Risk-profit analysis of regional energy service providers by regularized primal-dual interior point method

Abstract With the development of the electric market and smart grid, risk management is one of the key issues of optimal dispatch in the interconnected energy system. The uncertainty of market price will lead to the risk for the profit of the regional energy service providers (RESP). This paper firstly defines conditional robust profits (CRP) based conditional value-at-risk and uses it constructs a risk-averse model of a multi-regional interconnected energy system, which includes generator units, demand response, and energy storage system, model named as CRP-RESP. Then by building upon the notion of effective scenarios, the effective scenarios reduction technology (ESRT) is used to reduce the scale of the CRP-RESP model effectively. Besides, efficiently solve CRP-RESP and realize the privacy protection of RESP, CRP-RESP is decomposed by geographical region, and distributed computing is carried out by using regularized primal–dual interior point method (R-PDIPM) with disturbance terms. Finally, the effectiveness and reliability of the risk-averse model are tested with the case study. ESRT can not only effectively reduce the scale of the CRP-RESP model, but also obtain a high-quality risk scheduling scheme compared with other clustering methods. And the convergence ability of R-PDIPM with disturbance terms is verified from both theoretical and experimental aspects.

[1]  Enrico Zio,et al.  Analysis of robust optimization for decentralized microgrid energy management under uncertainty , 2015 .

[2]  Csaba Mészáros,et al.  Regularization techniques in interior point methods , 2012, J. Comput. Appl. Math..

[3]  A. Conejo,et al.  Optimal Involvement in Futures Markets of a Power Producer , 2008, IEEE Transactions on Power Systems.

[4]  Jacek Gondzio,et al.  Dynamic Non-diagonal Regularization in Interior Point Methods for Linear and Convex Quadratic Programming , 2019, J. Optim. Theory Appl..

[5]  Roger J.-B. Wets,et al.  Quantitative stability of variational systems: III.ε-approximate solutions , 1993, Math. Program..

[6]  Steven H. Low,et al.  Distributed algorithm for optimal power flow on a radial network , 2014, 53rd IEEE Conference on Decision and Control.

[7]  Kit Po Wong,et al.  Decomposition-coordination interior point method and its application to multi-area optimal reactive power flow , 2011 .

[8]  Jitka Dupacová,et al.  Scenario reduction in stochastic programming , 2003, Math. Program..

[9]  Francisco J. Prieto,et al.  A decomposition procedure based on approximate Newton directions , 2002, Math. Program..

[10]  Güzin Bayraksan,et al.  Identifying effective scenarios in distributionally robust stochastic programs with total variation distance , 2019, Math. Program..

[11]  R. Setiono Interior proximal point algorithm for linear programs , 1992 .

[12]  Miadreza Shafie-khah,et al.  Stochastic programming model for scheduling demand response aggregators considering uncertain market prices and demands , 2019 .

[13]  Zita Vale,et al.  A long-term risk management tool for electricity markets using swarm intelligence , 2010 .

[14]  Dongdong Zhang,et al.  Standardized modelling and economic optimization of multi-carrier energy systems considering energy storage and demand response , 2019, Energy Conversion and Management.

[15]  Zhao Yang Dong,et al.  Multiple Perspective-Cuts Outer Approximation Method for Risk-Averse Operational Planning of Regional Energy Service Providers , 2017, IEEE Transactions on Industrial Informatics.

[16]  Jamshid Aghaei,et al.  Risk-constrained optimal strategy for retailer forward contract portfolio , 2013 .

[17]  Michal Kaut,et al.  A Heuristic for Moment-Matching Scenario Generation , 2003, Comput. Optim. Appl..

[18]  Scott Kelly,et al.  Optimal operation of an energy hub considering the uncertainty associated with the power consumption of plug-in hybrid electric vehicles using information gap decision theory , 2019, International Journal of Electrical Power & Energy Systems.

