메뉴 건너뛰기




Volumn 12, Issue 4, 2015, Pages 491-518

A scalable solution framework for stochastic transmission and generation planning problems

Author keywords

Generation planning; Progressive Hedging; Stochastic mixed integer programming; Transmission planning

Indexed keywords


EID: 84946499591     PISSN: 1619697X     EISSN: 16196988     Source Type: Journal    
DOI: 10.1007/s10287-015-0229-y     Document Type: Article
Times cited : (77)

References (68)
  • 1
    • 79954622530 scopus 로고    scopus 로고
    • A multi-stage stochastic transmission expansion planning method
    • Akbari T, Rahimikian A, Kazemi A (2011) A multi-stage stochastic transmission expansion planning method. Energy Conv Manag 52(8–9):2844–2853
    • (2011) Energy Conv Manag , vol.52 , Issue.8-9 , pp. 2844-2853
    • Akbari, T.1    Rahimikian, A.2    Kazemi, A.3
  • 2
    • 0042526113 scopus 로고    scopus 로고
    • Transmission expansion planning: a mixed-integer LP approach
    • Alguacil N, Motto A, Conejo A (2003) Transmission expansion planning: a mixed-integer LP approach. IEEE Trans Power Syst 18(3):1070–1077
    • (2003) IEEE Trans Power Syst , vol.18 , Issue.3 , pp. 1070-1077
    • Alguacil, N.1    Motto, A.2    Conejo, A.3
  • 3
    • 0035425561 scopus 로고    scopus 로고
    • A mixed integer disjunctive model for transmission network expansion
    • Bahiense L, Oliveira G, Pereira M, Granville S (2001) A mixed integer disjunctive model for transmission network expansion. IEEE Trans Power Syst 16(3):560–565
    • (2001) IEEE Trans Power Syst , vol.16 , Issue.3 , pp. 560-565
    • Bahiense, L.1    Oliveira, G.2    Pereira, M.3    Granville, S.4
  • 4
    • 9644308639 scopus 로고
    • Partitioning procedures for solving mixed-variables programming problems
    • Benders J (1962) Partitioning procedures for solving mixed-variables programming problems. Numer Math 4(1):238–252
    • (1962) Numer Math , vol.4 , Issue.1 , pp. 238-252
    • Benders, J.1
  • 5
    • 0035339706 scopus 로고    scopus 로고
    • A greedy randomized adaptive search procedure for transmission expansion planning
    • Binato S, De Oliveira GC, De Araújo JL (2001) A greedy randomized adaptive search procedure for transmission expansion planning. IEEE Trans Power Syst 16(2):247–253
    • (2001) IEEE Trans Power Syst , vol.16 , Issue.2 , pp. 247-253
    • Binato, S.1    De Oliveira, G.C.2    De Araújo, J.L.3
  • 6
    • 0035339650 scopus 로고    scopus 로고
    • A new benders decomposition approach to solve power transmission network design problems
    • Binato S, Pereira M, Granville S (2001) A new benders decomposition approach to solve power transmission network design problems. IEEE Trans Power Syst 16(2):235–240
    • (2001) IEEE Trans Power Syst , vol.16 , Issue.2 , pp. 235-240
    • Binato, S.1    Pereira, M.2    Granville, S.3
  • 8
    • 0020543409 scopus 로고
    • Solving an electricity generating capacity expansion planning problem by generalized benders’ decomposition
    • Bloom JA (1983) Solving an electricity generating capacity expansion planning problem by generalized benders’ decomposition. Oper Res 31(1):84–100
    • (1983) Oper Res , vol.31 , Issue.1 , pp. 84-100
    • Bloom, J.A.1
  • 9
    • 0021389714 scopus 로고
    • Long-range generation planning using generalized benders’ decomposition: implementation and experience
    • Bloom JA, Caramanis M, Charny L (1984) Long-range generation planning using generalized benders’ decomposition: implementation and experience. Oper Res 32(2):290–313
