牵引变电站综合补偿方案的研究
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摘要
电力机车牵引比蒸气机车牵引和内燃机车牵引有许多优越性，所以电气化铁道在世界各国都得到了快速发展。但由于电力牵引负荷在运行中要产生大量的负序电流和谐波电流，这些电流注入电网后，会引起电力系统的电压、电流不对称和波形畸变，使电能质量下降，严重时还会威胁到电力系统的安全运行。因此，解决电气化铁道对电力系统的“污染”问题将是一个非常有意义的研究课题。
本文首先分析了电力牵引负荷产生的负序电流、谐波电流及低功率因数对电力系统和电力用户的影响，介绍了目前国内外对电气化铁道综合补偿的主要技术方案，并对各种技术方案进行了评价。然后以国内电气化铁道广泛采用YNd11接线的牵引变电站为研究对象，针对不同情况，深入研究了牵引变电站的几种综合补偿方案。
要治理电气化铁道对电力系统的污染，就必须了解电气化铁道的负荷特性，掌握其变化规律。本文列举了电力机车几种主要车型的结构以及它们产生的谐波电流。从分析YNd11接线变压器的牵引变电站负荷电流在变压器各绕组中分布的情况入手，导出了电气化铁道注入电力系统的负序电流、谐波电流的相关公式，得出了负序电流、谐波电流随电力机车负荷变化而变化的规律。为了便于分析综合补偿方案的效果，论文还给出了负序及谐波的有关标准规定。
滤波器除具有滤波作用外，还具有基波下向系统输送无功的特性。因此，合理设计滤波器，可使牵引变电站的功率因数及谐波同时满足要求。本文阐述了单调谐滤波器的结构及工作原理，列出了滤波器设计所需要的基本参数和技术参数的计算公式，并提出以设备投资最小为目标函数，以功率因数和滤波率为约束的滤波器优化设计数学模型。文中介绍了求解具有约束条件的非线性数学模型的算法——广义拉格朗日乘子算法的原理及步骤，即如何把具有约束条件的非线性数学模型转化为无约束条件的非线性数学模型进行求解；同时还介绍了无约束的非线性数学模型的求解算法——步长加速法的原理及步骤。利用C++Builder5.0对某牵引变电站进行了滤波器优化设计，结果表明滤波效果良好，在功率因数满足要求的前提下，可使谐波低于国标标准规定的限值。
随着技术的发展，新型的电力机车上已开始采用车载滤波器和变频调速技术，从而使谐波的问题有所缓解。但是随着电力牵引负荷的逐年增加，负序的问题却越来越突出。目
郑州大学工学硕士论文
前牵引变电站在进行综合补偿时，普遍忽视对负序电流的抑制。本文提出了在满足牵引变
电站无功补偿的前提下，使注入电力系统的负序电流最小的两相优化补偿方案。文中分析
了两供电臂负荷的负荷特性，对两供电臂正常运行时变压器各绕组中的功率因数及电压损
失进行公式推导及理论分析，得出了滞后相多补偿无功容量，引前相少补偿无功容量有利
于提高电压质量的结论。进而给出了以注入电力系统的负序电流最小为目标函数，以功率
因数及各相电压为约束条件，确定各相补偿容量的数学模型。利用c++B uilders.o编制了
根据负荷变化而调节两相补偿容量的程序。计算结果表明，两相优化补偿和常规补偿相比，
在功率因数达到同一给定值时，优化补偿对负序电流的抑制具有明显的效果，从而起到提
高电能质量的作用。
电力牵引负荷属于典型的不对称负荷，利用斯坦美兹(Steinmetz)原理，可以对其
进行平衡化处理。文中提出了一种基于斯坦美兹原理的三相补偿方案，导出了牵引变电站
各相的补偿容量和电流的计算公式，并采用C++ Bui lders.o编制了计算程序。给定功率因
数的期望值和两供电臂的负荷后，便可算出各相所需的补偿量。计算结果表明，该方案除
能达到理想的无功补偿效果外，还能消除负序电流。这对于提高电能质量将是很有意义的。
由于220kV电网比1 IOkV电网的短路容量大，对于负序和谐波有较强的承受能力，通
过提高牵引变电站的供电电压，还可减少其注入电网的负序电流和谐波电流，进而减少对
电力系统的影响。本文分析了哈大线电气化铁道采用的22OkV两相供电方案所存在的不足，
从缓解负序电流和谐波电流的角度讨论了采用220kV电源向牵引变电站供电的可行性，并
给出采用220kv三相供电的接线方案。
Nowadays, the electrified locomotives have an extremely rapid development all over the world because of its great advantage compared to internal-combustion engine. But this type of load during its operation generates tremendous negative sequence and harmonic currents which flow in the power system causing voltage, current asymmetric and wave distortion. This makes the power quality become worse. At present, with the development of electrified railway, the pollution engendered by the electrified locomotive is becoming more and more serious, even threats the safe and economic operation of the power system. Hence, it is a significative subject to study the comprehensive compensation of traction substation.
