CN110688778B - Prediction method of DC bias current on AC side under asymmetric impedance of MMC bridge arm - Google Patents

Prediction method of DC bias current on AC side under asymmetric impedance of MMC bridge arm Download PDF

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CN110688778B
CN110688778B CN201910984837.7A CN201910984837A CN110688778B CN 110688778 B CN110688778 B CN 110688778B CN 201910984837 A CN201910984837 A CN 201910984837A CN 110688778 B CN110688778 B CN 110688778B
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郑文迪
吴昕翀
邵振国
齐佩雯
周腾龙
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Fuzhou University
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Abstract

本发明涉及一种MMC桥臂阻抗不对称下的交流侧直流偏置电流预测方法,首先确定待预测系统的主回路参数;然后分析MMC稳态下偏置电流特性,得到MMC稳态下交流侧偏置电流的特性表达式;最后分析桥臂参数不对称下的偏置电流特性,得到桥臂参数不对称情况下的交流侧直流偏置电流。本发明能够有效预测交流侧的直流电流。

Figure 201910984837

The invention relates to a method for predicting the DC bias current of the AC side under the asymmetric impedance of the MMC bridge arm. First, the main loop parameters of the system to be predicted are determined; then the bias current characteristics under the MMC steady state are analyzed to obtain the AC side under the MMC steady state. The characteristic expression of the bias current; finally, the bias current characteristic under the asymmetric bridge arm parameters is analyzed, and the AC side DC bias current is obtained under the condition of the bridge arm parameter asymmetry. The present invention can effectively predict the DC current on the AC side.

Figure 201910984837

Description

MMC桥臂阻抗不对称下的交流侧直流偏置电流预测方法Prediction method of DC bias current on AC side under asymmetric impedance of MMC bridge arm

技术领域technical field

本发明涉及直流输电技术领域,特别是一种MMC桥臂阻抗不对称下的交流侧直流偏置电流预测方法。The invention relates to the technical field of DC power transmission, in particular to a method for predicting a DC bias current on an AC side under the condition of asymmetric impedance of an MMC bridge arm.

背景技术Background technique

直流输电技术被广泛应用及带来巨大经济效益的同时,也产生了一定技术和管理上的新问题,给交直流系统的运行带来新的挑战。其中,直流偏磁便是当前电力系统发展面临的新问题。所谓直流偏磁,是指某种原因出现的直流分量导致铁磁材料直流磁化直至饱和。因此,在电力系统中,诸如电力变压器、电流互感器等基于电磁感应原理设计,由铁芯构成主要磁通的电力设备都会受到直流偏磁问题的影响。While DC transmission technology is widely used and brings huge economic benefits, it also produces certain new problems in technology and management, which brings new challenges to the operation of AC and DC systems. Among them, DC bias is a new problem faced by the current power system development. The so-called DC bias refers to the DC component that occurs for some reason that causes the DC magnetization of the ferromagnetic material until saturation. Therefore, in the power system, such as power transformers, current transformers, etc., which are designed based on the principle of electromagnetic induction, and the power equipment whose main magnetic flux is composed of iron cores will be affected by the problem of DC bias.

实际投入运行的VSC-HVDC项目采用的拓扑结构主要有两电平、三电平及模块化多电平拓扑结构。其中,模块化多电平换流器(Modular Multilevel Converter, MMC)可以较好解决两电平和三电平换流器存在的固有缺陷,而且具有损耗低,输出电压谐波小等优点,备受业界的关注。不过,现有的偏磁模型针对的是传统输电工程中,单极大地回线运行以及太阳黑子运动产生磁暴这两种偏磁来源。而实际工程中,由于制造工艺、制造材料、运行工况等众多因素,MMC上、下桥臂参数会存在不完全对称的问题,也会引发交流侧电流的直流偏置,导致变压器的直流偏磁。随着系统运行年限的增加,桥臂参数的变化程度增大,因此这种情况下的偏磁问题是长期存在且会随着时间愈发严重,然而现有技术中却没有针对MMC-HVDC系统桥臂参数不对称下的情况提出有效的直流偏置电流预测方法。The topological structures used in the actual VSC-HVDC projects that are put into operation mainly include two-level, three-level and modular multi-level topologies. Among them, the Modular Multilevel Converter (MMC) can better solve the inherent defects of the two-level and three-level converters, and has the advantages of low loss and small output voltage harmonics, which is widely used. industry attention. However, the existing bias magnetism model is aimed at the two sources of bias magnetism in traditional power transmission projects, the operation of the monopole loop and the magnetic storm generated by the motion of sunspots. In actual engineering, due to many factors such as manufacturing process, manufacturing materials, operating conditions, etc., the parameters of the upper and lower arms of the MMC will not be completely symmetrical, and will also cause the DC bias of the AC side current, resulting in the DC bias of the transformer. magnetic. With the increase of the operating years of the system, the change degree of the bridge arm parameters increases, so the magnetic bias problem in this case exists for a long time and will become more serious with time. However, there is no MMC-HVDC system in the prior art. An effective DC bias current prediction method is proposed in the case of asymmetric bridge arm parameters.

