电力系统传输网络与负荷模型辨识及其在电压稳定分析中的应用
|
摘要
电力系统的发展和大区联网的实现,使得电力系统规模日益扩大、电网结构更加复杂,为国民经济带来显著效益的同时,也使电力系统运行点越来越接近稳定极限,整个系统发生电压失稳甚至电压崩溃的危险不断增加。电力系统仿真研究和各种具体分析都是建立在相应的数学模型基础上,各元件精确的数学模型能更准确地反映实际系统的动态过程,提高计算精度与可信度,有助于保证系统稳定安全运行、并提高分析决策水平,在电力系统的运行、控制、计算中具有现实意义。为了实现电力系统稳定安全运行,本文重点研究电力系统传输网络模型和非线性动态负荷模型的辨识及其在电压稳定分析中的应用。论文取得的主要研究成果和创新点如下：
1)提出改进的带遗忘因子的最小二乘法及其病态问题改善方法,实现多源、多负载电网模型的在线辨识。
针对复杂电力系统传输网络,基于基尔霍夫电压、电流定律,引入电压增益矩阵和电网阻抗矩阵,建立顾及线路耦合关系的多源、多负载电网稳态线性模型。与戴维南等值模型相比,该模型更利于理解和研究系统的整体运行效果。为了适应电网参数经常变化的特点,基于同步相量测量数据,采用带遗忘因子的递推最小二乘方法辨识该电网模型,实现电网阻抗参数的估计和跟踪；同时提出一种改进的基于奇异值分解的病态问题改善方法,提高了模型的辨识精度和可信度。最后通过两个简单电力系统进行仿真实验,结果表明本文所提方法可以有效用于多源、多负载电力系统传输网络模型的在线辨识。
2)提出基于电网模型的线路故障诊断和电压稳定分析方法
基于多源、多负载电力系统传输网络模型,研究其在线路故障诊断和电压稳定分析等方面的应用。首先根据电网模型计算并跟踪系统导纳矩阵的变化,根据矩阵各元素的变化情况,提出线路故障诊断方法。其次对耦合的电网模型进行解耦处理,提出一种静态电压稳定指标,表征系统当前运行点与稳定运行极限点的距离,方便判定各负荷节点的电压稳定性及薄弱程度,利于整个电网稳定监测。最后采用简单5节点系统和IEEE-30节点标准电力系统对所提出的线路故障诊断和电压稳定性分析方法进行验证。结果表明本文所提方法可以有效的判断系统线路故障发生点,并实时监测系统稳定运行状态。
3)提出电力系统非线性动态负荷模型辨识方法
针对Hill等提出的指数功率恢复模型的非线性和动态特性,采用二阶泰勒级数展开模型作为该模型的简化模型,提出一种基于频率加权最小二乘的Hartley调制函数算法进行模型参数的辨识。这是一种针对连续时间系统的直接辨识方法,该方法巧妙的避免了信号的数值微分处理及初始条件的确定,克服了传统离散系统辨识方法在连续系统模型和离散系统模型相互转换时引入的误差以及对采样周期的依赖。选择合适的调制函数参数可以有效提高系统辨识的抗噪能力。
为了克服Hartley调制函数方法参数选择复杂的缺点,简化辨识过程,充分考虑指数功率恢复模型的结构特征,本文提出一种基于离散傅里叶变换数值微分的交替最小二乘辨识方法。将非线性负荷模型辨识问题分解为两个线性最小二乘问题,采用交替辨识方法逐步估计负荷模型参数。针对负荷模型辨识过程中需要计算数值微分的特点,提出基于离散傅里叶变换的数值微分方法,有效减小数据噪声对辨识结果的影响,而且提高了计算速度。仿真结果表明,本文所提方法在含有明显噪声情况下仍然可以获得比较精确的辨识结果。
4)提出考虑非线性动态负荷模型动、静态特性的电压稳定分析方法
结合P-V曲线法,分析动态负荷模型参数对系统运行点位置的影响,研究负荷静态特性和动态特性如何影响着电压失稳事故的发生,提高了系统的稳定运行监控能力。通过实例分析,证明了系统在相同条件下,负荷特性将会影响P-V曲线上系统运行点的位置,从而导致系统离电压崩溃点更近或者更远。通过实时监测系统运行状态,在系统接近稳定运行极限时,及时采取无功补偿或切负荷等措施,防止发生电压失稳和电压崩溃等事故的发生。
The past decade has seen major restructuring and deregulation in the electric utility industry; significant changes have been taking place, bringing in the notion of competition and market strategies in the operation of electric power systems, and the need to reduce operating and capital costs. This economic pressure drives the trend to maximize the utilization of high-voltage equipment, operating at conditions closer to the system limits; however, this also put systems at a higher risk for collapse. For safe and efficient operating of large power systems, it is of paramount importance to provide real-time and accurate estimates of the voltage stability margin. Accurate grid models and load models are important in monitoring and protection of wide-area power systems.
This dissertation addresses issues in the estimation and application of power grid impedance matrices and dynamic load models based on synchronized phasor measurements, for improving monitoring and better operation of large power systems. The main results and innovations are listed as follows:
1) Online impedance estimation of power grids using a recursive least squares estimation algorithm with a forgetting factor.
For better understanding overall operation and performace of entire power systems, a multi-bus power grid model is obtained based on Kirchhoff's current and voltage laws. A recursive least squares estimation algorithm with a forgetting factor is presented to identify impedance parameters of the model. This approach is based on synchronized phasor measurements and makes it possible to track changing parameters. The algorithm is tested on two power systems using MATPOWER-generated data, and case studies are conducted for estimation of grid impedances. The results show that the proposed method is effective for online estimation of grid impedances.
2) Applications of grid impedance matrices to voltage stability margin analysis and fault detection.
Application of power grid impedance matrices to voltage stability margin analysis and fault detection is studied. Based on the Kirchhoff's law, the system admittance matrix can be obtained from the grid model. Then a method to dectect transmission line outage by observing grid impedance changes is proposed. A multi-port method for voltage stability margin prediction is proposed based on the estimated network impedance matrix. A simple5-bus system and the IEEE30-bus power system are used to investigate the proposed methods, and the results showed that the proposed method can be utilized for dectecting transmission line outage and online monitoring of voltage stability with high accuracy.
3) Identification of nonlinear dynamic load models of power systems.
A second order Taylor series expansion model is presented as the simplification of the popularly used exponential recovery dynamic load model. Then, a frequency weighted least-squares based Hartley modulating functions method is developed to estimate parameters of the load model, which effectively attenuates the effect of noises in the process of parameter identification. However, it is hard to choose the optimal parameters of the Hartley modulating fuction method.
To simplify the identification process and to improve the identification accuracy, considering the special characteristic of the exponential recovery dynamic load model, an alternating least squares approach is developed to decompose the nonlinear optimization problem of dynamic load parameter identification to two linear least squares problems, which can be solved in an alternating manner. Then, a DFT-based numerical derivative technique is proposed to attenuate the effect of noises in the process of parameter estimation. Simulation studies are conducted to demonstrate the accuracy of the proposed methods for identifying the dynamic load model in the presence of noticeable additive measurement noise.
4) Application of the dynamic load models to stability margin analysis.
P-V curves play an important role in understanding voltage instability. Under the same conditions in a power system, load characteristics affect the location of operating point in the P-V curves, which is distinctly important for voltage stability analysis. The influence of dynamic load characteristics on voltage stability is studied. Simulation analysis showed that load characteristics are critical for the stability of the system. The parameters of the dynamic load model are helpful for voltage stability analysis and protection.