Firstly, the harm to the power system and customers caused by electrified locomotives due to their characteristics of lower power factor, negative sequence current and harmonic currents is analyzed in the thesis. Secondly, the main several comprehensive compensation schemes of traction substation are introduced and evaluated. Finally, based on the widely used transformer with Yndll connection in traction substation, intensive observation is made on several compensation plans according to different conditions.
In order to deal with the pollution caused by electrified locomotive, its characteristics and rule of change must be mastered. In this thesis, the configuration of several main types of electric locomotive and harmonic currents generated by them are illustrated. Based on the analysis of the loading currents distributed in each phase winding of traction transformer, the corresponding formulas are deduced, these formulas can define how many negative sequence and harmonic currents swarm into power system from the transformer's high voltage side and how these change versus the loads. In order to assay the result of different methods, the relevant parts of National Standards of Power Quality are given, too.
Apart from filtering, filters can provide some fundamental reactive power to the power system. Hence, a filter could be designed to increase power factor of traction substation and decrease the harmonic currents. The configuration and principle of single-tuned passive filters are introduced, the basic parameters and relevant formulas are listed for the filter determination. Then a mathematic model for the filter optimization design is set up. The objective function is to minimize the total investment with qualified power factor and filtering rate. This is a nonlinear optimization problem. In this thesis, the extended Lagrange multiplication technique is applied. More over, the step-acceleration method is introduced to deal with nonlinear problem without constraints. As an example, the filter optimization design for traction substation is carried out using the C++ Builder 5.0. The designed filter works well. With the power factor satisfied, the harmonic currents are reduced to be lower than the required limit
s in the National Standards of Power Quality.
With the installation of filter on locomotives and the development of frequency converter, harmonic currents caused by the electric locomotive have been relieved. With the loads of locomotives increasing, the problems of negative sequence are becoming more and more noticeable that are ignored when traction substation is comprehensively compensated. In order to
deal with the problem, an two-phase optimization compensation plan is put forward in this thesis. It is to increase power factor and minimize the injected negative sequence currents. After the analysis of the characteristics of loads in the two power supplying arms, power factor, as well as the voltage loss in each phase of traction transformer, a conclusion is achieved that it is reasonable to over-compensate the lagging phase and less-compensate the leading phase. According to this analysis a mathematic model is set up aimed at minimizing the negative sequence currents with the constraints for power factor and each phase voltage considered, and the compensation capacity of each phase is determined. F
本文首先分析了电力牵引负荷产生的负序电流、谐波电流及低功率因数对电力系统和电力用户的影响，介绍了目前国内外对电气化铁道综合补偿的主要技术方案，并对各种技术方案进行了评价。然后以国内电气化铁道广泛采用YNd11接线的牵引变电站为研究对象，针对不同情况，深入研究了牵引变电站的几种综合补偿方案。
要治理电气化铁道对电力系统的污染，就必须了解电气化铁道的负荷特性，掌握其变化规律。本文列举了电力机车几种主要车型的结构以及它们产生的谐波电流。从分析YNd11接线变压器的牵引变电站负荷电流在变压器各绕组中分布的情况入手，导出了电气化铁道注入电力系统的负序电流、谐波电流的相关公式，得出了负序电流、谐波电流随电力机车负荷变化而变化的规律。为了便于分析综合补偿方案的效果，论文还给出了负序及谐波的有关标准规定。
滤波器除具有滤波作用外，还具有基波下向系统输送无功的特性。因此，合理设计滤波器，可使牵引变电站的功率因数及谐波同时满足要求。本文阐述了单调谐滤波器的结构及工作原理，列出了滤波器设计所需要的基本参数和技术参数的计算公式，并提出以设备投资最小为目标函数，以功率因数和滤波率为约束的滤波器优化设计数学模型。文中介绍了求解具有约束条件的非线性数学模型的算法——广义拉格朗日乘子算法的原理及步骤，即如何把具有约束条件的非线性数学模型转化为无约束条件的非线性数学模型进行求解；同时还介绍了无约束的非线性数学模型的求解算法——步长加速法的原理及步骤。利用C++Builder5.0对某牵引变电站进行了滤波器优化设计，结果表明滤波效果良好，在功率因数满足要求的前提下，可使谐波低于国标标准规定的限值。
随着技术的发展，新型的电力机车上已开始采用车载滤波器和变频调速技术，从而使谐波的问题有所缓解。但是随着电力牵引负荷的逐年增加，负序的问题却越来越突出。目
郑州大学工学硕士论文
前牵引变电站在进行综合补偿时，普遍忽视对负序电流的抑制。本文提出了在满足牵引变
电站无功补偿的前提下，使注入电力系统的负序电流最小的两相优化补偿方案。文中分析
了两供电臂负荷的负荷特性，对两供电臂正常运行时变压器各绕组中的功率因数及电压损
失进行公式推导及理论分析，得出了滞后相多补偿无功容量，引前相少补偿无功容量有利
于提高电压质量的结论。进而给出了以注入电力系统的负序电流最小为目标函数，以功率
因数及各相电压为约束条件，确定各相补偿容量的数学模型。利用c++B uilders.o编制了
根据负荷变化而调节两相补偿容量的程序。计算结果表明，两相优化补偿和常规补偿相比，
在功率因数达到同一给定值时，优化补偿对负序电流的抑制具有明显的效果，从而起到提
高电能质量的作用。
电力牵引负荷属于典型的不对称负荷，利用斯坦美兹(Steinmetz)原理，可以对其
