A sampling-based solution approach for electricity capacity expansion planning with chance constraint

Abstract In order to achieve carbon neutrality, several countries and regions have set specific targets for the reduction of carbon emissions. Although many policy makers agree on the uncertainty of the several factors which are involved in the planning of future energy systems, they have yet to consider the risks that their policies will incur, should they fail to meet current carbon emission targets. In this study, we propose a stochastic programming-based energy system model which takes into account various economic and technical uncertainty factors in addition to a chance-constraint, in order to assess the feasibility of meeting carbon emission targets. To determine the chance-constrained programming model efficiently, we propose a solution-based approach which adopts a sample average approximation approach. In addition, we combine the sampling-and-discarding approach with a newly devised heuristic algorithm that is suitable for our proposed model. Furthermore, as it is a numerical study, we apply our model and solution approach to evaluate the long-term capacity expansion plan under the carbon emission target within the Korean electricity sector. Through this numerical study, we verify both the solution quality and computational time of our solution approach, as well as the usability of our model for the trade-off analysis between costs and risks.

[1]  Dong Gu Choi,et al.  Comparative analysis of iterative approaches for incorporating learning-by-doing into the energy system models , 2020 .

[2]  George L. Nemhauser,et al.  An integer programming approach for linear programs with probabilistic constraints , 2010, Math. Program..

[3]  Tetsuo Tezuka,et al.  Implications of capacity expansion under uncertainty and value of information: The near-term energy planning of Japan , 2007 .

[4]  Jong-hyun Ryu,et al.  Effects of the move towards renewables on the power system reliability and flexibility in South Korea , 2020 .

[5]  Richard J. Giglio,et al.  Planning Electric Power Generation: A Nonlinear Mixed Integer Model Employing Benders Decomposition , 1977 .

[6]  Krishnendu Shaw,et al.  Low carbon chance constrained supply chain network design problem: a Benders decomposition based approach , 2016, Comput. Ind. Eng..

[7]  B. Hobbs,et al.  Analysis of multi-pollutant policies for the U.S. power sector under technology and policy uncertainty using MARKAL , 2010 .

[8]  Amit Kanudia,et al.  Modelling of uncertainties and price elastic demands in energy-environment planning for India , 1996 .

[9]  Raghu Pasupathy,et al.  Adaptive Sequential Sample Average Approximation for Solving Two-Stage Stochastic Linear Programs , 2021, SIAM J. Optim..

[10]  Martin Branda,et al.  Nonlinear Chance Constrained Problems: Optimality Conditions, Regularization and Solvers , 2016, Journal of Optimization Theory and Applications.

[11]  John P. Weyant,et al.  Electric sector investments under technological and policy-related uncertainties: a stochastic programming approach , 2013, Climatic Change.

[12]  Özlem Çavuş,et al.  A risk-averse approach for the planning of a hybrid energy system with conventional hydropower , 2021, Comput. Oper. Res..

[13]  Sarah M. Ryan,et al.  Scenario construction and reduction applied to stochastic power generation expansion planning , 2013, Comput. Oper. Res..

[14]  Peter Wild,et al.  Hedging the risk of increased emissions in long term energy planning , 2017 .

[15]  András Prékopa,et al.  ON PROBABILISTIC CONSTRAINED PROGRAMMING , 2015 .

[16]  Wolf-Peter Schill,et al.  Economic Effects of Renewable Energy Expansion: A Model-Based Analysis for Germany , 2011 .

[17]  T. González Grandón,et al.  Dynamic probabilistic constraints under continuous random distributions , 2020, Mathematical Programming.

[18]  Tamás Szántai,et al.  A Computer Code for Solution of Probabilistic-Constrained Stochastic Programming Problems , 1988 .

[19]  Guohe Huang,et al.  Multistage stochastic inexact chance-constraint programming for an integrated biomass-municipal solid waste power supply management under uncertainty , 2015 .

[20]  Peng Guo,et al.  Generating decision rules for flexible capacity expansion problem through gene expression programming , 2020, Comput. Oper. Res..

[21]  Alexander R. Barron,et al.  A near-term to net zero alternative to the social cost of carbon for setting carbon prices , 2020, Nature Climate Change.

[22]  Ed,et al.  The Stabil Stochastic Programming Model and Its Experimental Application to the Electrical Energy Sector of the Hungarian Economy Andr as Pr Ekopa , 1980 .

[23]  D. L. Woodruff,et al.  Modeling and solving a large-scale generation expansion planning problem under uncertainty , 2011 .

[24]  W. van Ackooij.  A Discussion of Probability Functions and Constraints from a Variational Perspective , 2020, Set-Valued and Variational Analysis.

[25]  Stein W. Wallace,et al.  Generating Scenario Trees for Multistage Decision Problems , 2001, Manag. Sci..

[26]  Ulrich Fahl,et al.  Uncertainty in the learning rates of energy technologies: An experiment in a global multi-regional energy system model , 2009 .

[27]  Guohe Huang,et al.  Chance-constrained two-stage fractional optimization for planning regional energy systems in British Columbia, Canada , 2015 .

[28]  Mohammad Marufuzzaman,et al.  An enhanced sample average approximation method for stochastic optimization , 2016 .

[29]  James R. Luedtke,et al.  A Sample Approximation Approach for Optimization with Probabilistic Constraints , 2008, SIAM J. Optim..

[30]  Jong-hyun Ryu,et al.  A long-term capacity expansion planning model for an electric power system integrating large-size renewable energy technologies , 2017, Comput. Oper. Res..

[31]  Hui Zhang,et al.  Chance Constrained Programming for Optimal Power Flow Under Uncertainty , 2011, IEEE Transactions on Power Systems.

[32]  Daiki Min,et al.  Evaluation of the long-term power generation mix: The case study of South Korea's energy policy , 2013 .

[33]  András Prékopa.  A class of stochastic programming decision problems , 1972 .

[34]  Dong Gu Choi,et al.  Multi-criteria decision analysis of electricity sector transition policy in Korea , 2020 .

[35]  Ekundayo Shittu,et al.  Generation capacity expansion under demand, capacity factor and environmental policy uncertainties , 2019, Comput. Ind. Eng..

[36]  J. Edmonds,et al.  Assessing China’s efforts to pursue the 1.5°C warming limit , 2021, Science.

[37]  A. Charnes,et al.  Chance-Constrained Programming , 1959 .

[38]  Marco C. Campi,et al.  A Sampling-and-Discarding Approach to Chance-Constrained Optimization: Feasibility and Optimality , 2011, J. Optim. Theory Appl..

[39]  John R. Birge,et al.  Introduction to Stochastic Programming , 1997 .

[40]  Dong Gu Choi,et al.  Uncertainty quantification and scenario generation of future solar photovoltaic price for use in energy system models , 2019, Energy.

[41]  Alexander Shapiro,et al.  Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications , 2009, J. Optimization Theory and Applications.