An efficient stochastic algorithm for mid-term scheduling of cascaded hydro systems
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摘要
Due to the stochastic and correlated attributes of natural inflows, the mid-term generation scheduling problem for cascaded hydro systems is a very challenging issue.This paper proposes a novel stochastic optimization algorithm using Latin hypercube sampling and Cholesky decomposition combined with scenario bundling and sensitivity analysis(LC-SB-SA) to address this problem.To deal with the uncertainty of natural inflows, Latin hypercube sampling is implemented to provide an adequate number of sampling scenarios efficiently, and Cholesky decomposition is introduced to describe the correlated natural inflows among cascaded stations.In addition, to overcome the difficulties in solving the objectives of all the scenarios, scenario bundling and sensitivity analysis algorithms are developed to improve the computational efficiency.Simulation results from both two-station and tenstation systems indicate that the proposed method has the merits in accuracy as well as calculation speed for the midterm cascaded hydro generation scheduling.The consideration of natural inflow correlation makes the formulated problem more realistic.
Due to the stochastic and correlated attributes of natural inflows, the mid-term generation scheduling problem for cascaded hydro systems is a very challenging issue.This paper proposes a novel stochastic optimization algorithm using Latin hypercube sampling and Cholesky decomposition combined with scenario bundling and sensitivity analysis(LC-SB-SA) to address this problem.To deal with the uncertainty of natural inflows, Latin hypercube sampling is implemented to provide an adequate number of sampling scenarios efficiently, and Cholesky decomposition is introduced to describe the correlated natural inflows among cascaded stations.In addition, to overcome the difficulties in solving the objectives of all the scenarios, scenario bundling and sensitivity analysis algorithms are developed to improve the computational efficiency.Simulation results from both two-station and tenstation systems indicate that the proposed method has the merits in accuracy as well as calculation speed for the midterm cascaded hydro generation scheduling.The consideration of natural inflow correlation makes the formulated problem more realistic.
Due to the stochastic and correlated attributes of natural inflows, the mid-term generation scheduling problem for cascaded hydro systems is a very challenging issue.This paper proposes a novel stochastic optimization algorithm using Latin hypercube sampling and Cholesky decomposition combined with scenario bundling and sensitivity analysis(LC-SB-SA) to address this problem.To deal with the uncertainty of natural inflows, Latin hypercube sampling is implemented to provide an adequate number of sampling scenarios efficiently, and Cholesky decomposition is introduced to describe the correlated natural inflows among cascaded stations.In addition, to overcome the difficulties in solving the objectives of all the scenarios, scenario bundling and sensitivity analysis algorithms are developed to improve the computational efficiency.Simulation results from both two-station and tenstation systems indicate that the proposed method has the merits in accuracy as well as calculation speed for the midterm cascaded hydro generation scheduling.The consideration of natural inflow correlation makes the formulated problem more realistic.