发明内容SUMMARY OF THE INVENTION

有鉴于此,本发明的目的是提出一种MMC桥臂阻抗不对称下的交流侧直流偏置电流预测方法,能够有效预测交流侧的直流电流。In view of this, the purpose of the present invention is to propose a method for predicting the DC bias current of the AC side under the asymmetric impedance of the MMC bridge arm, which can effectively predict the DC current of the AC side.

本发明采用以下方案实现:一种MMC桥臂阻抗不对称下的交流侧直流偏置电流预测方法,包括以下步骤:The present invention adopts the following scheme to realize: a method for predicting the DC bias current of the AC side under the asymmetric impedance of the MMC bridge arm, comprising the following steps:

确定待预测系统的主回路参数;Determine the main loop parameters of the system to be predicted;

根据待预测系统的主回路参数,采用式(1)计算桥臂参数不对称情况下的交流侧直流偏置电流:According to the main loop parameters of the system to be predicted, formula (1) is used to calculate the AC side DC bias current when the bridge arm parameters are asymmetric:

Figure BDA0002236362610000021
Figure BDA0002236362610000021

式中,Ivj_0表示桥臂参数不对称情况下的j相的交流侧直流偏置电流;Udc表示直流侧电压,Rpj表示第j相上桥臂的等效电阻,Rnj表示第j相下桥臂的等效电阻;其中,In the formula, I vj_0 represents the DC bias current of the j-phase AC side when the bridge arm parameters are asymmetric; U dc represents the DC side voltage, R pj represents the equivalent resistance of the upper bridge arm of the j-th phase, and R nj represents the j-th phase. Equivalent resistance of the lower arm of the phase; where,

Figure BDA0002236362610000022
Figure BDA0002236362610000022

Figure BDA0002236362610000023
Figure BDA0002236362610000023

式中,N表示每个桥臂上的子模块数量,Lpj表示第j相上桥臂的桥臂电感,ω表示电网角频率,C表示子模块中的电容,Lnj表示第j相下桥臂的桥臂电感。In the formula, N represents the number of sub-modules on each bridge arm, L pj represents the bridge arm inductance of the upper bridge arm of the j-th phase, ω represents the grid angular frequency, C represents the capacitance in the sub-modules, and L nj represents the lower-phase j-th phase. The leg inductance of the bridge leg.

进一步地,采用以下步骤得到式(1):Further, adopt the following steps to obtain formula (1):

步骤S1:分析MMC稳态下偏置电流特性,得到MMC稳态下交流侧偏置电流的特性表达式;Step S1: analyze the bias current characteristics under the MMC steady state, and obtain the characteristic expression of the AC side bias current under the MMC steady state;

步骤S2:分析桥臂参数不对称下的偏置电流特性,并根据步骤S1得到的MMC 稳态下交流侧偏置电流的特性表达式,得到桥臂参数不对称情况下的交流侧直流偏置电流。Step S2: analyze the bias current characteristics under the condition of asymmetric bridge arm parameters, and obtain the AC side DC bias under the condition of asymmetric bridge arm parameters according to the characteristic expression of the AC side bias current under the MMC steady state obtained in step S1 current.

进一步地,步骤S1具体包括以下步骤:Further, step S1 specifically includes the following steps:

步骤S11:根据基尔霍夫电流定律得到,第j相桥臂的电流ivj满足下式:Step S11: Obtained according to Kirchhoff's current law, the current i vj of the j-th phase bridge arm satisfies the following formula:

ivj=ipj-inji vj = i pj - i nj ;

式中,ipj表示第j相上桥臂电流,inj表示第j相下桥臂电流;In the formula, i pj represents the current of the upper bridge arm of the jth phase, and inj represents the current of the lower bridge arm of the jth phase;

定义桥臂共模电流为icirj,即表示第j相环流:The common mode current of the bridge arm is defined as i cirj , which means the j-th phase circulating current:

