A Symbolic Model Specification for Energy Efficiency Optimization Models

A Symbolic ModelSpecification forEnergy Efficiency

Optimization Models

INFORMS 2012

Emilio L. Cano andJavier M. Moguerza

Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model

Symbolic ModelSpecification

Representation

Solver Manager

ReproducibleResearch

References

A Symbolic Model Specificationfor Energy EfficiencyOptimization Models

Emilio L. Cano1 Javier M. Moguerza1

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

Annual Meeting 2012, Phoenix, AZ

October 14-17

INFORMS Annual Meeting 2012 1/32

http://www.enrima-project.eu


Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Outline

1 IntroductionEnRiMa ProjectDSS Description

2 Optimization ModelsDSS ModulesStrategic ModelOperational Model

3 Symbolic Model SpecificationRepresentationSolver Manager

4 Reproducible Research




Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Outline








Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Introduction

The overall objective of EnRiMa is todevelop a decision-support system (DSS)for operators of energy-efficient buildingsand spaces of public use.




Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Consortium




Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

EnRiMa DSS




Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Outline








Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Decision Scope

EnRiMaDSSStrategicModule

OperationalModule

StrategicDVs

StrategicConstraints

Upper-LevelOperational DVs

Upper-LevelEnergy-BalanceConstraints

Lower-LevelEnergy-BalanceConstraints

Lower-LevelOperational DVs




Optimization Models

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Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Strategic Constraints

spi = Gi ·∑

a′≤p,a′≥0

AGp−a′

i ·

(sia

′

i −∑

a′′≤p,a′′>a′

sda′,a′′

i

)

∀ i ∈ I, p ∈ P

z p,m,ti ,k ≤

∑k∈K

DT · AF p,m,ti · spi

∀ i ∈ I, p ∈ P , m ∈M, t ∈ T ∀ k ∈ KPF (i)




Optimization Models

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EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

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References

Upper-level Energy BalanceConstraints

∑i∈I

z p,m,ti ,k +

∑n∈NB(k,n,p,m,t),m

′∈M′B(k,n,p,m,t)

up,m,t ,m′

k ,n

−∑i∈I

yp,m,ti ,k −

∑n∈NS(k,n,p,m,t),m

′∈M′S(k,n,p,m,t)

wp,m,t ,m′

k ,n

−∑

j∈JSto

rip,m,tj ,k ≥ Dp,m,t

k −∑

j∈JSto

rop,m,tj ,k

−∑

j∈JPU

OD j ,k · xpj

∀ k ∈ K, p ∈ P , m ∈M, t ∈ T




Optimization Models

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Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Lower-level Energy BalanceConstraints

Ψt =δ

η· ξ ·

(ζ − Γt)

ln(ζ−Λt

Γt−Λt

) · 1

%

ϕ

,∀ t ∈ TO




Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Outline








Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Symbolic Model Specification

The SMS contains the mathematicalrepresentation of optimization models forall relevant energy subsystems and theirinteractions.

This mathematical representation iscomposed of variables, parameters, andrelations between them. Individualentities (variables and parameters) areidentified through the indices representingthe elements in different set.




Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Data-driven Modelling




Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Sets and Indices

> head(SMSsets(model1SMS)[,c(1,3,4,6,7,8,9)])

id tag sDes loc inSet aux subSet

1 1 NA Energy-creating technology sub NA NA FALSE

2 2 NA Energy-storing technology sub NA NA FALSE

3 3 NA Type of energy sub NA NA FALSE

4 4 NA Type of pollutant sub NA NA FALSE

5 5 NA Energy market sub NA NA FALSE

6 6 NA Long-term period sup NA NA FALSE

> cat(getSets(model1SMS, format = "tex", compact = FALSE))

\begin{description}

\item[$i$] Energy-creating technology.

\item[$j$] Energy-storing technology.

\item[$k$] Type of energy.

\item[$l$] Type of pollutant.

\item[$n$] Energy market.

\item[$p$] Long-term period.

\item[$m$] Mid-term period.

\item[$t$] Short-term period.

\item[$a$] Technology age. a = 0,...,P-1

\end{description}




Optimization Models

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Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Decision Variables

> head(SMSvars(model1SMS)[,c(1,2,4, 7,9)])

id symbol sDes units ind

1 1 si Generators to be installed Devices 1, 6

2 2 sd Generators to be decommissioned Devices 1, 6, 9

3 3 s Available generation capacity kW 1, 6

4 4 xi Storing devices to be installed Devices 2, 6

5 5 xd Storing devices to be decommissioned Devices 2, 6, 9

6 6 x Available storing capacity kWh 2, 6

> cat(getVars(model1SMS, format = "tex"))

\begin{description}

... ...

