Accepted Manuscript

Title: Minimization of operational cost for an off-gridrenewable hybrid system to generate electricity in residentialbuildings through the SVM and the BCGA methods

Author: Nedim Tutkun

PII: S0378-7788(14)00213-8DOI: http://dx.doi.org/doi:10.1016/j.enbuild.2014.03.003Reference: ENB 4889

To appear in: ENB

Received date: 14-9-2013Revised date: 13-2-2014Accepted date: 3-3-2014

Please cite this article as: N. Tutkun, Minimization of operational cost for anoff-grid renewable hybrid system to generate electricity in residential buildingsthrough the SVM and the BCGA methods, Energy and Buildings (2014),http://dx.doi.org/10.1016/j.enbuild.2014.03.003

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Minimization of operational cost for an off-grid renewable hybrid system to generate

electricity in residential buildings through the SVM and the BCGA methods

NedimTutkun

Department of Electrical & Electronic Engineering, Düzce University, 81620 Düzce, Turkey

Abstract

Recently Turkey’s electricity demand has shown a considerable increase due to its population

and economic growths. It is understandable that this may be very influential on electricity

price on market as well as other factors such as an increase in natural gas price etc. It should

be noted that the half of Turkey’s electricity generation is supplied from natural gas and 95%

of this source is imported from other countries. However, Turkey is rich in wind and solar

energy potentials to generate electricity and it is believed that this makes a considerable

impact on reducing high electricity unit cost to competitive one. In this regard, these

potentials can be utilized for electricity generation in order to meet a significant portion of the

power demanded by residential houses through a PV/wind system. The electricity cost of the

renewable system can be minimized by optimally scheduling generated and consumed

powers. In this paper, optimal power scheduling in such systems is carried out by using the

BCGA and the SVM methods. The results indicated that the proposed approach was able to

minimize the operation cost in the hybrid system through the optimal power scheduling.

Keywords

Genetic algorithms, Renewable systems, Optimal power scheduling, Support Vector

Machines

1. IntroductionRenewable energy systems have drawn great attention to reduce the fossil fuels consumption

by a large amount, to maintain a clean environment and to minimize the short-term energy

cost in residential houses in the last three decades. Among renewable energy systems,

photovoltaic (PV) panels and low power wind turbines are widely used to generate electricity.

A recent survey has shown that PV panels and small wind turbines are increasingly used for

power generation in smart buildings for many years [1]. It is a fact that PV systems are more

easily installed in buildings compared to wind turbines. However, neither PV nor wind turbine

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systems constantly produce power since they are irregular energy sources. Therefore power

may be insufficient to meet the demand for loads at some time intervals during a day. It is a

fact that a major problem in power systems is to maintain the balance between the generation

and consumption, hence smart power management is needed. One solution to this problem is

to add a battery bank to the system for home residence applications so that the surplus energy

can be stored to the battery bank when generation is greater than consumption or vice versa.

Adding the battery bank to the system inserts new constraints to the current ones and the

determination of number of battery is strongly dependent on renewable energy generation, the

load profile and the rated capacity of a battery.

The operational cost of this system should be minimized by scheduling generated and

consumed powers as much as possible for short term run. This is a typical constrained

optimization problem of power scheduling for a home residence. In off-grid systems some of

loads may be shed from the microgrid when generated power is less than consumed power

within 24 hours but in on-grid systems the power difference between load and generation is

supplied from the grid hence no load is shed. The power scheduling problem has been studied

by few researchers for last three decades.

Bakirtzis and Dokopoulos presented approach to solve short-term scheduling problem in a

small off-grid system including conventional and unconventional sources and an electrical

storage [2]. The system consists of diesel backup generators, wind turbine generators, and PV

arrays and a dynamic programming algorithm is used to minimize the fuel consumption.