Figure BDA0002236362610000031
Figure BDA0002236362610000031

步骤S12:设桥臂电流表示为以下多种频率成分叠加的形式:Step S12: Let the bridge arm current be expressed in the form of superposition of the following multiple frequency components:

Figure BDA0002236362610000032
Figure BDA0002236362610000032

式中,Ipj_0表示第j相上桥臂电流的直流分量,Inj_0表示第j相下桥臂电流的直流分量,Ipj_h

Figure BDA0002236362610000033
分别表示第j相桥臂电流h次谐波的幅值和初相角;In the formula, I pj_0 represents the DC component of the upper arm current of the jth phase, I nj_0 represents the DC component of the lower arm current of the jth phase, and I pj_h and
Figure BDA0002236362610000033
respectively represent the amplitude and initial phase angle of the h-th harmonic of the jth-phase bridge arm current;

取平均开关函数:Take the average switching function:

Figure BDA0002236362610000034
Figure BDA0002236362610000034

式中,Spj、Snj分别表示第j相上、下桥臂的开关函数,m为电压调制比,θj为交流系统第j相等效电动势初相角;In the formula, Spj and Snj represent the switching functions of the upper and lower arms of the jth phase, respectively, m is the voltage modulation ratio, and θ j is the initial phase angle of the equivalent electromotive force of the jth phase of the AC system;

令电容电流的集合平均值为桥臂电流与平均开关函数的乘积:Let the collective mean value of the capacitor current be the product of the bridge arm current and the mean switching function:

Figure BDA0002236362610000041
Figure BDA0002236362610000041

式中,ic,pj表示第j相上桥臂子模块电容电流集合平均值,ic,nj表示第j相下桥臂子模块电容电流集合平均值;In the formula , ic,pj represents the average value of the capacitor current set of the j-th upper bridge arm sub-module , and ic,nj represents the j-th phase lower bridge arm sub-module capacitor current set average value;

步骤S13:为了满足稳态运行,令电容电流的直流分量为0,即:Step S13: In order to satisfy the steady-state operation, let the DC component of the capacitor current be 0, that is:

Figure BDA0002236362610000042
Figure BDA0002236362610000042

式中,Ipj_1表示第j相上桥臂电流基频谐波的幅值,Inj_1表示第j相下桥臂电流基频谐波的幅值,

Figure BDA0002236362610000043
表示第j相桥臂电流基频谐波的初相角;In the formula, I pj_1 represents the amplitude of the fundamental frequency harmonic of the upper arm current of the jth phase, I nj_1 represents the amplitude of the fundamental frequency harmonic of the lower arm current of the jth phase,
Figure BDA0002236362610000043
Represents the initial phase angle of the fundamental frequency harmonic of the jth-phase bridge arm current;

步骤S13:采用下式计算MMC稳态下交流侧偏置电流的特性表达式:Step S13: Use the following formula to calculate the characteristic expression of the AC side bias current in the MMC steady state:

Figure BDA0002236362610000044
Figure BDA0002236362610000044

式中,Icirj_1表示第j相桥臂共模电流的基频分量。In the formula, I cirj_1 represents the fundamental frequency component of the common mode current of the j-th phase bridge arm.

进一步地,步骤S2具体包括以下步骤:Further, step S2 specifically includes the following steps:

步骤S21:仅考虑桥臂电流中的直流量与基频分量,将桥臂电压的基频增量表示为:Step S21: Considering only the DC quantity and the fundamental frequency component in the bridge arm current, the fundamental frequency increment of the bridge arm voltage is expressed as:

Figure BDA0002236362610000051
Figure BDA0002236362610000051

式中,

Figure BDA0002236362610000052
表示第j相上桥臂的电压增量的基频分量,
Figure BDA0002236362610000053
表示第j相下桥臂的电压增量的基频分量,Ipj_0表示第j相上桥臂电流的直流分量,Inj_0表示第j相下桥臂电流的直流分量;In the formula,
Figure BDA0002236362610000052
represents the fundamental frequency component of the voltage increment of the upper arm of the j-th phase,
Figure BDA0002236362610000053
Represents the fundamental frequency component of the voltage increment of the jth phase lower arm, I pj_0 represents the DC component of the jth phase upper bridge arm current, and I nj_0 represents the jth phase lower arm current DC component;

步骤S22:设j相交流输出电压基频量为:Step S22: Set the fundamental frequency of the j-phase AC output voltage as:

