铁磁谐振过电压非线性特性及其柔性抑制策略研究
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摘要
智能电网是世界电网未来的发展方向，其重要特征是“自愈”，即要求电网能够在线、实时并连续对系统安全性进行分析和评估，能够对系统进行在线诊断并能够对可能发生的系统故障进行及时预警，能够对已发生的系统故障进行预防、隔离和控制，使系统能够自我恢复，并能使电网各级防线之间紧密协调，能够抵御突发性事件和严重故障，并有效避免大范围连锁故障的发生，从而大幅提升电网的安全稳定性和供电可靠性，并大幅减少停电损失。
铁磁谐振发生在非线性电感和电容回路，谐振过程可能产生稳定的过电压和过电流，会对输配电装备和运行人员安全构成威胁，虽然国内外对铁磁谐振的产生机理、基本特性、发展规律和抑制措施进行了大量的研究，但是由于其谐振回路的复杂性和谐振类型的多样性，铁磁谐振抑制措施在某些谐振情况下抑制作用有限，造成电力系统关键设备可能承受较长时间的铁磁谐振过电压，可能使其产生绝缘损伤，最终可能造成设备损坏，因而铁磁谐振问题仍然是一个长期困扰电力系统安全运行的复杂问题。随着电网的发展，一方面配电网的快速发展造成配电系统参数变化范围急剧增大，配电网操作更加频繁，促使铁磁谐振发生率升高；另一方面超特高压系统对内部过电压倍数要求更为严格，铁磁谐振过电压可能会超过超特高压系统内部过电压水平。因此电力系统中的铁磁谐振问题愈发突出，亟需对铁磁谐振的非线性特性和铁磁谐振过电压的抑制进行深入研究。
目前铁磁谐振的基本特性分析和抑制方法研究大多基于铁磁谐振回路模型，该回路模型是对典型铁磁谐振回路简化而得到的，在一定程度上能够反映铁磁谐振的一般规律，为铁磁谐振研究奠定了基础，但是传统铁磁谐振模型需要精确的谐振电路模型和准确的系统参数，而在实际电力系统中，随着运行方式的改变谐振电路和系统参数都会随之发生变化，因此基于传统铁磁谐振模型的特性分析和抑制方法无法满足情况多变的现场应用。以目前研究成果为基础，本文提出了不依赖于铁磁谐振模型及参数，直接从铁磁谐振过电压时间序列入手进行铁磁谐振的非线性特性分析和抑制方法研究。首先针对铁磁谐振过电压时间序列的特点，选取适合铁磁谐振过电压的相空间重构算法，对铁磁谐振过电压时间序列进行相空间重构，可以挖掘铁磁谐振时间序列隐藏的系统信息，进而对铁磁谐振特有的非线性特性进行分析，从而对包含准周期和混沌在内的铁磁谐振过电压进行特征量提取和类型识别，能够为建立铁磁谐振过电压实时监测、在线分析以及主动抑制系统提供支持；其次在铁磁谐振过电压时间序列相空间重构的基础上，根据重构过程的关键参数建立铁磁谐振过电压时间序列的低阶多项式模型，并在此基础上研究铁磁谐振过电压时间序列的主动抑制策略，由此来论证直接通过铁磁谐振过电压时间序列得到抑制方法的可行性和有效性；最后基于以上研究，提出了一种采用高速全可控开关器件的铁磁谐振过电压灵活抑制方法也即柔性抑制方法，并分别搭建了考虑电压互感器(PT)铁芯磁滞效应的电磁暂态仿真模型和对应的实验室低压试验平台，基于仿真模型和试验平台详细分析了相关参数对铁磁谐振过电压抑制效果的影响，并对不同类型和不同谐振程度的铁磁谐振过电压进行了抑制研究。
本文通过理论分析、仿真计算和试验研究对铁磁谐振过电压时间序列的非线性特性和柔性抑制方法进行了详细的研究，结果表明：本文采用互信息法和Cao氏算法直接对铁磁谐振过电压进行相空间重构后可以得到有效的关键重构参数，能够得出与原铁磁谐振系统拓扑等价的重构吸引子，可以获取铁磁谐振系统的基本非线性特征，该方法不但克服了传统分析方法对精确铁磁谐振模型和系统参数的高度依赖，而且分析结果与传统分析方法高度一致；基于相空间重构，获得不同类型铁磁谐振过电压的两个重要的非线性特征量：重构吸引子的平均灰度和序列的最大Lyapunov指数，两者可以作为非周期谐振分类器的重要特征量，能够有效识别准周期和混沌铁磁谐振过电压；直接采用重构参数和过电压时间序列进行铁磁谐振数学建模，辨识得到了其二阶多项式模型，能够反映原铁磁谐振系统的基本数学特征，基于该数学模型所得到的铁磁谐振过电压抑制方法能够有效抑制不同类型的铁磁谐振过电压；基于以上研究，本文采用全控电力电子开关调整高频阻尼电阻投入特性，构造了一个电网频率意义下的等效连续可调电阻，进而实现不同类型铁磁谐振过电压的柔性抑制，仿真和试验研究表明阻尼电阻和高速开关门信号的占空比对铁磁谐振过电压抑制效果影响显著；对比研究结果表明，本文所提出的铁磁谐振过电压柔性抑制方法能够有效抑制不同类型和不同铁芯饱和程度的铁磁谐振过电压，在不显著增大设备负担的前提下能够弥补传统抑制方法的不足，且不会对系统造成谐波负担。
Smart grid is the direction for the world's power grid in the future, an importantfeature of which is "self-healing grid". This feature means that the power grid shouldhave the following abilities: real-time, online, continuous safe assessment and analysis;early warning, prevention and control for power accidents; and automatic faultdiagnosis, fault isolation and self-recovery. With such abilities, the security, stabilityand reliability of power grid can be significantly enhanced. The various defence lines ofpower grid are coordinated well so that the power grid owns the ability to defend someunexpected events and serious failures, which can effectively prevent the occurrence ofa wide range of cascading failures and significantly improve power supply reliabilityand reduce power losses.
Ferroresonance can occur in nonlinear inductance and capacitance circuit, it causesovervoltage and over-current that lasts for a long time and can even exist stably.Overvoltage and over-current may cause equipment failure and damage in powersystem. Therefore, the mechanism, the basic characteristics, the development law andthe suppression method of the ferroresonance are studied by a lot of scholars at homeand abroad. However, owning to the extremely various ferroresonance circuits and thevarious ferroresonance types, the effect of the present suppression method on theferroresonance under some certain condition may be limited. For this reason, powersystem key equipments may endure a long time ferroresonance overvoltage, makes itmay cause insulation damage and equipment damage. So, ferroresonance problem isstill a