考虑负荷和风电随机变化的电力系统概率最优潮流问题研究
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摘要
最优潮流是一种电力系统分析和优化的有效工具,在系统的安全运行、经济调度、可靠性分析、能量管理以及电力定价等方面得到了广泛的应用。在电力市场环境下,最优潮流不仅能为电力市场运营者提供最优决策,而且使这一决策过程更透明、更公平,因此在电力市场的阻塞管理、负荷管理,以及实时电价、无功定价、输电定价和可用传输能力等方面得到了广泛应用。以往的最优潮流分析方法大多基于确定的网络拓扑结构、系统元件参数及运行条件,然而,严格来说,上述各量是不确定或随机变化的,另外,具有随机性的风力发电在电力系统中不断涌现,也使系统中的不确定因素呈加剧趋势,这些不确定因素均对电力系统最优潮流分析提出新的挑战。本论文探讨了考虑负荷和风电随机变化的电力系统概率最优潮流问题,具体内容如下:
首先,对现有概率潮流算法进行比较,通过分析节点注入量互相关性对概率潮流解的影响,表明概率潮流分析时应当计及现实存在的注入量之间的互相关性。介绍了一次二阶矩法、计及协方差修正的线性化概率潮流、计及协方差修正的近似二阶概率潮流和两点估计法的基本理论,确定了节点注入量相互独立和互相关时各种算法的计算模型以及计算步骤。运用几种概率潮流算法在24节点系统上进行验证,并将各个算法的概率潮流解与相应的蒙特卡罗模拟解进行比较,结果表明,考虑协方差修正的近似二阶模型具有更高的准确度,但比其它算法耗费更多CPU时间。通过分析注入量互相关性对概率潮流解的影响,表明概率潮流分析时应当计及现实存在的注入量之间的相关性,否则会使结果产生较大误差。该部分内容不仅为其他研究者在选择概率潮流算法时提供参考,而且为在概率潮流分析中考虑节点注入量的互相关性提供了依据。
其次,针对风电随风速随机变化的特点,提出一种考虑无功功率—滑差特性的风电概率模型,进而采用概率潮流状态变量和异步机滑差联合迭代方法,进行含风电场电力系统概率潮流研究。该风电概率模型考虑风速的随机性,将风机输出的随机有功功率和吸收的随机无功功率描述为电压幅值、异步机的滑差和风轮机的电路参数的函数;联合迭代方法中,异步风力发电机的滑差作为新的修正量被引入,使用牛顿-拉夫逊方法求解关于潮流状态变量和滑差的联合迭代,因而迭代过程保持了牛顿-拉夫逊方法的平方收敛性。算例中假定风速服从Weibull分布,负荷服从正态分布,使用蒙特卡罗模拟方法对一经过修改的IEEE-14测试系统进行概率潮流计算,结果表明了所提方法的有效性;对风电场容量在系统中的不同比例进行分析,表明不适当的风电场容量会导致异常的概率潮流状况。
第三,引用一种基于次微分的半光滑Levenberg-Marquardt(L-M)方法,成功实现了最优潮流的求解问题。在利用非线性互补函数将OPF模型的KKT条件转化为半光滑非线性代数方程组后,采用基于次微分的半光滑L-M法求解,该方法属于牛顿法范畴,可通过对L-M参数的调整保证迭代系数矩阵的正定性,克服了系数矩阵的奇异引起的“病态”,且该方法在确定搜索方向时只需求解线性系统的近似解,适用于大规模系统的求解。算例中对Kojima-Shindo问题的分析表明,该方法能够用来求解半光滑方程组;也对电力系统算例的进行仿真,从收敛特性和计算精度方面对IEEE测试系统进行分析,结果表明了方法的有效性。
第四,考虑到系统参数的不确定性对系统优化的结果产生重要影响,运用一次二阶矩法来计及相关负荷的不确定性进行概率最优潮流分析。将概率最优潮流表述为随机非线性规划问题后,利用非线性互补函数将该问题的KKT条件进行转化,基于转化后的非线性代数方程组,利用一次二阶矩法确定了以待求量的数字特征表示的概率最优潮流模型,由于该模型包含不光滑函数,因此采用基于次微分的半光滑L-M方法求解。对五节点系统、IEEE-30和IEEE-118系统的算例分析中,将结果与两点估计法和蒙特卡罗模拟方法比较,表明所提方法具有较快的计算速度,而且与不确定变量的数目多少关系不大,故优于两点估计法和蒙特卡罗模拟方法;当没有输电阻塞发生时,所提方法显示了良好的计算性能;若发生输电阻塞,则将引起节点实时电价剧增,此时所提方法无法详细描述实时电价的PDF曲线。
最后,面对大量风电机组接入电力系统加剧了系统运行状况的不确定性问题,运用一次二阶矩法来计及风电的随机性,进行含风电场电力系统概率最优潮流研究。概率最优潮流模型中,风电场采用考虑无功功率—滑差特性的风电概率模型,不等式约束中除了机组出力约束、有载调压变压器变比约束、电压约束和支路电流约束,也考虑了风电场无功补偿容量约束、系统的分钟级爬坡能力约束;使用非线性互补函数将概率最优潮流的KKT条件转化为一组包含有不光滑函数的非线性代数方程组,然后基于一次二阶矩法确定了以待求量的数字特征表示的POPF模型,由于该模型包含不光滑函数,因此采用基于次微分的半光滑牛顿型方法求解。对修改的IEEE-30节点系统进行分析,与蒙特卡罗模拟方法进行比较,显示了所提方法良好的计算性能;结果也表明,适当的风电场容量可以节省系统燃料成本,且成本与节点实时电价的变化与理论分析是一致的,然而,随着风电场容量的增加,风电导致的可靠性成本越来越高,风电的价值也越来越小。
The optimal power flow (OPF), considering the system economical efficiency and security, has been commonly used as an efficient method in the power system analysis and optimization. It is applied widely in power system safety operation, the economic operation, reliability analysis, energy and power management and electricity price, etc. In the environment of power market, OPF not only provide the optimal decision for power market operator and make a decision process more transparent and more fair, so it is also applied widely in power market congestion management, load management, spot price, reactive power pricing and available transfer capability etc. The previous OPF methods are mostly based on the determinate network topological structure, the system component parameters and operation conditions. However, the quantities above mentioned are uncertain or random. In addition, the more and more random wind powers are connected into power system. It makes the uncertainties of system increase continually and the uncertainties bright the new challenges to the OPF analysis. The probabilistic optimal power flow (POPF) problem considering the random variation of load and wind farm output is researched in the dissertation. The main contents of the dissertation are as follows:
Firstly, the probabilistic load flow (PLF) calculation methods are researched and compared. The influence of the correlated nodal injections on the PLF is researched. Results show that the correlation among nodal injections should be considered in PLF analysis. It is introduced for the basic theory of the first-order second-moment method (FOSMM), the linearized model, the approximate second order model considering the correction of covariance and the two-point estimate method (2PEM), and it is determined for the calculation models and steps of the methods with the assumption of the independent and correlated nodal injections. The methods are verified on a 24-bus system. The results obtained from the methods are compared against more accurate results obtained from Monte Carlo simulation (MCS). Numerical results show that the approximate second order model is more accurate than the other algorithms with higher computation burden. The influence of the correlation on the PLF is demonstrated, which shows the correlation among nodal injections should be considered in PLF analysis. The errors will increase if ignoring the influence. The contents not only can be for reference for other researchers when selecting the PLF methods, but also provide the basis for considering the correlation among nodal injections in PLF analysis.
Secondly, due to wind power outputs varying with random wind, a probabilistic wind farm model considering the reactive power-slip characteristic is proposed. Then, a combined iteration method for the PLF state variables and the slip, applied to grid-connected induction wind power system, is presented. In the probabilistic model for wind farm, the uncertainties of wind speed is takes into account, and the real power injected and reactive power absorbed by the wind turbine are described as the function of the voltage magnitude, the slip of the induction machine and the circuit parameters of the wind turbines. In the unified iteration method, the slip of induction machine is introduced as the new correction value. The Newton-Raphson algorithm is used to solve the unified iteration of state variable and slip. Thus, the proposed method retains the quadratic convergence of the Newton-Raphson algorithm. With wind speed described as Weibull probability density function (PDF) and load described as normal distribution, the PLF is performed on the modified IEEE 14-bus system using MCS method. The results show the effectiveness of the proposed method, and show that the appropriate wind power capacity can improve the voltage profile. The different ratio of wind farm capacity with respect to the system overall real power load is researched. The results show that inappropriate wind farm capacity can lead to the exceptional power flow results.