Figure BDA0002236362610000054
Figure BDA0002236362610000054

式中,

Figure BDA0002236362610000055
表示第j相交流输出电压的基频分量;U表示第j相交流输出电压的基频电压的幅值;In the formula,
Figure BDA0002236362610000055
Represents the fundamental frequency component of the jth phase AC output voltage; U represents the amplitude of the fundamental frequency voltage of the jth phase AC output voltage;

对上、下桥臂阻抗进行区分,桥臂电压的基频波动满足:Distinguish the impedance of the upper and lower bridge arms, and the fundamental frequency fluctuation of the bridge arm voltage satisfies:

Figure BDA0002236362610000056
Figure BDA0002236362610000056

式中,

Figure BDA0002236362610000057
表示第j相上桥臂的电压基频分量,
Figure BDA0002236362610000058
表示第j相下桥臂的电压基频分量In the formula,
Figure BDA0002236362610000057
represents the voltage fundamental frequency component of the upper arm of the j-th phase,
Figure BDA0002236362610000058
Represents the voltage fundamental frequency component of the lower arm of the jth phase

步骤S23:综合考虑步骤S21-步骤S22,对于上桥臂有:Step S23: Considering step S21-step S22 comprehensively, for the upper bridge arm:

Figure BDA0002236362610000059
Figure BDA0002236362610000059

式中,Ipj_1表示第j相上桥臂电流的基频分量;In the formula, I pj_1 represents the fundamental frequency component of the upper arm current of the j-th phase;

则上桥臂电流基频量的计算采用下式:Then the calculation of the fundamental frequency of the upper arm current adopts the following formula:

Figure BDA0002236362610000061
Figure BDA0002236362610000061

其中,in,

Figure BDA0002236362610000062
Figure BDA0002236362610000062

则,不对称情况下的上桥臂电流的直流分量为:Then, the DC component of the upper arm current in the case of asymmetry is:

Figure BDA0002236362610000063
Figure BDA0002236362610000063

同理,不对称情况下的下桥臂直流分量为:In the same way, the DC component of the lower bridge arm in the case of asymmetry is:

Figure BDA0002236362610000064
Figure BDA0002236362610000064

其中,in,

Figure BDA0002236362610000065
Figure BDA0002236362610000065

步骤S23:得到桥臂参数不对称情况下的交流侧直流偏置电流表达式为:Step S23: Obtain the expression of the DC bias current of the AC side under the condition of asymmetric parameters of the bridge arm:

Figure BDA0002236362610000066
Figure BDA0002236362610000066

与现有技术相比,本发明有以下有益效果:Compared with the prior art, the present invention has the following beneficial effects:

1、本发明基于子模块电容电流特性得到MMC-HVDC稳态下交流侧直流偏置电流特性,实现环流基频量和交流直流量的相互转换,能够适用于任何基频环流存在引起交流侧出现直流电流的场景。1. The present invention obtains the DC bias current characteristics of the AC side under the steady state of the MMC-HVDC based on the capacitor current characteristics of the sub-modules, realizes the mutual conversion between the circulating current fundamental frequency and the alternating current and direct current, and can be applied to any fundamental frequency circulating current causes the AC side to appear. DC current scene.

2、本发明考虑模块化多电平换流器桥臂参数不对称的情况,提出以系统参数表示的交流侧直流偏置电流等效方法,无需额外监测设备,从而实现该场景下研究变压器直流偏磁问题时对系统阀侧的简化。对于待建直流输电工程,可以在确定系统参数时,利用本发明的方法从降低直流偏磁发生影响的角度辅助参数的确定;对于已投入运行的直流输电工程,可以借助本发明的方法,对桥臂参数不对称下的变压器直流偏磁影响进行评估,判断进行偏磁抑制的必要性。2. The present invention considers the asymmetry of the bridge arm parameters of the modular multi-level converter, and proposes an equivalent method of the AC side DC bias current represented by the system parameters without additional monitoring equipment, so as to realize the research on the DC voltage of the transformer in this scenario. A simplification of the valve side of the system when the bias is a problem. For the DC transmission project to be built, the method of the present invention can be used to assist the determination of parameters from the perspective of reducing the influence of DC bias when determining the system parameters; for the DC transmission project that has been put into operation, the method of the present invention can be used to The influence of the transformer DC bias under the asymmetric bridge arm parameters is evaluated, and the necessity of bias suppression is judged.

附图说明Description of drawings

图1为本发明实施例的方法流程示意图。FIG. 1 is a schematic flowchart of a method according to an embodiment of the present invention.

图2为三相MMC典型拓扑。Figure 2 shows a typical topology of a three-phase MMC.

