基于抛载试验和在线时域测试的同步发电机参数辨识新方法
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摘要
同步发电机是电力系统中最关键的一类设备。在电力系统分析中,同步发电机的模型有着极其重要的地位。对于电力系统的稳定性分析和控制设备的控制策略设计,都需要合理的发电机模型和准确的模型参数。
利用测量数据对参数进行辨识是确定同步发电机参数的主要方法。尽管已历经多年的发展,同步发电机的参数辨识仍然是一个颇具挑战性的课题。抛载试验和在线时域测试法与现有的其它方法相比有很多优点,因而近年来受到工业界和学术界较多关注。但是,在这两种基于测试的方法中,至今已有的研究还存在不足和缺点。对于抛载试验而言,在有测量噪声时,图形法难以被应用,而测量噪声是任何测试方法中都不可避免的;优化方法不仅需要提供参数初值,并且在有测量噪声时也可能导致较大的估计误差。在抛载试验下,由于计算需要,经常要在基于时间常数的运算电感模型和基于等值电路的模型之间做参数转换,虽然IEEE Std 1110-2002标准提供了在一定条件下的转换计算公式,但并没有提到转换中由于误差传递造成的参数误差问题,实际上,还没有任何文献对这个问题进行过研究。对于在线时域测试法而言,大多数现有的研究没有考虑饱和在扰动过程中的非线性影响。另外,有文献研究了发电机三阶模型的在线辨识,但已有的辨识模型还需要进一步发展,模型的非线性本质也要求引入更佳的非线性估计方法。
本论文主要针对测量噪声对参数估计结果的影响、模型参数转换中的误差问题及其解决方案、磁路饱和在扰动过程中的非线性影响,以及三阶模型的非线性特点,基于抛载试验和在线时域测试方法,对同步发电机的辨识模型和参数估计技术进行了比较系统深入的研究和探索,以提高参数估计的精度和估计中的抗噪声能力。
论文提出了一种在d轴抛载试验条件下估计同步发电机d轴同步电感和时间常数等参数的新方法。该方法的本质是同时辨识两个单输入单输出的传递函数的系数。从模型的层面,该方法是辨识基于时间常数的运算电感模型。首先,利用q轴电压、磁场电流以及它们的数值积分,构建线性回归方程组。其次,利用辅助变量法求解带有测量噪声的回归方程组的系数。最后,根据回归系数计算d轴参数。算例的大量测试结果表明所提方法比现有的图形法和数值优化法有更好的估计性能。
论文直接引入上述辨识单输入单输出传递函数的方法,在q轴抛载试验条件下,对同步发电机的q轴同步电感和时间常数也进行了估计。该方法实质上是辨识q轴运算电感。仿真结果表明了引入的这种方法的有效性。论文提出了一种利用辨识得到的运算电感模型来确定同步发电机d轴等值电路参数的方法。在抛载试验下,现有的研究或以辨识运算电感模型的参数为目的,或以辨识等值电路参数为目的,但没有探讨两类参数之间的转换问题。当辨识得到的参数在类型上不同于稳定分析软件需要的参数时,必须进行参数的转换。对于d轴只有1个阻尼绕组并且运算电感模型的参数已经估计得到的情况,IEEE Std 1110-2002标准建议采用解析公式直接计算等值电路参数。但是,由于辨识得到的运算电感模型的参数通常带有误差,用这种方式求取的等值电路参数值可能远离其真值。文献检索表明:还没有文献指出和研究过这个问题。为获得较为准确的等值电路参数值,论文将解析公式计算得到的等值电路参数值作为初值,然后基于发电机的混合状态模型,用预测误差法对等值电路参数进行估计。数值仿真结果表明按解析公式直接计算的方式存在大的误差,也表明所提方法在各种噪声情况下均能得到较准确的结果。本文所提方法能够作为IEEE Std 1110-2002标准关于该解析公式方法的一个补充。
论文考虑了当前大多数研究中所忽视的非线性饱和影响,提出了一个新的在线估计器。该估计器被用来辨识磁场绕组和d轴阻尼绕组的参数,不仅适用于凸极机,也适用于圆柱转子电机。仿真结果表明,若在参数辨识的过程中不考虑饱和作用,会造成较大的估计误差。大量噪声样本下的仿真结果表明提出的估计器既可以准确的捕获饱和在扰动过程中的非线性影响,而且具有较好的处理噪声的能力。
论文还提出了一个运用平方根无迹卡尔曼滤波器(Square-root unscented Kalman filter, SRUKF)来估计同步发电机参数的方法。首先,从参数估计的角度,发展了一个既适用于凸极机也适用于圆柱转子电机的三阶模型。然后,利用SRUKF对该模型进行了状态变量和未知参数的联合非线性估计。估计方法的基本特点是考虑模型的非线性。在测试系统上的仿真结果表明了所提方法的有效性。在联合估计的过程中,发电机参数稳定地收敛于稳态值,而估计的状态变量也与数值仿真得到的动态响应吻合。通过与常规的扩展卡尔曼滤波(Extended Kalman filter, EKF)方法的仿真比较,表明用所提出的方法能获得更准确的估计结果。
Synchronous machine is one of the key devices in power systems and synchronous machine models play an extremely important role in power system analysis. Power system stability analysis and designs of control strategies for control equipment are fully dependent on reasonable synchronous machine modeling and accurate parameters in models.
Parameter identification using measured data is the most important method for determining synchronous machine parameters. It is still a challenging topic although many researches have been conducted in this area in the past decades. Considerable efforts have been paid to load rejection tests and online time-domain tests for parameter identification of synchronous machines so far because of their advantages superior to other methods. However, there are deficiencies and shortcomings in existing researches of these two measurement-based methods. As well known, noises in measurements are unavoidable in any