Extended ADMMs for RPO of large-scale power systems with discrete controls

Extended ADMMs for RPO of large-scale power systems with discrete controls

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The reactive power optimization (RPO) problem of power systems is a mixed-integer nonlinear programming problem, which can be computationally expensive. This paper applies the alternating direction method of multipliers (ADMM) to solve it. By duplicating discrete control variables with one copy allowed to vary continuously, the RPO model is formulated as a modified model in which the objective function and constraints have a separable structure with respect to the continuous and discrete variables, except for the coupling constraint. We then applied the ADMM to solve this model with the separable structure, and hence the original problem is converted into two optimization sub-problems, which are nonlinear programming (NLP) and mixed-integer quadratic programming (MIQP) problems, respectively. To improve the convergence of the algorithm, we proposed an extended ADMM by adding the upper and lower limits on state variables into the MIQP sub-problem based on the sensitivities obtained in the NLP sub-problem. We also established a mechanism to filter out inactive inequality constraints in the MIQP sub-problem to improve computational speed. Moreover, numerical results tested on IEEE test systems and a real 739-bus system have shown the correctness of the proposed method and its adaptability for power systems with different sizes and configurations..


    1. 1)
      • 1. Ding, T., Liu, S., Yuan, W., et al: ‘A two-stage robust reactive power optimization considering uncertain wind power integration in active distribution networks’, IEEE Trans. Sustain. Energy, 2015, 7, (1), pp. 301311.
    2. 2)
      • 2. Ding, T., Liu, S., Wu, Z., et al: ‘Sensitivity-based relaxation and decomposition method to dynamic reactive power optimisation considering DGs in active distribution networks’, IET Gener. Trans. Distrib., 2017, 11, (1), pp. 3748.
    3. 3)
      • 3. Yang, Z., Bose, A., Zhong, H., et al: ‘Optimal reactive power dispatch with accurately modeled discrete control devices: a successive linear approximation approach’, IEEE Trans. Power Syst., 2017, 32, (3), pp. 24352444.
    4. 4)
      • 4. Liu, M., Tso, S.K., Cheng, Y., et al: ‘An extended nonlinear primal–dual interior-point algorithm for reactive-power optimization of large-scale power systems with discrete control variables’, IEEE Trans. Power Syst., 2003, 17, (4), pp. 982991.
    5. 5)
      • 5. Nie, Y., Du, Z., Wang, Z., et al: ‘PCPDIPM based optimal reactive power flow model with discrete variables’, Int. J. Electr. Power Energy Syst., 2015, 69, pp. 116122.
    6. 6)
      • 6. Soler, E.M., Asada, E.N., Costa, G.R.M.D.: ‘Penalty-based nonlinear solver for optimal reactive power dispatch with discrete controls’, IEEE Trans. Power Syst., 2013, 28, (3), pp. 21742182.
    7. 7)
      • 7. Morrison, D.R., Jacobson, S.H., Sauppe, J.J., et al: ‘Branch-and-bound algorithms: a survey of recent advances in searching, branching, and pruning’, Discret. Optim., 2016, 19, pp. 79102.
    8. 8)
      • 8. Zhao, J., Ju, L., Dai, Z., et al: ‘Voltage stability constrained dynamic optimal reactive power flow based on branch-bound and primal–dual interior point method’, Int. J. Electr. Power Energy Syst., 2015, 73, pp. 601607.
    9. 9)
      • 9. Capitanescu, F., Wehenkel, L.: ‘Sensitivity-based approaches for handling discrete variables in optimal power flow computations’, IEEE Trans. Power Syst., 2010, 25, (4), pp. 17801789.
    10. 10)
      • 10. Rahmaniani, R., Crainic, T.G., Gendreau, M., et al: ‘The Benders decomposition algorithm: a literature review’, Eur. J. Oper. Res., 2017, 259, (3), pp. 801817.
    11. 11)
      • 11. Gomez, T., Lumbreras, J., Parra, V.M.: ‘A security-constrained decomposition approach to optimal reactive power planning’, IEEE Trans. Power Syst., 1991, 6, (3), pp. 10691076.
    12. 12)
      • 12. Rabiee, A., Parniani, M.: ‘Voltage security constrained multi-period optimal reactive power flow using Benders and optimality condition decompositions’, IEEE Trans. Power Syst., 2013, 28, (2), pp. 696708.
    13. 13)
      • 13. Nasri, A., Kazempour, S.J., Conejo, A.J., et al: ‘Network-constrained ac unit commitment under uncertainty: a Benders’ decomposition approach’, IEEE Trans. Power Syst., 2015, 31, (1), pp. 412422.
    14. 14)
      • 14. Boyd, S., Parikh, N., Chu, E., et al: ‘Distributed optimization and statistical learning via the alternating direction method of multipliers’, Found. Trends Mach. Learn., 2011, 3, (1), pp. 1122.
    15. 15)
      • 15. Erseghe, T.: ‘Distributed optimal power flow using ADMM’, IEEE Trans. Power Syst., 2014, 29, (5), pp. 23702380.
    16. 16)
      • 16. Guo, K., Han, D.R., Wu, T.T.: ‘Convergence of alternating direction method for minimizing sum of two nonconvex functions with linear constraints’, Int. J. Comput. Math., 2017, 94, (8), pp. 16531669.
    17. 17)
      • 17. Yang, L., Pong, T.K., Chen, X.: ‘Alternating direction method of multipliers for a class of nonconvex and nonsmooth problems with applications to background/foreground extraction’, Mathematics, 2015, 10, (1), pp. 74110.
    18. 18)
      • 18. Alameer, A., Sezgin, A.: ‘Joint beamforming and network topology optimization of green cloud radio access networks’. IEEE Int. Symp. Turbo Codes Iterative Information Processing, Brest, France, September 2016, pp. 15.
    19. 19)
      • 19. Lin, F., Chen, C.: ‘An ADMM algorithm for load shedding in electric power grids’. American Control Conf., Boston, American, July 2016, pp. 50025007.
    20. 20)
      • 20. Alavian, A., Rotkowitz, M.C.: ‘Improving ADMM-based optimization of mixed integer objectives’. Information Sciences and Systems, MD, American, March 2017, pp. 16.
    21. 21)
      • 21. Zimmerman, R.D., Murillo-Sanchez, C.E., Thomas, R.J.: ‘MATPOWER: steady-state operations, planning, and analysis tools for power systems research and education’, IEEE Trans. Power Syst., 2011, 26, (1), pp. 1219.
    22. 22)
      • 22. GAMS Development Corporation: ‘GAMS, the solvers’ manual’, 2015. Available at, accessed January 2015.

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