Thirdly, based on the subdifferential, a semismooth Levenberg-Marquardt (L-M) method is successfully used to solve and the OPF problem. By introducing the nonlinear complementarity problem (NCP) function, the Karush-Kuhn-Tucker (KKT) conditions of OPF model are transformed equivalently into a set of semismooth nonlinear algebraic equations. Then the set of semismooth equations can be solved by a semismooth L-M method based on the subdifferential. The method belongs to Newton-type method. It can ensure the positive defmitiveness of the iterative coefficient matrix by using the L-M parameter, which avoids the ill-conditioning of iterative equations. The method, requiring only the approximate solution of a linear system at each iteration, is quite applicable to the large-scale cases. The feasibility of the proposed method for solving the nondifferentiable problem is verified on Kojima-Shindo problem, and the effectiveness of the proposed method is demonstrated by analyzing the convergence characteristic and computational precision of the method on the IEEE test systems.
Fourthly, owing to the impact of uncertain parameters on the system optimization results, a POPF algorithm based on the FOSMM is presented considering the uncertainty of correlated load. The POPF is first shown as the stochastic nonlinear programming problem. By introducing the NCP function, the KKT conditions of POPF system are transformed equivalently. Based on the transformed nonsmooth nonlinear algebraic equations, the FOSMM is used to determine the POPF model expressed by the numerical characteristic of variables. The model includes nonsmooth functions, so it can be solved by a semismooth L-M method based on the subdifferential. The proposed algorithm is verified by three test systems, i.e., the five-bus system, IEEE 30-bus and 118-bus systems. Results are compared with the 2PEM and MCS method. The proposed method has minor computational expense regardless of the number of uncertain variables and is computationally faster than the 2PEM and MCS method. The proposed method shows good performance when no line current is at its limit. If the case appears, the proposed method may not provide the explicit PDF curves of spot prices due to the exceptional spot prices caused by the congestion.
Finally, facing the increasing uncertain problem of system operation condition brought by more and more wind farms connected directly into power grid, the POPF calculation for grid-connected induction wind power system is researched, and the uncertainty of wind power is considered by the FOSMM. In the POPF model, wind farm is modeled by the probabilistic wind farm model considering the reactive power-slip characteristic, and the inequality constraints include not only the unit output constraints, the ratio constraints, the voltage constraints and the line current constraints but also the reactive compensation capacity constraints in wind farm and the system climbing capacity constraints per minute. By introducing the NCP function, the KKT conditions of POPF system are transformed equivalently. Based on the transformed nonsmooth nonlinear algebraic equations, the FOSMM is used to determine the POPF model expressed by the numerical characteristic of variables. The model includes nonsmooth functions, so it can be solved by a semismooth Newton-type method based on the subdifferential. The proposed algorithm is verified by the modified IEEE 30-bus system. Compared with the MCS method, the proposed method shows good performance. Results also show that the appropriate wind farm capacity can save the system fuel cost, and the changements of the costs and nodal spot prices keep the reasonable agreement with related theories. However, with the increasement of wind farm capacity, the reliability cost caused by wind power grows higher and higher and wind power value grows smaller and smaller.
首先,对现有概率潮流算法进行比较,通过分析节点注入量互相关性对概率潮流解的影响,表明概率潮流分析时应当计及现实存在的注入量之间的互相关性。介绍了一次二阶矩法、计及协方差修正的线性化概率潮流、计及协方差修正的近似二阶概率潮流和两点估计法的基本理论,确定了节点注入量相互独立和互相关时各种算法的计算模型以及计算步骤。运用几种概率潮流算法在24节点系统上进行验证,并将各个算法的概率潮流解与相应的蒙特卡罗模拟解进行比较,结果表明,考虑协方差修正的近似二阶模型具有更高的准确度,但比其它算法耗费更多CPU时间。通过分析注入量互相关性对概率潮流解的影响,表明概率潮流分析时应当计及现实存在的注入量之间的相关性,否则会使结果产生较大误差。该部分内容不仅为其他研究者在选择概率潮流算法时提供参考,而且为在概率潮流分析中考虑节点注入量的互相关性提供了依据。
其次,针对风电随风速随机变化的特点,提出一种考虑无功功率—滑差特性的风电概率模型,进而采用概率潮流状态变量和异步机滑差联合迭代方法,进行含风电场电力系统概率潮流研究。该风电概率模型考虑风速的随机性,将风机输出的随机有功功率和吸收的随机无功功率描述为电压幅值、异步机的滑差和风轮机的电路参数的函数;联合迭代方法中,异步风力发电机的滑差作为新的修正量被引入,使用牛顿-拉夫逊方法求解关于潮流状态变量和滑差的联合迭代,因而迭代过程保持了牛顿-拉夫逊方法的平方收敛性。算例中假定风速服从Weibull分布,负荷服从正态分布,使用蒙特卡罗模拟方法对一经过修改的IEEE-14测试系统进行概率潮流计算,结果表明了所提方法的有效性;对风电场容量在系统中的不同比例进行分析,表明不适当的风电场容量会导致异常的概率潮流状况。
第三,引用一种基于次微分的半光滑Levenberg-Marquardt(L-M)方法,成功实现了最优潮流的求解问题。在利用非线性互补函数将OPF模型的KKT条件转化为半光滑非线性代数方程组后,采用基于次微分的半光滑L-M法求解,该方法属于牛顿法范畴,可通过对L-M参数的调整保证迭代系数矩阵的正定性,克服了系数矩阵的奇异引起的“病态”,且该方法在确定搜索方向时只需求解线性系统的近似解,适用于大规模系统的求解。算例中对Kojima-Shindo问题的分析表明,该方法能够用来求解半光滑方程组;也对电力系统算例的进行仿真,从收敛特性和计算精度方面对IEEE测试系统进行分析,结果表明了方法的有效性。
第四,考虑到系统参数的不确定性对系统优化的结果产生重要影响,运用一次二阶矩法来计及相关负荷的不确定性进行概率最优潮流分析。将概率最优潮流表述为随机非线性规划问题后,利用非线性互补函数将该问题的KKT条件进行转化,基于转化后的非线性代数方程组,利用一次二阶矩法确定了以待求量的数字特征表示的概率最优潮流模型,由于该模型包含不光滑函数,因此采用基于次微分的半光滑L-M方法求解。对五节点系统、IEEE-30和IEEE-118系统的算例分析中,将结果与两点估计法和蒙特卡罗模拟方法比较,表明所提方法具有较快的计算速度,而且与不确定变量的数目多少关系不大,故优于两点估计法和蒙特卡罗模拟方法;当没有输电阻塞发生时,所提方法显示了良好的计算性能;若发生输电阻塞,则将引起节点实时电价剧增,此时所提方法无法详细描述实时电价的PDF曲线。
最后,面对大量风电机组接入电力系统加剧了系统运行状况的不确定性问题,运用一次二阶矩法来计及风电的随机性,进行含风电场电力系统概率最优潮流研究。概率最优潮流模型中,风电场采用考虑无功功率—滑差特性的风电概率模型,不等式约束中除了机组出力约束、有载调压变压器变比约束、电压约束和支路电流约束,也考虑了风电场无功补偿容量约束、系统的分钟级爬坡能力约束;使用非线性互补函数将概率最优潮流的KKT条件转化为一组包含有不光滑函数的非线性代数方程组,然后基于一次二阶矩法确定了以待求量的数字特征表示的POPF模型,由于该模型包含不光滑函数,因此采用基于次微分的半光滑牛顿型方法求解。对修改的IEEE-30节点系统进行分析,与蒙特卡罗模拟方法进行比较,显示了所提方法良好的计算性能;结果也表明,适当的风电场容量可以节省系统燃料成本,且成本与节点实时电价的变化与理论分析是一致的,然而,随着风电场容量的增加,风电导致的可靠性成本越来越高,风电的价值也越来越小。
The optimal power flow (OPF), considering the system economical efficiency and security, has been commonly used as an efficient method in the power system analysis and optimization. It is applied widely in power system safety operation, the economic operation, reliability analysis, energy and power management and electricity price, etc. In the environment of power market, OPF not only provide the optimal decision for power market operator and make a decision process more transparent and more fair, so it is also applied widely in power market congestion management, load management, spot price, reactive power pricing and available transfer capability etc. The previous OPF methods are mostly based on the determinate network topological structure, the system component parameters and operation conditions. However, the quantities above mentioned are uncertain or random. In addition, the more and more random wind powers are connected into power system. It makes the uncertainties of system increase continually and the uncertainties bright the new challenges to the OPF analysis. The probabilistic optimal power flow (POPF) problem considering the random variation of load and wind farm output is researched in the dissertation. The main contents of the dissertation are as follows:
Firstly, the probabilistic load flow (PLF) calculation methods are researched and compared. The influence of the correlated nodal injections on the PLF is researched. Results show that the correlation among nodal injections should be considered in PLF analysis. It is introduced for the basic theory of the first-order second-moment method (FOSMM), the linearized model, the approximate second order model considering the correction of covariance and the two-point estimate method (2PEM), and it is determined for the calculation models and steps of the methods with the assumption of the independent and correlated nodal injections. The methods are verified on a 24-bus system. The results obtained from the methods are compared against more accurate results obtained from Monte Carlo simulation (MCS). Numerical results show that the approximate second order model is more accurate than the other algorithms with higher computation burden. The influence of the correlation on the PLF is demonstrated, which shows the correlation among nodal injections should be considered in PLF analysis. The errors will increase if ignoring the influence. The contents not only can be for reference for other researchers when selecting the PLF methods, but also provide the basis for considering the correlation among nodal injections in PLF analysis.