[19]  Mingbo Liu,et al.  Incremental-Oriented ADMM for Distributed Optimal Power Flow With Discrete Variables in Distribution Networks , 2019, IEEE Transactions on Smart Grid.

[20]  Zhi Zhou,et al.  Energy Storage Arbitrage Under Day-Ahead and Real-Time Price Uncertainty , 2018, IEEE Transactions on Power Systems.

[21]  Lei Wang,et al.  Chance Constrained Optimization in a Home Energy Management System , 2018, IEEE Transactions on Smart Grid.

[22]  Alvaro Lorca,et al.  Power portfolio optimization considering locational electricity prices and risk management , 2014 .

[23]  Jitka Dupacová,et al.  Scenarios for Multistage Stochastic Programs , 2000, Ann. Oper. Res..

[24]  Stanislav Uryasev,et al.  Conditional Value-at-Risk for General Loss Distributions , 2002 .

[25]  Shuping Dang,et al.  Unit Commitment Model in Smart Grid Environment Considering Carbon Emissions Trading , 2016, IEEE Transactions on Smart Grid.

[26]  Sobhan Dorahaki,et al.  A novel two-stage structure for coordination of energy efficiency and demand response in the smart grid environment , 2018 .

[27]  A. Conejo,et al.  Multi-area coordinated decentralized DC optimal power flow , 1998 .

[28]  Chongqing Kang,et al.  Decentralized Intraday Generation Scheduling for Multiarea Power Systems via Dynamic Multiplier-Based Lagrangian Relaxation , 2017, IEEE Transactions on Power Systems.

[29]  Bernardo K. Pagnoncelli,et al.  Scenario reduction for stochastic programs with Conditional Value-at-Risk , 2018, Math. Program..

[30]  R. Rockafellar,et al.  Optimization of conditional value-at risk , 2000 .

[31]  Lei Wu,et al.  A Fully-Decentralized Consensus-Based ADMM Approach for DC-OPF With Demand Response , 2017, IEEE Transactions on Smart Grid.

[32]  Zita Vale,et al.  Dynamic electricity pricing for electric vehicles using stochastic programming , 2017 .

[33]  Luis Baringo,et al.  Day-Ahead Self-Scheduling of a Virtual Power Plant in Energy and Reserve Electricity Markets Under Uncertainty , 2019, IEEE Transactions on Power Systems.

[34]  B. H. Kim,et al.  A comparison of distributed optimal power flow algorithms , 2000 .

[35]  Yuanxiong Guo,et al.  Islanding-Aware Robust Energy Management for Microgrids , 2018, IEEE Transactions on Smart Grid.

[36]  Alfredo Vaccaro,et al.  A Range Arithmetic-Based Optimization Model for Power Flow Analysis Under Interval Uncertainty , 2013, IEEE Transactions on Power Systems.

[37]  Euhanna Ghadimi,et al.  Optimal Parameter Selection for the Alternating Direction Method of Multipliers (ADMM): Quadratic Problems , 2013, IEEE Transactions on Automatic Control.

[38]  Gabriela Hug,et al.  Toward Distributed/Decentralized DC Optimal Power Flow Implementation in Future Electric Power Systems , 2018, IEEE Transactions on Smart Grid.

[39]  Chen Zhang,et al.  A parallel method for solving the DC security constrained optimal power flow with demand uncertainties , 2018, International Journal of Electrical Power & Energy Systems.

[40]  Zhao Yang Dong,et al.  A Distributed Dual Consensus ADMM Based on Partition for DC-DOPF With Carbon Emission Trading , 2020, IEEE Transactions on Industrial Informatics.

[41]  Stephen M. Robinson,et al.  Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear-programming algorithms , 1974, Math. Program..

[42]  Vladimiro Miranda,et al.  Fuzzy modelling of power system optimal load flow , 1991 .

[43]  Jim Freeman Probability Metrics and the Stability of Stochastic Models , 1991 .