光伏时空概率模型及其在电力系统概率分析中的应用
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摘要
光伏发电具有绿色环保、无污染等优点，近年来得到了持续快速发展。然而，光伏发电属于典型的间歇式能源，输出功率严重依赖于辐照度等气象因素，具有较强的随机波动性，光伏发电的大规模接入将给电力系统的安全稳定、经济运行带来新的挑战。因此，需要利用概率理论和方法，充分考虑光伏功率的不确定性，定量评估光伏接入给电力系统规划与运行带来的深刻影响，为运行人员提供全面、科学的参考信息以及辅助决策信息。
本文在国家自然科学基金资助项目“输电网中长期状态的精细化模拟与概率评估的基础理论研究”(51177178)以及国家高技术研究发展计划(863计划)资助项目“含分布式电源的微电网关键技术研发”(2011AA05A107)的支持下，对考虑光伏电源输出功率随机性/时间相关性/空间相关性的概率建模方法，以及含光伏电力系统的概率潮流/概率最优潮流分析方法等基础性问题展开深入研究，并将其应用到电力系统与虚拟电厂的安全性和经济性分析中。具体内容如下：
1)基于非参数核密度估计的单变量光伏概率建模方法
针对现有光伏概率建模中需要假设参数分布和不能全面考虑各种随机因素影响的缺点，本文提出基于非参数核密度估计理论直接建立光伏电源输出功率的概率模型，并给出一种不依赖于总体真实分布的最优带宽改进模型和基于拟合优度检验及后验检验的综合检验指标。用地处重庆及杭州的光伏电站的实测数据进行仿真分析，验证了所提光伏概率建模方法和带宽选取方法的正确性、有效性以及对不同日照条件下光伏功率随机特性的适应性。
2)考虑空间相关性的光伏-负荷概率建模方法
位于相邻地区的光伏电源输出功率之间、光伏功率与气象条件敏感负荷之间存在一定的空间相关关系。现有研究在处理此类相关关系时，仅讨论了光伏的Beta概率模型，对光伏无法采用Beta等常规参数分布建模的情况，尚未涉及。针对该问题，本文基于等概率转换原则提出了一种考虑空间相关性的光伏-负荷概率建模方法，该方法能够处理服从任意分布的光伏和光伏、光伏和负荷之间的空间相关关系。在此基础上，结合Monte Carlo模拟，给出了一种考虑光伏-负荷空间相关性的概率潮流计算方法，并进一步引入中值拉丁超立方抽样技术以提高计算效率。以美国某光伏电站的实测数据和69节点配电系统为算例，验证了所提方法的有效性，并定量分析了光伏-负荷的相关性水平对配网安全、经济运行的影响。
3)考虑时间相关性的光伏概率建模方法
基于条件概率和两变量核密度估计理论，提出一种考虑时间相关性的光伏概率建模方法，该方法不仅可以计及光伏电源各时刻输出功率的随机波动性和相关性，而且还能够充分考虑光伏电源日功率输出起止时刻的不确定性。另外，针对所提时序建模概率方法，基于舍选法建立了光伏功率时序曲线的随机抽样方法。最后，应用美国、中国三座光伏电站输出功率的实测数据和34节点配电系统进行仿真分析，验证了所提方法的有效性及其对配电网日线损概率评估的适应性。
4)基于随机响应面法的含光伏电力系统概率潮流计算方法
基于随机响应面法提出了一种含光伏电力系统的概率潮流计算方法，并针对配点选择这一关键问题，引入基于线性无关原则的最优配点选择方法，进一步提高了概率潮流的计算速度和模拟精度。该方法能够快速、准确地实现概率潮流分析，无需借助级数展开式即可获取输出变量的概率分布，而且能够充分考虑光伏的非参数分布情况以及光伏-负荷之间的相关关系。以34节点配电系统和IEEE39节点输配电系统进行仿真分析，验证了所提算法的有效性，并分析了不同光伏概率模型及光伏-负荷相关性水平对概率潮流计算结果的影响。
5)含光伏虚拟电厂的概率最优潮流分析
为定量分析光伏、负荷等随机因素对虚拟电厂经济运行的影响，本文建立了含光伏虚拟电厂的概率最优潮流模型，并结合随机响应面和内点法提出一种概率最优潮流计算方法。所提最优潮流模型的目标函数中考虑了分布式能源(DER,distributed energy resource)和常规火电机组的发电费用、虚拟电厂的外购电费用以及虚拟电厂作为所辖DER总体的代表向外网售电的收益；约束条件中计及了DER出力上下限等技术约束以及网络安全约束等。算法方面，以内点法作为最优潮流的算法，并基于随机响应面法评估光伏及负荷的随机波动对最优潮流结果的影响。用IEEE30节点改进算例系统，验证了本文所提概率最优潮流分析方法的有效性，并对比分析了光伏接入以及不同光伏概率模型、光伏-负荷相关性水平对虚拟电厂经济运行的影响。
Solar photovoltaic (PV) generation with green and unpolluted strengths has kept upthe rapid pace of development in recent years, but it is an intermittent source of energy,whose power output depends seriously on the climate factors like solar irradiation,temperature and so on. Consequently the PV power is random. A large number of PVgenerators connected into power systems are a new challenge for the secure andeconomic operation of power system. The probabilistic analysis methods under thesufficient consideration of PV’s uncertain are thus employed for quantified evaluatingthe impact of PV generation on power system planning and operation. Consequently, therich, all-rounds, and comprehensive information can also be provided for power systemsoperators.