Secondly, due to wind power outputs varying with random wind, a probabilistic wind farm model considering the reactive power-slip characteristic is proposed. Then, a combined iteration method for the PLF state variables and the slip, applied to grid-connected induction wind power system, is presented. In the probabilistic model for wind farm, the uncertainties of wind speed is takes into account, and the real power injected and reactive power absorbed by the wind turbine are described as the function of the voltage magnitude, the slip of the induction machine and the circuit parameters of the wind turbines. In the unified iteration method, the slip of induction machine is introduced as the new correction value. The Newton-Raphson algorithm is used to solve the unified iteration of state variable and slip. Thus, the proposed method retains the quadratic convergence of the Newton-Raphson algorithm. With wind speed described as Weibull probability density function (PDF) and load described as normal distribution, the PLF is performed on the modified IEEE 14-bus system using MCS method. The results show the effectiveness of the proposed method, and show that the appropriate wind power capacity can improve the voltage profile. The different ratio of wind farm capacity with respect to the system overall real power load is researched. The results show that inappropriate wind farm capacity can lead to the exceptional power flow results.
Thirdly, based on the subdifferential, a semismooth Levenberg-Marquardt (L-M) method is successfully used to solve and the OPF problem. By introducing the nonlinear complementarity problem (NCP) function, the Karush-Kuhn-Tucker (KKT) conditions of OPF model are transformed equivalently into a set of semismooth nonlinear algebraic equations. Then the set of semismooth equations can be solved by a semismooth L-M method based on the subdifferential. The method belongs to Newton-type method. It can ensure the positive defmitiveness of the iterative coefficient matrix by using the L-M parameter, which avoids the ill-conditioning of iterative equations. The method, requiring only the approximate solution of a linear system at each iteration, is quite applicable to the large-scale cases. The feasibility of the proposed method for solving the nondifferentiable problem is verified on Kojima-Shindo problem, and the effectiveness of the proposed method is demonstrated by analyzing the convergence characteristic and computational precision of the method on the IEEE test systems.
Fourthly, owing to the impact of uncertain parameters on the system optimization results, a POPF algorithm based on the FOSMM is presented considering the uncertainty of correlated load. The POPF is first shown as the stochastic nonlinear programming problem. By introducing the NCP function, the KKT conditions of POPF system are transformed equivalently. Based on the transformed nonsmooth nonlinear algebraic equations, the FOSMM is used to determine the POPF model expressed by the numerical characteristic of variables. The model includes nonsmooth functions, so it can be solved by a semismooth L-M method based on the subdifferential. The proposed algorithm is verified by three test systems, i.e., the five-bus system, IEEE 30-bus and 118-bus systems. Results are compared with the 2PEM and MCS method. The proposed method has minor computational expense regardless of the number of uncertain variables and is computationally faster than the 2PEM and MCS method. The proposed method shows good performance when no line current is at its limit. If the case appears, the proposed method may not provide the explicit PDF curves of spot prices due to the exceptional spot prices caused by the congestion.
Finally, facing the increasing uncertain problem of system operation condition brought by more and more wind farms connected directly into power grid, the POPF calculation for grid-connected induction wind power system is researched, and the uncertainty of wind power is considered by the FOSMM. In the POPF model, wind farm is modeled by the probabilistic wind farm model considering the reactive power-slip characteristic, and the inequality constraints include not only the unit output constraints, the ratio constraints, the voltage constraints and the line current constraints but also the reactive compensation capacity constraints in wind farm and the system climbing capacity constraints per minute. By introducing the NCP function, the KKT conditions of POPF system are transformed equivalently. Based on the transformed nonsmooth nonlinear algebraic equations, the FOSMM is used to determine the POPF model expressed by the numerical characteristic of variables. The model includes nonsmooth functions, so it can be solved by a semismooth Newton-type method based on the subdifferential. The proposed algorithm is verified by the modified IEEE 30-bus system. Compared with the MCS method, the proposed method shows good performance. Results also show that the appropriate wind farm capacity can save the system fuel cost, and the changements of the costs and nodal spot prices keep the reasonable agreement with related theories. However, with the increasement of wind farm capacity, the reliability cost caused by wind power grows higher and higher and wind power value grows smaller and smaller.
引文
[1]周双喜,朱凌志,郭锡玖等.电力系统电压稳定性及其控制[M].北京:中国电力出版社,2004.
[2]李文沅.电力系统安全经济运行——模型与算法[M].重庆:重庆大学出版社,1998:74-76.
[3]J.Carpentier.Contribution to the economic dispatch problem[J].Bull.Soc.France Elect,1962,8:431-447.
[4]赵风云,王秀丽.输配电市场[M].北京:中国电力出版社,2003.
[5]陈树勇,戴慧珠,白晓明,等.风电场的发电可靠性模型及其应用[J].中国电机工程学报,2000,20(3):26-29.
[6]B.Borkowska.Probabilistic load flow[J].IEEE Trans.on Power Apparatus and Systems,1974,93(3):752-755.
[7]M.Sobierajski,Wroclaw.A method of stochastic load flow calculation[J].Archiv Fur Elektrotechnik,1978,60(1):37-40.
[8]G.T.Heydt.Stochastic Power Flow Calculations[C].IEEE Summer Power Meeting,San Francisco,CA,July,1975.
[9]P.W.Sauer,G.T.Heydt.A generalized stochastic power flow algorithms[C].IEEE Summer Meeting,Los Angeles.CA.July,1978.
[10]J.F.Dopazo,O.A.Klitin,A.M.Sasson.Stochastic load flows[J].IEEE Trans.on Power Apparatus and Systems,1975,94(2):299-309.
[11]A.P.Meliopoulos,A.G.Bakirtais,R.Kovacs.Power System Reliability Evaluation Using Stochastic Load Flows[J].IEEE Trans.on Power Apparatus and Systems,1984,103(5):1084-1091.
[12]R.N.Allan,M.R.G.Al-Shakarchi.Probabilistic techniques in AC load flow analysis[J].Proceedings of the Institution of Electrical Engineering,1977,124(2):154-160.
[13]A.M.Leite da Silva,V.L.Arienti,R.N.Allan.Probabilistic Load Flow Considering Dependence Between Input Nodal Powers[J].IEEE Trans.on Power Apparatus and Systems,1984,103(6):1524-1530.
[14]A.M.Leite da Silva,V.L.Arienti.Probabilistic load flow by a multilinear simulation algorithm[J].Proc.Inst.Elect.Eng.C:Generation,Transmission,Distribution,1990,137(4):276-282.
[15]A.M.Leite da Silva,S.M.P.Ribeiro,V.L.Arienti,et al.Probabilistic load flow techniques applied to power system expansion planning[J].IEEE Trans.Power Systems,1990,5(4):1047-1053.
[16]R.N.Allan,A.M.L.da Silva,R.C.Burchett.Evaluation methods and accuracy in probabilistic load flow solutions[J].IEEE Trans.on Power Apparatus and Systems,1981,100(5):2539-2546.
[17]X.Li,X.Chen,X.Yin,et al.The algorithm of probabilistic power flow retaining non-linearity[C].Proc.Int.Conf.Power System Technology,Kunming,China,2002.
[18]丁明,李生虎,黄凯.基于蒙特卡罗模拟的概率潮流计算[J].电网技术,2001,25(11):10-14,22.
[19]P.Zhang,S.T.Lee.Probabilistic load flow computation using the method of combined cumulants and Gram-Charlier expansion[J].IEEE Trans.on Power Systems,2004,19(1):676-682.
[20]林海源.交流模型下电力系统概率潮流计算[J].电力自动化设备,2006,26(6):53-56.
[21]C.-L.Su.Probabilistic load-flow computation using point estimate method[J].IEEE Trans.Power Systems,2005,20(4):1843-1851.
[22]J.M.Morales,J.P.Ruiz.Point estimate schemes to solve the probabilistic power flow[J].IEEE Trans.on Power Systems,2007,22(4):1594-1601.
[23]S.Aboreshaid,R.Billinton,M.F.Firuzabad.Probabilistic transient stability studies using the method of Bisection[J].IEEE Trans.on Power Systems,1996,11(4):1990-1995.
[24]崔凯,房大中,钟德成.电力系统暂态稳定性概率评估方法研究[J].电网技术,2005,29(1):44-49.
[25]F.F.Wu,Y.K.Tsai,Y.X.Yu.Probabilistic steady-state and dynamic security assessment[J].IEEE Trans.on Power Systems,1988,3(1):1-8.
[26]王克文,钟志勇,谢志棠等.混合使用中心矩与累加量的电力系统概率特征根分析方法[J].中国电机工程学报,2000,20(5):37-41.
