Transelec RET 2012

Generation and transmission capacity expansion planning under uncertainty using stochastic programming

Abstract

This study explored the co-optimization of generation and transmission investment decisions under hydro uncertainty conditions for the Chilean Central Interconnected System (‘Sistema Interconectado Central’, SIC) using stochastic mixed-integer programming. Generation and transmission capacity expansion planning (CEP) deals with deciding the investment decisions to make in order to minimize the total investment plus future operation costs for a power system over a certain horizon. Furthermore, as the CEP process involves long decision horizons (usually 10 to 20 years), forecasting of parameters such as demand, fuel prices and primary energy availability adds uncertainty to some of the problem parameters. Although remarkable advances have been made in optimization techniques, finding an optimal solution considering the uncertainty in the generation and transmission capacity expansion planning problem can still be extremely challenging.

The mathematical formulation of the CEP problem corresponds to a large-scale, mixed-integer, non-linear programming problem, which for a real power system is very difficult to solve. Thus, although ideally optimizing generation and transmission investment decisions simultaneously should provide the optimal expansion plan, traditionally these problems have been solved separately due to the computational challenges. Besides, prior to the mathematical formulation of the problem, the planner must carry out with diligence the essential task of categorizing the information and uncertainty. Some of the uncertain data such as demand growth, fuel prices, and hydro resources availability follow historical trends, making their uncertainty suitable to be expressed by means of probabilistic models.

In 2012, the installed hydro capacity of the SIC was approximately 44%. However, hydropower generation can vary significantly from year to year (70% of the total energy in 2002 but only 41% in 2012). This variation depends on weather conditions and the handling of the hydro reservoirs in previous years. Due to the large capacity of the hydro energy storage in the SIC and the hydro inflows variability, considering the hydro uncertainty in the CEP process is of utmost importance in order to maintain energy prices low and adequate reliability levels in the future. In order to include the hydro uncertainty in the CEP problem, this study uses the scenario-wise decomposition technique, which is anchored in the stochastic programming theory.

Stochastic programming is a framework for modeling optimization problems that involve uncertainty. Stochastic programming can be employed to find some policy that is feasible for all (or almost all) the possible data instances and maximizes the expectation of some function that includes decisions and random variables. In this study, a mixed-integer stochastic programming approach is applied to simultaneously solve the generation and transmission planning problem considering hydro uncertainty. The scenario-wise decomposition approach is an efficient tool for modeling uncertainties in stochastic programming. In this approach, the optimization problem is considered as deterministic for each scenario, but the problem is solved considering that the investment decision variables (first-stage decisions) are the same for each scenario. The constraints enforcing a unique capacity expansion plan are called non-anticipativity constraints in the optimization problem.

In order to reduce the mathematical optimization problem to a more manageable size, the modeling of the hydrologic variable was accomplished considering a reduced collection of historical scenarios (each scenario corresponding to a year of hydrological data for the different inflows), where each scenario has its own probability. This reduced collection was selected using clustering and the moment-matching technique. For the reduced collection to adequately represent the statistical properties of the complete 40-year set of historical hydro data it should contain a minimum number of scenarios (the more scenarios in the reduced collection, the more accurate the representation of the hydrologic uncertainty, but the larger the mathematical problem to solve). The authors conducted several analyses, and the available evidence seems to suggest that modeling with 3 to 5 scenarios (hydrological years) in the optimization problem should be enough to properly characterize the hydrologic uncertainty.

The capacity expansion plan obtained using the scenario-wise decomposition approach to co-optimize the generation and transmission investments was compared with the plans suggested by the CNE and the CDEC-SIC (which solves the generation and transmission expansion separately and with different levels of transmission and demand detail). The performance of each plan was calculated by running each plan in a more detailed operational model using the full hydrological dataset for the 15-year horizon, and then summing up the investment and expected operation costs associated to each plan. Although more work would be needed to improve the comparison between the expansion plans, the results show that the proposed methodology could provide solutions that are between 6% and 7% cheaper than the methodology currently employed in Chile.

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 (in press).

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 (in press).

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: This work started as a R&D collaboration with Transelec as a part of their RET initiative, leading to the CLAGTEE 2013 paper. After the project was finished, we independently kept working and produced additional methods and results leading to the other papers.