test. Unfortunately, the response curve method which is a popular technique under load rejection test cannot handle noisy measurements properly, whereas the optimization modeling method under load rejection test not only requires selection of initial parameter values but also may result in large estimation errors caused by measurement noises. Under load rejection test, it is often needed to implement parameter conversion between a time-constant-based operational inductance model and an equivalent-circuit based model due to requirements in calculations. Although a conversion formula under some condition is provided in the IEEE std 1110-2002, it failed to address errors of parameters which will be caused by error transfer in the conversion. In fact, this problem has never been presented in all existing researches. In online time-domain test, nonlinear dynamic saturation effects in a disturbance process have been missed in majority of previous work on online estimation of generator parameters. A third-order model for synchronous machine parameter online estimation has been used in a few published papers. However, the existing identification models need to be further improved and more effective estimation methods are required to deal with the non-linear feature of the third-order model.
In this thesis, new identification models and parameter estimation techniques are investigated systematically and deeply on the basis of load rejection test and online time-domain test. With an objective in improving accuracy of estimated parameters and increasing capacity of handling measurement-noises, the thesis focuses on effects of measurement noises on estimation results, errors in parameter conversion and solution to avoiding error transfers, nonlinear effects of magnetic saturation in a disturbance process and the nonlinear feature of third-order model.
A novel method for estimating d-axis parameters of synchronous generators under d-axis load rejection test is presented. The essence of the method is to simultaneously identify the coefficients of two single-input single-output transfer functions. From a viewpoint of modeling, it is a time-constant-based operational inductance model. Firstly, linear regression equations are constructed using the q-axis voltage, excitation current and their numerical integrations. Secondly, the regression coefficients with measurement noises are estimated using an instrumental variable approach. Finally, the d-axis parameters are calculated from the estimated regression coefficients. Simulation results indicate that the proposed method has a better performance than the traditional response curve method or optimization modeling method.
The method of single-input single-output transfer function is directly used to estimate q-axis synchronous inductance and time constants under load rejection test. Essentially, this method is to identify q-axis operational inductance. Simulation results demonstrate the effectiveness of the method.
