考虑并网风电随机波动的电力系统小干扰概率稳定研究
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摘要
大规模风电接入电网导致原来由可控可调度的同步电源组成的电力系统耦合了大量具有随机波动性的非同步电源,使得现代电力系统转变为随机—确定性耦合电力系统。这种耦合电力系统的稳定性问题使常规电力系统的稳定分析理论和方法遇到了新的挑战。
风电场的出力随风速而大幅度频繁波动使系统呈现多种运行方式,如何恰当地考虑风电不确定性和随机性对小干扰稳定的影响,模拟含大规模风电的电力系统的运行状态,是目前进行小干扰稳定计算时需要着重考虑的问题。本文针对大规模风电接入电力系统存在的小干扰稳定问题,结合我国特有的风电大规模、高集中、远距离输送的特点,围绕着风电功率的随机波动性和风机与常规机组的差异性,对含并网风电的电力系统小干扰概率稳定方面的问题进行了研究和探索,主要工作归纳如下。
建立适当的风电机组数学模型是研究大规模风电接入对电力系统小干扰稳定影响的基础,其模型和参数的准确度将直接关系到分析计算的精度。为此,本文详细建立了双馈风电机组的空气动力学模型、机械传动系统的轴系模型、桨距角控制系统模型、感应发电机模型、采用了矢量控制和前馈补偿策略的变频器控制系统模型；依据大规模风电场并网系统的小干扰稳定分析的需要,建立了风电场的动态等值模型；最后建立了系统中其它元件如同步机、励磁系统的动态模型以及输电线路、变压器、负荷的稳态模型,实现了完整的含双馈型风电场的电力系统小干扰稳定分析模型,为论文所进行的小干扰概率稳定分析奠定了基础。
运用概率统计的方法对含风电场的电力系统进行小干扰稳定分析的首要任务是合理地对风电场随机出力进行概率建模。为此,本文从影响风电场随机出力特性的主要因素出发,提出了包含风频分布模型、风速相关性模型和风电转换模型三部分的多风电场随机出力模型。算例分析表明,对于估计风频的Weibull分布模型,极大似然估计法的准确度更高,更能精确模拟实际风电场的风频分布；本文提出的风速相关性模型既保持了每个风电场的实测风速数据的概率分布特性,又准确模拟了风电场之间的相关水平,可以用于含风电场的电力系统小干扰概率稳定分析。
以前两部分研究内容中建立的双馈型风电场动态模型和考虑相关性的风电场随机出力模型为基础,对含风电场的小干扰概率稳定分析进行了研究。提出了一种基于2m+1点估计方案的小干扰概率稳定计算方法,通过与蒙特卡罗法的计算结果相比较,验证了算法的有效性,说明了利用2m+l点估计方案进行考虑风电场风速相关性的电力系统小干扰概率稳定分析的可行性,且具有计算精度高、求解速度快的特点。结合算例系统,通过设计不同的研究方案,详细分析了风电场接入位置、风电渗透率、风电相关性对小干扰概率稳定的影响。计算结果表明,对于互联电力系统,双馈型风电场替代本区域同步机出力会提高本区域内的局部模式和互联模式的阻尼比,对前者的影响程度最大,对其它区域内的局部模式几乎没有影响。随着风电渗透率的提高,上述情况下的阻尼比的改善程度越大,但随之而来带给系统阻尼的不确定性也越大。风电场的风速相关性对系统小干扰失稳概率和振荡模式的阻尼具有较大影响,相关度越高影响越大,影响的利弊取决于风电场的接入位置和系统潮流的变化,因此在进行小干扰概率稳定计算时有必要计及风速的相关性。算例分析结果说明了概率方法能够更加全面地刻画系统的小干扰稳定特性,为电力规划和运行人员提供更为丰富的关于系统小干扰稳定性的信息。
从概率分析的角度,提出了电力系统振荡稳定裕度(Oscillatory Stability Margin, OSM)概率评估模型,并结合风电随机出力模型、振荡稳定裕度确定性求解模型和蒙特卡罗仿真对该模型进行了求解。为了实现对系统振荡稳定裕度的随机特征和风险水平的整体把握和完整认知,提出了两类评估指标：概率指标和风险指标。结合算例系统,对风电场接入位置、风电装机容量以及风速相关性对振荡稳定裕度的影响进行深入了探讨。算例分析的结果表明,并网风电输出功率不确定性的存在,既可能给系统带来遭受损失的风险,也可能带来获得收益的机会,这取决于风电场的位置、风电装机容量和风速相关程度。本文提出的振荡稳定裕度概率评估为解决受风电波动性影响的电力系统振荡稳定性问题提供了一种新的思路和手段,利用评估指标解析表达式以及相关图表不但可直观反映各种因素对系统OSM的影响,还可为电力系统规划和运行提供指导意见和决策支持。
Power system stability plays a significant role in modern power industries. With increasing wind power penetration, the theory of power system stability needs to be improved, because the performance of power system are no longer only influenced by controllable synchronous generators, but also a large number of stochastic and fluctuating asynchronous generators (wind turbine generators, WTG), which makes the modern power system a complex stochastic-deterministic coupling power system.
