Review of Mathematical Methodology for Electric Power Optimization Problems


Electric power system is a physical energy system consisting of power generation, substations, transmission, distribution, and consumption. The objective of power system optimization is to improve power system security, economy, and reliability. This paper summarizes the classical mathematical optimization methods and modeling techniques of power system optimization associated with system planning, operation, and control. Along with the development of electric power industry, the concept of Energy Internet is addressed, which consists of power network, gas network, and transportation network. Under such new environments, electric power optimization faces some challenging with respect to the cooperation of multi-energy networks. According to the design structure and operational characteristics of the Energy Internet, some research areas of electric power optimization are presented from the view of mathematical optimization modeling and calculation. The aim is to provide some optimization methodology to solve the optimal issues of power system under the background of Energy Internet.

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Fig. 1


  1. 1.

    Liu, Y.: Analysis on and Inspiration of the “9.13” Islanding and Outage of Brazilian Remote Northwest Power Grid. Proc. CSEE 38(11), 3204–3213 (2018)

    Google Scholar 

  2. 2.

    Bogdan, Ž., Cehil, M., Kopjar, D.: Power system optimization. Energy 32(6), 955–960 (2007)

    Article  Google Scholar 

  3. 3.

    Seifi, H., Sepasian, M.S.: Electric power system planning. Springer, Berlin (2011)

    Google Scholar 

  4. 4.

    Niknam, T.: A new fuzzy adaptive hybrid particle swarm optimization algorithm for non-linear, non-smooth and non-convex economic dispatch problem. Appl. Energy 87(1), 327–339 (2010)

    Article  Google Scholar 

  5. 5.

    Qin, W., Zhang, J., Song, D.: An improved ant colony algorithm for dynamic hybrid flow shop scheduling with uncertain processing time. J. Intell. Manuf. 29, 1–14 (2015)

    Google Scholar 

  6. 6.

    Satoh, T., Nara, K.: Maintenance scheduling by using simulated annealing method for power plants. IEEE Trans. Power Syst. 6(2), 850–857 (1991)

    Article  Google Scholar 

  7. 7.

    Gupta, K.P., Jain, M.: Performance analysis of cellular radio system using artificial neural networks. Soc. Sci. Electron. Publ. 3(1), 5–13 (2017)

    Google Scholar 

  8. 8.

    Li, Y.F., Huang, G.H., Li, Y.P., et al.: Regional-scale electric power system planning under uncertainty–A multistage interval-stochastic integer linear programming approach. Energy Policy 38(1), 475–490 (2010)

    Article  Google Scholar 

  9. 9.

    Wang, X.Q., Huang, G.H., Lin, Q.G.: An interval mixed-integer non-linear programming model to support regional electric power systems planning with CO2 capture and storage under uncertainty. Environ. Syst. Res. 1(1), 1–13 (2012)

    Article  Google Scholar 

  10. 10.

    Ding, T., Hu, Y., Bie, Z.H.: Multi-stage stochastic programming with nonanticipativity constraints for expansion of combined power and natural gas systems. IEEE Trans. Power Syst. 33(1), 317–328 (2018)

    Article  Google Scholar 

  11. 11.

    WASP- GUIDEBOOK. International Atomic Energy Agency. Vienna (1984)

  12. 12.

    Wang, X.F.: Optimal Planning of Electric Power System. China Water Resources and Hydropower Press, Beijing (1990)

    Google Scholar 

  13. 13.

    Li, W., Yan, N.L., Zhang, S.X., et al.: Distributed multi-objective programming method for distributed power considering correlation. Autom. Electr. Power Syst. 41(9), 51–57 (2017)

    Google Scholar 

  14. 14.

    Du, A.H., Hu, Z.C., Song, Y.H., et al.: Distribution network planning considering the optimization of electric vehicle charging station layout. Power Syst. Technol. 35(11), 35–42 (2011)

    Google Scholar 

  15. 15.

    Lu, Q., Chen, L.J., Mei, S.W.: Typical application of game theory in power system and some prospects. Proc. CSEE 34(39), 5009–5017 (2014)

    Google Scholar 

  16. 16.

    Cheng, Y.H., Zhang, N., Kang, C.Q., et al.: Low-carbon grid planning considering demand side management. Autom. Electr. Power Syst. 40(23), 61–69 (2016)

    Google Scholar 

  17. 17.

