基于田口法的PSS参数优化以及PMU优化配置研究
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摘要
田口鲁棒设计法是结合日本经济发展经验创立的一种成熟的鲁棒设计实验方法。它从工程的角度出发,以最少的社会损失获得最好的产品品质为设计目的,在设计过程中采用正交表工具进行实验安排,并根据实验求出品质特性指标及信噪比(S/N)指标分别用于表征产品品质中与“与目标的差别”及“抵抗噪声的能力”的两方面的特性,然后根据各指标采用两阶段最佳化程序提炼出最经济有效的方案。它作为一种优秀的鲁棒设计方法,已经在众多工程领域当中大量应用。本文结合PSS参数优化问题和PMU优化配置问题的实际,基于田口鲁棒设计法的基本原理,主要进行了以下工作:
①电力系统稳定器(Power System Stabilizer, PSS)是抑制低频振荡的有效手段,其参数设计直接影响到PSS性能的优劣。为了使设计的PSS参数具有良好的鲁棒性,克服传统特征值分析方法设计PSS参数的缺点,本文基于田口鲁棒设计法的设计原理,以特定的李雅普诺夫函数计算出的信噪比(S/N)最大化为目标函数,采用遗传算法对鲁棒PSS参数进行优化设计。算例的仿真结果表明,PSS通过本文方法进行参数优化设计,更好地提取了系统中的有用信息,大大减少了计算量,具有良好的抑制振荡能力和鲁棒性,其综合性能优于传统方法。
②同步相量测量单元PMU( Phasor Measurement Unit)作为广域测量系统WAMS (Wide- Area Measurement Systems)的核心组件,已经开始应用于整个电力系统的实时分析和监控。传统的PMU配置方法在N-1情况下会丧失对系统的观测能力,而完全考虑N-1情况的配置方法虽然能克服在N-1情况下系统不可观测的缺点,但需要配置的PMU数目较多,经济性差。本文针对以上两种方法的缺点,将田口鲁棒设计法应用到PMU优化配置问题当中,提出一种最优成本-绩效比的PMU设计方案。通过基于复杂网络理论的互补性脆弱度指标集求出综合脆弱度指标来辨识重要线路,然后在方案设计过程中重点考虑对重要线路观测并充分考虑了方案对N-1噪声的鲁棒性。在设计实现时通过田口法品质特性指标和信噪比指标分别标示PMU配置方案的N-1观测能力和鲁棒性,最后采用两阶段最佳化程序对PMU配置方案进行设计得出最终方案。算例仿真表明,本方法设计的方案非常有效、实用。
通过以上两个问题中的成功应用实例可见,田口鲁棒设计法作为一种成熟、有效和经济的鲁棒设计实验方法,其理论成熟、简单有效、通用性好并且非常贴近工程实际,在电力系统工程问题的应用领域必有广泛的前景。
Taguchi robust design method is a very mature robust design experiment method which combined the economic development experience of Japan. From an engineering point of view its aim is to design the best products with minimal social losses. In the design process, orthogonal tools is used for experimental arrangements, the quality characteristics index and the signal to noise ratio (S /N) index are obtained by the experiments which are used to characterize product quality with the "difference between the target" and "the ability to resist noise" of the two properties, and then a two-stage process is used to extract the most cost-effective solution. As an excellent method of robust design, it has a large number of applications in many engineering fields. In this paper, by considering the actual of the PSS parameter optimization problem and the PMU optimization placement problem, based on the basic principle of Taguchi robust design method, mainly for the following work:
①Apply Power System Stabilizer (PSS) is an effective way to damp out low-frequency oscillations which parameters design has a direct effect on its performance. In order to improve the robustness of designed PSS parameters and overcome the shortcoming of the conventional Eigenvalue Analysis method which was used to design PSS parameters. This paper present a Genetic Algorithm (GA) designed PSS parameters which based on Taguchi robust method and Lyapunov Function. For the sake of reducing the computing time and considering enough information needed by the design, based on the Taguchi design method, the objective function of this design is to maximize the Signal Noise Ratio (SNR) calculated by the selected Lyapunov Function which can just show the information of the system needed by the PSS parameters design. At last, the testing result of two test systems show that the PSS parameters designed by the presented method has a good quality of robustness and ability of damping out the oscillations which is better than the PSS parameters designed by conventional method.
