takes only 4% of the total consumption,

which means that the investment in smart household appliances is high with respect to the amount

of energy you can control. The same holds for refrigeration.

The challenges in smart grids today are the need for a regulatory framework and standardization. In

the last few years Belgium started to provide legal provisions for smart grid concepts, such as

Demand Side Management. Supported by the EU energy policy, a number of definitions of new smart

grid concepts have been included in the national (and regional) laws and codes. Furthermore, the

transmission operators created new balancing products and cost-benefit analyses of smart meters to

allow the participation of loads and generation sources, such as solar panels, to connect to the

distribution grid. These changes show a positive evolution towards DSM participation and regulatory

acceptance. Yet a number of regulatory obstructions, such as pricing tariffs, need to be changed

before DSM can be implemented in a home. Dynamic pricing for residential users is at the moment

limited by Belgian legal provisions. The standardization will have an important impact on interest in

investment and market competitiveness. In the meanwhile there exist very few (inter)national smart

grid standards. Luckily a number of EU standardization institutions (CEN, CENELEC and ETSI) are

developing smart grid standards, e.g. smart utility meters [39].

12

1.2 Outline

In this section we will give a short description of the different chapters. Chapter 2 deals about the

different pricing schemes and their ability to reduce peak demands. The introduction of renewable

energy in our energy generation makes it difficult for the Distribution System Operators (DSOs) to

keep working as before, which gives uncertainty regarding DSO costs and revenues. The big challenge

in Europe today is to guarantee the grids stability for any situation while encouraging the integration

of renewables in a way that is socially and economically fair.

In chapter 3 the thermal -and electrical storage systems are dimensioned. The dimensioning of these

storage systems are important for obtaining an economical working of the HEMS. For example when

the battery is over dimensioned, it will never fully charge and a part of the battery capacity will be

unused. The opposite holds for an under dimensioning of the battery system. In this case the energy

of the PV installation will not be fully exploited. So it is of great importance that all the different

components are correctly tuned to each other.

Chapter 4 describes the models for the home battery, the thermal storage system (CHP unit and

thermal storage tank), the heat pump and the non-interruptible loads of the HEMS. These models are

used in the optimisation part of the HEMS, where the optimal operation schedule of each appliance

is determined. These models are a very basic description of the respective appliances, where the

dynamics are neglected for simplicity.

The different appliances that are modelled in the previous chapter will be used in Chapter 5 to build

the optimisation procedure. The optimisation is based on two optimisation objectives, namely the

overall energy cost and the comfort level of the user. The cost objective will be minimized and the

comfort level of the user will be maximized over the next 24 hours (i.e., next day) based on the

forecasted outdoor temperature, the power output of the PV installation over the next 24 hours and

the forecasted electricity -and natural gas price (CHP unit runs on natural gas). The Genetic Algorithm

(GA) in Matlab is used to solve the optimisation problem.

In chapter 6 three cases are examined to verify the effectiveness of the proposed HEMS model. The

first case is a single objective optimisation (cost only) where the effect of allowing flexibility to the

household appliances on the cost is examined. The second case is a multi-objective optimisation of

cost and comfort level of the user. According to [4] cost and comfort are contradictory, which means

that the cost of energy increases as the user wants more comfort. The cases are simulated for two

types of pricing schemes, namely a Time of Use (ToU) pricing scheme and a Real Time Pricing (RTP)

scheme.

The last chapter, chapter 7, ends with some conclusions based on the simulations done in chapter 6.

The last section of chapter 7 finishes with some final remarks based on a white paper written by the

Smart Grid team of Eandis.

13

Chapter 2

Pricing tariffs

Dynamic Pricing of electricity is a very important element in the study of a HEMS. By the end of 2013

the installed capacity of PV systems and wind turbines in Europe has reached 81 GW1 and 117 GW2

respectively. The variability of electricity generation due to renewables together with the variable

electricity consumption of households makes it difficult for the Distribution System Operators (DSOs)

to keep working as before. Of course this gives uncertainty regarding DSO costs and revenues. The

big challenge in Europe today is to guarantee the grids stability for any situation while encouraging

the integration of renewables in a way that is socially and economically fair. In [40], they propose

several recommendations regarding the design of distribution network tariffs. These

recommendations will be further outlined in this chapter.

2.1 Capacity versus Volumetric tariffs

Volume and capacity are the two factors that determine the consumer’s bill. Depending on the EU

country, the network tariff can be based on:

Volume: the consumers are charged on the total volume of energy they withdraw or feed

into the grid. The measuring unit is watt per hour (Wh, kWh, MWh).

Capacity: the consumers are charged on the maximum amount of energy they withdraw or

feed into the grid at any instance in time. Capacity is measured in watt (W, kW, MW). This

capacity can be:

- Fixed: contractually agreed maximum capacity and corresponding price

- Variable: tariff varies at several moments of a day and aims at shifting the

demand from one period to another. A day can have several peak periods

where the price is set high with respect to the rest of the day (see ToU

pricing below). Note that for a variable capacity tariff a smart meter needs

to be installed.

To make the difference between volumetric –and capacity tariffs clear we will illustrate this with an

example in Figure 8. If the two consumer (case 1 and case 2) would have a volumetric tariff their bill

will be the same, because they consume the same amount of energy (70 kWh). If their network tariff

would be based on the capacity the bill of consumer 1 will be lower than consumer 2, because the

peak load of consumer 1 is lower. In this example it is clear that the capacity based tariff is more fair,

because consumer 2 charges the grid more.

1 EPIA, Global Market Outlook for Photovoltaics 2014-2018, June 2014

2 EWEA, Wind in Power 2013 European Statistics, February 2014

14

In most EU member states the network tariff is mostly heavily based on total volume, with the

exception of some countries like the Netherlands, Finland and Spain where it is capacity based. The

question, “why should we reconsider the distribution network tariffs?” rises. In [40] they give several

grounded reasons to do so:

1. Due to the increased electrification of household appliances (e.g. HP and EV) the peak loads

at certain periods are increasing. Reinforcing the grid because of these few peak periods is

expensive and paid by all consumers. A cheaper solution is to shift a part of this demand at

lower consumption periods. This means that electricity consumption habits of the consumers

have to change. However volumetric tariffs only encourage consumers to reduce their overall

energy consumption, but does not encourage them to limit their immediate consumption to

a certain level.

2. Prosumers (households with PV installation on their roof) are not encouraged to reduce their

injection of energy at peak production times by aligning their own consumption with their

own production. It is very important to consider this when designing a HEMS.

3. In some countries there exists a net metering system where a prosumer receives credits for

at least a portion of the energy he injects into the grid. In Belgium this depends on the power

of your installation and the network tariff per kW for the use of the distribution grid. By

paying this tariff your electricity meter is turned back per kWh when you supply electricity to

the grid. This results in a lower net consumption and thus lower billing basis for the DSOs

while the grid development and maintenance cost, determined by the network capacity, do

not reduce. This and the higher local peak loads due to increased electrification create

revenue uncertainty for the DSO.

Figure 8: Demonstrates the inefficiency of volumetric systems to address capacity [40]

15

4. The connection of distributed energy sources result in higher tariffs paid by non-generators.

Prosumers can compensate this cost due to more self-consumption or net-metering, while

their share of network costs will be transferred to other consumers who cannot invest in

their own PV installation. This can be avoided if the prosumers were able to contribute to

grid stability through ‘’smart contracts’’ with the DSO or a capacity based tariff instead of a

volumetric one.

From this section we remember that [40]:

Grid users should be able to self-consume and self-generate as long as the costs for using the

grid services is reflected in their bill.

Make network tariff more capacity based, and less volumetric, in order to limit the revenue

uncertainty for the DSOs.

To reinforce the recommendation of a more capacity based network tariff, the case study of the

Netherlands will be outlined here [40]. In 2008, the Dutch government decided to switch from a

mixed tariff (combination of volumetric and capacity) to a system completely based on capacity. Two

arguments justified their change:

Network costs are mainly capacity driven and determined by peak loads

New tariffs were considered to introduce a simple billing between DSOs and retailer (only

one bill sent by the retailer, instead of separate bills sent by DSOs and retailers)

To inform and prepare the consumers for the change a large media campaign was organized. Among

other initiatives, like an awareness website created by DSOs and government, consumers with a large

connection and little consumption received a letter inviting them to check their real capacity needs.

In 2009 the capacity tariff was introduced for both electricity (≤ 80A) and gas (≤ 40m3/h). Together

with this change the energy tax was revised in order to compensate for the capacity tariff and avoid

public backlash. The variable component of the energy tax was increased and a fix tax reduction

ensured that households with a standard connection would approximately pay the same bill. The

transition to a new distribution tariff was a smart move of the Dutch government. It was transparent

for consumers, reduced their electricity bill (see Table 3) and reduced the revenue uncertainty for

the DSOs. This tariff change also led to a reduction in administration cost in the energy sector,

because it made it easier for DSOs to bill suppliers.

From this case study we remember that [40]:

Grid users should receive clear and appropriate information before and after new

distribution network tariffs are implemented.

Table 3 gives a detailed calculation of the electricity bill for the mixed tariff (2008) and the purely

capacity based tariff (2009). We indeed see that due to the fixed tax reduction of the Dutch

government the consumers bill reduces. This reduction is less pronounced as the consumption

volume increases (see Figure 9), which can be a motivation for the consumer to lower his

consumption.

16

2008 tariff Volume amount

Connection Fixed part

Variable part

32,64 euro 32,64

18 euro 18

0,0336 €/kWh 2000 kWh 67,20

Tax reduction 0-10 000 kWh

-199 euro -199

0,0752 €/kWh 150,4

€ 69,24

2009 tariff Volume amount

Connection Fixed part

Capacity charge (25A)

16,44 euro 16,44

18 euro 18

115,6 euro 115,6

Tax reduction 0-10 000 kWh

-318,62 euro -318,62

0,1085 €/kWh 2000 kWh 217

€ 48,42

Figure 9: Effect of the switch to capacity tariffs in the Netherlands in 2009 for different Volumes

(source: Liander) [40]

Table 3: Effect of the switch to capacity tariffs in the Netherlands in 2009 (source: Liander) [40]

17

2.2 Dynamic pricing schemes

In [41] they discuss several dynamic pricing tariffs and their ability to reduce peak loads. Each of

these pricing schemes has been examined in several pilot projects in Europe. During the discussion of

each of these pricing schemes we will mention the results of some pricing pilots.

1. Time of Use (ToU) pricing

ToU pricing tariffs changes several times a day and aims at shifting the demand from one

period to another. A day can have several peak periods where the price is set high with

respect to the rest of the day. Four levels of prices can be distinguished (peak, partial peak,

off peak and weekend tariff). Also a varying season tariff is possible. The peak periods of

consumption are fixed (mornings, evenings,..) and communicated in advance to the end

users. It is very important to notice that ToU pricing only shifts the peak load to another

period without reducing the total consumption. Several pilots were conducted in Europe

with ToU pricing- UK, France, Germany, Northern Ireland and Norway. In these pilots a peak

reduction varying from 0 to 12% is realized.

2. Critical Peak Pricing (CPP)

CPP offers lower tariffs during non-peak hours and substantially higher tariffs during peak

hours. The critical periods here are moments that the electricity price is high due to high

consumption (e.g. very cold or hot weather) or when the stability of the grid is jeopardized

(e.g. risk of black-out). The end user and utility company agree a maximum number -and

length of the peak periods, however the peak moments cannot be set in advance, because

these depend on weather conditions. Usually when the utility company expects a critical day

they inform the end users a day in advance. The number of critical days vary from 1-18 days

a year (San Diego Gas & Electric Company 2010). The TEMPO tariff pilot, that was an

experiment of EDF in France from 1989-1996 with 400 000 recruited end users, has used the

combination of CPP and ToU pricing in its program. This program realized an overall national

peak reduction of 4% and achieved a load shifting up to 30% (for a limited number of days

and hours a year. Dynamic pricing in combination with load control achieved a load shifting

of 50% in Sweden.

3. Critical Peak Rebate/Peak Time Rebate (CPR/PTR)

With a CPR scheme the end user is being rewarded if his consumption is less than what the

utility company expects during a few critical peak hours a year. These are usually very hot

summer afternoons or very cold winter evenings. The same as for CPP, the maximum

number and length of the critical periods are agreed upon beforehand. Just like CPP, the

exact timing cannot be predicted, because it depends on market dynamics, but usually the

end users are informed a day in advance of a critical day. In Europe the need of shifting

critical hours is less than in countries where the climate differences are more pronounced.

That’s why CPP and CPR is not used in a large number of pilot projects. CPP and CPR are

useful when there is a flexible load of significant consumption (e.g. air conditioning). Such

loads can be turned off or put in a less consumption mode during the peak moments. The

most CPP and CPR pilots are outside Europe-US, Australia and New Zealand. In these pilots a

load shift of up to 38% is achieved [42].

18

4. Real Time Pricing (RTP)

With the RTP scheme the electricity price is tied to the market price which can change on an

hourly basis. This electricity price is linked to the price on the APX, which is the stock market

for energy. The end users can be encouraged to reduce their consumption during high price

periods by alerting them when the electricity price reaches a certain threshold (e.g. by a text

message alert). To be truly effective smart appliances need to respond automatically to the

RTP scheme. A number of pilots that have not produced robust results show

the following percentages [42], [43]:

13% peak reduction on the basis of 3 European pilots

10% peak reduction on the basis of 12 American pilots

5. Inclining Block Rate (IBR) Pricing

With the IBR pricing scheme the price of electricity increases stepwise with the consumption.

The first block is the cheapest, sometimes even free, but the subsequent blocks are more

expensive as the consumption increases. IBR pricing schemes mainly aims at encouraging a

reduction in consumption. In Belgium the IBR system is in place since 2001, with the aim to

help low income consumers to keep their electricity bills within limits [44]. A few pilots in

Japan and California showed that IBR pricing is the most effective for a group of end users

with a very high consumption.

2.3 Essential components of a dynamic pricing approach

A dynamic pricing approach can have several end goals, like balancing demand and supply, prevent

grid extension or strengthening, achieve end-user energy saving, etc. According to [41] a dynamic

pricing approach consist of three elements:

The pricing scheme

Supportive technology

Feedback

The pricing schemes have been discussed in the section above. In this section we will discuss the

combination of supportive technology and feedback with dynamic pricing schemes.

2.3.1 Supportive Technology

Supportive technology covers a wide range of devices, such as smart meters –and appliances, In

House Displays (IHD), etc. Smart meters and IHD are a must in combination with dynamic pricing

schemes. The smart meter is needed for actual and real-time metering of the energy consumption

patterns. It makes a bi-directional communication possible between end-users and utility or

suppliers, depending on which party is responsible for the roll-out of the meters. The IHD provides in

several forms feedback to the end-user and has been shown that it improves the responsiveness of

the end-users [42]. In the next section we will discuss the different forms of feedback and the

potential to change the energy behaviour of the end-users. More complex technologies, like smart

appliances, can help to support the behaviour change of the end-users. These appliances can be

19

programmed to automatically respond to changes in information. In a HEMS these changes in

information can be price signals, the amount of available energy in your system and the preference

settings of the end-user. The main advantages of automation is that it allows very quick response to

information change and therefore more effective demand shifting /peak load reduction. The state-

wide California pricing pilot and the SMUD pilot in the US are well-known examples of automation in

combination with pricing schemes. In these countries electrical heating/cooling is wide spread and

can be programmed to respond to peak periods. In Figure 10 some results of different pricing pilots

in combination with automation are presented. As can be seen the level of response to pricing

schemes with automation are significantly larger than without automation. These results need of

course to be nuanced, because of the wide spread of electrical heating/cooling and the climate

circumstances in these countries (hot summers and cold winters). Such results will not be feasible in

Europe, since the climate circumstances and the availability of flexible loads, such as air conditioning,

are different. Several studies have shown that the consumer is concerned to hand over control of his

energy demand to another party. In the Netherlands 53% of the respondents said no to utility control

[45]. The same trend is observed in other European countries . A solution for this is the integration of

a HEMS where the demand control unit is located in the end-users home.