    Mohapatra, A.: Distributed slack bus algorithm for economic load dispatch. Dissertation (2012)

  18. 18.

    Carpentier, J.: Contribution à l’étude du dispatching économique[C] Bull. Soc. Française D’Electricité (1962)

  19. 19.

    Usoro, P., Rouhani, R., Mehra, R., et al.: Power system modelling for emergency state simulation. Math. Model. 4(2), 143–165 (1983)

    Article  Google Scholar 

  20. 20.

    Nemati, H., Latify, M.A., Yousefi, G.R.: Coordinated generation and transmission expansion planning for a power system under physical deliberate attacks. Int. J. Electr. Power Energy Syst. 96, 208–221 (2018)

    Article  Google Scholar 

  21. 21.

    Dumitru, P.: Study of a photovoltaic system with MPPT using Matlab. Carpath. J. Electr. Eng. 6(1), 25–33 (2012)

    Google Scholar 

  22. 22.

    Luo, H.Z., Bai, X.D., Peng, J.M.: Enhancing semidefinite relaxation for quadratically constrained quadratic programming via penalty methods. J. Optim. Theory Appl. 180, 964–992 (2019)

    MathSciNet  MATH  Article  Google Scholar 

  23. 23.

    Pineda, S., Fernandez-Blanco, R., Morales, J.M.: Time-adaptive unit commitment. IEEE Trans. Power Syst. 34(5), 3869–3878 (2019)

    Article  Google Scholar 

  24. 24.

    Gupta, P.P., Jain, P., Sharma, S. et al.: Reliability-security constrained unit commitment based on benders decomposition and mixed integer non-linear programming. In: International Conference on Computer, IEEE (2017)

  25. 25.

    Xiong, P., Singh, C.: A distributional interpretation of uncertainty sets in unit commitment under uncertain wind power. IEEE Trans. Sustain. Energy 10(1), 149–157 (2019)

    Article  Google Scholar 

  26. 26.

    Zhu, R.J., Wei, H., Bai, X.Q.: Wasserstein metric based distributionally robust approximate framework for unit commitment. IEEE Trans. Power Syst. 34(4), 2991–3001 (2019)

    Article  Google Scholar 

  27. 27.

    Zou, J., Ahmed, S., Sun, X.A.: Multistage stochastic unit commitment using stochastic dual dynamic integer programming. IEEE Trans. Power Syst. 34(4), 1814–1823 (2019)

    Article  Google Scholar 

  28. 28.

    Chen, X., Jin, L., Feng, L., et al.: Optimal control of AGC systems considering non-gaussian wind power uncertainty. IEEE Trans. Power Syst. 34(4), 2730–2743 (2019)

    Article  Google Scholar 

  29. 29.

    Wiener, N.: Cybernetics: Or Science About Control and Communication in Animals and Machines. Science Press, Beijing (1962)

    Google Scholar 

  30. 30.

    He, G.Y., Sun, Y.Y., Chang, N.C., et al.: On engineering implementation of the digital power system. China, Ser. E Technol. Sci. 51(11), 2021–2030 (2008)

    Article  Google Scholar 

  31. 31.

    Wang, Y.Y.: Game Model and Analysis of Power System with Wind Power Generation. Tsinghua University, Beijing (2012)

    Google Scholar 

  32. 32.

    Cai, H., Chen, Q.Y., Guan, Z.J., Huang, J.H.: Day-ahead optimal charging/discharging scheduling for electric vehicles in microgrids. Protect. Control Mod. Power Syst. 3(3), 93–107 (2018)

    Google Scholar 

  33. 33.

    Mei, S.W., Zhang, X.M.: Overview and prospect of application of advanced control theory in power system. Power Syst. Protect. Control 41(12), 143–153 (2013)

    Google Scholar 

  34. 34.

    Deng, C.J., Zhang, J.L.: Design of wireless robust measurement filter based on differential geometry. IET Wirel. Sens. Syst. 9(6), 340–346 (2019)

    Article  Google Scholar 

  35. 35.

    Molloy, T.L., Inga, J., Flad, M., Ford, J.J., Perez, T.: Inverse open-loop noncooperative differential games and inverse optimal control. IEEE Trans. Autom. Control 65(2), 897–904 (2020)

    Article  Google Scholar 

  36. 36.

    Luo, J.S., Zhang, C.: Optimal Operation of Power Systems. Published by Huazhong University of Technology Press, Wuhan (1990)

    Google Scholar 

  37. 37.

