An Optimal Power Flow Algorithm to Achieve Robust Operation Considering Load and Renewable Generation Uncertainties

Consideration of uncertain injections in optimal power flow (OPF) calculation is increasingly important because more renewable generators, whose outputs are variable and intermittent, are connected into modern power systems. Since it is often difficult to predict the variations of both load and renewable generator output accurately, this paper proposes an OPF algorithm to make optimized results not only have a high probability to achieve minimized generation cost, but also robust to the uncertain operating states. In this paper, the objective of the OPF is to minimize the generation cost of the scenario which has the largest probability to appear in the future. In order to make the OPF result be able to accommodate other possible scenarios, the OPF constraints are modified. Considering the probabilistic distributions of both load and renewable energy output, the modified constraints are derived from Taguchi's orthogonal array testing and probabilistic power flow calculation. The effectiveness of the proposed OPF method is demonstrated by the cases up to the system with 2736 buses.

[1]  J. Aguado,et al.  Cumulant-based probabilistic optimal power flow (P-OPF) with Gaussian and gamma distributions , 2005, IEEE Transactions on Power Systems.

[2]  Madhan Shridhar Phadke,et al.  Quality Engineering Using Robust Design , 1989 .

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

[4]  D. Ernst,et al.  Contingency Filtering Techniques for Preventive Security-Constrained Optimal Power Flow , 2007, IEEE Transactions on Power Systems.

[5]  Barbara Borkowska,et al.  Probabilistic Load Flow , 1974 .

[6]  Han Yu,et al.  Robust Transmission Network Expansion Planning Method With Taguchi's Orthogonal Array Testing , 2011, IEEE Transactions on Power Systems.

[7]  Anastasios G. Bakirtzis,et al.  Probabilistic evaluation of the performance of wind-diesel energy systems , 1994 .

[8]  A. Conejo,et al.  Scenario Reduction for Futures Market Trading in Electricity Markets , 2009, IEEE Transactions on Power Systems.

[9]  A.M. Stankovic,et al.  An application of interval analysis and optimization to electric energy markets , 2006, IEEE Transactions on Power Systems.

[10]  N. Growe-Kuska,et al.  Scenario reduction and scenario tree construction for power management problems , 2003, 2003 IEEE Bologna Power Tech Conference Proceedings,.

[11]  L. Wehenkel,et al.  Security management under uncertainty: From day-ahead planning to intraday operation , 2010, 2010 IREP Symposium Bulk Power System Dynamics and Control - VIII (IREP).

[12]  Zuyi Li,et al.  Risk-Constrained Bidding Strategy With Stochastic Unit Commitment , 2007, IEEE Transactions on Power Systems.

[13]  J. McCalley,et al.  Risk-Based Security and Economy Tradeoff Analysis for Real-Time Operation , 2007, IEEE Transactions on Power Systems.

[14]  O. Alsac,et al.  Optimal Load Flow with Steady-State Security , 1974 .

[15]  Yuping Wang,et al.  An orthogonal genetic algorithm with quantization for global numerical optimization , 2001, IEEE Trans. Evol. Comput..

[16]  Pravin Varaiya,et al.  Smart Operation of Smart Grid: Risk-Limiting Dispatch , 2011, Proceedings of the IEEE.

[17]  Louis Wehenkel,et al.  Day-ahead Security Assessment under Uncertainty Relying on the Combination of Preventive and Corrective Controls to Face Worst-Case Scenarios , 2011 .

[18]  M. Shahidehpour,et al.  Stochastic Security-Constrained Unit Commitment , 2007, IEEE Transactions on Power Systems.

[19]  Ronald N. Allan,et al.  Numerical techniques in probabilistic load flow problems , 1976 .

[20]  Li Wang,et al.  A Study on Generator Capacity for Wind Turbines Under Various Tower Heights and Rated Wind Speeds Using Weibull Distribution , 2008, IEEE Transactions on Energy Conversion.

[21]  V. Miranda,et al.  Fuzzy modelling of power system optimal load flow , 1991, [Proceedings] Conference Papers 1991 Power Industry Computer Application Conference.

[22]  Jiju Antony,et al.  Robust Design for Quality Engineering and Six Sigma , 2008 .

[23]  Werner Römisch,et al.  Scenario Reduction Algorithms in Stochastic Programming , 2003, Comput. Optim. Appl..

[24]  C. Cañizares,et al.  Probabilistic Optimal Power Flow in Electricity Markets Based on a Two-Point Estimate Method , 2006, IEEE Transactions on Power Systems.

[25]  R D Zimmerman,et al.  MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education , 2011, IEEE Transactions on Power Systems.

[26]  Yang Wang,et al.  Unit Commitment With Volatile Node Injections by Using Interval Optimization , 2011, IEEE Transactions on Power Systems.

[27]  A. Schellenberg,et al.  Enhancements to the Cumulant Method for Probabilistic Optimal Power Flow Studies , 2009, IEEE Transactions on Power Systems.

[28]  C. Lehmkoster,et al.  Security Constrained Optimal Power Flow for an Economical Operation of FACTS Devices in Liberalized Energy Markets , 2002, IEEE Power Engineering Review.

[29]  I. Erlich,et al.  A Stochastic Model for the Optimal Operation of a Wind-Thermal Power System , 2009, IEEE Transactions on Power Systems.

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

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

[32]  Cristina Corchero,et al.  Optimal Bidding Strategies for Thermal and Generic Programming Units in the Day-Ahead Electricity Market , 2010, IEEE Transactions on Power Systems.

[33]  Shaohua Zhang,et al.  Analysis of Probabilistic Optimal Power Flow Taking Account of the Variation of Load Power , 2008, IEEE Transactions on Power Systems.

[34]  T. T. Soong,et al.  Fundamentals of Probability and Statistics for Engineers , 2004 .

[35]  R. N. Kackar.  Off-Line Quality Control, Parameter Design, and the Taguchi Method , 1985 .

[36]  Kumaraswamy Ponnambalam,et al.  Probabilistic optimal power flow , 1998, Conference Proceedings. IEEE Canadian Conference on Electrical and Computer Engineering (Cat. No.98TH8341).