Reproducible Operations Research. An Application to Energy Systems Optimization

Transcription

1 IV Jornadas de Usuarios de R, /35. An to Energy Systems Optimization Investigación Operativa. Aplicación a la optimización de sistemas energéticos DEIO, Universidad Rey Juan Carlos, Madrid IV Jornadas de Usuarios de R, Barcelona 15 y 16 de noviembre de 2012

2 IV Jornadas de Usuarios de R, /35 Outline 1 2 Integrated 3 The EnRima Project

3 IV Jornadas de Usuarios de R, /35 Outline 1 2 Integrated 3 The EnRima Project

4 IV Jornadas de Usuarios de R, /35 OResearch The goal of reproducible research is to tie specific instructions to data analysis and experimental data so that results can be recreated, better understood and verified

5 IV Jornadas de Usuarios de R, /35 Workflow Needs Statistical Software Data Visualization Data Analysis Mathematical Representation Solver Input Generation Output Documentation

6 IV Jornadas de Usuarios de R, /35 Approaches Copy-paste Inconsistencies Errors Out-of-date non-reproducible Painful changes Black box Compiled software for specific solutions

7 IV Jornadas de Usuarios de R, /35 Outline 1 2 Integrated 3 The EnRima Project

8 IV Jornadas de Usuarios de R, /35 R as an Integrated Environment Advantages Open Source and Literate Programming capabilities. Integrated framework for SMS, data, equations and solvers. Data Analysis (pre- and post-), graphics and reporting.

9 IV Jornadas de Usuarios de R, /35 The SMS contains the mathematical representation of optimization models for all relevant energy subsystems and their interactions. This mathematical representation is composed of variables, parameters, and relations between them. Individual entities (variables and parameters) are identified through the indices representing the elements in different set.

10 IV Jornadas de Usuarios de R, /35 Data-driven Modelling

11 IV Jornadas de Usuarios de R, /35 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}

12 IV Jornadas de Usuarios de R, /35 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, sd Generators to be decommissioned Devices 1, 6, s Available generation capacity kw 1, xi Storing devices to be installed Devices 2, xd Storing devices to be decommissioned Devices 2, 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}

13 IV Jornadas de Usuarios de R, /35 Parameters > head(smspars(model1sms)[, c(1,2,4,7, 10)]) id symbol sdes units ind 1 1 D Energy demand kwh 3, 6, 7, G Generation capacity kw/device GS Storage capacity kw/device AG Generation aging factor kw/kwh 1, AS Storage aging factor kw/kw 2, 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}

14 IV Jornadas de Usuarios de R, /35 Equations > head(smseqs(model1sms)[,c(1,2,6,7,8)]) id symbol nature relation domain 1 1 eqavailg constraint eq 1, eqavails constraint eq 2, eqdecomlimg constraint lte 1, eqdecomlims constraint lte 2, eqenergybal constraint gte 3, 6, 7, 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 l NA vars 3 NA r NA pars 2 NA r 2 pars 4 NA r 3 vars 1 NA r 3 vars 2 NA l NA vars 6 NA > cat(geteq(model1sms, 1, format = "tex"))

15 IV Jornadas de Usuarios de R, /35 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}

16 IV Jornadas de Usuarios de R, /35 Complete Model

17 IV Jornadas de Usuarios de R, /35 Outline 1 2 Integrated 3 The EnRima Project

18 IV Jornadas de Usuarios de R, /35 Objective The overall objective of EnRiMa is to develop a decision-support system (DSS) for operators of energy-efficient buildings and spaces of public use.

19 IV Jornadas de Usuarios de R, /35 Consortium

20 IV Jornadas de Usuarios de R, /35 EnRiMa DSS

21 IV Jornadas de Usuarios de R, /35 Decision Scope Strategic DVs Strategic Module EnRiMaDSS Strategic Constraints Upper-Level Operational DVs Upper-Level Energy-Balance Constraints Lower-Level Operational DVs Operational Module Lower-Level Energy-Balance Constraints

22 IV Jornadas de Usuarios de R, /35 Instance

23 IV Jornadas de Usuarios de R, /35 Instance (cont.) > instancepars(model1instance, "CI")[sort(sample(1:975, 10, FALSE )),] i p a value 251 CHP CHP PV PV PV PV PV PV Wind Wind > instancesets(model1instance, c("i")) [1] "CHP" "PV" "Wind"

24 IV Jornadas de Usuarios de R, /35 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 = autumn.2017 = / ; Variables x(i, t) y(i, j, t) s(i, t) z ; Positive variable x ;

25 IV Jornadas de Usuarios de R, /35 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 ;

26 IV Jornadas de Usuarios de R, /35 Architecture

27 IV Jornadas de Usuarios de R, /35 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)

28 IV Jornadas de Usuarios de R, /35 DSS Integration

29 IV Jornadas de Usuarios de R, /35 Solution and report Sweave file example: % \documentclass[a4paper]{article} \usepackage{sweave} \title{example } \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",

30 IV Jornadas de Usuarios de R, /35 Solution and report (cont.) format = "tex", solver = "lp" ) #generate gams file wproblem(initstochimplem, filename = "myimplem.gms", format = "gams", solver = "lp" \section{} %Write the LaTeX equations \input{myimplem} \section{call to solver} <<>>= require(gdxrrw) gams("myimplem.gms \section{solution Analysis} <<>>= lst <- list(name='solvestat',form='full',compress=true)

31 IV Jornadas de Usuarios de R, /35 Solution and report (cont.) solverresults <- rgdx("mysol.gdx", lst) #Some analysis and charts over solverresults \end{document} 0.6 Energy Prices Simulation Optimisation Result Operational Decisions RTE 20 Price (EUR/kWh) PP SP Energy Type Electricity NG Operation Level CHP PV Time Periods Technology by Year

32 IV Jornadas de Usuarios de R, /35 Summary In this presentation the method used to represent and solve the optimization models developed within the EnRiMa DSS have been described

33 IV Jornadas de Usuarios de R, /35 Summary In this presentation the method used to represent and solve the optimization models developed within the EnRiMa DSS have been described Outlook Algebraic Modeling Languages for R solvers and APIs Extend representation formats: HTML, ODF,... Further formats: AMPL, XML,... user-friendly input release roptim library

34 IV Jornadas de Usuarios de R, /35 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 s FP7 project (number ) Project RIESGOS-CM: code S2009/ESP-1685 AGORANET project (IPT ) HAUS: IPT EDUCALAB: IPT DEMOCRACY4ALL: IPT CORPORATE COMMUNITY: IPT

35 IV Jornadas de Usuarios de R, /35 References COIN-OR Foundation. Internet, URL retrieved EnRiMa. Energy efficiency and risk management in public buildings GAMS. gdxrrw: interfacing gams and R. Internet, URL interfacing_gams_and_r. retrieved Josef Kallrath. Algebraic modeling languages: and overview. In Josef Kallrath, editor, Algebraic Modeling Systems, volume 104 of Applied Optimization, pages Springer Berlin Heidelberg, ISBN doi: / URL R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, URL ISBN Stefan Theussl. CRAN task view: Optimization and mathematical programming, URL

36 IV Jornadas de Usuarios de R, /35 Discussion