②Phasor Measurement Unit (PMU) as the core component of the Wide-Area Measurement Systems (WAMS) has begun to apply to the entire power system real-time analysis and monitoring. It is known that the traditional PMU placement methods will loss the observing capabilities of the power system under the N-1 condition, while fully considering the N-1 condition PMU Placement methods need too many PMUs to ensure the entire power system observing capabilities which economy is poor. For the sake of overcoming the shortcomings of the above methods, this paper presented a best cost - performance ratio PMU placement method based on the principles of Taguchi robust design method. In this paper, based on complex network theory, a set of integrated vulnerability index calculated by complementary vulnerability index set are used to identify the important lines in the system. By doing this, the aim of the design is to focus on ensure the important lines’observation and the robustness of the placement plan under the N-1 noise. In the design, the Taguchi quality characteristics and the S/N indexes is calculated to measure the PMU placement plan’s observing capabilities and robustness under the N-1 noise, at last, a two stage optimization procedure is used to determine the final plan. And finally, two testing system is used to test the performance of the PMU placement plan, the results show that this method is very effective and practical.
The successful application of the above two problems show, Taguchi robust design method as a mature, effective and economical robust design experiments method, its theoretical maturity, simple and effective, common good and very close to engineering practice, in Power System Engineering issues must have a broad prospect of application areas.
①电力系统稳定器(Power System Stabilizer, PSS)是抑制低频振荡的有效手段,其参数设计直接影响到PSS性能的优劣。为了使设计的PSS参数具有良好的鲁棒性,克服传统特征值分析方法设计PSS参数的缺点,本文基于田口鲁棒设计法的设计原理,以特定的李雅普诺夫函数计算出的信噪比(S/N)最大化为目标函数,采用遗传算法对鲁棒PSS参数进行优化设计。算例的仿真结果表明,PSS通过本文方法进行参数优化设计,更好地提取了系统中的有用信息,大大减少了计算量,具有良好的抑制振荡能力和鲁棒性,其综合性能优于传统方法。
②同步相量测量单元PMU( Phasor Measurement Unit)作为广域测量系统WAMS (Wide- Area Measurement Systems)的核心组件,已经开始应用于整个电力系统的实时分析和监控。传统的PMU配置方法在N-1情况下会丧失对系统的观测能力,而完全考虑N-1情况的配置方法虽然能克服在N-1情况下系统不可观测的缺点,但需要配置的PMU数目较多,经济性差。本文针对以上两种方法的缺点,将田口鲁棒设计法应用到PMU优化配置问题当中,提出一种最优成本-绩效比的PMU设计方案。通过基于复杂网络理论的互补性脆弱度指标集求出综合脆弱度指标来辨识重要线路,然后在方案设计过程中重点考虑对重要线路观测并充分考虑了方案对N-1噪声的鲁棒性。在设计实现时通过田口法品质特性指标和信噪比指标分别标示PMU配置方案的N-1观测能力和鲁棒性,最后采用两阶段最佳化程序对PMU配置方案进行设计得出最终方案。算例仿真表明,本方法设计的方案非常有效、实用。
通过以上两个问题中的成功应用实例可见,田口鲁棒设计法作为一种成熟、有效和经济的鲁棒设计实验方法,其理论成熟、简单有效、通用性好并且非常贴近工程实际,在电力系统工程问题的应用领域必有广泛的前景。
Taguchi robust design method is a very mature robust design experiment method which combined the economic development experience of Japan. From an engineering point of view its aim is to design the best products with minimal social losses. In the design process, orthogonal tools is used for experimental arrangements, the quality characteristics index and the signal to noise ratio (S /N) index are obtained by the experiments which are used to characterize product quality with the "difference between the target" and "the ability to resist noise" of the two properties, and then a two-stage process is used to extract the most cost-effective solution. As an excellent method of robust design, it has a large number of applications in many engineering fields. In this paper, by considering the actual of the PSS parameter optimization problem and the PMU optimization placement problem, based on the basic principle of Taguchi robust design method, mainly for the following work:
①Apply Power System Stabilizer (PSS) is an effective way to damp out low-frequency oscillations which parameters design has a direct effect on its performance. In order to improve the robustness of designed PSS parameters and overcome the shortcoming of the conventional Eigenvalue Analysis method which was used to design PSS parameters. This paper present a Genetic Algorithm (GA) designed PSS parameters which based on Taguchi robust method and Lyapunov Function. For the sake of reducing the computing time and considering enough information needed by the design, based on the Taguchi design method, the objective function of this design is to maximize the Signal Noise Ratio (SNR) calculated by the selected Lyapunov Function which can just show the information of the system needed by the PSS parameters design. At last, the testing result of two test systems show that the PSS parameters designed by the presented method has a good quality of robustness and ability of damping out the oscillations which is better than the PSS parameters designed by conventional method.