2.3.2 Feedback

Feedback is mainly intended to reduce the energy consumption of the end-user and make him more

aware of his consumption pattern with the aim of trying to change his energy consumption

behaviour. Feedback has gained a lot of attention in research and distinguishes three kinds of

feedback: direct, indirect and associative feedback [46]. Direct feedback consists of information that

is available on request and directly responds to changes in the energy consumption. The advantage

of this feedback is that it directly shows the impact of behavioural changes. Indirect feedback is

characterized by a time delay and is suitable to show the effect of changes in the heating

consumption. Associative/unintended feedback results from (associative) learning. For example

Figure 10: Impact of automation on peak reduction [42]

20

when the bill increases after you bought a new device. With the different types of feedback in mind

we will make a distinction between feedback of price changes and feedback of (changes in)

consumption patterns and volumes. In [47], a study on effective feedback to encourage a

behavioural change towards energy consumption reduction is carried out. In this study they conclude

with a number of recommendations. We will mention a few recommendations that are relevant for

this present work:

A smart meter and a user interface are a must. This user interface can be an In-House-

Display, a smartphone App or an ambient technology (e.g. changing light colours).

Feedback must last at least three months, but is preferably permanent. A minimum of three

months is necessary to have the potential to make a ‘new’ behaviour lasting.

The feedback is direct so that the end-user can immediately see the impact of his behaviour

on the energy consumption. This helps to make energy visible and to set priorities with

regard to behaviours that can be changed and how that will affect energy usage.

The feedback is detailed, providing information about devices, spaces, people and functions

(e.g. cooking, heating, …). Pilots showed that the more detailed the feedback, the more it is

effective in changing the energy behaviour.

The feedback is positive, graphical and symbolic. The most appreciated display of feedback is

a combination of graphical and textual information. Graphs are preferred to show historical

feedback. Feedback is positive and not providing too much information about what is not

achieved, but focus on the remaining saving potentials.

These feedback recommendations will be very important to help change the energy behaviour of

end-users. Although the control of the appliances in a HEMS is fully automated, these feedback

recommendations are still useful to give end-users the insight in their energy consumption and learn

them to deal with the fact that we have to consume energy when it is available. Of course this is just

possible to some extent and is the reason why we foresee a buffer in a HEMS.

As mentioned in the part about supportive technology, the combination of pricing schemes with

automated appliances significantly increased the peak reduction (see Figure 10). In [48] they

investigated the combination of a pricing scheme (ToU, CPP, CPR/PTR, RTP) with multiple supportive

technologies and feedback technologies. They noted that the combination generated a higher peak

reduction. The results of multiple large pricing pilots in the US [48] are shown in Figure 11. According

to [41] these results are easily explainable, because with such a wide range of technologies a large

section of different segments (types of households) can be reached. It is logical that with more

automated appliances a higher peak reduction can be reached, however this will not deliver the most

cost-efficient approach. A new Zealand pilot targeted a particular segment (high incomes, high age,

new houses) and found that the ToU pricing scheme worked fine in combination with energy saving

tips and a monthly bill that showed the realized shifts during peak periods per day [49].

21

2.4 Conclusions

In this section we will conclude with some recommendation and lessons regarding distribution

network tariffs and dynamic pricing tariffs.

Recommendations when designing distribution network tariffs [40]:

Grid users should be able to self-consume and self-generate as long as the costs for using the

grid services is reflected in their bill.

Make network tariff more capacity based, and less volumetric, in order to limit the revenue

uncertainty for the DSOs.

Grid users should receive clear and appropriate information before and after new

distribution network tariffs are implemented.

Grid users should receive compensation from the DSOs when adapting their energy

consumption/generation in response to signals (e.g. at peak times).

Figure 11: Multiple large pricing pilots vs. their percentage reduction in peak load [48] (w/tech: pricing scheme used in combination with automated appliances and feedback)

22

Lessons and recommendations regarding dynamic pricing tariffs [41]:

When focusing on load shifting only, this can increase the total consumption. If e.g. the off-

peak price is too low compared to the peak price it can create an increase in consumption.

ToU pricing schemes targets habitual behaviour, while CPR and CPP focuses on conscious and

less frequent behaviour.

People are not motivated by pricing incentives only. Environmental motives, well-being, are

motivators as well.

Load shifting can be achieved without technology by using fridge magnets and calendars that

indicate the peak periods in a day. Additional technology such as an In House Display

increases the response rate.

Combination of pricing schemes with the appropriate technology gives the largest reduction

in peak load and thus the largest response from the end-users.

2.5 Research questions

The topics that will be investigated in this master dissertation are the following ones:

1. What is the effect on the energy cost when we allow flexibility to some house hold

appliances?

2. What is the effect of the cost objective on the comfort objective and vice-versa?

3. What is the effect of different pricing schemes, ToU and RTP, on the performance of the

optimisation algorithm?

4. What is the effect of the battery degradation cost on the charging and discharging behaviour

of the battery?

23

Chapter 3

Dimensioning

In this chapter we will dimension the electrical and thermal storage system of a HEMS. The

dimensioning of these storage systems are important for obtaining an economical working of the

HEMS. For example when we over dimension the battery it will never fully charge and a part of the

battery capacity will be unused. The opposite holds for an under dimensioning of the battery system.

In this case the energy of the PV installation will not be fully exploited. So it is of great importance

that all the different components are correctly tuned to each other.

3.1 The PV-storage system

When an end-user wants to install a PV-storage system, then the question arises: What are the

advantages with respect to a system without storage? Some end-users will do it out of ideological

reasons other for economic reasons. To evaluate the cost advantage two conventional concepts are

proposed in [50], the self-consumption Zc and the self-sufficiency Zs.

Self-consumption Zc

The self-consumption stands for the share of the produced solar power that is instantaneously

consumed. It is defined as the ratio of the own consumed PV energy and the total produced solar

energy. For a classical PV system with no storage the self-consumption is determined by the

instantaneous consumption and thus depends on the load profile. A system with storage will have a

larger self-consumption, because the self-consumed PV energy is the sum of the instantaneous

consumption and the PV energy to charge the battery.

Self-sufficiency Zs

The self-sufficiency is the share of the required energy that instantaneously can be provided. It is

defined as the ratio of the consumed energy that is self-produced and the total consumed energy.

For a classical installation the self-produced energy is equal to the instantaneous consumed PV

energy. When storage is foreseen the energy that originates from the discharge of the battery has to

be taken into account. This means that not only the self-consumption, but also the self-sufficiency

increases when storage is integrated.

The question that arises: Which storage capacity needs to be foreseen such that these parameters

sufficiently increase and is justified with respect to the investment cost? In [50] a dimension method

is proposed that tries to achieve a balance between these aspects. This method will be further

discussed in this chapter.

24

3.1.1 General dimensioning criteria

When dimensioning a PV-storage system the power of the PV panels needs to be determined. In a

classical residential installation the optimal dimensioning is given by setting the annual production

equal to the annual consumption. This is of course a theoretical target, because the production of a

PV installation is influenced by different factors, such as weather, ageing, pollution of the panels, etc.

Also the annual consumption is variable due to different external factors. According to the VREG the

average consumption of a Belgian family (2 parents, 1 child) is 3500 kWh a year. To take all these

influencing factors into account the PV-installation is a bit over dimensioned in practice. Besides this

limitation, there are also limitations on the PV-power that can be installed:

Limitation on number of panels due to limited roof surface

Maximum legal PV power of 5 kW single phase and 10 kW three phase

Available budget

In practice the system efficiency lies around 80%, because there are some conversion losses in the

AC/DC inverter and the battery. This implies that the total energy use increases as the energy

exchange with the battery increases. Figure 12 gives the optimal ratio (PV production/consumption)

as a function of the effective battery capacity. For an effective capacity of 1kWh/MWh consumption

we need to install a PV installation of 1,11 p.u. ,which implies a production that is 11% higher than

the average annual consumption. The 11% higher production is to compensate for the losses,

because the system has a certain efficiency. The power of a PV installation is given in watt peak, Wp.

This is the electrical power output under ideal conditions (1000 W/m2 solar radiation, solar cell

temperature of 25oC). A standard solar panel with an efficiency of 15% and dimensions of 165x100

cm has a peak power of 250 Wp. The production (kWh) depends on the mean solar irradiation of the

sun and the orientation of the panels. The optimal orientation for Belgium is an inclination of 35o and

orientated to the south. The average solar irradiation in Gent lies around 123 W/m2 (58 W/m2 direct

radiation and 66 W/m2 diffuse radiation). It is important to know that an optimal orientation of the

PV installation does not imply a higher self-consumption. A higher self-consumptions can be obtained

by orientating the panels to the southwest, such that the consumption peak in the evening is better

captured by the PV installation.

Figure 12: Optimal ratio (production/consumption) as a function of the battery capacity [50]

25

In [50] the condition for a proper sizing is an equilibrium between the self-consumption Zc and the

self-sufficiency Zs. Based on measurements on 25 houses a method is developed that estimates the

optimal battery capacity. For a new installation the battery size and the power of the PV installation

can be optimally chosen. The boundary condition that is set for such a system is Zc = Zs. As can be

seen on Figure 13 this corresponds to a storage capacity of 0.98 kWh/MWh, an estimated annual

production of 1,11 p.u. and an estimated Zc = Zs = 55%. Implementing the optimal system is not

always possible due to some constraints that are mentioned above. When the peak power of the PV-

installation is constrained due to limited roof surface, an estimation of the annual production has to

be made. An application on PVGIS (Photovoltaic Geographical Information System) can be used to

make an estimation for the annually production

(http://re.jrc.ec.europa.eu/pvgis/apps4/pvest.php?lang=en&map=europe). When the average

production is estimated, we can calculate the ratio production/consumption and read the storage

capacity on Figure 13. To better understand this method, we will illustrate with a small example.

Example [50]:

Assume a house with a mean consumption of 4.5 MWh/year and a PV production of 2.7 MWh/year.

This is equal to a ratio of 2.7/4.5 = 0.6 p.u. From Figure 13, it follows that the optimal capacity is

approximately 0.65 kWh/MWh, which corresponds with a battery capacity of 0.65 x 4.5 = 2.9 kWh, a

Zc = 70% (green line) and a Zs = 40% (blue line).

Figure 13: Optimal storage capacity (top) and Zc, Zs as a function of PV production [50]

26

3.1.2 Battery types

Batteries form an essential part of the PV-storage system, therefore it is important to understand the

characteristics and limitations of a battery. We will discuss some important parameters which needs

to be taken into account when choosing an appropriate battery for your application.

The battery capacity is a measure for the amount of energy that can be stored and is usually

expressed in ampere-hour (Ah). Because the capacity is influenced by some external factors, such as

temperature and discharge current, it is expressed under standard conditions. Usually this is defined

as the product of 20 hours and the current the battery can supply for 20 hours at a standard

temperature of 20oC, while remaining above a specific voltage per cell. For example a battery with a

capacity of 100 Ah can deliver 5 A over a 20-hour period at 20oC. This brings us to another battery

parameter, namely the Charge-rate or C-rate. The C-rate is the speed at which a battery discharges

and is expressed relatively to the battery capacity. When we discharge with a constant current at a

1C rate, the battery will be fully discharged after one hour. In reality there will be some losses, due to

the internal resistance, through which the effective capacity will be lower than 100%. The effect of

temperature and discharge rate on the capacity is illustrated in Figure 14. Observe how the capacity

decreases as the C-rate increases. It seems that a temperature increase has an increase in capacity at

a constant C-rate. This may look as a positive effect, but the lifetime of the battery decreases with

the temperature (see later in Figure 17 left). As a rule of thumb we can say that the lifetime reduces

with a factor two per 10oC higher than 25oC.

The State Of Charge (SOC) and the Depth Of Charge (DOD) are the two parameters that are used to

monitor the performance of a battery. The SOC is a measure for the amount of energy the battery

contains at that moment and is the ratio of the current capacity and the rated capacity of the

battery. Because it is not directly measurable, the SOC is measured indirectly through a voltage

measurement or through other specific parameters of the battery. The DOD indicates the amount of

energy that is already consumed. It is expressed as a percentage of the rated capacity and is linked

with the SOC trough DOD = 100% - SOC. If the battery is completely discharged until the DOD reaches

100%, the lifetime of the battery reduces significantly. A good balance between a useful capacity and

a long lifetime is of great importance. The optimal DOD is however dependent on the battery type.

Some target values for different battery types are given in Table 4.

Figure 14: Battery capacity versus temperature and charge-rate [50]

27

The battery voltage is an important parameter when a battery needs to be charged. There are

several voltages defined for a battery. The nominal voltage is the voltage displayed on the

registration plate of the battery. A battery bank is composed of multiple cells, each with a type

specific voltage. A lead-acid battery cell has a nominal voltage of 2 V, a lithium battery has 3.6 V. By

combining these cells in series, the battery voltage can be tuned to the DC input voltage of the

inverter. The instantaneous voltage of the battery varies around the nominal one and depends on

the SOC.

The Open Circuit Voltage (OCV) is the voltage of the battery in no-load condition. The OCV can give

you an idea of the SOC of the battery. To obtain a proper measurement the battery needs to stabilize

after use. This can take up to 24 hours dependent on the battery type. To illustrate Figure 15 depicts

the relation between the SOC and the OCV of an AGM (Absorbent Glass Mat) battery. In this case the

relation is linear, but this varies depending on the type. The Closed Circuit Voltage (CCV) is the

voltage during charging and discharging mode of the battery. When a current flows through the

battery, there will be a voltage drop over the internal resistance of the battery. The larger the

current, the bigger the voltage drop. This means that the CCV tells us something about the charging

and discharging of the battery. A battery has a minimal allowed voltage, called the Cut-off voltage.

This is the voltage at the terminal of the battery when it is completely discharged. Discharging the

battery below the cut-off voltage often result in damaging the battery and needs to be avoided at all

time.

When charging a battery it is important to set the correct voltage at the terminal of the battery. The

charging happens in a couple of phases and is shown for a lead-acid-and a lithium-ion battery in

Figure 16. Charging a lead-acid battery happens in three stages. In a first stage the battery is charged

with a constant current and is known as the constant current charge. In this stage the battery is

charged until 70 to 80% of its capacity. The voltage increases until the absorption voltage is reached.

When this voltage is reached, the charger switches to the topping charge. In this phase the voltage is

kept constant and the current drops. When the battery is almost fully charged the third phase,

namely the float charge, is initiated. This phase compensates for the loss caused by the self-discharge

of the battery. The charging cycle of a lithium-ion battery (Figure 16-right) is for the two first phases

the same as a lead-acid battery, but with different voltage levels and a smaller tolerance. The cycle

contains now four phases, with an extra phase to charge the battery when the voltage goes below a

certain threshold value.

Figure 15: State Of Charge (SOC) as a function of the Open Circuit Voltage (OCV) for a AGM-battery [50]

28

To guarantee the lifetime of a battery the parameters of the charging cycle needs to be set in the

inverter. The Lifetime of a battery is an important parameter, due to the high investment cost of a

battery system. It is difficult to forecast and depends on the way the battery is used. For batteries

there are two types of lifetime, namely the calendar lifetime and the cycle lifetime. The calendar

lifetime is the expired time before a battery becomes unfunctional, whether the battery was active

or not. This is, among other things influenced by the temperature of the environment the battery

works in. Figure 17 (left) shows the influence of the temperature on the calendar lifetime. On the

other hand the cycle lifetime is the number of cycles a battery can go through until its capacity is

dropped to 80% of its rated capacity. A cycle is defined as one fully charge cycle followed by one fully

discharge cycle. The cycle lifetime given by the constructor is a target value and is strongly

dependent on the DOD that is imposed. A typical characteristic for a AGM battery is given in

Figure 17 (right). A lower DOD results in a higher cycle lifetime, but results in a smaller utilization of

the battery capacity. A tradeoff between lifetime and utilization of the battery has to be made.

Figure 16: The charging characteristic of a lead-acid (left) -and a Li-ion battery (right) [50]

Figure 17: Calendar lifetime of a Li-ion battery (left) and cycle lifetime for a AGM battery (right) [50]

29

To wrap up we will discuss a number of battery types that are qualified to use for residential energy

storage. Table 4 summarizes a number of parameters of different battery types. Note that for the

Nickel iron type battery the cost and cycle lifetime are still uncertain according to [50].

