An AC-QP optimal power flow algorithm considering wind forecast uncertainty

While renewable generation sources provide many economic and environmental benefits for the operation of power systems, their inherent stochastic nature introduces challenges from the perspective of reliability. Existing optimal power flow (OPF) methods must therefore be extended to consider forecast errors to mitigate in an economic manner the uncertainty that renewable generation introduces. This paper presents an AC-QP OPF solution algorithm that has been modified to include wind generation uncertainty. We solve the resulting stochastic optimization problem using a scenario based algorithm that is based on randomized methods that provide probabilistic guarantees of the solution. The proposed method produces an AC-feasible solution while satisfying reasonable reliability criteria. Test cases are included for the IEEE 14-bus network that has been augmented with 2 wind generators. The scalability, optimality and reliability achieved by the proposed method are then assessed.

[1]  A. Conejo,et al.  Economic Valuation of Reserves in Power Systems With High Penetration of Wind Power , 2009 .

[2]  Daniel K. Molzahn,et al.  Examining the limits of the application of semidefinite programming to power flow problems , 2011, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[3]  O. Alsaç,et al.  DC Power Flow Revisited , 2009, IEEE Transactions on Power Systems.

[4]  Bruce F. Wollenberg,et al.  Linear programming optimal power flow utilizing a trust region method , 2010, North American Power Symposium 2010.

[5]  S. Low,et al.  Zero Duality Gap in Optimal Power Flow Problem , 2012, IEEE Transactions on Power Systems.

[6]  John Lygeros,et al.  Probabilistic security-constrained AC optimal power flow , 2013, 2013 IEEE Grenoble Conference.

[7]  Allen J. Wood,et al.  Power Generation, Operation, and Control , 1984 .

[8]  John Lygeros,et al.  On the Road Between Robust Optimization and the Scenario Approach for Chance Constrained Optimization Problems , 2014, IEEE Transactions on Automatic Control.

[9]  F. Galiana,et al.  Stochastic Security for Operations Planning With Significant Wind Power Generation , 2008, IEEE Transactions on Power Systems.

[10]  Xu Andy Sun,et al.  Adaptive Robust Optimization for the Security Constrained Unit Commitment Problem , 2013, IEEE Transactions on Power Systems.

[11]  Giuseppe Carlo Calafiore,et al.  The scenario approach to robust control design , 2006, IEEE Transactions on Automatic Control.

[12]  Marco C. Campi,et al.  Non-convex scenario optimization with application to system identification , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[13]  Michael Chertkov,et al.  Chance-Constrained Optimal Power Flow: Risk-Aware Network Control under Uncertainty , 2012, SIAM Rev..

[14]  G. Papaefthymiou,et al.  MCMC for Wind Power Simulation , 2008, IEEE Transactions on Energy Conversion.

[15]  John Lygeros,et al.  Probabilistic guarantees for the N-1 security of systems with wind power generation , 2013 .

[16]  Goran Andersson,et al.  Analytical reformulation of security constrained optimal power flow with probabilistic constraints , 2013, 2013 IEEE Grenoble Conference.

[17]  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.

[18]  A. Conejo,et al.  Network-Constrained Multiperiod Auction for a Pool-Based Electricity Market , 2002, IEEE Power Engineering Review.

[19]  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.

[20]  R. Tempo,et al.  On the sample complexity of randomized approaches to the analysis and design under uncertainty , 2010, Proceedings of the 2010 American Control Conference.

[21]  A. Papavasiliou,et al.  Reserve Requirements for Wind Power Integration: A Scenario-Based Stochastic Programming Framework , 2011, IEEE Transactions on Power Systems.

[22]  John Lygeros,et al.  On the Connection Between Compression Learning and Scenario Based Single-Stage and Cascading Optimization Problems , 2015, IEEE Transactions on Automatic Control.

[23]  F. Bouffard,et al.  Stochastic security for operations planning with significant wind power generation , 2008, 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century.

[24]  Daniel K. Molzahn,et al.  Investigation of Non-zero Duality Gap Solutions to a Semidefinite Relaxation of the Optimal Power Flow Problem , 2014, 2014 47th Hawaii International Conference on System Sciences.

[25]  Steven H. Low,et al.  Convex Relaxation of Optimal Power Flow—Part I: Formulations and Equivalence , 2014, IEEE Transactions on Control of Network Systems.