Another approach to short term power scheduling was carried out by Marwali et al and it

proposes a model that incorporates a battery storage for peak load shaving with several

constraints including battery capacity, maximum PV capacity etc [3]. Kumar et al studied

economic analysis and power management of a stand-alone wind-PV hybrid energy system

using biogeography based on optimization algorithm [4]. Riffonneau et al presents a work on

optimal power management for grid connected PV systems with electrical storage using

optimal predictive power scheduling algorithm based on dynamic programming [5]. Palma-

Behnke et al put forward a novel energy management system for a renewable microgrid to

minimize the operation cost through the two-day ahead prediction of the weather conditions

[6]. Xiong Wu et al proposed an approach to the optimal scheduling of a microgrid with

various distributed generators and storage devices using the mixed integer linear

programming (MILP) method [7]. Another work on the optimal scheduling of smart homes’

energy consumption is carried out by Di Zhang et al using the MILP approach [8]. Morais et

al studied the energy management of the isolated low power hybrid renewable system and the

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optimal operation of a wind turbine, a PV panel, a fuel cell and a storage battery was achieved

by the MILP through the general algebraic modelling systems [9]. Liang and Liao presented a

study about fuzzy-optimization approach to solve the generation scheduling problem for wind

and solar energy systems in order to minimize total unit fuel cost [10]. Another investigation

such as by Lu and Shahidehpour applied a Lagrangian relaxation-based optimization

algorithm to determine the hourly charge/discharge commitment of a battery in a utility grid

and a network flow programming algorithm for the dispatch of committed battery units [11].

The power dispatch problem of distributed generators for optimal operation of a microgrid

was studied by Seon-Ju Ahn et al and the main objective was to minimize the fuel cost during

the grid-connected operation in this work [12]. Anusha et al presented a work on power

optimization problem with average delay constraint on the downlink of a Green Base Station

powered by solar or wind energy source as well as conventional sources such as diesel

generators or power grid. The main aim of this work was to minimize the energy drawn from

conventional energy sources using Markov Decision Problem approach [13]. Karami et al

studied the problem of the economic dispatch of the smart home integrated energy system and

the effects of the battery and electricity tariff in the system operation costs [14]. Khodr et al

used the virtual power producer for intelligent power scheduling under lab conditions [15].

Optimal dispatching method for smoothing power fluctuations of the PV/wind system with a

battery bank was proposed by Li et al [16]. Kadar carried out a work on power scheduling of

renewable power sources using the MILP technique to reduce the operational cost of the

system [17]. Precisely modelling and forecasting measured data play important role in various

power scheduling problems. Among several techniques, the support vector machines (SVM)

regression method is considerably attractive for a small number of prediction and modelling

and problems.

Mohandes et al, applied the SVM regression method to predict wind speed using the

measured data and compared the results with the latest neural network algorithm with the

multilayer perceptron in terms of performance [18]. Another researcher such as by

Kavaklioglu et al used the SVM regression to model Turkey’s electricity consumption and the

obtained results were meaningful [19]. Besides, the SVM regression method was also

employed for modelling a ground-coupled heat pump and new solar air heater systems [20].

In addition, techno-economic analysis of these systems was successfully carried out by the

SVM regression technique [21]. In order to reduce energy cost for small business energy

management strategy was accomplished by the Fuzzy Logic and graphical methods [22]. The

management of household energy was achieved by finding a compromise between user

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comfort and energy cost in terms of occupant expectations and physical constraints such as

energy price and power constraints [23].

This study investigates a proper power management for a 2kW off-grid PV/wind hybrid

system with electrical storage feeding a typical residential house located in a rural area. To

minimize the operation cost of this hybrid system was achieved by the binary-coded Genetic

Algorithm (GA) and the SVM regression methods for power scheduling. The system

description is given in Section 2 in which the hybrid system components are solely described

and presents the problem formulation containing the objective function and the constraint

equations. It also includes the forecasted wind, insolation and load profiles for 24 hours in the

location where the hybrid system was installed. The description of how the GA and SVM

techniques are also applied to the problem under consideration is presented in Section 2. The

obtained results and their discussion are stated in Section 3 and finally conclusion of the work

is asserted in Section 4.

2. System description and problem formulationA. System Components

The installed stand-alone renewable hybrid system is composed of wind turbines, PV panels

and batteries as shown in Fig. 1 and feeds a typical residential house in a remote area. A wind

turbine with permanent magnet synchronous generator generates 500W peak power and its

operation range varies from 2 to 25 m/s of wind speeds. Each monocrystalline PV panel has

235W peak power and no sun tracking system is used. There are two types of controller

employed to regulate the charging and discharging currents from the wind turbine and PV

arrays and their maximum charging currents of 20A and 10A respectively at 12 VDC. For

energy storage, three batteries used and each of them has the capacity of 2.4kWh. That is,

each battery can only be charged up to 2.4 kWh and discharged by 1.2 kWh in a time interval.

