CN112670987A - Power grid three-phase harmonic flow phasor matrix calculation method - Google Patents

Power grid three-phase harmonic flow phasor matrix calculation method Download PDF

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CN112670987A
CN112670987A CN202011601327.6A CN202011601327A CN112670987A CN 112670987 A CN112670987 A CN 112670987A CN 202011601327 A CN202011601327 A CN 202011601327A CN 112670987 A CN112670987 A CN 112670987A
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power flow
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power
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CN112670987B (en
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李传栋
林金榕
严翠云
杜培
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Electric Power Research Institute of State Grid Fujian Electric Power Co Ltd
State Grid Fujian Electric Power Co Ltd
Longyan Power Supply Co of State Grid Fujian Electric Power Co Ltd
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State Grid Fujian Electric Power Co Ltd
Longyan Power Supply Co of State Grid Fujian Electric Power Co Ltd
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Abstract

本发明涉及一种电网三相谐波潮流相量矩阵计算方法，包括步骤：设置谐波次数，设置谐波源统计模型初始值以及算法迭代误差限；采集包括变压器参数、线路参数、节点电压、发电机参数、负荷参数在内的参数，建立基波和谐波三相导纳矩阵；计算基波三相潮流；检测存在谐波源的节点，利用基波三相潮流结果，由谐波源统计模型预测谐波数据，进行谐波三相潮流计算；利用谐波三相网损功率更新基波三相负荷功率；判断前后节点注入功率误差是否小于预设的迭代误差限，若是则计算收敛，输出谐波三相潮流计算结果，否则返回重新计算基波三相潮流。本发明基于相量矩阵的思维进行程序架构，实现了大规模三相电网谐波潮流仿真的快速开发和高效计算。The invention relates to a method for calculating a three-phase harmonic power flow phasor matrix of a power grid, comprising the steps of: setting the harmonic order, setting the initial value of a harmonic source statistical model and an algorithm iteration error limit; collecting parameters including transformer parameters, line parameters, node voltages, Parameters including generator parameters and load parameters, establish fundamental wave and harmonic three-phase admittance matrix; calculate fundamental wave three-phase power flow; Statistical model predicts harmonic data and performs harmonic three-phase power flow calculation; uses harmonic three-phase network loss power to update fundamental three-phase load power; judges whether the injected power error of the front and rear nodes is less than the preset iteration error limit, and if so, the calculation converges , output the harmonic three-phase power flow calculation result, otherwise return to recalculate the fundamental wave three-phase power flow. The invention implements a program structure based on the thinking of the phasor matrix, and realizes the rapid development and efficient calculation of the large-scale three-phase power grid harmonic power flow simulation.

Description

一种电网三相谐波潮流相量矩阵计算方法A phasor matrix calculation method for three-phase harmonic power flow in power grid

技术领域technical field

本发明涉及电力系统安全技术领域，特别是一种电网三相谐波潮流相量矩阵计算方法。The invention relates to the technical field of power system security, in particular to a method for calculating a three-phase harmonic power flow phasor matrix of a power grid.

背景技术Background technique

电力系统的谐波问题在20世纪30年代就引起了人们的关注，随后由于现代工业技术的发展，电网中的非线性负荷大量增加，如工业中广泛应用的电弧和接触焊设备、矿热炉、硅铁炉、高频炉等，同时，电力电子技术的迅速发展，使晶闸管整流和换流技术得到广泛应用，这都使得电网中的谐波大量增加。谐波对电力系统的影响和危害是十分严重的，其主要表现为降低供电系统的功率因数、使电器设备过热，绝缘老化，产生振动和噪声，缩短用电设备的寿命、引起电力系统的并联和串联谐振损坏电容器等。为了解决上述谐波危害问题，70年代以来，各工业国家纷纷投入力量对谐波问题进行研究，作为谐波问题研究的重要内容，谐波潮流计算也得到了相应发展。The harmonic problem of the power system has attracted people's attention in the 1930s, and then due to the development of modern industrial technology, the nonlinear load in the power grid has increased greatly, such as arc and contact welding equipment, submerged arc furnaces, which are widely used in industry. , ferrosilicon furnace, high-frequency furnace, etc. At the same time, the rapid development of power electronic technology has made thyristor rectification and commutation technology widely used, which has caused a large increase in harmonics in the power grid. The influence and harm of harmonics to the power system is very serious, which is mainly manifested in reducing the power factor of the power supply system, overheating the electrical equipment, aging insulation, generating vibration and noise, shortening the life of the electrical equipment, and causing the parallel connection of the power system. and series resonance damage capacitors, etc. In order to solve the above-mentioned harmonic hazard problems, since the 1970s, various industrial countries have invested in research on harmonic problems. As an important part of harmonic research, harmonic power flow calculation has also been developed accordingly.

三相谐波潮流计算是研究谐波问题的重要内容，通过三相谐波潮流计算可以描绘电网络的三相谐波潮流分布，得出电网络三相各节点的谐波指标，这是评估电力系统安全运行的重要依据，根据三相谐波潮流计算结果还可分析谐波产生的原因，并进一步研究谐波治理措施。Three-phase harmonic power flow calculation is an important part of the study of harmonic problems. Through the three-phase harmonic power flow calculation, the three-phase harmonic power flow distribution of the electrical network can be depicted, and the harmonic indicators of each node of the three-phase electrical network can be obtained. It is an important basis for the safe operation of the power system. According to the calculation results of the three-phase harmonic power flow, the causes of harmonic generation can also be analyzed, and the harmonic control measures can be further studied.

当前的三相谐波潮流计算不适合运用于大规模三相网络，对谐波源的拓展不方便，因此程序的效率不高，不适合于工程实际情况。The current three-phase harmonic power flow calculation is not suitable for large-scale three-phase networks, and it is inconvenient to expand the harmonic source, so the efficiency of the program is not high, and it is not suitable for actual engineering conditions.

发明内容SUMMARY OF THE INVENTION

有鉴于此，本发明的目的是提出一种电网三相谐波潮流相量矩阵计算方法，基于相量矩阵的思维进行程序架构，实现了大规模三相电网谐波潮流仿真的快速开发和高效计算。In view of this, the purpose of the present invention is to propose a method for calculating a three-phase harmonic power flow phasor matrix of a power grid, and a program structure is carried out based on the thinking of the phasor matrix, so as to realize the rapid development and high efficiency of the large-scale three-phase power grid harmonic power flow simulation. calculate.

本发明采用以下方案实现：一种电网三相谐波潮流相量矩阵计算方法，具体包括以下步骤：The present invention adopts the following scheme to realize: a method for calculating a three-phase harmonic power flow phasor matrix of a power grid, which specifically includes the following steps:

设置谐波次数，设置谐波源统计模型初始值以及算法迭代误差限；Set the harmonic order, set the initial value of the harmonic source statistical model and the algorithm iteration error limit;

采集包括变压器参数、线路参数、节点电压、发电机参数、负荷参数在内的参数，建立基波和谐波三相导纳矩阵；Collect parameters including transformer parameters, line parameters, node voltage, generator parameters, load parameters, and establish fundamental wave and harmonic three-phase admittance matrices;

计算基波三相潮流；Calculate the fundamental three-phase power flow;

检测存在谐波源的节点，利用基波三相潮流结果，由谐波源统计模型预测谐波数据，进行谐波三相潮流计算；Detect nodes with harmonic sources, use the fundamental three-phase power flow results, predict the harmonic data by the harmonic source statistical model, and perform harmonic three-phase power flow calculations;

利用谐波三相网损功率更新基波三相负荷功率；The fundamental three-phase load power is updated by using the harmonic three-phase network loss power;

判断前后节点注入功率误差是否小于预设的迭代误差限，若是则计算收敛，输出谐波三相潮流计算结果，否则返回重新计算基波三相潮流。It is judged whether the injected power error of the front and rear nodes is less than the preset iterative error limit. If so, the calculation converges, and the harmonic three-phase power flow calculation result is output. Otherwise, it returns to recalculate the fundamental three-phase power flow.