complex problem for the safe operation of the power system for a long time. Withthe development of the power grid, the ferroresonance problem in power system isincreasingly prominent. On the one hand, the rapid development of power distributionnetwork makes the distribution system parameter variation range increase very sharpand the power distribution network operation is more frequent, which leads to a higherincidence of ferroresonance. On the other hand, the UHV system is very strict withinternal overvoltage, and ferroresonance overvoltage may exceed its internalovervoltage level and cause key equipment damage and even a wide range of accident.Therefore, it is urgent needed to study the nonlinear characteristics of ferroresonanceand then put forward a more feasible ferroresonance overvoltage suppression strategy.
At present, most of the study on the basic ferroresonance nonlinear characteristics analysis and its suppression method are based a basic ferroresonance circuit model. Themodel is simplified by a typical ferroresonance circuit. To a certain extent, the simplifymodel can explain the basic principle of ferroresonance and lay a solid foundation forthe study of the ferroresonance. However, the traditional ferroresonance model can onlybe established before acquiring the ferroresonance circuit and precise system parameters.In the actual power system, the ferroresonance circuit and its parameters change withthe change of the operation mode. Therefore, the characteristics and the suppressionmethod obtained based on the traditional ferroresonance model cannot satisfy the fieldapplication.
Based on the present research, this thesis proposes a new method to analyze thenonlinear characteristics of ferroresonance and then study the suppression method forferroresonance. The study is directly based the ferroresonance overvoltage time seriesand not relying on the accurate ferroresonance model and precise parameters. Firstly,aiming at the characteristics of the ferroresonance overvoltage, appropriate phase spacereconstruction methods are chosen to reconstruct the ferroresonance overvoltage timeseries. Base on the reconstruction, the hidden information of the overvoltage time seriescan be dig for ferroresonance nonlinear characteristics analysis. The nonlinearcharacteristics analysis can be used for extracting the nonlinear characteristics quantitiesof the ferroresonance, including quasi-periodic and chaotic ferroresonance, andidentifying their types. All of the study can be supported to establish an online real-timemonitoring, analysis and active suppression system. Secondly, based on the phase spacereconstruction of the ferroresonance overvoltage time series, a lower order polynomialmodel for ferroresonance is identified using the key parameters determined in phasespace reconstruction. Based on the model, an active suppression strategy based onovervoltage time series is studied to demonstrate that it is feasible and effective. Finally,based on the above research, a flexible suppression method by combining with thepower electronic technology for ferroresonance overvoltage is proposed. High-speedfully controllable switches are adopted in this method. Electromagnetic transientsimulation model considering the hysteresis characteristic of the PT and scale-downlaboratory test platform are established individually, based on that, the suppressioneffect of the changeable parameters on the ferroresonance overvoltage is analyzed indetail, and the suppressions on the different types and different resonance degrees offerroresonance overvoltage are investigated.