[27]王珂,连鸿波.电力市场概率网损分析[J].华东电力,2005,33(9):33-36.
[28]崔雅莉,别朝红,王锡凡.输电系统可用输电能力的概率模型及计算[J].电力系统自动化,2003,27(14):36-40.
[29]M.Blanchand,G.Desrochers.Generation of autocorrelated wind speeds for wind energy conversion system studies[J].Solar Energy,1984,33(6):571-579.
[30]C.G.Justus,W.R.Hargraves,A.Mikhail,et al.Methods for estimating wind speed frequency distributions[J].Journal of Applied Meteorology,1978,17(3):350-353.
[31]R.B.Corotis,A.B.Sigl,J.Klein.Probability models of wind velocity magnitude[J].Solar Energy,1978,20(6):483-493.
[32]S.H.Jangamshetti,V.G.Rau.Site matching of wind turbine generators:a case study[J].IEEE Trans.on Energy Conversion,1999,14(4):1537-1543.
[33]A.Balouktsis,D.Chassapis,T.D.Karapantsios.A nomogram method for estimating the energy produced by wind turbine generators[J].Solar Energy,2002,72(3):251-259.
[34]Y.Mulugetta,F.Drake.Assessment of solar and wind energy resources in Ethiopia.Ⅱ.Wind energy[J].Solar Energy,1996,57(4):323-334.
[35]吴学光,陈树勇等.最小误差逼近算法在风电场风能资源特性分析中的应用[J].电网技术,1998,22(7):69-74.
[36]姚国平,余岳峰,王志征.如东沿海地区风速数据分析及风力发电量计算[J].电力自动化设备,2004,24(4):12-14.
[37]雷亚洲,王伟胜,印永华等.基于机会约束规划的风电穿透功率极限计算[J].中国电机工程学报,2002,22(5):32-35.
[38]A.Garcia,J.L.Torres,E.Prieto,A.de Francisco.Fitting wind speed distributions:A case study[J].Solar Energy,1998,62(2):139-144.
[39]丁明,吴义纯,张立军.风电场风速概率分布参数计算方法的研究[J].中国电机工程学报,2005,25(10):107-110.
[40]雷亚洲.与风电并网相关的研究课题[J].电力系统自动化,2003,27(8):84-89.
[41]Z.Chen,E.Spooner.Grid power quality with variable speed wind turbines[J].IEEE Trans on Energy Conversion,2001,16(2):148-154.
[42]Z.Saad-Saoud,N.Jenkins.Models for predicting flicker induced by large wind turbines[J].IEEE Transactions on Energy Conversion,1999,14(3):743-748.
[43]A.E.Feijoo,J.Cidras,J.L.G.Dornelas.Wind speed simulation in wind farms for steady-state security assessment of electrical power systems[J].IEEE Trans on Energy Conversion,1999,14(4):1582-1588.
[44]A.E.Feijoo,J.Cidras.Modeling of wind farms in the load flow analysis[J].IEEE Trans on Power Systems,2000,15(1):110-115.
[45]吴俊玲,周双喜,孙建锋等.并网风力发电场的最大注入功率分析[J].电网技术,2004,28(20):28-32.
[46]王海超,周双喜,鲁宗相等.含风电场的电力系统潮流计算的联合迭代方法及应用[J].电网技术,2005,29(18):59-62.
[47]吴义纯,丁明,张立军.含风电场的电力系统潮流计算[J].中国电机工程学报,2005,25(4):36-39.
[48]N.D.Hatziargyriou,T.S.Karakatsanis,M.Papadopoulos.Probabilistic load flow in distribution systems containing dispersed wind power generation[J].IEEE Trans.on Power Systems,1993,8(1):159-165.
[49]P.Jorgensen,J.S.Christensen,J.O.Tande.Probabilistic load flow calculation using Monte Carlo techniques for distribution network with wind turbines[C].IEEE 8th Int.Conf.Harmonics and Quality of Power,1998,2:1146-1151.
[50]雷亚洲,王伟胜,印永华等.含风电场电力系统的有功优化潮流[J].电网技术,2002,26(6):18-21.
[51]陈海焱,陈金富,段献忠.含风电场电力系统经济调度的模糊建模及优化算法[J].电力系统自动化,2006,30(2):22-26.
[52]陈金富,陈海焱,段献忠.含大型风电场的电力系统多时段动态优化潮流[J].中国电机工程学报,2006,26(3):31-35.
[53]A.Larsson.Flicker emission of wind turbines caused by switching operation[J].IEEE Trans.on Energy Conversion,2002,17(1):119-123.
[54]E.Muljadi,H.E.McKenna.Power quality issues in a hybrid power system.IEEE Trans.Ind.Appl.,2002,38(3):803-809.
[55]V.Knazkins.Stability of power systems with large amounts of distributed generation[D].PhD.Dissertion,KTH Institution for Elektrotekniska System,2004.
[56]王志群等,朱守真,周双喜等.分布式发电对配电网电压分布的影响[J].电力系统自动化,2004,28(16):56-60.
[57]顾承红,艾芊.基于改进内点法的含风电场的系统最优潮流计算[J].中国电力,2007,40(1):89-93.
[58]诸骏伟.电力系统分析[M].北京:中国电力出版社,1995.
[59]H.W.Dommel,W.F.Tinney.Optimal power flow solutions[J].IEEE Trans.on Power Apparatus and Systems,1968,87(10):1866-1876.
[60]张伯明,陈寿孙.高等电力网络分析[M].北京:清华大学出版社,1996:241-253.
[61]D.Sun,B.Ashley,B.Brewer,et al.Optimal power flow by Newton approach [J].IEEE Trans.on Power Apparatus and Systems,1984,103(10):2684-2880.
[62]赵晋泉,侯志俭,吴际舜.改进最优潮流牛顿算法有效性的对策研究[J].中国电机工程学报,1999,19(12):70-75.
[63]李国庆,李雪峰,沈杰等.牛顿法和内点罚函数法相结合的概率可用功率交换能力计算[J].中国电机工程学报,2003,23(8):17-22.
[64]赵晋泉,侯志俭,吴际舜.牛顿最优潮流算法中离散控制量的新处理方法[J].电力系统自动化,1999,23(23):37-40,58.
[65]张永平,童小娇,吴复立等.基于非线性互补问题函数的半光滑牛顿最优潮流算法[J].中国电机工程学报,2004,24(9):130-135.
[66]X.Li,Y.Li,S.Zhang.A semismooth inexact Newton-type method for the solution of optimal power flow problem[J].WSEAS Trans.on Electronics, 2007,8(4):159-166.
[67]R.A.Jabr,A.H.Coonick,B.J.Cory.A primal-dual interior point method for optimal power flow dispatching[J].IEEE Trans.on Power Systems,2002,17(3):654-662.
[68]I.M.Nejdawi,K.A.Clements,et al.Nonlinear optimal power flow with intertemporal constraints[J].IEEE Power Engineering Review,2000,20(5):74-75.
[69]H.Wang,C.E.Murillo-Sanchez,et al.On computational issues of market-based optimal power flow[J].IEEE Trans.on Power Systems,2007,22(3):1185-1193.
[70]K.C.Almeida,R.Salgado.Optimal power flow solutions under variable load conditions[J].IEEE Trans.on Power Systems,2000,15(4):1204-1211.
[71]N.Karmarkar.A new polynomial-time algorithm for linear programming[J].Combinatorica.1984,4(4):373-395.
[72]P.E.Gill,W.Murray,M.A.Saunders,et al.On the projected Newton barrier methods for linear programming and an equivalence to Karmarkar's projective method[J].Math.Programming,1986,36(2):183-209.
[73]H.Wei,H.Sasaki,J.Kubokawa,et al.An interior point nonlinear programming for optimal power flow problems with a novel data structure[J].IEEE Trans.on Power Systems,1998,13(3):870-877.
[74]H.Wei,H.Sasaki,J.Kubokawa,et al.Large scale hydrothermal optimal power flow problems based on interior point nonlinear programming[J].IEEE Trans.on Power Systems,2000,15(1):396-403.
[75]袁越,久保川淳司,佐佐木博司等.基于内点法的含暂态稳定约束的最优潮流计算[J].电力系统自动化,2002,26(13):14-19.
[76]Y.Yuan,J.Kubokawa,H.Sasaki.A solution of optimal power flow with multi-contingency transient stability constraints[J].IEEE Trans.on Power Systems,2003,18(3):1094-1102.
[77]李尹,张伯明,孙宏斌等.基于非线性内点法的安全约束最优潮流(一)理论分析[J].电力系统自动化,2007,31(19):7-13.
[78]白晓清,韦化,Katsuki Fujisawa.求解最优潮流问题的内点半定规划法[J].中国电机工程学报,2008,28(19):56-64.
[79]钟德成,李渝曾.柔性交流输电系统潮流计算中改进的遗传算法[J].电力系统自动化,2000,24(2):48-50.