进一步地，所述设置谐波次数，设置谐波源统计模型初始值以及算法迭代误差限具体为：设置要计算的谐波次数，输入不同的谐波源的统计模型初始值，以及基波、谐波算法的迭代收敛误差值。Further, the setting of the harmonic order, the setting of the initial value of the harmonic source statistical model and the algorithm iteration error limit are specifically: setting the harmonic order to be calculated, inputting the initial value of the statistical model of different harmonic sources, and the fundamental wave, Iterative convergence error value for the harmonic algorithm.

进一步地，建立的基波三相导纳矩阵

Figure BDA0002871496610000021
为：Further, the established fundamental wave three-phase admittance matrix
Figure BDA0002871496610000021
for:

Figure BDA0002871496610000022
Figure BDA0002871496610000022

式中，

Figure BDA0002871496610000031
为基波三相线路的导纳矩阵，
Figure BDA0002871496610000032
为基波三相变压器的导纳矩阵；In the formula,
Figure BDA0002871496610000031
is the admittance matrix of the fundamental three-phase line,
Figure BDA0002871496610000032
is the admittance matrix of the fundamental three-phase transformer;

其中，基波三相线路的导纳矩阵

Figure BDA0002871496610000033
为：Among them, the admittance matrix of the fundamental wave three-phase line
Figure BDA0002871496610000033
for:

Figure BDA0002871496610000034
Figure BDA0002871496610000034

式中，nL表示线路总数，[CLf]与[CLt]为关联矩阵，

Figure BDA0002871496610000035
Figure BDA0002871496610000036
分别为线路t端和f端的三相电纳矩阵，上标i表示第i条线路；In the formula, nL represents the total number of lines, [C Lf ] and [C Lt ] are the correlation matrix,
Figure BDA0002871496610000035
Figure BDA0002871496610000036
are the three-phase susceptance matrices of the t-end and f-ends of the line, respectively, and the superscript i represents the ith line;

其中，

Figure BDA0002871496610000037
in,
Figure BDA0002871496610000037

Figure BDA0002871496610000038
Figure BDA0002871496610000038

Figure BDA0002871496610000039
Figure BDA0002871496610000039

式中，rL1,xL1分别表示线路正序电阻和电抗；rL2,xL2分别表示线路负序电阻和电抗；rL0,xL0分别表示线路零序电阻和电抗；In the formula, r L1 , x L1 represent the positive sequence resistance and reactance of the line respectively; r L2 , x L2 represent the negative sequence resistance and reactance of the line respectively; r L0 , x L0 represent the zero sequence resistance and reactance of the line respectively;

其中，基波三相变压器的导纳矩阵

Figure BDA00028714966100000310
为：Among them, the admittance matrix of the fundamental three-phase transformer
Figure BDA00028714966100000310
for:

Figure BDA0002871496610000041
Figure BDA0002871496610000041

其中，nT为变压器的总台数，[CTf]与[CTt]分别为关联矩阵；Among them, nT is the total number of transformers, [C Tf ] and [C Tt ] are the correlation matrices respectively;

Figure BDA0002871496610000042
Figure BDA0002871496610000042

式中，f表示首端，t表示末端，kf,kt分别表示f端变压器变比和t端变压器变比，上标q表示第q台变压器的零序电阻和电抗；In the formula, f represents the head end, t represents the end, k f , k t represent the transformer transformation ratio of the f terminal and the transformer transformation ratio of the t terminal, respectively, and the superscript q represents the zero-sequence resistance and reactance of the qth transformer;

Figure BDA0002871496610000043
Figure BDA0002871496610000043

其中，

Figure BDA0002871496610000044
in,
Figure BDA0002871496610000044

Figure BDA0002871496610000045
分别为第q台变压器的正序电阻和电抗，
Figure BDA0002871496610000046
分别为第q台变压器的负序电阻和电抗；
Figure BDA0002871496610000047
分别为第q台变压器的零序电阻和电抗。
Figure BDA0002871496610000045
are the positive sequence resistance and reactance of the qth transformer, respectively,
Figure BDA0002871496610000046
are the negative sequence resistance and reactance of the qth transformer, respectively;
Figure BDA0002871496610000047
are the zero-sequence resistance and reactance of the qth transformer, respectively.

进一步地，建立的谐波三相导纳矩阵

Figure BDA0002871496610000048
为：Further, the established harmonic three-phase admittance matrix
Figure BDA0002871496610000048
for:

Figure BDA0002871496610000049
Figure BDA0002871496610000049

式中，

Figure BDA00028714966100000410
为变压器谐波导纳矩阵，
Figure BDA00028714966100000411
为谐波线路导纳矩阵，
Figure BDA00028714966100000412
为负载谐波导纳矩阵，
Figure BDA00028714966100000413
为发电机谐波导纳矩阵。In the formula,
Figure BDA00028714966100000410
is the transformer harmonic admittance matrix,
Figure BDA00028714966100000411
is the harmonic line admittance matrix,
Figure BDA00028714966100000412
is the load harmonic admittance matrix,
Figure BDA00028714966100000413
is the generator harmonic admittance matrix.

进一步地，所述计算基波三相潮流具体为：对基础三相潮流方程修改为：Further, the calculation of the fundamental three-phase power flow is specifically: modifying the basic three-phase power flow equation as:

Figure BDA0002871496610000051
Figure BDA0002871496610000051

式中，Uabcx为三相电压实部，Uabcy为三相电压虚部，

Figure BDA0002871496610000052
为PV节点给定电压，ΔPabc为三相有功不平衡量，ΔQabc为三相无功不平衡量；pvbus、pqbus都为向量索引矩阵，由初始输入节点命名顺序决定；令误差修正量为：[Δxabc]＝[J]\[F]；J表示雅可比矩阵，F表示功率不平衡量矩阵；where U abcx is the real part of the three-phase voltage, U abcy is the imaginary part of the three-phase voltage,
Figure BDA0002871496610000052
Set the voltage for the PV node, ΔP abc is the three-phase active power unbalance, ΔQ abc is the three-phase reactive power unbalance; pvbus and pqbus are vector index matrices, which are determined by the naming sequence of the initial input nodes; let the error correction amount be: [ Δx abc ]=[J]\[F]; J represents the Jacobian matrix, and F represents the power imbalance matrix;

修正电压如下：The correction voltage is as follows:

Figure BDA0002871496610000053
Figure BDA0002871496610000053

式中，i1为pqbus的电压实部对应的索引向量，i2为pqbus的电压虚部对应的索引向量，i3为pvbus的电压实部对应的索引向量，i4为pvbus的电压虚部对应的索引向量，由初始输入节点命名顺序决定；Δxabc为电压误差修正量矩阵；In the formula, i 1 is the index vector corresponding to the voltage real part of pqbus, i 2 is the index vector corresponding to the voltage imaginary part of pqbus, i 3 is the index vector corresponding to the voltage real part of pvbus, and i 4 is the voltage imaginary part of pvbus The corresponding index vector is determined by the naming order of the initial input nodes; Δx abc is the voltage error correction matrix;

判断F是否大于预设的基波三相迭代误差值，若是，则循环执行上述计算；若否，则结束三相基波潮流计算，储存三相基波潮流结果。Determine whether F is greater than the preset fundamental wave three-phase iteration error value, if so, execute the above calculation in a loop; if not, end the three-phase fundamental wave power flow calculation and store the three-phase fundamental wave power flow result.