1)提出改进的带遗忘因子的最小二乘法及其病态问题改善方法,实现多源、多负载电网模型的在线辨识。
针对复杂电力系统传输网络,基于基尔霍夫电压、电流定律,引入电压增益矩阵和电网阻抗矩阵,建立顾及线路耦合关系的多源、多负载电网稳态线性模型。与戴维南等值模型相比,该模型更利于理解和研究系统的整体运行效果。为了适应电网参数经常变化的特点,基于同步相量测量数据,采用带遗忘因子的递推最小二乘方法辨识该电网模型,实现电网阻抗参数的估计和跟踪；同时提出一种改进的基于奇异值分解的病态问题改善方法,提高了模型的辨识精度和可信度。最后通过两个简单电力系统进行仿真实验,结果表明本文所提方法可以有效用于多源、多负载电力系统传输网络模型的在线辨识。
2)提出基于电网模型的线路故障诊断和电压稳定分析方法
基于多源、多负载电力系统传输网络模型,研究其在线路故障诊断和电压稳定分析等方面的应用。首先根据电网模型计算并跟踪系统导纳矩阵的变化,根据矩阵各元素的变化情况,提出线路故障诊断方法。其次对耦合的电网模型进行解耦处理,提出一种静态电压稳定指标,表征系统当前运行点与稳定运行极限点的距离,方便判定各负荷节点的电压稳定性及薄弱程度,利于整个电网稳定监测。最后采用简单5节点系统和IEEE-30节点标准电力系统对所提出的线路故障诊断和电压稳定性分析方法进行验证。结果表明本文所提方法可以有效的判断系统线路故障发生点,并实时监测系统稳定运行状态。
3)提出电力系统非线性动态负荷模型辨识方法
针对Hill等提出的指数功率恢复模型的非线性和动态特性,采用二阶泰勒级数展开模型作为该模型的简化模型,提出一种基于频率加权最小二乘的Hartley调制函数算法进行模型参数的辨识。这是一种针对连续时间系统的直接辨识方法,该方法巧妙的避免了信号的数值微分处理及初始条件的确定,克服了传统离散系统辨识方法在连续系统模型和离散系统模型相互转换时引入的误差以及对采样周期的依赖。选择合适的调制函数参数可以有效提高系统辨识的抗噪能力。
为了克服Hartley调制函数方法参数选择复杂的缺点,简化辨识过程,充分考虑指数功率恢复模型的结构特征,本文提出一种基于离散傅里叶变换数值微分的交替最小二乘辨识方法。将非线性负荷模型辨识问题分解为两个线性最小二乘问题,采用交替辨识方法逐步估计负荷模型参数。针对负荷模型辨识过程中需要计算数值微分的特点,提出基于离散傅里叶变换的数值微分方法,有效减小数据噪声对辨识结果的影响,而且提高了计算速度。仿真结果表明,本文所提方法在含有明显噪声情况下仍然可以获得比较精确的辨识结果。
4)提出考虑非线性动态负荷模型动、静态特性的电压稳定分析方法
结合P-V曲线法,分析动态负荷模型参数对系统运行点位置的影响,研究负荷静态特性和动态特性如何影响着电压失稳事故的发生,提高了系统的稳定运行监控能力。通过实例分析,证明了系统在相同条件下,负荷特性将会影响P-V曲线上系统运行点的位置,从而导致系统离电压崩溃点更近或者更远。通过实时监测系统运行状态,在系统接近稳定运行极限时,及时采取无功补偿或切负荷等措施,防止发生电压失稳和电压崩溃等事故的发生。
The past decade has seen major restructuring and deregulation in the electric utility industry; significant changes have been taking place, bringing in the notion of competition and market strategies in the operation of electric power systems, and the need to reduce operating and capital costs. This economic pressure drives the trend to maximize the utilization of high-voltage equipment, operating at conditions closer to the system limits; however, this also put systems at a higher risk for collapse. For safe and efficient operating of large power systems, it is of paramount importance to provide real-time and accurate estimates of the voltage stability margin. Accurate grid models and load models are important in monitoring and protection of wide-area power systems.
This dissertation addresses issues in the estimation and application of power grid impedance matrices and dynamic load models based on synchronized phasor measurements, for improving monitoring and better operation of large power systems. The main results and innovations are listed as follows:
1) Online impedance estimation of power grids using a recursive least squares estimation algorithm with a forgetting factor.
For better understanding overall operation and performace of entire power systems, a multi-bus power grid model is obtained based on Kirchhoff's current and voltage laws. A recursive least squares estimation algorithm with a forgetting factor is presented to identify impedance parameters of the model. This approach is based on synchronized phasor measurements and makes it possible to track changing parameters. The algorithm is tested on two power systems using MATPOWER-generated data, and case studies are conducted for estimation of grid impedances. The results show that the proposed method is effective for online estimation of grid impedances.
2) Applications of grid impedance matrices to voltage stability margin analysis and fault detection.
Application of power grid impedance matrices to voltage stability margin analysis and fault detection is studied. Based on the Kirchhoff's law, the system admittance matrix can be obtained from the grid model. Then a method to dectect transmission line outage by observing grid impedance changes is proposed. A multi-port method for voltage stability margin prediction is proposed based on the estimated network impedance matrix. A simple5-bus system and the IEEE30-bus power system are used to investigate the proposed methods, and the results showed that the proposed method can be utilized for dectecting transmission line outage and online monitoring of voltage stability with high accuracy.
3) Identification of nonlinear dynamic load models of power systems.
A second order Taylor series expansion model is presented as the simplification of the popularly used exponential recovery dynamic load model. Then, a frequency weighted least-squares based Hartley modulating functions method is developed to estimate parameters of the load model, which effectively attenuates the effect of noises in the process of parameter identification. However, it is hard to choose the optimal parameters of the Hartley modulating fuction method.
To simplify the identification process and to improve the identification accuracy, considering the special characteristic of the exponential recovery dynamic load model, an alternating least squares approach is developed to decompose the nonlinear optimization problem of dynamic load parameter identification to two linear least squares problems, which can be solved in an alternating manner. Then, a DFT-based numerical derivative technique is proposed to attenuate the effect of noises in the process of parameter estimation. Simulation studies are conducted to demonstrate the accuracy of the proposed methods for identifying the dynamic load model in the presence of noticeable additive measurement noise.
4) Application of the dynamic load models to stability margin analysis.
P-V curves play an important role in understanding voltage instability. Under the same conditions in a power system, load characteristics affect the location of operating point in the P-V curves, which is distinctly important for voltage stability analysis. The influence of dynamic load characteristics on voltage stability is studied. Simulation analysis showed that load characteristics are critical for the stability of the system. The parameters of the dynamic load model are helpful for voltage stability analysis and protection.
引文
[1]袁季修.防御大停电的广域保护和紧急控制.中国电力出版社,2007.
[2]Y. Harmand, M. Trotignon, J. F. Lesigne, et al. Analysis of a voltage collapse-incident and proposal for a time-based hierarchical containment scheme. CIGRE session paper 38/39-02,1990.
[3]赵遵廉.电力系统安全稳定导则学习和辅导.北京：中国电力出版社,2001.
[4]A. Kurita, T. Sakurai. The power system failure on July 23,1987 in Tokyo. Proceeding of the 27th conference on decision and control, Austin, Texas, USA, 1988.
[5]CIGRE WG34.08. Isolation and restoration policies against system collapse. Technical brochure,200,2002.
[6]王梅义,吴竞昌,蒙定中.大电网系统技术第2版.北京：水利电力出版社,1991.
[7]刘肇旭,印永华,郑美特,等.南方互联电力系统中期动态稳定破坏事故调查与分析.电网技术,1996,20(7)：53-58.
[8]雷晓蒙.台湾省1999年7月29日的大停电事故的教训和启示.中国电力,1999,32(12)：55-57.
[9]U.S.-Canada Power System outage Task Force. Final report on the August 14, 2003 blackout in the Unite States and Canada:causes and recommendations. 2004.
[10]唐斯庆,张弥,李建设,等.海南电网“9·26”大面积停电事故的分析与总结.电网技术,2006,30(1)：1-7.
[11]陈庆前,尹项根,侯慧,等.从2008年雪灾分析电力系统的结构缺陷.中国电力,2008,41(12)：1-5.
[12]倪以信,陈寿孙,张宝霖.动态电力系统的理论和分析.北京：清华大学出版社,2002.
[13]T. V. Cutsem, C. Vournas. Voltage stability of electric power systems. Springer, 1998.
[14]A. Greenwood. Electrical transients in power systems,2nd edition. Wiley Interscience,1991.
[15]K. E. Martin. Phasor measurements at the Bonneville power administration. Power Systems and Communications Infrastructures for the Future, Beijing, China,2002.
[16]K. E. Martin. Phasor measurements at the Bonneville power administration. Power Systems and Communications Infrastructures for the Future, Beijing, China,2002.
[17]蔡运清,汪磊,M.Kip,等.广域保护(稳控)技术的现状及展望.电网技术,2004,28(8)：20-25.
[18]Y. J. Yoon. Study of the utilization and benefits of phasor measurement units for large scale power system state estimation. Master thesis, Texas A&M University, 2005.
[19]Eastern Interconnection Phasor Project. Metrics for determining the impact of phasor measurements on power system state estimation.2006.
[20]S. Chakrabarti, E. Kyriakides, D. G. Eliades. Placement of synchronized measurements for power system observability. IEEE Transactions on Power Delivery,2009,24(1):12-19.
[21]Y. Z. Cheng, X. Hu, B. Gou. A new state estimation using synchronized phasor measurements. IEEE International Symposium on Circuits and systems,2008. 2817-2820.
[22]张文涛,邱宇峰,郑旭军.GPS及其在电力系统中的应用.电网技术,1996,20(5)：38-40.
