Optimal Placing of Wind Turbines: Modelling the Uncertainty
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- 英文论文题名：Optimal Placing of Wind Turbines: Modelling the Uncertainty
- 论文作者：Timo Leenman ; Frank Phillipson
- 英文论文作者：Timo Leenman ; Frank Phillipson ; TNO
- 年：2015
- 作者机构：TNO,Delft,the Netherlands;
- 英文论文关键词：Optimizing energy generation ; wind turbines placement ; transportation losses ; optimization methods
- 会议召开时间：2015-03-01
- 会议录名称：Journal of Clean Energy Technologies Vol.3 No.2
- 语种：英文
- 分类号：TM614
- 学会代码：CDYA
- 学会名称：成都亚昂教育咨询有限公司
- 页数：15
- 文件大小：2150k
- 原文格式：D
摘要
When looking at the optimal place to locate a wind turbine, trade-offs have to be made between local placement and spreading: transmission loss favours local placements and the correlation between the stochastic productions of wind turbines favours spreading. In this paper steps are described to determine the locations of new wind mills that minimize energy loss on the High Voltage power grid. A vindication of the used power grid model is provided, the simulation procedure for stochastic wind power is described and the required mathematical optimization models are described as well as implemented. Results are shown and their relation to real life problems is discussed. The analysis leads to the observation that in reality the entire Dutch coast is popular to locate wind turbines but the only region where this leads to actual reduction of the losses is the North(Groningen and Friesland). Next to this, at the current share of wind energy in the total network load, a spreading strategy to reduce variance of total wind power production does not seem advisable. At higher penetration(30%or more) spreading will become important.
When looking at the optimal place to locate a wind turbine, trade-offs have to be made between local placement and spreading: transmission loss favours local placements and the correlation between the stochastic productions of wind turbines favours spreading. In this paper steps are described to determine the locations of new wind mills that minimize energy loss on the High Voltage power grid. A vindication of the used power grid model is provided, the simulation procedure for stochastic wind power is described and the required mathematical optimization models are described as well as implemented. Results are shown and their relation to real life problems is discussed. The analysis leads to the observation that in reality the entire Dutch coast is popular to locate wind turbines but the only region where this leads to actual reduction of the losses is the North(Groningen and Friesland). Next to this, at the current share of wind energy in the total network load, a spreading strategy to reduce variance of total wind power production does not seem advisable. At higher penetration(30%or more) spreading will become important.
When looking at the optimal place to locate a wind turbine, trade-offs have to be made between local placement and spreading: transmission loss favours local placements and the correlation between the stochastic productions of wind turbines favours spreading. In this paper steps are described to determine the locations of new wind mills that minimize energy loss on the High Voltage power grid. A vindication of the used power grid model is provided, the simulation procedure for stochastic wind power is described and the required mathematical optimization models are described as well as implemented. Results are shown and their relation to real life problems is discussed. The analysis leads to the observation that in reality the entire Dutch coast is popular to locate wind turbines but the only region where this leads to actual reduction of the losses is the North(Groningen and Friesland). Next to this, at the current share of wind energy in the total network load, a spreading strategy to reduce variance of total wind power production does not seem advisable. At higher penetration(30%or more) spreading will become important.
引文
[1]C.Ababei and R.Kavasseri,“Efficient network reconfiguration using minimum cost maximum flow-based branch exchanges and random walks-based loss estimations,”IEEE Transactions on Power Systems,vol.326,no.1,2011.
[2]M.E.Baran and F.F.Wu,“Network reconfiguration in distribution systems for loss reduction and load balancing,”IEEE Transactions on Power Delivery,vol.4,no.2,1989.
[3]R.S.Rao and S.V.L.Narasimham,“Optimal capacitor placement in a radial distribution system using plant growth simulation algorithm,”World Academy of Science,Engineering and Technology,vol.45,2008.
[4]C.Wang and M.H.Nehrir,“Analytical approaches for optimal placement of distributed generation sources in power systems,”IEEE Transactions on Power Systems,vol.19,no.4,2004.