If the sum of generation and storage is less than demand, some of controllable loads must be

shed. If the total generation is greater than the demand, the surplus energy is stored in the

batteries and the excess generation is dissipated by a voltage-controlled resistive load as heat.

This is necessary to maintain the stability of the system in terms of output frequency and

voltage.

B. Optimal Power Scheduling

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The power scheduling in a renewable hybrid system is usually formulated as a constrained

optimization problem. This problem is based on minimization of operation cost by taking into

account for all the constraints expressed for the renewable hybrid system. Wind and insolation

profiles strongly depending on weather conditions were obtained for an hour time interval in a

year. In order to reduce an hour time interval to 15-minute time interval the number of

measured data was increased by the SVM regression modelling for a better power scheduling.

It should be emphasized that wind power generation is primarily dispatched in the hybrid

system if solely sufficient.

The operation of hybrid system is divided into three modes as follows: (i) surplus energy is

stored in the batteries, (ii) the batteries are discharged when the generated power is

insufficient, (iii) some of the loads is shed from the system the total power generation is

insufficient. With the optimal power scheduling, all the loads may be supplied by the hybrid

system without shedding and may help find minimal operational cost during a week or month.

For necessary optimal power scheduling, the total cost minimization function Fc can be

expressed as

����= ������(∑ [��������(��) + ��������(��)+ ��������(��)−����=1 ��������(��)+��������(��) − ��������(��)]) (1)

subject to

1. ∑ ����(��) + ����(��) + ����(��)− ����(��)− ����(��) + ����(��)− ����(��)����=1 = 02. ���������� ≤ ����(��) ≤ ����������3. ���������� ≤ ����(��) ≤ ����������4. ����(��) ≤ 400��5. ����(��) ≤ 200��6. ����(��)− ������(��− 1) ≤ 07. ������(0) = 200��where cw, cs, cd, cc, cu and ce are unit costs of wind, PV, discharged, charged, undelivered and

excess powers and the unit costs of these energy sources are 0.03€/kWh, 0.03€/kWh,

0.045€/kWh, 0.03€/kWh, 0.15€/kWh and zero respectively. Besides, Pw, Ps, Pl, Pc, Pd, Pu, Pe

and Pst are wind power generated by a wind turbine, power generated by PV panels, power

demand for loads, power charged in the batteries, power discharged from the batteries,

undelivered power, excess power and storage power correspondingly. The unit costs of wind,

PV and the batteries were estimated using annual cost analysis given in [1], [9] and [15].

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Figure 2 shows the yearly averaged wind and PV power generations, and power demand

variations with 15-minute time interval for one week schedule.

C. Support Vector Machines

The SVM method, first developed by Vapnik, is widely used for solving classification,

modelling and regression problems [24]. The SVM regression technique can be obtained as

follows: Let y be a function of n input variables of x. The given training data set of and

( ),…,( , ) is used to find the best model using a linear formulation expressed as

(2)

where is the obtained model output, is the weight vector, sign represents the vector

inner product and is the bias term.

It is fact that the most of real world problems cannot be modelled by linear equation models.

However, the SVM regression technique allows us to model nonlinear real world problems by

a nonlinear kernel function of .

(3)

It is now main problem to determine the proper nonlinear function maps of which fit to

best . In the SVM regression model, should be as flat as possible to obtain a best

generalized performance which requires that is to be minimized for each training test

data given by

(4)

where is the error margin.

In Eq. (4) no feasible constraints are guaranteed but the slack variables of and are

introduced to make them feasible. Despite few types of loss functions, SVM regression with

insensitive loss function is employed in this investigation. It is insensitive to small

errors and applies to a penalty when the errors are greater than acceptable margin of . The

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main objective is to estimate the parameters and that minimize the cost function and this

inevitably leads to a convex optimization problem stated by

(5)

where C is regularization parameter which determines the penalty to estimate the errors.

