A bi-objective DC-optimal power flow model using linear relaxation-based second order cone programming and its Pareto Frontier

Abstract The DC optimal power flow (DC-OPF) plays an important role in the operation and planning of modern power systems. In this paper, a bi-objective DC-OPF model minimizing both network losses and generation costs is introduced, which can further be converted into a single objective model via the weighted sum method. Furthermore, the Pareto Frontier is employed to solve this problem. In the mathematical view, the model is a special non-convex quadratic constraints quadratic programming problem. In order to obtain a continuous Pareto Frontier, the original non-convex feasible region is relaxed to its convex hull using a linear relaxation-based second order cone programming method. Compared with the semi-definite relaxation method, the proposed method can greatly reduce the number of dummy variables and the complexity of solutions. Finally, simulations on eight small systems and four practical, large systems are performed, in addition to the comparison of a Monte Carlo simulation. The results verify the effectiveness of the proposed algorithm.

[1]  Pu Li,et al.  Probabilistic analysis for optimal power flow under uncertainty , 2010 .

[2]  S. M. Shahidehpour,et al.  Short-term generation scheduling with transmission and environmental constraints using an augmented Lagrangian relaxation , 1995 .

[3]  Hongbin Sun,et al.  Absolute Value Constraint Based Method for Interval Optimization to SCED Model , 2014, IEEE Transactions on Power Systems.

[4]  R. Yokoyama,et al.  Improved genetic algorithms for optimal power flow under both normal and contingent operation states , 1997 .

[5]  Jiuping Pan,et al.  Review of usage-based transmission cost allocation methods under open access , 2000 .

[6]  Q. Wu,et al.  Downside Risk Constrained Probabilistic Optimal Power Flow With Wind Power Integrated , 2016, IEEE Transactions on Power Systems.

[7]  R. Bacher,et al.  Unlimited point algorithm for OPF problems. Discussion , 1999 .

[8]  M. A. Abido,et al.  Optimal power flow using particle swarm optimization , 2002 .

[9]  Hongbin Sun,et al.  A Bi-Level Branch and Bound Method for Economic Dispatch With Disjoint Prohibited Zones Considering Network Losses , 2015, IEEE Transactions on Power Systems.

[10]  Q. H. Wu,et al.  Optimal Power System Dispatch With Wind Power Integrated Using Nonlinear Interval Optimization and Evidential Reasoning Approach , 2016, IEEE Transactions on Power Systems.

[11]  Deqiang Gan,et al.  Stability-constrained optimal power flow , 2000 .

[12]  A. M. Jubril,et al.  Solving Multi-Objective Economic Dispatch Problem Via Semidefinite Programming , 2013, IEEE Transactions on Power Systems.

[13]  A. Diniz,et al.  A Dynamic Piecewise Linear Model for DC Transmission Losses in Optimal Scheduling Problems , 2011, IEEE Transactions on Power Systems.

[14]  Hongbin Sun,et al.  Optimal Power Flow With the Consideration of Flexible Transmission Line Impedance , 2016, IEEE Transactions on Power Systems.

[15]  William F. Tinney,et al.  Optimal Power Flow Solutions , 1968 .

[16]  C. Patvardhan,et al.  Useful multi-objective hybrid evolutionary approach to optimal power flow , 2003 .

[17]  Mengshi Li,et al.  Mean-variance model for power system economic dispatch with wind power integrated , 2014 .

[18]  Xiaoqing Bai,et al.  Semi-definite programming-based method for security-constrained unit commitment with operational and optimal power flow constraints , 2009 .

[19]  M. A. Abido.  Environmental/economic power dispatch using multiobjective evolutionary algorithms , 2003 .

[20]  Hongbin Sun,et al.  Big-M Based MIQP Method for Economic Dispatch With Disjoint Prohibited Zones , 2014, IEEE Transactions on Power Systems.

[21]  Federico Milano,et al.  Multiobjective optimization for pricing system security in electricity markets , 2003 .

[22]  Hongbin Sun,et al.  Interval Power Flow Analysis Using Linear Relaxation and Optimality-Based Bounds Tightening (OBBT) Methods , 2015 .

[23]  Chen Wang,et al.  Optimal Power Flow Solution Incorporating Wind Power , 2012, IEEE Systems Journal.

[24]  Fangxing Li,et al.  DCOPF-Based LMP simulation: algorithm, comparison with ACOPF, and sensitivity , 2007, 2008 IEEE/PES Transmission and Distribution Conference and Exposition.

[25]  Hongbin Sun,et al.  Exact Penalty Function Based Constraint Relaxation Method for Optimal Power Flow Considering Wind Generation Uncertainty , 2015, IEEE Transactions on Power Systems.

[26]  Vassilios Petridis,et al.  Optimal power flow by enhanced genetic algorithm , 2002 .

[27]  Claudio A. Canizares,et al.  Multiobjective optimal power flows to evaluate voltage security costs in power networks , 2003 .

[28]  Thomas J. Overbye,et al.  A comparison of the AC and DC power flow models for LMP calculations , 2004, 37th Annual Hawaii International Conference on System Sciences, 2004. Proceedings of the.

[29]  Ferial El-Hawary,et al.  Optimal environmental dispatching of electric power systems via an improved Hopfield neural network model , 1995 .

[30]  Hsiao-Dong Chiang,et al.  Power-current hybrid rectangular formulation for interior-point optimal power flow , 2009 .

[31]  M. Kojima,et al.  Second order cone programming relaxation of nonconvex quadratic optimization problems , 2001 .

[32]  G. Lambert-Torres,et al.  A hybrid particle swarm optimization applied to loss power minimization , 2005, IEEE Transactions on Power Systems.

[33]  Pandelis N. Biskas,et al.  Decentralised security constrained DC-OPF of interconnected power systems , 2004 .

[34]  R. Bacher,et al.  Unlimited point algorithm for OPF problems , 1997, Proceedings of the 20th International Conference on Power Industry Computer Applications.

[35]  R. Adapa,et al.  A review of selected optimal power flow literature to 1993. I. Nonlinear and quadratic programming approaches , 1999 .