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Solving OPF using linear approximations: fundamental analysis and numerical demonstration

Solving OPF using linear approximations: fundamental analysis and numerical demonstration

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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)
      • J. Carpentier .
        1. Carpentier, J.: ‘Contribution to the economic dispatch problem’, Bull. Soc. Francaise Elect., 1962, 3, (8), pp. 431447.
        . Bull. Soc. Francaise Elect. , 8 , 431 - 447
    2. 2)
      • J.A. Momoh , R. Adapa , M.E. El-Hawary .
        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.
        . IEEE Trans. Power Syst. , 1 , 96 - 104
    3. 3)
      • J.A. Momoh , M. El-Hawary , R. Adapa .
        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.
        . IEEE Trans. Power Syst. , 1 , 105 - 111
    4. 4)
      • M.A. Abido .
        4. Abido, M.A.: ‘Optimal power flow using particle swarm optimization’, Int. J. Electr. Power Energy Syst., 2002, 24, (7), pp. 563571.
        . Int. J. Electr. Power Energy Syst. , 7 , 563 - 571
    5. 5)
      • K. Pandya , S. Joshi .
        5. Pandya, K., Joshi, S.: ‘A survey of optimal power flow methods’, J. Theor. Appl. Inf. Technol., 2008, 4, (5), pp. 450458.
        . J. Theor. Appl. Inf. Technol. , 5 , 450 - 458
    6. 6)
      • J. Lavaei , S.H. Low .
        6. Lavaei, J., Low, S.H.: ‘Zero duality gap in optimal power flow problem’, IEEE Trans. Power Syst., 2012, 27, (1), pp. 92107.
        . IEEE Trans. Power Syst. , 1 , 92 - 107
    7. 7)
      • R. Madani , S. Sojoudi , J. Lavaei .
        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.
        . IEEE Trans. Power Syst. , 1 , 199 - 211
    8. 8)
      • S. Sojoudi , J. Lavaei .
        8. Sojoudi, S., Lavaei, J.: ‘Physics of power networks makes hard optimization problems easy to solve’. IEEE Power and Energy Society General Meeting, 2012.
        . IEEE Power and Energy Society General Meeting
    9. 9)
      • M. Farivar , S.H. Low .
        9. Farivar, M., Low, S.H.: ‘Branch flow model: relaxations and convexification &: part I’, IEEE Trans. Power Syst., 2013, 28, (3), pp. 25542564.
        . IEEE Trans. Power Syst. , 3 , 2554 - 2564
    10. 10)
      • C. Coffrin , H.L. Hijazi , P.V. Hentenryck .
        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.
        . IEEE Trans. Power Syst. , 4 , 3008 - 3018
    11. 11)
      • R. Madani , M. Ashraphijuo , J. Lavaei .
        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.
        . IEEE Trans. Power Syst. , 2 , 1297 - 1307
    12. 12)
      • Z. Yang , H. Zhong , Q. Xia .
        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.
        . J. Energy Eng.
    13. 13)
      • Q. Wang , A. Yang , F. Wen .
        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.
        . J. Mod. Power Syst. Clean Energy , 2 , 142 - 149
    14. 14)
      • B. Hu , H. Wang , S. Yao .
        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.
        . Prot. Control Mod. Power Syst. , 1 , 1 - 11
    15. 15)
      • H. Wang , C.E. Murillo-Sanchez , R.D. Zimmerman .
        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.
        . IEEE Trans. Power Syst. , 3 , 1185 - 1193
    16. 16)
      • B. Stott , O. Alsaç . (2012)
        16. Stott, B., Alsaç, O.: ‘Optimal power flow: Basic requirements for real-life problems and their solutions’, White paper, 2012.
        .
    17. 17)
      • A. Gómez-Expósito , A.J. Conejo , C.A. Cañizares . (2009)
        17. Gómez-Expósito, A., Conejo, A.J., Cañizares, C.A.: ‘Electric energy systems analysis and Operation’ (CRC, Boca Raton, FL, USA, 2009).
        .
    18. 18)
      • A. Castillo , P. Lipka , J.P. Watson .
        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.
        . IEEE Trans. Power Syst. , 4 , 2752 - 2763
    19. 19)
      • M. Ilic , S. Cvijic , J.H. Lang .
        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.
        . IEEE Power and Energy Society General Meeting
    20. 20)
      • C. Coffrin , P.V. Hentenryck .
        20. Coffrin, C., Hentenryck, P.V.: ‘A linear-programming approximation of AC power flows’, INFORMS J. Comput., 2014, 26, (4), pp. 718734.
        . INFORMS J. Comput. , 4 , 718 - 734
    21. 21)
      • T.N.d. Santos , L.A. Diniz .
