메뉴 건너뛰기




Volumn 1, Issue 1, 2014, Pages 15-27

Convex relaxation of optimal power flow - Part i: Formulations and equivalence

Author keywords

Convex relaxation; optimal power flow; power systems; quadratically constrained quadratic program (QCQP); second order cone program (SOCP); semidefinite program (SDP); semidefinite relaxation

Indexed keywords

ACOUSTIC GENERATORS; QUADRATIC PROGRAMMING; RELAXATION PROCESSES; STANDBY POWER SYSTEMS;

EID: 84905407867     PISSN: None     EISSN: 23255870     Source Type: Journal    
DOI: 10.1109/TCNS.2014.2309732     Document Type: Article
Times cited : (969)

References (70)
  • 2
    • 0000767626 scopus 로고
    • Contribution to the economic dispatch problem
    • (in French)
    • J. Carpentier, "Contribution to the economic dispatch problem," Bull. Soc. Francoise Electr., vol. 3, no. 8, pp. 431-447, 1962 (in French).
    • (1962) Bull. Soc. Francoise Electr. , vol.3 , Issue.8 , pp. 431-447
    • Carpentier, J.1
  • 3
    • 84914405497 scopus 로고
    • Optimal power flow solutions
    • Oct.
    • H. W. Dommel and W. F. Tinney, "Optimal power flow solutions," IEEE Trans. Power App. Syst., vol. 87, no. 10, pp. 1866-1876, Oct. 1968.
    • (1968) IEEE Trans. Power App. Syst. , vol.87 , Issue.10 , pp. 1866-1876
    • Dommel, H.W.1    Tinney, W.F.2
  • 5
    • 0026151499 scopus 로고
    • A survey of the optimal power flow literature
    • May
    • M. Huneault and F. D. Galiana, "A survey of the optimal power flow literature," IEEE Trans. Power Syst., vol. 6, no. 2, pp. 762-770, May 1991.
    • (1991) IEEE Trans. Power Syst. , vol.6 , Issue.2 , pp. 762-770
    • Huneault, M.1    Galiana, F.D.2
  • 6
    • 0033079737 scopus 로고    scopus 로고
    • A review of selected optimal power flow literature to 1993. Part I: Nonlinear and quadratic programming approaches
    • Feb.
    • J. A. Momoh, M. E. El-Hawary, and R. Adapa, "A review of selected optimal power flow literature to 1993. Part I: Nonlinear and quadratic programming approaches," IEEE Trans. Power Syst., vol. 14, no. 1, pp. 96-104, Feb. 1999.
    • (1999) IEEE Trans. Power Syst. , vol.14 , Issue.1 , pp. 96-104
    • Momoh, J.A.1    El-Hawary, M.E.2    Adapa, R.3
  • 7
    • 0033079460 scopus 로고    scopus 로고
    • A review of selected optimal power flow literature to 1993. Part II: Newton, linear programming and interior point methods
    • Feb.
    • J. A. Momoh, M. E. El-Hawary, and R. Adapa, "A review of selected optimal power flow literature to 1993. Part II: Newton, linear programming and interior point methods," IEEE Trans. Power Syst., vol. 14, no. 1, pp. 105-111, Feb. 1999.
    • (1999) IEEE Trans. Power Syst. , vol.14 , Issue.1 , pp. 105-111
    • Momoh, J.A.1    El-Hawary, M.E.2    Adapa, R.3
  • 8
    • 77953967659 scopus 로고    scopus 로고
    • A survey of optimal power flow methods
    • K. S. Pandya and S. K. Joshi, "A survey of optimal power flow methods," J. Theor. Appl. Inf. Technol., vol. 4, no. 5, pp. 450-458, 2008.
    • (2008) J. Theor. Appl. Inf. Technol. , vol.4 , Issue.5 , pp. 450-458
    • Pandya, K.S.1    Joshi, S.K.2
  • 9
    • 84870872545 scopus 로고    scopus 로고
    • Optimal power flow: A bibliographic survey I: Formulations and deterministic methods
    • Sep.
    • S. Frank, I. Steponavice, and S. Rebennack, "Optimal power flow: A bibliographic survey, I: Formulations and deterministic methods," Energy Syst., vol. 3, pp. 221-258, Sep. 2012.