Battery type Power density [W/l]

Energy density [Wh/l]

Cost *€/kWh/cell+

Lifetime [# cycles]

η efficiency

[%]

Weight [kg/l]

DOD [%]

Flooded Lead Acid

85 60 0.1 1100 60-70 2 50

AGM Valve Regulated Lead-acid

110 100 0.44 450 85-95 2 40

Gel Valve Regulated Lead-acid

90 80 0.4 900 90-95 2 70

Lithium-iron phosphate

427 280 0.3 2000 85-92 2.34 80

Nickel-metal hydride

218 200 0.45 1000 66-85 2.75 60

Nickel-iron 77 30 ? ? 65-85 1.3 80

The lead-acid battery is the oldest and most well-known battery type. Due to a low cost this type of

battery is still the most used one. The electrodes are manufactured from lead and lead oxide and are

submerged in an electrolyte consisting of a blend of sulfur acid and distilled water. The lead-acid

batteries can be divided into two categories, namely the Valve Regulated Lead-acid (VRLA) and the

Flooded Lead-acid (FLA). During charging, the electrodes must be completely submerged in the

electrolyte at all times to avoid damage to the battery cells. This requires a regular maintenance of

the battery by adding distilled water, because the electrolyte escapes as gas during the chemical

reaction. Due to the explosiveness of the gas, ventilation needs to be foreseen. This makes the FLA

battery less fit for residential use.

The VRLA battery is developed to eliminate the necessity of adding distilled water and to make it

possible to use a lead-acid cell in every position. The chemical process is not 100% efficient, which

means that in time a VRLA battery will run dry. This indicates that maintenance is still necessary, but

less frequent than for a FLA battery. Within the group of VRLA batteries a distinction based on the

transport medium is made. In this way they distinguish the Gel- and AGM (Absorbent Glass Mat)

VRLA battery. Gel cells add silica dust to the electrolyte, forming a thick gel. This reduces the

movement inside the battery case and makes it possible to use it in every position. Many gel

batteries also use a one-way valve instead of open vents. This helps the internal gasses to recombine

Table 4: Parameter values of some commonly used battery types [50]

30

back into water and reduces the gas leaks. Gel cells must be charged at a lower voltage (C/20) than

flooded or AGM cells to prevent excess gas from damaging the cells. Fast charging them may lead to

permanent damage to the cells. These batteries are sometimes referred to as ‘silicone batteries’.

AGM batteries hold their electrolyte in the glass mats and does not freely flood the plates (which is

the case in a FLA battery). The absorbent glass mats are used to absorb the electrolyte and provides

channels for oxygen gasses which will participate in the recombination reaction to prevent the

escape of hydrogen and oxygen gasses. Due to the physical properties of gelled electrolytes, the

power of a Gel battery declines faster than an AGM battery as the temperature drops below 0oC.

AGM batteries are good for high current -and power applications.

The Lithium-iron phosphate (LFP) battery is commercially available since 2006 and is evolved from

the classical lithium-ion battery. LFP batteries have a high energy density and perform well in the

field of safety, lifetime and power density. These features make the LFP battery ideal for electrical

vehicles, electrical equipment and residential storage. A disadvantage with respect to the FLA is the

higher cost. In several applications, especially solar power, efficiency is of great importance. The

round trip energy efficiency (discharge from 100% to 0% and back to 100% charged) of the average

lead-acid battery lies around 80%. The round trip energy efficiency of a LFP battery is 92%. The

charge process of lead-acid batteries becomes inefficient when the SOC reaches 80%. In contrast a

LFP battery will still achieve 90% efficiency under shallow discharge conditions [51].

The Nickel-metal hydride (NiMH) battery is developed in the eighties with the first application in the

aerospace, because of its high energy density and long lifetime. Just as the VRLA battery, also the

NiMH battery is completely sealed and requires little maintenance. NiMH and NiCad batteries are

one of the most difficult batteries to charge accurately. For Li-ion and lead acid batteries you can

control overcharge by setting a maximum charge voltage. The nickel based batteries do not have a

‘float charge’ voltage, so the charging is based on forcing a current through the battery. The voltage

to do this is not fixed like other battery types. Charging these cells in parallel is difficult, because it is

not sure that each cell or pack of cells has the same impedance, which means that some will take

more current than other cells, even when they are fully charged. This indicates that each string in a

parallel pack will need a separate charging circuit or we need to balance the current in another way.

For example by using resistors that dominate the current control. The charging efficiency of a NiMH

battery is typically 66%, meaning that you need to put 150 Ah into the battery for every 100 Ah you

get out. The faster you charge, the worst this gets. NiMH batteries are sensitive to damage on

overcharge when the charge rate is higher than C/10. Charging a battery of 100 Ah with a C/10 rate,

meaning charging with a current of 10 A, takes 10 hours to fully charge [52].

The Nickel-iron (NiFe) battery is invented by Edison in 1901 and is still often called the ‘Edison

battery’. This type of battery has a good resistant against both overcharge and deep discharge. It is a

very robust battery which is tolerant of abuse and can have a very long lifetime, even if treated bad.

The battery manufacturer Iron Edison sells NiFe batteries of 100 Ah with a cycle life of 11000 cycles

at a DOD of 80% and a lifetime on float of 30 years. The battery storage life is even 85 years. This

type of battery costs 808 $/kWh or 733 €/kWh, but has a very low cost per kWh per cycle (0.07

€/kWh/cycle) due to its high cycle lifetime [53]- [54]. According to [50] the lifetime of NiFe batteries

is not proven yet, but looks promising for residential storage.

31

3.1.3 Sizing the PV-storage system

In this section we will dimension the PV-storage system with the method explained above. In a first

step we will sum up all possible electrical devices in a house and their corresponding daily

consumption to get an idea of the energy demand for each appliance. Furthermore we assume a

house with characteristic data given in Table 5.

The consumption data profile of some appliances are found in [55]. These consumption profiles will

be used in the present work to examine the demand response possibilities of some appliances. The

profiles are not necessary for the sizing of the PV-storage system, but give an idea how much energy

a typical device consumes in a day.

Appliance Energy consumption [Wh] Duration [h] Peak power [W]

Dishwasher 1433 2,2 1180

Washing machine 230 1 1000

Tumble dryer 1358 1 2950

Oven 750 0,5 3000

Micro wave oven 500 0,5 750

Deep fryer 1850 0,75 1800

cooker hood 90 0,75 150

Refrigerator 1497 24 135

Freezer 580 24 100

TV,radio,modem 1830 4 500

Computer 290 3 100

Flat iron 1340 2,5 1200

Coffee set 170 0,25 1100

Vacuum cleaner 1460 1,5 1000

Lighting 1410 4 350

Laptop 210 5 90

Total 14998 24 15405

Average yearly consumption 3.5 MWh

Grid connection 40A, single phase

Favourable roof surface 37 m2

Roof orientation SE

Roof inclination 30o

Table 5: characteristic data of a typical Belgium house [50]

Table 6: Average energy consumption per day for some typical household appliances [50]- [55]

32

We see that the peak power is very high, but the different appliances will never work at the same

moment. This implies that there will be a certain dispersion of the total power. Besides many devices

will rarely work at their peak power. In a next step, we will determine the storage capacity based on

the data given in Table 5. The yearly consumption of 3.5 MWh gives a mean daily consumption of

approximately 10 kWh. Of course this does not correspond with the nearly 15 kWh given in Table 6,

because not all appliances will be used every day. From the research in [50], it seems that

1kWh/MWh is approximately a good estimation for the storage capacity. Note that this corresponds

with the criterion Zc = Zs in Figure 13.

From equation (1) it follows that we need a battery with a useful capacity of 3.5 kWh. Depending on

the type of battery a maximum Depth Of Charge (DOD) will be taken into account. The DOD indicates

how much energy the battery delivers. Another important battery parameter is the State Of Charge

(SOC). This parameter is linked to the DOD as follows DOD = 100%-SOC and is a measure for the

amount of energy the battery possesses at that moment. Note that the DOD and SOC are been

expressed as a percentage of the maximum capacity of the battery. In Table 7 the DOD of different

battery types is given.

Battery type DOD [%]

Flooded Lead Acid (FLA)

50

AGM Valve Regulated Lead-Acid (AGM VRLA)

40

Gel Valve Regulated Lead-Acid (GEL VRLA)

70

Lithium-iron phosphate (LFP)

80

Nickel-metal hydride (NiMH)

60

Nickel-iron (NiFe) 80

The effect of this parameter and other parameters on the lifetime of the battery is already discussed

in the previous section. If we choose the Lithium Iron Phosphate (LFP) battery with a DOD of 80%

than the real battery capacity in kWh is:

(1)

Table 7: Maximum Depth Of Charge (DOD) for different battery types

(2)

33

The capacity of a battery is usually expressed in Ah (Ampere hour). If we assume that the inverter

works at a DC voltage of 48 V, the real battery capacity in Ah is:

In practice a packet LFP batteries with a capacity of 100 Ah can easily be constructed. The last

parameter that needs to be determined is the peak power of our PV installation. As already

mentioned above batteries work with a certain efficiency (charge-and discharge efficiency). From

Figure 13 it follows that the optimal PV production is 11% (1.11 p.u.) higher than the yearly

consumption. Therefore the yearly PV production is estimated at:

The optimal orientated installation in Flanders has a yield of 950 kWh/kWp [50]. Given the SE

orientation and a roof inclination of 30o a correction factor of 0.96 follows from Table 8. This gives us

the following peak power for our PV installation.

Correction factor for a specific orientation and roof inclination

Inclination Orientation

0o 30o 60o 90o

West 0.93 0.90 0.78 0.55

South East 0.93 0.96 0.88 0.66

South 0.93 1 0.91 0.68

South West 0.93 0.96 0.88 0.66

West 0.93 0.90 0.78 0.55

Table 8: Correction factor for a specific orientation and roof inclination (source: HESPUL) [56]

Annually consumption 3.5 MWh

Power of PV panels 4.5 kWp

Estimated annually production 3.9 MWh

Battery type LFP

Capacity of home battery 100 Ah (48 V)

Estimated self-consumption Zc 55%

Estimated self-sufficiency Zs 55%

Table 9: Summary of the results of chapter 3

34

To obtain the desired peak power of 4.3 kWp we use 18 panels of 250 Wp. The total peak power is

then 4.5 kWp. The surface of one panel is 1.6 m2, which mean that the total area is 28,8 m2 ( = 18 x

1.6 m2). This is feasible, because the available roof surface is 37 m2. To wrap up the result are

summarized in Table 9.

3.2 Thermal Storage System

The thermal storage system consists of a Combined Heat and Power (CHP) unit, a Heat pump (HP)

and a hot water tank. A CHP unit is a device that simultaneously produces useful heat and electricity

from a single fuel source. The CHP or co-generation is widely used in large industry due to its efficient

use of fuel. The generated electricity is consumed on-site and the recovered heat is used in an

industrial process or fed into a district heating network [57]. The same concept can be used on a

smaller scale in buildings. These types of CHP units are called micro-CHP units. Micro-CHP systems

are powered by different prime movers, but the most advanced ones are fuel cells, Stirling engine

and internal combustion engine [58]. Studies have been established to assess the performance of an

building-integrated micro-CHP. In [59] such a study is conducted and demonstrated in terms of

primary energy saving and CO2 emission reduction. These two concepts have led to an growing

interest of integrating micro-CHP systems in buildings. The size of an micro-CHP unit can vary from an

electrical output of 1 kWe for a single family house to over 15 kWe for office buildings or small hotels.

For the CHP unit with an Internal Combustion Engine (ICE) as prime mover, the four-stroke spark

ignition engine is typically used. These engines are typically fuelled with natural gas, because of the

lower emissions (CO2) with relation to other fossil fuels such as gasoline or diesel. Approximately

one-third of the fuel energy is converted into mechanical work that drives the generator to produce

electricity. A part of the energy is recovered from the exhaust gasses by the heat recovery system.

Figure 18: A basic configuration of a micro-CHP unit with thermal storage [58]

35

The exhaust gasses have a temperature of 300-600 oC, which indicates that an significant amount of

heat still can be recovered. In general commercially available ICE based micro-CHP units have an

electrical efficiency of 24-30% and an thermal efficiency of 60-70%. This means that an overall

efficiency of 70-80% can be reached. Commercially available micro-CHP systems based on ICEs will be

summarized later in this chapter. A basic configuration of a micro-CHP unit with thermal storage is

shown in Figure 18. The water is drawn below from the tank and first passes the engine cooling heat

exchanger. This is typically a plate heat exchanger that cools the engine. The hot engine cooling

water than passes further to the exhaust gas heat exchanger where the hot gasses further heat up

the water. The thermal buffering is used to improve the thermal efficiency and reduce the duty cycle

of the system. An increasing duty cycle results in a reduced lifetime of the unit and a reduction in fuel

efficiency. The thermal buffering is usually implemented as an insulated tank of which the

temperature is limited to 100oC, because the cooling of the engine must be maintained. The space

heating and domestic hot water circuits run from the thermal storage tank by means of heat

exchangers. Instead of water, the energy storage medium can be a combination of water and a phase

change material (PCM). This improves the storage efficiency, because a smaller volume can be used.

A smaller volume results in smaller heating losses to the environment and thus improves the

efficiency [58].

In [60] a CHP unit is used in combination with a Heat Pump (HP). A CHP-HP system has the potential

to reduce the heat pump energy consumption during cold periods by using the heat recovered from

the PGU (Power Generator Unit), which is another name for CHP unit. This could improve the overall

efficiency and reduce the operational cost. In this article they present the design and feasibility study

of a CHP-HP system in a single family home. The operation cost of a CHP-HP system is compared to

the operation cost of a conventional HP system. Figure 19 represents the basic configuration of the

CHP-HP system proposed in [60]. In this configuration the electrical power to operate the heat pump

is foreseen by the CHP unit. The recovered heat from the CHP unit is used to provide additional heat

to the space heating -and hot water circuit of the building. This recovered heat is first used to provide

the space heating demand and the remaining is used to provide hot water for the building. An

auxiliary electrical heater and a gas fired boiler is foreseen to provide additional energy, when the

recovered heat is not sufficient.

Figure 19: Schematic diagram of CHP-HP system [60]

36

3.2.1 Sizing the Thermal Storage and CHP unit

Based on the two concepts shown above, we propose the following configuration (see Figure 20) of

the thermal storage system we will use in this work. A dimensioning of the different components will

be conducted based on space heating demand -and hot water consumption data.

The natural gas FNG comes in the ICE of the CHP unit and simultaneously produces heat QEG and

electrical power PCHP. The heat is recovered in the heat recovery system and delivered (QCHP) to the

thermal storage tank. This hot water (Qhot water) is then supplied to the hot water circuit of the

building. The electrical power that the CHP unit produces is fed to the HP that delivers Qspace heating to

the building. The excess of produced electrical power is than supplied to the grid or battery. If there

is less production, the difference is buffered by the battery, grid or directly by the PV-system. To size

the CHP unit we must notice that the hot water demand is the restricting factor in this problem,

because hot water can only be replenished by the CHP unit. This is a choice we make to keep the

control logic of our HEMS simple, because there also exist heat pumps that can heat up water. The

useful heat QCHP can be written as:

( )

A CHP unit has an electrical efficiency ηe, which means that the fuel energy FNG and electrical energy

PCHP are coupled with the following equation:

The heat recovery system has a thermal efficiency ηHRS, this implies that Qw can be written as:

(3)

(4)

Figure 20: Schematic diagram of thermal storage system

37

( )

If we insert equation (4) and (5) into equation (3) we obtain the relation between the electrical -and

thermal output of a CHP unit.

( )

( )

, ( )-

From these equations we can also derive the total efficiency of a CHP unit.

( )

The next step is to look at the daily hot water consumption profile. According to [61] the historically

most widely used hot water profile has been the so called ‘ASHRAE draw profile’. In [61] they made a

review of the source data (Perlman,1985). From this review two important considerations have been

revealed: first, all monitored data is from Canadian residences, and second, typically houses with two

adults and two children where a cloth washer and dishwasher are present. This data is given as a

percentage of the total daily hot water consumption (see Figure 21). So if we multiply this data with

the daily consumption of hot water, we obtain a consumption profile in liter per hour. A single family

house (4 members) consumes approximately 150 l/day according to [62]. This corresponds to an

energy of:

( )

(5)

(6)

(7)

38

We have assumed that cold water at 16 oC comes in and is heated to the desired 60 oC. We need 5.11

kWh of energy to cover the heat demand in a day. If we assume that we have a time available of 1

hour to heat the water in the storage tank to the desired temperature, than we need a CHP unit with

a thermal power output of approximately 5 kW. In the next section we will sum a number a

commercially available micro-CHP units. To see if the 5 kWth is a feasible power for the given hot

water profile a small model is made in Simulink. The following first-order differential equation, which

represents the thermal energy flow in the thermal storage system, is implemented in Simulink.