[23]熊敏,施慧.两地功角相量监测系统在电力系统中的应用.中国电力,1998,31(2)：7-9.
[24]李丹等.华北电网广域实时动态监测系统.电网技术,2004,28(23).
[25]王兆家,岑宗浩,陈汉中.华东电网多功能功角实时监测系统的开发及应用.电网技术,2002,26(8)：44-48.
[26]钟波,于峥.广域电网相量测量系统在西北电网的开发及应用.中国电力,2005,38(12)：2003.
[27]J. Xiao, X. Xie, H. Li, et al. Power system dynamic security assessment via synchrophasor Monitoring.2004 International Conference on Power System Technology-POWERCON,2004.
[28]王正风,葛斐,戴长春.基于PMU的电力系统建模及参数辨识.继电器,2007,35(S)：378-382.
[29]范琦,穆钢,王克英.基于同步相量测量的线路参数在线测量的实验研究.东北电力学院学报,2002,22(4)：1-5.
[30]常乃超,兰洲,甘德强,等.广域测量系统在电力系统分析及控制中的应用综述.电网技术,2005,29(10)：46-52.
[31]张伯明,陈寿孙.高等电力网络分析.清华大学出版社,1999.
[32]P. Zaroo, A. G. Exposito. Power system Parameter Estimation:A Survey. IEEE Transactions on Power Systems,2000,15 (1):216-222.
[33]罗化伟.基于快速戴维南等值的电力系统静态电压稳定性研究：[硕士学位论文].湖南大学,2009.
[34]孙华东,周孝信,李若梅.计及感应电动机负荷的静态电压稳定性分析.中国电机工程学报,2005,25(24)：1-7.
[35]B. Milosevic, M. Begovic. Voltage-stability protection and control using a wide-area network of phasor measurements. IEEE Transactions on Power Systems,2003,18:121-127.
[36]G. Verbic, F. Gubina. A new concept of voltage-collapse protection based on local phasors. IEEE Transactions on Power Delivery,2004,19 (2):576-581.
[37]M. Zima, M. Larsson, P. Korba, et al. Design aspects for wide-area monitoring and control systems. Proceedings of the IEEE,2005,93 (5):980-996.
[38]Y. Wang, W.Y. Li, J.P. Lu. A new node voltage stability index based on local voltage phasors. Electric Power Systems Research,2009,79:265-271.
[39]S. Corsi, G. N. Taranto. A real-time voltage instability identification algorithm based on local phasor measurements. IEEE Transactions on Power Systems, 2008,23:1271-1279.
[40]G. Fusco, A. Losi, M. Russo. Constrained least squares methods for parameter tracking of power system steady-state equivalent circuits. IEEE Transactions on Power Delivery,2000,15, (3):1073-2000.
[41]K. Vu, M. M. Begovic, D. Novosel, et al. Use of local measurements to estimate voltage-stability margin. IEEE Transactions on Power Systems,1999,14: 1029-1034.
[42]M. H. Haque. On-line monitoring of maximum permissible loading of a power system within voltage stability limits. IEE Proceedings Generation, Transmission & Distribution,2003,150:107-112.
[43]李娟,刘修宽,曹国臣,等.一种面向节点的电网等值参数跟踪估计方法的研究.中国电机工程学报,2003,23(3)：30-33.
[44]K. Ohtsuka, S. Yokokava, H. Tanaka, et al. An equivalent of multi-machine power systems and its identification for online application to decentralized stabilizers. IEEE Transactions on Power Systems,1989,4 (2):687-693.
[45]Y. Gong, N. Schulz, A. Guzman. Synchrophasor-Based Real-Time Voltage Stability Index. Proceedings of the 32nd Annual Western Protective Relay Conference,2005:1-8.
[46]梁志瑞,于成洋.基于同步相量测量的电力系统等值及电压稳定评估.电力科学与工程,2005.33-36.
[47]段俊东,郭志忠.基于广域测量的在线电压稳定监视.继电器,2006,34(15)：24-28.
[48]L. Ljung. System identification:theory for the user. Englewood Cliffs, NJ: Prentice-Hall,1987.
[49]K. H. E. Liu, S. L. Lim. Parameter error identification and estimation in power system state estimation. IEEE Transactions on Power Systems,1995,10 (1): 200-209.
[50]O. Alsac, N. Vempati, B. Stott, et al. Generalized state estimation. IEEE Transactions on Power Systems,1998,13 (3):1069-1075.
[51]W. E. Larimor. Canonical variate analysis in identification, filtering and adaptive control. Proc.29th IEEE Conference on Decision and Control,1990. 596-604.
[52]P. V. Overschee, B.D. Moor. Subspace Identification for Linear Systems:Theory, Implementation, and Applications. Kluwer Academic Publishers,1996 Data driven weighted estimation,1996.
[53]W. Liu, F. Wu, S. Lun. Estimation of parameter errors from measurement residuals in state estimation. IEEE Transactions on Power Systems,1992,7 (1): 81-89.
[54]I. W. Slutsker, S. Mokhtari, K. A. Clements. Real time recursive parameter estimation in energy management systems. IEEE Transactions on Power Systems,1996,11 (3):1393-1399.
[55]王进,苏盛,李欣然.电力系统综合负荷模型的辨识算法研究.华北电力技术,2002,11：8-12.
[56]F. Ding, T. W. Chen, Identification of Hammerstein nonlinear ARMAX systems. Automatica,2005,41 (9):1479-1489.
[57]Y. Shi, F. Ding, T. W. Chen, Multirate crosstalk identification in xDSL systems. IEEE Transactions on Communications,2006,54 (10):1878-1886.
[58]J. V. Milanovic, I. A. Hiskens. Effects of dynamic load model parameters on damping of oscillations in power systems. Electric Power Systems Research, 1995,33:53-61.
[59]Y. V. Makarov, V. A. Maslennikov, D. J. Hill. Revealing loads having the biggest influence on power system small disturbance stability. IEEE Transactions on Power Systems,1996,11:2018-2023.
[60]G. D. Prasad, M. A. Al-Mulhim. Comparative assessment of the effect of dynamic load models on voltage stability. International Journal of Electrical Power & Energy Systems,1997,19:305-309.
[61]A. Borghetti, R. Caldon, C. A. Nucci. Generic dynamic load models in long-term voltage stability studies. International Journal of Electrical Power & Energy Systems,2000,22:291-301.
[62]鞠平.电力系统负荷建模理论与实践.电力系统自动化,1999,19(1)：1-7.
[63]贺仁睦.负荷模型在电力系统计算中的作用及发展.华北电力学院学报,1985,3：1-8.
[64]周文,贺仁睦,章健,等.电力负荷建模问题研究综述.现代电力,1999,2：83-89.
[65]C. Concordia, S. Ihara. Load representation in power system stability studies. IEEE Transactions on Power Systems,1982,101 (4):969-977.
[66]CIGRE Task Force. Load modeling and dynamics. Electra,1990,1 (130): 124-141.
[67]CIGRE Task Force. Modeling of voltage collapse including dynamic phenomena. Electra,1993,1 (147):71-77.
[68]IEEE Task Force. Standard load models for power flow and dynamic performance simulation. IEEE Transactions on Power Systems,1995,10 (3): 1302-1313.
[69]J. Ma, R. M. He, D. J. Hill. Load modeling by finding support vectors of load data from field measurements. IEEE Transactions on Power Systems,2006,21 (2):726-735.
[70]P. Ju, F. Wu, Z. Y. Shao, et al. Composite load models based on field measurements and their applications in dynamic analysis. IET Proceeding of Generation Transmission and Distribution,2007,1 (5):751-760.
[71]张红斌,汤涌,李柏青.差分方程负荷模型参数分散性的研究.2006,26(18)：1-5.
[72]鞠平,马大强.电力系统负荷建模.中国电力出版社,2008.
[73]卫志农,鞠平.电力负荷在线建模方法.中国电机工程学报,1995,15(6)：361-368.
[74]W. S. Kao, C. J. Lin, C.T. Huang, et al. Comparison of simulated power system dynamics applying various load models with actual recorded data. IEEE Transactions on Power Systems,1994,9:248-254.
[75]D. N. Kosterev, C. W. Taylor, W. A. Mittelstadt. Model validation for the August 10,1996 WSCC system outage. IEEE Transactions on Power Systems,1999,14: 967-979.
[76]IEEE Task Force on Load Representation for Dynamic Performance. Load representation for dynamic performance analysis. IEEE Transactions on Power Systems,1993,8:472-482.
[77]IEEE Task Force on Load Representation for Dynamic Performance. Bibliography on load models for power flow and dynamic performance simulation. IEEE Transactions on Power Systems,1995,10:523-538.