    • (2012) Energy Syst. , vol.3 , pp. 221-258
    • Frank, S.1    Steponavice, I.2    Rebennack, S.3
  • 10
    • 84870955285 scopus 로고    scopus 로고
    • Optimal power flow: A bibliographic survey, II: Nondeterministic and hybrid methods
    • Sep.
    • S. Frank, I. Steponavice, and S. Rebennack, "Optimal power flow: A bibliographic survey, II: Nondeterministic and hybrid methods," Energy Syst., vol. 3, pp. 259-289, Sep. 2013.
    • (2013) Energy Syst. , vol.3 , pp. 259-289
    • Frank, S.1    Steponavice, I.2    Rebennack, S.3
  • 11
    • 84890476081 scopus 로고    scopus 로고
    • History of optimal power flow and formulations (OPF Paper 1)
    • Dec.
    • M. B. Cain, R. P. O'Neill, and A. Castillo, "History of optimal power flow and formulations (OPF Paper 1)," Tech. Rep., US FERC, Dec. 2012.
    • (2012) Tech. Rep., US FERC
    • Cain, M.B.1    O'Neill, R.P.2    Castillo, A.3
  • 12
    • 84904341188 scopus 로고    scopus 로고
    • The IV formulation and linear approximations of the AC optimal power flow problem (OPF Paper 2)
    • Dec.
    • R. P. O'Neill, A. Castillo, and M. B. Cain, "The IV formulation and linear approximations of the AC optimal power flow problem (OPF Paper 2)," Tech. Rep., US FERC, Dec. 2012.
    • (2012) Tech. Rep., US FERC
    • O'Neill, R.P.1    Castillo, A.2    Cain, M.B.3
  • 13
    • 84890530855 scopus 로고    scopus 로고
    • The computational testing ofAC optimal power flow using the current voltage formulations (OPF Paper 3)
    • Dec.
    • R. P.O'Neill, A. Castillo, and M. B. Cain, "The computational testing ofAC optimal power flow using the current voltage formulations (OPF Paper 3)," Tech. Rep., US FERC, Dec. 2012.
    • (2012) Tech. Rep., US FERC
    • O'Neill, R.P.1    Castillo, A.2    Cain, M.B.3
  • 14
    • 84904333490 scopus 로고    scopus 로고
    • Survey of approaches to solving the ACOPF (OPF Paper 4)
    • Mar.
    • A. Castillo and R. P. O'Neill, "Survey of approaches to solving the ACOPF (OPF Paper 4)," Tech. Rep., US FERC, Mar. 2013.
    • (2013) Tech. Rep., US FERC
    • Castillo, A.1    O'Neill, R.P.2
  • 15
    • 84890494395 scopus 로고    scopus 로고
    • Computational performance of solution techniques applied to the ACOPF (OPF Paper 5)
    • Mar.
    • A. Castillo and R. P. O'Neill, "Computational performance of solution techniques applied to the ACOPF (OPF Paper 5)," Tech. Rep., US FERC, Mar. 2013.
    • (2013) Tech. Rep., US FERC
    • Castillo, A.1    O'Neill, R.P.2
  • 16
    • 0016062145 scopus 로고
    • Fast decoupled load flow
    • May
    • B. Stott and O. Alsaç, "Fast decoupled load flow," IEEE Trans. Power App. Syst., vol. 93, no. 3, pp. 859-869, May 1974.
    • (1974) IEEE Trans. Power App. Syst. , vol.93 , Issue.3 , pp. 859-869
    • Stott, B.1    Alsaç, O.2
  • 17
    • 0025472139 scopus 로고
    • Further developments in LP-based optimal power flow
    • Aug.
    • O. Alsaç, J. Bright, M. Prais, and B. Stott, "Further developments in LP-based optimal power flow," IEEE Trans. Power Syst., vol. 5, no. 3, pp. 697-711, Aug. 1990.
    • (1990) IEEE Trans. Power Syst. , vol.5 , Issue.3 , pp. 697-711
    • Alsaç, O.1    Bright, J.2    Prais, M.3    Stott, B.4
  • 20
    • 68349130530 scopus 로고    scopus 로고
    • DC power flow revisited
    • Aug.
    • B. Stott, J. Jardim, and O. Alsaç, "DC power flow revisited," IEEE Trans. Power Syst., vol. 24, no. 3, pp. 1290-1300, Aug. 2009.
    • (2009) IEEE Trans. Power Syst. , vol.24 , Issue.3 , pp. 1290-1300
    • Stott, B.1    Jardim, J.2    Alsaç, O.3
  • 22
    • 33747619180 scopus 로고    scopus 로고
    • Radial distribution load flow using conic programming
    • Aug.