This dissertation is supported by “Research on the basic theories of mid-long termprobabilistic modeling and evaluation of transmission power system”, subsidized by theNational Natural Science Foundation of China, No.51177178, and “The key technologyresearch and development of micro-grid incorporating distributed generators”,subsidized by The National High Technology Research and Development of China863Program, No.2011AA05A107. The study is carried out for probabilistic modelingmethods considering the randomness/chronological/spatial correlation of PV generation,probabilistic power flow and probabilistic optimal power flow calculation methods forpower system containing PV generators. And finally they are applied into the secure andeconomic analysis of power system or virtual power plant. The detailed study includes:
1) The probabilistic modeling method of PV generation based on nonparametrickernel density estimation theory
The present probabilistic PV power modeling methods are usually based onparametric density estimations which rest on some probabilistic assumption, and cannotconsider the effects of all the stochastic factors involved. A new probabilistic modelingmethod of PV power is proposed based on nonparametric kernel density estimation andan improved optimal bandwidth selecting method without depending on the realdistribution is also developed. The comprehensive test index is also presented based onthe goodness-of-fit and posteriori tests. The proposed probabilistic modeling andbandwidth selection methods are verified using PV power data of Chongqing andHangzhou, which are quite different in sunshine condition. The test results also demonstrate the adaptability of the new probabilistic modeling method to PV powerwith distinct stochastic characteristics.
2) The probabilistic modeling method for PV generation considering the spatialcorrelation
The power outputs of PV at the adjacent locations are correlated with each otherand also with the loads which are sensitive to weather conditions. Thus, this dissertationproposes a probabilistic modeling method considering such correlation. The correlationsbetween PV outputs and loads obeying different probability distributions can beconsidered by the proposed method. And a probabilistic power flow analysis methodbased on Monte Carlo is also developed to deal with the randomness and correlation ofPV outputs and loads. The Latin Hypercube Sampling method, an efficient samplingmethod, is also incorporated to decrease the computation burden. The measured powerdata of PV generators in USA and the69-node distribution network are used todemonstrate the correctness and effectiveness of the presented method and analyze theimpacts of different PV probabilistic models and correlations between PV outputs andloads on the probabilistic power flow of distribution networks.
3) The chronological probability modeling method for PV generation
A chronological probability modeling method for PV generation is proposed on thebasis of conditional probability and nonparametric kernel density estimation. In additionto randomness of PV power, the correlation of PV powers between adjacent time pointsand the uncertainty of start and end moments of PV output can be represented. Thestochastic sampling method of PV time series is also proposed based on the rejectionsampling technique. The power data of three PV generators in different regions withdistinct weather conditions and34-node distribution network are used to demonstratethe correctness, effectiveness and adaptability of the presented method and itsapplication in the probabilistic evaluation of daily network loss of distribution network.
4) The probabilistic power flow analysis method based on stochastic responsesurface method for power systems incorporating PV generation
Based on stochastic response surface method, a probabilistic power flow analysismethod for power system incorporating PV generation is proposed. The collocationpoint selecting method based on linearly independent is also introduced to chooseoptimal collocation points. The proposed method can rapidly solve the probabilisticpower flow with high accuracy as well as considering the nonparametric model of PVgeneration and the correlations between PV outputs and loads. The34-node distribution system and IEEE39-node test system are used to verify the correctness andeffectiveness of the proposed method. The impacts of different probabilistic models ofPV generation and correlations between PV outputs and loads on the probabilisticpower flow are also analyzed.
5) The probabilistic optimal power flow analysis method for virtual power plantcontaining PV generation
In order to reflect the impacts of random factors, like PV power and loads, on theeconomic operation of virtual power plant, a probabilistic optimal power flow analysismethod is proposed by combining the stochastic response surface method and interiorpoint method. The optimal power flow model minimizing the generation cost for virtualpower plant containing PV generation is established. The interior point method isemployed to solve the optimal power flow and the stochastic response surface method isused to deal with the randomness of PV outputs and loads. The modified IEEE30-bustest system is used to verify the correctness and effectiveness of the proposed method.The impacts of the PV generation on virtual power plant are also analyzed.