( )

The hot water tank is modeled as a closed system, where heat is extracted through a heat exchanger

(see Figure 18). We assume that the CHP unit works at its nominal power when turned on, so

dynamical behaviour is neglected in this simple model. The first term at the right part of equation (8)

represents the input heat energy from the CHP unit, the second term is the heat extracted by the hot

water circuit of the building, and the last term represents the heat losses to the environment. We

assume that the tank is placed in an non-heated room with an ambient temperature Tambient of 15oC.

The heat losses to the environment can then be written as:

( )

The overall heat transfer coefficient UTS is given by [58]:

Where,

(8)

Figure 21: Hot water usage profile [61]

39

Is the radiation term. The convective heat transfer coefficient for the thermal storage were taken as

free convection in water and air. The conductivity coefficient and thicknesses L were taken from [58].

This gives a global heat transfer coefficient of:

We assume a thermal storage V that is equal to the average daily hot water consumption, which is

150 liters in our case. The typical height of a storage tank is 1.2 m. If we assume the tank has a

cylindrical form, this gives us a surface ATS of:

√

Now that all parameters are known the simulation in Simulink is run. Figure 22 shows the

temperature of the hot water inside the tank. We have started with an initial water temperature of

16 oC inside the tank. As can be seen on Figure 22 this takes approximately one hour until the water

temperature reaches 60oC. After that the temperature is controlled within the desired temperature

range of 50-60oC. From these simulations we can conclude that the chosen CHP unit with a thermal

output of 5 kW is a feasible choice to cover for the hot water demand profile given in Figure 21.

Figure 23 shows the thermal output power of the CHP unit. The first on period is the largest, due to

the cold water at the start. To finish the part of the CHP unit, we will show a number of commercial

available CHP units and their characteristics. This information is shown in Table 10.

Figure 22: Temperature of hot water inside thermal storage tank

40

CHP unit ECOWILL, freewatt,

ecoPOWER 1.0

ecoPOWER 3.0/4.7

SenerTec Dachs

ZuhauseKraftwerk

Yanmar

Engine Honda GE160EV

Marathon engine

Dachs Volkswagen CNG 2.0

Miller Cycle gas engine

Cylinders 1-cylinder 1-cylinder 1-cylinder 4-cylinder 3-cylinder

Electrical efficiency

26.3% 24.7% 27% 33.5% 31.5%

Thermal efficiency

65.7% 65.7% 61% (72%) 56.4% 53.5%

Overall efficiency

92.0% 88.9% 88% (99%) 90% 85%

Electrical/ Thermal output

1.0 kW/2.5 kW

1.3–4.7 kW/4.0-12.5

kW

5.5 kW/ 12.5 kW (14.8kW)

19 kW/32 kW 10 kW/16.8 kW

Voltage 230 V, 50/60 Hz, single

phase

400 V, 50 Hz, 3 ~

230/400 V, 50

Hz, 3 ~

400 V / 50 Hz, 3 ~

240/120 ACV, 60 Hz, single

phase

Sound level < 52 dB (A) < 52 dB (A) 52–56 dB (A) < 50 dB (A) 56 dB (A)

Maintenance interval

6000 hours 4000 hours 3500 hours 5000 hours 10000 hours

Table 10: Commercial available micro-CHP units [58]

Figure 23: Thermal power output of CHP unit

41

3.2.2 Sizing The Heat Pump

To determine the power of a heat pump, the heat losses of the building need to be determined. The

calculation of these losses are stipulated in the norm NBN EN 12831 [B22] and- specific for Belgium

applications- in the NBN B 62-003 [B2] norm. For the calculation of the heat losses, the worst case

scenario is assumed. This means that the heat installation needs to deliver the heat demand at the

lowest possible outdoor temperature. In [63] they propose that the total thermal heating power

(ΦHL) that need to be installed is a sum of the transmission losses (ΦT), the natural-and/or mechanical

ventilation losses (ΦV ) and a term that takes the required heating power into account (ΦRH):

( )

With i the number of heated rooms. In [64] a heat load calculation of a single family house using the

CLTD/GLF (Cooling Load Temperature Difference/Gain-Loss Factor) method is carried out. These

calculations are based on the house with a floor plan shown in Figure 24. The heat transfer

coefficients U of the roof-and wall construction, the doors and the windows are shown in Table 11.

For each room we have to calculate the heat loss by transmission. This typically consist of different

terms, depending on whether the room has a window, partition wall or outer wall. The general

formula for the heat transfer loss by transmission is given by:

(W)

Where U is the heat transfer coefficient and A the heat exchanging surface. For an outer wall the

temperature difference is Ti – To, where Ti is the indoor temperature and To is the outdoor

temperature. For the inner/partition wall we use a temperature difference of Ti – Ta, where Ta is the

adjacent room temperature. For simplicity we assume that adjacent rooms that are not heated have

a temperature of 15oC. This is an assumption we make to make the calculations a bit easier. For

clarity we will do the calculation for the living room. The calculation for the other rooms are similar

and are summarized in Table 13.

(9)

Item U [W/m2K]

Roof construction Conventional roof-attic-ceiling combination

0.28

Wall construction Brick, insulation, gypsum wallboard Partition wall

0.34

0. 4

Doors Wood, solid core

1.82

Windows Clear double-pane glass in wood frames 3 mm thick The window glass has a 600 mm overhang at the top. Assume closed, medium-colour venetian blinds.

2.84

Table 11: The heat transfer coefficients of the different construction items in a house [64]

42

The living room has one outer wall and two partition walls. The outer west wall has a window and

door with the dimensions given in Figure 24. The heat loss through this wall is given by:

( ) ( ) ( ( ))

In the introduction we have mentioned that the heat losses are calculated for the worst case

scenario. According to the NBN B 62-003 [B2] norm the temperature of the worst case scenario that

need to be taken into account in the region East-Flanders is -8oC. The average indoor temperature is

assumed to be 20oC. The garage is typically a room that is not heated. As mentioned above, this

room has a temperature of 15oC. Now the heat losses through the partition walls can be calculated.

For the partition wall between living room and garage we obtain:

( )

( ) ( )

The heat losses through the door, the window and the roof still needs to be determined. These

values are respectively :

( ) ( ( ))

( ) ( ( ))

( ) ( ( ))

If we add everything up we become the transmission heat loss of the living room in equation (10).

Figure 24: House floor plan of a single family house [64]

1 2

3

43

The formula that is used to calculate the ventilation loss in a room is shown in the equation below

[63]. The ventilation flow is determined by the nature of the ventilation systems, where we make a

distinction between natural ventilation and forced ventilation. The ventilation guidelines for the

different areas in a house are found in a source book called the Residential Exposure Assessment.

The table from this book is for convenience shown in Figure 25.

( ) ( ) (W)

Where:

HV is the heat transfer coefficient by ventilation (W/K)

qV is the ventilation flow in the room (m3/h)

ρa is the mass density of air (1.2 kg/m3)

ca is the specific heat capacity of air (0.278 Wh/kg.K)

The ventilation flow is calculated with the Air exchange Rate (ACH) values given in Figure 25. The

general formula is given by

Where V is the volume of the living area. The living room falls in the class of the living areas and

requires a ventilation rate of 0.35 h-1 [65]. This corresponds to a ventilation flow of

( )

If we fill in all the parameters we obtain a ventilation loss of:

( ( ))

(10)

(11)

Figure 25: Air Exchange Rates (ACH) for different environments in a single family house [65]

44

The last term of equation (9), namely the required heating power φRH, still need to be determined. In

[63] they propose the next formula to calculate φRH

(W)

Where:

Af is the floor area of the heated room (in m2)

fRH (W/m2) is the heating factor, which depends on the heat-up time and the adopted

temperature drop of the room temperature when the heating system is turned off. In

Table 12 a number of target values for fRH are given.

If we assume the heat-up time is one hour with an temperature drop of 2K (fRH = 22), the required

heating power for the living room is

( )

This gives us for the living room a total thermal heating power of:

Heat-up time (h)

Residential

1 K 2 K 3 K

Heating factor fRH (W/K)

1 11 22 45

2 6 11 22

3 4 9 16

4 2 7 13

The same approach is used for the other rooms. The calculations for these rooms are carried out in

Excel and summarized in Table 13. From the calculations it follows that the total required thermal

heating power that need to be installed is approximately 8.2 kWth. If we use a heat pump with a

Coefficient Of Performance (COP) of 3 we need a heat pump with a rated power of 2.7 kWe.

A last thing that needs to be determined is the heat gain rate Gt (Wh/h) of the house. The heat gain

rate is the rate the house looses heat to the outside through the outside walls, doors, windows and

roof. It actually expresses how good or bad the house is isolated. The expression for Gt is given by the

equation below and is a function of the inside-and outside temperature at every instant t.

( ) (Wh/h)

Table 12: Heating factor for different heat-up times and temperature drops [63]

45

G0 (W/K) describes the amount of heat loss per K difference between inside -and outside

temperature. This parameter depends on the heat transfer coefficients U and areas A of the outer

parts of the house. The calculation for G0 is carried out in Excel, but for clarity this parameter will be

determined for the living room. In equation (10) and (11) the transmission and ventilation loss of the

living room is determined for the case of an inside temperature of 20oC and an outside temperature

of -8oC. As already mentioned G0 is the amount of heat lost per K difference between the indoor -and

outdoor temperature. This gives us for the living room a G0 factor of:

( )

The same approach is used for the other heated rooms, which are carried out in Excel. This gives us a

total heat gain rate Gt of:

( ) (Wh/h)

This parameter will be later used in the modeling part of the heat pump in chapter 4. To wrap up the

result of this chapter are summarized in the table below.

Battery capacity CBat 4.8 kWh

Rated power of PV panels 4.5 kWp

Rated power of CHP unit 5 kWth

Volume of thermal storage 150 l

Rated power of heat pump 2.7 kWe

Environment ( ) ( ) ( ) ( )

Living room (fRH=22,ACH =0.35)

632 345.6 980 1957.6

Kitchen (fRH=22,qV = 25 l/s)

447.3 840.7 496.5 1784.5

Bedroom 1+2 (fRH=11,ACH =0.35)

686.5 239.5 335.8 1261.8

Bedroom 3+bath (fRH=11,ACH = 0.35)

958.4 472.5 662.5 2093.4

Utility (fRH=6, qV = 7.5 l/s)

640.6 252.2 183.2 1076

Total 3364.8 2150.5 2657.9 8172.3

Table 13: The calculation of the total heating power for each room of a single family house

(12)

Table 14: The dimensioning results of chapter 3

46

Chapter 4

Modelling

In this chapter the models for the home battery, the thermal storage system (CHP unit and thermal

storage), the heat pump and the non-interruptible loads, namely the washing machine, the

dishwasher and the cloth dryer, will be determined. Also the operating constraints of each appliance

will be described in this chapter. The decision vector that is sent by the scheduling module to the

monitor module (see Figure 2) is written as [4]:

, -

Where

,

- is the power that is feed into or withdrawn from the

battery at every time slot N.

,

- is the power that is withdrawn or feed into the grid at

every time slot N.

,

- is the working status of the heat pump at every time slot N.

,

- is the working status of the combined heat and power

unit at every time slot N.

,

- are the starting times of the non-interruptible loads, where

WM: Washing machine, DW: Dishwasher, CD: Cloth dryer.

Note that Pbat and Pgrid are double vectors, SHP and SCHP are binary vectors, and Tstart is a discrete

vector.

4.1 The Battery

The HEMS needs to prevent the home energy storage battery from overcharge and overdischarge by

controlling the SOC within a specified range [SOCmin,SOCmax], where SOCmin and SOCmax are the

minimum and maximum allowable SOC of the battery. This constraint is depicted in the equation

below.

The batteries SOC associated with the charge and discharge of the battery is calculated by the

following equations, respectively [4]:

(13)

47

Where Cbat is the rated battery capacity in kWh, PBat,tch and PBat,t

disch represent the charging -and

discharging power of the battery at timeslot t, ηch and ηdisch are the charging -and discharging

efficiency of the battery system. Note that this also includes the efficiency of the inverter (see

Figure 26). For safety the charging and discharging powers should be controlled such that it is smaller

or equal to the maximum allowable values. This results in two other constraints that need to be

fulfilled:

A schematic diagram of a grid-interactive PV- system with battery is shown in Figure 26. The battery

and PV-system are coupled on the same DC-bus, such that only one inverter is needed instead of

two. The coupling with the battery is via a Maximum Power Point (MPP) controller that controls the

working point such that the PV panels work at their maximum power and delivers the right DC-

voltage at the exit. In practice the control logic such that the above constraints are satisfied is

implemented in the inverter.

(14)

(15)

(16)

Figure 26: Schematic diagram of a grid-interactive PV-system with DC -coupling [50]

48

4.2 The Thermal Storage System

As shown in Figure 20 the thermal storage system consists of the CHP unit, the thermal storage tank

and the heat pump. The CHP unit and the thermal storage tank will be modeled together. The heat

pump that satisfies the space heating demand of the house will be modeled separately.

4.2.1 The thermal storage tank and CHP unit

The thermal storage tank and CHP unit are used to deliver the hot water demand of the house. It is

clear that in this problem the temperature of the hot water in the thermal storage need to be

controlled. The user consumes hot water at approximately 50oC-60oC. When the temperature of the

hot water exceeds one of these bounds, it gives the HEMS a signal to start or stop the CHP unit. The

first order differential equations represented in equation (8) will be used to model the temperature

inside the thermal storage tank. For convenience equation (8) is repeated here.

( )

The equation will be rewritten in a more convenient form, such that it can later be used in the

optimisation part in Chapter 5. We first start by rewriting equation (8) [66]:

( ) ( )

( ) ( )

( )

By integrating both sides one gets:

∫( )

Where

If we solve equation (17) we obtain the temperature inside the thermal storage tank at every instant

in time [4]:

(

* [

] [ (

*]

(17)

(18)

49

Where and

are the hot water temperatures (oC) inside the hot water tank in time slots t and

t+1; and

are the temperatures of the ambient environment and inlet water in time slot

t; C is the equivalent thermal mass (Wh/K); is the length of a timeslot in hours; G is the product of

the surface area and thermal resistance of the thermal storage tank (W/K). , and are

calculated according to the following equations, respectively:

(W/K)

(K/W)

(kW)

Where is the density of water (1000 kg/m3), is the hot water flow rate in time slot t (l/h)

and the specific heat capacity of water (J/kg K). is the rated power of the CHP unit (kW) and

is the status of the CHP unit in timeslot t (1 = ON, 0 = OFF). In the model of the CHP unit we

assume that the CHP unit works at its rated power when turned on. This is done for simplicity, such

that we do not have to take the dynamic behaviour into account. Note that in equation (21) the

relation between the electrical –and thermal output of a CHP unit is used (see equation (6)). In order

to ensure the comfort preference of the user, the CHP unit should regulate the hot water

temperature within a prespecified range set by the user:

4.2.2 The heat pump

The model for the space heating/cooling load developed in [67] is adopted in this thesis. In this

model, the room temperature is calculated as

Where and

are the room temperatures (oC) in time slots t and t+1 respectively; is

the length of a time slot; is the heat gain rate of the house given in equation (12); is the energy

needed to change the temperature of the air in the room by 1 K (Wh/K); is the heating capacity

of the heat pump unit (=COP*PHP) and is the working status of the heat pump in time slot t (1 =

ON, 0 = OFF). To change the air in the room by 1 K, the energy required (Wh/K) is calculated as

(Wh/K)

Where is the specific heat capacity of air for a typical room condition and is the volume

of the house. The specific heat capacity of air is 1.012 J/(g K). This can also be written as

Because 1 g of air is 1/1290 m3 and 1 J is 1/3600 Wh. This results in a of

(19)

(20)

(21)

(22)

(23)

50

( )

See Figure 24 for Vhouse. Now the room temperature is expressed as a function of the working status

of the heat pump ( ), the room temperature can be controlled within a prespecified range set by

the user.

Where and

stands for the minimum and maximum room temperatures.