In this thesis, the nonlinear characteristics of the ferroresonance overvoltage time series and its flexible suppression method are carried out in detail though theoreticalanalysis, simulation and experiment research. The results are as follows:
Mutual information method and Cao method are adopted to reconstruct the pahsespace of the ferroresonance overvoltage. Based on the phase space reconstruction, thereconstructed attractor in sense of topological equivalent can be acquired, which can beused to analyze the nonlinear characteristics of the ferroresonance. The method used inthis thesis overcomes the traditional analysis method, which depends on the accurateferroresonance model and its precise parameters. The results of the method used in thisthesis are agreed with that of the traditional method. Based on the phase spacereconstruction, two important nonlinear characteristics quantities can be furtherobtained: the average gray value of the reconstructed attractor and the largest Lyapunovexponent of the overvoltage time series. The two nonlinear characteristics quantities ofthe ferroresonance overvoltage time series can be to classify the non-periodicferroresonance. A two-order polynomial model is identified using the reconstructionparameters and the ferroresonance overvoltage time series rather than extracting fromthe ferroresonance circuit. The model can represent the basic characteristics of theoriginal ferroresonance system. A feedback control method proposed based on theidentified model can suppress different types of ferroresonance overvoltage successfully.Fully controlled power electronic switches are adopted in this thesis to adjust the highfrequency damping resistance characteristics to realize ferroresonance suppression. Thesimulation and experiment research show that the damping resistance and duty cycle forputting into the damping resistor influence the suppression effect significantly.Comparison results show that the he proposed flexible ferroresonance overvoltagesuppression method can effectively restrain different types and different core saturationdegrees of ferroresonance overvoltage. The method can make up for the inadequacy oftraditional suppression method and not increase the burden to equipment. Moreover, themethod will not cause harmonic load for the system.
铁磁谐振发生在非线性电感和电容回路，谐振过程可能产生稳定的过电压和过电流，会对输配电装备和运行人员安全构成威胁，虽然国内外对铁磁谐振的产生机理、基本特性、发展规律和抑制措施进行了大量的研究，但是由于其谐振回路的复杂性和谐振类型的多样性，铁磁谐振抑制措施在某些谐振情况下抑制作用有限，造成电力系统关键设备可能承受较长时间的铁磁谐振过电压，可能使其产生绝缘损伤，最终可能造成设备损坏，因而铁磁谐振问题仍然是一个长期困扰电力系统安全运行的复杂问题。随着电网的发展，一方面配电网的快速发展造成配电系统参数变化范围急剧增大，配电网操作更加频繁，促使铁磁谐振发生率升高；另一方面超特高压系统对内部过电压倍数要求更为严格，铁磁谐振过电压可能会超过超特高压系统内部过电压水平。因此电力系统中的铁磁谐振问题愈发突出，亟需对铁磁谐振的非线性特性和铁磁谐振过电压的抑制进行深入研究。
目前铁磁谐振的基本特性分析和抑制方法研究大多基于铁磁谐振回路模型，该回路模型是对典型铁磁谐振回路简化而得到的，在一定程度上能够反映铁磁谐振的一般规律，为铁磁谐振研究奠定了基础，但是传统铁磁谐振模型需要精确的谐振电路模型和准确的系统参数，而在实际电力系统中，随着运行方式的改变谐振电路和系统参数都会随之发生变化，因此基于传统铁磁谐振模型的特性分析和抑制方法无法满足情况多变的现场应用。以目前研究成果为基础，本文提出了不依赖于铁磁谐振模型及参数，直接从铁磁谐振过电压时间序列入手进行铁磁谐振的非线性特性分析和抑制方法研究。首先针对铁磁谐振过电压时间序列的特点，选取适合铁磁谐振过电压的相空间重构算法，对铁磁谐振过电压时间序列进行相空间重构，可以挖掘铁磁谐振时间序列隐藏的系统信息，进而对铁磁谐振特有的非线性特性进行分析，从而对包含准周期和混沌在内的铁磁谐振过电压进行特征量提取和类型识别，能够为建立铁磁谐振过电压实时监测、在线分析以及主动抑制系统提供支持；其次在铁磁谐振过电压时间序列相空间重构的基础上，根据重构过程的关键参数建立铁磁谐振过电压时间序列的低阶多项式模型，并在此基础上研究铁磁谐振过电压时间序列的主动抑制策略，由此来论证直接通过铁磁谐振过电压时间序列得到抑制方法的可行性和有效性；最后基于以上研究，提出了一种采用高速全可控开关器件的铁磁谐振过电压灵活抑制方法也即柔性抑制方法，并分别搭建了考虑电压互感器(PT)铁芯磁滞效应的电磁暂态仿真模型和对应的实验室低压试验平台，基于仿真模型和试验平台详细分析了相关参数对铁磁谐振过电压抑制效果的影响，并对不同类型和不同谐振程度的铁磁谐振过电压进行了抑制研究。