进行平衡化处理。文中提出了一种基于斯坦美兹原理的三相补偿方案，导出了牵引变电站
各相的补偿容量和电流的计算公式，并采用C++ Bui lders.o编制了计算程序。给定功率因
数的期望值和两供电臂的负荷后，便可算出各相所需的补偿量。计算结果表明，该方案除
能达到理想的无功补偿效果外，还能消除负序电流。这对于提高电能质量将是很有意义的。
由于220kV电网比1 IOkV电网的短路容量大，对于负序和谐波有较强的承受能力，通
过提高牵引变电站的供电电压，还可减少其注入电网的负序电流和谐波电流，进而减少对
电力系统的影响。本文分析了哈大线电气化铁道采用的22OkV两相供电方案所存在的不足，
从缓解负序电流和谐波电流的角度讨论了采用220kV电源向牵引变电站供电的可行性，并
给出采用220kv三相供电的接线方案。
Nowadays, the electrified locomotives have an extremely rapid development all over the world because of its great advantage compared to internal-combustion engine. But this type of load during its operation generates tremendous negative sequence and harmonic currents which flow in the power system causing voltage, current asymmetric and wave distortion. This makes the power quality become worse. At present, with the development of electrified railway, the pollution engendered by the electrified locomotive is becoming more and more serious, even threats the safe and economic operation of the power system. Hence, it is a significative subject to study the comprehensive compensation of traction substation.
Firstly, the harm to the power system and customers caused by electrified locomotives due to their characteristics of lower power factor, negative sequence current and harmonic currents is analyzed in the thesis. Secondly, the main several comprehensive compensation schemes of traction substation are introduced and evaluated. Finally, based on the widely used transformer with Yndll connection in traction substation, intensive observation is made on several compensation plans according to different conditions.
In order to deal with the pollution caused by electrified locomotive, its characteristics and rule of change must be mastered. In this thesis, the configuration of several main types of electric locomotive and harmonic currents generated by them are illustrated. Based on the analysis of the loading currents distributed in each phase winding of traction transformer, the corresponding formulas are deduced, these formulas can define how many negative sequence and harmonic currents swarm into power system from the transformer's high voltage side and how these change versus the loads. In order to assay the result of different methods, the relevant parts of National Standards of Power Quality are given, too.
Apart from filtering, filters can provide some fundamental reactive power to the power system. Hence, a filter could be designed to increase power factor of traction substation and decrease the harmonic currents. The configuration and principle of single-tuned passive filters are introduced, the basic parameters and relevant formulas are listed for the filter determination. Then a mathematic model for the filter optimization design is set up. The objective function is to minimize the total investment with qualified power factor and filtering rate. This is a nonlinear optimization problem. In this thesis, the extended Lagrange multiplication technique is applied. More over, the step-acceleration method is introduced to deal with nonlinear problem without constraints. As an example, the filter optimization design for traction substation is carried out using the C++ Builder 5.0. The designed filter works well. With the power factor satisfied, the harmonic currents are reduced to be lower than the required limit
s in the National Standards of Power Quality.
With the installation of filter on locomotives and the development of frequency converter, harmonic currents caused by the electric locomotive have been relieved. With the loads of locomotives increasing, the problems of negative sequence are becoming more and more noticeable that are ignored when traction substation is comprehensively compensated. In order to
deal with the problem, an two-phase optimization compensation plan is put forward in this thesis. It is to increase power factor and minimize the injected negative sequence currents. After the analysis of the characteristics of loads in the two power supplying arms, power factor, as well as the voltage loss in each phase of traction transformer, a conclusion is achieved that it is reasonable to over-compensate the lagging phase and less-compensate the leading phase. According to this analysis a mathematic model is set up aimed at minimizing the negative sequence currents with the constraints for power factor and each phase voltage considered, and the compensation capacity of each phase is determined. F
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