Hence this optimization problem can be expressed as

(6)

where , , and are the Lagrange multipliers.

In order to obtain minimum error, the partial derivatives of with respect to , , and

should be taken and then set to zero. Taking account of Karush–Kuhn–Tucker conditions the

above equations can be rewritten as

(7)

where .

Finally the model equation can be expressed as

(8)

The kernel function used for SVM regression is the radial basis function given by

(9)

where is the width of radial basis function.

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For proper modelling of the insolation rate and wind speed, parameters of and are

estimated to be 100 and 0.01, and 250 and 0.01 respectively. Since there is no straight-

forward formula to determine them, these parameters are estimated by using a metaheuristic

method. Application of the SVM method to measured data of wind speed and insolation rate

in order to obtain a regression model is shown in Figs 3 and 4. As shown in Fig. 3, the

developed model for insolation rate is well-fitted and the squared correlation coefficient is in

acceptable range. The constructed model for wind speed is illustrated in Fig. 4 and it is

relatively well-fitted to measured values.

D. Application of Binary-Coded GA

To obtain the low-cost power scheduling for a typical residential house, the binary-coded GA

software was developed in MATLAB® environment. In the design of the software power

demand, charging and discharging powers were considered to be a variable. There were two

types of load profiles: one covered all necessary electrical appliances, lighting, heating and

cooling etc; the other consisted of some of necessary electrical appliances and lighting

devices. Maximum of second load profile was 65% of peak value of the first load profile for

each time interval hence its search space was determined between upper and lower limits of

power demand. The excess and undelivered powers were then calculated by satisfying the

constraints given by (1).

The genetic process was initialized by a randomly generated binary population with 100

strings as shown in Figure 5. Each binary-coded string was 30 bit length and each of variables

was equal to 10 bit. For fitness calculation, each substring was converted to real numbers

between the predetermined ranges. Eq. (1) was assigned to be the objective function and the

reciprocal of the objective function was considered to be the fitness function. Thus, fitness for

ith population member can simply be calculated by

(10)

where A is a positive integer number for proper fitness scaling, Fci is the ith total cost and is

the error margin used to avoid making the denominator zero.

The selection was carried out by using the tournament selection algorithm and selected

population were crossed over by the uniform crossover approach with the probability of 0.65.

In order to avoid early convergence flip mutation was implemented on the crossed over

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population with the probability of 0.001. The elitist strategy was carried out to maintain the

best string in each generation.

It should be noted that the binary-coded GA is more convenient than real-coded GA for

optimal power scheduling problem since real crossover and mutation outcomes were out of

the specified range. Therefore they must be linearly mapped for each generation and this

breaks the natural process of the genetic algorithm.

3. Results and DiscussionsThe designed software was run for 150 generations to obtain the lowest operation cost in the

proposed renewable hybrid system. As seen from Figure 6, the operation cost exhibited sharp

decrease around 25 generations but after that it became almost unchanged. This means that

with current parameters of the GA software there is no a better solution found to the problem.

However changing crossover and mutation probability rates and population size may improve

the performance of the GA software for the proposed approach but it is not beyond this

investigation. Nonetheless, the binary-coded GA software managed to considerably reduce

the operation cost as shown in Figure 6. The operation cost was initially around 3¢ but after

25 generations it was fixed at 2.48¢ hence the total reduction was about 22% of maximum

cost. It should also be emphasized that the bit length of each variable may affect on this

reduction. Figure 7 shows the scheduled power demand and charging and discharging powers

in the proposed system. As previously shown in Figure 4 the daily average power demand

was around 0.66kW and minimum and maximum power demand were about 0.390kW and

0.968kW respectively. Without power scheduling, the difference between power generation

and consumption is negative at between 0:00-1:00, 4:15-9:30 and 17:15-24:00 hours and

positive at between 1:00-4:15 and 9:30-17:15 hours on the daily basis operation. However, in

the GA based power scheduling, the power demand varied from 0.254 to 0.715kW and its

average was around 0.458kW. It is clear that average scheduled power demand decreased by

almost 25% of unscheduled power demand. The undelivered power is comparatively

minimized in power scheduling operation with battery bank and there is much more power

delivered to the load as shown in Figure 8. It should be noticed that time interval in positive

power difference curve becomes larger than one in unscheduled power difference curve. This

may be explained by proper power management of the hybrid system with an electrical

storage. Figure 9 shows variations of the excess and undelivered powers for power scheduling

of the proposed hybrid system. Generated power is mostly greater than consumed power in