Deterministic strategies used for small signal stability analysis of power systems as affected by penetration of large scale wind generation are limited since they are carried out based on a specified operating condition. However, since the wind generation is primarily determined by wind speed and thus fluctuating constantly, the operating conditions of the system are stochastically uncertain. Therefore, a more comprehensive probabilistic stability research that considering the uncertainties and intermittence of wind power should be conducted to assess the influence of wind generation on the power system stability from the viewpoint of probability. This dissertation studied and explored the probabilistic analysis of small-signal stability of power systems as affected by stochastic variation of grid-connected wind generation. The primary contents and original contributions of this dissertation are as follows:
Dynamic modelling of wind turbine generator is the basis of researching the impact of wind power on power system small signal stability. For this purpose, the status equations of the aerodynamic model, shaft system model, pitch control model, converters model with application of vector control and feed-forward decoupling control strategies of the doubly-fed induction generator (DFIG) are established for analyzing small signal stability. Furthermore, in order to investigate the effects of large scale wind farms connected to an existing power grid on the small signal analysis of power system, the whole wind farm is modelled as an aggregated wind farm model by one equivalent wind generator, whose parameters can be modelled as an equivalent of the parallel connection of single generators. Apart from this, models for synchronous generators, excitation systems, transmission lines and transformers are also presented.
The primary task of small signal stability analysis of wind integrated power systems by using the probabilistic method is to reasonably simulate the probabilistic production of wind farms. Therefore, considering the main factors affecting stochastic characteristic of wind power, probabilistic production model of multiple wind farms is developed. This model consists of three parts:wind speed frequency distribution model, wind speed correlation model and wind speed-power output transformation model. By comparing the calculated results getting from different estimation methods, it can be seen that maximal likelihood method was better in fitting the wind speed distribution. The proposed wind speed correlation model is verified from three aspects:goodness of fit test, two-dimensional kernel smoothing density estimate and aggregated power output comparison. The results show that the proposed wind speed correlation model preserves the marginal distribution of wind speed at each wind site and the correlation structure of multiple wind site, which can be applied to small signal stability analysis of power system containing wind farms.
Based on the dynamic model of grid-connected wind farms with DFIG type and the probabilistic production model of multiple wind farms, a probabilistic methodology for small signal stability analysis of power system with correlated wind sources is presented. The approach based on the2m+1point estimate scheme and Cornish Fisher expansion, the orthogonal transformation technique is used to deal with the correlation of wind farms. A case study is carried out on two test system and the probabilistic indexes for eigenvalue analysis are computed from the statistical processing of the obtained results. The accuracy and efficiency of the proposed method are confirmed by comparing with the results of Monte Carlo simulation. The numerical results indicate that the proposed method can actually capture the probabilistic characteristics of mode properties of the power systems with correlated wind sources. Test results show that the dampings of local mode and inter-area mode tend to be improved when a synchronous generator involved in these oscillatory modes is replaced by the wind farms within the same area. Additionally, it appears that wind farms do not affect local modes in distant areas. Furthermore, the presence of correlated wind speeds increases the fluctuation of wind farms'output, which leads to a considerable influence on the probability of small signal instability and damping of oscillatory mode. It is necessary to consider the correlation among wind farms in the probabilistic small signal stability problem to build more exact models.
At last, author provides an attempt to include probabilistic character of wind power into the power system oscillatory stability margin (OSM) analysis. The probabilistic production model of multiple wind farms is applied to generate the wind speed samples. The mathematical model of OSM for wind farm integrated power system is formulated and is calculated by the integration-based eigenvalue tracing approach. Considering the uncertainties of the wind power, several statistical indices are presented to evaluate OSM. Monte Carlo simulation is used to calculate these statistics. The impact of wind power uncertainty on OSM restricted by inter-area mode is investigated in two test system, respectively, for different wind farm locations, wind power penetration levels and wind speed correlation (WSC) degrees. For both interconnected systems, wind power uncertainty variation is found to have a positive or negative impact on the probabilistic OSM. The impact depends on the locations of the wind farms (the degree of network congestion), the wind power penetration level and wind speed correlation degree. Statistical indices allow visualizing the above phenomena and, which is more important, can be used to assist power system operators and planners in quantitatively assessing the impact of wind generation and certain operating decisions with respect to changing operating conditions. The risk index provides system operators and planners with information necessary for decision making, including risk threshold selection. Hopefully, the analysis presented in this paper can be extended to include possible preventive and remedial measures necessary to improve the probability of oscillatory stability or maintain a certain OSM in the actual system operation.