进一步地，所述检测存在谐波源的节点，利用基波三相潮流结果，由谐波源统计模型预测谐波数据，进行谐波三相潮流计算具体为：Further, in the detection of nodes with harmonic sources, using the fundamental wave three-phase power flow results, the harmonic data is predicted by the harmonic source statistical model, and the harmonic three-phase power flow calculation is performed as follows:

利用参数标记检测含有谐波源标记的节点，并判断是否有多个谐波源在同一节点；若有，则考虑谐波源之间的相互影响；若无，则不考虑谐波源之间的相互影响；Use parameter markers to detect nodes containing harmonic source markers, and determine whether there are multiple harmonic sources at the same node; if so, consider the mutual influence between harmonic sources; if not, do not consider the interaction between harmonic sources mutual influence;

各次谐波电流：

Figure BDA0002871496610000068
Each harmonic current:
Figure BDA0002871496610000068

若在同一节点有多个谐波源时考虑它们的相互影响，由国标得到考虑谐波源之间相互影响的公式为：If there are multiple harmonic sources at the same node to consider their mutual influence, the formula for considering the mutual influence between harmonic sources obtained from the national standard is:

Figure BDA0002871496610000061
Figure BDA0002871496610000061

式中，harmonich为第h次谐波电流含有率，Iabcx、Iabcy由基波潮流得到，

Figure BDA0002871496610000062
分别为谐波源1与谐波源2的谐波三相电流；Kh为给定系数；where harmonic h is the h-th harmonic current content, I abcx and I abcy are obtained from the fundamental power flow,
Figure BDA0002871496610000062
are the harmonic three-phase currents of harmonic source 1 and harmonic source 2 respectively; K h is a given coefficient;

由

Figure BDA0002871496610000063
得到各节点各次谐波三相电压，由谐波三相电压得到谐波三相损耗,利用谐波源节点的谐波损耗更新此节点的三相功率；其中，
Figure BDA0002871496610000064
为三相谐波电压矩阵，
Figure BDA0002871496610000065
为网络谐波导纳矩阵，
Figure BDA0002871496610000066
为三相谐波功率。Depend on
Figure BDA0002871496610000063
Obtain the harmonic three-phase voltage of each node, obtain the harmonic three-phase loss from the harmonic three-phase voltage, and use the harmonic loss of the harmonic source node to update the three-phase power of this node; among them,
Figure BDA0002871496610000064
is the three-phase harmonic voltage matrix,
Figure BDA0002871496610000065
is the network harmonic admittance matrix,
Figure BDA0002871496610000066
is the three-phase harmonic power.

进一步地，所述判断前后节点注入功率误差是否小于预设的迭代误差限，若是则计算收敛，输出谐波三相潮流计算结果，否则返回重新计算基波三相潮流具体为：Further, whether the injected power error of the node before and after the judgment is less than the preset iterative error limit, if so, the calculation is converged, and the harmonic three-phase power flow calculation result is output, otherwise the return to recalculate the fundamental wave three-phase power flow is specifically:

Figure BDA0002871496610000067
Figure BDA0002871496610000067

式中，

Figure BDA0002871496610000071
为第k次循环得到的三相功率值矩阵，
Figure BDA0002871496610000072
为第k-1次循环得到的三相功率值矩阵；判断[ΔSabc(k)]是否小于预设的谐波迭代误差值，若否，则返回重新计算基波三相潮流，若是，结束并输出谐波三相潮流计算结果。In the formula,
Figure BDA0002871496610000071
is the three-phase power value matrix obtained in the kth cycle,
Figure BDA0002871496610000072
is the three-phase power value matrix obtained in the k-1th cycle; judge whether [ΔS abc (k)] is less than the preset harmonic iteration error value, if not, return to recalculate the fundamental three-phase power flow, if so, end And output the harmonic three-phase power flow calculation results.

本发明还提供了一种电网三相谐波潮流相量矩阵计算系统，包括存储器、处理器以及存储于存储器上并能够在处理器上运行的计算机程序指令，当处理器运行该计算机程序指令时，能够实现如上文所述的方法步骤。The present invention also provides a grid three-phase harmonic power flow phasor matrix calculation system, comprising a memory, a processor, and a computer program instruction stored in the memory and capable of running on the processor. When the processor runs the computer program instruction , the method steps as described above can be implemented.

与现有技术相比，本发明有以下有益效果：本发明基于相量矩阵的思维进行程序架构，实现了大规模三相电网谐波潮流仿真的快速开发和高效计算。Compared with the prior art, the present invention has the following beneficial effects: the present invention implements a program structure based on the thinking of phasor matrix, and realizes rapid development and efficient calculation of large-scale three-phase power grid harmonic power flow simulation.

具体实施方式Detailed ways

下面结合实施例对本发明做进一步说明。The present invention will be further described below in conjunction with the embodiments.

应该指出，以下详细说明都是示例性的，旨在对本申请提供进一步的说明。除非另有指明，本文使用的所有技术和科学术语具有与本申请所属技术领域的普通技术人员通常理解的相同含义。It should be noted that the following detailed description is exemplary and intended to provide further explanation of the application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

需要注意的是，这里所使用的术语仅是为了描述具体实施方式，而非意图限制根据本申请的示例性实施方式。如在这里所使用的，除非上下文另外明确指出，否则单数形式也意图包括复数形式，此外，还应当理解的是，当在本说明书中使用术语“包含”和/或“包括”时，其指明存在特征、步骤、操作、器件、组件和/或它们的组合。It should be noted that the terminology used herein is for the purpose of describing specific embodiments only, and is not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly dictates otherwise, the singular is intended to include the plural as well, furthermore, it is to be understood that when the terms "comprising" and/or "including" are used in this specification, it indicates that There are features, steps, operations, devices, components and/or combinations thereof.

本实施例提供了一种电网三相谐波潮流相量矩阵计算方法，具体包括以下步骤：This embodiment provides a method for calculating a three-phase harmonic power flow phasor matrix of a power grid, which specifically includes the following steps:

设置谐波次数，设置谐波源统计模型初始值以及算法迭代误差限；Set the harmonic order, set the initial value of the harmonic source statistical model and the algorithm iteration error limit;

采集包括变压器参数、线路参数、节点电压、发电机参数、负荷参数在内的参数，建立基波和谐波三相导纳矩阵；Collect parameters including transformer parameters, line parameters, node voltage, generator parameters, load parameters, and establish fundamental wave and harmonic three-phase admittance matrices;

计算基波三相潮流；Calculate the fundamental three-phase power flow;

检测存在谐波源的节点，利用基波三相潮流结果，由谐波源统计模型预测谐波数据，进行谐波三相潮流计算；Detect nodes with harmonic sources, use the fundamental three-phase power flow results, predict the harmonic data by the harmonic source statistical model, and perform harmonic three-phase power flow calculations;

利用谐波三相网损功率更新基波三相负荷功率；The fundamental three-phase load power is updated by using the harmonic three-phase network loss power;

判断前后节点注入功率误差是否小于预设的迭代误差限，若是则计算收敛，输出谐波三相潮流计算结果，否则返回重新计算基波三相潮流。It is judged whether the injected power error of the front and rear nodes is less than the preset iterative error limit. If so, the calculation converges, and the harmonic three-phase power flow calculation result is output. Otherwise, it returns to recalculate the fundamental three-phase power flow.