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daytime in particular around the period from 10:00 to 16:00 hours and this extra generated

power is called excess power. This power reaches its maximum and minimum about at

midday and midnight respectively as expected. Surprisingly the excess power reaches 727W

about at 12:30 hours and it is larger than average power demand. Whereas, maximum of the

undelivered power is 139W about at 21:15 hours and it may be around zero if an additional

PV panel or a wind turbine should be integrated to the hybrid system.

Variation of the unit cost of the hybrid system against 15 minute time intervals is shown in

Figure 10. Minimum and maximum unit costs of the hybrid system are 0.9¢ and 3.62¢ at

12:00 and 1:00 hours respectively. Average unit cost is around 2.1¢ in this hybrid system for a

week schedule but it contains no maintenance and investment costs. It should be noted that

the unit cost is strongly dependent on power demand as well as other parameters and shows a

similar trend with power demand such that it decreases when power demand is low and

increases when it is high.

4. ConclusionIt is shown that the binary-coded GA method may successfully be applied to obtain optimal

power scheduling with a 15-minute time interval and manages to considerably minimize

operation unit cost in the proposed hybrid system. Besides the balance between electricity

generation and consumption in the microgrid hybrid system is almost maintained by the

proposed approach. The real-time implementation of this approach may be applicable to the

slightly large off-grid renewable PV/wind hybrid systems. Finally, this proposed approach

may be improved by extending the forecasted number of data for wind speed and insolation

rate measurements by the SVM regression method in order to obtain 1-minute or 5-minute

time interval.

References[1] Kellogg, W. D. et al., “Generation of unit sizing and cost analysis for stand-alone wind, PV and hybrid

wind/PV systems”, IEEE Energy Conversion, vol. 13, pp. 70-75, 1998.[2] Bakirtzis, A. G. and Dokopoulos, P. S., “Short term generation scheduling in a small autonomous system

with unconventional energy sources”, IEEE Trans. on Power Systems, vol. 3, pp. 1230-1236, 1988.[3] Marwali, M. K. C. et al, “Short term generation scheduling in photovoltaic-utility grid with battery storage”,

IEEE Trans. on Power Systems, vol. 13, pp. 1057–1062, 1998.[4] Kumar et al., “Economic analysis and power management of a stand-alone wind/photovoltaic hybrid energy

system using biogeography based optimization algorithm”, Swarm and Evolutionary Computation, vol. 8, pp. 33-43, 2013.

[5] Riffonneau Y. et al., “Optimal power flow management for grid connected PV systems with batteries,” IEEE Trans. on Sustainable Energy, vol. 2, No. 3, pp. 309-320, 2011.

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[6] Palma-Behnke, R. Et al., “Energy management system for a renewable based microgrid with a demand side management mechanism”, IEEE Symposium on Computational Intelligence Applications in Smart Grid, pp. 1-8, 2011.

[7] Xiong Wu et al., “Optimal generation scheduling of a microgrid”, 3rd IEEE PES International Conference and Exhibition on Innovative Smart Grid Technologies, pp. 1-7, 2012.

[8] Di Zhang et al., “Optimal scheduling of smart homes energy consumption with microgrid”, The First International Conference on Smart Grids, Green Communications and IT Energy-Aware Technologies, pp. 70-75, 2011.

[9] Morais, H. et al, “Optimal scheduling of a renewable micro-grid in an isolated load area using mixed-integer linear programming,” Renewable Energy, vol. 35, pp. 151–156, 2010.

[10] Liang R. H. And Liao, J. H., “A fuzzy-optimization approach for generation scheduling with wind and solar energy systems”, IEEE Transactions on Power Systems, vol. 22, pp. 1665-1674, 2007.