图3为本发明实施例的MMC子模块数与偏置电流的关系示意图。FIG. 3 is a schematic diagram of the relationship between the number of MMC sub-modules and the bias current according to an embodiment of the present invention.

具体实施方式Detailed ways

下面结合附图及实施例对本发明做进一步说明。The present invention will be further described below with reference to the accompanying drawings and 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.

如图1所示,本实施例提供了一种MMC桥臂阻抗不对称下的交流侧直流偏置电流预测方法,其中典型的三相MMC典型拓扑如图2所示。图中,子模块采用半桥结构,每个桥臂由N个相同的子模块(SM)、桥臂电感L0以及等效电阻R0串联而成。各电气量正方向按图示进行定义。O点、O’分别表示直流侧、交流侧零电位参考点,v表示MMC交流出口处。交流系统用理想电压源usj进行等效 (j=a、b、c,表示交流三相)。交流系统经过联结电抗器Lac接至MMC交流出口处。 uvj表示j相交流出口处电压,ivj表示j相交流侧电流。irj表示桥臂电流(r=p表示上桥臂,r=n表示下桥臂),urj表示某一桥臂上所有子模块电压之和。Udc表示直流侧电压,Idc表示直流输电电流。As shown in FIG. 1 , this embodiment provides a method for predicting the DC bias current on the AC side under the condition of asymmetric impedance of the MMC bridge arm, where a typical topology of a typical three-phase MMC is shown in FIG. 2 . In the figure, the sub-module adopts a half-bridge structure, and each bridge arm consists of N identical sub-modules (SM), bridge arm inductance L 0 and equivalent resistance R 0 in series. The positive direction of each electric quantity is defined as shown in the figure. Point O and O' represent the zero-potential reference points on the DC side and the AC side, respectively, and v represents the AC outlet of the MMC. The AC system is equivalent to an ideal voltage source u sj (j=a, b, c, representing three phases of AC). The AC system is connected to the AC outlet of the MMC through the connection reactor L ac . u vj represents the voltage at the j-phase AC outlet, and i vj represents the j-phase AC side current. i rj represents the bridge arm current (r=p represents the upper bridge arm, r=n represents the lower bridge arm), and urj represents the sum of the voltages of all sub-modules on a certain bridge arm. U dc represents the DC side voltage, and I dc represents the DC transmission current.

本实施例具体包括以下步骤:This embodiment specifically includes the following steps:

确定待预测系统的主回路参数(包括系统的电压调制比、交流侧系统电压、桥臂阻抗、电容器参数、子模块数目等);Determine the main loop parameters of the system to be predicted (including the voltage modulation ratio of the system, the AC side system voltage, bridge arm impedance, capacitor parameters, the number of sub-modules, etc.);

根据待预测系统的主回路参数,采用式(1)计算桥臂参数不对称情况下的交流侧直流偏置电流:According to the main loop parameters of the system to be predicted, formula (1) is used to calculate the AC side DC bias current when the bridge arm parameters are asymmetric:

Figure BDA0002236362610000081
Figure BDA0002236362610000081

式中,Ivj_0表示桥臂参数不对称情况下的j相的交流侧直流偏置电流;Udc表示直流侧电压,Rpj表示第j相上桥臂的等效电阻,Rnj表示第j相下桥臂的等效电阻;其中,In the formula, I vj_0 represents the DC bias current of the j-phase AC side when the bridge arm parameters are asymmetric; U dc represents the DC side voltage, R pj represents the equivalent resistance of the upper bridge arm of the j-th phase, and R nj represents the j-th phase. Equivalent resistance of the lower arm of the phase; where,

Figure BDA0002236362610000082
Figure BDA0002236362610000082

Figure BDA0002236362610000083
Figure BDA0002236362610000083

式中,N表示每个桥臂上的子模块数量,Lpj表示第j相上桥臂的桥臂电感,ω表示电网角频率,C表示子模块中的电容,Lnj表示第j相下桥臂的桥臂电感。In the formula, N represents the number of sub-modules on each bridge arm, L pj represents the bridge arm inductance of the upper bridge arm of the j-th phase, ω represents the grid angular frequency, C represents the capacitance in the sub-modules, and L nj represents the lower-phase j-th phase. The leg inductance of the bridge leg.