在本实施例中，所述设置谐波次数，设置谐波源统计模型初始值以及算法迭代误差限具体为：设置要计算的谐波次数，输入不同的谐波源的统计模型初始值，以及基波、谐波算法的迭代收敛误差值。In this embodiment, the setting of the harmonic order, the setting of the initial value of the statistical model of the harmonic source and the error limit of the algorithm iteration are specifically: setting the harmonic order to be calculated, inputting the initial value of the statistical model of different harmonic sources, and Iterative convergence error values for fundamental and harmonic algorithms.

在本实施例中，建立的基波三相导纳矩阵

Figure BDA0002871496610000081
为：In this embodiment, the established fundamental wave three-phase admittance matrix
Figure BDA0002871496610000081
for:

Figure BDA0002871496610000082
Figure BDA0002871496610000082

式中，

Figure BDA0002871496610000083
为基波三相线路的导纳矩阵，
Figure BDA0002871496610000084
为基波三相变压器的导纳矩阵；In the formula,
Figure BDA0002871496610000083
is the admittance matrix of the fundamental three-phase line,
Figure BDA0002871496610000084
is the admittance matrix of the fundamental three-phase transformer;

其中，基波三相线路的导纳矩阵

Figure BDA0002871496610000085
为：Among them, the admittance matrix of the fundamental wave three-phase line
Figure BDA0002871496610000085
for:

Figure BDA0002871496610000086
Figure BDA0002871496610000086

式中，nL表示线路总数，[CLf]与[CLt]为关联矩阵，

Figure BDA0002871496610000087
Figure BDA0002871496610000091
分别为线路t端和f端的三相电纳矩阵，上标i表示第i条线路；In the formula, nL represents the total number of lines, [C Lf ] and [C Lt ] are the correlation matrix,
Figure BDA0002871496610000087
Figure BDA0002871496610000091
are the three-phase susceptance matrices of the t-end and f-ends of the line, respectively, and the superscript i represents the ith line;

其中，

Figure BDA0002871496610000092
in,
Figure BDA0002871496610000092

Figure BDA0002871496610000093
Figure BDA0002871496610000093

Figure BDA0002871496610000094
Figure BDA0002871496610000094

式中，rL1,xL1分别表示线路正序电阻和电抗；rL2,xL2分别表示线路负序电阻和电抗；rL0,xL0分别表示线路零序电阻和电抗；In the formula, r L1 , x L1 represent the positive sequence resistance and reactance of the line respectively; r L2 , x L2 represent the negative sequence resistance and reactance of the line respectively; r L0 , x L0 represent the zero sequence resistance and reactance of the line respectively;

其中，基波三相变压器的导纳矩阵

Figure BDA0002871496610000095
为(由于变压器的导纳模型和变压器的接线有关，这里只以Ynyn12接线为例说明)：Among them, the admittance matrix of the fundamental three-phase transformer
Figure BDA0002871496610000095
(Because the admittance model of the transformer is related to the wiring of the transformer, here only the wiring of Ynyn12 is used as an example):

Figure BDA0002871496610000096
Figure BDA0002871496610000096

其中，nT为变压器的总台数，[CTf]与[CTt]分别为关联矩阵；Among them, nT is the total number of transformers, [C Tf ] and [C Tt ] are the correlation matrices respectively;

Figure BDA0002871496610000097
Figure BDA0002871496610000097

式中，f表示首端，t表示末端，kf,kt分别表示f端变压器变比和t端变压器变比，上标q表示第q台变压器的零序电阻和电抗；In the formula, f represents the head end, t represents the end, k f , k t represent the transformer transformation ratio of the f terminal and the transformer transformation ratio of the t terminal, respectively, and the superscript q represents the zero-sequence resistance and reactance of the qth transformer;

Figure BDA0002871496610000101
Figure BDA0002871496610000101

其中，

Figure BDA0002871496610000102
in,
Figure BDA0002871496610000102

Figure BDA0002871496610000103
分别为第q台变压器的正序电阻和电抗，
Figure BDA0002871496610000104
分别为第q台变压器的负序电阻和电抗；
Figure BDA0002871496610000105
分别为第q台变压器的零序电阻和电抗。
Figure BDA0002871496610000103
are the positive sequence resistance and reactance of the qth transformer, respectively,
Figure BDA0002871496610000104
are the negative sequence resistance and reactance of the qth transformer, respectively;
Figure BDA0002871496610000105
are the zero-sequence resistance and reactance of the qth transformer, respectively.

其中，in,

Figure BDA0002871496610000106
Figure BDA0002871496610000106

式中，

Figure BDA0002871496610000107
为第i台变压器零序阻抗，
Figure BDA0002871496610000108
为第i台变压器负序阻抗，
Figure BDA0002871496610000109
为第i台变压器正序阻抗，
Figure BDA00028714966100001010
为第i台变压器零序电纳，
Figure BDA00028714966100001011
为第i台变压器负序电纳，
Figure BDA00028714966100001012
为第i台变压器正序电纳；In the formula,
Figure BDA0002871496610000107
is the zero-sequence impedance of the i-th transformer,
Figure BDA0002871496610000108
is the negative sequence impedance of the i-th transformer,
Figure BDA0002871496610000109
is the positive sequence impedance of the i-th transformer,
Figure BDA00028714966100001010
is the zero-sequence susceptance of the i-th transformer,
Figure BDA00028714966100001011
is the negative sequence susceptance of the i-th transformer,
Figure BDA00028714966100001012
is the positive sequence susceptance of the i-th transformer;

关联矩阵为：The correlation matrix is:

Figure BDA00028714966100001013
Figure BDA00028714966100001013

Figure BDA0002871496610000111
Figure BDA0002871496610000111

式中，Lf为线路首端排列，nB为节点数，Lt为线路末端排列，Tf为变压器首端排列，Tt为变压器末端排列；In the formula, Lf is the arrangement of the head end of the line, nB is the number of nodes, Lt is the arrangement of the end of the line, Tf is the arrangement of the head end of the transformer, and Tt is the arrangement of the end of the transformer;

在本实施例中，建立的谐波三相导纳矩阵

Figure BDA0002871496610000112
为：In this embodiment, the established harmonic three-phase admittance matrix
Figure BDA0002871496610000112
for:

Figure BDA0002871496610000113
Figure BDA0002871496610000113

式中，

Figure BDA0002871496610000114
为变压器谐波导纳矩阵，
Figure BDA0002871496610000115
为谐波线路导纳矩阵，
Figure BDA0002871496610000116
为负载谐波导纳矩阵，
Figure BDA0002871496610000117
为发电机谐波导纳矩阵。In the formula,
Figure BDA0002871496610000114
is the transformer harmonic admittance matrix,
Figure BDA0002871496610000115
is the harmonic line admittance matrix,
Figure BDA0002871496610000116
is the load harmonic admittance matrix,
Figure BDA0002871496610000117
is the generator harmonic admittance matrix.