[5]A.D.T.Le,M.A.Kashem,M.Negnevitsky,and G.Ledwich,“Optimal Distributed Generation parameters for reducing losses with economic consideration,”Research paper for the Australian Research Council,2007.
[6]V.H.M.Quezada,J.R.Abbad,and T.G.S.Roman,“Assessment of energy distribution losses for increasing penetration of Distributed Generation,”IEEE Transactions on Power Systems,vol.21,no.2,2006.
[7]N.N.Croes,“Impact of distributed energy generation on energy loss:Finding the optimal mix,”MSc thesis,University of Groningen and TNO,2011.
[8]N.Croes,F.Phillipson,and M.Schreuder,“Tactical congestion management:The optimal mix of decentralised generators in a district,”Integration of Renewables into the Distribution Grid,2012.
[9]G.A.Orfanos,P.S.Georgilakis,and N.D.Hatziargyriou,“Transmission Expansion Planning of Systems With Increasing Wind Power Integration,”2012.
[10]Z.Hu,X.Zhou,and W.T.Jewel,“Optimal generation expansion planning with integration of variable renewables and bulk energy storage systems,”in Proc.2013 1st IEEE Conference on Technologies for Sustainability(Sus Tech),2013,pp.1-8.
[11]E Y.Ivanova,N.I.Voropai,and E.Handschin,“A multi-criteria approach to expansion planning of wind power plants in electric power systems,”Power Tech,pp.1-4,2005.
[12]A.E.Feijoo,J.Cidras,and J.L.G.Dornelas,“Wind speed simulation in wind farms for steady-state security assessment of electrical power systems,”IEEE Transactions on Energy Conversions,vol.14,no.4,pp.1582-1588,1999.
[13]G.Papaefthymiou and B.Kloeckl,“MCMC for Wind Power Simulation,”IEEE Transactions on Energy Conversion,vol.23,no.1,2008.
[14]G.Carpinelli,G.Celli,F.Pilo,and A.Russo,“Distributed generation sizing and siting under uncertainty,”presented at IEEE Porto Power Tech Conference,2001.
[15]R.L.Y.Chen,“Models and Algorithms for Stochastic Network Design and Flow Problems:Applications in Truckload Procurement Auctions and Renewable Energy,”Ph D Thesis,University of Michigan,2010.
[16]C.Kraemer,K.Goldermann,C.Breue,P.Awate,and A.Moser,“Optimal positioning of renewable energy units,”Energy Tech.,pp.1-5,2013.
[17]K.Purchala,L.Meeus,D.Van Dommelen,and R.Belmans,“Usefulness of DC Power Flow for Active Power Flow Analysis,”in Proc.IEEE PES General Meeting,2005.
[18]D.Crevier,“Approximate Transmission Network Models for Use in Analysis and Design,”MIT Energy Laboratory Report,1972.
[19]R.K.Ahuja,T.L.Magnanti,and J.B.Orlin,Network Flows,Englewood Cliffs:Prentice-Hall,1993.
[20]P.Tseng and D.Bertsekas,“An-relaxation method for separable convex cost generalized network flow problems,”in Proc.the 5th International IPCO Conference,Vancouver,1996.
[21]B.Stott,J.Jardim,and O.Alsac,“DC Power Flow Revisited,”IEEE Transactions on Power Systems,vol.24,no.3,2009.
[22]D.Bertsimas and J.N.Tsitsiklis,Introduction to Linear Optimization,Athena Scientific,Belmont,Massachusetts,1997.
[23]R.A.Johnson and D.W.Wichern,Applied Multivariate Statistical Analysis,Prentice-Hall,Upper Saddle River,2007.
[24]D.R.Jensen,“Multivariate distributions having Weibull properties,”Journal of Multivariate Analysis,vol.9,pp.267-277,1979.
[25]D.R.Jensen,“A generalization of the multivariate Rayleigh distribution,”The Indian Journal of Statistics,vol.32,pp.193-208,1970.
[26]M.Steinbach,“Markowitz revisited:Mean-variance models in financial portfolio analysis,”SIAM Review,vol.43,pp.31-85,2001.
