a strategic planning model for energy efficiency in public buildings

SEIO 2012, Madrid, April 20 2012 1/44

IntroductionModelling

Symbolic Model Specification

A Strategic Planning Model for Energy Efficiencyin Public Buildings

Emilio L. Cano1 Javier M. Moguerza1

1Department of Statistics and Operations ResearchUniversity Rey Juan Carlos, Spain

XXXIII Congreso Nacional de Estadıstica eInvestigacion Operativa

Emilio L. Cano and Javier M. Moguerza Strategic Model Planning: Energy Efficiency & Risk Mgmt.




Outline

1 IntroductionEnRiMa Project

2 ModellingModel DescriptionDecision VariablesConstraints and Objectives

3 Symbolic Model SpecificationModel Generation Through R




Symbolic Model SpecificationEnRiMa Project

Outline








Introduction

The model described in this talk has been developed withinthe project EnRiMa: Energy Efficiency and Risk Managementin Public Buildings, funded by the EC.

The overall objective of EnRiMa is to develop adecision-support system (DSS) for operators ofenergy-efficient buildings and spaces of public use.





EnRiMa DSS





Model DescriptionDecision VariablesConstraints and Objectives

Outline









Scheme of the Project

EnRiMaDSSStrategicModule

OperationalModule

StrategicDVs

StrategicConstraints

Upper-LevelOperational DVs

Upper-LevelEnergy-BalanceConstraints

Lower-LevelEnergy-BalanceConstraints

Lower-LevelOperational DVs






Strategic Model

The strategic model is used in order to make strategic decisionsconcerning which technologies to install and/or de- commission inthe long term. In an attempt to tackle short- and long-termdecisions as a whole, the strategic model includes a simplifiedversion of operational energy-balance constraints, and theoperational model, in turn, includes the realisation of the strategicdecisions as parameters. In this way, both models feed back toeach other.






Embedded Operational Model

Time resolution

m Mid-term period; m ∈M.

p Long-term period; p ∈ P.t Short-term period; t ∈ T .

The model includes the realisation of short-term decisions (t) thatare scaled to a long-term period (p) through a mid-termrepresentative profile (m).






Energy Technologies and MarketsOther Relevant Sets

i Energy-creating technology; i ∈ I.j Energy-absorbing technology; j ∈ J .k Energy type; k ∈ K.n Energy market; n ∈ N .

l Pollutant; l ∈ L.






Outline









Strategic DecisionsLong Term

Energy-creating technologies (i)

spi Available capacity (kW )

sdp,qi Number of devices to be decommissioned

sipi Number of devices to be installed

We denote by energy-creating technologies those technologies thatprovide the energy demanded by the building (e.g. Combined Heatand Power, Photovoltaic, etc.)






Strategic DecisionsLong Term

Energy-absorbing technologies (j )

xpj Available capacity (kWh)

xdp,qj Capacity to be decommissioned

xipj Capacity to be installed

We denote by energy-absorbing technologies those technologiesthat allow the building to demand less input energy. Thesetechnologies can be storing technologies (e.g. batteries) or passivemeasures (e.g. isolation).






Embedded Operational DecisionsShort Term

Basic variables∗

up,m,t ,mmk ,n Purchase of energy (kWh)

wp,m,t ,mmk ,n Sale of energy (kWh)

yp,m,ti ,k Input of energy k to technology i (kWh)

qip,m,tk ,j Energy type k added to storage technology j (kWh)

qop,m,tk ,j Energy type k released from storage technology j

(kWh)

∗mm 6= m deals with energy traded in forward markets.






Operational DecisionsShort Term

Calculated variables

z p,m,ti ,k Output of energy type k from technology i (kWh)

rp,m,tk ,j Energy type k to be stored in technology j (kWh)

ep,m,t Energy consumption (kWh)






Energy-dispatching Decision Flow

Market

Demand

Purchases

Fictitious

Generation Technologies

StorageTechnologies

N

K

J

ISales

K y

u

u

u

w

u

w

z

qiqo

qi






Outline









Constraints

Strategic

Available generating technologies calculation

Available storing technologies calculation

Generation technologies decommissioning limit

Storage technologies decommissioning limit

Budget limit

Emissions limit

Physical limit for energy-creation technologies installation

Physical limit for energy-absorbing technologies installation

Efficiency constraint

Primary energy calculation






Constraints

Embedded Operational Constraints

Energy balance

Technologies short-term availability

Energy output calculation

Energy stored calculation

Energy discharging limit

Energy storage lower limit

Energy storage upper limit






Strategic Constraints

Available generating technologies calculation

The available capacity to generate a type of energy for eachtechnology in a long-term period equals the number of totaldevices available times their nominal capacity, corrected by theaging factor.

spi = Gi

p∑a1=0

AGp−a1i

(sia1i −

p∑a2=a1+1

sda1,a2i

)p ∈ P, i ∈ I.