具体的，发电机谐波阻抗(忽略发电机电阻)为：Specifically, the generator harmonic impedance (ignoring generator resistance) is:

Figure BDA0002871496610000118
Figure BDA0002871496610000118

e表示第e台发电机；

Figure BDA0002871496610000119
为第e台发电机的零序电抗，
Figure BDA00028714966100001110
为第e台发电机的负序电抗，
Figure BDA00028714966100001111
为第e台发电机的正序电抗；e represents the e-th generator;
Figure BDA0002871496610000119
is the zero-sequence reactance of the e-th generator,
Figure BDA00028714966100001110
is the negative sequence reactance of the e-th generator,
Figure BDA00028714966100001111
is the positive sequence reactance of the e-th generator;

Figure BDA00028714966100001112
Figure BDA00028714966100001112

Figure BDA00028714966100001113
Figure BDA00028714966100001113

Figure BDA00028714966100001114
Figure BDA00028714966100001114

nB为系统的节点数，当节点存在发电机时，该节点对应的第h次谐波导纳为

Figure BDA0002871496610000121
若不存在发电机，对应谐波导纳则为0；nB is the number of nodes in the system. When there is a generator at the node, the hth harmonic admittance corresponding to this node is
Figure BDA0002871496610000121
If there is no generator, the corresponding harmonic admittance is 0;

Figure BDA0002871496610000122
Figure BDA0002871496610000122

nh为要计算的谐波总次数。nh is the total number of harmonics to be calculated.

其中，负荷谐波阻抗为：Among them, the load harmonic impedance is:

Figure BDA0002871496610000123
Figure BDA0002871496610000123

Figure BDA0002871496610000124
Figure BDA0002871496610000124

p代表第p个负荷；Sa,Sb,Sc分别为节点给定a相、b相、c相的功率，Pa,Pb,Pc为节点给定的a相、b相、c相有功功率，Qa,Qb,Qc为节点给定的a相、b相、c相无功功率，

Figure BDA0002871496610000125
为第p个负荷节点a相电压；p represents the p-th load; S a , S b , and S c are the powers of the a-phase, b-phase, and c-phase given by the node, respectively; P a , P b , and P c are the a-phase, b-phase, c-phase active power, Q a , Q b , Q c are the a-phase, b-phase, c-phase reactive power given by the node,
Figure BDA0002871496610000125
is the phase a voltage of the p-th load node;

Figure BDA0002871496610000126
Figure BDA0002871496610000126

Figure BDA0002871496610000127
Figure BDA0002871496610000127

Figure BDA0002871496610000128
Figure BDA0002871496610000128

当节点存在负荷时，该节点对应的第h次谐波导纳为

Figure BDA0002871496610000129
若不存在负荷，对应谐波导纳则为0；When the node has load, the hth harmonic admittance corresponding to the node is
Figure BDA0002871496610000129
If there is no load, the corresponding harmonic admittance is 0;

Figure BDA00028714966100001210
Figure BDA00028714966100001210

其中，谐波线路为：Among them, the harmonic circuit is:

Figure BDA0002871496610000131
Figure BDA0002871496610000131

Figure BDA0002871496610000132
Figure BDA0002871496610000132

rL1,xL1分别为线路正序电阻和电抗；rL2,xL2分别为线路负序电阻和电抗；rL0,xL0分别为线路零序电阻和电抗，i表示第i条线路r L1 , x L1 are the positive sequence resistance and reactance of the line, respectively; r L2 , x L2 are the negative sequence resistance and reactance of the line, respectively; r L0 , x L0 are the zero-sequence resistance and reactance of the line, and i represents the i-th line

Figure BDA0002871496610000133
Figure BDA0002871496610000133

Figure BDA0002871496610000134
Figure BDA0002871496610000134

Figure BDA0002871496610000135
Figure BDA0002871496610000135

关联矩阵Correlation matrix

Figure BDA0002871496610000136
Figure BDA0002871496610000136

Figure BDA0002871496610000137
Figure BDA0002871496610000137

Figure BDA0002871496610000138
Figure BDA0002871496610000138

Figure BDA0002871496610000139
Figure BDA0002871496610000139

其中，变压器谐波矩阵为：Among them, the transformer harmonic matrix is:

Figure BDA0002871496610000141
Figure BDA0002871496610000141

Figure BDA0002871496610000142
Figure BDA0002871496610000142

Figure BDA0002871496610000143
Figure BDA0002871496610000143

Figure BDA0002871496610000144
Figure BDA0002871496610000144

关联矩阵：Correlation matrix:

Figure BDA0002871496610000145
Figure BDA0002871496610000145

Figure BDA0002871496610000146
Figure BDA0002871496610000146

Figure BDA0002871496610000147
Figure BDA0002871496610000147

Figure BDA0002871496610000148
Figure BDA0002871496610000148

综上，谐波总导纳矩阵为：In summary, the total harmonic admittance matrix is:

Figure BDA0002871496610000149
Figure BDA0002871496610000149

在本实施例中，所述计算基波三相潮流具体为：In this embodiment, the calculation of the fundamental wave three-phase power flow is specifically:

电压电流细胞相量Voltage Current Cell Phasor

Figure BDA0002871496610000151
Figure BDA0002871496610000151

Figure BDA0002871496610000152
Figure BDA0002871496610000152

基本三相潮流方程表示为The basic three-phase power flow equation is expressed as

Figure BDA0002871496610000153
Figure BDA0002871496610000153

Figure BDA0002871496610000154
Figure BDA0002871496610000154

Figure BDA0002871496610000155
Figure BDA0002871496610000155

Figure BDA0002871496610000156
Figure BDA0002871496610000156

Figure BDA0002871496610000157
Figure BDA0002871496610000157

[Iabcx]＝[Gabc][Uabcx]-[Babc][Uabcy][I abcx ]=[G abc ][U abcx ]-[B abc ][U abcy ]

Iabcy＝[Gabc][Uabcy]+[Babc][Uabcx]I abcy =[G abc ][U abcy ]+[B abc ][U abcx ]

Figure BDA0002871496610000158
Figure BDA0002871496610000158

Figure BDA0002871496610000159
Figure BDA0002871496610000159

Figure BDA0002871496610000161
Figure BDA0002871496610000161

Figure BDA0002871496610000162
Figure BDA0002871496610000162

Figure BDA0002871496610000163
Figure BDA0002871496610000163

Figure BDA0002871496610000164
Figure BDA0002871496610000164

[Iax],[Ibx],[Icx]分别为a相、b相、c相电流实部矩阵，[Iay],[Iby],[Icy]分别为a相、b相、c相电流虚部矩阵，[Uax],[Ubx],[Ucx]分别为a相、b相、c相电压实部矩阵，[Uay],[Uby],[Ucy]分别为a相、b相、c相电压虚部矩阵，

Figure BDA0002871496610000165
为节点注入有功功率矩阵，
Figure BDA0002871496610000166
为节点注入无功功率矩阵，[Babc]为电纳矩阵，[Gabc]为电导矩阵，
Figure BDA0002871496610000167
为三相功率矩阵，[Uabcx]为三相电压实部矩阵，[Iabcx]为三相电流实部矩阵，[Uabcy]为三相电压虚部矩阵，[Iabcy]为三相电流虚部矩阵，
Figure BDA0002871496610000168
为三相基波导纳矩阵；[I ax ], [I bx ], [I cx ] are the current real part matrices of the a-phase, b-phase and c-phase respectively, [I ay ], [I by ], [I cy ] are the a-phase, b-phase respectively , c-phase current imaginary part matrix, [U ax ], [U bx ], [U cx ] are a-phase, b-phase, c-phase voltage real part matrix, [U ay ], [U by ], [U cy ] are the voltage imaginary part matrices of phase a, phase b and phase c, respectively,
Figure BDA0002871496610000165
Inject the active power matrix into the node,
Figure BDA0002871496610000166
inject reactive power matrix for the node, [B abc ] is the susceptance matrix, [G abc ] is the conductance matrix,
Figure BDA0002871496610000167
is the three-phase power matrix, [U abcx ] is the three-phase voltage real part matrix, [I abcx ] is the three-phase current real part matrix, [U abcy ] is the three-phase voltage imaginary part matrix, [I abcy ] is the three-phase current matrix imaginary part matrix,
Figure BDA0002871496610000168
is the three-phase fundamental wave admittance matrix;

电网运行中发电机母线一般电压均是受控的，电压受控的母线处无功功率就不可控，因此对于基础方程修订如下。During the operation of the power grid, the voltage of the generator bus is generally controlled, and the reactive power at the bus where the voltage is controlled is not controllable. Therefore, the basic equation is revised as follows.