1 Capitals are used to represent complex quantities.
2 Here capitals represent normal real DC quantities.
3 Note that it is necessary that the balances sum up to zero,or,total power production equals total power consumption.This is because the DC power flow model assumes that no power losses occur.Power losses are neglected while computing the power flow solution.Afterwards,when the power flow solution has been computed,an estimate is made of the losses that have occurred.
4 Do not confuse this decision variable xi with the symbol xij or x,used in the previous chapter to denote line reactance.Notational conventions in power engineering demand the use of xij for reactance,and in mathematical programming it is customary to denote first stage decision variables by xi.
5 The scenario set S is a kind of finite discretization of the sample space Ω of M: in fact, the expectation in the objective function could have been written ∫_wΩ·(∑_(ij)eA(y_ij~w)~2r_ij)dw, whereas the approximation by introducing the scenario set S looks like ∑_xesp~x(∑_(ij)eA(y_ij~x)~2r_ij)
6 This is the choice made to produce the results in the next section.
7 The large supply at Beverwijk is explained by offshore wind farms at the height of Noord Holland.The large supplies at Maasvlakte and Geertruidenberg are explained by the large number of Combined Heat and Power(CHP)systems used by greenhouses and industry.Borssele is home to a nuclear power plant.
8 Note that this is purely theoretical because of the following.In our model extra DG power is compensated by decreasing supply of the original supply nodes.This choice was made in order to approximate the situation in which all commercial power plants in the country take equal share in the compensation.When the share of DG becomes too large,this approximation fails.
9 This concerns the HV grid:whether spreading strategies on a MV network scale would be desirable from a technical point of view,should be investigated in a different case study.
[2]M.E.Baran and F.F.Wu,“Network reconfiguration in distribution systems for loss reduction and load balancing,”IEEE Transactions on Power Delivery,vol.4,no.2,1989.
[3]R.S.Rao and S.V.L.Narasimham,“Optimal capacitor placement in a radial distribution system using plant growth simulation algorithm,”World Academy of Science,Engineering and Technology,vol.45,2008.
[4]C.Wang and M.H.Nehrir,“Analytical approaches for optimal placement of distributed generation sources in power systems,”IEEE Transactions on Power Systems,vol.19,no.4,2004.
[5]A.D.T.Le,M.A.Kashem,M.Negnevitsky,and G.Ledwich,“Optimal Distributed Generation parameters for reducing losses with economic consideration,”Research paper for the Australian Research Council,2007.
[6]V.H.M.Quezada,J.R.Abbad,and T.G.S.Roman,“Assessment of energy distribution losses for increasing penetration of Distributed Generation,”IEEE Transactions on Power Systems,vol.21,no.2,2006.
[7]N.N.Croes,“Impact of distributed energy generation on energy loss:Finding the optimal mix,”MSc thesis,University of Groningen and TNO,2011.
[8]N.Croes,F.Phillipson,and M.Schreuder,“Tactical congestion management:The optimal mix of decentralised generators in a district,”Integration of Renewables into the Distribution Grid,2012.
[9]G.A.Orfanos,P.S.Georgilakis,and N.D.Hatziargyriou,“Transmission Expansion Planning of Systems With Increasing Wind Power Integration,”2012.
[10]Z.Hu,X.Zhou,and W.T.Jewel,“Optimal generation expansion planning with integration of variable renewables and bulk energy storage systems,”in Proc.2013 1st IEEE Conference on Technologies for Sustainability(Sus Tech),2013,pp.1-8.
[11]E Y.Ivanova,N.I.Voropai,and E.Handschin,“A multi-criteria approach to expansion planning of wind power plants in electric power systems,”Power Tech,pp.1-4,2005.
[12]A.E.Feijoo,J.Cidras,and J.L.G.Dornelas,“Wind speed simulation in wind farms for steady-state security assessment of electrical power systems,”IEEE Transactions on Energy Conversions,vol.14,no.4,pp.1582-1588,1999.