②Phasor Measurement Unit (PMU) as the core component of the Wide-Area Measurement Systems (WAMS) has begun to apply to the entire power system real-time analysis and monitoring. It is known that the traditional PMU placement methods will loss the observing capabilities of the power system under the N-1 condition, while fully considering the N-1 condition PMU Placement methods need too many PMUs to ensure the entire power system observing capabilities which economy is poor. For the sake of overcoming the shortcomings of the above methods, this paper presented a best cost - performance ratio PMU placement method based on the principles of Taguchi robust design method. In this paper, based on complex network theory, a set of integrated vulnerability index calculated by complementary vulnerability index set are used to identify the important lines in the system. By doing this, the aim of the design is to focus on ensure the important lines’observation and the robustness of the placement plan under the N-1 noise. In the design, the Taguchi quality characteristics and the S/N indexes is calculated to measure the PMU placement plan’s observing capabilities and robustness under the N-1 noise, at last, a two stage optimization procedure is used to determine the final plan. And finally, two testing system is used to test the performance of the PMU placement plan, the results show that this method is very effective and practical.
The successful application of the above two problems show, Taguchi robust design method as a mature, effective and economical robust design experiments method, its theoretical maturity, simple and effective, common good and very close to engineering practice, in Power System Engineering issues must have a broad prospect of application areas.
引文
[1] Grudinin N,Roytelman I.Heading off Emergencies in Large Electric Grids[J].IEEE Spectrum, 1997,34 (4):42-47.
[2]卢卫星,舒印标,史连军.美国西部电力系统1996年8月10日大停电事故[J].电网技术,1996,20(9):40-42.
[3]印永华,郭剑波等.美加“814”大停电事故初步分析以及应吸取的教训[J].电网技术,2003,27(10):8-16.
[4]鲁顺,高立群,王坷等.莫斯科大停电分析及启示[J].继电器,2006,34(16):27-31.
[5]李春艳,陈洲,肖孟金等.西欧“11.4”大停电分析及对华中电网的启示[J].高电压技术,2008,32(1):163-167.
[6]莫逆,梅生伟,车文妍.提高电力系统小干扰稳定性的全状态H∞控制器[J].清华大学学报(自然科学版),2009,49(7):929-933.
[7] T.C. Yang.Applying H∞optimization method to power system stabilizer design parts 1& 2[J].Elect. Power Energy Syst.,1997,19(1):29-43.
[8]陈柔伊,张尧,钟庆,蔡广林.分散H∞控制器在电力系统阻尼控制中的应用[J].华南理工大学学报(自然科学版),2009,37(2):118-126.
[9] S. J. Kim,Y. H. Moon and K. H. Kim.Low-order robust power system stabilizer for single-machine systems:an LMI approach [C].IEEE Industrial Electronics IECON 2006-32nd Annual Conference on 6-10 Nov. 2006:742-747.
[10]袁金腾,王秀明,姜志国.基于LMI的电力系统广域附加阻尼控制[J].东北电力大学学报,2009,29(4):50-54.
[11] Chen S,Malik O P.Power system stabilizer design usingμsynthesis [J].IEEE Transactions on Energy Conversion,1995,10(1):175-181.
[12] Chen G,Sugie T.μ-Analysis and synthesis of state feedback systems based on multipliers and LMI's[C].IEEE Proceedings of the American Control Conference,1998,537-541.