引文
[1]Arce A, Ohishi T, Soares S(2002)Optimal dispatch of generating units of the Itaipu hydroelectric plant. IEEE Trans Power Syst 17(1):154–158
[2]Wang J, Huang W, Ma G et al(2015)An improved partheno genetic algorithm for multi-objective economic dispatch in cascaded hydropower systems. Int J Electr Power Energy Syst67:591–597
[3]Quintana VH, Chikhani AY(1981)A stochastic model for midterm operation planning of hydro-thermal systems with random reservoir inflows. IEEE Trans Power App Syst PAS100(3):1119–1127
[4]Wang C, Zhou J, Lu P et al(2015)Long-term scheduling of large cascade hydropower stations in Jinsha River, China.Energy Convers Manag 90:476–487
[5]Yu Z, Sparrow FT, Bowen BH(1998)A new long-term hydro production scheduling method for maximizing the profit of hydroelectric systems. IEEE Trans Power Syst 13(1):66–71
[6]Zhao TTG, Zhao JS, Liu P et al(2015)Evaluating the marginal utility principle for long-term hydropower scheduling. Energy Convers Manag 106:213–223
[7]Zhao YJ, Chen X, Jia QS et al(2010)Long-term scheduling for cascaded hydro energy systems with annual water consumption and release constraints. IEEE Trans Auto Sci Eng 7(4):969–976
[8]Wu L, Shahidehpour M, Li ZY(2008)GENCO’s risk-constrained hydrothermal scheduling. IEEE Trans Power Syst23(4):1847–1858
[9]Wu L, Shahidehpour M(2011)Optimal coordination of stochastic hydro and natural gas supplies in midterm operation of power systems. IET Gener Transm Distrib 5(5):577–587
[10]Helseth A, Gjelsvik A, Mo B et al(2013)A model for optimal scheduling of hydro thermal systems including pumped-storage and wind power. IET Gener Transm Distrib 7(12):1426–1434
[11]Matos VL, Finardi EC(2012)A computational study of a stochastic optimization model for long term hydrothermal scheduling. Int J Electr Power Energy Syst 43(1):1443–1452
[12]Mahor A, Rangnekar S(2012)Short term generation scheduling of cascaded hydro electric system using novel self adaptive inertia weight PSO. Int J Electr Power Energy Syst 34:1–9
[13]Guedes LSM, Vieira DAG, Lisboa AC et al(2015)A continuous compact model for cascaded hydro-power generation and preventive maintenance scheduling. Int J Electr Power Energy Syst 73:702–710
[14]Mantawy AH, Soliman SA, El-Hawary ME(2013)The longterm hydro-scheduling problem—a new algorithm. Electr PowerSyst Res 64:67–72
[15]Li C, Yan R, Zhou J(1990)Stochastic optimization of interconnected multi-reservoir power systems. IEEE Trans Power Syst 5(4):1487–1496
[16]Sherkat VR, Campo R, Moslehi K et al(1985)Stochastic longterm hydrothermal optimization for a multireservoir system.IEEE Trans Power App Syst PAS 104(8):2040–2050
[17]Bruno HD, Marcelo AT, AndréLMM(2013)Parallel computing applied to the stochastic dynamic programming for long term operation planning of hydrothermal power systems. Eur J Oper Res 229(1):212–222
[18]Flach BC, Barroso LA, Pereira MVF(2010)Long-term optimal allocation of hydro generation for a price-maker company in a competitive market:latest developments and a stochastic dual dynamic programming approach. IET Gener Transm Distrib4(2):299–314
[19]Geoffrey P(2015)Stochastic inflow modeling for hydropower scheduling problems. Eur J Oper Res 246:496–504
[20]Pereira MVF, Pinto LMVG(1991)Multi-stage stochastic optimization applied to energy planning. Math Progr 52:359–375
[21]Baslis CG, Bakirtzis AG(2011)MMiidd--Tteerrmmssttoocchhaassttiiccsscchheedduull--ing of a price-maker hydro producer with pumped storage. IEEE Trans Power Syst 26(4):1856–1865
[22]Feng YH, Ryan SM(2014)Scenario reduction for stochastic unit commitment with wind penetration. In:Proceedings of IEEE PES general meeting, National Harbo, USA, 27–31 July2014, 5 pp
[23]Gil E, Aravena I, Cardenas R(2015)Generation capacity expansion planning under hydro uncertainty using stochastic mixed integer programming and scenario reduction. IEEE Trans Power Syst 30(4):1838–1847
