负荷动特性的建模及其对电压稳定的影响研究
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摘要
负荷动态特性对电力系统的动态行为具有重要的影响,是引起电力系统电压稳定问题的关键因素。本文以负荷动特性的建模及其对电压稳定的影响为主线,研究内容包括负荷时变性问题、负荷动特性的分类与综合方法、小干扰电压稳定分析的模型和指标、暂态电压稳定分析的模型和快速判断方法。
采用对实测负荷动特性进行分类与综合的方法来解决负荷建模中的负荷时变性问题。基于随机过程相关性原理,提出了基于实测响应空间的负荷动特性分类方法。该方法以负荷动特性的实测响应空间为特征向量空间,首先对各个样本的实测响应进行时间坐标的标准化,再计算实测响应空间各样本间的相关系数,最后采用系统聚类法按样本间的相关系数值进行分类。实测响应空间具有能够直接、准确地反映负荷特性样本对应的负荷构成的本质特征的优点,工程应用实例表明了该方法的分类结果准确、实现简便。
提出了基于实测响应空间的负荷动特性直接综合方法,以建立同类负荷特性中不同样本的通用负荷模型。该方法首先通过求得某类负荷特性中所有样本的重心作为该类负荷特性的聚类中心,再通过对聚类中心等效样本进行参数辨识以得到该类负荷特性的综合模型参数。建模实践表明该方法得到的某类负荷特性的综合模型参数能够较好的描述该类负荷特性中的所有样本,其物理意义清晰、计算量小。并且,采用判别分析法对新采集的负荷特性样本进行归类,以修正各类负荷特性的聚类中心,进而修正各个类的综合模型参数。这样,修正的综合模型参数就能够反映负荷特性发生的新变化,从而提高了综合模型参数的准确性。
通过对电力系统在任一时间断面上从某个负荷母线向系统侧看进去部分进行戴维南等值,并对负荷采用三阶感应电动机并联恒阻抗动态模型,构建了系统电压稳定分析的微分代数方程组(DAE)模型,并推导出系统小干扰电压稳定分析的线性化方程的状态矩阵的解析表达式。系统研究了负荷模型参数与负荷节点PV曲线上小干扰电压稳定极限点位置的关系。并得出了此等值系统的小干扰电压稳定性本质上是负荷中感应电动机部分的静态稳定性,负荷中感应电动机部分采用三阶模型和一阶模型得到系统平衡点的小干扰电压稳定性是一致的结论。因而在负荷中感应电动机部分采用一阶模型条件下提出了一个在线小干扰电压稳定状态指标Ls。推导出了指标Ls的解析表达式,算例分析表明Ls计算量小、线性特性较好、变化幅度大、适合于在线表征系统当前运行点各个负荷节点的电压稳定程度。
提出了一种负荷采用三阶感应电动机并联恒阻抗动态模型时电力系统暂态电压稳定的快速判断方法。推导出了此动态负荷模型下电力系统数学模型的一般化描述。针对采用牛顿法求取故障后系统主导不稳定平衡点(CUEP)存在的初值选取难题,提出了一种实用但不失严谨的解决方案:通过识别给定故障的主导负荷母线,对主导负荷母线以外系统由故障后稳定平衡点(SEP)处的状态进行戴维南等值,对负荷中的感应电动机采用其稳态等值电路,再由感应电动机的转矩特性求得CUEP附近的一个点作为近似的CUEP,以此为迭代初值以可靠求得CUEP;并采用二阶正规型来近似CUEP的稳定流形的方法求得近似的SEP的吸引域的局部边界。算例分析表明应用该方法判断电力系统的暂态电压稳定性具有较高的准确度。
Electric load dynamic characteristic has great relation to the dynamic behavior of power system, and it is the key factor of causing the voltage instability problem. This dissertation makes the load dynamic characteristic modeling and its influence to voltage stability as keystone; and its research contents include load time-variation character problem, classification and synthesis for dynamic load characteristics, analyzing model and method for small disturbance voltage stability, analyzing model and quick judgment method for transient voltage stability.
The classification and synthesis for dynamic load characteristics is used to settle the time-variation character problem in measurement-based load modeling. Based on the random process correlation theory, a new dynamic load characteristics classification method is presented. It uses the field measured response space as the character vector space of dynamic load characteristics. First, the measured response of each dynamic load characteristics sample is standardized in time coordination, then the correlation coefficients of all the samples in measured response space is computed, at last, the system clustering method is used to make the samples classification. The measured response can reflect the load composition character of each sample very good. The project instance shows that the classification result of the method is veracious, and the realization of the method is convenient.