[80]余健明,刘恒,王海燕等.基于学习策略的遗传算法在最优潮流中的应用[J].西安理工大学学报,2007,23(4):370-374.
[81]J.Yuryevich,K.P.Wong.Evolutionary programming based optimal power flow algorithm[J].IEEE Trans.on Power Systems,1999,14(4):1245-1250.
[82]D.C.Walters,G.B.Sheble.Genetic algorithm solution of economic dispatch with valve pointloading[J].IEEE Trans.on Power Systems,1993,8(3):1325-1332.
[83]K.Iba.Reactive power optimization by genetic algorithm[J].IEEE Trans.on Power Systems,1994,9(2):685-692.
[84]H.T.Yang,P.C.Yang.C.L.Huang.Evolutionary programming based economic dispatch for units with non-smooth fuel cost functions[J].IEEE Trans.on Power Systems,1996,11(1):112-118.
[85]K.Y.Lee,X.Bai,Y.M.Park.Optimization method for reactive power planning by using a modified simple genetic algorithm[J].IEEE Trans.on Power Systems,1997,10(4):1843-1849.
[86]K.P.Wong,Y.W.Wong.Hybrid genetic/simulated annealing approach to short-term multiple-fuel-constrained generation scheduling[J].IEEE Trans on Power Systems,1997,12(2):776-784.
[87]蔡昌春,丁晓群,王斌.混沌模拟退火算法在无功优化中的应用[J].高电压技术,2008,34(3):578-582.
[88]L.Chen,S.Matoba,H.Inabe,T.Okabe.Surrogate constraint method for optimal power flow[J].IEEE Trans on Power Systems,1998,13(3):1084-1089.
[89]J.H.Park,Y.S.Kim,I.K.Eom,K.Y.Lee.Economic load dispatch for piecewise quadratic cost function using Hopfield neural network[J].IEEE Trans on Power Systems,1993,8(3):1030-1038.
[90]C.T.Su,G.J.Chiou.A fast computation Hopfield method to economic dispatch of power systems[J].IEEE Trans on Power Systems,1997,12(4):1759-1764.
[91]C.T.Su,C.T.Lin.New approach with a Hopfield modeling framework to economic dispatch[J].IEEE Trans on Power Systems,2000,15(2):541-545.
[92]杨波,赵遵廉,陈允平等.一种求解最优潮流问题的改进粒子群优化算法[J].电网技术,2006,30(11):6-10.
[93]李婷,赖旭芝,吴敏.基于双种群粒子群优化新算法的最优潮流求解[J].中南大学学报(自然科学版),2007,38(1):133-137.
[94]段肩平,贺成才.基于改进粒子群优化算法的电力系统有功最优潮流[J].华中电力,2008,21(1):18-20,24.
[95]娄素华,吴耀武,熊信艮.电力系统无功优化的变尺度混沌优化算法[J].电网技术,2005,29(11):20-24.
[96]谭涛亮,张尧.基于遗传禁忌混合算法的电力系统无功优化[J].电网技术, 2004,28(11):57-61.
[97]汪剑,游大海,徐天奇.基于改进的Tabu搜索算法的电力系统无功优化[J].华中电力,2005,18(4):17-20.
[98]任晓莉,程红丽,刘健.基于禁忌搜索算法的变电站电压无功优化控制[J].继电器,2008,36(8):31-34,39.
[99]刘耀年,李迎红,张冰冰等.基于人工鱼群算法的最优潮流计算[J].电工电能新技术,2006,25(4):30-33,66.
[100]G.J.Hahn,S.S.Shapiro.Statistical models in engineering[M].New York:Weily,1967.
[101]S.Kaplan.On the method of discrete probability distributions in risk and reliability calculation-application to seismic risk assessment[J].Risk Anal.,1981,1(3):189-196.
[102]M.Madrigal,K.Ponnambalam,V.H.Quintana.Probabilistic optimal power flow[C].IEEE Canadian Conference on Electrical and Computer Engineering,1998,1:385-388.
[103]A.Schellenberg,W.Rosehart,J.Aguado.Cumulant based probabilistic optimal power flow(P-OPF)[C].8th International Conference on Probabilistic Methods Applied to Power Systems,2004:506-511.
[104]A.Schellenberg,W.Rosehart,J.Aguado.Cumulant-based probabilistic optimal power flow(P-OPF) with Gaussian and gamma distributions[J].IEEE Trans.on Power Systems,2005,20(2):773-781.
[105]G.Verbic,C.A.Canizares.Probabilistic optimal power flow in electricity markets based on a Two-Point Estimate method[J].IEEE Trans.on Power Systems,2006,21(4):1883-1893.
[106]刘健,徐精求,董海鹏.配电网概率负荷分析及其应用[J].电网技术,2004,28(6):67-70.
[107]吴红斌,丁明,李生虎等.发电机和负荷模型对暂态稳定性影响的概率分析[J].电网技术,2004,28(1):19-21.
[108]戴剑锋,王海超,周双喜等.基于负荷裕度随机特性的电压失稳概率问题研究[J].中国电机工程学报,2006,26(13):26-30.
[109]张建芬,王克文,宗秀红等.几种概率潮流模型的准确性比较分析[J].郑州大学学报(工学版),2003,24(4):32-36.
[110]E.vRosenblueth.Two-point estimates in probabilities[J].Applied Mathematical Modelling,1981,5(5):329-335.
[111]H.P.Hong.An efficient point estimate method for probabilistic analysis[J].Reliability Engineering and System Safety,1998,59(3):261-267.
[112]C.-L.Su,C.-N.Lu.Two-point estimate method for quantifying transfer capability uncertainty[J].IEEE Trans.on Power Systems,2005,20(2):573-579.
[113]K.W.Wang,C.T.Tse,K.M.Tang.Algorithm for power system dynamic stability studies taking account the variation of load power[J].Electrical Power System Research,1998,46(3):221-227.
[114]C.R.Fuerte-Esquivel,J.H.Tovar-Hernandez,G.Gutierrez-Alcaraz,and F.Cisneros-Torres.Discussion of modeling of wind farms in the load flow analysis[J].IEEE Trans.Power Syst.,2001,16(4):951.
[115]J.Mur and A.A.Bayod.Wind power variability model Part Ⅰ-Foundations[C].9th Int.Conf.Electrical Power Quality and Utilisation,Barcelona,Spain,2007:1-6.
[116]J.Mur and A.A.Bayod.Wind power variability model Part Ⅱ-Probabilistic power flow[C].9th Int.Conf.Electrical Power Quality and Utilisation,Barcelona,Spain,2007:1-6.
[117]N.D.Hatziargyriou,T.S.Karakatsanis,and M.I.Lorentzou.Voltage control settings to increase wind power based on probabilistic load flow[J].Electrical Power Energy Syst.,2005,27(9-10):656-661.
[118]P.Chen,Z.Chen,B.Bak-Jensen,R.Villafafila,and S.Sorensen.Study of power fluctuation from dispersed generations and loads and its impact on a distribution network through a probabilistic approach[C].9th Int.Conf.Electrical Power Quality and Utilisation,Barcelona,Spain,2007:1-5.
[119]L.L.Freris.Wind energy conversion system[M].Englewood Cliffs,NJ:Prentice-Hall,1990.
[120]S.H.Jangamshetti and V.G.Rau.Optimum siting of wind turbine generators [J].IEEE Trans.Energy Conv.,2001,16(1):8-13.
[121]申洪,王伟胜,戴慧珠.变速恒频风力发电机组的无功功率极限[J].电网技术,2003,27(11):60-63.
[122]吴俊玲.大型风电场并网运行的若干技术问题研究[D],北京,清华大学,2004.
[123]G.Celli,S.Mocci,F.Pilo and R.Cicoria.Probabilistic optimization of MV distribution network in presence of distributed generation[C].14th Power Systems Computation ConE,Sevilla,Spain,2002:1-7.
[124]C.R.Fuerte-Esquivel and E.Acha.A Newton-type algorithm for the control of power flow in electrical power network[J].IEEE Trans.Power Syst.,1997,12(4):1474-1480.
[125]M.Papadopolos,P.Malatestas,and N.Hatziargyriou.Simulation and analysis of small and medium size power systems containing wind turbines[J].IEEE Trans.Power Syst.,1991,6(4):1453-1458.
[126]G.S.Stavrakakis and G.N.Kariniotakis.A general simulation algorithm for the accurate assessment of isolated diesel-Wind turbines systems interation.Part Ⅰ:A general multimachine power system model[J].IEEE Trans.Energy Conv.,1995,10(3):577-583.
[127]J.Carpentier.Contribution to the economic dispatch problem[J].Bull.Soc.Franc.Elect.,1962,3(8):431-447.
[128]G.F.Reid,L.Hasdorf.Economic dispatch using quadratic programming[J].IEEE Trans.on Power Apparatus and Systems,1973,92(6):2015-2023.