[24]Pappala VS, Erlich I, Rohrig K et al(2009)A stochastic model for the optimal operation of a wind-thermal power system. IEEE Trans Power Syst 24(2):940–950
[25]Delgado C, Domínguez-Navarro JA(2014)Point estimate method for probabilistic load flow of an unbalanced power distribution system with correlated wind and solar sources. Int J Electr Power Energy Syst 61:267–278
[26]Pereira MVF, Oliveira GC, Costa CCG et al(1984)Stochastic streamflow models for hydroelectric systems. Water Resour Res20:379–390
[27]Xie M, Zhou J, Li C et al(2015)Long-term generation scheduling of Xiluodu and Xiangjiaba cascade hydro plants considering monthly streamflow forecasting error. Energy Convers Manage 105:368–376
[28]Li X, Li TJ, Wei JH et al(2014)Hydro unit commitment via mixedintegerlinearprogramming:acase study of the Three GorgesP roject,China. IEEE Trans Power Syst29(3):1232–1241
[29]Shukla A, Singh SN(2016)Clustering based unit commitment with wind power uncertainty. Energy Convers Manage111:89–102
[30]Díaz G, Casielles PG, Coto J(2014)Simulation of spatially correlated wind power in small geographic areas—sampling methods and evaluation. Int J Electr Power Energy Syst63:513–522
[31]Azizipanah-Abarghooee R, Niknam T, Malekpour M et al(2015)Optimal power flow based TU/CHP/PV/WPP coordination in view of wind speed, solar irradiance and load correlations. Energy Convers Manage 96:131–145
[32]Cooper HJ, Goodwin GC, Feuer A et al(2012)Design of scenarios for constrained stochastic optimization via vector quantization. In:Proceedings of American control conference,Montreal, USA, 27–29 June 2012, 5 pp
[33]Greene S, Dobson I, Alvarado FL(2002)Sensitivity of transfer capability margins with a fast formula. IEEE Trans Power Syst17(1):34–40
[34]Ge XL, Zhang LZ, Shu J et al(2014)Short-term hydropower optimal scheduling considering the optimization of water time delay. Electr Power Syst Res 110:188–197
[2]Wang J, Huang W, Ma G et al(2015)An improved partheno genetic algorithm for multi-objective economic dispatch in cascaded hydropower systems. Int J Electr Power Energy Syst67:591–597
[3]Quintana VH, Chikhani AY(1981)A stochastic model for midterm operation planning of hydro-thermal systems with random reservoir inflows. IEEE Trans Power App Syst PAS100(3):1119–1127
[4]Wang C, Zhou J, Lu P et al(2015)Long-term scheduling of large cascade hydropower stations in Jinsha River, China.Energy Convers Manag 90:476–487
[5]Yu Z, Sparrow FT, Bowen BH(1998)A new long-term hydro production scheduling method for maximizing the profit of hydroelectric systems. IEEE Trans Power Syst 13(1):66–71
[6]Zhao TTG, Zhao JS, Liu P et al(2015)Evaluating the marginal utility principle for long-term hydropower scheduling. Energy Convers Manag 106:213–223
[7]Zhao YJ, Chen X, Jia QS et al(2010)Long-term scheduling for cascaded hydro energy systems with annual water consumption and release constraints. IEEE Trans Auto Sci Eng 7(4):969–976
[8]Wu L, Shahidehpour M, Li ZY(2008)GENCO’s risk-constrained hydrothermal scheduling. IEEE Trans Power Syst23(4):1847–1858
[9]Wu L, Shahidehpour M(2011)Optimal coordination of stochastic hydro and natural gas supplies in midterm operation of power systems. IET Gener Transm Distrib 5(5):577–587
[10]Helseth A, Gjelsvik A, Mo B et al(2013)A model for optimal scheduling of hydro thermal systems including pumped-storage and wind power. IET Gener Transm Distrib 7(12):1426–1434
[11]Matos VL, Finardi EC(2012)A computational study of a stochastic optimization model for long term hydrothermal scheduling. Int J Electr Power Energy Syst 43(1):1443–1452
[12]Mahor A, Rangnekar S(2012)Short term generation scheduling of cascaded hydro electric system using novel self adaptive inertia weight PSO. Int J Electr Power Energy Syst 34:1–9