Available storing technologies calculation

The available capacity to store a type of energy for each technologyin a long-term period equals the number of total devices availabletimes their nominal capacity, corrected by the aging factor.

xpj = GSj

p∑a1=0

ASp−a1i

(xia1j −

p∑a2=a1+1

xda1,a2j

)p ∈ P, j ∈ J







Generation technologies decommissioning limit

The number of devices to be decommissioned must be less thanthe number of devices previously installed.

∑a1>p

sdp,a1i ≤ sipi p ∈ P, i ∈ I







Storage technologies decommissioning limit

The number of devices to be decommissioned must be less thanthe number of devices previously installed.

∑a1>p

xdp,a1j ≤ xipj p ∈ P, j ∈ J







Budget limit

The total investment in technologies must be lower than a specifiedbudget limit. This includes installation and decommissioning costs.

∑i∈I

CI p,0i ·Gi · sipi +

∑j∈J

CISp,0j ·GSj · xi

pj

+∑i∈I

Gi

(p∑

a1=0

CDp−a1i

p∑a2=a1+1

sda1,a2i

)

+∑j∈J

(p∑

a1=0

CDSp−a1j

p∑a2=a1+1

xda1,a2j

)≤ ILp p ∈ P







Emissions limit

The total emissions must be lower than the allowed limit per year.

∑m∈M

DM pm

(∑i∈I

∑k∈K

∑t∈T

Hi ,k ,l · yp,m,ti ,k

∑n∈N

∑k∈K

∑t∈T

Ci ,l ,n · up,m,t ,mmk ,n

)≤ PLp

l

p ∈ P, l ∈ L







Physical limit for energy-creation technologies installation

The available capacity of a given energy-creation technology, islimited by the physical space needed. This is a function of bothbuilding and technology configuration. For example, for PVtechnologies it would be the ratio roof/technology surfaces. Notethat the function must return the appropriate units.

spi ≤ f (BuildPars,TechPars i) p ∈ P, i ∈ I







Physical limit for energy-absorbing technologies installation

The available capacity of a given energy-absorbing technology islimited by the physical space needed. This is a function of bothbuilding and technology configuration. Note that the functionmust return the appropriate units.

xpj ≤ f (BuildPars,TechPars j ) p ∈ P, j ∈ J







Efficiency constraint

Minimum efficiency required in the building.

∑p∈P

∑m∈M

∑t∈T

∑k∈K

(Dp,m,t

k +∑m∈M

∑n∈N

wp,m,t ,mmk ,n

)≥ EF ·

∑p∈P

∑m∈M

∑t∈T

ep,m,t







Primary energy calculation

The primary energy (not from a fictitious market) consumed is thesum of the processed energy of each type and the one used as aninput fuel.

ep,m,t =∑m∈M

∑k∈K

∑n∈N

(up,m,t ,mmk ,n · Bk ,n +

∑n∈N

up,m,t ,mmk ,n

)p ∈ P, m ∈M, t ∈ T






Operational Constraints

Energy Balance

The energy supplied must meet the energy demand minus theenergy saved due to absorbing technologies. It is composed of theenergy produced with energy-creating technologies plus the energypurchased in the market minus the energy for sale, energy forstorage and energy for production. On the demand side, the energyreleased from storage and the energy saved with passivetechnologies diminish the total demand.






Operational ConstraintsEnergy Balance Equation

∑i∈I

z p,m,ti ,k +

∑n∈NB(k)

∑mm∈MA

up,m,t ,mmk ,n

−∑i∈I

yp,m,ti ,k −

∑mm∈MS

∑n∈NS(k)

wp,m,t ,mmk ,n

∑j∈JS

qip,m,tk ,j ≥ Dp,m,t

k

−∑j∈JS

qop,m,tk ,j −

∑j∈JPS

Φp,m,tj −

∑j∈JPU

ODk ,j · xpj ·D

p,m,tk

p ∈ P, m ∈M, t ∈ T, k ∈ K

Passive technologies can be modelled in two ways:space-measurable ones, and unitary-measurable ones.