    Fan, M.T., Zhang, Z.P.: Mathematical Model and Computational Method of Power System Optimization. China Electric Power Press, Beijing (2012)

    Google Scholar 

  38. 38.

    Han, D., Yan, Z.: Evaluating the impact of smart grid technologies on generation expansion planning under uncertainties. Int. Trans. Electr. Energy Syst. 26(5), 934–951 (2016)

    Article  Google Scholar 

  39. 39.

    Han, D., Yan, Z., Zhang, D.T., et al.: Assessing the impact of advanced technologies on utilization improvement of substations. J. Electr. Eng. Technol. 10(5), 1921–1929 (2015)

    Article  Google Scholar 

  40. 40.

    Xu, X.Y., Yan, Z., Shahidehpour, M., Wang, H., Chen, S.J.: Power system voltage stability evaluation considering renewable energy with correlated variabilities. IEEE Trans. Power Syst. 33(3), 3236–3245 (2018)

    Article  Google Scholar 

  41. 41.

    Lv, M.X., Lou, S.H., Wu, Y.W., et al.: Unit commitment of a power system including battery swap stations under a low-carbon economy. Energies 11(7), 1898–1909 (2018)

    Article  Google Scholar 

  42. 42.

    Yin, L.J., Li, X.Y., GAO, L.L., et al.: A novel mathematical model and multi-objective method for the low-carbon flexible job shop scheduling problem. Sustain. Comput. Inform. Syst. 13, 15–30 (2017)

    Google Scholar 

  43. 43.

    Shen, Y., Yao, W., Wen J, J.Y.: Adaptive wide-area power oscillation damper design for photovoltaic plant considering delay compensation. IET Gen. Transm. Distrib. 11(18), 4511–4519 (2018)

    Article  Google Scholar 

  44. 44.

    Mei, S.W., Wei, W., Liu, F.: Game theoretical perspective of power system control and decision making: a brief review of engineering game theory. Control Theory Appl. (2018)

  45. 45.

    Lu, Q., Chen, Y., Huang, J.X., et al.: A directional entrapment modification on the polyethylene surface by the amphiphilic modifier of stearyl-alcohol poly(ethylene oxide) ether. Appl. Surf. Sci. 441, 130–137 (2018)

    Article  Google Scholar 

  46. 46.

    Yang, L., Chen, Y.D., Luo, A., et al.: Effect of phase locked loop on the small-signal perturbation modeling and stability analysis for three-phase LCL-type grid-connected inverter in weak grid. IET Renew. Power Gen. 13(1), 86–93 (2018)

    Article  Google Scholar 

  47. 47.

    Zhou, X.P., Chen, Y.D., Luo, A., et al.: A microgrid cluster structure and its autonomous coordination control strategy. Int. J. Electr. Power Energy Syst. 100(4), 69–80 (2018)

    Article  Google Scholar 

  48. 48.

    Zhang, H.G., Li, Y.S., Gao, W.Z.: Distributed optimal energy management for energy internet. IEEE Trans. Ind. Inform. 13(6), 3081–3097 (2017)

    Article  Google Scholar 

  49. 49.

    Li, Q., Gao, D.W., Zhang, H.G., Wu, Z.P., Wang, F.Y.: Consensus-based distributed economic dispatch control method in power systems. IEEE Trans. Smart Grid 10(1), 941–954 (2019)

    Article  Google Scholar 

  50. 50.

    Shi, W., Ling, Q., Yuan, K., Wu, G., Yin, W.: On the linear convergence of the ADMM in decentralized consensus optimization. IEEE Trans. Signal Process. 62(7), 1750–1761 (2014)

    MathSciNet  MATH  Article  Google Scholar 

  51. 51.

    Mhanna, S., Verbič, G., Chapman, A.C.: Adaptive ADMM for distributed AC optimal power flow. IEEE Trans. Power Syst. 34(3), 2025–2035 (2019)

    Article  Google Scholar 

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Correspondence to Xiao-Jiao Tong.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 11671125).

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Han, D., Tong, X. Review of Mathematical Methodology for Electric Power Optimization Problems. J. Oper. Res. Soc. China 8, 295–309 (2020).

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  • Mathematical optimization
  • Electric power system
  • Energy Internet
  • Modeling and algorithm

Mathematics Subject Classification

  • 90