        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.
        . IEEE Trans. Power Syst. , 2 , 508 - 519
    22. 22)
      • H. Zhong , Q. Xia , Y. Wang .
        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.
        . IEEE Trans. Power Syst. , 3 , 2232 - 2241
    23. 23)
      • H. Zhang , V. Vittal , G.T. Heydt .
        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.
        . Innovative Smart Grid Technol. Conf. Asia (ISGT Asia) , 1 - 5
    24. 24)
      • H. Zhang , G.T. Heydt , V. Vittal .
        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.
        . IEEE Trans. Power Syst. , 3 , 3471 - 3479
    25. 25)
      • T. Akbari , M.T. Bina .
        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.
        . IET Gener. Transm. Distrib. , 5 , 1117 - 1123
    26. 26)
      • J. Yang , N. Zhang , C. Kang .
        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.
        . IEEE Trans. Power Syst. , 5 , 3607 - 3617
    27. 27)
      • S.M. Fatemi , S. Abedi , G.B. Gharehpetian .
        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.
        . IEEE Trans. Power Syst. , 6 , 3012 - 3023
    28. 28)
      • Z. Yang , H. Zhong , Q. Xia .
        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.
        . Electr. Power Syst. Res. , 63 - 71
    29. 29)
      • Z. Yang , H. Zhong , A. Bose .
        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.
        . IEEE Trans. Power Syst. , 99 , 1
    30. 30)
      • B. Stott , J. Jardim , O. Alsac .
        30. Stott, B., Jardim, J., Alsac, O.: ‘Dc power flow revisited’, IEEE Trans. Power Syst., 2009, 24, (3), pp. 12901300.
        . IEEE Trans. Power Syst. , 3 , 1290 - 1300
    31. 31)
      • S. Lu , N. Zhou , N.P. Kumar .
        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.
        . IEEE Transmission and Distribution Conf. and Exposition
    32. 32)
      • Y. Qi , D. Shi , D. Tylavsky .
        32. Qi, Y., Shi, D., Tylavsky, D.: ‘Impact of assumptions on Dc power flow model accuracy’. North American Power Symp. (NAPS), 2012.
        . North American Power Symp. (NAPS)
    33. 33)
      • Z. Yang , H. Zhong , Q. Xia .
        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.
        . IET Gener., Transm. Distrib. , 14 , 3654 - 3662
    34. 34)
      • Z. Yang , A. Bose , H. Zhong .
        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.
        . IEEE Trans. Power Syst. , 3 , 2435 - 2444
    35. 35)
      • R.D. Zimmerman , C.E. Murillo-Sánchez , R.J. Thomas .
        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.
        . IEEE Trans. Power Syst. , 1 , 12 - 19
    36. 36)
      • J.S. Al-Sumait , A.K. Al-Othman , J.K. Sykulski .
        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.
        . Int. J. Electr. Power Energy Syst. , 10 , 720 - 730
    37. 37)
      • L.S. Coelho , V.C. Mariani .
        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.
        . IEEE Trans. Power Syst. , 2 , 989 - 996
    38. 38)
      • C. Chao-Lung .
        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.
        . IEEE Trans. Power Syst. , 4 , 1690 - 1699
    39. 39)
      • J. Zhong , K. Bhattacharya .
        39. Zhong, J., Bhattacharya, K.: ‘Toward a competitive market for reactive power’, IEEE Trans. Power Syst., 2002, 17, (4), pp. 12061215.
        . IEEE Trans. Power Syst. , 4 , 1206 - 1215
    40. 40)
      • A.J. Wood , B.F. Wollenberg . (1996)
        40. Wood, A.J., Wollenberg, B.F.: ‘Power generation, operation and Control’ (John Wiley & Sons, New York, 1996, 2nd edn.).
        .
    41. 41)
      • T.J. Overbye , X. Cheng , Y. Sun .
        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.
        . Proc. 37th Hawaii Int. Conf. System Sciences
    42. 42)
      • E. Litvinov , Z. Tongxin , G. Rosenwald .
        42. Litvinov, E., Tongxin, Z., Rosenwald, G., et al: ‘Marginal loss modeling in Lmp calculation’, IEEE Trans. Power Syst., 2004, 19, (2), pp. 880888.
        . IEEE Trans. Power Syst. , 2 , 880 - 888
    43. 43)
      • Z. Yang , A. Bose , H. Zhong .
        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..
        . IEEE Trans. Power Syst. , 5 , 4080 - 4090
    44. 44)
      • A. Helseth .
        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.
        . 2012 9th Int. Conf. the European Energy Market , 1 - 8
    45. 45)
      • 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].
        .
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