[78]R. M. He, J. Ma, D. J. Hill. Composite load modeling via measurement approach. IEEE Transactions on Power Systems,2006,21:663-672.
[79]J. Ma, D. Han, R. M. He, Z. Y. Dong, et al. Reducing identified parameters of measurement-based composite load model. IEEE Transactions on Power Systems,2008,23:76-83.
[80]W. S. Kao. Dynamic load modeling in power system stability studies. IEEE Transactions on Power Systems,1995,10 (2):907-914.
[81]M. Taleb, M. Akbaba, E. A. Abdullah. Aggregation of induction machines for power system dynamic studies. IEEE Transactions on Power Systems,1994,9 (4):2042-2048.
[82]陈谦,孙建波,蔡敏,等.考虑配电网络综合负荷模型的参数确定.中国电机工程学报,2008,28(16)：45-50.
[83]鞠平,潘学萍,韩敬东.3种感应电动机综合负荷模型的比较.电力系统自动化,1999,23(19)：40-47.
[84]B. K. Choi, H. D. Chiang, Y. Li, et al. Measurement-based dynamic load models: derivation, comparison, and validation. IEEE Transactions on Power Systems, 2006,21 (3):1276-1283.
[85]B. K. Choi, H. D. Chiang, Y. Li, et al. Development of composite load models of power systems using online measurement data. Journal of Electrical Engineering & Technoogyl,2006,1 (2):161-169.
[86]B. K. Choi, H. D. Chiang, S. T. Cain. Justification of some field observations of dynamic load behaviors:analytical and numerical approach. Power and Energy Society General Meeting-Conversion and Delivery of Electrical Energy in the 21st Century,2008.1-7.
[87]B. K. Choi, H. D. Chiang. Multiple solutions and plateau phenomenon in measurement-based load model development:issues and suggestions. IEEE Transactions on Power Systems,2009,24 (2):824-831.
[88]G. D. Prasad, M. A. Al-Mulhim, G. D. Ray, et al. Comparative assessment of the effect of dynamic load models on voltage stability. Electrical Power & Energy Systems,1997,19 (5):305-309.
[89]F. Dai, J. V. Milanovic, N. Jenkins. The influence of measurement delays on estimated load model parameters. Ninth International Conference on Harmonics and Quality of Power,2000,1 (1):324-328.
[90]A. Maitra, A. Gaikwaad, P. Pourbeik, et al. Load models parameter derivation using an automated algorithm and measured data. Power and Energy Society General Meeting-Conversion and Delivery of Electrical Energy in the 21st Century,2008.1-7.
[91]I. R. Navarro. Dynamic load models for power systems-Estimation of time-varying parameters during normal operation. Licentiate thesis, Lund University,2002.
[92]D. J. Hill. Nonlinear dynamic load models with recovery for voltage stability studies. IEEE Transactions on Power Systems,1993,8:166-176.
[93]W. Xu, Y. Mansour. Voltage stability analysis using generic dynamic load models. IEEE Transactions on Power Systems,1994,9:479-493.
[94]M. M. Begovic, R. Q. Mills. Load identification and voltage stability monitoring. IEEE Transactions on Power Systems,1995,10(1):109-116.
[95]Y. J. Jeng, C. C. Yeh. Cluster-based blind nonlinear-channel estimation. IEEE Transactions on Signal Process,1997,45 (5):1161-1172.
[96]张强.非线性结构的神经网络LM系统辨识方法.振动工程学报,2004,17：986-988.
[97]M. Enqvist. A weighting method for approximate nonlinear system identification. Proceedings on the 46th IEEE Conference on Decision and Control,2007:5104-5109.
[98]强明辉,张京娥.基于MATLAB的递推最小二乘辨识与仿真.自动化与仪 器仪表,2008,6：4-5.
[99]J. H. Wang, P. K. Hopke, T. M. Hancewicz, et al. Application of modified alternating least squares regression to spectroscopic image analysis. Analytica Chimica Acta,2003,476:93-109.
[100]苟北,陈陈,提兆旭.Prony算法在电力系统负荷动态模型辨识中的应用研究.电力系统自动化,1997,21：21-24.
[101]程颖,鞠平,吴峰.负荷模型参数辨识的粒子群优化法及其与基因算法比较.电力系统自动化,2003,11：25-29.
[102]章健,贺仁睦,韩民晓.直接优化方法及其在负荷模型参数辨识中的应用.现代电力,1996,13(4)：8-14.
[103]D. Karisson, D. J. Hill. Modeling and identification of nonlinear dynamic loads in power systems. IEEE Transactions on Power Systems,1994,9 (1):157-166.
[104]J. C. Wang, H. D. Jiang, C. L. Chang, et al. Development of a frequency-dependent composite load model using the measurement approach. IEEE Transactions on Power Systems,1994,9:1546-1556.
[105]I. A. Hiskens. Nonlinear dynamic model evaluation from disturbance measurements. IEEE Transactions on Power Systems,2001,16 (4):702-710.
[106]王进,李欣然,苏盛.用阻尼最小二乘优化算法实现电力系统综合静态负荷建模.长沙电力学院学报,2004,19(1)：40-46.
[107]P. Ju, E. Handschin, D. Karlsson. Nonlinear dynamic load modeling:model and parameter estimation. IEEE Transactions on Power Systems,1996,11 (4): 1689-1696.
[108]D. Han, J. Ma, R. M. He, et al. A real application of measurement-based load modeling in large-scale power grids and its validation. IEEE Transactions on Power Systems,2009,24:1756-1764.
[109]V. Knyazkin, C. A. Canzares, L. H. Soder. On the parameter estimation and modeling of aggregate power system loads. IEEE Transactions on Power Systems,2004,19:1023-1031.
[110]P. Jazayeri, W. Rosehart, D. T. Westwick. A multistage algorithm for identification of nonlinear aggregate power system loads. IEEE Transactions on Power Systems,2007,22:1072-1079.
[111]M. Matsubara, Y. Usui, S. Sugimoto. Identification of continuous-time MIMO systems via sampled data. International Journal of Innovative Computing Information and Control,2006,2 (5):1119-1136.
[112]M. Dehghani, S. K. Y. Nikravesh. Estimation of synchronous generator parameters in a large scale power system. International Journal of Innovative Computing Information and Control,2009,5 (8):2141-2150.
[113]苏永春.电力系统电压稳定理论若干关键问题研究：[博士学位论文].华中科技大学,2010.
[114]A. Souza, J. Souza, A. Silva. Online voltage stability monitoring. IEEE Transactions on Power Systems,2000,15 (4):1300-1305.
[115]黄志刚,邬炜,韩英铎.基于同步相量测量的电压稳定评估算法.电力系统自动化,2002,26(2)：28-33.
[116]陈衍.电力系统稳态分析.北京：中国电力出版社,1995.
[117]C. W. Taylor. Power system voltage stability. New York, McGraw-Hill,1994.
[118]T. V. Cutsem, C. Vourmas. Voltage stability of electric power system. Norwell, MA, USA:Kluwer Academic Publishers,1998.
[119]沈莹.基于支持向量机的负荷建模的研究：[硕士学位论文].郑州大学,2007.
[120]潘文霞,陈允平,沈祖诒.电力系统电压稳定性研究综述.电网技术,2001,25(9)：51-54.
[121]张艳萍.受端系统小扰动电压稳定问题的研究：[博士学位论文].华北电力大学(北京),2008.
[122]祝晶.基于支持向量机的负荷建模的研究：[硕士学位论文].湖南大学,2006.
[123]Y. Kataoka, Y. Shinoda. Voltage stability limit of electric power systems with generator reactive power constraints considered. IEEE Transactions on Power System,2005,20 (2):951-962.
[124]徐晓春.电力系统在线电压静态稳定分析方法和应用研究：[硕士学位论文].东南大学,2009.
[125]中国电力科学研究院.中国版BPA潮流程序用户手册,2002.
[126]吴潘.基于分岔理论的电力系统电压稳定及无功优化研究：[硕士学位论文].长沙理工大学,2010.
[127]江伟,王成山,余贻鑫,等.直接计算静态电压稳定临界点的新方法.中国电机工程学报,2006,26(10)：1-6.
[128]李村晓.电力系统综合负荷模型辨识策略研究及建模平台开发：[硕士学位论文].湖南大学,2007.
[129]樊宇璐.基于改进连续潮流法的电力系统静态电压稳定裕度研究：[硕士学 位论文].广西大学,2009.
[130]王立德.电力系统综合负荷模型结构研究：[硕士学位论文].湖南大学,2008.