    • (1984) Oper Res , vol.32 , Issue.2 , pp. 290-313
    • Bloom, J.A.1    Caramanis, M.2    Charny, L.3
  • 12
    • 0032597546 scopus 로고    scopus 로고
    • Transmission network expansion planning under an improved genetic algorithm. In: Proceedings of the 21st 1999 IEEE international conference on power industry computer applications, 1999, pp 315–321
    • da Silva EL, Gil HA, Areiza JM (1999) Transmission network expansion planning under an improved genetic algorithm. In: Proceedings of the 21st 1999 IEEE international conference on power industry computer applications, 1999, pp 315–321, IEEE
    • (1999) IEEE
    • da Silva, E.L.1    Gil, H.A.2    Areiza, J.M.3
  • 14
    • 33751071102 scopus 로고    scopus 로고
    • Scenario reduction in stochastic programming
    • Dupačová J, Gröwe-Kuska N, Römisch W (2003) Scenario reduction in stochastic programming. Math Program 95(3):493–511
    • (2003) Math Program , vol.95 , Issue.3 , pp. 493-511
    • Dupačová, J.1    Gröwe-Kuska, N.2    Römisch, W.3
  • 15
    • 84946510356 scopus 로고    scopus 로고
    • EIA: Energy Information Administration, Electricity Power Annual (2014) Retrieved August 30, 2014, from
    • EIA: Energy Information Administration, Electricity Power Annual (2014) Retrieved August 30, 2014, from URL http://www.eia.gov/electricity/annual/html/epa_01_01.html
  • 16
    • 84946510357 scopus 로고    scopus 로고
    • Energy Exemplar PLEXOS Software (2014)
    • Energy Exemplar PLEXOS Software (2014) URL http://energyexemplar.com/software/plexos-desktop-edition/
  • 17
    • 84866165983 scopus 로고    scopus 로고
    • Scenario construction and reduction applied to stochastic power generation expansion planning
    • Feng Y, Ryan SM (2013) Scenario construction and reduction applied to stochastic power generation expansion planning. Comput Oper Res 40(1):9–23
    • (2013) Comput Oper Res , vol.40 , Issue.1 , pp. 9-23
    • Feng, Y.1    Ryan, S.M.2
  • 18
    • 85027909472 scopus 로고    scopus 로고
    • Solution sensitivity-based scenario reduction for stochastic unit commitment
    • Feng Y, Ryan SM (2014) Solution sensitivity-based scenario reduction for stochastic unit commitment. Comput Manag Sci 1–34
    • (2014) Comput Manag Sci , pp. 1-34
    • Feng, Y.1    Ryan, S.M.2
  • 19
    • 84946510358 scopus 로고    scopus 로고
    • Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs
    • Gade D, Hackebeil G, Ryan S, Watson J, Wets R, Woodruff D (2014) Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs. Under review
    • (2014) Under review
    • Gade, D.1    Hackebeil, G.2    Ryan, S.3    Watson, J.4    Wets, R.5    Woodruff, D.6
  • 20
    • 0035008821 scopus 로고    scopus 로고
    • Stigler’s diet problem revisited
    • Garille S, Gass S (2001) Stigler’s diet problem revisited. Oper Res 49(1):1–13
    • (2001) Oper Res , vol.49 , Issue.1 , pp. 1-13
    • Garille, S.1    Gass, S.2
  • 21
    • 0014848305 scopus 로고
    • Transmission network estimation using linear programming
    • Garver LL (1970) Transmission network estimation using linear programming. IEEE Trans Power Apparatus Syst 7:1688–1697
    • (1970) IEEE Trans Power Apparatus Syst , vol.7 , pp. 1688-1697
    • Garver, L.L.1
  • 22
    • 0015419856 scopus 로고
    • Generalized benders decomposition
    • Geoffrion AM (1972) Generalized benders decomposition. J Optim Theory Appl 10(4):237–260
    • (1972) J Optim Theory Appl , vol.10 , Issue.4 , pp. 237-260
    • Geoffrion, A.M.1
  • 23
    • 84946497528 scopus 로고
