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Decision Making under Uncertainty:R implementation for Energy Efficient Buildings

Emilio L. Cano1 Javier M. Moguerza1

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

The 8th International R Users Meeting

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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Outline

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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Outline

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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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.

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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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.

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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Consortium

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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Outline

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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EnRiMa DSS

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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Outline

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Optimization Scope

Strategic Model

Strategic decisions concerningwhich technologies to installand/or decommission in the longterm

Operational Model

Energy portfolio selection in theshort term

Interaction

The strategic model includesa simplified version ofoperational energy-balanceconstraints

The operational modelincludes the realisation ofthe strategic decisions asparameters

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

Use R! 2012, Vanderbilt University, Nashville, June 14 2012 9/1

Optimization Scope

Strategic Model

Strategic decisions concerningwhich technologies to installand/or decommission in the longterm

Operational Model

Energy portfolio selection in theshort term

Interaction

The strategic model includesa simplified version ofoperational energy-balanceconstraints

The operational modelincludes the realisation ofthe strategic decisions asparameters

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

Use R! 2012, Vanderbilt University, Nashville, June 14 2012 9/1

Optimization Scope

Strategic Model

Strategic decisions concerningwhich technologies to installand/or decommission in the longterm

Operational Model

Energy portfolio selection in theshort term

Interaction

The strategic model includesa simplified version ofoperational energy-balanceconstraints

The operational modelincludes the realisation ofthe strategic decisions asparameters

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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Scheme of the Project

EnRiMaDSSStrategicModule

OperationalModule

StrategicDVs

StrategicConstraints

Upper-LevelOperational DVs

Upper-LevelEnergy-BalanceConstraints

Lower-LevelEnergy-BalanceConstraints

Lower-LevelOperational DVs

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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Scenario trees

Decision Time

1 2 543 6 7 98

Stage 1 Stage 2 Stage 3

Scenario 1

Scenario 2

Scenario 3

Scenario 4

Scenario 5

Scenario 6

Illustrative scenario tree

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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Outline

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Objective Function (example)

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

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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Constraints (two examples)

Energy Balance (operational):∑i∈I

zp,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

Emissions limit (strategic):

∑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

≤ PLpl

p ∈ P, l ∈ L

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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Outline

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Symbolic Model Specification

The formulation reached models complex systems

Moreover, the Symbolic Model Specification should be:

FlexibleReplicableReproducibleScalablePortable

Thus, a suitable structure is needed

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Data model

Model and Instance Classes, data attributes, input/output methods

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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Outline

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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Algebraic Languages

Needs

Statistical Software

Data Visualization

Data Analysis

MathematicalRepresentation

Solver InputGeneration

OutputDocumentation

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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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.

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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R Code Example

> cat(getEq(mySMS , 1, format = "gams"), "\n")

genTechAvail(p,i) .. s(i,p) =e= G(i)*Sum((a), AG(i,a)*(

si(i,p)-Sum((q), sd(i,p,q))) ;

> cat(getEq(mySMS , 1, format = "tex"), "\n")

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

\in \mathcal{ A }} \mathit{AG}_{i}^{a} \cdot \left (

\mathit{si}_{i}^{p}- \sum _{q \in \mathcal{ Q }} \

mathit{sd}_{i}^{p,q} \right ) \qquad \forall \;p \in

\mathcal{ P },\; i \in \mathcal{ I }

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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Solution and report

Sweave 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",

format = "tex",

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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Solution and report (cont.)

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

#Some analysis and charts over solverResults object

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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Solution and report (cont.)

@

\end{document}

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Summary

In this presentation the models developed for the EnRiMaDSS have been described

An integrated framework allows to integrate analysis,representation and solution of optimization problems

Examples of use have been presented

Outlook

Integration of scenarios for stochastic optimizationExtend representation formats: HTML, ODF, . . .Further formats: AMPL, MPS, XML, . . .A contributed package?

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

Use R! 2012, Vanderbilt University, Nashville, June 14 2012 25/1

Summary

In this presentation the models developed for the EnRiMaDSS have been described

An integrated framework allows to integrate analysis,representation and solution of optimization problems

Examples of use have been presented

Outlook

Integration of scenarios for stochastic optimizationExtend representation formats: HTML, ODF, . . .Further formats: AMPL, MPS, XML, . . .A contributed package?

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References

[1] Michel Berkelaar and others. lpSolve: Interface to Lp solve v. 5.5 to solvelinear/integer programs, 2011. URLhttp://CRAN.R-project.org/package=lpSolve. R package version 5.6.6.

[2] COIN-OR Foundation. Internet, 2012. URL http://www.coin-or.org/. retrieved2012-06-12.

[3] A.J. Conejo, M. Carrion, and J.M. Morales. Decision Making Under Uncertainty inElectricity Markets. International Series in Operations Research and ManagementScience Series. Springer, 2010. ISBN 9781441974204. URLhttp://books.google.es/books?id=zta0qWS_W98C.

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

[5] 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.

[6] Chris Marnay, Joseph Chard, Kristina Hamachi, Tim Lipman, Mithra Moezzi,Boubekeur Ouaglal, and Afzal Siddiqui. Modeling of customer adoption ofdistributed energy resources. Technical report, Lawrence Berkeley NationalLaboratory, 2001. URL http://der.lbl.gov/publications/

modeling-customer-adoption-distributed-energy-resources.

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation

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References (cont.)

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

[8] Afzal S. Siddiqui, Chris Marnay, Jennifer L. Edwards, Ryan Firestone, SrijayGhosh, and Michael Stadler. Effects of carbon tax on microgrid combined heatand power adoption. Journal of Energy Engineering, 131(1):2–25, 2005. doi:10.1061/(ASCE)0733-9402(2005)131:1(2). URLhttp://link.aip.org/link/?QEY/131/2/1.

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Acknowledgements

R-project

GAMS Software

EnRiMa project partners

Project RIESGOS-CM: code S2009/ESP-1685

This work has been partially funded by the projects:

Energy Efficiency and Risk Management in Public Buildings (EnRiMa) EC’s FP7project (number 260041)AGORANET 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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Discussion

Thanks for your attention !

emilio.lopez@urjc.es

@emilopezcano

Emilio L. Cano and Javier M. Moguerza Decision Making under Uncertainty: R implementation