4.3 The non-interruptible loads

In this dissertation, a washing machine (WM), dishwasher (DW) and cloth dryer (CD) are taken as

non-interruptible appliances. These appliances have two statuses, namely ON or OFF. Once they have

turned on, they must keep working until their task is completed. The task starting time and the

number of time slots needed for completing the task of each appliance is set by the user. These

appliances should meet the constraints [4]:

∑

Where * + is the time slot in which the task of appliance a is started;

is

the number of time slots that are needed to complete the task of appliance a. The first constraint of

equation (25) expresses that the task should be finished within a prespecified time interval set by the

user. The second constraint expresses the non-interruptible nature of the appliance, namely once it

starts they must complete their entire cycle. The last constraint expresses the number of time slots

each appliance need to complete its task. For simplicity it is assumed that the appliances work at

their rated power during operation. The power of appliance a in time slot t is calculated as

Where Pa is the rated power of appliance a.

(24)

(25)

(26)

51

Chapter 5

Optimisation

The different appliances that are modelled in the previous chapter will be used here to build the

optimisation procedure. The optimisation is based on two optimisation objectives, namely the overall

energy cost and the comfort level of the user. The energy cost is minimized and the comfort of the

user is maximized over the next 24 hours (i.e., next day) based on the forecasted outdoor

temperature, the power output of the PV installation over the next 24 hours and the forecasted

electricity -and natural gas price (CHP unit runs on natural gas). The Genetic Algorithm (GA) [68] in

Matlab will be used to carry out the optimisation. From chapter 1 it became clear that the Particle

Swarm Optimisation (PSO) is a frequent used optimisation algorithm in literature. Matlab also has

this algorithm, but it can only be used for unconstraint problems. In this work an algorithm that

solves constraint problems with both continuous and discrete variables is needed. The GA is a

method for both solving constraint and unconstraint problems based on natural selection that

mimics the biological evolution. At each time step the algorithm randomly selects individuals from

the population and uses them as parents to produce the children for the next generation. There are

three types of children [68]:

Elite children are individuals in the current population with the best fitness values. These

individuals automatically survive the next generation.

Crossover children are individuals that are created by combining the vectors of a pair of

parents.

Mutation children are created by introducing random changes or mutations to a single

parent.

Figure 27: Schematic diagram that illustrates the three types of children [68]

52

5.1 The Cost Objective

The overall net energy price over the scheduling horizon is formulated in equation (27), which

consists of four terms: the first term represents the overall electricity cost of buying electricity from

the grid, the second term stands for the overall revenue of selling electricity to the grid, the third

term stands for the degradation cost of the home energy storage battery and the last term denotes

the cost of buying natural gas for the CHP unit.

∑ ( )

∑ ( )

∑

∑

(€/kWh) is the electricity price at timeslot t when the user buys electricity from the grid; and

(€/kWh) is the electricity price at timeslot t when the user sells electricity to the grid. Note that

( ) means that power is withdrawn from the grid and ( ) that

power is feed into the grid. is the battery degradation cost (€/kWh) and (€/kWh) is the

price of natural gas at timeslot t. The term

is the power flow of natural gas in kW (see equation

(4), FNG); is the working status of the CHP unit in timeslot t and is the length of a timeslot in

hours.

A detailed description and calculation method of the batteries degradation cost can be found in [69].

For convenience the most important formulas are shown here. The degradation cost cdeg of a battery

can be calculated by

Where Cc is the battery capital cost in € and LE is the battery life throughput energy in kWh. Battery

lifetime is expressed in number of cycles, measured at a reference DOD (Depth Of Discharge) and a

reference temperature. In order to reflect the impact of temperature on lifetime, LE is defined in [69]

as follows:

Where LN is the battery lifetime in number of cycles at a reference condition, i.e., ambient

temperature T = 20oC, DOD = 80%; Es is the total energy storage of the battery under reference

condition in kWh; ηTem is the temperature dependence factor and is defined as the ratio of the actual

lifetime LC to the reference one LN, as shown below.

(27)

(28)

53

5.2 The Comfort Objective

In practice a residential user want to reduce his energy price without losing comfort. There are

different comfort concerns depending on the type of home appliance. For example, for space heating

and hot water demand, the user pays more attention to temperature, however, for the washing

machine, dishwasher and cloth dryer, he focuses on when the task of these appliances are

completed. Therefore in [4], a set of comfort level indicators are proposed based on appliance type.

The comfort cost function is formulated as

∑

Where A ={HP, TS, WM, DW, CD}; is the comfort level indicator of appliance a and NA is the

number of controllable appliances in the HEMS.

5.2.1 Heat Pump (HP)

To quantify the user’s comfort level under the operation of the HP, [4] proposes a comfort level

indicator whose definition is based on the assumption that when the room temperature is equal to

the user setting temperature, the user is most comfortable. If the room temperature deviates from

the setting value to a certain extent, the user comfort level will be decreased. The indicator is

calculated as

∑

Where *

+ and

is determined by

Where is the desired room temperature set by the user and

and are the two

parameters that are related to the temperature dead band of the heat pump. According to the

definition of in equation (30), it is within the range of [0 100], where zero means the user is most

comfortable and 100 the user is least comfortable. The comfort level indicator is visualised in

Figure 28. The indoor temperature horizon is divided into three zones:

A comfortable zone: lies within [

-

A tolerable zone: is larger than

, but smaller than or

is smaller than

, but larger than

(29)

(30)

54

An intolerable zone: is larger than or smaller than

.

5.2.2 Thermal Storage (TS)

The definition of comfort level indicator is similar to that of the heat pump and is calculated as

∑

Where *

+ and

is determined by

and are user setting parameters whose meanings are similar to the parameter of

the heat pump comfort level indicator. Just as also lies within the range of [0 100] and can be

divided into three zones.

(31)

Figure 28: Relationship among parameters of HP comfort level indicator [4]

55

5.2.3 The non-interruptible appliances

A user’s comfort level for the non-interruptible loads (WM, DW, CD) is determined by the finishing

time of these appliances. The user will be most comfortable if the appliance starts on the moment

the user wants. In reality the user can tolerate some delay, which makes the non-interruptible

appliances flexible loads. Of course this delay is limited, which means that if the delay is too long, the

user will be unsatisfied. The comfort level indicators for WM, DW and CD share the same expression

and are calculated as

(

)

(

) (

)

Where * +, namely the Washing machine, Dish washer and Cloth dryer.

and

specify the valid working interval for appliance a. If appliance a starts within the

interval ,

-, where

is the delay the user can tolerate and is the

preferred starting time of the user, the user is most satisfied. is the number of timeslots

appliance a need to finish its task. The comfort level of the user decreases as the appliance starting

time is beyond the delay set by the user. The relationship between these parameters is depicted in

Figure 29. Also this indicator is divided into three zones, namely the comfortable zone, the tolerable

zone and the invalid zone. The comfort level indicator Ia is in the range [0 100] too and has the same

meaning as the comfort level indicator of the HP and TS.

(32)

Figure 29: Relationships among parameters of WM, DW and CD comfort level indicators [4]

56

5.3 Multi-objective Optimisation Model

The multi-objective optimisation model for the HEMS is formulated as

( ) ( ) ( ) ( ) ( ) ( )

In this model, the working status of HP and CHP in each time slot and the task starting times of WM,

DW and CD are decision variables. Minimizing the energy cost and maximizing the user comfort level

(which corresponds to minimizing the comfort level indicators Fcomfort) are the two objectives of this

problem. For implementation reasons the multi-objective optimisation model proposed in (33) is

transformed into a single objective optimisation model by weighting method [4], which means that

we can take a tradeoff between the cost -and comfort objective by changing α.

( )

( ) ( ) ( ) ( ) ( ) ( )

Where α is called the user preference factor, 0 ≤ α ≤1, through which the residential user can take a

tradeoff between the energy cost and the comfort level conveniently. The reason why we transform

the model to a single objective optimisation model, is because the genetic algorithm (GA) in Matlab

cannot work with integer variables for multi-objective problems. The syntax for the GA in Matlab is

as follows:

( )

Where fitnessfcn is the objective function (= Ftotal); nvars is the dimension of fitnessfcn (= 7); A*x ≤ b

are the inequality constraints; Aeq*x = beq are the equality constraints; LB and UB are the lower-and

upper bounds of the variables; nonlcon are the nonlinear constraints (not applicable here); IntCon is

a vector with the integer variables and options changes the default optimisation parameters by the

values given in options. Because GA does not accept equality constraints for problems with integer

variables, the equality constraints have to be transformed into inequality constraints as follows:

The Aeq matrix and beq vector are than included in the A matrix and b vector respectively. The syntax

now looks as follows:

( , - , - , - )

(33)

(34)

57

5.3.1 The equality constraints

The equality constraint expresses that production (PV panels, CHP unit and grid) equals consumption

at any moment in time. The control vector of the HEMS is shown below (see introduction of

chapter 4).

, -

Where Pbat and Pgrid are continuous variables and SHP,SCHP and Tstart are integer variables. As reference

we assume that Pgrid >0 when power is withdrawn from it and Pgrid <0 when power is feed into the

grid. For the battery we take an opposite reference, namely Pbat <0 means that the battery delivers

power to the loads or the grid and Pbat>0 indicates that the battery is being charged. With these

references in mind we can write out the equality constraint as follows:

∑

Where A = {WM, DW, CD} and Ptcl is the critical load power, which is not controlled by the HEMS. If

we put all the control variables on the left side of the equality sign and the known ones on the right

side we can write (36) in the form Aeq.x = beq.

∑

The variable is a discrete vector. This vector represents the starting times of the non-

interruptible loads and is determined in the first time slot of the scheduling horizon. The equation

above can then be rewritten as:

(35)

(36)

Figure 30: Power distribution relationships of the HEMS in smart grid [4]

58

∑

If we use the definitions given in chapter 4, the control variables can be written as:

∑

Where St are the working statuses (ON/OFF) of the corresponding appliances. The right hand side of

equation (37) can be written in matrix form, such that we obtain the form Aeq.x = beq. For one

timeslot we obtain the following coefficient row aeq for the right hand side and column vector beq for

the left hand side of equation (37).

, -

[

∑

]

The scheduling horizon consists of Nslot time slots, which means that Aeq has Nslot rows and 7*Nslot

columns; beq will be a column vector with size Nslot. This gives us the following matrices Aeq and beq:

[

]

[

∑

∑

∑

]

Aeq is a diagonal matrix with the coefficients of equation (37) on the main diagonal. This matrix can

be interpreted as follows: each row represents a timeslot t, and each column represents the control

variables of the corresponding time slot t. For example if we look to the first row of Aeq, the first

element of length 7 represents the control variables of timeslot 1, the second column of the second

timeslot and so on. Because at each time slot t, the consumption needs to be covered, we only get

the coefficients of (37) on the main diagonal.

(37)

(38)

59

5.3.2 The inequality constraints

The inequality constraints depicted in chapter 4 describe the operating constraints of each home

appliance. Some constraints are imposed by the residential user, for example max. and min. room

temperature, others are due to operational restrictions. For example the SOC of the battery must

maintain a minimum charge of 20% in order to obtain an acceptable lifetime of the home battery.

The home battery

We will first start by writing out the inequality matrix Abat of the battery. Equation (13) depicts the

charging constraint of the battery. For convenience this constraint is repeated here.

is calculated in two ways, depending on whether the battery is in charging -or discharging state.

The matrix will be written out for the charging state only. The discharging state is done in a similar

way. The charging state of the home storage battery is depicted in equation (14) and repeated

below.

If we put equation (14) into (13) we get

The equation is multiplied with the batteries capacity Cbat, such that we obtain the energy in the

battery at every timeslot t. The inequality constraint needs to be in the form A.x ≤b. This means that

the second equation from above needs to be multiplied with -1.

Equation (39) in matrix form looks as follows:

[

(

)

(

)

]

(39)

(40)

60

The top part of matrix (40) represents the first equation of (39), the bottom part represents the

second one. In (39) one can see that the present energy content of the battery is depending on the

energy content of the previous time step. This effect can be seen in the matrix , where at each

time step (each row in (40) represents a time slot) a zero row is replaced by ( ). The

same holds for the lower part of (40). In this way a lower triangle matrix is obtained with dimension

2Nslot x 7Nslot. The b vector of (39) is a 2Nslot column vector and is shown in (41).

[ (

)

(

)

]

The same matrix can be built for the discharging state of the battery, with the difference that the

matrix has row elements equal to (

). The b vector is the same as in (41). In block

matrix representation the A -and b matrix for the battery looks as follows:

[

]

[

]

The HP

The constraint of the HP operation is determined by the room temperature set by the residential

user. This constraint is depicted in (24) and repeated here.

The room temperature TtRoom is modeled in chapter 4 by equation (23):

Combining these two equations results in the following inequality constraints:

(41)

(42)

61

if the equations above are further written out with (12) we get:

(

*

(

*

If we write (43) in the form A.x ≤ b we obtain:

[

(

.

/

.

/

.

/

)

(

.

/

.

/

.

/

)

]

[

(

(

*

(

*

(

*

(

*

∑(

*

(

*

∑ (

*

)

(

(

*

(

*

(

*

(

*

∑(

*

(

*

∑ (

*

)

]

(43)

(44)

62

To understand how the matrices in (44) are obtained the first equation in (43) will be written out for

first two time slots. T0Room is the initial room temperature, which is considered known.

(

*

(

*

(

*

[(

*

]

The last equation is obtained by evaluating T1Room in the second equation. The first row of matrix A

and b in (44) is obtained by rewriting equation T1Room. Note that each decision vector Xi, i = 0,…,Nslot-1,

is a column vector of length 7.

(

*

↔ 0

1 [

]

(

*

The same approach is applied on equation T2Room, we get:

(

*

(

*

(

*

↔ 0 .

/

1

[

]

.

/

.

/

63

The CHP unit

Similar to the HP, the CHP unit should maintain the hot water temperature within a prespecified

range set by the user (see (22)). This constraint is for convenience repeated here.

The temperature of the hot water inside the thermal storage tank is modeled in (18):

(

* [

] [ (

*]

Combining the two expressions results in the inequality constraints that limits the operation

boundary of the CHP unit. These constraints are expressed by

(

* [

] [ (

*]

(

* [

] [ (

*]

To know how to build up the matrices, the first equation in (45) will be written out for the first two

time slots. T0TS is the initial temperature of the hot water. For the first timeslot we get:

(

* [

] [ (

*]

↔

.

/ [

] 0 .

/1

For reducing the writing of symbols, we have replaced (

) with q0.

↔ 0 .

/1

.

/ 0 .

/1

↔ 0 ( .

/) 1 [

]

(

* [ (

*]

For the second timeslot we obtain the following expression:

(

* [

] [ (

*]

Substituting T1TS into the equation above results in:

,

(

) ( )-

(

) ( )

↔ (

*

(

* ,

(

)-

( )

(45)

64

↔ [ (

*

(

* ( ) ( ) ] [

]

,

(

)-

(

)

A pattern can be seen in these equations, namely in the second time step, the coefficients of the

previous time step are multiplied with

of the next time step. Rewriting equations (45) in the

form A.x ≤ b results in the following matrices. The top part of represents the first equation of

(45) and the bottom part the second equation. The same holds for .

[

(

(

)

(

)

(

.

/)

(

)

∏

(

)

)

(

(

)

(

)

(

.

/)

(

)

∏

(

)

)

]

[

(

,

(

)-

,

(

)-

(

)

,

(

)- ∏

(

)

(

)

)

(

,

(

)-

,

(

)-

(

)

,

(

)- ∏

(

)

(

)

)

]

(46)

65

The non-interruptible loads

For the non-interruptible loads it is important that the corresponding appliance carries out its job

within a prespecified time interval set by the user. The constraints of these type of appliances are

expressed in (25). It is important to keep in mind that the starting times of the non-interruptible

loads are discrete quantities and are determined in the first time slot of the scheduling horizon. To

satisfy the residential user, the appliance’s task should start within the time interval (see (25)):

Where * +, namely the Washing machine, Dish washer and Cloth dryer.

The starting times of the non-interruptible appliances are determined by the intlinprog solver

in Matlab. The syntax for this solver looks as follows:

intlinprog(fa,nvars,[],[],Aeqa,beq

a,LB,UB)

Where Aeqa and beq

a are represented in (47)

[

(

)

(

)

]

Where and

represent the start and end position of the ones in matrix .

The cost function fa is a column vector that is the product of the rated power of appliance a (Pa in

kW) and the price scheme of electricity (€/kWh). The price scheme is adapted, where the price is set

to zero when there is enough PV production (e.g. 2 kW). In this way the solver will prefer to schedule

the appliance during PV production. The second term in intlinprog specifies the number of variables,

which is the number of timeslots (Nslot) in our case. Note that each variable in (47) is binary, where

zero means OFF and one means ON. The third and fourth term are meant for the inequality

equations, but this is not applicable here. The equality equation (47) expresses that appliance a can

start its operation between time slot , ,

- and must take timeslots to finish its

operation. The last two terms in intlinprog represent the lower-and upper bound of each variable.

