Minimisation of active power losses and number of control adjustments in the optimal reactive dispatch problem

Minimisation of active power losses and number of control adjustments in the optimal reactive dispatch problem

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Trade-offs between power system's optimal operational performance and the minimal number of control adjustments necessary to attain a desired operating point make optimal reactive dispatch (ORD) solutions practical to system operators. In this study, a multi-objective ORD model that provides, in terms of weighting factors, trade-offs between minimal active power losses in transmission systems and minimal number of control adjustments in generator voltages, tap ratios and shunt controls is featured. This multi-objective ORD is formulated as a mixed-integer non-linear programming (MINLP) problem, and the proposed resolution methodology is based on translating the original MINLP problem into non-linear programming (NLP) problem deploying a sigmoid function, enabling the use of NLP solvers. Both original MINLP and translated NLP models are implemented in GAMS and numerical tests with IEEE test-systems with up to 300 buses are conducted using DICOPT, KNITRO and CONOPT solvers to validate the proposed ORD model and its resolution methodology. Results demonstrate the relation between active power losses and the number of adjustments in control variables, which is valuable information for operation planning. Another fundamental result is the high computational performance of the method when compared to specialized MINLP solvers.


    1. 1)
      • 1. Carpentier, J.L.: ‘Contribution á létude du dispatching économique’, Bull. Soc. Fran. Elec., 1962, 3, (8), pp. 431447.
    2. 2)
      • 2. Dommel, H.W., Tinney, W.F.: ‘Optimal power flow solutions’, IEEE Trans. Power Appar. Syst., 1968, PAS-87, (10), pp. 18661876.
    3. 3)
      • 3. Sasson, A.M., Viloria, F., Aboytes, F.: ‘Optimal load flow solution using the Hessian matrix’, IEEE Trans. Power Appar. Syst., 1973, PAS-92, (1), pp. 3141.
    4. 4)
      • 4. Sun, D.I., Ashley, B., Brewer, B., et al: ‘Optimal power flow by Newton approach’, IEEE Trans. Power Appar. Syst., 1984, PAS-103, (10), pp. 28642880.
    5. 5)
      • 5. Granville, S.: ‘Optimal reactive dispatch through interior point methods’, IEEE Trans. Power Syst., 1994, 9, (1), pp. 136146.
    6. 6)
      • 6. Lavaei, J., Low, S.H.: ‘Zero duality gap in optimal power flow problem’, IEEE Trans. Power Syst., 2012, 27, (1), pp. 92107.
    7. 7)
      • 7. Quintana, V.H., Torres, G.L., Medina-Palomo, J.: ‘Interior-point methods and their applications to power systems: a classification of publications and software codes’, IEEE Trans. Power Syst., 2000, 15, (1), pp. 170176.
    8. 8)
      • 8. Capitanescu, F., Wehenkel, L.: ‘Experiments with the interior-point method for solving large scale optimal power flow problems’, Electr. Power Syst. Res., 2013, 95, pp. 276283.
    9. 9)
      • 9. Pandya, K.S., Joshi, S.K.: ‘A survey of optimal power flow methods’, J. Theor. Appl. Inf. Technol., 2008, 4, pp. 450458.
    10. 10)
      • 10. Frank, S., Steponavice, I., Rebemmack, S.: ‘Optimal power flow: a bibliographic survey I – formulations and deterministic methods’, Energy Syst., 2012, 3, pp. 221258.
    11. 11)
      • 11. Frank, S., Steponavice, I., Rebemmack, S.: ‘Optimal power flow: a bibliographic survey II – non-deterministic and hybrid methods’, Energy Syst., 2012, 3, pp. 259289.
    12. 12)
      • 12. Mohseni-Bonab, S.M., Rabiee, A.: ‘Optimal reactive power dispatch: a review, and a new stochastic voltage stability constrained multi-objective model at the presence of uncertain wind power generation’, IET Gener. Transm. Distrib., 2017, 11, pp. 815829 (14).
    13. 13)
      • 13. Tinney, W.F., Bright, J.M., Demaree, K.D., et al: ‘Some deficiencies in optimal power flow’, IEEE Trans. Power Syst., 1988, 3, (2), pp. 676683.
    14. 14)
      • 14. Capitanescu, F., Wehenkel, L.: ‘Redispatching active and reactive powers using a limited number of control actions’, IEEE Trans. Power Syst., 2011, 26, pp. 12211230.
    15. 15)
      • 15. Capitanescu, F.: ‘Critical review of recent advances and further developments needed in AC optimal power flow’, Electr. Power Syst. Res., 2016, 136, pp. 5768.
    16. 16)
      • 16. Azmy, A.M.: ‘Optimal power flow to manage voltage profiles in interconnected networks using expert systems’, IEEE Trans. Power Syst., 2007, 22, (4), pp. 16221628.
    17. 17)
      • 17. Capitanescu, F., Rosehart, W., Wehenkel, L.: ‘Optimal power flow computations with constraints limiting the number of control actions’. PowerTech, 2009 IEEE Bucharest, Bucharest, Romania, 28 June–2 July 2009, vol. 1, pp. 18.
    18. 18)
      • 18. Liu, W.H.E., Gupa, X.: ‘Fuzzy constrait enforcement and control actions curtailment in an optimal power flow’, IEEE Trans. Power Syst., 1996, 11, pp. 639645.
    19. 19)
      • 19. Miettinen, K.: ‘Nonlinear multiobjective optimization’ (Kluwer Academic Publishers, Boston, MA, USA, 1999, 1st edn.).
    20. 20)
      • 20. Murray, W., Ng, K.M.: ‘An algorithm for nonlinear optimization problems with binary variables’, Comput. Optim. Appl., 2010, 47, (2), pp. 257288.
    21. 21)
      • 21. de Oliveira, E.J., da Silva, I.C.Jr., Pereira, J.L.R., et al: ‘Transmission system expansion planning using a sigmoid function to handle integer investment variables’, IEEE Trans. Power Syst., 2005, 20, (3), pp. 16161621.
    22. 22)
      • 22. GAMS: ‘General algebraic modeling systems’, Gams distribution 24.0, 2013.
    23. 23)
      • 23. Viswanathan, J., Grossmann, I.E.: ‘Discrete and continuous optimizer’, Engineering Design Research Center (EDRC) at Carnegie Mellon University, 1990.
    24. 24)
      • 24. Waltz, R.A., Plantenga, T.D.: ‘Knitro user's manual’ (Ziena Optimization, Inc., 2010), version 7.0. Available at
    25. 25)
      • 25. Drud, S.A.: ‘Conopt’, Math. Program., 1985, 31, pp. 153191.
    26. 26)
      • 26. Drud, S.A.: ‘A large-scale GRG code’, ORSA J. Comput., 1992, 6, pp. 207216.
    27. 27)
      • 27. IBM: IBM ILOG CPLEX Optimizer, IBM, available at, 2015, cplex
    28. 28)
      • 28. Quesada, I., Grossmann, I.E.: ‘An LP/NLP based branch and bound algorithm for convex MINLP optimization problems’, Comput. Chem. Eng., 1992, 16, pp. 937947.
    29. 29)
      • 29. Mazzini, A.P.: ‘Development of continuous and discrete optimization strategies to problems of optimal power flow’. PhD thesis, São Carlos School of Engineering, University of São Paulo, 2016.

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