Investigación Operativa Reproducible. Aplicación a la o o optimización de sistemas energéticos

ReproducibleOperations Research

IV Jornadas R

Emilio L. CanoJavier M. Moguerza

Introduction

Reproducible Research

Framework

Symbolic Model Specification

Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

Reproducible Operations Research.

An Application to Energy Systems

OptimizationInvestigacion Operativa Reproducible. Aplicacion a la

optimizacion de sistemas energeticos

Emilio L. Cano1 Javier M. Moguerza1

1DEIO, Universidad Rey Juan Carlos, Madrid

IV Jornadas de Usuarios de R, Barcelona

15 y 16 de noviembre de 2012

IV Jornadas de Usuarios de R, 2012 1/35

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IV Jornadas R


Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

Outline

1 IntroductionReproducible Research

2 Integrated FrameworkSymbolic Model Specification

3 ApplicationThe EnRima ProjectDSS DescriptionSolver ManagerReporting


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IV Jornadas R


Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

Outline





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IV Jornadas R


Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

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


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IV Jornadas R


Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

Workflow

NeedsStatistical Software

Data Visualization

Data Analysis

MathematicalRepresentation

Solver Input Generation

Output Documentation


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Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

Approaches

Copy-paste

Inconsistencies

Errors

Out-of-date

non-reproducible

Painful changes

Black boxCompiled software for specific solutions


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IV Jornadas R


Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

Outline





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IV Jornadas R


Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

R as an Integrated Environment

Advantages

Open Source

Reproducible Research and Literate Programmingcapabilities.

Integrated framework for SMS, data, equationsand solvers.

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


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IV Jornadas R


Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography


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.


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IV Jornadas R


Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

Data-driven Modelling


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Introduction


Framework


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Bibliography

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}


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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}


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Bibliography

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}


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Introduction


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Bibliography

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"))


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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}


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Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

Complete Model


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IV Jornadas R


Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

Outline





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IV Jornadas R


Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

Objective

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


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IV Jornadas R


Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

Consortium


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IV Jornadas R


Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

EnRiMa DSS


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IV Jornadas R


Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

Decision Scope

EnRiMaDSSStrategicModule

OperationalModule

StrategicDVs

StrategicConstraints

Upper-LevelOperational DVs

Upper-LevelEnergy-BalanceConstraints

Lower-LevelEnergy-BalanceConstraints

Lower-LevelOperational DVs


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Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

Instance


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Introduction


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Bibliography

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"


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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 ;


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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 ;


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Introduction


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Reporting

Bibliography

Architecture


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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)


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Bibliography

DSS Integration


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Solution and reportSweave file example:

%

\documentclass[a4paper]{article}

\usepackage{Sweave}

\title{Example Symbolic Model Specification}

\author{urjc}

\begin{document}

\maketitle

\section{Data analysis}

<<>>=

# Some code for importing the

# Symbolic Model and analyzing the

# input data ...

#Generate tex file

wProblem(myImplem,

filename = "myImplem.tex",


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Bibliography

Solution and report (cont.)

format = "tex",

solver = "lp" )

#generate gams file

wProblem(initStochImplem,

filename = "myImplem.gms",

format = "gams",

solver = "lp" )

@

\section{Symbolic Model Specification}

%Write the LaTeX equations

\input{myImplem}

\section{Call to solver}

<<>>=

require(gdxrrw)

gams("myImplem.gms --outfile=mySol.gdx")

@

\section{Solution Analysis}

<<>>=

lst <- list(name='solvestat',form='full',compress=TRUE)


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Solution and report (cont.)

solverResults <- rgdx("mySol.gdx", lst)

#Some analysis and charts over solverResults object

@

\end{document}

0.2

0.4

0.6

0.2

0.4

0.6

PP

SP

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Time Periods

Pric

e (E

UR

/kW

h)

Energy Type

Electricity

NG

Energy Prices SimulationOptimisation Result − Operational Decisions

Technology by Year

Ope

ratio

n Le

vel

5

10

15

20

2013 2014 2015 2016 2017

CHP

2013 2014 2015 2016 2017

PV

5

10

15

20

RTE


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IV Jornadas R


Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

Summary

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

OutlookAlgebraic Modeling Languages for R solversand APIsExtend representation formats: HTML,ODF, . . .Further formats: AMPL, XML, . . .user-friendly inputrelease roptim library


http://www.urjc.es


IV Jornadas R


Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

Summary

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

OutlookAlgebraic Modeling Languages for R solversand APIsExtend representation formats: HTML,ODF, . . .Further formats: AMPL, XML, . . .user-friendly inputrelease roptim library


http://www.urjc.es


IV Jornadas R


Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

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-2011-0869-430000CORPORATE COMMUNITY: IPT-2011-0871-430000


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IV Jornadas R


Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

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.

Josef Kallrath. Algebraic modeling languages: Introduction and overview. InJosef Kallrath, editor, Algebraic Modeling Systems, volume 104 ofApplied Optimization, pages 3–10. Springer Berlin Heidelberg, 2012.ISBN 978-3-642-23591-7. doi: 10.1007/978-3-642-23592-4 1. URLhttp://dx.doi.org/10.1007/978-3-642-23592-4_1.

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.urjc.es

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://dx.doi.org/10.1007/978-3-642-23592-4_1

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

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


IV Jornadas R


Introduction


Framework


Application

EnRiMa Project

DSS Description

Solver Manager

Reporting

Bibliography

Discussion

¡ Gracias !

[email protected]

@emilopezcano


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Documents

Investigación Operativa Reproducible. Aplicación a la o o optimización de sistemas energéticos