对基础三相潮流方程修改为：The basic three-phase power flow equation is modified as:

Figure BDA0002871496610000171
Figure BDA0002871496610000171

式中，Uabcx为三相电压实部，Uabcy为三相电压虚部，

Figure BDA0002871496610000172
为PV节点给定电压，ΔPabc为三相有功不平衡量，ΔQabc为三相无功不平衡量；pvbus、pqbus都为向量索引矩阵，由初始输入节点命名顺序决定；令误差修正量为：[Δxabc]＝[J]\[F]；J表示三相雅可比矩阵，F表示三相功率不平衡量矩阵；where U abcx is the real part of the three-phase voltage, U abcy is the imaginary part of the three-phase voltage,
Figure BDA0002871496610000172
Set the voltage for the PV node, ΔP abc is the three-phase active power unbalance, ΔQ abc is the three-phase reactive power unbalance; pvbus and pqbus are vector index matrices, which are determined by the naming sequence of the initial input nodes; let the error correction amount be: [ Δx abc ]=[J]\[F]; J represents the three-phase Jacobian matrix, and F represents the three-phase power unbalance matrix;

修正电压如下：The correction voltage is as follows:

Figure BDA0002871496610000173
Figure BDA0002871496610000173

式中，i1为pqbus的电压实部对应的索引向量，i2为pqbus的电压虚部对应的索引向量，i3为pvbus的电压实部对应的索引向量，i4为pvbus的电压虚部对应的索引向量，由初始输入节点命名顺序决定；Δxabc为三相电压误差修正量；In the formula, i 1 is the index vector corresponding to the voltage real part of pqbus, i 2 is the index vector corresponding to the voltage imaginary part of pqbus, i 3 is the index vector corresponding to the voltage real part of pvbus, and i 4 is the voltage imaginary part of pvbus The corresponding index vector is determined by the naming sequence of the initial input nodes; Δx abc is the three-phase voltage error correction amount;

判断F是否大于预设的基波三相迭代误差值，若是，则循环执行上述计算；若否，则结束三相基波潮流计算，储存三相基波潮流结果。Determine whether F is greater than the preset fundamental wave three-phase iteration error value, if so, execute the above calculation in a loop; if not, end the three-phase fundamental wave power flow calculation and store the three-phase fundamental wave power flow result.

在本实施例中，所述检测存在谐波源的节点，利用基波三相潮流结果，由谐波源统计模型预测谐波数据，进行谐波三相潮流计算具体为：In this embodiment, the detection of nodes with harmonic sources, using the fundamental wave three-phase power flow results, and predicting the harmonic data by the harmonic source statistical model, the calculation of harmonic three-phase power flow is specifically:

利用参数标记检测含有谐波源标记的节点，并判断是否有多个谐波源在同一节点；若有，则考虑谐波源之间的相互影响；若无，则不考虑谐波源之间的相互影响；Use parameter markers to detect nodes containing harmonic source markers, and determine whether there are multiple harmonic sources at the same node; if so, consider the mutual influence between harmonic sources; if not, do not consider the interaction between harmonic sources mutual influence;

各次谐波电流：

Figure BDA0002871496610000181
Each harmonic current:
Figure BDA0002871496610000181

若在同一节点有多个谐波源时考虑它们的相互影响，由国标得到考虑谐波源之间相互影响的公式为：If there are multiple harmonic sources at the same node to consider their mutual influence, the formula for considering the mutual influence between harmonic sources obtained from the national standard is:

Figure BDA0002871496610000182
Figure BDA0002871496610000182

式中，harmonich为第h次谐波电流含有率，Iabcx、Iabcy由基波潮流得到，

Figure BDA0002871496610000183
分别为谐波源1与谐波源2的谐波三相电流；Kh为给定系数；where harmonic h is the h-th harmonic current content, I abcx and I abcy are obtained from the fundamental power flow,
Figure BDA0002871496610000183
are the harmonic three-phase currents of harmonic source 1 and harmonic source 2 respectively; K h is a given coefficient;

由

Figure BDA0002871496610000184
得到各节点各次谐波三相电压，由谐波三相电压得到谐波三相损耗,利用谐波源节点的谐波损耗更新此节点的三相功率；其中，
Figure BDA0002871496610000185
为三相谐波电压矩阵，
Figure BDA0002871496610000186
为三相谐波导纳矩阵，
Figure BDA0002871496610000187
为三相谐波功率矩阵。Depend on
Figure BDA0002871496610000184
Obtain the harmonic three-phase voltage of each node, obtain the harmonic three-phase loss from the harmonic three-phase voltage, and use the harmonic loss of the harmonic source node to update the three-phase power of this node; among them,
Figure BDA0002871496610000185
is the three-phase harmonic voltage matrix,
Figure BDA0002871496610000186
is the three-phase harmonic admittance matrix,
Figure BDA0002871496610000187
is the three-phase harmonic power matrix.

在本实施例中，所述判断前后节点注入功率误差是否小于预设的迭代误差限，若是则计算收敛，输出谐波三相潮流计算结果，否则返回重新计算基波三相潮流具体为：In this embodiment, whether the injected power error of the node before and after the judgment is less than the preset iterative error limit, if so, the calculation converges, and the harmonic three-phase power flow calculation result is output, otherwise the return to recalculate the fundamental wave three-phase power flow is specifically:

Figure BDA0002871496610000188
Figure BDA0002871496610000188

式中，

Figure BDA0002871496610000189
为第k次循环得到的三相功率值矩阵，
Figure BDA00028714966100001810
为第k-1次循环得到的三相功率值矩阵；判断[ΔSabc(k)]是否小于预设的谐波迭代误差值，若否，则返回重新计算基波三相潮流，若是，结束并输出谐波三相潮流计算结果。In the formula,
Figure BDA0002871496610000189
is the three-phase power value matrix obtained in the kth cycle,
Figure BDA00028714966100001810
is the three-phase power value matrix obtained in the k-1th cycle; judge whether [ΔS abc (k)] is less than the preset harmonic iteration error value, if not, return to recalculate the fundamental three-phase power flow, if so, end And output the harmonic three-phase power flow calculation results.

本实施例还提供了一种电网三相谐波潮流相量矩阵计算系统，包括存储器、处理器以及存储于存储器上并能够在处理器上运行的计算机程序指令，当处理器运行该计算机程序指令时，能够实现如上文所述的方法步骤。This embodiment also provides a power grid three-phase harmonic power flow phasor matrix calculation system, including a memory, a processor, and computer program instructions stored in the memory and capable of running on the processor. When the processor runs the computer program instructions , the method steps as described above can be implemented.