In order to build the common load model of a dynamic load characteristics classification, a new dynamic load characteristics synthesis method that directly synthesizes the field measured load characteristics is presented. This method uses the center of gravity of all the samples in a dynamic load characteristics classification as the clustering center of this classification, and by doing parameter identification of the clustering center equivalent sample, the synthetic load model of this classification is gained. The load modeling practice showed that the synthetic model gained from this method can represent different dynamic load characteristics samples in a classification very good, and the method has the advantages of clear physical meaning and small computing. Moreover, the distinguish analysis is used to determine the classification ascription of the new dynamic load characteristics samples, and the new clustering center of each classification including new dynamic load characteristics is gained, then the amendatory synthetic load model parameters of the corresponding classification is also gained. In this way, the amendatory synthetic load model parameters can reflect the new changes of actual load characteristic, and the nicety of synthetic load model parameters’representing the load characteristic is improved.
The Thevenin equivalent circuit is used to represent the system side as seen from a load bus of power system at any time, and the third order induction motor paralleled with const impedance dynamic model is used to represent the load, the differential and algebraic equations (DAE) model of analyzing the voltage stability of the system is built up. And the analytic expression of the state matrix of the linear small disturbance equation of the equivalent system is deduced. The relation of the dynamic load model parameters and the position of the small disturbance voltage stability limit point in the PV curve are systematically analyzed. The conclusions that the essence of the small disturbance voltage stability of the equivalent system is the steady stability of the induction motor part in load, and the small disturbance voltage stability of equilibrium points of the system is the same whether first order model or third order model is used to represent the induction motor part in load are gained. So in the condition of the first order model is used to represent the induction motor part in load, a new on-line small disturbance voltage stability state index Ls is presented. The analytic expression of Ls is deduced. The instances analysis shows that the computation of Ls is small, the linear characteristic of Ls is good, and the variation magnitude of Ls is big, so it is suitable for on-line reflecting the voltage stability degree of load buses at the current operating point of the system.
A method which can quickly determine the transient voltage stability of power system considering the third order induction motor paralleled with const impedance dynamic load model is presented. The general representation of the mathematics model of power system with this dynamic load model is deduced. Aimed at the problem of choosing the initial value when the Newton method is used to compute the controlling unstable equilibrium point(CUEP) of the post fault system, a practical and rigorous solving scheme is presented: by identifying the controlling load bus of the given fault, and using the Thevenin equivalent circuit to represent the rest of the system at the state of the stable equilibrium point(SEP) of the post fault system, and then using the torque characteristics of induction motor, a point near the CUEP is gained to be the initial value. The second order normal form is used to approximate the stable manifold of CUEP, and the approximating local boundary of the region of attraction of SEP is gained. The instances analysis shows that the nicety of the method is high when it is used to determine the transient voltage stability of power system.
采用对实测负荷动特性进行分类与综合的方法来解决负荷建模中的负荷时变性问题。基于随机过程相关性原理,提出了基于实测响应空间的负荷动特性分类方法。该方法以负荷动特性的实测响应空间为特征向量空间,首先对各个样本的实测响应进行时间坐标的标准化,再计算实测响应空间各样本间的相关系数,最后采用系统聚类法按样本间的相关系数值进行分类。实测响应空间具有能够直接、准确地反映负荷特性样本对应的负荷构成的本质特征的优点,工程应用实例表明了该方法的分类结果准确、实现简便。
提出了基于实测响应空间的负荷动特性直接综合方法,以建立同类负荷特性中不同样本的通用负荷模型。该方法首先通过求得某类负荷特性中所有样本的重心作为该类负荷特性的聚类中心,再通过对聚类中心等效样本进行参数辨识以得到该类负荷特性的综合模型参数。建模实践表明该方法得到的某类负荷特性的综合模型参数能够较好的描述该类负荷特性中的所有样本,其物理意义清晰、计算量小。并且,采用判别分析法对新采集的负荷特性样本进行归类,以修正各类负荷特性的聚类中心,进而修正各个类的综合模型参数。这样,修正的综合模型参数就能够反映负荷特性发生的新变化,从而提高了综合模型参数的准确性。
通过对电力系统在任一时间断面上从某个负荷母线向系统侧看进去部分进行戴维南等值,并对负荷采用三阶感应电动机并联恒阻抗动态模型,构建了系统电压稳定分析的微分代数方程组(DAE)模型,并推导出系统小干扰电压稳定分析的线性化方程的状态矩阵的解析表达式。系统研究了负荷模型参数与负荷节点PV曲线上小干扰电压稳定极限点位置的关系。并得出了此等值系统的小干扰电压稳定性本质上是负荷中感应电动机部分的静态稳定性,负荷中感应电动机部分采用三阶模型和一阶模型得到系统平衡点的小干扰电压稳定性是一致的结论。因而在负荷中感应电动机部分采用一阶模型条件下提出了一个在线小干扰电压稳定状态指标Ls。推导出了指标Ls的解析表达式,算例分析表明Ls计算量小、线性特性较好、变化幅度大、适合于在线表征系统当前运行点各个负荷节点的电压稳定程度。
提出了一种负荷采用三阶感应电动机并联恒阻抗动态模型时电力系统暂态电压稳定的快速判断方法。推导出了此动态负荷模型下电力系统数学模型的一般化描述。针对采用牛顿法求取故障后系统主导不稳定平衡点(CUEP)存在的初值选取难题,提出了一种实用但不失严谨的解决方案:通过识别给定故障的主导负荷母线,对主导负荷母线以外系统由故障后稳定平衡点(SEP)处的状态进行戴维南等值,对负荷中的感应电动机采用其稳态等值电路,再由感应电动机的转矩特性求得CUEP附近的一个点作为近似的CUEP,以此为迭代初值以可靠求得CUEP;并采用二阶正规型来近似CUEP的稳定流形的方法求得近似的SEP的吸引域的局部边界。算例分析表明应用该方法判断电力系统的暂态电压稳定性具有较高的准确度。
Electric load dynamic characteristic has great relation to the dynamic behavior of power system, and it is the key factor of causing the voltage instability problem. This dissertation makes the load dynamic characteristic modeling and its influence to voltage stability as keystone; and its research contents include load time-variation character problem, classification and synthesis for dynamic load characteristics, analyzing model and method for small disturbance voltage stability, analyzing model and quick judgment method for transient voltage stability.
