Reactive Power Scheduling Using Quadratic Convex Relaxation ‎

Document Type : Research paper

Authors

Faculty of Engineering and Technology, Shahrekord University (SKU), Shahrekord, Iran.‎

Abstract

In this paper, quadratic convex relaxation (QCR) is used to relax AC optimal power flow (AC-OPF) used for reactive power scheduling (RPS) of the power system. The objective function is system active power loss minimization to optimally determine the tap position of tap-changers, the reactive power output of generating units, synchronous condensers, shunt capacitor banks, and reactors. The nonlinear and non-convex terms due to trigonometric functions cause the problem to be non-convex which results in trapping in local minimum or even not converging in large size power systems. Therefore, in this paper, the nonlinear terms and trigonometric function are relaxed by linear and quadratic functions. Furthermore, the product of two variables and multi-variables are relaxed by McCormick bilinear and multi-linear expressions, converting the AC-OPF of RPS to quadratic constraint programming (QCP) optimization problem. The proposed RPS method is studied based on IEEE RTS 24-bus test system. The results show the accuracy of the proposed (QCR) method to relax the AC-OPF optimization problem of RPS.   

Keywords

References

  1. Wang, R.G. Wen and R. S. Yang, “On the procurement and pricing of reactive power service in the electricity market environment,” IEEE PES Gen. Meet., vol. 1, pp. 1120-1124, 2004.
  2. Zhong and K. Bhattacharya, “Reactive power management in deregulated power systems-A Review,” IEEE PES Wint. Meet., vol. 2, pp. 1287-1292, 2002.
  3. L. Lo and Y. A. Alturki, “Toward reactive power markets. Part 1: reactive power allocation”, IET Gener., Transm. Distrib., vol. 153, no. 1, pp. 59-70, 2006.
  4. V. Menezes, L.C.P. da Silva and V.F. da Costa, “Dynamic VAr sources scheduling for improving voltage stability margin,” IEEE Trans. Power Syst., vol. 18, no. 2, pp. 969 – 971, 2003.
  5. -T. Su and Ch.-T. Lin, “Fuzzy-based voltage/reactive power scheduling for voltage security improvement and loss reduction,” IEEE Trans. Power Deliv., vol. 16, no. 2, pp. 319-323, 2001.
  6. Sarkar and S.A. Khaparde, “Reactive Power Constrained OPF Scheduling With 2-D Locational Marginal Pricing,” IEEE Trans. Power Syst., vol. 28, no. 1, pp. 503-512, 2013.
  7. Kumar, S.C. Srivastava and S.N. Singh, “A Zonal Congestion Management Approach Using Real and Reactive Power Rescheduling,” IEEE Trans. Power Syst., vol. 19, no. 1, pp. 554-562, 2004.
  8. Corsi, P. Marannino, N. Losignore, G. Moreschini and G. Piccini, “Coordination between the reactive power scheduling function and the hierarchical voltage control of the EHV ENEL system,” IEEE Trans. Power Syst., vol. 10, no. 2, pp. 686-694, 1995.
  9. Venkatesh, G. Sadasivam and M.A. Khan, “A new optimal reactive power scheduling method for loss minimization and voltage stability margin maximization using successive multi-objective fuzzy LP technique,” IEEE Trans. Power Syst., vol. 15, no. 2, pp. 844-851, 2000.
  10. D. Youssef, “Implicit generator and SVC modelling for contingency scheduling of reactive power dispatch,” IET Gener. Transm. Distribut., vol. 142, no. 5, pp. 527-534, 1995.
  11. V. Castro, C. Moreira and L. M. Carvalho, “Hierarchical optimisation strategy for energy scheduling and volt/var control in autonomous clusters of microgrids,” ET Renew. Power Gener., vol. 14, no. 1, pp. 27-38, 2020.
  12. Pirouzi, J. Aghaei, M. A. Latify, G. R. Yousefi and G. Mokryani, “A Robust Optimization Approach for Active and Reactive Power Management in Smart Distribution Networks Using Electric Vehicles,” IEEE Syst J., vol. 12, no. 3, pp. 2699-2710, 2018.
  13. Mahzouni-Sani, A. Hamidi, D. Nazarpour and S. Golshannavaz, “Multi-objective linearised optimal reactive power dispatch of wind-integrated transmission networks,” IET Gener. Transm. Distrib., vol. 13, no. 13, pp. 2686-2696, 2019.
  14. A. Cañizares, K. Bhattacharya, I. El-Samahy, H. Haghighat, J. Pan and C. Tang, “Re-defining the reactive power dispatch problem in the context of competitive electricity markets,” IET Gener. Transm. Distrib., vol. 4, no. 2, pp. 162-177, 2010.
  15. Rabiee, H. A. Shayanfar and N. Amjady, “Reactive power pricing – problems and a proposal for a competitive market,” IEEE Power Energy Magaz., pp. 19-32, 2009.
  16. Amjady, A. Rabiee and H. A. Shayanfar, “Pay-as-bid based reactive power market,” Energy Convers. Manage., vol. 51, no. 2, pp. 367-81, 2010.
  17. Rabiee, H. A. Shayanfar and N. Amjady, “Coupled energy and reactive power market clearing considering power system security,” Energy Convers. Manage., vol. 50, no. 4, pp. 907-15, 2009.
  18. H. Rather, Z. Chen, P. Thogersen and P. Lund, “Dynamic Reactive Power Compensation of Large-Scale Wind Integrated Power System,” IEEE Trans. Power Syst., vol. 30, no. 5, pp. 2516-2526, 2015.
  19. Hijazi, C. Coffrin and P. V. Hentenryck, “Convex quadratic relaxations for mixed-integer nonlinear programs in power systems,” Math. Program. Comput., vol. 9, pp. 321-367, 2017.
  20. McCormick, “Computability of global solutions to factorable nonconvex programs: part i—convex underestimating problems,” Math. Program., vol. 10, pp. 146–175, 1976.
  21. Reliability Test System Task Force, “The IEEE Reliability Test System–1996,” IEEE Trans. Power Syst., vol. 14, no. 3, pp. 1010-1020, 1999.
  22. Generalized Algebraic Modeling Systems (GAMS), [Online] Available: http://www.gams.com.
Journal of Operation and Automation in Power Engineering
Volume 10, Issue 3
December 2022
Pages 214-218

Files

History

  • Receive Date: 21 July 2021
  • Revise Date: 09 October 2021
  • Accept Date: 31 October 2021

Share

How to cite

Statistics