以上所述，仅是本发明的较佳实施例而已，并非是对本发明作其它形式的限制，任何熟悉本专业的技术人员可能利用上述揭示的技术内容加以变更或改型为等同变化的等效实施例。但是凡是未脱离本发明技术方案内容,依据本发明的技术实质对以上实施例所作的任何简单修改、等同变化与改型，仍属于本发明技术方案的保护范围。The above are only preferred embodiments of the present invention, and are not intended to limit the present invention in other forms. Any person skilled in the art may use the technical content disclosed above to make changes or modifications to equivalent changes. Example. However, any simple modifications, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solutions of the present invention still belong to the protection scope of the technical solutions of the present invention.

Claims (8)

1.一种电网三相谐波潮流相量矩阵计算方法，其特征在于，包括以下步骤：1. a power grid three-phase harmonic power flow phasor matrix calculation method, is characterized in that, comprises the following steps: 设置谐波次数，设置谐波源统计模型初始值以及算法迭代误差限；Set the harmonic order, set the initial value of the harmonic source statistical model and the algorithm iteration error limit; 采集包括变压器参数、线路参数、节点电压、发电机参数、负荷参数在内的参数，建立基波和谐波三相导纳矩阵；Collect parameters including transformer parameters, line parameters, node voltage, generator parameters, load parameters, and establish fundamental wave and harmonic three-phase admittance matrices; 计算基波三相潮流；Calculate the fundamental three-phase power flow; 检测存在谐波源的节点，利用基波三相潮流结果，由谐波源统计模型预测谐波数据，进行谐波三相潮流计算；Detect nodes with harmonic sources, use the fundamental three-phase power flow results, predict the harmonic data by the harmonic source statistical model, and perform harmonic three-phase power flow calculations; 利用谐波三相网损功率更新基波三相负荷功率；The fundamental three-phase load power is updated by using the harmonic three-phase network loss power; 判断前后节点注入功率误差是否小于预设的迭代误差限，若是则计算收敛，输出谐波三相潮流计算结果，否则返回重新计算基波三相潮流。It is judged whether the injected power error of the front and rear nodes is less than the preset iterative error limit. If so, the calculation converges, and the harmonic three-phase power flow calculation result is output. Otherwise, it returns to recalculate the fundamental three-phase power flow. 2.根据权利要求1所述的一种电网三相谐波潮流相量矩阵计算方法，其特征在于，所述设置谐波次数，设置谐波源统计模型初始值以及算法迭代误差限具体为：设置要计算的谐波次数，输入不同的谐波源的统计模型初始值，以及基波、谐波算法的迭代收敛误差值。2. a kind of power grid three-phase harmonic power flow phasor matrix calculation method according to claim 1, is characterized in that, described setting harmonic order, setting harmonic source statistical model initial value and algorithm iteration error limit are specifically: Set the harmonic order to be calculated, input the initial value of the statistical model for different harmonic sources, and the iterative convergence error value of the fundamental and harmonic algorithms. 3.根据权利要求1所述的一种电网三相谐波潮流相量矩阵计算方法，其特征在于，建立的基波三相导纳矩阵
Figure FDA0002871496600000011
为：3. A kind of grid three-phase harmonic power flow phasor matrix calculation method according to claim 1, is characterized in that, the established fundamental wave three-phase admittance matrix
Figure FDA0002871496600000011
for:
Figure FDA0002871496600000012
Figure FDA0002871496600000012
 式中，
Figure FDA0002871496600000013
为基波三相线路的导纳矩阵，
Figure FDA0002871496600000014
为基波三相变压器的导纳矩阵；In the formula,
Figure FDA0002871496600000013
is the admittance matrix of the fundamental three-phase line,
Figure FDA0002871496600000014
is the admittance matrix of the fundamental three-phase transformer; 其中，基波三相线路的导纳矩阵
Figure FDA0002871496600000015
为：Among them, the admittance matrix of the fundamental wave three-phase line
Figure FDA0002871496600000015
for:
Figure FDA0002871496600000021
Figure FDA0002871496600000021
 式中，nL表示线路总数，[CLf]与[CLt]为关联矩阵，
Figure FDA0002871496600000022
Figure FDA0002871496600000023
与
Figure FDA0002871496600000024
分别为线路t端和f端的三相电纳矩阵，上标i表示第i条线路；In the formula, nL represents the total number of lines, [C Lf ] and [C Lt ] are the correlation matrix,
Figure FDA0002871496600000022
Figure FDA0002871496600000023
and
Figure FDA0002871496600000024
are the three-phase susceptance matrices of the t-end and f-ends of the line, respectively, and the superscript i represents the ith line; 其中，
Figure FDA0002871496600000025
in,
Figure FDA0002871496600000025
Figure FDA0002871496600000026
Figure FDA0002871496600000026
Figure FDA0002871496600000027
Figure FDA0002871496600000027
 式中，rL1,xL1分别表示线路正序电阻和电抗；rL2,xL2分别表示线路负序电阻和电抗；rL0,xL0分别表示线路零序电阻和电抗；In the formula, r L1 , x L1 represent the positive sequence resistance and reactance of the line respectively; r L2 , x L2 represent the negative sequence resistance and reactance of the line respectively; r L0 , x L0 represent the zero sequence resistance and reactance of the line respectively; 其中，基波三相变压器的导纳矩阵
Figure FDA0002871496600000028
为：Among them, the admittance matrix of the fundamental three-phase transformer
Figure FDA0002871496600000028
for:
Figure FDA0002871496600000029
Figure FDA0002871496600000029
 其中，nT为变压器的总台数，[CTf]与[CTt]分别为关联矩阵；Among them, nT is the total number of transformers, [C Tf ] and [C Tt ] are the correlation matrices respectively;
Figure FDA0002871496600000031
Figure FDA0002871496600000031
 式中，f表示首端，t表示末端，kf,kt分别表示f端变压器变比和t端变压器变比，上标q表示第q台变压器的零序电阻和电抗；In the formula, f represents the head end, t represents the end, k f , k t respectively represent the transformer transformation ratio of the f terminal and the transformer transformation ratio of the t terminal, and the superscript q represents the zero-sequence resistance and reactance of the qth transformer;
Figure FDA0002871496600000032
Figure FDA0002871496600000032
 其中，
Figure FDA0002871496600000033
in,
Figure FDA0002871496600000033
Figure FDA0002871496600000034
分别为第q台变压器的正序电阻和电抗，
Figure FDA0002871496600000035
分别为第q台变压器的负序电阻和电抗；
Figure FDA0002871496600000036
分别为第q台变压器的零序电阻和电抗。
Figure FDA0002871496600000034
are the positive sequence resistance and reactance of the qth transformer, respectively,
Figure FDA0002871496600000035
are the negative sequence resistance and reactance of the qth transformer, respectively;
Figure FDA0002871496600000036
are the zero-sequence resistance and reactance of the qth transformer, respectively. 4.根据权利要求1所述的一种电网三相谐波潮流相量矩阵计算方法，其特征在于，建立的谐波三相导纳矩阵
Figure FDA0002871496600000037
为：4. a kind of grid three-phase harmonic power flow phasor matrix calculation method according to claim 1 is characterized in that, the established harmonic three-phase admittance matrix
Figure FDA0002871496600000037
for:
Figure FDA0002871496600000038
Figure FDA0002871496600000038
 式中，
Figure FDA0002871496600000039
为变压器谐波导纳矩阵，
Figure FDA00028714966000000310
为谐波线路导纳矩阵，
Figure FDA00028714966000000311
为负载谐波导纳矩阵，
Figure FDA00028714966000000312
