Fondecyt 1151270

Power Systems Capacity Expansion Planning Under Uncertainty

Abstract

In electric power systems, Capacity Expansion Planning (CEP) involves decisions about location, sizing and timing of new generation and transmission to minimize the total operation and investment cost over a certain time horizon. As CEP is usually performed for long planning horizons (over 10 years), uncertainty in the models’ inputs is an issue that needs to be addressed by planners. The uncertainty can be dealt with by either improving forecasting techniques (which can only be improved up to a certain point) or by improving the decision-making models such that their outcomes are more robust to changes in the modeling assumptions. The main goal of this study is to develop, implement, and test stochastic programming methods for obtaining generation and transmission investment plans for real-sized systems that are robust to the uncertainty of the input parameters in a reasonable time and without oversimplifying the problem.

Stochastic programming is a framework for modeling optimization problems involving uncertainty, assuming that the probability distributions associated to the data are known or can be estimated. Stochastic programming can be used to formulate a stochastic CEP as a Stochastic Mixed-Integer Program (SMIP) capable of finding a generation and transmission investment plan that is feasible for all (or almost all) the possible data instances and minimizes the expected value of the investment and operation cost. The mathematical formulation of the deterministic CEP problem corresponds to a large-scale mixed-integer programming problem, which for real power systems is very difficult to solve. Thus, incorporating uncertainty implies the solution of even larger optimization problems that usually can only be solved after making considerable simplifications to it.

The work on this research will be conducted on three areas: 1) Representation and modeling of uncertainty in the input parameters; 2) Formulation and solution of the stochastic CEP problem for different types of uncertainty; and 3) Decomposition and parallelization of the SMIP problem.

In a stochastic CEP, the nature of the stochastic input parameter will determine the structure of the SMIP. For example, demand uncertainty will affect the Right-Hand-Side of the SMIP, while fuel price and emissions price uncertainty will affect the objective function. This work will use techniques grounded on the stochastic programming area, particularly scenario-wise decomposition (for uncertainty related to hydro and renewable energy availability, load growth, and fuel and emissions price) and chance constrained optimization (for uncertainty related to generation and transmission reliability). As the complexity of the SMIP problem increases with the detail of the stochastic input parameter representation, this work will apply scenario reduction and clustering techniques to the multi-dimensional data to reduce it to a discrete number of scenarios. Furthermore, because of the size and complexity of stochastic CEP optimization problems in real power systems, this work will also explore decomposition and parallelization techniques for solving them faster and without recurring to oversimplification of the power flow formulation. This part of the work will start implementing decomposition by scenario of SMIP-based CEP problems using progressive hedging.

Expected outcomes of this research are: 1) A suite of models and methods for making generation and transmission investment decisions in deterministic and stochastic environments; 2) Market models of the Chilean interconnected systems for stochastic capacity expansion planning; 3) Sensitivity analysis of capacity expansion plans to changes in the modeling assumptions; 4) A measure of the value of the stochastic solution and of the expected value of perfect information, and recommendations about the minimum number of discrete scenarios to use for each type of uncertainty; 5) Optimized reduced representations of the stochastic inputs for using in electricity market models; and 6) Decomposition and parallelization techniques for reducing simulation times in large stochastic CEP problems. It is expected that the open source availability of tools and methods generated during the project execution will have significant impact on stimulating and encouraging further research and education in this area.

Journal papers

Esteban Gil, Ignacio Aravena, Raúl Cárdenas, “Generation capacity expansion planning under hydro uncertainty using stochastic mixed integer programming and scenario reduction”, IEEE Transactions on Power Systems, vol. 30, no. 4, pp. 1838-1847, July 2015.

DOI: 10.1109/TPWRS.2014.2351374.

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Ignacio Aravena, Esteban Gil, “Hydrological scenario reduction for stochastic optimization in hydrothermal power systems”, Applied Stochastic Models in Business and Industry, vol. 31, no. 2, pp. 231-240, March/April 2015.

DOI: 10.1002/asmb.2027.

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Conference papers

William Gandulfo, Esteban Gil, Ignacio Aravena, “Generation Capacity Expansion Planning under Demand Uncertainty Using Stochastic Mixed-Integer Programming”, 2014 IEEE Power & Energy Society General Meeting (IEEE-PES-GM 2014), National Harbour, USA, Jul. 27-31, 2014. DOI: 10.1109/PESGM.2014.6939368.

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Ignacio Aravena, Raúl Cárdenas, Esteban Gil, Victor Hinojosa, Patricio Reyes, Juan C. Araneda, “Co-optimization of generation and transmission investment decisions under hydro uncertainty using stochastic mixed-integer programming”, 10^th Latin-American Congress on Electric Power Generation, Transmission and Distribution (CLAGTEE 2013), Viña del Mar, Chile, Oct. 6-9, 2013.

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NOTE: Some of these papers may be prior to the commencement of the project.