Hybrid Corrector Interior Point Method for Optimal Power Flow

Abstract

Abstract: A hybrid corrector interior point method was proposed. The proposed algorithm combines effectively the predictor corrector and centrality correction methods, which optimize the search direction by dynamically choosing the proposition of the corrector direction in Newton direction, which can improve the effect of centrality correction and then speed up the convergence of the algorithm. The algorithm was simulated for IEEE 57, IEEE 118, IEEE 300 bus systems and three real systems. The numerical results demonstrate that, compared with the multiple centrality correction interior point method, the proposed algorithm can lead to convergence with a smaller number of iterations and faster computational time. Moreover, the comparison studies also show that the algorithm can be more robust than that traditional predictorcorrector interior point method and its variants.

Key words: hybrid corrector, interior point method, nonlinear programming, optimal power flow

CLC Number:

TM732

XIE Liang-1, JIANG Xiao-Dong-2, LI Shao-Hua-1. Hybrid Corrector Interior Point Method for Optimal Power Flow[J]. Journal of Shanghai Jiaotong University, 2011, 45(06): 804-808.

References

［1］Sun D I, Ashley B, Brewer B, et al. Optimal power flow by Newton approach ［J］. IEEE Transactions on Power Apparatus and Systems, 1997, PAS103 (10): 28642880.

［2］Sttot B, Marinho J L. Linear programming for powersystem network security applications ［J］. IEEE Trans on Power Apparatus and Systems, 1979, PAS98 (3): 837848.

［3］Nanda J, Kothari D P, Srivastava S C. New optimal powerdispatch algorithm using Fletcher’s quadratic programming method ［J］. IEE ProceedingsGeneration, Transmission and Distribution, 1989, 136(3): 153161.

［4］刘盛松，蔣传文，侯志俭.基于最优潮流的最大传输能力计算［J］.上海交通大学学报， 2004， 38(8)： 12331237．

LIU Shengsong，JIANG Chuanwen，HOU Zhijian. Optimal power flow based total transfer capability calculation ［J］. Journal of Shanghai Jiaotong University，2004，38(8)：12331237.

［5］Granville S. Optimal reactive dispatch through interior point methods ［J］. IEEE Transactions on Power Systems, 1994, 9(1): 136146.

［6］Megiddo N. Pathways to the optimal set in linear programming ［M］. New York: SpringerVerlag, 1989: 131158.

［7］Mehrotra S. On the implementation of a primaldual interior point method ［J］. SIAM Journal on Optimization, 1992, 2(4): 575601.

［8］Carpenter T J, Lustig I J, Mulvey J M, et al. Higherorder predictorcorrector interiorpoint methods with applications to quadratic objectives ［J］. SIAM Journal on Optimization, 1993, 3(4): 696725.

［9］Gondzio J. Multiple centrality corrections in a primaldual method for linear programming ［J］. Computational Optimization and Applications, 1996, 6(2): 137156.

［10］Wu YuChi, Debs A S， Marsten R E. A direct nonlinear predictorcorrector primaldual interior point algorithm for optimal power flows ［J］. IEEE Transactions on Power Systems, 1994, 9(2): 876883.

［11］Rider M J, Paucar V L, Garcia A V, et al. A higher order interior point method to minimize active power loss in electric energy systems［C］//Large Engineering Systems Conference on Power Engineering. Montreal: IEEE Press, 2003: 189193.

［12］Torres G L, Quintana V H. On a nonlinear multiplecentrality corrections interiorpoint method for optimal power flow ［J］. IEEE Transactions on Power Systems, 2001, 16(2): 222228.

［13］Wei H, Sasaki H, Kubakawa J, et al. An interior point nonlinear programming for optimal power flow problems with a novel data structure ［J］. IEEE Transactions on Power Systems, 1998, 13(3): 870877.

［14］Colombo M, Gondzio J. Further development of multiple centrality correctors for interior point methods ［J］. Computational Optimization and Applications, 2008, 41(3): 277305.

［15］Cartis C. Some disadvantages of a Mehrotratype primaldual corrector interior point algorithm for linear programming ［J］. Applied Numerical Mathematics, 2009, 59(5): 11101119.

[1]	LI Zhen, XU Bingqing, LI Qingbo, YAN Xiongwei, LI Boya. Gliding Vehicle Trajectory Planning Based on Sequential Convex Optimization Algorithm [J]. Air & Space Defense, 2021, 4(4): 50-56.
[2]	JIANG Wen-ying (姜文英), LIN Yan* (林焰), CHEN Ming (陈明), YU Yan-yun (于雁云). Research on the Optimization Approach for Cargo Oil Tank Design Based on the Improved Particle Swarm Optimization Algorithm [J]. Journal of shanghai Jiaotong University (Science), 2015, 20(5): 565-570.
[3]	TANG Lei1,XIE Xinlian1，WANG Chenwu2. Model of Tramp Ship Scheduling with Variable Speed Based on Set Partition Approach [J]. Journal of Shanghai Jiaotong University, 2013, 47(06): 909-915.
[4]	ZHANG Bao-ji (张宝吉). Shape Optimization of Bow Bulbs with Minimum Wave-Making Resistance Based on Rankine Source Method [J]. Journal of shanghai Jiaotong University (Science), 2012, 17(1): 65-069.
[5]	ZHANG Bao- Ji. Optimization Design of Hull Lines Based on Hybrid Optimization Algorithm [J]. Journal of Shanghai Jiaotong University, 2012, 46(08): 1238-1242.
[6]	ZHANG Baoji1，MA Kun2 . Optimization Design of Hull Lines Based on Rankine Source Method [J]. Journal of Shanghai Jiaotong University, 2010, 44(10): 1414-1417.
[7]	YANG Hong-jie, SHEN Zhu-jiang, WANG Jian-hua, ZHANG Zhou-yun. 3D Upper Bound Limit Analysis for c-φ Materials [J]. Journal of Shanghai Jiao Tong University, 2003, 37(12): 1923-1926.