[131]林舜江.负荷动特性的建模及其对电压稳定的影响研究：[博士学位论文].湖南大学,2008.
[132]李日波.电网戴维南等值及静态电压稳定性研究：[硕士学位论文].湖南大学,2010.
[133]李连伟.基于戴维南等值的静态电压稳定极限快速计算方法研究：[硕士学位论文].湖南大学,2009.
[134]葛维春.电力系统电压稳定性与电压崩溃的研究：[博士学位论文].哈尔滨工业大学与华北电力学院联合培养,1992.
[135]李宝国,鲁宝春,巴金祥.一种绘制PV曲线的快速方法.继电器,2002,30(2)：13-15.
[136]段俊东,郭志忠.一种可在线确定电压稳定运行范围的方法.中国电机工程学报,2006,26(4)：113-118.
[137]V. Ajjarapu, B. Lee. Bibliography on voltage stability. IEEE Transactions on Power Systems,1998,13 (1):115-125.
[138]B. H. Chowdhury, C. W. Taylor. Voltage Stability Analysis:V-Q Power Flow Simulation versus Dynamic Simulation. IEEE Transactions on Power Systems, 2001,15(4):1354-1359.
[139]H. Sun, X. Zhou, R. Li. Accuracy analysis of static voltage stability indices based on power flow model. IEEE/PES T&D 2005 Asia Pacific, Dalian, China, 2005.
[140]P. Kessel, H. Glavitsch. Estimating the voltage stability of a power system. IEEE Transactions on Power Delivery,1986,1 (3):346-354
[141]余贻鑫,贾宏杰,严雪飞.可准确跟踪鞍节点分岔的改进局部电压稳定指标LI.电网技术,1999,23(5)：19-23.
[142]D. Marelli, M. Fu. A continuous-time linear system identification method for slowly sampled data. IEEE Transactions on Signal Processing,2010,58 (5): 2521-2533.
[143]H. Gamier, M. Mensler, A. Richard. Continuous-time model identification from sampled data:implementation issues and performance evaluation. International Journal of Control,2003,76 (13):1337-1357.
[144]H. Unbehauen, G. P. Rao. A review of identification in continuous-time systems. Annual reviews in Control,1998,22 (27):145-171.
[145]G. P. Rao, H. Unbehauen. Identification of continuous-time systems. IEE Proceeding Control Theory Application,2006,153 (2):185-220.
[146]P. C. Young, H. Gamier. Identification and estimation of continuous-time, data-based mechanistic (DBM) models for environmental systems. Environmental Modeling & Software,2006,21 (8):1055-1072.
[147]S. Daniel-Berhel, H. Unbehauen. Physical parameters estimation of the nonlinear continuous-time dynamics of a DC motor using Hartley modulating functions method. Journal of the Franklin Institute,1999,336 (3):481-501.
[148]D. K. Rollins, N. Bhandari, A. M. Bassily, et al. A continuous-time nonlinear dynamic predictive modeling method for Hammerstein process. Industrial & Engineering Chemistry Research,2003,42 (4):860-872.
[149]F. X. Wu, L. Mu. Separable parameter estimation method for nonlinear biological system. The 3rd International Conference on Bioinformatics and Biomedical Engineering, Beijing China,2009.1-4.
[150]W. Rosehart, D. Westwick, P. Jazayeri, et al. Separable identification of nonlinear aggregate power system loads. Electric Power Systems Research, 2009,79 (2):346-354.
[151]邓勇,郭瑞碰,黄劫,等.电网参数辨识与实时拓扑检错系统的开发与应用.2007,1：15-17.
[152]S. A. Arefifar, W. Xu. Online tracking of power system impedance parameters and filed experiences. IEEE Transactions on Power Delivery,2009,24 (4): 1781-1788.
[153]李超,房大中,周雪松.负荷动态特性对孤网电压稳定性的影响.天津理工大学学报,2007,23(4)：54-58.
[154]宗秀红,张尧,董泰福.计及负荷动态特性的电压稳定概率特征根分析.继电器,2008,36(4)：19-26.
[155]李欣然,贺仁睦,章健,等.负荷特性对电力系统静态电压稳定性的影响和静态电压稳定性广义实用判据.中国电机工程学报,1999,19(4)：23-30.
[156]张伶俐,周文,章健,等.面向综合的电力负荷特性建模.中国电机工程学报,1999,19(9)：71-75.
[157]J. Y. Wen, L. Jiang, Q. H. Wu, et al. Power system load modeling by learning based on system measurements. IEEE Transactions on Power Delivery,2003, 18:364-371.
[158]E. Vaahedi, H. M. Z. El-Din, W. W. Price. Dynamic load modeling in large scale stability studies. IEEE Transactions on Power Systems,1988,3 (3):1039-1045.
[159]王进,李欣然,苏盛.一种电力系统综合负荷模型辨识的改进算法研究.电力系统及其自动化学报,2002,14(2)：12-15.
[160]郭琼,姚晓宁.浅析电力系统负荷对电压稳定性的影响.电力系统及其自动化学报,2004,16(3)：61-65.
[161]H. Wang, L. Qian, E. Dougherty. Inference of gene regulatory networks using S-system:a unified approach. IET Systems Biology,2010,4 (2):145-156.
[162]周轶,菅浩然,李致家,等.基于递推最小二乘改进算法的洪水预报模型研究.河海大学学报,2007,35(1)：77-80.
[163]J. Yang, T. W. Chen, M. Wu. Online impedance matrix estimation of interconnected power systems. IEEE Electrical Power and Energy Conference 2009, Montreal, Canada,2009.1-5.
[164]A.G. Phadke. Synchronized phasor measurements in power systems. IEEE Computer Applications in Power,1993,6 (2):10-15.
[165]R.D.Zimmerman, D. Gan. MATPOWER User's Manual. School of Electrical Engineering, Cornell University, Version 3.2,2007.
[166]http://www.ee.washington.edu/research/pstca,1993.
[167]Power Systems Test Case Archive,30 bus power flow test case. University of Washington College of Engineering. Available:http://www.ee.washington.edu /research/pstca/pf30/pg_tca30bus.htm,1993.
[168]C. Canizares. Voltage stability assessment:concepts, practices and tools. IEEE-PES Power Systems Stability Subcommittee Special Publication, SP101PSS,2002.
[169]J. Yang, W. X. Li, T. W. Chen, et al. Online estimation and application of power grid impedance matrices based on synchronized phasor measurements. IET Generation, Transmission & Distribution,2010,4, (9):1052-1059.
[170]J. Yang, M Wu, Y. He, et al. A continuous-time identification method for parameter estimation of nonlinear dynamic load models of power systems. International Journal of Innovative Computing, Information and Control, (Accepted).
[171]J. Yang, W. X. Li, T. W. Chen, et al. Identification of nonlinear dynamic load models using an alternating least squares approach. The Fourth International Conference on Electric Utility Deregulation and Restructuring and Power Technologies, Weihai, China,2011.1155-1160.
[172]R. Chartrand. Numerical differentiation of noisy, non smooth data. ISRN Applied Mathematics,2005,2011:1-11.
[173]J. Yang, M. Wu, Y. He, et al. Identification and application of nonlinear dynamic load models. Journal of Control Theory and Application, (Accepted).
[2]Y. Harmand, M. Trotignon, J. F. Lesigne, et al. Analysis of a voltage collapse-incident and proposal for a time-based hierarchical containment scheme. CIGRE session paper 38/39-02,1990.
[3]赵遵廉.电力系统安全稳定导则学习和辅导.北京：中国电力出版社,2001.
[4]A. Kurita, T. Sakurai. The power system failure on July 23,1987 in Tokyo. Proceeding of the 27th conference on decision and control, Austin, Texas, USA, 1988.
[5]CIGRE WG34.08. Isolation and restoration policies against system collapse. Technical brochure,200,2002.
[6]王梅义,吴竞昌,蒙定中.大电网系统技术第2版.北京：水利电力出版社,1991.
[7]刘肇旭,印永华,郑美特,等.南方互联电力系统中期动态稳定破坏事故调查与分析.电网技术,1996,20(7)：53-58.
[8]雷晓蒙.台湾省1999年7月29日的大停电事故的教训和启示.中国电力,1999,32(12)：55-57.
[9]U.S.-Canada Power System outage Task Force. Final report on the August 14, 2003 blackout in the Unite States and Canada:causes and recommendations. 2004.
[10]唐斯庆,张弥,李建设,等.海南电网“9·26”大面积停电事故的分析与总结.电网技术,2006,30(1)：1-7.
[11]陈庆前,尹项根,侯慧,等.从2008年雪灾分析电力系统的结构缺陷.中国电力,2008,41(12)：1-5.