在本实施例中,采用以下步骤得到式(1):In the present embodiment, the following steps are adopted to obtain formula (1):

步骤S1:分析MMC稳态下偏置电流特性,得到MMC稳态下交流侧偏置电流的特性表达式;Step S1: analyze the bias current characteristics under the MMC steady state, and obtain the characteristic expression of the AC side bias current under the MMC steady state;

步骤S2:分析桥臂参数不对称下的偏置电流特性,并根据步骤S1得到的MMC 稳态下交流侧偏置电流的特性表达式,得到桥臂参数不对称情况下的交流侧直流偏置电流。Step S2: analyze the bias current characteristics under the condition of asymmetric bridge arm parameters, and obtain the AC side DC bias under the condition of asymmetric bridge arm parameters according to the characteristic expression of the AC side bias current under the MMC steady state obtained in step S1 current.

在本实施例中,步骤S1具体包括以下步骤:In this embodiment, step S1 specifically includes the following steps:

步骤S11:根据基尔霍夫电流定律得到,第j相桥臂的电流ivj满足下式:Step S11: Obtained according to Kirchhoff's current law, the current i vj of the j-th phase bridge arm satisfies the following formula:

ivj=ipj-inji vj = i pj - i nj ;

式中,ipj表示第j相上桥臂电流,inj表示第j相下桥臂电流;In the formula, i pj represents the current of the upper bridge arm of the jth phase, and inj represents the current of the lower bridge arm of the jth phase;

定义桥臂共模电流为icirj,即表示第j相环流:The common mode current of the bridge arm is defined as i cirj , which means the j-th phase circulating current:

Figure BDA0002236362610000091
Figure BDA0002236362610000091

步骤S12:设桥臂电流表示为以下多种频率成分叠加的形式:Step S12: Let the bridge arm current be expressed in the form of superposition of the following multiple frequency components:

Figure BDA0002236362610000092
Figure BDA0002236362610000092

式中,Ipj_0表示第j相上桥臂电流的直流分量,Inj_0表示第j相下桥臂电流的直流分量,Ipj_h

Figure BDA0002236362610000093
分别表示第j相桥臂电流h次谐波的幅值和初相角;In the formula, I pj_0 represents the DC component of the upper arm current of the jth phase, I nj_0 represents the DC component of the lower arm current of the jth phase, and I pj_h and
Figure BDA0002236362610000093
respectively represent the amplitude and initial phase angle of the h-th harmonic of the jth-phase bridge arm current;

取平均开关函数:Take the average switching function:

Figure BDA0002236362610000101
Figure BDA0002236362610000101

式中,Spj、Snj分别表示第j相上、下桥臂的开关函数,m为电压调制比,θj为交流系统第j相等效电动势初相角;In the formula, Spj and Snj represent the switching functions of the upper and lower arms of the jth phase, respectively, m is the voltage modulation ratio, and θ j is the initial phase angle of the equivalent electromotive force of the jth phase of the AC system;

令电容电流的集合平均值为桥臂电流与平均开关函数的乘积:Let the collective mean value of the capacitor current be the product of the bridge arm current and the mean switching function:

Figure BDA0002236362610000102
Figure BDA0002236362610000102

式中,ic,pj表示第j相上桥臂子模块电容电流集合平均值,ic,nj表示第j相下桥臂子模块电容电流集合平均值;In the formula , ic,pj represents the average value of the capacitor current set of the j-th upper bridge arm sub-module , and ic,nj represents the j-th phase lower bridge arm sub-module capacitor current set average value;

步骤S13:为了满足稳态运行,令电容电流的直流分量为0,即:Step S13: In order to satisfy the steady-state operation, let the DC component of the capacitor current be 0, that is:

Figure BDA0002236362610000103
Figure BDA0002236362610000103

式中,Ipj_1表示第j相上桥臂电流基频谐波的幅值,Inj_1表示第j相下桥臂电流基频谐波的幅值,

Figure BDA0002236362610000104
表示第j相桥臂电流基频谐波的初相角;In the formula, I pj_1 represents the amplitude of the fundamental frequency harmonic of the upper arm current of the jth phase, I nj_1 represents the amplitude of the fundamental frequency harmonic of the lower arm current of the jth phase,
Figure BDA0002236362610000104
Represents the initial phase angle of the fundamental frequency harmonic of the jth-phase bridge arm current;

步骤S13:采用下式计算MMC稳态下交流侧偏置电流的特性表达式:Step S13: Use the following formula to calculate the characteristic expression of the AC side bias current in the MMC steady state:

Figure BDA0002236362610000105
Figure BDA0002236362610000105

式中,Icirj_1表示第j相桥臂共模电流的基频分量。In the formula, I cirj_1 represents the fundamental frequency component of the common mode current of the j-th phase bridge arm.