Because each variable is binary (1/0) the lower bound vector LB is a zero vector and the upper bound

vector UB is a unit vector. The intlinprog solver returns a binary vector of length Nslot with exact

successive ones. The position of the first one element determines the start time of the non-

interruptible appliance a.

(47)

66

Chapter 6

Case studies

In this chapter simulations are performed to examine the effectiveness of the proposed HEMS

strategy. The simulation programs are coded in Matlab and are run on a Windows 10 (64 bit) Intel®

Core™ i3-5005U CPU @ 2 GHz computer with an 8 GB memory. Three cases will be investigated, all

using the same production -and consumption profile. The scheduling horizon is 24 hours, and is

divided evenly into 96 timeslots of 15 minutes; that is Nslot = 96, ∆t = 0.25 h. The data of the used

pricing schemes, namely Real Time Pricing (RTP) scheme and Time of Use pricing (ToU) scheme, are

from [70] and [71] respectively. The RTP pricing scheme data is taken from the Belpex site. Belpex is a

power exchange for anonymous, cleared, short term trading in electricity and is composed of three

market segments, namely Belpex DAM, Belpex CIM and Belpex SRM. For more information the

reader is referred to the website of Belpex (www.Belpex.be). The ToU pricing scheme is found in an

Canadian master thesis [71]. We will use two type of ToU pricing schemes. One has two pricing

levels, namely an Off-Peak price from 12 pm – 7 am and a standard price from 8 am - 12 pm. The

second is a three-level ToU scheme with an Off-Peak price from 12 pm – 8 am, a standard price from

12 am – 4 pm and an On-Peak price from 8 am – 12 am and from 4 pm – 12 pm. A PV production

profile [72] and critical load profile [72] is hard to find online and is provided by my promoter Bart

Meersman and counsellor Dimitar Bozalakov. The forecasted outdoor temperature is taken from a

website named AccuWeateher.com [73]. This was the temperature in Gent in the month March. The

pricing schemes, PV production profile, critical load profile and outdoor temperature are shown in

Figure 31- Figure 34 respectively.

Figure 32: Forecasted PV power profile [72] Figure 31: Critical load profile of residential household [72]

67

Figure 33: Electricity pricing schemes [70]- [71]

Figure 34: Forecasted Outdoor temperature [73]

68

6.1 Case 0

In case 0 we want to investigate how the energy cost changes when we allow some flexibility to the

household appliances. In a first simulation (case 00) the room temperature boundary is set to

,

- , where Tset is the user’s temperature set point (Tsetroom = 20oC), the

temperature in the Thermal Storage (TS) water tank is limited to ,

-, with

equal to 55oC. The starting times of the non-interruptible appliances are not regulated and are

set equal to the ideal starting times , (see Table 15). In a second simulation (case 01) the

temperature boundaries are selected wider. For the TS tank the temperature of the hot water is

regulated within the temperature range of [50oC, 60oC]. The boundaries of the room temperature

depend on the moment of the day and are represented in Figure 35. In the night we allow a

temperature band of 2oC around the temperature set point of the user. From 6 am – 8 am the

temperature band is reduced to 0.5oC, because than the residential user is awake. During the day,

the temperature band is elected wider again, because no one is at home normally. When the

residential user comes home in the evening, the temperature band is narrowed again. The non-

interruptible loads are controlled within a minimum and maximum time slot as explained in section

4.3 of chapter 4. These boundaries for the washing machine (WM), the dishwasher (DW) and the

cloth dryer (CD) are taken from [4]. For convenience of the reader the values are shown in Table 15.

Parameter Washing machine (WM)

Dish washer (DW)

Cloth dryer (CD)

(time slot) 37 37 77

(time slot) 76 84 96

(time slot) 48 56 80

(time slot) 4 4 8

(time slot) 4 4 4

Rated power (kW) 0.5 1 4

Table 15: Parameter setting of WM, DW and CD [4]

Figure 35: Room temperature band over a day

69

Each of the cases explained above, namely case 00 and case 01, are run five times. After each run the

net energy cost, the battery degradation cost, the revenue of selling electricity to the grid and the

purchase cost are noted. The battery degradation cost is calculated according to equation (28) for a

LFP (Lithium-iron phosphate ) battery. This type of battery has the following specification given in

Table 16, where LN is the battery life cycle time, Es is the energy capacity of the battery, ηTem is the

temperature dependence factor, DOD is the depth of charge and CC is the investment cost of the

battery.

LN 2000 cycles

Es 4,8 kWh

ηTem 0,9

DOD 0,8

CC € 2212

If we fill in these values in (28) we obtain an battery degradation cost of € 0.32/kWh. The selling price

of electricity to the grid determines the revenue the HEMS makes. According to [2] the selling price

of electricity should be 5% lower when supplied to the grid, compared to the buying price in every

specific instance. This ensures that the utility companies have a profit margin and the HEMS creates

more value for the installed renewable energy source, by enabling a higher penetration of renewable

energy at the residence. The simulations are done with the two-level ToU pricing scheme shown in

Figure 33. The results of the simulations are shown in Table 17. Note that these values are average

values of the five runs. Std. stands for the standard deviation between the five runs.

Case 0 Purchase cost (€)

Std.

Battery cost (€)

Std.

Sales revenue

(€)

Std.

Net cost (€)

Std.

No flexibility (case 00)

4.73 0.12 2.27 0.11 1.84 0.06 5.16 0.08

Flexibility (case 01) 4.09 0.18 2.21 0.17 1.57 0.09 4.75 0.18

From the last column in Table 17 we see that in the case where we allow some flexibility of the home

appliances the net energy cost is smaller than the case were there is no or little operation flexibility

of the home appliances (€ 0.41 difference). The purchase cost and sales revenue is larger in case 00.

This can be explained by Figure 36 and Figure 37. In these figures we see that the power flow with

the grid is a bit larger in the case of no flexibility. Note that the maximum power exchange with the

grid is limited between 3 kW for feeding power into the grid and 4 kW for extracting power from the

grid. The reason for that is because we want to limit the power exchange with the grid, such that the

own produced PV energy is used as much as possible. The battery degradation cost is a bit smaller in

the case where flexibility is allowed. The power exchange of the battery and grid for the two cases

are shown in Figure 36 and Figure 37 respectively. The lower graph on these figures depict the state

of charge of the battery as a percentage of the energy content of the battery (=4.8 kWh).

Table 16: Parameters for a Lithium-iron phosphate (LFP) battery

Table 17: Simulation results of case 0 (scheduling horizon = 24 h)

70

Figure 36: Simulation results in case of no flexibility of home appliance

Figure 37: Simulation results in case of flexibility of home appliances

71

The state of charge of the battery reaches about 90% of its capacity in both cases. In the first part of

the day (0-12 h), the battery is barely being charged, because there is no PV power available. When

the sun starts to shine (see blue and green graph on figure PGrid), the battery is being charged. Note

that at the same moment the excess PV power is feed into the grid. The maximum charging- and

discharging power of the battery is assumed to be 2 kW, as indicated by the green dotted line on

graph PBattery. On this graph we see that during PV production the battery charges with a power

smaller than 2 kW. A reason for this phenomenon is because a part of the PV power is instantaneous

consumed. The batteries state of charge (SOC) is regulated between 20% and 100%. The 20% SOC is

because the Depth of Discharge (DOD) of an LFP battery is set to 80% (DOD = 1-SOC) such that the

expected life time is not jeopardized. In order to force the algorithm to charge the battery during PV

production, we set the battery degradation cost negative. In this way the algorithm thinks it sells the

energy to the battery and makes profit. When there is no PV production, the degradation cost is set

to its normal positive value. The use of a battery degradation cost is of great importance to obtain a

profitable situation, such that the battery is being charged or discharged in a reasonable way. From

simulations without a battery degradation cost the algorithm bought electricity from the grid to

charge the battery and discharged in the next time slot to the loads, such that the net electricity cost

is reduced (see case 2). Of course this is not a profitable situation.

Figure 38: Simulation results in case of no flexibility of home appliances

72

In Figure 38 and Figure 39 the electrical power outputs of the Heat Pump (HP) and the Combined

Heat and Power unit (CHP) are depicted in the top graphs. Note that these appliances have two

working conditions, namely ON or OFF. When they are ON they work on their rated power, which is

2.7 kWe for the HP and 1.7 kWe for the CHP unit. The course of the room temperature and the hot

water temperature inside the Thermal Storage tank (TS) are shown in the lower graphs. The

temperature boundaries are depicted as green dotted lines. The first thing that stands out is that the

temperature boundaries are sometimes crossed. This is due to the fact that the HP and CHP unit are

modeled in a way where they only have two working conditions. So it is possible that at a certain

timeslot the temperature is within bounds, for example close to the upper bound. When the

algorithm decides to turn on the appliance (HP or CHP unit) it outputs heat at rated power such that

the temperature in the next timeslot exceeds the upper temperature bound. It is clear that in the

case of flexibility the CHP unit is less active than in the other case. This results of course in less fuel

consumption and thus in a lower energy cost. The influence of the HP is not very clear, because the

temperature band is much smaller, but we see that it is less active when the temperature band is

wider. A last remark that can be made is that the Genetic Algorithm used in Matlab is not very robust

for the constrained problem in this thesis. The results between different runs of the same case are

always different, which makes it hard to draw good conclusions. Nevertheless, based on the standard

deviation given in Table 17, this case (case 0) shows that allowing flexibility in the operation of the

home appliances results in a decrease of the net energy cost.

Figure 39: Simulation results in case of flexibility of home appliances

73

6.2 Case 1

In case 1 the effect of comfort and cost as an objective will be examined. As explained in the

introduction chapter cost and comfort are contradictory, which means that the cost will be larger

(smaller) if the comfort level is higher (lower). This effect will be investigated in this case for the

three level Time of Use (ToU) pricing scheme and the Real time Pricing (RTP) scheme. The RTP

scheme only contains the price of electricity per kWh, without distribution cost, taxes, etc. As

explained in chapter 1 (see Figure 5) the price on your electricity bill consists of several parts (energy,

distribution cost, transport cost, taxes,…) and energy is only a third of the total cost. So to be a bit

realistic, the RTP scheme will be added with a cost that represents the grid compensation

(=distribution cost, transport cost, taxes, etc.). This grid compensation will be calculated by taking the

maximum electricity price in the RTP scheme and divide it by a third. The maximum electricity price

of the RTP scheme is about 4 cents per kWh (see Figure 33), which results in a grid compensation

price of 12 cents per kWh. The residential user can make a tradeoff by changing the user preference

factor α. α equal to one means that the algorithm only minimizes the cost objective, whereas α equal

to zeros indicates that the algorithm will only take the comfort objective into account. In case 1 the

user preference factor α will be set to 0, 0.5 and 1, where 0.5 means that cost and comfort are

considered equally important for the user. As mentioned in the comfort objective section (5.2) of

chapter 5, the comfort level indicators are defined as a function that increases when the control

quantity, temperature for heat pump (HP) and CHP unit and starting time for the non-interruptible

appliances, deviates from the user’s set point. The margins in this case are chosen small, with a

for the HP and a

for the CHP unit. If the HP and

CHP unit control the room temperature and hot water temperature respectively within ,

with the room temperature -and hot water temperature set point respectively, the comfort level

indicator will be at its minimal value. Therefore, the smaller α, the smaller the operation limits for the

thermal appliances and thus the less flexible they are. The results of the simulations are shown in

Table 18 and Figure 40.

Three –level Time of Use pricing scheme

α Purchase

cost (€)

Std.

Battery cost (€)

Std.

Sales revenue

(€)

Std.

Net cost (€)

Std.

Comfort level

indicator

Std.

0 4,85 0.01 1,92 0.05 2,13 0.04 4,63 0.06 6,3 1.7

0.5 4,33 0.21 2,25 0.21 2 0.18 4,57 0.18 16.8 5.3

1 4,12 0.13 2 0.14 1,91 0.17 4,21 0.21 24,1 6

Real Time Pricing scheme

α Purchase

cost (€)

Std.

Battery cost (€)

Std.

Sales revenue

(€)

Std.

Net cost (€)

Std.

Comfort level

indicator

Std.

0 5.47 0.04 2.15 0.4 2.11 0.06 5.51 0.41 4.8 2.4

0.5 5 0.09 2.14 0.15 1.98 0.08 5.17 0.17 22 6.9

1 4.9 0.08 2 0.12 1.8 0.15 5.09 0.2 28.9 5.6

Table 18: Simulation results of case 1 (scheduling horizon = 24 h)

74

From Table 18 or Figure 40 we see that the net energy cost decreases and the comfort level indicator

increases with increasing α. Important to remember is that a higher comfort level indicator indicates

that the most comfortable bounds set by the user are exceeded (within a reasonable margin) and

thus that the user is less comfortable. This indicator is defined within the range of [0 100], where

zero means that the user is most comfortable and 100 indicates that the user is least comfortable. As

mentioned before the user preference factor α is a way the residential user can take a tradeoff

between cost and comfort level. A higher α means that the consumer finds cost more important than

comfort and vice-versa. The sales revenue decreases slightly with increasing α. The net cost is larger

for the case with the RTP scheme. This is probably due to the fact that the difference between the

maximum and minimum electricity price is smaller in the case for the RTP scheme than for the ToU

pricing scheme. The battery cost and sales revenue are from the same magnitude in both cases

(around € 2). This indicates that the algorithm controls the battery and exchange with the grid in a

similar way for both cases (see Figure 41 and Figure 42). The only significant difference between the

ToU -and RTP scheme is the purchase cost, which is smaller in the case with the ToU pricing scheme.

Note that the results given in Table 18 are average values of five different simulation runs. The blue

and red lines of Figure 40 are not fitting lines, but are just drawn to indicate the rising and falling

trend of the net cost and comfort level indicator respectively. The influence of the user’s preference

factor α is shown in Figure 43 (α=0) and Figure 44 (α=1). In these figures we see that the power that is

put back in the grid is smaller when α equals to one. This is also confirmed by looking to the sales

revenue, which is a bit smaller for α = 1. There is some variation between the different simulation

runs for a fixed α. This is because the genetic algorithm (GA) is stochastic, which means that it makes

random choices of the initial population it starts calculating with. Normally you can choose a fix initial

population in GA, but this options is not available for problems with discrete variables.

Figure 40: The net energy cost and comfort level as a function of the user’s preference factor α for the case with the three-level ToU pricing scheme

75

Figure 42: Power flow for case with RTP scheme for α = 0.5

Figure 41: Power flow for case with ToU pricing scheme for α = 0.5

76

Figure 43: Power flow for α=0 (ToU-3 level)

Figure 44: Power flow for α=1 (ToU-3 level)

77

6.3 Case 2

In this case we will investigate the influence of the battery degradation cost on the operation of the

optimisation model. We will do this for a user preference factor α of 1 and look how the different

parts (purchase cost and sales revenue) of the cost change. This will be done for a ToU pricing

scheme and a RTP pricing scheme, such that we can compare it with the results of the previous case.

According to [4] the battery degradation cost is a way to assure a profitable situation of the battery

performance. The results of the simulations are shown in Table 19.

Time of Use (ToU) – 3 level

Case Purchase cost

(€) Std.

σ Sales revenue

(€) Std.

σ

Without battery degradation cost

4.31 0.02 1.87 0.1

With battery degradation cost

4.12 0.13 1,91 0.17

Real Time Pricing scheme

Case Purchase cost

(€) Std.

σ Sales revenue

(€) Std.

σ

Without battery degradation cost

4.83 0.09 1.83 0.1

With battery degradation cost

4.9 0.08 1.8 0.15

If the purchase cost in this case is compared with the previous case were a battery degradation cost

is foreseen, a smaller purchase cost is obtained in the latter one. The difference is 0.19 euro (€ 4.31-

€ 4.12) for the case with the ToU pricing scheme. The difference is small, but nevertheless present.