[13]G.Papaefthymiou and B.Kloeckl,“MCMC for Wind Power Simulation,”IEEE Transactions on Energy Conversion,vol.23,no.1,2008.
[14]G.Carpinelli,G.Celli,F.Pilo,and A.Russo,“Distributed generation sizing and siting under uncertainty,”presented at IEEE Porto Power Tech Conference,2001.
[15]R.L.Y.Chen,“Models and Algorithms for Stochastic Network Design and Flow Problems:Applications in Truckload Procurement Auctions and Renewable Energy,”Ph D Thesis,University of Michigan,2010.
[16]C.Kraemer,K.Goldermann,C.Breue,P.Awate,and A.Moser,“Optimal positioning of renewable energy units,”Energy Tech.,pp.1-5,2013.
[17]K.Purchala,L.Meeus,D.Van Dommelen,and R.Belmans,“Usefulness of DC Power Flow for Active Power Flow Analysis,”in Proc.IEEE PES General Meeting,2005.
[18]D.Crevier,“Approximate Transmission Network Models for Use in Analysis and Design,”MIT Energy Laboratory Report,1972.
[19]R.K.Ahuja,T.L.Magnanti,and J.B.Orlin,Network Flows,Englewood Cliffs:Prentice-Hall,1993.
[20]P.Tseng and D.Bertsekas,“An-relaxation method for separable convex cost generalized network flow problems,”in Proc.the 5th International IPCO Conference,Vancouver,1996.
[21]B.Stott,J.Jardim,and O.Alsac,“DC Power Flow Revisited,”IEEE Transactions on Power Systems,vol.24,no.3,2009.
[22]D.Bertsimas and J.N.Tsitsiklis,Introduction to Linear Optimization,Athena Scientific,Belmont,Massachusetts,1997.
[23]R.A.Johnson and D.W.Wichern,Applied Multivariate Statistical Analysis,Prentice-Hall,Upper Saddle River,2007.
[24]D.R.Jensen,“Multivariate distributions having Weibull properties,”Journal of Multivariate Analysis,vol.9,pp.267-277,1979.
[25]D.R.Jensen,“A generalization of the multivariate Rayleigh distribution,”The Indian Journal of Statistics,vol.32,pp.193-208,1970.
[26]M.Steinbach,“Markowitz revisited:Mean-variance models in financial portfolio analysis,”SIAM Review,vol.43,pp.31-85,2001.
1 Capitals are used to represent complex quantities.
2 Here capitals represent normal real DC quantities.
3 Note that it is necessary that the balances sum up to zero,or,total power production equals total power consumption.This is because the DC power flow model assumes that no power losses occur.Power losses are neglected while computing the power flow solution.Afterwards,when the power flow solution has been computed,an estimate is made of the losses that have occurred.
4 Do not confuse this decision variable xi with the symbol xij or x,used in the previous chapter to denote line reactance.Notational conventions in power engineering demand the use of xij for reactance,and in mathematical programming it is customary to denote first stage decision variables by xi.
5 The scenario set S is a kind of finite discretization of the sample space Ω of M: in fact, the expectation in the objective function could have been written ∫_wΩ·(∑_(ij)eA(y_ij~w)~2r_ij)dw, whereas the approximation by introducing the scenario set S looks like ∑_xesp~x(∑_(ij)eA(y_ij~x)~2r_ij)
6 This is the choice made to produce the results in the next section.
7 The large supply at Beverwijk is explained by offshore wind farms at the height of Noord Holland.The large supplies at Maasvlakte and Geertruidenberg are explained by the large number of Combined Heat and Power(CHP)systems used by greenhouses and industry.Borssele is home to a nuclear power plant.
8 Note that this is purely theoretical because of the following.In our model extra DG power is compensated by decreasing supply of the original supply nodes.This choice was made in order to approximate the situation in which all commercial power plants in the country take equal share in the compensation.When the share of DG becomes too large,this approximation fails.
9 This concerns the HV grid:whether spreading strategies on a MV network scale would be desirable from a technical point of view,should be investigated in a different case study.