Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

access icon free Solving OPF using linear approximations: fundamental analysis and numerical demonstration

Due to the unique advantages in computational robustness and convergence, the linear approximation approach is and will remain to be an important method to solve the optimal power flow (OPF) problem, especially for industrial applications. The DC power flow method, which is currently used in the majority of power industries, is the representative. Many studies extend the DC power flow method by including voltage magnitude, reactive power, and losses. This study provides a detailed analysis and breakdown investigation of existing linear approximations of the OPF problem. The formulation and accuracy of existing linear approximations are compared. Taking advantage of the decoupled formulation of linear approximations, the property of power flow equations is illustrated from a new perspective. Why reactive power flow equations are hard to linearise is explained theoretically. The numerical performance of existing linear approximations is demonstrated in IEEE and Polish test systems. Evidence from the theoretical analysis and numerical studies shows that the accuracy of linear approximations could be substantially improved using a mathematical transformation of the non-linear voltage magnitude term. This finding provides a new research direction for solving the OPF problem using linear approximations.

References

    1. 1)
      • 5. Pandya, K., Joshi, S.: ‘A survey of optimal power flow methods’, J. Theor. Appl. Inf. Technol., 2008, 4, (5), pp. 450458.
    2. 2)
      • 21. Santos, T.N.d., Diniz, L.A.: ‘A dynamic piecewise linear model for DC transmission losses in optimal scheduling problems’, IEEE Trans. Power Syst., 2011, 25, (2), pp. 508519.
    3. 3)
      • 26. Yang, J., Zhang, N., Kang, C., et al: ‘A state-Independent linear power flow model with accurate estimation of voltage magnitude’, IEEE Trans. Power Syst., 2017, 32, (5), pp. 36073617.
    4. 4)
      • 7. Madani, R., Sojoudi, S., Lavaei, J.: ‘Convex relaxation for optimal power flow problem: mesh networks’, IEEE Trans. Power Syst., 2015, 30, (1), pp. 199211.
    5. 5)
      • 29. Yang, Z., Zhong, H., Bose, A., et al: ‘A linearized OPF model with reactive power and voltage magnitude: a pathway to improve the Mw-only DC OPF’, IEEE Trans. Power Syst., 2017, PP, (99), pp. 1-1, DOI: 10.1109/TPWRS.2017.2718551.
    6. 6)
      • 37. Coelho, L.S., Mariani, V.C.: ‘Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect’, IEEE Trans. Power Syst., 2006, 21, (2), pp. 989996.
    7. 7)
      • 36. Al-Sumait, J.S., Al-Othman, A.K., Sykulski, J.K.: ‘Application of pattern search method to power system valve-Point economic load dispatch’, Int. J. Electr. Power Energy Syst., 2007, 29, (10), pp. 720730.
    8. 8)
      • 45. ‘Recent ISO software enhancements and future software and modeling plans’, available at: https://www.ferc.gov/industries/electric/indus-act/rto/rto-iso-soft-2011.pdf, [accessed 9 July 2017].
    9. 9)
      • 4. Abido, M.A.: ‘Optimal power flow using particle swarm optimization’, Int. J. Electr. Power Energy Syst., 2002, 24, (7), pp. 563571.
    10. 10)
      • 15. Wang, H., Murillo-Sanchez, C.E., Zimmerman, R.D., et al: ‘On computational issues of market-based optimal power flow’, IEEE Trans. Power Syst., 2007, 22, (3), pp. 11851193.
    11. 11)
      • 28. Yang, Z., Zhong, H., Xia, Q., et al: ‘A novel network model for optimal power flow with reactive power and network losses’, Electr. Power Syst. Res., 2017, 144, pp. 6371.
    12. 12)
      • 30. Stott, B., Jardim, J., Alsac, O.: ‘Dc power flow revisited’, IEEE Trans. Power Syst., 2009, 24, (3), pp. 12901300.
    13. 13)
      • 22. Zhong, H., Xia, Q., Wang, Y., et al: ‘Dynamic economic dispatch considering transmission losses using quadratically constrained quadratic program method’, IEEE Trans. Power Syst., 2013, 28, (3), pp. 22322241.
    14. 14)
      • 39. Zhong, J., Bhattacharya, K.: ‘Toward a competitive market for reactive power’, IEEE Trans. Power Syst., 2002, 17, (4), pp. 12061215.
    15. 15)
      • 23. Zhang, H., Vittal, V., Heydt, G.T., et al: ‘A relaxed AC optimal power flow model based on a Taylor series’. Innovative Smart Grid Technol. Conf. Asia (ISGT Asia), 2013, pp. 15.
    16. 16)
      • 17. Gómez-Expósito, A., Conejo, A.J., Cañizares, C.A.: ‘Electric energy systems analysis and Operation’ (CRC, Boca Raton, FL, USA, 2009).
    17. 17)
      • 33. Yang, Z., Zhong, H., Xia, Q., et al: ‘Optimal power flow based on successive linear approximation of power flow equations’, IET Gener., Transm. Distrib., 2016, 10, (14), pp. 36543662.
    18. 18)
      • 41. Overbye, T.J., Cheng, X., Sun, Y.: ‘A comparison of the AC and DC power flow models for LMP calculations’. Proc. 37th Hawaii Int. Conf. System Sciences, 2004.
    19. 19)