    • Analysis of the linearized power flow model in Benders decomposition. System Optimization Lab., Dept. of Operations Research, Stanford University. Technical report
    • Granville S, Pereira MVF (1985) Analysis of the linearized power flow model in Benders decomposition. System Optimization Lab., Dept. of Operations Research, Stanford University. Technical report, SOL 85–04
    • (1985) SOL , pp. 04-85
    • Granville, S.1    Pereira, M.V.F.2
  • 25
    • 84864524056 scopus 로고    scopus 로고
    • Pyomo: modeling and solving mathematical programs in python
    • Hart W, Watson J, Woodruff D (2011) Pyomo: modeling and solving mathematical programs in python. Math Program Comput 3(3):219–260
    • (2011) Math Program Comput , vol.3 , Issue.3 , pp. 219-260
    • Hart, W.1    Watson, J.2    Woodruff, D.3
  • 26
    • 33845332357 scopus 로고    scopus 로고
    • Overview of transmission expansion planning using real options analysis. In: Proceedings of the 37th annual North American power symposium, 2005, pp 497–502
    • Hedman K, Gao F, Sheble G (2005) Overview of transmission expansion planning using real options analysis. In: Proceedings of the 37th annual North American power symposium, 2005, pp 497–502, IEEE
    • (2005) IEEE
    • Hedman, K.1    Gao, F.2    Sheble, G.3
  • 27
    • 0001281946 scopus 로고
    • Optimization methods for electric utility resource planning
    • Hobbs BF (1995) Optimization methods for electric utility resource planning. Eur J Oper Res 83(1):1–20
    • (1995) Eur J Oper Res , vol.83 , Issue.1 , pp. 1-20
    • Hobbs, B.F.1
  • 28
    • 0033340486 scopus 로고    scopus 로고
    • Stochastic programming-based bounding of expected production costs for multiarea electric power systems
    • Hobbs BF, Ji YD (1999) Stochastic programming-based bounding of expected production costs for multiarea electric power systems. Oper Res 47(6):836–848
    • (1999) Oper Res , vol.47 , Issue.6 , pp. 836-848
    • Hobbs, B.F.1    Ji, Y.D.2
  • 29
    • 0037321138 scopus 로고    scopus 로고
    • A heuristic for moment-matching scenario generation
    • Høyland K, Kaut M, Wallace SW (2003) A heuristic for moment-matching scenario generation. Comput Optim Appl 24(2–3):169–185
    • (2003) Comput Optim Appl , vol.24 , Issue.2-3 , pp. 169-185
    • Høyland, K.1    Kaut, M.2    Wallace, S.W.3
  • 30
    • 34249830842 scopus 로고
    • Monte carlo (importance) sampling within a benders decomposition algorithm for stochastic linear programs
    • Infanger G (1992) Monte carlo (importance) sampling within a benders decomposition algorithm for stochastic linear programs. Ann Oper Res 39(1):69–95
    • (1992) Ann Oper Res , vol.39 , Issue.1 , pp. 69-95
    • Infanger, G.1
  • 31
    • 84856301035 scopus 로고    scopus 로고
    • Modeling and solving a large-scale generation expansion planning problem under uncertainty
    • Jin S, Ryan SM, Watson JP, Woodruff DL (2011) Modeling and solving a large-scale generation expansion planning problem under uncertainty. Energy Syst 2(3–4):209–242
    • (2011) Energy Syst , vol.2 , Issue.3-4 , pp. 209-242
    • Jin, S.1    Ryan, S.M.2    Watson, J.P.3    Woodruff, D.L.4
  • 32
    • 84906497552 scopus 로고    scopus 로고
    • Temporal versus stochastic granularity in thermal generation capacity planning with wind power
    • Jin S, Botterud A, Ryan SM (2014) Temporal versus stochastic granularity in thermal generation capacity planning with wind power. IEEE Trans Power Syst 29(5):2033–2041
    • (2014) IEEE Trans Power Syst , vol.29 , Issue.5 , pp. 2033-2041