A method to accurately determine d-axis equivalent circuit parameters from an operational inductance model is presented. In existing researches, either a time-constant based operational inductance model or an equivalent-circuit based model is obtained under load rejection test. However, the parameter conversion between the two models was not discussed. It is necessary to perform a parameter conversion when estimated parameters are different from those required by stability analysis software. In the case where the d-axis is represented by one damper winding and the parameters in operational inductance model have been estimated, the IEEE Std 1110-2002 has recommended that equivalent-circuit parameters be calculated using analytical formulas. However, the direct computation method using the analytical formulas may result in unreasonable parameter values which deviate far away from their true values because of the errors that always exist in the measurement-based operational inductance model. Literature searches indicate that this issue has not been addressed so far. To obtain accurate equivalent circuit parameters, the thesis presents a two-step method. Initial values of equivalent circuit parameters are computed first using the analytical formulas; and then a prediction error method is used to estimate the parameters using a hybrid state model of generator. Simulation results demonstrate that the direct computation method using the analytical formulas does cause large parameter errors whereas the presented method is very effective under any designated noise level. The presented method can be used as a complement to the analytical formula method given in the IEEE Std 1110-2002.
Majority of previous work on online estimation of generator parameters ignored the nonlinear dynamic saturation effect in a disturbance process. In the thesis, a new estimator is presented to incorporate the saturation effect in a disturbance process. The estimator focuses on recognizing field winding and d-axis damper winding parameters of both salient-pole and round-rotor generators. Simulation results demonstrate that neglecting the saturation effect in an identification procedure will create a large estimation error. Simulation results from a lot of noisy samples also demonstrate that the proposed estimator not only can accurately capture the non-linear dynamic saturation effect in a disturbance process but also has a good capacity of handling measurement noises.
A new method to estimate the parameters of a synchronous generator using the square-root unscented Kalman filter (SRUKF) is also presented in the thesis. A new third-order model for the parameter estimation of both round rotor and salient generators is developed first and then the SRUKF method is applied to the third-order model to perform the joint estimation of state variables and unknown generator parameters. The essential feature of the presented estimation method is incorporation of nonlinearity of the model. Simulation results demonstrate the effectiveness of the proposed method in parameter estimation of synchronous generator. The estimation processes of generator parameters steadily converge to the estimated values, whereas the estimation processes of state variables are consistent with the dynamic responses in the numerical simulations. Simulations indicate that the presented method can obtain more accurate results than the traditional extended Kalman filter (EKF) method.
利用测量数据对参数进行辨识是确定同步发电机参数的主要方法。尽管已历经多年的发展,同步发电机的参数辨识仍然是一个颇具挑战性的课题。抛载试验和在线时域测试法与现有的其它方法相比有很多优点,因而近年来受到工业界和学术界较多关注。但是,在这两种基于测试的方法中,至今已有的研究还存在不足和缺点。对于抛载试验而言,在有测量噪声时,图形法难以被应用,而测量噪声是任何测试方法中都不可避免的;优化方法不仅需要提供参数初值,并且在有测量噪声时也可能导致较大的估计误差。在抛载试验下,由于计算需要,经常要在基于时间常数的运算电感模型和基于等值电路的模型之间做参数转换,虽然IEEE Std 1110-2002标准提供了在一定条件下的转换计算公式,但并没有提到转换中由于误差传递造成的参数误差问题,实际上,还没有任何文献对这个问题进行过研究。对于在线时域测试法而言,大多数现有的研究没有考虑饱和在扰动过程中的非线性影响。另外,有文献研究了发电机三阶模型的在线辨识,但已有的辨识模型还需要进一步发展,模型的非线性本质也要求引入更佳的非线性估计方法。