[12]倪以信,陈寿孙,张宝霖.动态电力系统的理论和分析.北京：清华大学出版社,2002.
[13]T. V. Cutsem, C. Vournas. Voltage stability of electric power systems. Springer, 1998.
[14]A. Greenwood. Electrical transients in power systems,2nd edition. Wiley Interscience,1991.
[15]K. E. Martin. Phasor measurements at the Bonneville power administration. Power Systems and Communications Infrastructures for the Future, Beijing, China,2002.
[16]K. E. Martin. Phasor measurements at the Bonneville power administration. Power Systems and Communications Infrastructures for the Future, Beijing, China,2002.
[17]蔡运清,汪磊,M.Kip,等.广域保护(稳控)技术的现状及展望.电网技术,2004,28(8)：20-25.
[18]Y. J. Yoon. Study of the utilization and benefits of phasor measurement units for large scale power system state estimation. Master thesis, Texas A&M University, 2005.
[19]Eastern Interconnection Phasor Project. Metrics for determining the impact of phasor measurements on power system state estimation.2006.
[20]S. Chakrabarti, E. Kyriakides, D. G. Eliades. Placement of synchronized measurements for power system observability. IEEE Transactions on Power Delivery,2009,24(1):12-19.
[21]Y. Z. Cheng, X. Hu, B. Gou. A new state estimation using synchronized phasor measurements. IEEE International Symposium on Circuits and systems,2008. 2817-2820.
[22]张文涛,邱宇峰,郑旭军.GPS及其在电力系统中的应用.电网技术,1996,20(5)：38-40.
[23]熊敏,施慧.两地功角相量监测系统在电力系统中的应用.中国电力,1998,31(2)：7-9.
[24]李丹等.华北电网广域实时动态监测系统.电网技术,2004,28(23).
[25]王兆家,岑宗浩,陈汉中.华东电网多功能功角实时监测系统的开发及应用.电网技术,2002,26(8)：44-48.
[26]钟波,于峥.广域电网相量测量系统在西北电网的开发及应用.中国电力,2005,38(12)：2003.
[27]J. Xiao, X. Xie, H. Li, et al. Power system dynamic security assessment via synchrophasor Monitoring.2004 International Conference on Power System Technology-POWERCON,2004.
[28]王正风,葛斐,戴长春.基于PMU的电力系统建模及参数辨识.继电器,2007,35(S)：378-382.
[29]范琦,穆钢,王克英.基于同步相量测量的线路参数在线测量的实验研究.东北电力学院学报,2002,22(4)：1-5.
[30]常乃超,兰洲,甘德强,等.广域测量系统在电力系统分析及控制中的应用综述.电网技术,2005,29(10)：46-52.
[31]张伯明,陈寿孙.高等电力网络分析.清华大学出版社,1999.
[32]P. Zaroo, A. G. Exposito. Power system Parameter Estimation:A Survey. IEEE Transactions on Power Systems,2000,15 (1):216-222.
[33]罗化伟.基于快速戴维南等值的电力系统静态电压稳定性研究：[硕士学位论文].湖南大学,2009.
[34]孙华东,周孝信,李若梅.计及感应电动机负荷的静态电压稳定性分析.中国电机工程学报,2005,25(24)：1-7.
[35]B. Milosevic, M. Begovic. Voltage-stability protection and control using a wide-area network of phasor measurements. IEEE Transactions on Power Systems,2003,18:121-127.
[36]G. Verbic, F. Gubina. A new concept of voltage-collapse protection based on local phasors. IEEE Transactions on Power Delivery,2004,19 (2):576-581.
[37]M. Zima, M. Larsson, P. Korba, et al. Design aspects for wide-area monitoring and control systems. Proceedings of the IEEE,2005,93 (5):980-996.
[38]Y. Wang, W.Y. Li, J.P. Lu. A new node voltage stability index based on local voltage phasors. Electric Power Systems Research,2009,79:265-271.
[39]S. Corsi, G. N. Taranto. A real-time voltage instability identification algorithm based on local phasor measurements. IEEE Transactions on Power Systems, 2008,23:1271-1279.
[40]G. Fusco, A. Losi, M. Russo. Constrained least squares methods for parameter tracking of power system steady-state equivalent circuits. IEEE Transactions on Power Delivery,2000,15, (3):1073-2000.
[41]K. Vu, M. M. Begovic, D. Novosel, et al. Use of local measurements to estimate voltage-stability margin. IEEE Transactions on Power Systems,1999,14: 1029-1034.
[42]M. H. Haque. On-line monitoring of maximum permissible loading of a power system within voltage stability limits. IEE Proceedings Generation, Transmission & Distribution,2003,150:107-112.
[43]李娟,刘修宽,曹国臣,等.一种面向节点的电网等值参数跟踪估计方法的研究.中国电机工程学报,2003,23(3)：30-33.
[44]K. Ohtsuka, S. Yokokava, H. Tanaka, et al. An equivalent of multi-machine power systems and its identification for online application to decentralized stabilizers. IEEE Transactions on Power Systems,1989,4 (2):687-693.
[45]Y. Gong, N. Schulz, A. Guzman. Synchrophasor-Based Real-Time Voltage Stability Index. Proceedings of the 32nd Annual Western Protective Relay Conference,2005:1-8.
[46]梁志瑞,于成洋.基于同步相量测量的电力系统等值及电压稳定评估.电力科学与工程,2005.33-36.
[47]段俊东,郭志忠.基于广域测量的在线电压稳定监视.继电器,2006,34(15)：24-28.
[48]L. Ljung. System identification:theory for the user. Englewood Cliffs, NJ: Prentice-Hall,1987.
[49]K. H. E. Liu, S. L. Lim. Parameter error identification and estimation in power system state estimation. IEEE Transactions on Power Systems,1995,10 (1): 200-209.
[50]O. Alsac, N. Vempati, B. Stott, et al. Generalized state estimation. IEEE Transactions on Power Systems,1998,13 (3):1069-1075.
[51]W. E. Larimor. Canonical variate analysis in identification, filtering and adaptive control. Proc.29th IEEE Conference on Decision and Control,1990. 596-604.
[52]P. V. Overschee, B.D. Moor. Subspace Identification for Linear Systems:Theory, Implementation, and Applications. Kluwer Academic Publishers,1996 Data driven weighted estimation,1996.
[53]W. Liu, F. Wu, S. Lun. Estimation of parameter errors from measurement residuals in state estimation. IEEE Transactions on Power Systems,1992,7 (1): 81-89.
[54]I. W. Slutsker, S. Mokhtari, K. A. Clements. Real time recursive parameter estimation in energy management systems. IEEE Transactions on Power Systems,1996,11 (3):1393-1399.
[55]王进,苏盛,李欣然.电力系统综合负荷模型的辨识算法研究.华北电力技术,2002,11：8-12.
[56]F. Ding, T. W. Chen, Identification of Hammerstein nonlinear ARMAX systems. Automatica,2005,41 (9):1479-1489.
[57]Y. Shi, F. Ding, T. W. Chen, Multirate crosstalk identification in xDSL systems. IEEE Transactions on Communications,2006,54 (10):1878-1886.
[58]J. V. Milanovic, I. A. Hiskens. Effects of dynamic load model parameters on damping of oscillations in power systems. Electric Power Systems Research, 1995,33:53-61.
[59]Y. V. Makarov, V. A. Maslennikov, D. J. Hill. Revealing loads having the biggest influence on power system small disturbance stability. IEEE Transactions on Power Systems,1996,11:2018-2023.
[60]G. D. Prasad, M. A. Al-Mulhim. Comparative assessment of the effect of dynamic load models on voltage stability. International Journal of Electrical Power & Energy Systems,1997,19:305-309.
[61]A. Borghetti, R. Caldon, C. A. Nucci. Generic dynamic load models in long-term voltage stability studies. International Journal of Electrical Power & Energy Systems,2000,22:291-301.
[62]鞠平.电力系统负荷建模理论与实践.电力系统自动化,1999,19(1)：1-7.
[63]贺仁睦.负荷模型在电力系统计算中的作用及发展.华北电力学院学报,1985,3：1-8.
[64]周文,贺仁睦,章健,等.电力负荷建模问题研究综述.现代电力,1999,2：83-89.
[65]C. Concordia, S. Ihara. Load representation in power system stability studies. IEEE Transactions on Power Systems,1982,101 (4):969-977.
[66]CIGRE Task Force. Load modeling and dynamics. Electra,1990,1 (130): 124-141.
[67]CIGRE Task Force. Modeling of voltage collapse including dynamic phenomena. Electra,1993,1 (147):71-77.