    • R. A. Jabr, "Radial distribution load flow using conic programming," IEEE Trans. Power Syst., vol. 21, no. 3, pp. 1458-1459, Aug. 2006.
    • (2006) IEEE Trans. Power Syst. , vol.21 , Issue.3 , pp. 1458-1459
    • Jabr, R.A.1
  • 23
    • 44649096459 scopus 로고    scopus 로고
    • Semidefinite programming for optimal power flow problems
    • X. Bai, H. Wei, K. Fujisawa, and Y. Wang, "Semidefinite programming for optimal power flow problems," Int. J. Elect. Power Energy Syst., vol. 30, no. 6-7, pp. 383-392, 2008.
    • (2008) Int. J. Elect. Power Energy Syst. , vol.30 , Issue.6-7 , pp. 383-392
    • Bai, X.1    Wei, H.2    Fujisawa, K.3    Wang, Y.4
  • 24
    • 84856282519 scopus 로고    scopus 로고
    • Zero duality gap in optimal power flow problem
    • Feb.
    • J. Lavaei and S. H. Low, "Zero duality gap in optimal power flow problem," IEEE Trans. Power Syst., vol. 27, no. 1, pp. 92-107, Feb. 2012.
    • (2012) IEEE Trans. Power Syst. , vol.27 , Issue.1 , pp. 92-107
    • Lavaei, J.1    Low, S.H.2
  • 25
    • 79960930294 scopus 로고    scopus 로고
    • A semidefinite programming method with graph partitioning technique for optimal power flow problems
    • X. Bai and H. Wei, "A semidefinite programming method with graph partitioning technique for optimal power flow problems," Int. J. Elect. Power Energy Syst., vol. 33, no. 7, pp. 1309-1314, 2011.
    • (2011) Int. J. Elect. Power Energy Syst. , vol.33 , Issue.7 , pp. 1309-1314
    • Bai, X.1    Wei, H.2
  • 26
    • 84860247520 scopus 로고    scopus 로고
    • Exploiting sparsity in SDP relaxations of the OPF problem
    • May
    • R. A. Jabr, "Exploiting sparsity in SDP relaxations of the OPF problem," IEEE Trans. Power Syst., vol. 27, no. 2, pp. 1138-1139, May 2012.
    • (2012) IEEE Trans. Power Syst. , vol.27 , Issue.2 , pp. 1138-1139
    • Jabr, R.A.1
  • 27
    • 84886085006 scopus 로고    scopus 로고
    • Implementation of a large-scale optimal power flow solver based on semidefinite programming
    • Nov.
    • D. Molzahn, J. Holzer, B. Lesieutre, and C. DeMarco, "Implementation of a large-scale optimal power flow solver based on semidefinite programming," IEEE Trans. Power Syst., vol. 28, no. 4, pp. 3987-3998, Nov. 2013.
    • (2013) IEEE Trans. Power Syst. , vol.28 , Issue.4 , pp. 3987-3998
    • Molzahn, D.1    Holzer, J.2    Lesieutre, B.3    Demarco, C.4
  • 29
    • 85032752455 scopus 로고    scopus 로고
    • Semidefinite relaxation of quadratic optimization problems
    • May
    • Z. Luo, W. Ma, A. M. C. So, Y. Ye, and S. Zhang, "Semidefinite relaxation of quadratic optimization problems," IEEE Signal Process. Mag., vol. 27, no. 3, pp. 20-34, May 2010.
    • (2010) IEEE Signal Process. Mag. , vol.27 , Issue.3 , pp. 20-34
    • Luo, Z.1    Ma, W.2    So, A.M.C.3    Ye, Y.4    Zhang, S.5
  • 30
    • 84930149896 scopus 로고    scopus 로고
    • Convex relaxation of optimal power flow, II: Exactness
    • to be published
    • S. H. Low, "Convex relaxation of optimal power flow, II: Exactness," IEEE Trans. Control Netw. Syst., 2014, to be published.
    • (2014) IEEE Trans. Control Netw. Syst.
    • Low, S.H.1
  • 31
    • 85008029051 scopus 로고    scopus 로고
    • Smart operation of smart grid: Risk-limiting dispatch
    • Jan.