[13]Guedes LSM, Vieira DAG, Lisboa AC et al(2015)A continuous compact model for cascaded hydro-power generation and preventive maintenance scheduling. Int J Electr Power Energy Syst 73:702–710
[14]Mantawy AH, Soliman SA, El-Hawary ME(2013)The longterm hydro-scheduling problem—a new algorithm. Electr PowerSyst Res 64:67–72
[15]Li C, Yan R, Zhou J(1990)Stochastic optimization of interconnected multi-reservoir power systems. IEEE Trans Power Syst 5(4):1487–1496
[16]Sherkat VR, Campo R, Moslehi K et al(1985)Stochastic longterm hydrothermal optimization for a multireservoir system.IEEE Trans Power App Syst PAS 104(8):2040–2050
[17]Bruno HD, Marcelo AT, AndréLMM(2013)Parallel computing applied to the stochastic dynamic programming for long term operation planning of hydrothermal power systems. Eur J Oper Res 229(1):212–222
[18]Flach BC, Barroso LA, Pereira MVF(2010)Long-term optimal allocation of hydro generation for a price-maker company in a competitive market:latest developments and a stochastic dual dynamic programming approach. IET Gener Transm Distrib4(2):299–314
[19]Geoffrey P(2015)Stochastic inflow modeling for hydropower scheduling problems. Eur J Oper Res 246:496–504
[20]Pereira MVF, Pinto LMVG(1991)Multi-stage stochastic optimization applied to energy planning. Math Progr 52:359–375
[21]Baslis CG, Bakirtzis AG(2011)MMiidd--Tteerrmmssttoocchhaassttiiccsscchheedduull--ing of a price-maker hydro producer with pumped storage. IEEE Trans Power Syst 26(4):1856–1865
[22]Feng YH, Ryan SM(2014)Scenario reduction for stochastic unit commitment with wind penetration. In:Proceedings of IEEE PES general meeting, National Harbo, USA, 27–31 July2014, 5 pp
[23]Gil E, Aravena I, Cardenas R(2015)Generation capacity expansion planning under hydro uncertainty using stochastic mixed integer programming and scenario reduction. IEEE Trans Power Syst 30(4):1838–1847
[24]Pappala VS, Erlich I, Rohrig K et al(2009)A stochastic model for the optimal operation of a wind-thermal power system. IEEE Trans Power Syst 24(2):940–950
[25]Delgado C, Domínguez-Navarro JA(2014)Point estimate method for probabilistic load flow of an unbalanced power distribution system with correlated wind and solar sources. Int J Electr Power Energy Syst 61:267–278
[26]Pereira MVF, Oliveira GC, Costa CCG et al(1984)Stochastic streamflow models for hydroelectric systems. Water Resour Res20:379–390
[27]Xie M, Zhou J, Li C et al(2015)Long-term generation scheduling of Xiluodu and Xiangjiaba cascade hydro plants considering monthly streamflow forecasting error. Energy Convers Manage 105:368–376
[28]Li X, Li TJ, Wei JH et al(2014)Hydro unit commitment via mixedintegerlinearprogramming:acase study of the Three GorgesP roject,China. IEEE Trans Power Syst29(3):1232–1241
[29]Shukla A, Singh SN(2016)Clustering based unit commitment with wind power uncertainty. Energy Convers Manage111:89–102
[30]Díaz G, Casielles PG, Coto J(2014)Simulation of spatially correlated wind power in small geographic areas—sampling methods and evaluation. Int J Electr Power Energy Syst63:513–522
[31]Azizipanah-Abarghooee R, Niknam T, Malekpour M et al(2015)Optimal power flow based TU/CHP/PV/WPP coordination in view of wind speed, solar irradiance and load correlations. Energy Convers Manage 96:131–145
[32]Cooper HJ, Goodwin GC, Feuer A et al(2012)Design of scenarios for constrained stochastic optimization via vector quantization. In:Proceedings of American control conference,Montreal, USA, 27–29 June 2012, 5 pp
[33]Greene S, Dobson I, Alvarado FL(2002)Sensitivity of transfer capability margins with a fast formula. IEEE Trans Power Syst17(1):34–40
[34]Ge XL, Zhang LZ, Shu J et al(2014)Short-term hydropower optimal scheduling considering the optimization of water time delay. Electr Power Syst Res 110:188–197