The difference in purchase cost is less pronounced for the RTP scheme (€ 4.83 ↔ € 4.9). Based on

the standard deviation we can say that the influence of the battery degradation cost is negligible for

the case with the RTP scheme. The sales revenue are of the same order in both cases. The effect of

the battery degradation cost for the case with the ToU pricing scheme can be seen on Figure 45 and

Figure 46. On the bottom graph of Figure 45 (the State of Charge) we see that at the first half of the

day (0-12 h) the battery charges and discharges continuously, while in the case with a degradation

cost (bottom graph Figure 46) the battery shows less charging and discharging cycles. These charging

and discharging cycles are not good for the batteries lifetime and need to be avoided. So we can

conclude that the implementation of a battery degradation cost results in a more profitable situation

with less charging and discharging cycles of the battery. The model shows a different behaviour for

the RTP scheme as can be seen on Figure 47. When we do not foresee a degradation cost the battery

charges in the night during the low price period and discharges when the price rises again. This

behaviour is clearly visible from 0-10 h on Figure 47. We do not see this behaviour when a battery

degradation cost is present in the model (see Figure 48).

Table 19: Simulation results of case 2 (scheduling horizon = 24 h)

78

Figure 46: Power flow for case with battery degradation cost (ToU-3 level)

Figure 45: Power flow for case without battery degradation cost (ToU-3 level)

79

Figure 48: Power flow for case with battery degradation cost (RTP scheme)

Figure 47: Power flow for case without battery degradation cost (RTP scheme)

80

Chapter 7

Conclusions

To study the behaviour of different home appliances and their flexibility a Home Energy

Management System (HEMS) is proposed in this thesis. It proposes a framework of HEMS including a

grid, PV, a thermal storage tank and a home energy storage battery. A multi-objective optimisation

algorithm for HEMS is proposed, which minimizes electricity cost and maximizes the comfort of the

residential user simultaneously. The algorithm controls the operation of schedulable home

appliances, such as a washing machine (WM), a dish washer (DW) and a cloth dryer (CD). It also

controls two heating appliances, namely a heat pump (HP) and a combined heat and power (CHP)

unit along with the power distribution among the grid and the home battery. These appliances are

controlled according to the electricity price, the price of natural gas (NG), forecasted power output of

the PV, forecasted outdoor temperature and user preferences. The residential user has the ability of

selling electricity to the grid for revenue. In order to quantify the user’s comfort level, a set of

comfort level indicators proposed by [4] are used. These comfort level indicators are proposed based

on the home appliance’s characteristics and user’s preferences. At the begin of this present work a

number of research questions were asked to investigate the influence of some parameters. These

questions are repeated here for the convenience of the reader (see section 2.5).

The topics that will be investigated in this thesis are the following ones:

1. What is the effect on the energy cost when we allow flexibility to some house hold

appliances?

2. What is the effect of the cost objective on the comfort objective and vice-versa?

3. What is the effect of different pricing schemes, Time of Use (ToU) and Real time Pricing

(RTP), on the performance of the optimisation algorithm?

4. What is the effect of the battery degradation cost on the charging and discharging behaviour

of the battery?

The first question is investigated in case 0. From this case it became clear that allowing flexibility to

the home appliances results in a lower energy cost. This case is carried out with a two-level ToU

pricing scheme that has an off peak –and standard rate price. The difference between allowing and

not allowing flexibility results in a net energy cost gain of € 0.41 (see Table 17). This is of the same

magnitude that was obtained in [4].

The second and third question are studied in case 1. The user’s preference α is a way for the

residential user to take a tradeoff between cost and comfort level. The factor α is set to 0, 0.5 and 1,

where zero means that only the comfort level of the user is considered, one indicates that only the

cost objective is minimized and 0.5 means that cost and comfort are considered equally. The model is

run for the three values of α. The results confirm the conclusion given in [4], namely that the cost –

and comfort objective are contradictory. This means that maximising the comfort results in a higher

cost and vice-versa. The algorithm behaves pretty much the same for a three-level ToU -or RTP

81

scheme if we look at the power distribution among grid and battery. There is a slight difference in

the energy cost, where the algorithm obtains a smaller cost for the ToU scheme. This effect can be

explained by the fact that the price difference between min. and max. is larger in the ToU scheme,

which means that the algorithm has the opportunity to buy cheap electricity during the off peak

period.

In the last case we examined the effect of the battery degradation cost on the performance of the

algorithm. This is carried out for two pricing schemes, namely three-level ToU -and RTP scheme. For

the ToU pricing scheme we saw that the presence of a battery degradation cost resulted in less

charging and discharging cycles of the battery (see Figure 45-Figure 46), which is of course a

profitable situation w.r.t. the batteries lifetime. The presence of a degradation cost also resulted in a

smaller purchase cost, and thus a smaller net energy cost. The algorithm shows a completely

different behaviour for the RTP scheme. With the presence of a degradation cost the battery barely

charges in the first part of the day (see Figure 48, 0-10 h) and even shows small charging –and

discharging cycles. When the degradation cost is omitted the power distribution of the battery

changes. During the first part of the day (0-10 h) we now see that the battery charges when the

electricity price is low and discharges to the loads when the price rises again (see Figure 47, 0- 10 h).

Because of the small difference between the low price -and high price period, the effect on the

energy cost is small. As can be seen on Table 19 the average purchase cost is € 4.83 when there is no

degradation cost and € 4.9 when a degradation cost is presence. Note that these are average values

of five different runs, where in one of the simulation runs without a degradation cost the purchase

cost was € 4.73. This again confirms that the genetic algorithm is not robust for the type of

optimisation problem we are solving here.

To end with the next section discusses the vision of Eandis about the transition to green energy.

Eandis has published a white paper called ‘The Journey to Green Energy’ [74] where they tell their

vision about the energy transition. Eandis is the largest Distribution System Operator (DSO) of

Belgium, so it is interesting to know how they will tackle the problem of a major change in our energy

production and thus distribution.

82

7.1 Final Remarks

The motive of adapting our energy generation towards green is the worldwide concern of global

warming. Adapting our energy generation towards green is one way to deal with the global warming

problem, but changing our consumption behaviour is a crucial step in this transition. According to

Eandis the transition towards a ‘’green’’ landscape is a gradual process where the biggest challenge

will be to act in the right way at the right time to facilitate this transition. ‘’Flexibility’’ in consumption

and production will play an important role, but adding them into our energy landscape will only be

possible if the right policies, control systems and market mechanisms evolve at the same pace [74].

The journey towards green energy will result mostly in decentralized electricity generation, which

means that the solution also has to be found in a decentralized manner. Every element (demand,

generation and storage) need to participate to keep the system balanced. Nowadays “ demand drives

generation”, but as we want to evolve towards a green energy landscape the shift towards

“generation drives demand” must be introduced. There are many solutions to achieve this and new

solutions will emerge, but focusing on only one solution is not a good idea. The impact of industrial

consumers is of course larger than in the residential domain, but Eandis believes that the residential

domain will be needed in the future. For now the focus will be on the industrial consumers while

preparing for the change in behaviour of residential customers. One of the reason for this, is because

certain pilot projects such as Address, Ecogrid and Linear have shown that the financial benefits for

residential users are currently very low. Eandis believes that a socio-cultural change will be

necessary, but hopes that the necessary technology (storage and load shifting automation) will allow

to achieve the necessary flexibility with minimized impact. A way to achieve this demand-shifting is

via financial signals, for example dynamic pricing schemes, or controlled by a technical signal that is

centrally or locally created based on the situation of the market or network [74].

The change towards a green energy production does not imply that we should only allow renewable

generation in our network, because we will still need for example the gas fired plants filling the gaps

between generation and demand. This until other technology, e.g. storage, can take over. As a result

of the intermittency of renewable generation we need to provide additional flexible power to fill the

gap between the available renewable generation and the demand. This fact makes renewable energy

such as wind and solar expensive, because the cost of producing green energy is the sum of the wind

turbines and solar panels + the cost of the necessary balancing power to maintain the network

balanced. If we look at Figure 49 we see that the integration cost of wind energy is as large as the

generation cost of it. One of the effects of decentralized generation is that the energy will circulate in

two directions in the network. The first challenge is controlling the voltage and guaranteeing the

security of the network with a highly bi-directional load flow. The second challenge will be to bring

the generation electrically as close as possible to the demand. This will reduce the amount of

investment required and the losses in the network. Working on the right network architecture is

crucial to realize a financial benefit, reduce network losses and allow green energy to be more

present in the network. The way to do this is to maximize the integration of local generation on

demand feeders. This will allow power to flow through the shortest way to the consumer and results

in fewer losses and voltage problems [74].

83

Tariff schemes are a way to handle the “pull” type of demand response by just sending new pricing

tariffs and hope the consumer will react [74]. The most dynamic model used is to communicate the

electricity prices day-ahead to customers. The danger of pricing/tariff schemes is an overreaction

that results in a heavy unbalance or congestion problem, as there is not always a feedback loop. Each

control model will only converge if you adjust your actions based on the obtained results. This means

that based on the situation of the network, you should be able to adjust the tariff schemes

dynamically. Several pilot projects, such as Linear and Ecogrid, showed that the financial result of

residential demand response is so low nowadays that the business opportunity is still negative.

However Eandis believes that the journey to green will continue and at some point the residential

demand will need to contribute to balance the system. Think of the increasing electrification of

house hold appliances, such as a heat pump and an electrical vehicle [74].

The start of using balancing power on distribution networks will need a great number of participants,

because of the smaller impact than large industrial consumers. This implies that an aggregator will

have to contract a lot more customers to ensure the continuous availability of flexibility resources he

is selling to a Transmission System Operator (TSO) like Elia for example. As the number of clients

increase it is difficult to have a deterministic view on what is happening on the network when the

aggregator acts for balancing purposes. Residential and smaller consumers will at some point in the

future start to participate in the market. However it will not be possible to determine their actions in

a deterministic way nor control them directly. Reactions from the market will come in a stochastic

base, not only in volume but also in reaction time. Control systems will have to act in a total different

way, where central control will have to make room for local automation systems that react to local

signals, perhaps together with global broadcasted information. This will become more important and

even crucial [74].

Figure 49: Levelized Cost Of Energy (LCOE) for wind turbines [74]

84

When looking to an energy problem we have to consider three types of efficiency that compose the

global efficiency. These three types of efficiencies are the energy efficiency, the financial efficiency

and the green efficiency. In most cases these efficiencies are contradictory, which means that it is

hard to focus on one of them without restricting the other two (see Figure 50). The first type of

efficiency, namely energy efficiency, focuses on using as little energy as possible. For example to

maximize the efficiency of heating -or refrigeration processes, it is a matter of finding the right

balance between adding energy to and keep energy inside your process. This does not necessary

mean consuming when there is excess of green energy or during low price periods. To obtain a

maximal financial efficiency we need to consume electricity at the lowest possible cost. This does not

imply that consuming during low price periods that the consumption will be less. When we wait

longer, for example until a low price period, before turning on heating or cooling systems, this will

probably result in a lower energy efficiency because the system will have consumed more before

reaching the desired temperature. Finally green efficiency will demand to maximize the use of green

energy such that the amount of CO2 emissions reduce. Trying to maximize green energy will need

some kind of storage and balancing power to keep the system balanced. As known this costs a lot of

money, which will result in a lower financial efficiency [74].

We will end with some interesting features related to demand response. On low voltage feeders a

congestion normally leads to a voltage problem. Too much local production will lead to over-voltage

and too much demand results in an under-voltage. Acting based on a local voltage measurement may

be a solution for congestion problems. Controllers can start appliances that absorb the excess of

produced energy, which otherwise should be curtailed. This not only solves the voltage problem, but

also increases the energy efficiency. Another example can be an electrical vehicle charger that

reduce its current based on the voltage drop it causes. Besides of maintaining the voltage level, also

the frequency is an important parameter for maintaining a balanced network. The use of local

frequency relays on heavy consuming appliances, such as a water boiler and heat pump, can resolve

frequency problems. If the trigger to shut off is set to a frequency just above the trigger for

frequency containment reserves (49.8 Hz), this will cut off a large part of the demand that may

prevent a further drop or at least help limit the impact of the frequency drop. The remaining problem

is to decide how long they have to be cut off and how we need to start them up again. The restart

may cause a problem, because when for example all boilers are restarted at the same moment this

may cause another frequency drop. A sequential start up can be a solution [74].

Figure 50: Triangle of efficiency [74]

85

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91

Appendix

Matlab code tic

clc;

clear all;

%%

%%%%%%%%%%%%%%%%%%

% Initialisation %

%%%%%%%%%%%%%%%%%%

disp('Initialisation...');

%% Parameters input

type='single'; % single objective optimisation

timesteps = 96; % # of timesteps

alpha = 1; % users's preference factor -> alpha*Fcost+(1-alpha)*Fcomfort

N_slot = 96; % 96 timeslots of 15 min

% dpunitstotal = 4; % Total number of controllable appliances:(1)Battery % (2) Grid (3) Heat Pump (HP) % (4) Combined Heat

and Power Unit (CHPU) % (5) Washing machine (WM) % (6) Dishwasher (DW) %(7) Cloth dryer (CD)

dpname = ['battery,','grid,','HVAC,','CHPU,','WM','DW','CD'];

dpinclude = [1,2,3,4,5,6,7]; % Appliances that are included

dpunits = length(dpinclude); % effective number of appliances

ngen = dpunits * timesteps; % number of variables

92

%battery

nu_bat = 0.90*0.97; %efficiency battery*efficiency inverter

dt = 0.25; % 15 min = 1/4 h

Emax = 4.8*4*dt; % maximum storage capacity of battery 4.8 kWh

E0 = 0.2*Emax; % minimum energy content of battery

E_init = 0.2*Emax; % energy in battery @ t=0

P_max = 2; %Max. charging power of battery [kW]

P_min = 2; %Max. discharging power of battery [kW]

L_N = 2000; % cycle lifetime of battery [# cycles]

DOD = 0.8; %Depth of discharge of battery = max. amount of energy the battery can deliver as a percentage of Emax

n_Tem = 0.9; %actual lifetime/reference lifetime

C_c = 2212; %battery capital cost [euro]

C_d = C_c/(L_N*Emax*n_Tem*DOD); %battery degradation cost [euro/kWh]

data = load('DATA'); % loading PV -and load profile, pricing schemes

% prices

%daprce = data.RTP(1:timesteps) + max(data.RTP(1:timesteps))*3;

daprce = data.ToU_2(1:timesteps); % Buying price of electricity [euro/kWh]

revenue = 0.95*daprce; % Selling price of electricity to the grid [euro/kWh]

NG = data.NG_max(1:timesteps); %Buying price scheme of natural gas [euro/kWh]

degcost = C_d*[ones(40,1);-ones(28,1);ones(28,1)]; % Degradation cost scheme of battery [euro/kWh]

% Input

P_PV = data.P_PV(1:timesteps)./max(data.P_PV)*4.5; %PV production [kW];4.5 kWp

P_cl = data.P_critic1(1:timesteps); % Critical load profile [kW]

Ft = data.Ft(1:timesteps); %hot water usage profile [l/h];

T_outdoor = data.T_outdoor(1:timesteps); % outdoor temperature in deg. C

y=load('case01'); %Loading results of previous simulation run

T_room = y.T_room; %Room temperature used to calculate comfort cost function of HP

T_w = y.T_water; %Hot water temperature used to calculate comfort cost function of Thermal storage tank

93

% limits

lb1 = [-Emax -5 0 0 1 1 1]; lb2 = [-P_min -3 0 0 0 0 0]; %lower bound limits

ub1 = [10 10 1 1 96 96 96]; ub2 = [P_max 4 1 1 0 0 0]; %upper bound limits

lb = horzcat(lb1,Horzcat(timesteps-1,lb2)); %makes lower bound row of length 7*timesteps

ub = horzcat(ub1,Horzcat(timesteps-1,ub2)); %makes upper bound row of length 7*timesteps

%CHPU

P_CHPU = 1.7; %rated power of CHPU [kW]

nu_e = 0.247; % electrical efficiency of CHPU

nu_HX = 0.657; % thermal efficiency of heat recovery system

nu_CHPU = nu_e/(1-nu_e)*1/nu_HX; %P_CHPU = nu_CHPU*Q_CHPU

T_TS_max = (60-2.5)*(alpha==0)+(60-1.25)*(alpha==0.5)+60*(alpha==1); % max. temp. of thermal storage

T_TS_min = (50+2.5)*(alpha==0)+(50+3.75)*(alpha==0.5)+50*(alpha==1); % min. temp. of thermal storage

T_env = 15; % environment temperature of thermal store

T_in = 16; % inlet temperature of water

G_TS = 0.50588*1.754; %ratio of the surface area of tank to thermal resistance of the tank U_TS*A_TS [W/K]