[13]富饶,黄琳.基于LMI的μ方法及其在电力系统中的应用[J].中国电机工程学报,2002,22(10):50-54.
[14] Abdel-Magid Y L,Abido M A.Optimal Multiobjective Design of Robust Power System Stabilizers Using Genetic Algorithms [J].IEEE Trans on Power Systems,2003,18(3):1125-1132.
[15] Karnik S.R,Raju A.B,Raviprakasha M.S.Genetic Algorithm based Robust Power System Stabilizer Design using Taguchi Principle[C].Emerging Trends in Engineering and Technology,2008. ICETET '08. First International Conference on 16-18 July 2008:887-892.
[16]刘新东,江全元,曹一家.N–1条件下不失去可观测性的PMU优化配置方法[J].中国电机工程学报,2009,29(10):47-51.
[17] Denegri G B,Invernizzi M,Milano F.A security oriented approachto PMU positioning for advanced monitoring of a transmission grid[C].IEEE International Conference on Power System Technology,Kunming,China,2002.
[18]晓刚,陶佳,江全元,等.考虑高风险连锁故障的PMU配置方法[J].电力系统自动化,2008,32(4):11-14.
[19] Doyle J C.Analysis of feedback systems with structured uncertainties [C].Proceedings of IEE, Part D,1982,129:240-250.
[20] Fan M K H,Tits A L,Doyle J C.Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics [J].IEEE Transactionson Automatic Control,Jan. 1991,36(1):25-38.
[21] Taguchi G,Chowdhury S,Taguchi S.Robust Engineering[M].New York:McGraw-Hill, 2000.
[22] Wu Y.Taguchi Mechods for Robust Design[M].New York:ASME,2000.
[23]金天雄,金石男,江平开等.有限元法与田口方法相结合模拟研究交联聚乙烯电缆绝缘中的水树现象[J].绝缘材料,2008,41(3):45-48.
[24] M. Bounou,S.Lefebvre and X. Dai Do.Improving the quality of an optimal power flow solution by Taguchi method [J].Elect. Power Energy Syst,1995,17(2):113-118.
[25]贺小明,于忠奇,来新民.基于田口法的大型锻件微观组织健壮参数控制方法[J].塑性工程学报2008,15(4):94-97.
[26]薛禹胜,郝思鹏,刘俊勇,等.关于低频振荡分析方法的评述[J].电力系统自动化,2009,33(3) :1-8.
[27] P. Kunder.Power system stability and control[M].McGraw-Hill Inc.,New York,1994.
[28]王锡凡,方万良,杜正春.现代电力系统分析[M].北京:科学出版社,2003.
[29]刘取.电力系统稳定性及发电机励磁控制[M].北京:中国电力出版社,2007.
[30]余耀南.动态电力系统[M].北京:水利电力出版社,1985.
[31] F.R.Schleif, et al.Damping for the Northwest-Southwest Tieline Oscillations–an analog study [J].IEEE Transactions on Power Apparatus and Systems.Vol.85,No.12,Dec. 1966.
[32] D.K. Kosterev,C. Taylor,W.A. Mittelstadt.Modal validation for the August 10, 1996 WSCC system outage [J].IEEE Transactions on Power systems,1999,14(3):967-979.
[33] D.K. Kosterev,W.A. Mittelstadt,M. Viles,et al.Modal validation and analysis of WSCC system oscillations following Alberta separation on August 4,2000.Final Report by Bonneville Power Administration and BC Hydro,2001.
[34]李庚银,邵俊松,周明.电力系统低频振荡及振荡解列策略研究综述[C].全国高等学校的电力系统及其自动化专业第十六届学术年会论文集,吉林省吉林市,2000.
[35]王梅义,吴竞昌,蒙定中.大电网系统技术[M].北京:中国电力出版社,1995.
[36]张晓明,庞晓燕,陈苑文,刘增煌,田芳.四川电网低频振荡及控制措施[J].中国电力,2000,33(6):35-39.
[37] LARSON E V,SWANN S A.Applying power systems stabilizers,Part I-III[J].IEEE Transactions on Power Apparatus and Systems,1981,100(9):3017-3046.