\item[$ \mathit{s}_{i}^{p}$] Available generation capacity (kW).

... ...

\item[$ \mathit{r}_{j,k}^{p,m,t}$] Energy stored (kWh).

\item[$ \mathit{c}_{}^{}$] TotalCost (EUR).

\item[$ \mathit{e}_{}^{p,m,t}$] Primary energy consumed (kWh).

\end{description}




Optimization Models

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Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Parameters

> head(SMSpars(model1SMS)[, c(1,2,4,7, 10)])

id symbol sDes units ind

1 1 D Energy demand kWh 3, 6, 7, 8

2 2 G Generation capacity kW/Device 1

3 3 GS Storage capacity kW/Device 2

4 4 AG Generation aging factor kW/kWh 1, 11

5 5 AS Storage aging factor kW/kW 2, 11

6 6 AV Technology availability factor kW/kW 1, 6, 7, 8

> cat(getPars(model1SMS, format = "tex"))

\begin{description}

\item[$ \mathit{D}_{k}^{p,m,t}$] Energy demand (kWh).

\item[$ \mathit{G}_{i}^{}$] Generation capacity (kW/Device).

\item[$ \mathit{GS}_{j}^{}$] Storage capacity (kW/Device).

... ...

\item[$ \mathit{IL}_{}^{}$] Investment limit (EUR).

... ...

\end{description}




Optimization Models

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Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Equations

> head(SMSeqs(model1SMS)[,c(1,2,6,7,8)])

id symbol nature relation domain

1 1 eqAvailg constraint eq 1, 6

2 2 eqAvails constraint eq 2, 6

3 3 eqDecomLimg constraint lte 1, 6

4 4 eqDecomLims constraint lte 2, 6

5 5 eqEnergyBal constraint gte 3, 6, 7, 8

6 6 eqOutputCalc constraint eq 1, 6, 7, 8, 20

> head(model1SMS@terms[,c(1,6,7,8,9,10,11)])

id eq side parent nature item setSums

1 1 1 l NA vars 3 NA

2 2 1 r NA pars 2 NA

3 3 1 r 2 pars 4 NA

4 4 1 r 3 vars 1 NA

5 5 1 r 3 vars 2 NA

6 1 2 l NA vars 6 NA

> cat(getEq(model1SMS, 1, format = "tex"))




Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Equations (cont.)

\mathit{s}_{i}^{p} = \mathit{G}_{i}^{} \cdot

\sum _{ \mathit{a'} \leq \mathit{p} , \mathit{a'}\geq \mathit{0} } \mathit{AG}_{i}^{\mathit{p}-\mathit{a'}}\cdot \left ( \mathit{si}_{i}^{\mathit{a'}}-\sum _{ \mathit{a''} \leq \mathit{p} ,

\mathit{a''} > \mathit{a'} }

\mathit{sd}_{i}^{\mathit{a'},\mathit{a''}} \right)

\qquad \forall \;i \in \mathcal{I},\; p \in \mathcal{P}




Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Instance




Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Instance (cont.)

> instancePars(model1Instance, "CI")[sort(sample(1:975,

10, FALSE )),]

i p a value

251 CHP 22 19 1021.45984

313 CHP 25 12 830.54032

450 PV 16 4 18.57636

476 PV 17 14 24.96507

517 PV 20 1 17.00000

578 PV 22 21 30.70389

581 PV 23 2 17.51000

586 PV 23 7 20.29889

669 Wind 6 3 212.18000

758 Wind 15 2 206.00000

> instanceSets(model1Instance, c("i"))

[1] "CHP" "PV" "Wind"




Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Problem

> wProblem(example1Instance, "basicExample.gms", "gams", "lp")

*GAMS file created with R

$if NOT set outfile $set outfile outSol

Sets

i Technology / RTE, PV, CHP/

j Period / winter, spring, summer, autumn/

t Year / 2013, 2014, 2015, 2016, 2017/

;

...

parameter

D(j,t) Demand Level

/ winter .2013 = 5.25

spring .2013 = 5.83333333333333

...

autumn .2017 = 7.75833333333333

/ ;

Variables

x(i, t)

y(i, j, t)

s(i, t)

z

;

Positive variable x ;




Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


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References

Problem (cont.)Positive variable y ;

Positive variable s ;

;

Equations

eqAvail (i,t) Available technologies capacity calculation

eqDemand (j,t) Production plan for demand

eqCapacity (i,j,t) Technologies capacity

Cost Total Cost

;

eqAvail(i,t) .. s(i,t) =e= s(i,t-1)+x(i,t)-x(i,t-LT(i)) ;

eqDemand(j,t) .. Sum((i), y(i,j,t)) =e= D(j,t) ;

eqCapacity(i,j,t) .. y(i,j,t) =l= G(i,j,t)*s(i,t) ;

Cost .. z =e= Sum((t), (Sum((i), CI(i,t)*x(i,t))+Sum((i,j), CO(i,j,t)*DT(j,t)*y(i,j,t)))) ;

Model Deterministic1 /all/;

solve Deterministic1 using lp minimizing z ;

scalars modelstat, solvestat, obj;

modelstat = Deterministic1.modelstat;

solvestat = Deterministic1.solvestat;

obj = Deterministic1.objVal;

execute_unload '%outfile%', modelstat, solvestat, obj, x, y, s, z ;




Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Architecture




Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Architecture (cont.)

> # .... Data preparation

> load("./data/exampleCMS.RData")

> wProblem(mod1Instance, "example.gms", "gams", "lp")

> #

> # solve

> gams("example.gms --outfile=exampleSol.gdx")

> #

> ## import solution

> oldOpt <- options(stringsAsFactors= FALSE)

> importGams(model1Instance)<- "exampleSol.gdx"

> options(oldOpt)

> #

> getsolution(model1Instance)




Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

DSS Integration




Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Outline








Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Reproducible OResearch

The goal of reproducible research is to tiespecific instructions to data analysis andexperimental data so that results can berecreated, better understood and verified




Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Summary

In this presentation the method used torepresent and solve the optimizationmodels developed within the EnRiMaDSS have been described

An integrated framework allows torepresent the models in several formatsboth human and machine readable.

OutlookIntegration of dual-level scenario treesExtend representation formats: HTML,ODF, . . .Further formats: AMPL, XML, . . .user-friendly input




Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Summary

In this presentation the method used torepresent and solve the optimizationmodels developed within the EnRiMaDSS have been described

An integrated framework allows torepresent the models in several formatsboth human and machine readable.

OutlookIntegration of dual-level scenario treesExtend representation formats: HTML,ODF, . . .Further formats: AMPL, XML, . . .user-friendly input




Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Acknowledgements

R-project

GAMS Software

EnRiMa project partners

This work has been partially funded by the projects:

Energy Efficiency and Risk Management in Public Buildings (EnRiMa) EC’sFP7 project (number 260041)Project RIESGOS-CM: code S2009/ESP-1685AGORANET project (IPT-430000-2010-32)HAUS: IPT-2011-1049-430000EDUCALAB: IPT-2011-1071-430000DEMOCRACY4ALL: IPT-2011-0869-430000

CORPORATE COMMUNITY: IPT-2011-0871-430000




Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

References

COIN-OR Foundation. Internet, 2012. URL http://www.coin-or.org/.retrieved 2012-06-12.

EnRiMa. Energy efficiency and risk management in public buildings.www.enrima-project.eu, 2012.

GAMS. gdxrrw: interfacing gams and R. Internet, 2012. URLhttp://support.gams-software.com/doku.php?id=gdxrrw:

interfacing_gams_and_r. retrieved 2012-03-06.

R Development Core Team. R: A Language and Environment for StatisticalComputing. R Foundation for Statistical Computing, Vienna, Austria,2012. URL http://www.R-project.org/. ISBN 3-900051-07-0.

Stefan Theussl. CRAN task view: Optimization and mathematicalprogramming, 2012. URL http://cran.r-project.org/.



http://www.coin-or.org/

www.enrima-project.eu

http://support.gams-software.com/doku.php?id=gdxrrw:interfacing_gams_and_r

http://support.gams-software.com/doku.php?id=gdxrrw:interfacing_gams_and_r

http://www.R-project.org/

http://cran.r-project.org/


Optimization Models

INFORMS 2012


Introduction

EnRiMa Project

DSS Description

Optimization Models

DSS Modules

Strategic Model

Operational Model


Representation

Solver Manager


References

Discussion

Thanks for your attention !

[email protected]

@emilopezcano



Documents

A Symbolic Model Specification for Energy Efficiency Optimization Models