本论文主要针对测量噪声对参数估计结果的影响、模型参数转换中的误差问题及其解决方案、磁路饱和在扰动过程中的非线性影响,以及三阶模型的非线性特点,基于抛载试验和在线时域测试方法,对同步发电机的辨识模型和参数估计技术进行了比较系统深入的研究和探索,以提高参数估计的精度和估计中的抗噪声能力。
论文提出了一种在d轴抛载试验条件下估计同步发电机d轴同步电感和时间常数等参数的新方法。该方法的本质是同时辨识两个单输入单输出的传递函数的系数。从模型的层面,该方法是辨识基于时间常数的运算电感模型。首先,利用q轴电压、磁场电流以及它们的数值积分,构建线性回归方程组。其次,利用辅助变量法求解带有测量噪声的回归方程组的系数。最后,根据回归系数计算d轴参数。算例的大量测试结果表明所提方法比现有的图形法和数值优化法有更好的估计性能。
论文直接引入上述辨识单输入单输出传递函数的方法,在q轴抛载试验条件下,对同步发电机的q轴同步电感和时间常数也进行了估计。该方法实质上是辨识q轴运算电感。仿真结果表明了引入的这种方法的有效性。论文提出了一种利用辨识得到的运算电感模型来确定同步发电机d轴等值电路参数的方法。在抛载试验下,现有的研究或以辨识运算电感模型的参数为目的,或以辨识等值电路参数为目的,但没有探讨两类参数之间的转换问题。当辨识得到的参数在类型上不同于稳定分析软件需要的参数时,必须进行参数的转换。对于d轴只有1个阻尼绕组并且运算电感模型的参数已经估计得到的情况,IEEE Std 1110-2002标准建议采用解析公式直接计算等值电路参数。但是,由于辨识得到的运算电感模型的参数通常带有误差,用这种方式求取的等值电路参数值可能远离其真值。文献检索表明:还没有文献指出和研究过这个问题。为获得较为准确的等值电路参数值,论文将解析公式计算得到的等值电路参数值作为初值,然后基于发电机的混合状态模型,用预测误差法对等值电路参数进行估计。数值仿真结果表明按解析公式直接计算的方式存在大的误差,也表明所提方法在各种噪声情况下均能得到较准确的结果。本文所提方法能够作为IEEE Std 1110-2002标准关于该解析公式方法的一个补充。
论文考虑了当前大多数研究中所忽视的非线性饱和影响,提出了一个新的在线估计器。该估计器被用来辨识磁场绕组和d轴阻尼绕组的参数,不仅适用于凸极机,也适用于圆柱转子电机。仿真结果表明,若在参数辨识的过程中不考虑饱和作用,会造成较大的估计误差。大量噪声样本下的仿真结果表明提出的估计器既可以准确的捕获饱和在扰动过程中的非线性影响,而且具有较好的处理噪声的能力。
论文还提出了一个运用平方根无迹卡尔曼滤波器(Square-root unscented Kalman filter, SRUKF)来估计同步发电机参数的方法。首先,从参数估计的角度,发展了一个既适用于凸极机也适用于圆柱转子电机的三阶模型。然后,利用SRUKF对该模型进行了状态变量和未知参数的联合非线性估计。估计方法的基本特点是考虑模型的非线性。在测试系统上的仿真结果表明了所提方法的有效性。在联合估计的过程中,发电机参数稳定地收敛于稳态值,而估计的状态变量也与数值仿真得到的动态响应吻合。通过与常规的扩展卡尔曼滤波(Extended Kalman filter, EKF)方法的仿真比较,表明用所提出的方法能获得更准确的估计结果。
Synchronous machine is one of the key devices in power systems and synchronous machine models play an extremely important role in power system analysis. Power system stability analysis and designs of control strategies for control equipment are fully dependent on reasonable synchronous machine modeling and accurate parameters in models.
Parameter identification using measured data is the most important method for determining synchronous machine parameters. It is still a challenging topic although many researches have been conducted in this area in the past decades. Considerable efforts have been paid to load rejection tests and online time-domain tests for parameter identification of synchronous machines so far because of their advantages superior to other methods. However, there are deficiencies and shortcomings in existing researches of these two measurement-based methods. As well known, noises in measurements are unavoidable in any test. Unfortunately, the response curve method which is a popular technique under load rejection test cannot handle noisy measurements properly, whereas the optimization modeling method under load rejection test not only requires selection of initial parameter values but also may result in large estimation errors caused by measurement noises. Under load rejection test, it is often needed to implement parameter conversion between a time-constant-based operational inductance model and an equivalent-circuit based model due to requirements in calculations. Although a conversion formula under some condition is provided in the IEEE std 1110-2002, it failed to address errors of parameters which will be caused by error transfer in the conversion. In fact, this problem has never been presented in all existing researches. In online time-domain test, nonlinear dynamic saturation effects in a disturbance process have been missed in majority of previous work on online estimation of generator parameters. A third-order model for synchronous machine parameter online estimation has been used in a few published papers. However, the existing identification models need to be further improved and more effective estimation methods are required to deal with the non-linear feature of the third-order model.