[38]李颖,贺仁睦.负荷与PSS的相互作用对系统动态稳定的影响[J].电力系统自动化,2004,28(8):40 -44.
[39]牛振勇,杜正春,方万良,等.基于进化策略的多机系统PSS参数优化[J].中国电机工程学报,2004,24(2):22 - 27.
[40]胡晓波,杨利民,陈中,等.基于人工鱼群算法的PSS参数优化[J].电力自动化设备,2009,29(2):47-50.
[41]蒋平,黄霆,罗建裕.基于增强连续禁忌算法的PSS参数优化[J].电力自动化设备,2004,24(12):19-22.
[42] Abdel-Magid Y L,Abido M A,Al-Baiyat S,et al.Simultaneous Stabilization of Multi-machine Power Systems via Genetic Algorithms [J].IEEE Trans on Power Systems,1999,14(4):1428-1439.
[43]李顺昕,马进,贺仁睦.基于Prony辨识的自适应PSS的设计及研究[J].现代电力,2006,23(1) :1-5.
[44] Zhao Qiaoe,Su Xiaolin, Zhou Shuangx.Research of Power System Stabilizer Based on Prony On-line Identification and Neural Network Control[J].IEEE Electrical Machines and Systems,2008,ICEMS 2008. International Conference on 17-20 Oct. 2008:146-150.
[45]闵勇,丁仁杰,韩英铎,等.一次系统事故的同步相量测量结果分析[J].电力系统自动化,1998,22(7):10-13.
[46] Baldwin T,Mili L,Boisen M and Adapa R .Power System Observability with Minimal Phasor Measurement Placement[J].IEEE Transactions on Power Systems 1993,8(2),707-715.
[47]彭疆南,孙元章,王海风.考虑系统完全可观测性的PMU最优配置方法[J].电力系统自动化,2003,27(4):10-16.
[48]罗毅,赵冬梅.电力系统PMU最优配置数字规划算法[J].电力系统自动化,2006,30(9):20-25.
[49]孙旻,熊俊杰,张杰等.基于最大测量树法的电力系统PMU优化配置[J].电力自动化设备,2008,28(8):73-76.
[50]彭春华.基于免疫BPSO算法与拓扑可观性的PMU最优配置[J].电工技术学报,2008,23(6):119-124.
[51]卢强,王仲鸿,韩英铎.输电系统最优控制[M].北京:科学出版社,1984.
[52]倪以信,陈寿孙,张宝霖.动态电力系统的理论和分析[M].北京:清华大学出版社,2002.
[53]刘豹.现代控制理论(第二版)[M].北京:机械工业出版社,2000.
[54]雷英杰等.MATLAB遗传算法工具箱及应用[M].西安:西安电子科技大学出版社,2005.
[55] Milano F.An open source power system analysis toolbox[J].IEEE Transactions on Power Systems,2005,20(3):1199-1206.
[56] Monticelli A,Wu F F.Network Observability Theory[J].IEEE Trans on Power Apparatus and Systems,1985,4 (5):1042-1048.
[57]倪向萍,梅生伟,张雪敏.基于复杂网络理论的输电线路脆弱度评估方法[J].电力系统自动化,2008,32(4):1-6.
[2]卢卫星,舒印标,史连军.美国西部电力系统1996年8月10日大停电事故[J].电网技术,1996,20(9):40-42.
[3]印永华,郭剑波等.美加“814”大停电事故初步分析以及应吸取的教训[J].电网技术,2003,27(10):8-16.
[4]鲁顺,高立群,王坷等.莫斯科大停电分析及启示[J].继电器,2006,34(16):27-31.
[5]李春艳,陈洲,肖孟金等.西欧“11.4”大停电分析及对华中电网的启示[J].高电压技术,2008,32(1):163-167.
[6]莫逆,梅生伟,车文妍.提高电力系统小干扰稳定性的全状态H∞控制器[J].清华大学学报(自然科学版),2009,49(7):929-933.
[7] T.C. Yang.Applying H∞optimization method to power system stabilizer design parts 1& 2[J].Elect. Power Energy Syst.,1997,19(1):29-43.