C = 150*4186/3600; %equivalent thermal mass m_TS*c_p [Wh/K]

Bt = Ft*4186/3600; %[W/K]

Rt = (Bt+G_TS).^-1;%[K/W]

Q_CHPU = 1/nu_CHPU*P_CHPU*1000; % Thermal power of CHPU [W]

T_set_w = 55;% user set point of hot water temperature

dT_L = 2.5;dT_U=2.5;% Temperature band of thermal store

Tw_m = T_TS_min;Tw_mm = T_TS_max;

tau = Rt*C;

G = G_TS;

dT_m = max(T_set_w-Tw_m,Tw_mm-T_set_w);

f_t = exp(-dt*tau.^-1);

T_n = T_in;

94

%HP

P_HVAC = 2.7; % rated power of HP [kW]

COP = 2;%COP of HP

Q_HVAC = COP*P_HVAC*1000;

T_room_mm = 21;%max room temperature [C]

T_room_m = 19; % min room temperature in [C]

T_set_r = 20; % user set point of room temperature [C]

T_room_max = ([(T_set_r+2)*ones(24,1);

(T_set_r+0.5)*ones(8,1);(T_set_r+2)*ones(36,1);(T_set_r+0.5)*ones(20,1);(T_set_r+2)*ones(8,1)])*(alpha==1)+

(T_room_mm*ones(t mesteps,1))*(alpha==0)+((T_room_mm+0.5)*ones(timesteps,1))*(alpha==0.5); % Upper bound of room temperature

T_room_min = ([(T_set_r-2)*ones(24,1); (T_set_r-0.5)*ones(8,1);(T_set_r-2)*ones(36,1);(T_set_r-0.5)*ones(20,1);

(T_set_r-2)*ones(8,1)])*(alpha==1)+(T_room_m*ones(timesteps,1))*(alpha==0)+((T_room_m-0.5)*ones(timesteps,1))*(alpha==0.5); %

Lower bound of room temperature

DT_m = max(T_set_r-T_room_m,T_room_mm-T_set_r);

DT_L = 1;DT_U=1; % Temperature band of HP [C]

G0 = 195.7; %Gt = G0*(Tt_outdoor-Tt_room)-> heat gain rate of the house [Wh/h.K]

dc = 4*216; %energy to change temp of air by 1 degree Celsius [Wh/K]

T_room_init = 20; %initial room temperature [C]

Gt = G0*(T_outdoor-T_room); % heat gain rate of the house [Wh/h]

%WM

N_task_WM = 4; % # of time slots needed to finish job

N_max_WM = 76; % Time slot at which job needs to be finished

N_min_WM = 37;% Time slot at which job may start WM

P_WM = 0.5; % rated power of WM

P =

[daprce(1:40);daprce(41)/2;daprce(42)/4;zeros(20,1);daprce(63)*0.2;daprce(64)*0.4;daprce(65)*0.6;daprce(66)*0.8;daprce(67:96]

;% Electricity price->made zero during PV production

95

f1 = P_WM*P; % Electricity cost function for WM

Aeq1 = [zeros(1,N_min_WM),ones(1,N_max_WM-N_task_WM-N_min_WM),zeros(1,timesteps-(N_min_WM+N_max_WM-N_task_WM-N_min_WM))];

beq1 = N_task_WM;

LB = zeros(timesteps,1);

UB = ones(timesteps,1);

U_WM = intlinprog(f1,timesteps,[],[],Aeq1,beq1,LB,UB);% Determine optimal starting time WM

N_start_WM = find(U_WM,1,'first')*(alpha==1)+48*(alpha==0); %Starting time of WM

%DW

N_task_DW = 4; % # of time slots needed to finish job

N_max_DW = 84;% Time slot at which job needs to be finished

N_min_DW = 37;% Time slot at which job may start DW

P_DW = 1; % Rated power of DW

f2 = P_DW*P;% Electricity cost function for DW

Aeq2= [zeros(1,N_min_DW),ones(1,N_max_DW-N_task_DW-N_min_DW),zeros(1,timesteps-(N_min_DW+N_max_DW-N_task_DW-N_min_DW))];

beq2 = N_task_DW;

U_DW = intlinprog(f2,timesteps,[],[],Aeq2,beq2,LB,UB);% Determine optimal starting time DW

N_start_DW = find(U_DW,1,'first')*(alpha==1)+56*(alpha==0);%Starting time of DW

%CD

N_task_CD = 8; % # of time slots needed to finish job

N_max_CD = 93;% Time slot at which job needs to be finished

N_min_CD = 77;% Time slot at which job may start CD

P_CD = 4; % Rated power of CD

f3 = P_CD*P;% Electricity cost function for CD

Aeq3= [zeros(1,N_min_CD),ones(1,N_max_CD-N_task_CD-N_min_CD),zeros(1,timesteps-(N_min_CD+N_max_CD-N_task_CD-N_min_CD))];

beq3 = N_task_CD;

96

U_CD = intlinprog(f3,timesteps,[],[],Aeq3,beq3,LB,UB);% Determine optimal starting time CD

N_start_CD = find(U_CD,1,'first')*(alpha==1)+80*(alpha==0);%Starting time of CD

%% Construction of cost- and comfort functions

DPcostfunctions=DPcostfunction(dpinclude);

Degcost = degcostfcn(dpinclude);

Rev_cost = revenuecostfcn(dpinclude);

Comfortfunctions = Comfortfunction(dpinclude);

NonIntfcn = NonIntcomfortfcn(dpinclude);

HP_comfort = HP_comfortfcn(dpinclude);

CHP_comfort = CHP_comfortfcn(dpinclude);

[Fcost,Fcomfort]=Parametratie(timesteps,dpunits,DPcostfunctions,Comfortfunctions);

F_deg = Parametratie_bat(timesteps,dpunits,Degcost);

F_revenue = Parametratie_bat(timesteps,dpunits,Rev_cost);

F_nonIntcomfort = Parametratie_comfort(timesteps,dpunits,NonIntfcn);

F_HP = Parametratie_comfort(timesteps,dpunits,HP_comfort);

F_CHP = Parametratie_comfort(timesteps,dpunits,CHP_comfort);

Ydeg = str2func(strcat('@(x,degcost)',F_deg));

Yrev = str2func(strcat('@(x,revenue)',F_revenue));

Ycost=str2func(strcat('@(x,revenue,daprce,degcost,NG,nu_e,P_CHPU)',Fcost));

Ycomfort=str2func(strcat('@(x,T_set_r,T_room_m,T_room_mm,DT_m,DT_L,DT_U,T_room,Gt,dc,Q_HVAC,N_slot,T_set_w,dT_L,dT_U,Tw_m,Tw_

mm,f_t,G,Bt,Rt,dT_m,T_w,T_env,T_n,Q_CHPU)',Fcomfort));

YnonInt = str2func(strcat('@(x)',F_nonIntcomfort));

Y_HP = str2func(strcat('@(x,T_set_r,T_room_m,T_room_mm,DT_m,DT_L,DT_U,T_room,Gt,dc,Q_HVAC,N_slot)',F_HP));

Y_CHP = str2func(strcat('@(x,N_slot,T_set_w,dT_L,dT_U,Tw_m,Tw_mm,f_t,G,Bt,Rt,dT_m,T_w,T_env,T_n,Q_CHPU)',F_CHP));

%% Construction of equality vector beq

beq1 = b_vector_eq(timesteps,P_PV,P_cl,P_WM,U_WM,P_DW,U_DW,P_CD,U_CD);

beq = [beq1;-beq1];

97

%% Construction of equality matrix Aeq

veq =[1 -1 P_HVAC -P_CHPU 0 0 0];

Aeq1 = A_matrix_eq(timesteps,dpunits,veq);

Aeq = [Aeq1;-Aeq1];

%% Construction of inequality matrix A

% battery

%charge

v_ch =[dt*nu_bat 0 0 0 0 0 0];

A_ch_max = A_matrix_ch_max(timesteps,dpunits,v_ch);

A_ch_min = -A_ch_max;

A_ch = [A_ch_max;A_ch_min];

%discharge

v_disch =[dt/nu_bat 0 0 0 0 0 0];

A_disch_max = A_matrix_ch_max(timesteps,dpunits,v_disch);

A_disch_min = -A_disch_max;

A_disch = [A_disch_max;A_disch_min];

A_bat = [A_ch;A_disch];

%HVAC

cst1 = (1-G0*dt/dc);

v_HVAC = [0 0 dt/(dc)*Q_HVAC 0 0 0 0];

A_HVAC_max = A_matrix_HVAC(timesteps,dpunits,cst1,v_HVAC);

A_HVAC_min = -A_HVAC_max;

A_HVAC = [A_HVAC_max; A_HVAC_min];

%CHPU+Thermal storage

a = Rt.*(1-exp(-(Rt*C).^-1*dt))*Q_CHPU;

b = exp(-(Rt*C).^-1*dt);

98

A_CHPU_max = A_matrix_CHP(timesteps,dpunits,a,b);

A_CHPU_min = -A_CHPU_max;

A_CHPU = [A_CHPU_max;A_CHPU_min];

%WM

v_WM = [0 0 0 0 1 0 0];

A_WM_max = A_matrix_nonInt(timesteps,dpunits,v_WM);

A_WM = [A_WM_max;-A_WM_max];

%DW

v_DW = [0 0 0 0 0 1 0];

A_DW_max = A_matrix_nonInt(timesteps,dpunits,v_DW);

A_DW = [A_DW_max;-A_DW_max];

%CD

v_CD = [0 0 0 0 0 0 1];

A_CD_max = A_matrix_nonInt(timesteps,dpunits,v_CD);

A_CD = [A_CD_max;-A_CD_max];

%Total A

A = [A_bat;A_HVAC;A_CHPU;Aeq;A_WM;A_DW;A_CD];

%% Construction of inequality vector b

% battery

b_ch = [E_init;Emax*ones(timesteps-1,1);-E_init;-E0*ones(timesteps-1,1)];

b_disch = b_ch;

b_bat = [b_ch;b_disch];

99

%HVAC

b_HVAC_max = b_vector_HVAC(timesteps,T_room_max,T_room_init,G0,cst1,dt,dc,T_outdoor);

b_HVAC_min = b_vector_HVAC_min(timesteps,T_room_min,T_room_init,G0,cst1,dt,dc,T_outdoor);

b_HVAC = [b_HVAC_max;b_HVAC_min];

%CHPU+Thermal storage

c = G_TS*Rt*T_env + Bt.*Rt*T_in;

d = (1-exp(-(Rt*C).^-1*dt));

b_CHPU_max = b_vector_CHP_max(timesteps,T_TS_max,T_set_w,b,c,d);

b_CHPU_min = b_vector_CHP_min(timesteps,T_TS_min,T_set_w,b,c,d);

b_CHPU = [b_CHPU_max;b_CHPU_min];

%WM

b_WM_max = [N_max_WM-N_task_WM;zeros(timesteps-1,1)];

b_WM_min = [-N_min_WM;zeros(timesteps-1,1)];

b_WM = [b_WM_max;b_WM_min];

%DW

b_DW_max = [N_max_DW-N_task_DW;zeros(timesteps-1,1)];

b_DW_min = [-N_min_DW;zeros(timesteps-1,1)];

b_DW = [b_DW_max;b_DW_min];

%CD

b_CD_max = [N_max_CD-N_task_CD;zeros(timesteps-1,1)];

b_CD_min = [-N_min_CD;zeros(timesteps-1,1)];

b_CD = [b_CD_max;b_CD_min];

%Total b

b = [b_bat;b_HVAC;b_CHPU;beq;b_WM;b_DW;b_CD];

100

%%

%%%%%%%%%%%%%%%%%%%%%%%

% DISPATCH ALGORITHME %

%%%%%%%%%%%%%%%%%%%%%%%

disp('Optimalisation...');

if(isequal(type,'single'))

disp('Single objective optimisation...');

optionsGA = gaoptimset('TolFun',1e-4,'TolCon',1e-4,'PopulationSize',200, 'Generations', ngen*200,'Display','iter');

[x,fval,exitflag] = ga(@(x)MultiObj(x,alpha, daprce, revenue, degcost, NG, nu_e, P_CHPU, T_set_r, T_room_m, T_room_mm,

DT_m, DT_L, DT_U, T_room, Gt, dc, Q_HVAC, N_slot, T_set_w, dT_L, dT_U, Tw_m, Tw_mm, f_t, G, Bt, Rt, dT_m, T_w, Q_CHPU, T_env,

T_n, Ycost, Ycomfort), ngen, A, b, [], [], lb, ub, [], Binvar(timesteps,[3 4 5 6 7]), optionsGA);

else

disp('Error type!');

end

%%

%%%%%%%%%%%%%%%%%%%%%%%

% RESULTS %

%%%%%%%%%%%%%%%%%%%%%%%

disp('Processing results...');

if(isequal(type,'single'))

disp('Single objective results...');

fvaltot=(fval(:,1));

[minimum, ind]=min(fvaltot);

for j=1:ngen

xopt(j)=x(ind,j);

end

for i=1:1

fval_opt(i) = fval(ind,i);

end

else

101

disp('Error type!');

end

toc

% Putting simulation results in a table

xopt_new = round(xopt*10.^1)/10.^1;

setpoints = reshape(xopt_new, dpunits, [])';

SOC = cumsum(setpoints(:,1)*dt);% Calculating State Of Charge of battery

T_room = RoomTempConstr(setpoints(:,3),T_room_init,G0,dc,Q_HVAC,T_outdoor);% Calculating room temperature profile

T_water = WaterTemp(setpoints(:,4),T_set_w,G_TS,Bt,Rt,C,T_in,T_env,Q_CHPU);% Calculating hot water temperature profile

results = [(1:1:timesteps)' round((setpoints(:,1)-setpoints(:,2)+P_HVAC*setpoints(:,3)-P_CHPU*setpoints(:,4)-beq1)*10)/10

setpoints(:,1), setpoints(:,2), setpoints(:,3)*P_HVAC, T_room, setpoints(:,4)*P_CHPU, T_water, SOC,

[N_start_WM;setpoints(2:timesteps,5)],P_WM*U_WM,(1:1:timesteps)',[N_start_DW;setpoints(2:timesteps,6)],

P_DW*U_DW,[N_start_CD;setpoints(2:timesteps,7)], P_CD*U_CD, daprce, revenue(1:timesteps), degcost, NG];

dataset = mat2dataset(results);

dataset(:,:);

dataset.Properties.VarNames = {'Timeslot','equality_test', 'P_Bat','P_Grid','P_HVAC','T_room','P_CHPU','T_water',

'SOC','N_start_WM','P_WM','Timeslot1','N_start_DW','P_DW','N_start_CD','P_CD', 'Buying', 'Selling','degcost','NG'}

% Printing results on screen

fval %fitness value of cost function

disp('Results')

%energy cost

fcost_net = Ycost(x,revenue,daprce,degcost,NG,nu_e,P_CHPU) %net energy cost

f_deg = Ydeg(x,degcost) %battery degradation cost

f_rev = -Yrev(x,revenue) %Sales revenue

f_purchase = fcost_net-f_deg+f_rev %Purchase cost of energy

102

%comfort cost of each appliance

fcomfort =

1/5*(Ycomfort(x,T_set_r,T_room_m,T_room_mm,DT_m,DT_L,DT_U,T_room,Gt,dc,Q_HVAC,N_slot,T_set_w,dT_L,dT_U,Tw_m,Tw_mm,f_t,G,Bt,Rt

,dT_m,T_water,T_env,T_n,Q_CHPU)- YnonInt(x) + YnonInt([0 0 0 0 N_start_WM N_start_DW N_start_CD, zeros(1,ngen-7)])) %Total

comfort cost

f_HP = Y_HP(x,T_set_r,T_room_m,T_room_mm,DT_m,DT_L,DT_U,T_room,Gt,dc,Q_HVAC,N_slot)%comfort cost of heat pump

f_CHP = Y_CHP(x,N_slot,T_set_w,dT_L,dT_U,Tw_m,Tw_mm,f_t,G,Bt,Rt,dT_m,T_water,T_env,T_n,Q_CHPU)%comfort cost of CHP unit

f_nonInt = YnonInt([0 0 0 0 N_start_WM N_start_DW N_start_CD, zeros(1,ngen-7)]) %comfort cost of non-interruptible appliances

fcomfort_test = 1/5*(f_HP + f_CHP + f_nonInt) %Total comfort cost test

save('case01'); % saving the results