本文通过理论分析、仿真计算和试验研究对铁磁谐振过电压时间序列的非线性特性和柔性抑制方法进行了详细的研究，结果表明：本文采用互信息法和Cao氏算法直接对铁磁谐振过电压进行相空间重构后可以得到有效的关键重构参数，能够得出与原铁磁谐振系统拓扑等价的重构吸引子，可以获取铁磁谐振系统的基本非线性特征，该方法不但克服了传统分析方法对精确铁磁谐振模型和系统参数的高度依赖，而且分析结果与传统分析方法高度一致；基于相空间重构，获得不同类型铁磁谐振过电压的两个重要的非线性特征量：重构吸引子的平均灰度和序列的最大Lyapunov指数，两者可以作为非周期谐振分类器的重要特征量，能够有效识别准周期和混沌铁磁谐振过电压；直接采用重构参数和过电压时间序列进行铁磁谐振数学建模，辨识得到了其二阶多项式模型，能够反映原铁磁谐振系统的基本数学特征，基于该数学模型所得到的铁磁谐振过电压抑制方法能够有效抑制不同类型的铁磁谐振过电压；基于以上研究，本文采用全控电力电子开关调整高频阻尼电阻投入特性，构造了一个电网频率意义下的等效连续可调电阻，进而实现不同类型铁磁谐振过电压的柔性抑制，仿真和试验研究表明阻尼电阻和高速开关门信号的占空比对铁磁谐振过电压抑制效果影响显著；对比研究结果表明，本文所提出的铁磁谐振过电压柔性抑制方法能够有效抑制不同类型和不同铁芯饱和程度的铁磁谐振过电压，在不显著增大设备负担的前提下能够弥补传统抑制方法的不足，且不会对系统造成谐波负担。
Smart grid is the direction for the world's power grid in the future, an importantfeature of which is "self-healing grid". This feature means that the power grid shouldhave the following abilities: real-time, online, continuous safe assessment and analysis;early warning, prevention and control for power accidents; and automatic faultdiagnosis, fault isolation and self-recovery. With such abilities, the security, stabilityand reliability of power grid can be significantly enhanced. The various defence lines ofpower grid are coordinated well so that the power grid owns the ability to defend someunexpected events and serious failures, which can effectively prevent the occurrence ofa wide range of cascading failures and significantly improve power supply reliabilityand reduce power losses.
Ferroresonance can occur in nonlinear inductance and capacitance circuit, it causesovervoltage and over-current that lasts for a long time and can even exist stably.Overvoltage and over-current may cause equipment failure and damage in powersystem. Therefore, the mechanism, the basic characteristics, the development law andthe suppression method of the ferroresonance are studied by a lot of scholars at homeand abroad. However, owning to the extremely various ferroresonance circuits and thevarious ferroresonance types, the effect of the present suppression method on theferroresonance under some certain condition may be limited. For this reason, powersystem key equipments may endure a long time ferroresonance overvoltage, makes itmay cause insulation damage and equipment damage. So, ferroresonance problem isstill a complex problem for the safe operation of the power system for a long time. Withthe development of the power grid, the ferroresonance problem in power system isincreasingly prominent. On the one hand, the rapid development of power distributionnetwork makes the distribution system parameter variation range increase very sharpand the power distribution network operation is more frequent, which leads to a higherincidence of ferroresonance. On the other hand, the UHV system is very strict withinternal overvoltage, and ferroresonance overvoltage may exceed its internalovervoltage level and cause key equipment damage and even a wide range of accident.Therefore, it is urgent needed to study the nonlinear characteristics of ferroresonanceand then put forward a more feasible ferroresonance overvoltage suppression strategy.