[129]覃振成,乐秀璠,蓝澜等.基于改进非线性预报-校正内点法的最优潮流[J],电力系统自动化,2005,29(9):25-30.
[130]I.M.Nejdawi,K.A.Clements,P.W.Davis.An efficient interior point method for sequential quadratic programming based optimal power flow[J].IEEE Trans.Power Syst.,2000,15(4):1179-1183.
[131]刘盛松,侯志俭,蒋传文.基于信赖域内点法的最优潮流算法[J].电力系统自动化,2003,27(6):26-30.
[132]G.L.Torres,V.H.Quintana.Optimal power flow by a nonlinear complementarity method[J].IEEE Trans.Power Syst.,2000,15(3):1028-1033.
[133]F.Facchinei,C.Kanzow.A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems[J].Mathematical Programming,1997,76(3):493-512.
[134]L.Qi.Convergence analysis of some algorithms for solving nonsmooth equations[J].Mathematics of Operations research,1993,18(1):227-244.
[135]F.H.Clarke.Optimization and Nonsmooth Analysis[M].Wiley,New York,NY:1983.
[136]T.De Luca,F.Faccinei,C.Kanzow.A semismooth equation approach to the solution of nonlinear complementarity problems[J].Mathematical Programming,1996,75(3):407-439.
[137]L.Grippo,F.Lampariello,S.Lucidi.A Nonmonotone Line Search Technique for Newton's Method[J].SIAM Journal on Numerical Analysis,1986,23(4):707-716.
[138]J.-S.Pang and S.A.Gabriel,NE/SQP:A robust algorithm for the nonlinear complementarity problem[J].Mathematical Programming,1993,60(1-3):295-337.
[139]R.D.Zimmerman,C.E.MURILLO-SANCHEZ,D.Q.GAN.Documentation for Matpower version3[EB/OL][M].http://www.pserc.cornell.edu/matpower/matpower.html,2006.
[140]M.E.El-Hawary and G.A.N.Mbamalu.A comparison of probabilistic perturbation and deterministic based optimal power flow solutions[J].IEEE Trans.Power Syst.,1991,6(3):1099-1105.
[141]R.Y.Rubinstein.Simulation and the Monte Carlo Method[M].New York:Wiley,1981.
[142]雷亚洲.随机规划理论在风电并网系统分析中的应用研究[D].北京:中国电力科学研究院,2001.
[2]李文沅.电力系统安全经济运行——模型与算法[M].重庆:重庆大学出版社,1998:74-76.
[3]J.Carpentier.Contribution to the economic dispatch problem[J].Bull.Soc.France Elect,1962,8:431-447.
[4]赵风云,王秀丽.输配电市场[M].北京:中国电力出版社,2003.
[5]陈树勇,戴慧珠,白晓明,等.风电场的发电可靠性模型及其应用[J].中国电机工程学报,2000,20(3):26-29.
[6]B.Borkowska.Probabilistic load flow[J].IEEE Trans.on Power Apparatus and Systems,1974,93(3):752-755.
[7]M.Sobierajski,Wroclaw.A method of stochastic load flow calculation[J].Archiv Fur Elektrotechnik,1978,60(1):37-40.
[8]G.T.Heydt.Stochastic Power Flow Calculations[C].IEEE Summer Power Meeting,San Francisco,CA,July,1975.
[9]P.W.Sauer,G.T.Heydt.A generalized stochastic power flow algorithms[C].IEEE Summer Meeting,Los Angeles.CA.July,1978.
[10]J.F.Dopazo,O.A.Klitin,A.M.Sasson.Stochastic load flows[J].IEEE Trans.on Power Apparatus and Systems,1975,94(2):299-309.
[11]A.P.Meliopoulos,A.G.Bakirtais,R.Kovacs.Power System Reliability Evaluation Using Stochastic Load Flows[J].IEEE Trans.on Power Apparatus and Systems,1984,103(5):1084-1091.
[12]R.N.Allan,M.R.G.Al-Shakarchi.Probabilistic techniques in AC load flow analysis[J].Proceedings of the Institution of Electrical Engineering,1977,124(2):154-160.
[13]A.M.Leite da Silva,V.L.Arienti,R.N.Allan.Probabilistic Load Flow Considering Dependence Between Input Nodal Powers[J].IEEE Trans.on Power Apparatus and Systems,1984,103(6):1524-1530.
[14]A.M.Leite da Silva,V.L.Arienti.Probabilistic load flow by a multilinear simulation algorithm[J].Proc.Inst.Elect.Eng.C:Generation,Transmission,Distribution,1990,137(4):276-282.
[15]A.M.Leite da Silva,S.M.P.Ribeiro,V.L.Arienti,et al.Probabilistic load flow techniques applied to power system expansion planning[J].IEEE Trans.Power Systems,1990,5(4):1047-1053.
[16]R.N.Allan,A.M.L.da Silva,R.C.Burchett.Evaluation methods and accuracy in probabilistic load flow solutions[J].IEEE Trans.on Power Apparatus and Systems,1981,100(5):2539-2546.
[17]X.Li,X.Chen,X.Yin,et al.The algorithm of probabilistic power flow retaining non-linearity[C].Proc.Int.Conf.Power System Technology,Kunming,China,2002.
[18]丁明,李生虎,黄凯.基于蒙特卡罗模拟的概率潮流计算[J].电网技术,2001,25(11):10-14,22.
[19]P.Zhang,S.T.Lee.Probabilistic load flow computation using the method of combined cumulants and Gram-Charlier expansion[J].IEEE Trans.on Power Systems,2004,19(1):676-682.
[20]林海源.交流模型下电力系统概率潮流计算[J].电力自动化设备,2006,26(6):53-56.
[21]C.-L.Su.Probabilistic load-flow computation using point estimate method[J].IEEE Trans.Power Systems,2005,20(4):1843-1851.
[22]J.M.Morales,J.P.Ruiz.Point estimate schemes to solve the probabilistic power flow[J].IEEE Trans.on Power Systems,2007,22(4):1594-1601.
[23]S.Aboreshaid,R.Billinton,M.F.Firuzabad.Probabilistic transient stability studies using the method of Bisection[J].IEEE Trans.on Power Systems,1996,11(4):1990-1995.
[24]崔凯,房大中,钟德成.电力系统暂态稳定性概率评估方法研究[J].电网技术,2005,29(1):44-49.
[25]F.F.Wu,Y.K.Tsai,Y.X.Yu.Probabilistic steady-state and dynamic security assessment[J].IEEE Trans.on Power Systems,1988,3(1):1-8.
[26]王克文,钟志勇,谢志棠等.混合使用中心矩与累加量的电力系统概率特征根分析方法[J].中国电机工程学报,2000,20(5):37-41.
[27]王珂,连鸿波.电力市场概率网损分析[J].华东电力,2005,33(9):33-36.
[28]崔雅莉,别朝红,王锡凡.输电系统可用输电能力的概率模型及计算[J].电力系统自动化,2003,27(14):36-40.
[29]M.Blanchand,G.Desrochers.Generation of autocorrelated wind speeds for wind energy conversion system studies[J].Solar Energy,1984,33(6):571-579.
[30]C.G.Justus,W.R.Hargraves,A.Mikhail,et al.Methods for estimating wind speed frequency distributions[J].Journal of Applied Meteorology,1978,17(3):350-353.
[31]R.B.Corotis,A.B.Sigl,J.Klein.Probability models of wind velocity magnitude[J].Solar Energy,1978,20(6):483-493.
[32]S.H.Jangamshetti,V.G.Rau.Site matching of wind turbine generators:a case study[J].IEEE Trans.on Energy Conversion,1999,14(4):1537-1543.
[33]A.Balouktsis,D.Chassapis,T.D.Karapantsios.A nomogram method for estimating the energy produced by wind turbine generators[J].Solar Energy,2002,72(3):251-259.
[34]Y.Mulugetta,F.Drake.Assessment of solar and wind energy resources in Ethiopia.Ⅱ.Wind energy[J].Solar Energy,1996,57(4):323-334.
[35]吴学光,陈树勇等.最小误差逼近算法在风电场风能资源特性分析中的应用[J].电网技术,1998,22(7):69-74.
[36]姚国平,余岳峰,王志征.如东沿海地区风速数据分析及风力发电量计算[J].电力自动化设备,2004,24(4):12-14.
[37]雷亚洲,王伟胜,印永华等.基于机会约束规划的风电穿透功率极限计算[J].中国电机工程学报,2002,22(5):32-35.
[38]A.Garcia,J.L.Torres,E.Prieto,A.de Francisco.Fitting wind speed distributions:A case study[J].Solar Energy,1998,62(2):139-144.
[39]丁明,吴义纯,张立军.风电场风速概率分布参数计算方法的研究[J].中国电机工程学报,2005,25(10):107-110.
[40]雷亚洲.与风电并网相关的研究课题[J].电力系统自动化,2003,27(8):84-89.