风电场的出力随风速而大幅度频繁波动使系统呈现多种运行方式,如何恰当地考虑风电不确定性和随机性对小干扰稳定的影响,模拟含大规模风电的电力系统的运行状态,是目前进行小干扰稳定计算时需要着重考虑的问题。本文针对大规模风电接入电力系统存在的小干扰稳定问题,结合我国特有的风电大规模、高集中、远距离输送的特点,围绕着风电功率的随机波动性和风机与常规机组的差异性,对含并网风电的电力系统小干扰概率稳定方面的问题进行了研究和探索,主要工作归纳如下。
建立适当的风电机组数学模型是研究大规模风电接入对电力系统小干扰稳定影响的基础,其模型和参数的准确度将直接关系到分析计算的精度。为此,本文详细建立了双馈风电机组的空气动力学模型、机械传动系统的轴系模型、桨距角控制系统模型、感应发电机模型、采用了矢量控制和前馈补偿策略的变频器控制系统模型；依据大规模风电场并网系统的小干扰稳定分析的需要,建立了风电场的动态等值模型；最后建立了系统中其它元件如同步机、励磁系统的动态模型以及输电线路、变压器、负荷的稳态模型,实现了完整的含双馈型风电场的电力系统小干扰稳定分析模型,为论文所进行的小干扰概率稳定分析奠定了基础。
运用概率统计的方法对含风电场的电力系统进行小干扰稳定分析的首要任务是合理地对风电场随机出力进行概率建模。为此,本文从影响风电场随机出力特性的主要因素出发,提出了包含风频分布模型、风速相关性模型和风电转换模型三部分的多风电场随机出力模型。算例分析表明,对于估计风频的Weibull分布模型,极大似然估计法的准确度更高,更能精确模拟实际风电场的风频分布；本文提出的风速相关性模型既保持了每个风电场的实测风速数据的概率分布特性,又准确模拟了风电场之间的相关水平,可以用于含风电场的电力系统小干扰概率稳定分析。
以前两部分研究内容中建立的双馈型风电场动态模型和考虑相关性的风电场随机出力模型为基础,对含风电场的小干扰概率稳定分析进行了研究。提出了一种基于2m+1点估计方案的小干扰概率稳定计算方法,通过与蒙特卡罗法的计算结果相比较,验证了算法的有效性,说明了利用2m+l点估计方案进行考虑风电场风速相关性的电力系统小干扰概率稳定分析的可行性,且具有计算精度高、求解速度快的特点。结合算例系统,通过设计不同的研究方案,详细分析了风电场接入位置、风电渗透率、风电相关性对小干扰概率稳定的影响。计算结果表明,对于互联电力系统,双馈型风电场替代本区域同步机出力会提高本区域内的局部模式和互联模式的阻尼比,对前者的影响程度最大,对其它区域内的局部模式几乎没有影响。随着风电渗透率的提高,上述情况下的阻尼比的改善程度越大,但随之而来带给系统阻尼的不确定性也越大。风电场的风速相关性对系统小干扰失稳概率和振荡模式的阻尼具有较大影响,相关度越高影响越大,影响的利弊取决于风电场的接入位置和系统潮流的变化,因此在进行小干扰概率稳定计算时有必要计及风速的相关性。算例分析结果说明了概率方法能够更加全面地刻画系统的小干扰稳定特性,为电力规划和运行人员提供更为丰富的关于系统小干扰稳定性的信息。
从概率分析的角度,提出了电力系统振荡稳定裕度(Oscillatory Stability Margin, OSM)概率评估模型,并结合风电随机出力模型、振荡稳定裕度确定性求解模型和蒙特卡罗仿真对该模型进行了求解。为了实现对系统振荡稳定裕度的随机特征和风险水平的整体把握和完整认知,提出了两类评估指标：概率指标和风险指标。结合算例系统,对风电场接入位置、风电装机容量以及风速相关性对振荡稳定裕度的影响进行深入了探讨。算例分析的结果表明,并网风电输出功率不确定性的存在,既可能给系统带来遭受损失的风险,也可能带来获得收益的机会,这取决于风电场的位置、风电装机容量和风速相关程度。本文提出的振荡稳定裕度概率评估为解决受风电波动性影响的电力系统振荡稳定性问题提供了一种新的思路和手段,利用评估指标解析表达式以及相关图表不但可直观反映各种因素对系统OSM的影响,还可为电力系统规划和运行提供指导意见和决策支持。
Power system stability plays a significant role in modern power industries. With increasing wind power penetration, the theory of power system stability needs to be improved, because the performance of power system are no longer only influenced by controllable synchronous generators, but also a large number of stochastic and fluctuating asynchronous generators (wind turbine generators, WTG), which makes the modern power system a complex stochastic-deterministic coupling power system.