    • P. P. Varaiya, F. F. Wu, and J. W. Bialek, "Smart operation of smart grid: Risk-limiting dispatch," Proc. IEEE, vol. 99, no. 1, pp. 40-57, Jan. 2011.
    • (2011) Proc. IEEE , vol.99 , Issue.1 , pp. 40-57
    • Varaiya, P.P.1    Wu, F.F.2    Bialek, J.W.3
  • 33
  • 34
    • 0031146910 scopus 로고    scopus 로고
    • Coarse-grained distributed optimal power flow
    • May
    • B. H. Kim and R. Baldick, "Coarse-grained distributed optimal power flow," IEEE Trans. Power Syst., vol. 12, no. 2, pp. 932-939, May 1997.
    • (1997) IEEE Trans. Power Syst. , vol.12 , Issue.2 , pp. 932-939
    • Kim, B.H.1    Baldick, R.2
  • 35
    • 0032593003 scopus 로고    scopus 로고
    • A fast distributed implementation of optimal power flow
    • Aug.
    • R. Baldick, B. H. Kim, C. Chase, and Y. Luo, "A fast distributed implementation of optimal power flow," IEEE Trans. Power Syst., vol. 14, no. 3, pp. 858-864, Aug. 1999.
    • (1999) IEEE Trans. Power Syst. , vol.14 , Issue.3 , pp. 858-864
    • Baldick, R.1    Kim, B.H.2    Chase, C.3    Luo, Y.4
  • 36
    • 60149101724 scopus 로고    scopus 로고
    • Decentralized optimal power flow control for overlapping areas in power systems
    • Feb.
    • G. Hug-Glanzmann and G. Andersson, "Decentralized optimal power flow control for overlapping areas in power systems," IEEE Trans. Power Syst., vol. 24, no. 1, pp. 327-336, Feb. 2009.
    • (2009) IEEE Trans. Power Syst. , vol.24 , Issue.1 , pp. 327-336
    • Hug-Glanzmann, G.1    Andersson, G.2
  • 37
    • 0037275802 scopus 로고    scopus 로고
    • Adecomposition methodology applied to the multi-area optimal power flow problem
    • F. J. Nogales, F. J. Prieto, and A. J. Conejo, "Adecomposition methodology applied to the multi-area optimal power flow problem," Ann. Oper. Res., vol. 120, pp. 99-116, 2003.
    • (2003) Ann. Oper. Res. , vol.120 , pp. 99-116
    • Nogales, F.J.1    Prieto, F.J.2    Conejo, A.J.3
  • 39
    • 84886051238 scopus 로고    scopus 로고
    • Dynamic network energy management via proximal message passing
    • M. Kraning, E. Chu, J. Lavaei, and S. Boyd, "Dynamic network energy management via proximal message passing," Found. Trends Optim., vol. 1, no. 2, pp. 70-122, 2013.
    • (2013) Found. Trends Optim. , vol.1 , Issue.2 , pp. 70-122
    • Kraning, M.1    Chu, E.2    Lavaei, J.3    Boyd, S.4
  • 40
    • 79956350391 scopus 로고    scopus 로고
    • Options for control of reactive power by distributed photovoltaic generators
    • Jun.
    • K. Turitsyn, P. Su?lc, S. Backhaus, and M. Chertkov, "Options for control of reactive power by distributed photovoltaic generators," Proc. IEEE, vol. 99, no. 6, pp. 1063-1073, Jun. 2011.
    • (2011) Proc. IEEE , vol.99 , Issue.6 , pp. 1063-1073
    • Turitsyn, K.1    Sulc, P.2    Backhaus, S.3    Chertkov, M.4
  • 42
    • 84861646861 scopus 로고    scopus 로고
    • Lagrangian duality and branch-and-bound algorithms for optimal power flow
    • Mar./Apr.
    • D. T. Phan, "Lagrangian duality and branch-and-bound algorithms for optimal power flow," Oper. Res., vol. 60, no. 2, pp. 275-285, Mar./Apr. 2012.
    • (2012) Oper. Res. , vol.60 , Issue.2 , pp. 275-285
    • Phan, D.T.1
  • 45
    • 0024480765 scopus 로고
    • Optimal capacitor placement on radial distribution systems
    • Nov.
    • M. E. Baran and F. F. Wu, "Optimal capacitor placement on radial distribution systems," IEEE Trans. Power Del., vol. 4, no. 1, pp. 725-734, Nov. 1989.