[41]Z.Chen,E.Spooner.Grid power quality with variable speed wind turbines[J].IEEE Trans on Energy Conversion,2001,16(2):148-154.
[42]Z.Saad-Saoud,N.Jenkins.Models for predicting flicker induced by large wind turbines[J].IEEE Transactions on Energy Conversion,1999,14(3):743-748.
[43]A.E.Feijoo,J.Cidras,J.L.G.Dornelas.Wind speed simulation in wind farms for steady-state security assessment of electrical power systems[J].IEEE Trans on Energy Conversion,1999,14(4):1582-1588.
[44]A.E.Feijoo,J.Cidras.Modeling of wind farms in the load flow analysis[J].IEEE Trans on Power Systems,2000,15(1):110-115.
[45]吴俊玲,周双喜,孙建锋等.并网风力发电场的最大注入功率分析[J].电网技术,2004,28(20):28-32.
[46]王海超,周双喜,鲁宗相等.含风电场的电力系统潮流计算的联合迭代方法及应用[J].电网技术,2005,29(18):59-62.
[47]吴义纯,丁明,张立军.含风电场的电力系统潮流计算[J].中国电机工程学报,2005,25(4):36-39.
[48]N.D.Hatziargyriou,T.S.Karakatsanis,M.Papadopoulos.Probabilistic load flow in distribution systems containing dispersed wind power generation[J].IEEE Trans.on Power Systems,1993,8(1):159-165.
[49]P.Jorgensen,J.S.Christensen,J.O.Tande.Probabilistic load flow calculation using Monte Carlo techniques for distribution network with wind turbines[C].IEEE 8th Int.Conf.Harmonics and Quality of Power,1998,2:1146-1151.
[50]雷亚洲,王伟胜,印永华等.含风电场电力系统的有功优化潮流[J].电网技术,2002,26(6):18-21.
[51]陈海焱,陈金富,段献忠.含风电场电力系统经济调度的模糊建模及优化算法[J].电力系统自动化,2006,30(2):22-26.
[52]陈金富,陈海焱,段献忠.含大型风电场的电力系统多时段动态优化潮流[J].中国电机工程学报,2006,26(3):31-35.
[53]A.Larsson.Flicker emission of wind turbines caused by switching operation[J].IEEE Trans.on Energy Conversion,2002,17(1):119-123.
[54]E.Muljadi,H.E.McKenna.Power quality issues in a hybrid power system.IEEE Trans.Ind.Appl.,2002,38(3):803-809.
[55]V.Knazkins.Stability of power systems with large amounts of distributed generation[D].PhD.Dissertion,KTH Institution for Elektrotekniska System,2004.
[56]王志群等,朱守真,周双喜等.分布式发电对配电网电压分布的影响[J].电力系统自动化,2004,28(16):56-60.
[57]顾承红,艾芊.基于改进内点法的含风电场的系统最优潮流计算[J].中国电力,2007,40(1):89-93.
[58]诸骏伟.电力系统分析[M].北京:中国电力出版社,1995.
[59]H.W.Dommel,W.F.Tinney.Optimal power flow solutions[J].IEEE Trans.on Power Apparatus and Systems,1968,87(10):1866-1876.
[60]张伯明,陈寿孙.高等电力网络分析[M].北京:清华大学出版社,1996:241-253.
[61]D.Sun,B.Ashley,B.Brewer,et al.Optimal power flow by Newton approach [J].IEEE Trans.on Power Apparatus and Systems,1984,103(10):2684-2880.
[62]赵晋泉,侯志俭,吴际舜.改进最优潮流牛顿算法有效性的对策研究[J].中国电机工程学报,1999,19(12):70-75.
[63]李国庆,李雪峰,沈杰等.牛顿法和内点罚函数法相结合的概率可用功率交换能力计算[J].中国电机工程学报,2003,23(8):17-22.
[64]赵晋泉,侯志俭,吴际舜.牛顿最优潮流算法中离散控制量的新处理方法[J].电力系统自动化,1999,23(23):37-40,58.
[65]张永平,童小娇,吴复立等.基于非线性互补问题函数的半光滑牛顿最优潮流算法[J].中国电机工程学报,2004,24(9):130-135.
[66]X.Li,Y.Li,S.Zhang.A semismooth inexact Newton-type method for the solution of optimal power flow problem[J].WSEAS Trans.on Electronics, 2007,8(4):159-166.
[67]R.A.Jabr,A.H.Coonick,B.J.Cory.A primal-dual interior point method for optimal power flow dispatching[J].IEEE Trans.on Power Systems,2002,17(3):654-662.
[68]I.M.Nejdawi,K.A.Clements,et al.Nonlinear optimal power flow with intertemporal constraints[J].IEEE Power Engineering Review,2000,20(5):74-75.
[69]H.Wang,C.E.Murillo-Sanchez,et al.On computational issues of market-based optimal power flow[J].IEEE Trans.on Power Systems,2007,22(3):1185-1193.
[70]K.C.Almeida,R.Salgado.Optimal power flow solutions under variable load conditions[J].IEEE Trans.on Power Systems,2000,15(4):1204-1211.
[71]N.Karmarkar.A new polynomial-time algorithm for linear programming[J].Combinatorica.1984,4(4):373-395.
[72]P.E.Gill,W.Murray,M.A.Saunders,et al.On the projected Newton barrier methods for linear programming and an equivalence to Karmarkar's projective method[J].Math.Programming,1986,36(2):183-209.
[73]H.Wei,H.Sasaki,J.Kubokawa,et al.An interior point nonlinear programming for optimal power flow problems with a novel data structure[J].IEEE Trans.on Power Systems,1998,13(3):870-877.
[74]H.Wei,H.Sasaki,J.Kubokawa,et al.Large scale hydrothermal optimal power flow problems based on interior point nonlinear programming[J].IEEE Trans.on Power Systems,2000,15(1):396-403.
[75]袁越,久保川淳司,佐佐木博司等.基于内点法的含暂态稳定约束的最优潮流计算[J].电力系统自动化,2002,26(13):14-19.
[76]Y.Yuan,J.Kubokawa,H.Sasaki.A solution of optimal power flow with multi-contingency transient stability constraints[J].IEEE Trans.on Power Systems,2003,18(3):1094-1102.
[77]李尹,张伯明,孙宏斌等.基于非线性内点法的安全约束最优潮流(一)理论分析[J].电力系统自动化,2007,31(19):7-13.
[78]白晓清,韦化,Katsuki Fujisawa.求解最优潮流问题的内点半定规划法[J].中国电机工程学报,2008,28(19):56-64.
[79]钟德成,李渝曾.柔性交流输电系统潮流计算中改进的遗传算法[J].电力系统自动化,2000,24(2):48-50.
[80]余健明,刘恒,王海燕等.基于学习策略的遗传算法在最优潮流中的应用[J].西安理工大学学报,2007,23(4):370-374.
[81]J.Yuryevich,K.P.Wong.Evolutionary programming based optimal power flow algorithm[J].IEEE Trans.on Power Systems,1999,14(4):1245-1250.
[82]D.C.Walters,G.B.Sheble.Genetic algorithm solution of economic dispatch with valve pointloading[J].IEEE Trans.on Power Systems,1993,8(3):1325-1332.
[83]K.Iba.Reactive power optimization by genetic algorithm[J].IEEE Trans.on Power Systems,1994,9(2):685-692.
[84]H.T.Yang,P.C.Yang.C.L.Huang.Evolutionary programming based economic dispatch for units with non-smooth fuel cost functions[J].IEEE Trans.on Power Systems,1996,11(1):112-118.
[85]K.Y.Lee,X.Bai,Y.M.Park.Optimization method for reactive power planning by using a modified simple genetic algorithm[J].IEEE Trans.on Power Systems,1997,10(4):1843-1849.
[86]K.P.Wong,Y.W.Wong.Hybrid genetic/simulated annealing approach to short-term multiple-fuel-constrained generation scheduling[J].IEEE Trans on Power Systems,1997,12(2):776-784.
[87]蔡昌春,丁晓群,王斌.混沌模拟退火算法在无功优化中的应用[J].高电压技术,2008,34(3):578-582.
[88]L.Chen,S.Matoba,H.Inabe,T.Okabe.Surrogate constraint method for optimal power flow[J].IEEE Trans on Power Systems,1998,13(3):1084-1089.
[89]J.H.Park,Y.S.Kim,I.K.Eom,K.Y.Lee.Economic load dispatch for piecewise quadratic cost function using Hopfield neural network[J].IEEE Trans on Power Systems,1993,8(3):1030-1038.
[90]C.T.Su,G.J.Chiou.A fast computation Hopfield method to economic dispatch of power systems[J].IEEE Trans on Power Systems,1997,12(4):1759-1764.
[91]C.T.Su,C.T.Lin.New approach with a Hopfield modeling framework to economic dispatch[J].IEEE Trans on Power Systems,2000,15(2):541-545.