[68]IEEE Task Force. Standard load models for power flow and dynamic performance simulation. IEEE Transactions on Power Systems,1995,10 (3): 1302-1313.
[69]J. Ma, R. M. He, D. J. Hill. Load modeling by finding support vectors of load data from field measurements. IEEE Transactions on Power Systems,2006,21 (2):726-735.
[70]P. Ju, F. Wu, Z. Y. Shao, et al. Composite load models based on field measurements and their applications in dynamic analysis. IET Proceeding of Generation Transmission and Distribution,2007,1 (5):751-760.
[71]张红斌,汤涌,李柏青.差分方程负荷模型参数分散性的研究.2006,26(18)：1-5.
[72]鞠平,马大强.电力系统负荷建模.中国电力出版社,2008.
[73]卫志农,鞠平.电力负荷在线建模方法.中国电机工程学报,1995,15(6)：361-368.
[74]W. S. Kao, C. J. Lin, C.T. Huang, et al. Comparison of simulated power system dynamics applying various load models with actual recorded data. IEEE Transactions on Power Systems,1994,9:248-254.
[75]D. N. Kosterev, C. W. Taylor, W. A. Mittelstadt. Model validation for the August 10,1996 WSCC system outage. IEEE Transactions on Power Systems,1999,14: 967-979.
[76]IEEE Task Force on Load Representation for Dynamic Performance. Load representation for dynamic performance analysis. IEEE Transactions on Power Systems,1993,8:472-482.
[77]IEEE Task Force on Load Representation for Dynamic Performance. Bibliography on load models for power flow and dynamic performance simulation. IEEE Transactions on Power Systems,1995,10:523-538.
[78]R. M. He, J. Ma, D. J. Hill. Composite load modeling via measurement approach. IEEE Transactions on Power Systems,2006,21:663-672.
[79]J. Ma, D. Han, R. M. He, Z. Y. Dong, et al. Reducing identified parameters of measurement-based composite load model. IEEE Transactions on Power Systems,2008,23:76-83.
[80]W. S. Kao. Dynamic load modeling in power system stability studies. IEEE Transactions on Power Systems,1995,10 (2):907-914.
[81]M. Taleb, M. Akbaba, E. A. Abdullah. Aggregation of induction machines for power system dynamic studies. IEEE Transactions on Power Systems,1994,9 (4):2042-2048.
[82]陈谦,孙建波,蔡敏,等.考虑配电网络综合负荷模型的参数确定.中国电机工程学报,2008,28(16)：45-50.
[83]鞠平,潘学萍,韩敬东.3种感应电动机综合负荷模型的比较.电力系统自动化,1999,23(19)：40-47.
[84]B. K. Choi, H. D. Chiang, Y. Li, et al. Measurement-based dynamic load models: derivation, comparison, and validation. IEEE Transactions on Power Systems, 2006,21 (3):1276-1283.
[85]B. K. Choi, H. D. Chiang, Y. Li, et al. Development of composite load models of power systems using online measurement data. Journal of Electrical Engineering & Technoogyl,2006,1 (2):161-169.
[86]B. K. Choi, H. D. Chiang, S. T. Cain. Justification of some field observations of dynamic load behaviors:analytical and numerical approach. Power and Energy Society General Meeting-Conversion and Delivery of Electrical Energy in the 21st Century,2008.1-7.
[87]B. K. Choi, H. D. Chiang. Multiple solutions and plateau phenomenon in measurement-based load model development:issues and suggestions. IEEE Transactions on Power Systems,2009,24 (2):824-831.
[88]G. D. Prasad, M. A. Al-Mulhim, G. D. Ray, et al. Comparative assessment of the effect of dynamic load models on voltage stability. Electrical Power & Energy Systems,1997,19 (5):305-309.
[89]F. Dai, J. V. Milanovic, N. Jenkins. The influence of measurement delays on estimated load model parameters. Ninth International Conference on Harmonics and Quality of Power,2000,1 (1):324-328.
[90]A. Maitra, A. Gaikwaad, P. Pourbeik, et al. Load models parameter derivation using an automated algorithm and measured data. Power and Energy Society General Meeting-Conversion and Delivery of Electrical Energy in the 21st Century,2008.1-7.
[91]I. R. Navarro. Dynamic load models for power systems-Estimation of time-varying parameters during normal operation. Licentiate thesis, Lund University,2002.
[92]D. J. Hill. Nonlinear dynamic load models with recovery for voltage stability studies. IEEE Transactions on Power Systems,1993,8:166-176.
[93]W. Xu, Y. Mansour. Voltage stability analysis using generic dynamic load models. IEEE Transactions on Power Systems,1994,9:479-493.
[94]M. M. Begovic, R. Q. Mills. Load identification and voltage stability monitoring. IEEE Transactions on Power Systems,1995,10(1):109-116.
[95]Y. J. Jeng, C. C. Yeh. Cluster-based blind nonlinear-channel estimation. IEEE Transactions on Signal Process,1997,45 (5):1161-1172.
[96]张强.非线性结构的神经网络LM系统辨识方法.振动工程学报,2004,17：986-988.
[97]M. Enqvist. A weighting method for approximate nonlinear system identification. Proceedings on the 46th IEEE Conference on Decision and Control,2007:5104-5109.
[98]强明辉,张京娥.基于MATLAB的递推最小二乘辨识与仿真.自动化与仪 器仪表,2008,6：4-5.
[99]J. H. Wang, P. K. Hopke, T. M. Hancewicz, et al. Application of modified alternating least squares regression to spectroscopic image analysis. Analytica Chimica Acta,2003,476:93-109.
[100]苟北,陈陈,提兆旭.Prony算法在电力系统负荷动态模型辨识中的应用研究.电力系统自动化,1997,21：21-24.
[101]程颖,鞠平,吴峰.负荷模型参数辨识的粒子群优化法及其与基因算法比较.电力系统自动化,2003,11：25-29.
[102]章健,贺仁睦,韩民晓.直接优化方法及其在负荷模型参数辨识中的应用.现代电力,1996,13(4)：8-14.
[103]D. Karisson, D. J. Hill. Modeling and identification of nonlinear dynamic loads in power systems. IEEE Transactions on Power Systems,1994,9 (1):157-166.
[104]J. C. Wang, H. D. Jiang, C. L. Chang, et al. Development of a frequency-dependent composite load model using the measurement approach. IEEE Transactions on Power Systems,1994,9:1546-1556.
[105]I. A. Hiskens. Nonlinear dynamic model evaluation from disturbance measurements. IEEE Transactions on Power Systems,2001,16 (4):702-710.
[106]王进,李欣然,苏盛.用阻尼最小二乘优化算法实现电力系统综合静态负荷建模.长沙电力学院学报,2004,19(1)：40-46.
[107]P. Ju, E. Handschin, D. Karlsson. Nonlinear dynamic load modeling:model and parameter estimation. IEEE Transactions on Power Systems,1996,11 (4): 1689-1696.
[108]D. Han, J. Ma, R. M. He, et al. A real application of measurement-based load modeling in large-scale power grids and its validation. IEEE Transactions on Power Systems,2009,24:1756-1764.
[109]V. Knyazkin, C. A. Canzares, L. H. Soder. On the parameter estimation and modeling of aggregate power system loads. IEEE Transactions on Power Systems,2004,19:1023-1031.
[110]P. Jazayeri, W. Rosehart, D. T. Westwick. A multistage algorithm for identification of nonlinear aggregate power system loads. IEEE Transactions on Power Systems,2007,22:1072-1079.
[111]M. Matsubara, Y. Usui, S. Sugimoto. Identification of continuous-time MIMO systems via sampled data. International Journal of Innovative Computing Information and Control,2006,2 (5):1119-1136.
[112]M. Dehghani, S. K. Y. Nikravesh. Estimation of synchronous generator parameters in a large scale power system. International Journal of Innovative Computing Information and Control,2009,5 (8):2141-2150.
[113]苏永春.电力系统电压稳定理论若干关键问题研究：[博士学位论文].华中科技大学,2010.
[114]A. Souza, J. Souza, A. Silva. Online voltage stability monitoring. IEEE Transactions on Power Systems,2000,15 (4):1300-1305.
[115]黄志刚,邬炜,韩英铎.基于同步相量测量的电压稳定评估算法.电力系统自动化,2002,26(2)：28-33.
[116]陈衍.电力系统稳态分析.北京：中国电力出版社,1995.
[117]C. W. Taylor. Power system voltage stability. New York, McGraw-Hill,1994.
[118]T. V. Cutsem, C. Vourmas. Voltage stability of electric power system. Norwell, MA, USA:Kluwer Academic Publishers,1998.
[119]沈莹.基于支持向量机的负荷建模的研究：[硕士学位论文].郑州大学,2007.