The classification and synthesis for dynamic load characteristics is used to settle the time-variation character problem in measurement-based load modeling. Based on the random process correlation theory, a new dynamic load characteristics classification method is presented. It uses the field measured response space as the character vector space of dynamic load characteristics. First, the measured response of each dynamic load characteristics sample is standardized in time coordination, then the correlation coefficients of all the samples in measured response space is computed, at last, the system clustering method is used to make the samples classification. The measured response can reflect the load composition character of each sample very good. The project instance shows that the classification result of the method is veracious, and the realization of the method is convenient.
In order to build the common load model of a dynamic load characteristics classification, a new dynamic load characteristics synthesis method that directly synthesizes the field measured load characteristics is presented. This method uses the center of gravity of all the samples in a dynamic load characteristics classification as the clustering center of this classification, and by doing parameter identification of the clustering center equivalent sample, the synthetic load model of this classification is gained. The load modeling practice showed that the synthetic model gained from this method can represent different dynamic load characteristics samples in a classification very good, and the method has the advantages of clear physical meaning and small computing. Moreover, the distinguish analysis is used to determine the classification ascription of the new dynamic load characteristics samples, and the new clustering center of each classification including new dynamic load characteristics is gained, then the amendatory synthetic load model parameters of the corresponding classification is also gained. In this way, the amendatory synthetic load model parameters can reflect the new changes of actual load characteristic, and the nicety of synthetic load model parameters’representing the load characteristic is improved.
The Thevenin equivalent circuit is used to represent the system side as seen from a load bus of power system at any time, and the third order induction motor paralleled with const impedance dynamic model is used to represent the load, the differential and algebraic equations (DAE) model of analyzing the voltage stability of the system is built up. And the analytic expression of the state matrix of the linear small disturbance equation of the equivalent system is deduced. The relation of the dynamic load model parameters and the position of the small disturbance voltage stability limit point in the PV curve are systematically analyzed. The conclusions that the essence of the small disturbance voltage stability of the equivalent system is the steady stability of the induction motor part in load, and the small disturbance voltage stability of equilibrium points of the system is the same whether first order model or third order model is used to represent the induction motor part in load are gained. So in the condition of the first order model is used to represent the induction motor part in load, a new on-line small disturbance voltage stability state index Ls is presented. The analytic expression of Ls is deduced. The instances analysis shows that the computation of Ls is small, the linear characteristic of Ls is good, and the variation magnitude of Ls is big, so it is suitable for on-line reflecting the voltage stability degree of load buses at the current operating point of the system.
A method which can quickly determine the transient voltage stability of power system considering the third order induction motor paralleled with const impedance dynamic load model is presented. The general representation of the mathematics model of power system with this dynamic load model is deduced. Aimed at the problem of choosing the initial value when the Newton method is used to compute the controlling unstable equilibrium point(CUEP) of the post fault system, a practical and rigorous solving scheme is presented: by identifying the controlling load bus of the given fault, and using the Thevenin equivalent circuit to represent the rest of the system at the state of the stable equilibrium point(SEP) of the post fault system, and then using the torque characteristics of induction motor, a point near the CUEP is gained to be the initial value. The second order normal form is used to approximate the stable manifold of CUEP, and the approximating local boundary of the region of attraction of SEP is gained. The instances analysis shows that the nicety of the method is high when it is used to determine the transient voltage stability of power system.
引文
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