    • (1989) IEEE Trans. Power Del. , vol.4 , Issue.1 , pp. 725-734
    • Baran, M.E.1    Wu, F.F.2
  • 46
    • 0024480990 scopus 로고
    • Optimal sizing of capacitors placed on a radial distribution system
    • Jan.
    • M. E. Baran and F. F. Wu, "Optimal sizing of capacitors placed on a radial distribution system," IEEE Trans. Power Del., vol. 4, no. 1, pp. 735-743, Jan. 1989.
    • (1989) IEEE Trans. Power Del. , vol.4 , Issue.1 , pp. 735-743
    • Baran, M.E.1    Wu, F.F.2
  • 47
    • 0025402362 scopus 로고
    • On the existence and uniqueness of load flow solution for radial distribution power networks
    • Mar.
    • H.-D. Chiang and M. E. Baran, "On the existence and uniqueness of load flow solution for radial distribution power networks," IEEE Trans. Circuits Syst., vol. 37, no. 3, pp. 410-416, Mar. 1990.
    • (1990) IEEE Trans. Circuits Syst. , vol.37 , Issue.3 , pp. 410-416
    • Chiang, H.-D.1    Baran, M.E.2
  • 48
    • 0026175328 scopus 로고
    • A decoupled load flow method for distribution power networks: Algorithms, analysis and convergence study
    • Jun.
    • H.-D. Chiang, "A decoupled load flow method for distribution power networks: Algorithms, analysis and convergence study," Int. J. Elect. Power Energy Syst., vol. 13, no. 3, pp. 130-138, Jun. 1991.
    • (1991) Int. J. Elect. Power Energy Syst. , vol.13 , Issue.3 , pp. 130-138
    • Chiang, H.-D.1
  • 49
    • 0025251059 scopus 로고
    • New method for the analysis of distribution networks
    • Jan.
    • R. Cespedes, "New method for the analysis of distribution networks," IEEE Trans. Power Del., vol. 5, no. 1, pp. 391-396, Jan. 1990.
    • (1990) IEEE Trans. Power Del. , vol.5 , Issue.1 , pp. 391-396
    • Cespedes, R.1
  • 50
    • 0032592951 scopus 로고    scopus 로고
    • Reliable load flow technique for radial distribution networks
    • Aug.
    • A. G. Expósito and E. R. Ramos, "Reliable load flow technique for radial distribution networks," IEEE Trans. Power Syst., vol. 14, no. 13, pp. 1063-1069, Aug. 1999.
    • (1999) IEEE Trans. Power Syst. , vol.14 , Issue.13 , pp. 1063-1069
    • Expósito, A.G.1    Ramos, E.R.2
  • 52
    • 84864284002 scopus 로고    scopus 로고
    • Convex models of distribution system reconfiguration
    • Aug.
    • J. A. Taylor and F. S. Hover, "Convex models of distribution system reconfiguration," IEEE Trans. Power Syst., vol. 27, no. 3, pp. 1407-1413, Aug. 2012.
    • (2012) IEEE Trans. Power Syst. , vol.27 , Issue.3 , pp. 1407-1413
    • Taylor, J.A.1    Hover, F.S.2
  • 53
    • 84897672390 scopus 로고    scopus 로고
    • Geometry of power flows and optimization in distribution networks
    • J. Lavaei, D. Tse, and B. Zhang, "Geometry of power flows and optimization in distribution networks," IEEE Trans. Power Syst., vol. 29, no. 2, pp. 572-583, 2014.
    • (2014) IEEE Trans. Power Syst. , vol.29 , Issue.2 , pp. 572-583
    • Lavaei, J.1    Tse, D.2    Zhang, B.3
  • 55
    • 0024001725 scopus 로고
    • A compensation-based power flow method for weakly meshed distribution and transmission networks
    • May
    • D. Shirmohammadi, H. W. Hong, A. Semlyen, and G. X. Luo, "A compensation-based power flow method for weakly meshed distribution and transmission networks," IEEE Trans. Power Syst., vol. 3, no. 2, pp. 753-762, May 1988.
    • (1988) IEEE Trans. Power Syst. , vol.3 , Issue.2 , pp. 753-762
    • Shirmohammadi, D.1    Hong, H.W.2    Semlyen, A.3    Luo, G.X.4
  • 57
    • 84880898174 scopus 로고    scopus 로고
    • Branch flow model: Relaxations and convexification (parts i II)
    • Aug.