Deterministic strategies used for small signal stability analysis of power systems as affected by penetration of large scale wind generation are limited since they are carried out based on a specified operating condition. However, since the wind generation is primarily determined by wind speed and thus fluctuating constantly, the operating conditions of the system are stochastically uncertain. Therefore, a more comprehensive probabilistic stability research that considering the uncertainties and intermittence of wind power should be conducted to assess the influence of wind generation on the power system stability from the viewpoint of probability. This dissertation studied and explored the probabilistic analysis of small-signal stability of power systems as affected by stochastic variation of grid-connected wind generation. The primary contents and original contributions of this dissertation are as follows:
Dynamic modelling of wind turbine generator is the basis of researching the impact of wind power on power system small signal stability. For this purpose, the status equations of the aerodynamic model, shaft system model, pitch control model, converters model with application of vector control and feed-forward decoupling control strategies of the doubly-fed induction generator (DFIG) are established for analyzing small signal stability. Furthermore, in order to investigate the effects of large scale wind farms connected to an existing power grid on the small signal analysis of power system, the whole wind farm is modelled as an aggregated wind farm model by one equivalent wind generator, whose parameters can be modelled as an equivalent of the parallel connection of single generators. Apart from this, models for synchronous generators, excitation systems, transmission lines and transformers are also presented.
The primary task of small signal stability analysis of wind integrated power systems by using the probabilistic method is to reasonably simulate the probabilistic production of wind farms. Therefore, considering the main factors affecting stochastic characteristic of wind power, probabilistic production model of multiple wind farms is developed. This model consists of three parts:wind speed frequency distribution model, wind speed correlation model and wind speed-power output transformation model. By comparing the calculated results getting from different estimation methods, it can be seen that maximal likelihood method was better in fitting the wind speed distribution. The proposed wind speed correlation model is verified from three aspects:goodness of fit test, two-dimensional kernel smoothing density estimate and aggregated power output comparison. The results show that the proposed wind speed correlation model preserves the marginal distribution of wind speed at each wind site and the correlation structure of multiple wind site, which can be applied to small signal stability analysis of power system containing wind farms.
Based on the dynamic model of grid-connected wind farms with DFIG type and the probabilistic production model of multiple wind farms, a probabilistic methodology for small signal stability analysis of power system with correlated wind sources is presented. The approach based on the2m+1point estimate scheme and Cornish Fisher expansion, the orthogonal transformation technique is used to deal with the correlation of wind farms. A case study is carried out on two test system and the probabilistic indexes for eigenvalue analysis are computed from the statistical processing of the obtained results. The accuracy and efficiency of the proposed method are confirmed by comparing with the results of Monte Carlo simulation. The numerical results indicate that the proposed method can actually capture the probabilistic characteristics of mode properties of the power systems with correlated wind sources. Test results show that the dampings of local mode and inter-area mode tend to be improved when a synchronous generator involved in these oscillatory modes is replaced by the wind farms within the same area. Additionally, it appears that wind farms do not affect local modes in distant areas. Furthermore, the presence of correlated wind speeds increases the fluctuation of wind farms'output, which leads to a considerable influence on the probability of small signal instability and damping of oscillatory mode. It is necessary to consider the correlation among wind farms in the probabilistic small signal stability problem to build more exact models.
At last, author provides an attempt to include probabilistic character of wind power into the power system oscillatory stability margin (OSM) analysis. The probabilistic production model of multiple wind farms is applied to generate the wind speed samples. The mathematical model of OSM for wind farm integrated power system is formulated and is calculated by the integration-based eigenvalue tracing approach. Considering the uncertainties of the wind power, several statistical indices are presented to evaluate OSM. Monte Carlo simulation is used to calculate these statistics. The impact of wind power uncertainty on OSM restricted by inter-area mode is investigated in two test system, respectively, for different wind farm locations, wind power penetration levels and wind speed correlation (WSC) degrees. For both interconnected systems, wind power uncertainty variation is found to have a positive or negative impact on the probabilistic OSM. The impact depends on the locations of the wind farms (the degree of network congestion), the wind power penetration level and wind speed correlation degree. Statistical indices allow visualizing the above phenomena and, which is more important, can be used to assist power system operators and planners in quantitatively assessing the impact of wind generation and certain operating decisions with respect to changing operating conditions. The risk index provides system operators and planners with information necessary for decision making, including risk threshold selection. Hopefully, the analysis presented in this paper can be extended to include possible preventive and remedial measures necessary to improve the probability of oscillatory stability or maintain a certain OSM in the actual system operation.
引文
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