[8]陈柔伊,张尧,钟庆,蔡广林.分散H∞控制器在电力系统阻尼控制中的应用[J].华南理工大学学报(自然科学版),2009,37(2):118-126.
[9] S. J. Kim,Y. H. Moon and K. H. Kim.Low-order robust power system stabilizer for single-machine systems:an LMI approach [C].IEEE Industrial Electronics IECON 2006-32nd Annual Conference on 6-10 Nov. 2006:742-747.
[10]袁金腾,王秀明,姜志国.基于LMI的电力系统广域附加阻尼控制[J].东北电力大学学报,2009,29(4):50-54.
[11] Chen S,Malik O P.Power system stabilizer design usingμsynthesis [J].IEEE Transactions on Energy Conversion,1995,10(1):175-181.
[12] Chen G,Sugie T.μ-Analysis and synthesis of state feedback systems based on multipliers and LMI's[C].IEEE Proceedings of the American Control Conference,1998,537-541.
[13]富饶,黄琳.基于LMI的μ方法及其在电力系统中的应用[J].中国电机工程学报,2002,22(10):50-54.
[14] Abdel-Magid Y L,Abido M A.Optimal Multiobjective Design of Robust Power System Stabilizers Using Genetic Algorithms [J].IEEE Trans on Power Systems,2003,18(3):1125-1132.
[15] Karnik S.R,Raju A.B,Raviprakasha M.S.Genetic Algorithm based Robust Power System Stabilizer Design using Taguchi Principle[C].Emerging Trends in Engineering and Technology,2008. ICETET '08. First International Conference on 16-18 July 2008:887-892.
[16]刘新东,江全元,曹一家.N–1条件下不失去可观测性的PMU优化配置方法[J].中国电机工程学报,2009,29(10):47-51.
[17] Denegri G B,Invernizzi M,Milano F.A security oriented approachto PMU positioning for advanced monitoring of a transmission grid[C].IEEE International Conference on Power System Technology,Kunming,China,2002.
[18]晓刚,陶佳,江全元,等.考虑高风险连锁故障的PMU配置方法[J].电力系统自动化,2008,32(4):11-14.
[19] Doyle J C.Analysis of feedback systems with structured uncertainties [C].Proceedings of IEE, Part D,1982,129:240-250.
[20] Fan M K H,Tits A L,Doyle J C.Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics [J].IEEE Transactionson Automatic Control,Jan. 1991,36(1):25-38.
[21] Taguchi G,Chowdhury S,Taguchi S.Robust Engineering[M].New York:McGraw-Hill, 2000.
[22] Wu Y.Taguchi Mechods for Robust Design[M].New York:ASME,2000.
[23]金天雄,金石男,江平开等.有限元法与田口方法相结合模拟研究交联聚乙烯电缆绝缘中的水树现象[J].绝缘材料,2008,41(3):45-48.
[24] M. Bounou,S.Lefebvre and X. Dai Do.Improving the quality of an optimal power flow solution by Taguchi method [J].Elect. Power Energy Syst,1995,17(2):113-118.
[25]贺小明,于忠奇,来新民.基于田口法的大型锻件微观组织健壮参数控制方法[J].塑性工程学报2008,15(4):94-97.
[26]薛禹胜,郝思鹏,刘俊勇,等.关于低频振荡分析方法的评述[J].电力系统自动化,2009,33(3) :1-8.
[27] P. Kunder.Power system stability and control[M].McGraw-Hill Inc.,New York,1994.
[28]王锡凡,方万良,杜正春.现代电力系统分析[M].北京:科学出版社,2003.
[29]刘取.电力系统稳定性及发电机励磁控制[M].北京:中国电力出版社,2007.
[30]余耀南.动态电力系统[M].北京:水利电力出版社,1985.
[31] F.R.Schleif, et al.Damping for the Northwest-Southwest Tieline Oscillations–an analog study [J].IEEE Transactions on Power Apparatus and Systems.Vol.85,No.12,Dec. 1966.
[32] D.K. Kosterev,C. Taylor,W.A. Mittelstadt.Modal validation for the August 10, 1996 WSCC system outage [J].IEEE Transactions on Power systems,1999,14(3):967-979.
