This repository contains code that reproduces the results of the paper Improvements to Modern Portfolio Theory based models applied to electricity systems. Pre-print is available at: https://arxiv.org/abs/2105.08182. Published version is available at https://doi.org/10.1016/j.eneco.2022.106047.
With the increase of variable renewable energy sources (VRES) share in electricity systems, manystudies were developed in order to determine their optimal technological and spatial mix. Modern PortfolioTheory (MPT) has been frequently applied in this context. However, some crucial aspects, important inenergy planning, are not addressed by these analyses. We, therefore, propose several improvements andevaluate how each change in formulation impacts results. More specifically, we address generation costs, system demand, and firm energy output, present a formal model and apply it to the case of Brazil. Wefound that, after including our proposed modifications, the resulting efficient frontier differs strongly fromthe one obtained in the original formulation. Portfolios with high output standard deviation are not ableto provide a firm output level at competitive costs. Furthermore, we show that diversification plays animportant role in smoothing output from VRES portfolios.
- R
- CPLEX
If required packages are not installed, run install.packages(c("tidyverse", "corrr", "lubridate", "lhs", "furrr", "geosphere", "ggrepel")) in R.
The following files are required to run the model:
- parameters.R: Define main execution parameters.
- Plantdata.rds: Power plants data, except time series.
- WindSolar.rds: Time series for wind and PV power plants. Available at https://zenodo.org/record/4924020.
Rscript main.R
Open main.R and press Ctrl+Shift+S (Source)
The path to CPLEX oplrun executable must be defined in file parameters.R before running the script. In Linux systems the default installation folder (for version 12.10) is /opt/ibm/ILOG/CPLEX_Studio1210/opl/bin/x86-64_linux/. This is probably not necessary in Windows systems. If CPLEX is not available in the system, it is possible to download the file Results.rds containing the results and generate the figures. This file contains the results from an execution using CPLEX 12.10.0, R 4.0.3, tidyverse 1.3.0, lubridate 1.7.9.2, lhs 1.1.1, furrr 0.2.2, corrr 0.4.3, geosphere 1.5-10. To run without CPLEX, there are two possible ways:
- Run
Rscript main.R noCPLEX, in command line. - Change CPLEX variable to FALSE in file parameters.R.
Change variable NumThreads in parameters.R file to define the number of threads to be used in some routines. This option has no impact on CPLEX optimization. Each thread requires RAM space, so it is recommended to not set this value too high, unless there is enough available RAM.
After running the script, file Results.rds is created in results/ folder. Name and location of file Results.rds can be changed in the parameters.R file before script execution. All figures are also exported in PDF format.
Results from CPLEX can vary slightly depending on the system specs, operating system, CPLEX Version, etc. However, those differences are minimal and do not impact the conclusions.
File Results.rds contains a list of tibbles, as described below.
- ExecParam: Each row is a scenario and the parameters used to run it.
- MainResults: In this tibble, each row is an optimization run. All data, except what is related to individual plants, is here, such as cost, standard deviation, portfolio mean generation, etc.
- PlantResults: Individual power plant capacity for each run.
- MultiplierResults: VaR, CVaR and multiplier for each run in order to achieve the required CVaR value.