    • Jin, S.1    Botterud, A.2    Ryan, S.M.3
  • 33
    • 78649451140 scopus 로고    scopus 로고
    • Wind integration studies: optimization vs simulation
    • Kahn E (2010) Wind integration studies: optimization vs simulation. Electr J 23(9):51–64
    • (2010) Electr J , vol.23 , Issue.9 , pp. 51-64
    • Kahn, E.1
  • 34
    • 0037843031 scopus 로고    scopus 로고
    • Classification of publications and models on transmission expansion planning
    • Latorre G, Cruz RD, Areiza JM, Villegas A (2003) Classification of publications and models on transmission expansion planning. IEEE Trans Power Syst 18(2):938–946
    • (2003) IEEE Trans Power Syst , vol.18 , Issue.2 , pp. 938-946
    • Latorre, G.1    Cruz, R.D.2    Areiza, J.M.3    Villegas, A.4
  • 35
    • 0028550745 scopus 로고
    • Chopin, a heuristic model for long term transmission expansion planning
    • Latorre-Bayona G, Perez-Arriaga IJ (1994) Chopin, a heuristic model for long term transmission expansion planning. IEEE Trans Power Syst 9(4):1886–1894
    • (1994) IEEE Trans Power Syst , vol.9 , Issue.4 , pp. 1886-1894
    • Latorre-Bayona, G.1    Perez-Arriaga, I.J.2
  • 36
    • 0030235440 scopus 로고    scopus 로고
    • Progressive hedging and tabu search applied to mixed integer (0,1) multistage stochastic programming
    • Løkketangen A, Woodruff DL (1996) Progressive hedging and tabu search applied to mixed integer (0,1) multistage stochastic programming. J Heuristics 2:111–128
    • (1996) J Heuristics , vol.2 , pp. 111-128
    • Løkketangen, A.1    Woodruff, D.L.2
  • 37
    • 79952068952 scopus 로고    scopus 로고
    • Exploration of resource and transmission expansion decisions in the western renewable energy zone initiative
    • Mills A, Phadke A, Wiser R (2011) Exploration of resource and transmission expansion decisions in the western renewable energy zone initiative. Energy Policy 39(3):1732–1745
    • (2011) Energy Policy , vol.39 , Issue.3 , pp. 1732-1745
    • Mills, A.1    Phadke, A.2    Wiser, R.3
  • 38
    • 84886910449 scopus 로고    scopus 로고
    • An evaluation of solar valuation methods used in utility planning and procurement processes. Technical report
    • Mills A, Wiser R (2012) An evaluation of solar valuation methods used in utility planning and procurement processes. Technical report. Lawrence Berkeley National Laboratory
    • (2012) Lawrence Berkeley National Laboratory
    • Mills, A.1    Wiser, R.2
  • 39
    • 84882618891 scopus 로고    scopus 로고
    • Changes in the economic value of variable generation at high penetration levels: a pilot case study of california. Technical report
    • Mills A, Wiser R (2012) Changes in the economic value of variable generation at high penetration levels: a pilot case study of california. Technical report. Lawrence Berkeley National Laboratory
    • (2012) Lawrence Berkeley National Laboratory
    • Mills, A.1    Wiser, R.2
  • 40
    • 84946510360 scopus 로고    scopus 로고
    • Engineering–economic methods for power transmission planning under uncertainty and renewable resource policies. Ph.D
    • The Johns Hopkins University, Baltimor
    • Munoz FD (2014) Engineering–economic methods for power transmission planning under uncertainty and renewable resource policies. Ph.D. thesis, The Johns Hopkins University, Baltimore
    • (2014) thesis
    • Munoz, F.D.1
  • 41
    • 84891561294 scopus 로고    scopus 로고
    • An engineering–economic approach to transmission planning under market and regulatory uncertainties: WECC case study