    • M. Farivar and S. H. Low, "Branch flow model: Relaxations and convexification (parts I, II)," IEEE Trans. Power Syst., vol. 28, no. 3, pp. 2554-2572, Aug. 2013.
    • (2013) IEEE Trans. Power Syst. , vol.28 , Issue.3 , pp. 2554-2572
    • Farivar, M.1    Low, S.H.2
  • 59
    • 0034186807 scopus 로고    scopus 로고
    • Stability-constrained optimal power flow
    • May
    • D. Gan, R. J. Thomas, and R. D. Zimmerman, "Stability-constrained optimal power flow," IEEE Trans. Power Syst., vol. 15, no. 2, pp. 535-540, May 2000.
    • (2000) IEEE Trans. Power Syst. , vol.15 , Issue.2 , pp. 535-540
    • Gan, D.1    Thomas, R.J.2    Zimmerman, R.D.3
  • 61
    • 84924348258 scopus 로고    scopus 로고
    • Optimal power flow: Basic requirements for real-life problems and their solutions
    • Jul.
    • B. Stott and O. Alsaç, "Optimal power flow: Basic requirements for real-life problems and their solutions," White paper, Jul. 2012.
    • (2012) White Paper
    • Stott, B.1    Alsaç, O.2
  • 63
    • 47849109874 scopus 로고
    • Positive definite completions of partial Hermitian matrices
    • R. Grone, C. R. Johnson, E. M. Sá, and H. Wolkowicz, "Positive definite completions of partial Hermitian matrices," Linear Algebr. Appl., vol. 58, pp. 109-124, 1984.
    • (1984) Linear Algebr. Appl. , vol.58 , pp. 109-124
    • Grone, R.1    Johnson, C.R.2    Sá, E.M.3    Wolkowicz, H.4
  • 64
    • 0035238840 scopus 로고    scopus 로고
    • Exploiting sparsity in semidefinite programming via matrix completion I: General framework
    • M. Fukuda, M. Kojima, K. Murota, and K. Nakata, "Exploiting sparsity in semidefinite programming via matrix completion I: General framework," SIAM J. Optim., vol. 11, pp. 647-674, 2001.
    • (2001) SIAM J. Optim. , vol.11 , pp. 647-674
    • Fukuda, M.1    Kojima, M.2    Murota, K.3    Nakata, K.4
  • 65
    • 1542337154 scopus 로고    scopus 로고
    • Exploiting sparsity in semidefinite programming via matrix completion II: Implementation and numerical results
    • K. Nakata, K. Fujisawa, M. Fukuda, M. Kojima, and K. Murota, "Exploiting sparsity in semidefinite programming via matrix completion II: Implementation and numerical results," Math. Program., vol. 95, no. 2, pp. 303-327, 2003.
    • (2003) Math. Program. , vol.95 , Issue.2 , pp. 303-327
    • Nakata, K.1    Fujisawa, K.2    Fukuda, M.3    Kojima, M.4    Murota, K.5
  • 66
    • 84886090661 scopus 로고    scopus 로고
    • Geometry of the injection region of power networks
    • May
    • B. Zhang and D. Tse, "Geometry of the injection region of power networks," IEEE Trans. Power Syst., vol. 28, no. 2, pp. 788-797, May 2013.
    • (2013) IEEE Trans. Power Syst. , vol.28 , Issue.2 , pp. 788-797
    • Zhang, B.1    Tse, D.2
  • 68
    • 0029410321 scopus 로고
    • Fast decoupled power flow for unbalanced radial distribution systems
    • Nov.
    • R. D. Zimmerman and H.-D. Chiang, "Fast decoupled power flow for unbalanced radial distribution systems," IEEE Trans. Power Syst., vol. 10, no. 4, pp. 2045-2052, Nov. 1995.
    • (1995) IEEE Trans. Power Syst. , vol.10 , Issue.4 , pp. 2045-2052
    • Zimmerman, R.D.1    Chiang, H.-D.2
  • 70
    • 34250833384 scopus 로고
    • Network reconfiguration in distribution systems for loss reduction and load balancing
    • Apr.
    • M. E. Baran and F. F. Wu, "Network reconfiguration in distribution systems for loss reduction and load balancing," IEEE Trans. Power Del., vol. 4, no. 2, pp. 1401-1407, Apr. 1989.
    • (1989) IEEE Trans. Power Del. , vol.4 , Issue.2 , pp. 1401-1407
    • Baran, M.E.1    Wu, F.F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.