[33] D.K. Kosterev,W.A. Mittelstadt,M. Viles,et al.Modal validation and analysis of WSCC system oscillations following Alberta separation on August 4,2000.Final Report by Bonneville Power Administration and BC Hydro,2001.
[34]李庚银,邵俊松,周明.电力系统低频振荡及振荡解列策略研究综述[C].全国高等学校的电力系统及其自动化专业第十六届学术年会论文集,吉林省吉林市,2000.
[35]王梅义,吴竞昌,蒙定中.大电网系统技术[M].北京:中国电力出版社,1995.
[36]张晓明,庞晓燕,陈苑文,刘增煌,田芳.四川电网低频振荡及控制措施[J].中国电力,2000,33(6):35-39.
[37] LARSON E V,SWANN S A.Applying power systems stabilizers,Part I-III[J].IEEE Transactions on Power Apparatus and Systems,1981,100(9):3017-3046.
[38]李颖,贺仁睦.负荷与PSS的相互作用对系统动态稳定的影响[J].电力系统自动化,2004,28(8):40 -44.
[39]牛振勇,杜正春,方万良,等.基于进化策略的多机系统PSS参数优化[J].中国电机工程学报,2004,24(2):22 - 27.
[40]胡晓波,杨利民,陈中,等.基于人工鱼群算法的PSS参数优化[J].电力自动化设备,2009,29(2):47-50.
[41]蒋平,黄霆,罗建裕.基于增强连续禁忌算法的PSS参数优化[J].电力自动化设备,2004,24(12):19-22.
[42] Abdel-Magid Y L,Abido M A,Al-Baiyat S,et al.Simultaneous Stabilization of Multi-machine Power Systems via Genetic Algorithms [J].IEEE Trans on Power Systems,1999,14(4):1428-1439.
[43]李顺昕,马进,贺仁睦.基于Prony辨识的自适应PSS的设计及研究[J].现代电力,2006,23(1) :1-5.
[44] Zhao Qiaoe,Su Xiaolin, Zhou Shuangx.Research of Power System Stabilizer Based on Prony On-line Identification and Neural Network Control[J].IEEE Electrical Machines and Systems,2008,ICEMS 2008. International Conference on 17-20 Oct. 2008:146-150.
[45]闵勇,丁仁杰,韩英铎,等.一次系统事故的同步相量测量结果分析[J].电力系统自动化,1998,22(7):10-13.
[46] Baldwin T,Mili L,Boisen M and Adapa R .Power System Observability with Minimal Phasor Measurement Placement[J].IEEE Transactions on Power Systems 1993,8(2),707-715.
[47]彭疆南,孙元章,王海风.考虑系统完全可观测性的PMU最优配置方法[J].电力系统自动化,2003,27(4):10-16.
[48]罗毅,赵冬梅.电力系统PMU最优配置数字规划算法[J].电力系统自动化,2006,30(9):20-25.
[49]孙旻,熊俊杰,张杰等.基于最大测量树法的电力系统PMU优化配置[J].电力自动化设备,2008,28(8):73-76.
[50]彭春华.基于免疫BPSO算法与拓扑可观性的PMU最优配置[J].电工技术学报,2008,23(6):119-124.
[51]卢强,王仲鸿,韩英铎.输电系统最优控制[M].北京:科学出版社,1984.
[52]倪以信,陈寿孙,张宝霖.动态电力系统的理论和分析[M].北京:清华大学出版社,2002.
[53]刘豹.现代控制理论(第二版)[M].北京:机械工业出版社,2000.
[54]雷英杰等.MATLAB遗传算法工具箱及应用[M].西安:西安电子科技大学出版社,2005.
[55] Milano F.An open source power system analysis toolbox[J].IEEE Transactions on Power Systems,2005,20(3):1199-1206.
[56] Monticelli A,Wu F F.Network Observability Theory[J].IEEE Trans on Power Apparatus and Systems,1985,4 (5):1042-1048.
[57]倪向萍,梅生伟,张雪敏.基于复杂网络理论的输电线路脆弱度评估方法[J].电力系统自动化,2008,32(4):1-6.