    • Munoz FD, Hobbs BF, Ho J, Kasina S (2014) An engineering–economic approach to transmission planning under market and regulatory uncertainties: WECC case study. IEEE Trans Power Syst 29(1):307–317
    • (2014) IEEE Trans Power Syst , vol.29 , Issue.1 , pp. 307-317
    • Munoz, F.D.1    Hobbs, B.F.2    Ho, J.3    Kasina, S.4
  • 42
    • 84870584305 scopus 로고    scopus 로고
    • Efficient proactive planning to accommodate renewables. In: IEEE Power and Energy Society General Meeting
    • Munoz FD, Hobbs BF, Kasina S (2012) Efficient proactive planning to accommodate renewables. In: IEEE Power and Energy Society General Meeting, pp 1–7
    • (2012) pp 1–7
    • Munoz, F.D.1    Hobbs, B.F.2    Kasina, S.3
  • 43
    • 84946510362 scopus 로고    scopus 로고
    • New bounding and decomposition methods for MILP investment problems: multi-area transmission and generation planning under policy constraints
    • Munoz FD, Hobbs BF, Watson JP (2014) New bounding and decomposition methods for MILP investment problems: multi-area transmission and generation planning under policy constraints. JHU Working Paper
    • (2014) JHU Working Paper
    • Munoz, F.D.1    Hobbs, B.F.2    Watson, J.P.3
  • 44
    • 84946510363 scopus 로고    scopus 로고
    • Endogenous assessment of the capacity value of solar PV in generation investment planning studies
    • Munoz FD, Mills AD (2015) Endogenous assessment of the capacity value of solar PV in generation investment planning studies. Sandia Technical Report
    • (2015) Sandia Technical Report
    • Munoz, F.D.1    Mills, A.D.2
  • 45
    • 84876451528 scopus 로고    scopus 로고
    • Approximations in power transmission planning: implications for the cost and performance of renewable portfolio standards
    • Munoz FD, Sauma EE, Hobbs BF (2013) Approximations in power transmission planning: implications for the cost and performance of renewable portfolio standards. J Regul Econ 43(3):305–338
    • (2013) J Regul Econ , vol.43 , Issue.3 , pp. 305-338
    • Munoz, F.D.1    Sauma, E.E.2    Hobbs, B.F.3
  • 46
    • 0029407206 scopus 로고
    • Large scale transmission network planning using optimization and heuristic techniques
    • Oliveira G, Costa A, Binato S (1995) Large scale transmission network planning using optimization and heuristic techniques. IEEE Trans Power Syst 10(4):1828–1834
    • (1995) IEEE Trans Power Syst , vol.10 , Issue.4 , pp. 1828-1834
    • Oliveira, G.1    Costa, A.2    Binato, S.3
  • 47
    • 84946510364 scopus 로고    scopus 로고
    • Recent ISO software enhancements and future software and modeling plans. Retrieved August 30, 2014
    • ONeill RP, Dautel T, Krall E (2011) Recent ISO software enhancements and future software and modeling plans. Retrieved August 30, 2014, from URL http://www.ferc.gov/industries/electric/indus-act/rto/rto-iso-soft-2011.pdf
    • (2011) from URL
    • ONeill, R.P.1    Dautel, T.2    Krall, E.3
  • 48
    • 84883599947 scopus 로고    scopus 로고
    • A model and approach to the challenge posed by optimal power systems planning
    • O’Neill RP, Krall EA, Hedman KW, Oren SS (2013) A model and approach to the challenge posed by optimal power systems planning. Math Program 140(2):239–266
    • (2013) Math Program , vol.140 , Issue.2 , pp. 239-266
    • O’Neill, R.P.1    Krall, E.A.2    Hedman, K.W.3    Oren, S.S.4
  • 49
    • 84880066582 scopus 로고    scopus 로고
    • Multiarea stochastic unit commitment for high wind penetration in a transmission constrained network