本文在国家自然科学基金资助项目“输电网中长期状态的精细化模拟与概率评估的基础理论研究”(51177178)以及国家高技术研究发展计划(863计划)资助项目“含分布式电源的微电网关键技术研发”(2011AA05A107)的支持下，对考虑光伏电源输出功率随机性/时间相关性/空间相关性的概率建模方法，以及含光伏电力系统的概率潮流/概率最优潮流分析方法等基础性问题展开深入研究，并将其应用到电力系统与虚拟电厂的安全性和经济性分析中。具体内容如下：
1)基于非参数核密度估计的单变量光伏概率建模方法
针对现有光伏概率建模中需要假设参数分布和不能全面考虑各种随机因素影响的缺点，本文提出基于非参数核密度估计理论直接建立光伏电源输出功率的概率模型，并给出一种不依赖于总体真实分布的最优带宽改进模型和基于拟合优度检验及后验检验的综合检验指标。用地处重庆及杭州的光伏电站的实测数据进行仿真分析，验证了所提光伏概率建模方法和带宽选取方法的正确性、有效性以及对不同日照条件下光伏功率随机特性的适应性。
2)考虑空间相关性的光伏-负荷概率建模方法
位于相邻地区的光伏电源输出功率之间、光伏功率与气象条件敏感负荷之间存在一定的空间相关关系。现有研究在处理此类相关关系时，仅讨论了光伏的Beta概率模型，对光伏无法采用Beta等常规参数分布建模的情况，尚未涉及。针对该问题，本文基于等概率转换原则提出了一种考虑空间相关性的光伏-负荷概率建模方法，该方法能够处理服从任意分布的光伏和光伏、光伏和负荷之间的空间相关关系。在此基础上，结合Monte Carlo模拟，给出了一种考虑光伏-负荷空间相关性的概率潮流计算方法，并进一步引入中值拉丁超立方抽样技术以提高计算效率。以美国某光伏电站的实测数据和69节点配电系统为算例，验证了所提方法的有效性，并定量分析了光伏-负荷的相关性水平对配网安全、经济运行的影响。
3)考虑时间相关性的光伏概率建模方法
基于条件概率和两变量核密度估计理论，提出一种考虑时间相关性的光伏概率建模方法，该方法不仅可以计及光伏电源各时刻输出功率的随机波动性和相关性，而且还能够充分考虑光伏电源日功率输出起止时刻的不确定性。另外，针对所提时序建模概率方法，基于舍选法建立了光伏功率时序曲线的随机抽样方法。最后，应用美国、中国三座光伏电站输出功率的实测数据和34节点配电系统进行仿真分析，验证了所提方法的有效性及其对配电网日线损概率评估的适应性。
4)基于随机响应面法的含光伏电力系统概率潮流计算方法
基于随机响应面法提出了一种含光伏电力系统的概率潮流计算方法，并针对配点选择这一关键问题，引入基于线性无关原则的最优配点选择方法，进一步提高了概率潮流的计算速度和模拟精度。该方法能够快速、准确地实现概率潮流分析，无需借助级数展开式即可获取输出变量的概率分布，而且能够充分考虑光伏的非参数分布情况以及光伏-负荷之间的相关关系。以34节点配电系统和IEEE39节点输配电系统进行仿真分析，验证了所提算法的有效性，并分析了不同光伏概率模型及光伏-负荷相关性水平对概率潮流计算结果的影响。
5)含光伏虚拟电厂的概率最优潮流分析
为定量分析光伏、负荷等随机因素对虚拟电厂经济运行的影响，本文建立了含光伏虚拟电厂的概率最优潮流模型，并结合随机响应面和内点法提出一种概率最优潮流计算方法。所提最优潮流模型的目标函数中考虑了分布式能源(DER,distributed energy resource)和常规火电机组的发电费用、虚拟电厂的外购电费用以及虚拟电厂作为所辖DER总体的代表向外网售电的收益；约束条件中计及了DER出力上下限等技术约束以及网络安全约束等。算法方面，以内点法作为最优潮流的算法，并基于随机响应面法评估光伏及负荷的随机波动对最优潮流结果的影响。用IEEE30节点改进算例系统，验证了本文所提概率最优潮流分析方法的有效性，并对比分析了光伏接入以及不同光伏概率模型、光伏-负荷相关性水平对虚拟电厂经济运行的影响。
Solar photovoltaic (PV) generation with green and unpolluted strengths has kept upthe rapid pace of development in recent years, but it is an intermittent source of energy,whose power output depends seriously on the climate factors like solar irradiation,temperature and so on. Consequently the PV power is random. A large number of PVgenerators connected into power systems are a new challenge for the secure andeconomic operation of power system. The probabilistic analysis methods under thesufficient consideration of PV’s uncertain are thus employed for quantified evaluatingthe impact of PV generation on power system planning and operation. Consequently, therich, all-rounds, and comprehensive information can also be provided for power systemsoperators.