[11] Lu B. and Shahidehpour, M., “Short-term scheduling of battery in a grid-connected PV/battery system”, IEEE Transactions on Power Systems, vol. 20, pp. 1053-1061, 2005.

[12] Seon A. and Moon S. “Economic scheduling of distributed generators in a microgrid considering various constraints”, IEEE Power & Energy Society General Meeting, pp. 1-6, 2009.

[13] Lalitha, A. et al., “Power-optimal scheduling for a Green Base station with delay constraints”, National Conference on Communications, pp. 1-5, 2013.

[14] Karami H. et al, “Optimal scheduling of residential energy system including combined heat and power system and storage device”, Electric Power Components and Systems, vol. 41:8, pp. 765-781, 2013.

[15] Khodr, H. et al, “Intelligent renewable microgrid scheduling controlled by a virtual power producer: A laboratory experience,” Renewable Energy, vol. 48, pp. 269-275, 2012.

[16] L. Li, Q. Ding, H. Li and M. Dan, “Optimal dispatching method for smoothing power fluctuations of the wind-photovoltaic-battery hybrid generation system,” IEEE PES ISGT, pp. 1-6, 2012.

[17] P. Kadar, “Scheduling the generation of renewable power sources,” 5th Slovakian-Hungarian Joint Symposium on Applied Machine Intelligence and Informatics, pp. 255-263, 2007.

[18] M.A. Mohandes et al, “Support vector machines for wind speed prediction,” Renewable Energy, 29, 939–947, 2004.

[19] K. Kavaklioglu, “Modeling and prediction of Turkey’s electricity consumption using Support Vector Regression,” Applied Energy 88, 368–375, 2011.

[20] H. Esen et al, “Modelling a ground-coupled heat pump system by a support vector machine,” Renewable Energy, 33, 1814-1823, 2008.

[21] H. Esen, M. Inalli, M. Esen, “Technoeconomic appraisal of a ground source heat pump system for a heating season in eastern Turkey,” Energy Conversion and Management, 47, 1281-1297, 2006.

[22] H. Zhang et al, “Fuzzy logic based energy management strategy for commercial buildings integrating photovoltaic and storage systems” Energy and Buildings, 54, 196-206, 2012.

[23] R. Missaoui et al, “Managing energy smart homes according to energy prices: analysis of a building energy management system,” Energy and Buildings, 71, 155-167, 2014.

[24] Vapnik, V. N., The Nature of Statistical Learning Theory. NY: Springer-Verlag, 1995.

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Figure 1. The installed PV/wind hybrid system for a typical residential house.

0

750

1500

0 113 226 339 452 565 678

Power (W)

Number of Time Inverval

Load Wind PV

Figure 2. Variation of power generation and demand with time for one week schedule.

Figure 3. Modelling insolation rate using the SVM regression.

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Figure 4. Modelling wind speed using the SVM regression.

Calculate the fitness

Select the individuals

Mutate the population

Copy the best string

Reached maximum number of generation?

YES

NO

Randomly generate a population

STOP

Crossover the population

Figure 5. The flowchart of the GA process.

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2.45

2.85

3.25

0 25 50 75 100 125 150

Operation Cost (¢/kWh)

Generation

Figure 6. Variation of operation cost for the proposed hybrid system with generation.

0

400

800

0 113 226 339 452 565 678

Power (W)

Number of Time Interval

Load Charge Discharge

Figure 7. Variation of scheduled power demand, charging and discharging powers with time.

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15

-650

-200

250

700

1150

0 14 28 42 56 70 84 98

Power (W)

Time Interval

unscheduled

scheduled

Figure 8. Variation of power difference under scheduled and unscheduled operation.

0

400

800

0 113 226 339 452 565 678

Power (W)

Number of Time Interval

Excess Undelivered

Figure 9. Variations of excess and undelivered powers with time.

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0.8

2.5

4.2

0 112 224 336 448 560 672

Operational Cost (¢/kWh)

Number of Time Interval

Figure 10. Variation of the unit cost against number of time interval.

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HIGHLIGHTS II

Optimal power scheduling problem in a PV/Wind system is solved by the BCGA

method

The SVM regression method is used to estimate new data points for better

scheduling

Application of this work can be possible to slightly large PV/wind hybrid systems