    • Papavasiliou A, Oren SS (2013) Multiarea stochastic unit commitment for high wind penetration in a transmission constrained network. Oper Res 61(3):578–592
    • (2013) Oper Res , vol.61 , Issue.3 , pp. 578-592
    • Papavasiliou, A.1    Oren, S.S.2
  • 50
    • 84881028803 scopus 로고    scopus 로고
    • Transmission planning under uncertainties of wind and load: sequential approximation approach
    • Park H, Baldick R (2013) Transmission planning under uncertainties of wind and load: sequential approximation approach. IEEE Trans Power Syst 28(3):2395–2402
    • (2013) IEEE Trans Power Syst , vol.28 , Issue.3 , pp. 2395-2402
    • Park, H.1    Baldick, R.2
  • 52
    • 84858059229 scopus 로고    scopus 로고
    • A combined deterministic and sampling-based sequential bounding method for stochastic programming. In: Proceedings of the 2011 winter simulation conference (Wsc)
    • Pierre-Louis P, Bayraksan G, Morton DP (2011) A combined deterministic and sampling-based sequential bounding method for stochastic programming. In: Proceedings of the 2011 winter simulation conference (Wsc), pp 4167–4178
    • (2011) pp 4167–4178
    • Pierre-Louis, P.1    Bayraksan, G.2    Morton, D.P.3
  • 53
    • 82855172402 scopus 로고    scopus 로고
    • Reduced network modeling of WECC as a market design prototype. In: IEEE Power and Energy Society General Meeting
    • Price JE, Goodin J (2011) Reduced network modeling of WECC as a market design prototype. In: IEEE Power and Energy Society General Meeting, pp 1–6
    • (2011) pp 1–6
    • Price, J.E.1    Goodin, J.2
  • 54
    • 84946510367 scopus 로고    scopus 로고
    • PSR Netplan Software (2012)
    • PSR Netplan Software (2012) URL http://www.psr-inc.com.br/portal/psr/servicos/modelos_de_apoio_a_decisao/studio_plan/netplan/
  • 55
    • 18944370802 scopus 로고    scopus 로고
    • Reinforcement scheduling convergence in power systems transmission planning
    • Reis FS, Carvalho P, Ferreira L (2005) Reinforcement scheduling convergence in power systems transmission planning. IEEE Trans Power Syst 20(2):1151–1157
    • (2005) IEEE Trans Power Syst , vol.20 , Issue.2 , pp. 1151-1157
    • Reis, F.S.1    Carvalho, P.2    Ferreira, L.3
  • 56
    • 0000514655 scopus 로고
    • Scenarios and policy aggregation in optimization under uncertainty
    • Rockafellar RT, Wets RJB (1991) Scenarios and policy aggregation in optimization under uncertainty. Math Oper Res 16(1):119–147
    • (1991) Math Oper Res , vol.16 , Issue.1 , pp. 119-147
    • Rockafellar, R.T.1    Wets, R.J.B.2
  • 57
    • 0028371606 scopus 로고
    • A hierarchical decomposition approach for transmission network expansion planning
    • Romero R, Monticelli A (1994) A hierarchical decomposition approach for transmission network expansion planning. IEEE Trans Power Syst 9(1):373–380
    • (1994) IEEE Trans Power Syst , vol.9 , Issue.1 , pp. 373-380
    • Romero, R.1    Monticelli, A.2
  • 58
    • 84893156958 scopus 로고    scopus 로고
    • Toward scalable, parallel progressive hedging for stochastic unit commitment. In: 2013 IEEE Power and Energy Society General Meeting (PES), pp 1–5
    • Ryan SM, Wets RJB, Woodruff DL, Silva-Monroy C, Watson JP (2013) Toward scalable, parallel progressive hedging for stochastic unit commitment. In: 2013 IEEE Power and Energy Society General Meeting (PES), pp 1–5, IEEE
    • (2013) IEEE
    • Ryan, S.M.1    Wets, R.J.B.2    Woodruff, D.L.3    Silva-Monroy, C.4    Watson, J.P.5
  • 59
    • 0035341667 scopus 로고    scopus 로고
    • A mixed integer linear programming model for transmission expansion planning with generation location selection