This dissertation is supported by “Research on the basic theories of mid-long termprobabilistic modeling and evaluation of transmission power system”, subsidized by theNational Natural Science Foundation of China, No.51177178, and “The key technologyresearch and development of micro-grid incorporating distributed generators”,subsidized by The National High Technology Research and Development of China863Program, No.2011AA05A107. The study is carried out for probabilistic modelingmethods considering the randomness/chronological/spatial correlation of PV generation,probabilistic power flow and probabilistic optimal power flow calculation methods forpower system containing PV generators. And finally they are applied into the secure andeconomic analysis of power system or virtual power plant. The detailed study includes:
1) The probabilistic modeling method of PV generation based on nonparametrickernel density estimation theory
The present probabilistic PV power modeling methods are usually based onparametric density estimations which rest on some probabilistic assumption, and cannotconsider the effects of all the stochastic factors involved. A new probabilistic modelingmethod of PV power is proposed based on nonparametric kernel density estimation andan improved optimal bandwidth selecting method without depending on the realdistribution is also developed. The comprehensive test index is also presented based onthe goodness-of-fit and posteriori tests. The proposed probabilistic modeling andbandwidth selection methods are verified using PV power data of Chongqing andHangzhou, which are quite different in sunshine condition. The test results also demonstrate the adaptability of the new probabilistic modeling method to PV powerwith distinct stochastic characteristics.
2) The probabilistic modeling method for PV generation considering the spatialcorrelation
The power outputs of PV at the adjacent locations are correlated with each otherand also with the loads which are sensitive to weather conditions. Thus, this dissertationproposes a probabilistic modeling method considering such correlation. The correlationsbetween PV outputs and loads obeying different probability distributions can beconsidered by the proposed method. And a probabilistic power flow analysis methodbased on Monte Carlo is also developed to deal with the randomness and correlation ofPV outputs and loads. The Latin Hypercube Sampling method, an efficient samplingmethod, is also incorporated to decrease the computation burden. The measured powerdata of PV generators in USA and the69-node distribution network are used todemonstrate the correctness and effectiveness of the presented method and analyze theimpacts of different PV probabilistic models and correlations between PV outputs andloads on the probabilistic power flow of distribution networks.
3) The chronological probability modeling method for PV generation
A chronological probability modeling method for PV generation is proposed on thebasis of conditional probability and nonparametric kernel density estimation. In additionto randomness of PV power, the correlation of PV powers between adjacent time pointsand the uncertainty of start and end moments of PV output can be represented. Thestochastic sampling method of PV time series is also proposed based on the rejectionsampling technique. The power data of three PV generators in different regions withdistinct weather conditions and34-node distribution network are used to demonstratethe correctness, effectiveness and adaptability of the presented method and itsapplication in the probabilistic evaluation of daily network loss of distribution network.
4) The probabilistic power flow analysis method based on stochastic responsesurface method for power systems incorporating PV generation
Based on stochastic response surface method, a probabilistic power flow analysismethod for power system incorporating PV generation is proposed. The collocationpoint selecting method based on linearly independent is also introduced to chooseoptimal collocation points. The proposed method can rapidly solve the probabilisticpower flow with high accuracy as well as considering the nonparametric model of PVgeneration and the correlations between PV outputs and loads. The34-node distribution system and IEEE39-node test system are used to verify the correctness andeffectiveness of the proposed method. The impacts of different probabilistic models ofPV generation and correlations between PV outputs and loads on the probabilisticpower flow are also analyzed.
5) The probabilistic optimal power flow analysis method for virtual power plantcontaining PV generation
In order to reflect the impacts of random factors, like PV power and loads, on theeconomic operation of virtual power plant, a probabilistic optimal power flow analysismethod is proposed by combining the stochastic response surface method and interiorpoint method. The optimal power flow model minimizing the generation cost for virtualpower plant containing PV generation is established. The interior point method isemployed to solve the optimal power flow and the stochastic response surface method isused to deal with the randomness of PV outputs and loads. The modified IEEE30-bustest system is used to verify the correctness and effectiveness of the proposed method.The impacts of the PV generation on virtual power plant are also analyzed.
引文
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