[92]杨波,赵遵廉,陈允平等.一种求解最优潮流问题的改进粒子群优化算法[J].电网技术,2006,30(11):6-10.
[93]李婷,赖旭芝,吴敏.基于双种群粒子群优化新算法的最优潮流求解[J].中南大学学报(自然科学版),2007,38(1):133-137.
[94]段肩平,贺成才.基于改进粒子群优化算法的电力系统有功最优潮流[J].华中电力,2008,21(1):18-20,24.
[95]娄素华,吴耀武,熊信艮.电力系统无功优化的变尺度混沌优化算法[J].电网技术,2005,29(11):20-24.
[96]谭涛亮,张尧.基于遗传禁忌混合算法的电力系统无功优化[J].电网技术, 2004,28(11):57-61.
[97]汪剑,游大海,徐天奇.基于改进的Tabu搜索算法的电力系统无功优化[J].华中电力,2005,18(4):17-20.
[98]任晓莉,程红丽,刘健.基于禁忌搜索算法的变电站电压无功优化控制[J].继电器,2008,36(8):31-34,39.
[99]刘耀年,李迎红,张冰冰等.基于人工鱼群算法的最优潮流计算[J].电工电能新技术,2006,25(4):30-33,66.
[100]G.J.Hahn,S.S.Shapiro.Statistical models in engineering[M].New York:Weily,1967.
[101]S.Kaplan.On the method of discrete probability distributions in risk and reliability calculation-application to seismic risk assessment[J].Risk Anal.,1981,1(3):189-196.
[102]M.Madrigal,K.Ponnambalam,V.H.Quintana.Probabilistic optimal power flow[C].IEEE Canadian Conference on Electrical and Computer Engineering,1998,1:385-388.
[103]A.Schellenberg,W.Rosehart,J.Aguado.Cumulant based probabilistic optimal power flow(P-OPF)[C].8th International Conference on Probabilistic Methods Applied to Power Systems,2004:506-511.
[104]A.Schellenberg,W.Rosehart,J.Aguado.Cumulant-based probabilistic optimal power flow(P-OPF) with Gaussian and gamma distributions[J].IEEE Trans.on Power Systems,2005,20(2):773-781.
[105]G.Verbic,C.A.Canizares.Probabilistic optimal power flow in electricity markets based on a Two-Point Estimate method[J].IEEE Trans.on Power Systems,2006,21(4):1883-1893.
[106]刘健,徐精求,董海鹏.配电网概率负荷分析及其应用[J].电网技术,2004,28(6):67-70.
[107]吴红斌,丁明,李生虎等.发电机和负荷模型对暂态稳定性影响的概率分析[J].电网技术,2004,28(1):19-21.
[108]戴剑锋,王海超,周双喜等.基于负荷裕度随机特性的电压失稳概率问题研究[J].中国电机工程学报,2006,26(13):26-30.
[109]张建芬,王克文,宗秀红等.几种概率潮流模型的准确性比较分析[J].郑州大学学报(工学版),2003,24(4):32-36.
[110]E.vRosenblueth.Two-point estimates in probabilities[J].Applied Mathematical Modelling,1981,5(5):329-335.
[111]H.P.Hong.An efficient point estimate method for probabilistic analysis[J].Reliability Engineering and System Safety,1998,59(3):261-267.
[112]C.-L.Su,C.-N.Lu.Two-point estimate method for quantifying transfer capability uncertainty[J].IEEE Trans.on Power Systems,2005,20(2):573-579.
[113]K.W.Wang,C.T.Tse,K.M.Tang.Algorithm for power system dynamic stability studies taking account the variation of load power[J].Electrical Power System Research,1998,46(3):221-227.
[114]C.R.Fuerte-Esquivel,J.H.Tovar-Hernandez,G.Gutierrez-Alcaraz,and F.Cisneros-Torres.Discussion of modeling of wind farms in the load flow analysis[J].IEEE Trans.Power Syst.,2001,16(4):951.
[115]J.Mur and A.A.Bayod.Wind power variability model Part Ⅰ-Foundations[C].9th Int.Conf.Electrical Power Quality and Utilisation,Barcelona,Spain,2007:1-6.
[116]J.Mur and A.A.Bayod.Wind power variability model Part Ⅱ-Probabilistic power flow[C].9th Int.Conf.Electrical Power Quality and Utilisation,Barcelona,Spain,2007:1-6.
[117]N.D.Hatziargyriou,T.S.Karakatsanis,and M.I.Lorentzou.Voltage control settings to increase wind power based on probabilistic load flow[J].Electrical Power Energy Syst.,2005,27(9-10):656-661.
[118]P.Chen,Z.Chen,B.Bak-Jensen,R.Villafafila,and S.Sorensen.Study of power fluctuation from dispersed generations and loads and its impact on a distribution network through a probabilistic approach[C].9th Int.Conf.Electrical Power Quality and Utilisation,Barcelona,Spain,2007:1-5.
[119]L.L.Freris.Wind energy conversion system[M].Englewood Cliffs,NJ:Prentice-Hall,1990.
[120]S.H.Jangamshetti and V.G.Rau.Optimum siting of wind turbine generators [J].IEEE Trans.Energy Conv.,2001,16(1):8-13.
[121]申洪,王伟胜,戴慧珠.变速恒频风力发电机组的无功功率极限[J].电网技术,2003,27(11):60-63.
[122]吴俊玲.大型风电场并网运行的若干技术问题研究[D],北京,清华大学,2004.
[123]G.Celli,S.Mocci,F.Pilo and R.Cicoria.Probabilistic optimization of MV distribution network in presence of distributed generation[C].14th Power Systems Computation ConE,Sevilla,Spain,2002:1-7.
[124]C.R.Fuerte-Esquivel and E.Acha.A Newton-type algorithm for the control of power flow in electrical power network[J].IEEE Trans.Power Syst.,1997,12(4):1474-1480.
[125]M.Papadopolos,P.Malatestas,and N.Hatziargyriou.Simulation and analysis of small and medium size power systems containing wind turbines[J].IEEE Trans.Power Syst.,1991,6(4):1453-1458.
[126]G.S.Stavrakakis and G.N.Kariniotakis.A general simulation algorithm for the accurate assessment of isolated diesel-Wind turbines systems interation.Part Ⅰ:A general multimachine power system model[J].IEEE Trans.Energy Conv.,1995,10(3):577-583.
[127]J.Carpentier.Contribution to the economic dispatch problem[J].Bull.Soc.Franc.Elect.,1962,3(8):431-447.
[128]G.F.Reid,L.Hasdorf.Economic dispatch using quadratic programming[J].IEEE Trans.on Power Apparatus and Systems,1973,92(6):2015-2023.
[129]覃振成,乐秀璠,蓝澜等.基于改进非线性预报-校正内点法的最优潮流[J],电力系统自动化,2005,29(9):25-30.
[130]I.M.Nejdawi,K.A.Clements,P.W.Davis.An efficient interior point method for sequential quadratic programming based optimal power flow[J].IEEE Trans.Power Syst.,2000,15(4):1179-1183.
[131]刘盛松,侯志俭,蒋传文.基于信赖域内点法的最优潮流算法[J].电力系统自动化,2003,27(6):26-30.
[132]G.L.Torres,V.H.Quintana.Optimal power flow by a nonlinear complementarity method[J].IEEE Trans.Power Syst.,2000,15(3):1028-1033.
[133]F.Facchinei,C.Kanzow.A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems[J].Mathematical Programming,1997,76(3):493-512.
[134]L.Qi.Convergence analysis of some algorithms for solving nonsmooth equations[J].Mathematics of Operations research,1993,18(1):227-244.
[135]F.H.Clarke.Optimization and Nonsmooth Analysis[M].Wiley,New York,NY:1983.
[136]T.De Luca,F.Faccinei,C.Kanzow.A semismooth equation approach to the solution of nonlinear complementarity problems[J].Mathematical Programming,1996,75(3):407-439.
[137]L.Grippo,F.Lampariello,S.Lucidi.A Nonmonotone Line Search Technique for Newton's Method[J].SIAM Journal on Numerical Analysis,1986,23(4):707-716.
[138]J.-S.Pang and S.A.Gabriel,NE/SQP:A robust algorithm for the nonlinear complementarity problem[J].Mathematical Programming,1993,60(1-3):295-337.
[139]R.D.Zimmerman,C.E.MURILLO-SANCHEZ,D.Q.GAN.Documentation for Matpower version3[EB/OL][M].http://www.pserc.cornell.edu/matpower/matpower.html,2006.
[140]M.E.El-Hawary and G.A.N.Mbamalu.A comparison of probabilistic perturbation and deterministic based optimal power flow solutions[J].IEEE Trans.Power Syst.,1991,6(3):1099-1105.
[141]R.Y.Rubinstein.Simulation and the Monte Carlo Method[M].New York:Wiley,1981.
[142]雷亚洲.随机规划理论在风电并网系统分析中的应用研究[D].北京:中国电力科学研究院,2001.
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