At present, most of the study on the basic ferroresonance nonlinear characteristics analysis and its suppression method are based a basic ferroresonance circuit model. Themodel is simplified by a typical ferroresonance circuit. To a certain extent, the simplifymodel can explain the basic principle of ferroresonance and lay a solid foundation forthe study of the ferroresonance. However, the traditional ferroresonance model can onlybe established before acquiring the ferroresonance circuit and precise system parameters.In the actual power system, the ferroresonance circuit and its parameters change withthe change of the operation mode. Therefore, the characteristics and the suppressionmethod obtained based on the traditional ferroresonance model cannot satisfy the fieldapplication.
Based on the present research, this thesis proposes a new method to analyze thenonlinear characteristics of ferroresonance and then study the suppression method forferroresonance. The study is directly based the ferroresonance overvoltage time seriesand not relying on the accurate ferroresonance model and precise parameters. Firstly,aiming at the characteristics of the ferroresonance overvoltage, appropriate phase spacereconstruction methods are chosen to reconstruct the ferroresonance overvoltage timeseries. Base on the reconstruction, the hidden information of the overvoltage time seriescan be dig for ferroresonance nonlinear characteristics analysis. The nonlinearcharacteristics analysis can be used for extracting the nonlinear characteristics quantitiesof the ferroresonance, including quasi-periodic and chaotic ferroresonance, andidentifying their types. All of the study can be supported to establish an online real-timemonitoring, analysis and active suppression system. Secondly, based on the phase spacereconstruction of the ferroresonance overvoltage time series, a lower order polynomialmodel for ferroresonance is identified using the key parameters determined in phasespace reconstruction. Based on the model, an active suppression strategy based onovervoltage time series is studied to demonstrate that it is feasible and effective. Finally,based on the above research, a flexible suppression method by combining with thepower electronic technology for ferroresonance overvoltage is proposed. High-speedfully controllable switches are adopted in this method. Electromagnetic transientsimulation model considering the hysteresis characteristic of the PT and scale-downlaboratory test platform are established individually, based on that, the suppressioneffect of the changeable parameters on the ferroresonance overvoltage is analyzed indetail, and the suppressions on the different types and different resonance degrees offerroresonance overvoltage are investigated.
In this thesis, the nonlinear characteristics of the ferroresonance overvoltage time series and its flexible suppression method are carried out in detail though theoreticalanalysis, simulation and experiment research. The results are as follows:
Mutual information method and Cao method are adopted to reconstruct the pahsespace of the ferroresonance overvoltage. Based on the phase space reconstruction, thereconstructed attractor in sense of topological equivalent can be acquired, which can beused to analyze the nonlinear characteristics of the ferroresonance. The method used inthis thesis overcomes the traditional analysis method, which depends on the accurateferroresonance model and its precise parameters. The results of the method used in thisthesis are agreed with that of the traditional method. Based on the phase spacereconstruction, two important nonlinear characteristics quantities can be furtherobtained: the average gray value of the reconstructed attractor and the largest Lyapunovexponent of the overvoltage time series. The two nonlinear characteristics quantities ofthe ferroresonance overvoltage time series can be to classify the non-periodicferroresonance. A two-order polynomial model is identified using the reconstructionparameters and the ferroresonance overvoltage time series rather than extracting fromthe ferroresonance circuit. The model can represent the basic characteristics of theoriginal ferroresonance system. A feedback control method proposed based on theidentified model can suppress different types of ferroresonance overvoltage successfully.Fully controlled power electronic switches are adopted in this thesis to adjust the highfrequency damping resistance characteristics to realize ferroresonance suppression. Thesimulation and experiment research show that the damping resistance and duty cycle forputting into the damping resistor influence the suppression effect significantly.Comparison results show that the he proposed flexible ferroresonance overvoltagesuppression method can effectively restrain different types and different core saturationdegrees of ferroresonance overvoltage. The method can make up for the inadequacy oftraditional suppression method and not increase the burden to equipment. Moreover, themethod will not cause harmonic load for the system.
引文
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