      • 11. Madani, R., Ashraphijuo, M., Lavaei, J.: ‘Promises of conic relaxation for contingency-constrained optimal power flow problem’, IEEE Trans. Power Syst., 2016, 31, (2), pp. 12971307.
    20. 20)
      • 43. Yang, Z., Bose, A., Zhong, H., et al: ‘LMP revisited: a linear model for the loss-embedded LMP’, IEEE Trans. Power Syst., 2017, 32, (5), pp. 40804090..
    21. 21)
      • 3. Momoh, J.A., El-Hawary, M., Adapa, R.: ‘A review of selected optimal power flow literature to 1993. Part II: Newton, linear programming and interior point methods’, IEEE Trans. Power Syst., 1999, 14, (1), pp. 105111.
    22. 22)
      • 14. Hu, B., Wang, H., Yao, S.: ‘Optimal economic operation of isolated community microgrid incorporating temperature controlling devices’, Prot. Control Mod. Power Syst., 2017, 2, (1), pp. 111.
    23. 23)
      • 2. Momoh, J.A., Adapa, R., El-Hawary, M.E.: ‘A review of selected optimal power flow literature to 1993. Part I. Nonlinear and quadratic programming approaches’, IEEE Trans. Power Syst., 1999, 14, (1), pp. 96104.
    24. 24)
      • 24. Zhang, H., Heydt, G.T., Vittal, V., et al: ‘An improved network model for transmission expansion planning considering reactive power and network losses’, IEEE Trans. Power Syst., 2013, 28, (3), pp. 34713479.
    25. 25)
      • 18. Castillo, A., Lipka, P., Watson, J.P., et al: ‘A successive linear programming approach to solving the IV-ACOPF’, IEEE Trans. Power Syst., 2016, 31, (4), pp. 27522763.
    26. 26)
      • 1. Carpentier, J.: ‘Contribution to the economic dispatch problem’, Bull. Soc. Francaise Elect., 1962, 3, (8), pp. 431447.
    27. 27)
      • 44. Helseth, A.: ‘A linear optimal power flow model considering nodal distribution of losses’. 2012 9th Int. Conf. the European Energy Market, 2012, pp. 18.
    28. 28)
      • 6. Lavaei, J., Low, S.H.: ‘Zero duality gap in optimal power flow problem’, IEEE Trans. Power Syst., 2012, 27, (1), pp. 92107.
    29. 29)
      • 8. Sojoudi, S., Lavaei, J.: ‘Physics of power networks makes hard optimization problems easy to solve’. IEEE Power and Energy Society General Meeting, 2012.
    30. 30)
      • 25. Akbari, T., Bina, M.T.: ‘Linear approximated formulation of Ac optimal power flow using binary discretisation’, IET Gener. Transm. Distrib., 2016, 10, (5), pp. 11171123.
    31. 31)
      • 20. Coffrin, C., Hentenryck, P.V.: ‘A linear-programming approximation of AC power flows’, INFORMS J. Comput., 2014, 26, (4), pp. 718734.
    32. 32)
      • 10. Coffrin, C., Hijazi, H.L., Hentenryck, P.V.: ‘The QC relaxation: a theoretical and computational study on optimal power flow’, IEEE Trans. Power Syst., 2016, 31, (4), pp. 30083018.
    33. 33)
      • 34. 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.
    34. 34)
      • 12. Yang, Z., Zhong, H., Xia, Q., et al: ‘Review the OPF problem from the fundamentals: challenges and state-of-the-art algorithms’, J. Energy Eng., accepted, DOI: 10.1061/(ASCE)EY.1943-7897.0000510.
    35. 35)
      • 38. Chao-Lung, C.: ‘Improved genetic algorithm for power economic dispatch of units with valve-Point effects and multiple fuels’, IEEE Trans. Power Syst., 2005, 20, (4), pp. 16901699.
    36. 36)
      • 16. Stott, B., Alsaç, O.: ‘Optimal power flow: Basic requirements for real-life problems and their solutions’, White paper, 2012.
    37. 37)
      • 35. Zimmerman, R.D., Murillo-Sánchez, 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.
    38. 38)
      • 19. Ilic, M., Cvijic, S., Lang, J.H., et al: ‘Operating beyond today's PV curves: challenges and potential benefits’. IEEE Power and Energy Society General Meeting, 2015.
    39. 39)
      • 13. Wang, Q., Yang, A., Wen, F., et al: ‘Risk-based security-constrained economic dispatch in power systems’, J. Mod. Power Syst. Clean Energy, 2013, 1, (2), pp. 142149.
    40. 40)
      • 31. Lu, S., Zhou, N., Kumar, N.P., et al: ‘Improved Dc power flow method based on empirical knowledge of the system’. IEEE Transmission and Distribution Conf. and Exposition, 2010.
    41. 41)
      • 40. Wood, A.J., Wollenberg, B.F.: ‘Power generation, operation and Control’ (John Wiley & Sons, New York, 1996, 2nd edn.).
    42. 42)
      • 27. Fatemi, S.M., Abedi, S., Gharehpetian, G.B., et al: ‘Introducing a novel DC power flow method with reactive power considerations’, IEEE Trans. Power Syst., 2015, 30, (6), pp. 30123023.
    43. 43)
      • 42. Litvinov, E., Tongxin, Z., Rosenwald, G., et al: ‘Marginal loss modeling in Lmp calculation’, IEEE Trans. Power Syst., 2004, 19, (2), pp. 880888.
    44. 44)
      • 9. Farivar, M., Low, S.H.: ‘Branch flow model: relaxations and convexification &: part I’, IEEE Trans. Power Syst., 2013, 28, (3), pp. 25542564.
    45. 45)
      • 32. Qi, Y., Shi, D., Tylavsky, D.: ‘Impact of assumptions on Dc power flow model accuracy’. North American Power Symp. (NAPS), 2012.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-gtd.2017.1078
Loading

Related content

content/journals/10.1049/iet-gtd.2017.1078
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address