[120]潘文霞,陈允平,沈祖诒.电力系统电压稳定性研究综述.电网技术,2001,25(9)：51-54.
[121]张艳萍.受端系统小扰动电压稳定问题的研究：[博士学位论文].华北电力大学(北京),2008.
[122]祝晶.基于支持向量机的负荷建模的研究：[硕士学位论文].湖南大学,2006.
[123]Y. Kataoka, Y. Shinoda. Voltage stability limit of electric power systems with generator reactive power constraints considered. IEEE Transactions on Power System,2005,20 (2):951-962.
[124]徐晓春.电力系统在线电压静态稳定分析方法和应用研究：[硕士学位论文].东南大学,2009.
[125]中国电力科学研究院.中国版BPA潮流程序用户手册,2002.
[126]吴潘.基于分岔理论的电力系统电压稳定及无功优化研究：[硕士学位论文].长沙理工大学,2010.
[127]江伟,王成山,余贻鑫,等.直接计算静态电压稳定临界点的新方法.中国电机工程学报,2006,26(10)：1-6.
[128]李村晓.电力系统综合负荷模型辨识策略研究及建模平台开发：[硕士学位论文].湖南大学,2007.
[129]樊宇璐.基于改进连续潮流法的电力系统静态电压稳定裕度研究：[硕士学 位论文].广西大学,2009.
[130]王立德.电力系统综合负荷模型结构研究：[硕士学位论文].湖南大学,2008.
[131]林舜江.负荷动特性的建模及其对电压稳定的影响研究：[博士学位论文].湖南大学,2008.
[132]李日波.电网戴维南等值及静态电压稳定性研究：[硕士学位论文].湖南大学,2010.
[133]李连伟.基于戴维南等值的静态电压稳定极限快速计算方法研究：[硕士学位论文].湖南大学,2009.
[134]葛维春.电力系统电压稳定性与电压崩溃的研究：[博士学位论文].哈尔滨工业大学与华北电力学院联合培养,1992.
[135]李宝国,鲁宝春,巴金祥.一种绘制PV曲线的快速方法.继电器,2002,30(2)：13-15.
[136]段俊东,郭志忠.一种可在线确定电压稳定运行范围的方法.中国电机工程学报,2006,26(4)：113-118.
[137]V. Ajjarapu, B. Lee. Bibliography on voltage stability. IEEE Transactions on Power Systems,1998,13 (1):115-125.
[138]B. H. Chowdhury, C. W. Taylor. Voltage Stability Analysis:V-Q Power Flow Simulation versus Dynamic Simulation. IEEE Transactions on Power Systems, 2001,15(4):1354-1359.
[139]H. Sun, X. Zhou, R. Li. Accuracy analysis of static voltage stability indices based on power flow model. IEEE/PES T&D 2005 Asia Pacific, Dalian, China, 2005.
[140]P. Kessel, H. Glavitsch. Estimating the voltage stability of a power system. IEEE Transactions on Power Delivery,1986,1 (3):346-354
[141]余贻鑫,贾宏杰,严雪飞.可准确跟踪鞍节点分岔的改进局部电压稳定指标LI.电网技术,1999,23(5)：19-23.
[142]D. Marelli, M. Fu. A continuous-time linear system identification method for slowly sampled data. IEEE Transactions on Signal Processing,2010,58 (5): 2521-2533.
[143]H. Gamier, M. Mensler, A. Richard. Continuous-time model identification from sampled data:implementation issues and performance evaluation. International Journal of Control,2003,76 (13):1337-1357.
[144]H. Unbehauen, G. P. Rao. A review of identification in continuous-time systems. Annual reviews in Control,1998,22 (27):145-171.
[145]G. P. Rao, H. Unbehauen. Identification of continuous-time systems. IEE Proceeding Control Theory Application,2006,153 (2):185-220.
[146]P. C. Young, H. Gamier. Identification and estimation of continuous-time, data-based mechanistic (DBM) models for environmental systems. Environmental Modeling & Software,2006,21 (8):1055-1072.
[147]S. Daniel-Berhel, H. Unbehauen. Physical parameters estimation of the nonlinear continuous-time dynamics of a DC motor using Hartley modulating functions method. Journal of the Franklin Institute,1999,336 (3):481-501.
[148]D. K. Rollins, N. Bhandari, A. M. Bassily, et al. A continuous-time nonlinear dynamic predictive modeling method for Hammerstein process. Industrial & Engineering Chemistry Research,2003,42 (4):860-872.
[149]F. X. Wu, L. Mu. Separable parameter estimation method for nonlinear biological system. The 3rd International Conference on Bioinformatics and Biomedical Engineering, Beijing China,2009.1-4.
[150]W. Rosehart, D. Westwick, P. Jazayeri, et al. Separable identification of nonlinear aggregate power system loads. Electric Power Systems Research, 2009,79 (2):346-354.
[151]邓勇,郭瑞碰,黄劫,等.电网参数辨识与实时拓扑检错系统的开发与应用.2007,1：15-17.
[152]S. A. Arefifar, W. Xu. Online tracking of power system impedance parameters and filed experiences. IEEE Transactions on Power Delivery,2009,24 (4): 1781-1788.
[153]李超,房大中,周雪松.负荷动态特性对孤网电压稳定性的影响.天津理工大学学报,2007,23(4)：54-58.
[154]宗秀红,张尧,董泰福.计及负荷动态特性的电压稳定概率特征根分析.继电器,2008,36(4)：19-26.
[155]李欣然,贺仁睦,章健,等.负荷特性对电力系统静态电压稳定性的影响和静态电压稳定性广义实用判据.中国电机工程学报,1999,19(4)：23-30.
[156]张伶俐,周文,章健,等.面向综合的电力负荷特性建模.中国电机工程学报,1999,19(9)：71-75.
[157]J. Y. Wen, L. Jiang, Q. H. Wu, et al. Power system load modeling by learning based on system measurements. IEEE Transactions on Power Delivery,2003, 18:364-371.
[158]E. Vaahedi, H. M. Z. El-Din, W. W. Price. Dynamic load modeling in large scale stability studies. IEEE Transactions on Power Systems,1988,3 (3):1039-1045.
[159]王进,李欣然,苏盛.一种电力系统综合负荷模型辨识的改进算法研究.电力系统及其自动化学报,2002,14(2)：12-15.
[160]郭琼,姚晓宁.浅析电力系统负荷对电压稳定性的影响.电力系统及其自动化学报,2004,16(3)：61-65.
[161]H. Wang, L. Qian, E. Dougherty. Inference of gene regulatory networks using S-system:a unified approach. IET Systems Biology,2010,4 (2):145-156.
[162]周轶,菅浩然,李致家,等.基于递推最小二乘改进算法的洪水预报模型研究.河海大学学报,2007,35(1)：77-80.
[163]J. Yang, T. W. Chen, M. Wu. Online impedance matrix estimation of interconnected power systems. IEEE Electrical Power and Energy Conference 2009, Montreal, Canada,2009.1-5.
[164]A.G. Phadke. Synchronized phasor measurements in power systems. IEEE Computer Applications in Power,1993,6 (2):10-15.
[165]R.D.Zimmerman, D. Gan. MATPOWER User's Manual. School of Electrical Engineering, Cornell University, Version 3.2,2007.
[166]http://www.ee.washington.edu/research/pstca,1993.
[167]Power Systems Test Case Archive,30 bus power flow test case. University of Washington College of Engineering. Available:http://www.ee.washington.edu /research/pstca/pf30/pg_tca30bus.htm,1993.
[168]C. Canizares. Voltage stability assessment:concepts, practices and tools. IEEE-PES Power Systems Stability Subcommittee Special Publication, SP101PSS,2002.
[169]J. Yang, W. X. Li, T. W. Chen, et al. Online estimation and application of power grid impedance matrices based on synchronized phasor measurements. IET Generation, Transmission & Distribution,2010,4, (9):1052-1059.
[170]J. Yang, M Wu, Y. He, et al. A continuous-time identification method for parameter estimation of nonlinear dynamic load models of power systems. International Journal of Innovative Computing, Information and Control, (Accepted).
[171]J. Yang, W. X. Li, T. W. Chen, et al. Identification of nonlinear dynamic load models using an alternating least squares approach. The Fourth International Conference on Electric Utility Deregulation and Restructuring and Power Technologies, Weihai, China,2011.1155-1160.
[172]R. Chartrand. Numerical differentiation of noisy, non smooth data. ISRN Applied Mathematics,2005,2011:1-11.
[173]J. Yang, M. Wu, Y. He, et al. Identification and application of nonlinear dynamic load models. Journal of Control Theory and Application, (Accepted).