    • Samarakoon H, Shrestha R, Fujiwara O (2001) A mixed integer linear programming model for transmission expansion planning with generation location selection. Int J Electr Power Energy Syst 23(4):285–293
    • (2001) Int J Electr Power Energy Syst , vol.23 , Issue.4 , pp. 285-293
    • Samarakoon, H.1    Shrestha, R.2    Fujiwara, O.3
  • 60
    • 33847689868 scopus 로고    scopus 로고
    • Transmission network expansion planning considering uncertainty in demand
    • Silva I, Rider M, Romero R, Murari C (2006) Transmission network expansion planning considering uncertainty in demand. IEEE Trans Power Syst 21(4):1565–1573
    • (2006) IEEE Trans Power Syst , vol.21 , Issue.4 , pp. 1565-1573
    • Silva, I.1    Rider, M.2    Romero, R.3    Murari, C.4
  • 61
    • 0023349730 scopus 로고
    • Large sample properties of simulations using latin hypercube sampling
    • Stein M (1987) Large sample properties of simulations using latin hypercube sampling. Technometrics 29(2):143–151
    • (1987) Technometrics , vol.29 , Issue.2 , pp. 143-151
    • Stein, M.1
  • 62
    • 0035532141 scopus 로고    scopus 로고
    • Estimating the number of clusters in a data set via the gap statistic
    • Tibshirani R, Walther G, Hastie T (2001) Estimating the number of clusters in a data set via the gap statistic. J R Stat Soc Ser B Stat Methodol 63:411–423
    • (2001) J R Stat Soc Ser B Stat Methodol , vol.63 , pp. 411-423
    • Tibshirani, R.1    Walther, G.2    Hastie, T.3
  • 63
    • 84867723903 scopus 로고    scopus 로고
    • The economics of planning electricity transmission to accommodate renewables: using two-stage optimisation to evaluate flexibility and the cost of disregarding uncertainty
    • van der Weijde AH, Hobbs BF (2012) The economics of planning electricity transmission to accommodate renewables: using two-stage optimisation to evaluate flexibility and the cost of disregarding uncertainty. Energy Econ 34(6):2089–2101
    • (2012) Energy Econ , vol.34 , Issue.6 , pp. 2089-2101
    • van der Weijde, A.H.1    Hobbs, B.F.2
  • 64
    • 84946510369 scopus 로고    scopus 로고
    • VENTYX PROMOD IV Software (2014)
    • VENTYX PROMOD IV Software (2014) URL http://www.ventyx.com/en/enterprise/business-operations/business-products/promod-iv
  • 66
    • 84864520668 scopus 로고    scopus 로고
    • Pysp: modeling and solving stochastic programs in python
    • Watson JP, Woodruff D, Hart W (2012) Pysp: modeling and solving stochastic programs in python. Math Program Comput 4(2):109–149
    • (2012) Math Program Comput , vol.4 , Issue.2 , pp. 109-149
    • Watson, J.P.1    Woodruff, D.2    Hart, W.3
  • 67
    • 80053098461 scopus 로고    scopus 로고
    • Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems
    • Watson J, Woodruff D (2011) Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems. Comput Manag Sci 8(4):355–370
    • (2011) Comput Manag Sci , vol.8 , Issue.4 , pp. 355-370
    • Watson, J.1    Woodruff, D.2
  • 68
    • 84906504333 scopus 로고    scopus 로고
    • A new approach to model load levels in electric power systems with high renewable penetration
    • Wogrin S, Duenas P, Delgadillo A, Reneses J (2014) A new approach to model load levels in electric power systems with high renewable penetration. IEEE Trans Power Syst 29(5):2210–2218
    • (2014) IEEE Trans Power Syst , vol.29 , Issue.5 , pp. 2210-2218
    • Wogrin, S.1    Duenas, P.2    Delgadillo, A.3    Reneses, J.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.