为发电机谐波导纳矩阵。In the formula,
Figure FDA0002871496600000039
is the transformer harmonic admittance matrix,
Figure FDA00028714966000000310
is the harmonic line admittance matrix,
Figure FDA00028714966000000311
is the load harmonic admittance matrix,
Figure FDA00028714966000000312
is the generator harmonic admittance matrix. 5.根据权利要求1所述的一种电网三相谐波潮流相量矩阵计算方法，其特征在于，所述计算基波三相潮流具体为：对基础三相潮流方程修改为：5. a kind of power grid three-phase harmonic power flow phasor matrix calculation method according to claim 1, is characterized in that, described calculating fundamental wave three-phase power flow is specifically: amend basic three-phase power flow equation to be:
Figure FDA0002871496600000041
Figure FDA0002871496600000041
 式中，Uabcx为三相电压实部，Uabcy为三相电压虚部，
Figure FDA0002871496600000042
为PV节点设定的电压，ΔPabc为abc三相有功不平衡量，ΔQabc为abc三相无功不平衡量；pvbus、pqbus都为向量索引矩阵，由初始输入节点命名顺序决定；令误差修正量为：[Δxabc]＝[J]\[F]；J表示雅可比矩阵，F表示功率不平衡量矩阵；where U abcx is the real part of the three-phase voltage, U abcy is the imaginary part of the three-phase voltage,
Figure FDA0002871496600000042
The voltage set for the PV node, ΔP abc is the abc three-phase active power unbalance, ΔQ abc is the abc three-phase reactive power unbalance; pvbus and pqbus are vector index matrices, which are determined by the naming sequence of the initial input nodes; let the error correction amount is: [Δx abc ]=[J]\[F]; J represents the Jacobian matrix, and F represents the power imbalance matrix; 修正电压如下：The correction voltage is as follows:
Figure FDA0002871496600000043
Figure FDA0002871496600000043
 式中，i1为pqbus的电压实部对应的索引向量，i2为pqbus的电压虚部对应的索引向量，i3为pvbus的电压实部对应的索引向量，i4为pvbus的电压虚部对应的索引向量，由初始输入节点命名顺序决定；Δxabc为电压误差修正量矩阵；In the formula, i 1 is the index vector corresponding to the voltage real part of pqbus, i 2 is the index vector corresponding to the voltage imaginary part of pqbus, i 3 is the index vector corresponding to the voltage real part of pvbus, and i 4 is the voltage imaginary part of pvbus The corresponding index vector is determined by the naming order of the initial input nodes; Δx abc is the voltage error correction matrix; 判断F是否大于预设的基波三相迭代误差值，若是，则循环执行上述计算；若否，则结束三相基波潮流计算，储存三相基波潮流结果。Determine whether F is greater than the preset fundamental wave three-phase iteration error value, if so, execute the above calculation in a loop; if not, end the three-phase fundamental wave power flow calculation and store the three-phase fundamental wave power flow result. 6.根据权利要求1所述的一种电网三相谐波潮流相量矩阵计算方法，其特征在于，所述检测存在谐波源的节点，利用基波三相潮流结果，由谐波源统计模型预测谐波数据，进行谐波三相潮流计算具体为：6 . The method for calculating a three-phase harmonic power flow phasor matrix of a power grid according to claim 1 , wherein the detection of a node with a harmonic source is performed by using the fundamental wave three-phase power flow result, and statistics from the harmonic source are used. 7 . The model predicts the harmonic data and performs the harmonic three-phase power flow calculation as follows: 利用参数标记检测含有谐波源标记的节点，并判断是否有多个谐波源在同一节点；若有，则考虑谐波源之间的相互影响；若无，则不考虑谐波源之间的相互影响；Use parameter markers to detect nodes containing harmonic source markers, and determine whether there are multiple harmonic sources at the same node; if so, consider the mutual influence between harmonic sources; if not, do not consider the interaction between harmonic sources mutual influence; 各次谐波电流：
Figure FDA0002871496600000051
Each harmonic current:
Figure FDA0002871496600000051
 若在同一节点有多个谐波源时考虑它们的相互影响，由国标得到考虑谐波源之间相互影响的公式为：If there are multiple harmonic sources at the same node to consider their mutual influence, the formula for considering the mutual influence between harmonic sources obtained from the national standard is:
Figure FDA0002871496600000052
Figure FDA0002871496600000052
 式中，harmonich为第h次谐波电流含有率，Iabcx、Iabcy由基波潮流得到的电流实部和虚部，
Figure FDA0002871496600000053
分别为谐波源1与谐波源2的谐波三相电流；Kh为给定系数；where harmonic h is the h-th harmonic current content, I abcx and I abcy are the current real and imaginary parts obtained from the fundamental power flow,
Figure FDA0002871496600000053
are the harmonic three-phase currents of harmonic source 1 and harmonic source 2 respectively; K h is a given coefficient; 由
Figure FDA0002871496600000054
得到各节点各次谐波三相电压，由谐波三相电压得到谐波三相损耗,利用谐波源节点的谐波损耗更新此节点的三相功率；其中，
Figure FDA0002871496600000055
为三相谐波电压，
Figure FDA0002871496600000056
为网络谐波导纳矩阵，
Figure FDA0002871496600000057
为三相谐波功率。Depend on
Figure FDA0002871496600000054
Obtain the harmonic three-phase voltage of each node, obtain the harmonic three-phase loss from the harmonic three-phase voltage, and use the harmonic loss of the harmonic source node to update the three-phase power of this node; among them,
Figure FDA0002871496600000055
is the three-phase harmonic voltage,
Figure FDA0002871496600000056
is the network harmonic admittance matrix,
Figure FDA0002871496600000057
is the three-phase harmonic power. 7.根据权利要求1所述的一种电网三相谐波潮流相量矩阵计算方法，其特征在于，所述判断前后节点注入功率误差是否小于预设的迭代误差限，若是则计算收敛，输出谐波三相潮流计算结果，否则返回重新计算基波三相潮流具体为：7 . The method for calculating a three-phase harmonic power flow phasor matrix of a power grid according to claim 1 , wherein whether the injected power error of the node before and after the judgment is less than a preset iterative error limit, and if so, the calculation is converged and the output Harmonic three-phase power flow calculation result, otherwise return to recalculate fundamental three-phase power flow. Specifically:
Figure FDA0002871496600000061
Figure FDA0002871496600000061
 式中，
Figure FDA0002871496600000062
为第k次循环得到的三相功率值矩阵，
Figure FDA0002871496600000063
为第k-1次循环得到的三相功率值矩阵；判断[ΔSabc(k)]是否小于预设的谐波迭代误差值，若否，则返回重新计算基波三相潮流，若是，结束并输出谐波三相潮流计算结果。In the formula,
Figure FDA0002871496600000062
is the three-phase power value matrix obtained in the kth cycle,
Figure FDA0002871496600000063
is the three-phase power value matrix obtained from the k-1th cycle; judge whether [ΔS abc (k)] is less than the preset harmonic iteration error value, if not, return to recalculate the fundamental three-phase power flow, if so, end And output the harmonic three-phase power flow calculation results. 8.一种电网三相谐波潮流相量矩阵计算系统，其特征在于，包括存储器、处理器以及存储于存储器上并能够在处理器上运行的计算机程序指令，当处理器运行该计算机程序指令时，能够实现如权利要求1-7任一项所述的方法步骤。8. A power grid three-phase harmonic power flow phasor matrix computing system, characterized in that, comprising a memory, a processor and a computer program instruction stored on the memory and able to run on the processor, when the processor runs the computer program instruction , the method steps of any one of claims 1-7 can be implemented.
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