Technologies short-term availability

The energy that can be supplied by a technology is constrained bythe availability of the technology.

z p,m,ti ,k ≤ DT ·Ap,m,t

i · spip ∈ P, m ∈M, t ∈ T, i ∈ I, k = KF (i)







Energy output calculation

The total energy output by each technology for a type of energyoutput is the sum of all the energy outputs over the energy inputs,computed as the energy input corrected by the conversion factor.

z p,m,ti ,kk =

∑k∈KI (i)

(Ei ,k ,kk

)−1 · yp,m,ti ,k

p ∈ P, m ∈M, t ∈ T, i ∈ I, kk ∈ KO(i)







Energy stored calculation

The energy stored each period is the energy stored in the previousperiod, plus the energy sent to storage, minus the energy releasedfrom storage. All flows are corrected by the losses ratio parameters.

rp,m,tk ,j = OSk ,j · r

p,m,t−1k ,j + OIk ,j · qi

p,m,t−1k ,j −OOk ,j · qo

p,m,t−1k ,j

p ∈ P, m ∈M, t ∈ T, k ∈ K, j ∈ JS







Energy discharging limit

The amount of energy that may be discharged from anyenergy-storage technology is limited by the storage level.

qop,m,tk ,j ≤ ORk ,j · r

p,m,tk ,j

p ∈ P, m ∈M, t ∈ T, k ∈ K, j ∈ JS







Energy storage lower limit

The amount of energy that may be stored from any energy-storagetechnology must be greater than the capacity installed corrected bythe minimum charge allowed.

rp,m,tk ,j ≥ OAk ,j · x

pj

p ∈ P, m ∈M, t ∈ T, k ∈ K, j ∈ JS







Energy storage upper limit

The amount of energy that may be stored in any energy-storagetechnology must be lower than the capacity installed, corrected bythe maximum charge allowed.

rp,m,tk ,j ≤ OBk ,j · x

pj

p ∈ P, m ∈M, t ∈ T, k ∈ K, j ∈ JS






Objective Function

Minimize total cost

The objective is to minimize the total cost. It is composed of thecost of installing and maintaining technologies (both energycreating and energy absorbing), the operational cost of thetechnologies and the cost of purchasing energy in the market. Thesales of energy and subsidies are incomes that we have to subtractfrom the total cost.






Objective Function

min∑p∈P

∑i∈I

CI p,0i ·Gi · sipi

∑j∈J

CISp,0j ·GSj · xi

pj

+∑i∈I

Gi

p∑a1=0

CDp−a1i

p∑a2=a1+1

sda1,a2i

+∑j∈J

p∑a1=0

CDSp−a1j

p∑a2=a1+1

xda1,a2j

+

∑m∈M

DM pm

∑i∈I

∑k∈K

∑t∈T

COp,m,ti,k · zp,m,t

i,k

+∑

m∈MDM p

m

∑j∈J

∑k∈K

∑t∈T

COSp,m,tk,j · rp,m,t

k,j

−∑

m∈MDM p

m

∑i∈I

∑k∈K

∑n∈NS(k)

∑mm∈MA

∑t∈T

PPp,m,ti,k,n · u

p,m,t,mmk,n

−∑

m∈MDM p

m

∑i∈I

∑k∈K

∑n∈NS(k)

∑mm∈MS

∑t∈T

SPp,m,ti,k,n · w

p,m,t,mmk,n

−∑i∈I

SU pi ·Gi · si

pi





Model Generation Through RSummary

Outline









Algebraic LanguagesFrom Data to Models

Needs

Statistical Software

Data Visualization

Data Analysis

MathematicalRepresentation

Solver InputGeneration

OutputDocumentation






R as an Integrated Environment

Advantages

Open Source

Reproducible Research and Literate Programming capabilities.

Integrated framework for SMS, data, equations and solvers.

Data Analysis (pre- and post-), graphics and reporting.






Summary

In this presentation the strategic model for the EnRiMa DSShas been described.

It has been developed in a sequential way from the “atomic”elements of the models.

The Symbolic Model Specification generates outputdocumentation and algebraic language definitions for solvers.

Outlook

Extension to a stochastic optimisation formulation.Symbolic Model Specification enhancement.GUI for the EnRiMa DSS.






Discussion

Thanks for your attention !

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a strategic planning model for energy efficiency in public buildings

Technology

objectives strategic

energy eciency risk

operators of energy

energy type

strategic decisions

risk management

public buildings emilio

introduction enrima