In this thesis, new identification models and parameter estimation techniques are investigated systematically and deeply on the basis of load rejection test and online time-domain test. With an objective in improving accuracy of estimated parameters and increasing capacity of handling measurement-noises, the thesis focuses on effects of measurement noises on estimation results, errors in parameter conversion and solution to avoiding error transfers, nonlinear effects of magnetic saturation in a disturbance process and the nonlinear feature of third-order model.
A novel method for estimating d-axis parameters of synchronous generators under d-axis load rejection test is presented. The essence of the method is to simultaneously identify the coefficients of two single-input single-output transfer functions. From a viewpoint of modeling, it is a time-constant-based operational inductance model. Firstly, linear regression equations are constructed using the q-axis voltage, excitation current and their numerical integrations. Secondly, the regression coefficients with measurement noises are estimated using an instrumental variable approach. Finally, the d-axis parameters are calculated from the estimated regression coefficients. Simulation results indicate that the proposed method has a better performance than the traditional response curve method or optimization modeling method.
The method of single-input single-output transfer function is directly used to estimate q-axis synchronous inductance and time constants under load rejection test. Essentially, this method is to identify q-axis operational inductance. Simulation results demonstrate the effectiveness of the method.
A method to accurately determine d-axis equivalent circuit parameters from an operational inductance model is presented. In existing researches, either a time-constant based operational inductance model or an equivalent-circuit based model is obtained under load rejection test. However, the parameter conversion between the two models was not discussed. It is necessary to perform a parameter conversion when estimated parameters are different from those required by stability analysis software. In the case where the d-axis is represented by one damper winding and the parameters in operational inductance model have been estimated, the IEEE Std 1110-2002 has recommended that equivalent-circuit parameters be calculated using analytical formulas. However, the direct computation method using the analytical formulas may result in unreasonable parameter values which deviate far away from their true values because of the errors that always exist in the measurement-based operational inductance model. Literature searches indicate that this issue has not been addressed so far. To obtain accurate equivalent circuit parameters, the thesis presents a two-step method. Initial values of equivalent circuit parameters are computed first using the analytical formulas; and then a prediction error method is used to estimate the parameters using a hybrid state model of generator. Simulation results demonstrate that the direct computation method using the analytical formulas does cause large parameter errors whereas the presented method is very effective under any designated noise level. The presented method can be used as a complement to the analytical formula method given in the IEEE Std 1110-2002.
Majority of previous work on online estimation of generator parameters ignored the nonlinear dynamic saturation effect in a disturbance process. In the thesis, a new estimator is presented to incorporate the saturation effect in a disturbance process. The estimator focuses on recognizing field winding and d-axis damper winding parameters of both salient-pole and round-rotor generators. Simulation results demonstrate that neglecting the saturation effect in an identification procedure will create a large estimation error. Simulation results from a lot of noisy samples also demonstrate that the proposed estimator not only can accurately capture the non-linear dynamic saturation effect in a disturbance process but also has a good capacity of handling measurement noises.
A new method to estimate the parameters of a synchronous generator using the square-root unscented Kalman filter (SRUKF) is also presented in the thesis. A new third-order model for the parameter estimation of both round rotor and salient generators is developed first and then the SRUKF method is applied to the third-order model to perform the joint estimation of state variables and unknown generator parameters. The essential feature of the presented estimation method is incorporation of nonlinearity of the model. Simulation results demonstrate the effectiveness of the proposed method in parameter estimation of synchronous generator. The estimation processes of generator parameters steadily converge to the estimated values, whereas the estimation processes of state variables are consistent with the dynamic responses in the numerical simulations. Simulations indicate that the presented method can obtain more accurate results than the traditional extended Kalman filter (EKF) method.
引文
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