步骤S2具体包括以下步骤:Step S2 specifically includes the following steps:

步骤S21:要计算MMC参数不对称下的交流侧偏置电流,需先求得此时环流的基频量。为了简化分析,仅考虑桥臂电流中的直流量与基频分量,将桥臂电压的基频增量表示为:Step S21: To calculate the AC side bias current under the asymmetric MMC parameters, it is necessary to first obtain the fundamental frequency of the circulating current at this time. In order to simplify the analysis, only the DC and fundamental frequency components in the bridge arm current are considered, and the fundamental frequency increment of the bridge arm voltage is expressed as:

Figure BDA0002236362610000111
Figure BDA0002236362610000111

式中,

Figure BDA0002236362610000112
表示第j相上桥臂的电压增量的基频分量,
Figure BDA0002236362610000113
表示第j相下桥臂的电压增量的基频分量,Ipj_0表示第j相上桥臂电流的直流分量,Inj_0表示第j相下桥臂电流的直流分量;In the formula,
Figure BDA0002236362610000112
represents the fundamental frequency component of the voltage increment of the upper arm of the j-th phase,
Figure BDA0002236362610000113
Represents the fundamental frequency component of the voltage increment of the jth phase lower arm, I pj_0 represents the DC component of the jth phase upper bridge arm current, and I nj_0 represents the jth phase lower arm current DC component;

步骤S22:设j相交流输出电压基频量为:Step S22: Set the fundamental frequency of the j-phase AC output voltage as:

Figure BDA0002236362610000114
Figure BDA0002236362610000114

式中,

Figure BDA0002236362610000115
表示第j相交流输出电压的基频分量;U表示第j相交流输出电压的基频电压的幅值;In the formula,
Figure BDA0002236362610000115
Represents the fundamental frequency component of the jth phase AC output voltage; U represents the amplitude of the fundamental frequency voltage of the jth phase AC output voltage;

对上、下桥臂阻抗进行区分,桥臂电压的基频波动满足:Distinguish the impedance of the upper and lower bridge arms, and the fundamental frequency fluctuation of the bridge arm voltage satisfies:

Figure BDA0002236362610000116
Figure BDA0002236362610000116

式中,

Figure BDA0002236362610000117
表示第j相上桥臂的电压基频分量,
Figure BDA0002236362610000118
表示第j相下桥臂的电压基频分量;In the formula,
Figure BDA0002236362610000117
represents the voltage fundamental frequency component of the upper arm of the j-th phase,
Figure BDA0002236362610000118
represents the voltage fundamental frequency component of the lower arm of the jth phase;

步骤S23:综合考虑步骤S21-步骤S22,对于上桥臂有:Step S23: Considering step S21-step S22 comprehensively, for the upper bridge arm:

Figure BDA0002236362610000121
Figure BDA0002236362610000121

式中,Ipj_1表示第j相上桥臂电流的基频分量;In the formula, I pj_1 represents the fundamental frequency component of the upper arm current of the j-th phase;

则上桥臂电流基频量的计算采用下式:Then the calculation of the fundamental frequency of the upper arm current adopts the following formula:

Figure BDA0002236362610000122
Figure BDA0002236362610000122

其中,in,

Figure BDA0002236362610000123
Figure BDA0002236362610000123

则,不对称情况下的上桥臂电流的直流分量为:Then, the DC component of the upper arm current in the case of asymmetry is:

Figure BDA0002236362610000124
Figure BDA0002236362610000124

同理,不对称情况下的下桥臂直流分量为:In the same way, the DC component of the lower bridge arm in the case of asymmetry is:

Figure BDA0002236362610000125
Figure BDA0002236362610000125

其中,in,

Figure BDA0002236362610000126
Figure BDA0002236362610000126

步骤S23:得到桥臂参数不对称情况下的交流侧直流偏置电流表达式为:Step S23: Obtain the expression of the DC bias current of the AC side under the condition of asymmetric parameters of the bridge arm:

Figure BDA0002236362610000131
Figure BDA0002236362610000131

特别的,为了验证本实施例的有效性,本实施例基于PSCAD/EMTDC搭建真双级MMC直流输电系统电磁暂态模型,模型主回路参数见表1。改变A相上桥臂电抗器参数,其余桥臂参数均保持为基准值,进行多组仿真,记录交流侧输出电流的直流分量,所记录的偏置电流仿真值与采用本实施例的方法计算值进行对比,如表2所示,误差仅为0.03%,证明本实施例所提出的桥臂参数不对称情况下交流侧直流偏置电流等效模型的正确性。In particular, in order to verify the effectiveness of this embodiment, this embodiment builds an electromagnetic transient model of a true two-stage MMC direct current transmission system based on PSCAD/EMTDC, and the main circuit parameters of the model are shown in Table 1. Change the reactor parameters of the upper arm of the A-phase, and keep the parameters of the other arms as the reference values, carry out multiple sets of simulations, record the DC component of the output current on the AC side, and the recorded bias current simulation value is calculated by using the method of this embodiment. As shown in Table 2, the error is only 0.03%, which proves the correctness of the equivalent model of the DC bias current on the AC side when the bridge arm parameters proposed in this embodiment are asymmetrical.

表1模型主回路参数Table 1 Model main circuit parameters

参数名称parameter name 参数值parameter value 交流侧额定电压/kVAC side rated voltage/kV 220220 直流侧额定电压/kVDC side rated voltage/kV ±320±320 子模块电容/mFSubmodule capacitance/mF 1010 桥臂电抗器/mHBridge arm reactor/mH 5050 平波电抗器/mHSmoothing reactor/mH 5050 桥臂等效电阻/RBridge arm equivalent resistance/R 0.10.1 桥臂子模块数Number of bridge arm submodules 2020 额定调制比Nominal modulation ratio 0.85 0.85

表2交流侧直流偏置电流解析计算值与仿真值对比的部分结果Table 2 Part of the results of the comparison between the analytical calculation value and the simulation value of the DC bias current on the AC side

Figure BDA0002236362610000132
Figure BDA0002236362610000132

Figure BDA0002236362610000141
Figure BDA0002236362610000141

以待建直流输电工程参数设计时,利用本实施例的方法辅助子模块数目的确定为例。考虑可能出现的桥臂参数不对称情况为上桥臂电抗值高于基准值10%,方法中除了子模块数目作为变量,其余参数不变。得到图3所示,MMC交流侧偏置电流随的变化情况。在子模块数目小于150时,偏置电流会随子模块数目的增加而增大,特别是当120<N<150时,偏置电流增加的速度加快。因此,考虑工程投入后会出现的桥臂参数不对称情况引发的偏磁问题,子模块数目并非越多越好。Take the method of this embodiment as an example to assist the determination of the number of sub-modules when designing the parameters of the DC power transmission project to be built. Considering the possible asymmetry of the bridge arm parameters, the reactance value of the upper bridge arm is 10% higher than the reference value. In the method, except the number of sub-modules as a variable, the rest of the parameters remain unchanged. As shown in Figure 3, the change of the bias current on the AC side of the MMC is obtained. When the number of sub-modules is less than 150, the bias current will increase with the increase of the number of sub-modules, especially when 120<N<150, the rate of increase of the bias current is accelerated. Therefore, considering the bias problem caused by the asymmetry of the bridge arm parameters that will occur after the project is invested, the number of sub-modules is not the better.

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 (4)

1.一种MMC桥臂阻抗不对称下的交流侧直流偏置电流预测方法,其特征在于,1. an AC side DC bias current prediction method under asymmetric impedance of MMC bridge arm, is characterized in that, 确定待预测系统的主回路参数;Determine the main loop parameters of the system to be predicted; 根据待预测系统的主回路参数,采用式(1)计算桥臂参数不对称情况下的交流侧直流偏置电流:According to the main loop parameters of the system to be predicted, formula (1) is used to calculate the AC side DC bias current when the bridge arm parameters are asymmetric:
Figure FDA0003020857430000011
Figure FDA0003020857430000011
式中,m表示电压调制比,Ivj_0表示桥臂参数不对称情况下j相的交流侧直流偏置电流;Udc表示直流侧电压,Rpj表示第j相上桥臂的等效电阻,Rnj表示第j相下桥臂的等效电阻;其中,In the formula, m represents the voltage modulation ratio, I vj_0 represents the AC side DC bias current of the j-phase when the bridge arm parameters are asymmetrical; U dc represents the DC side voltage, R pj represents the equivalent resistance of the upper bridge arm of the jth phase, R nj represents the equivalent resistance of the lower arm of the jth phase; where,
Figure FDA0003020857430000012
Figure FDA0003020857430000012
Figure FDA0003020857430000013
Figure FDA0003020857430000013
式中,N表示每个桥臂上的子模块数量,Lpj表示第j相上桥臂的桥臂电感,ω表示电网角频率,C表示子模块中的电容,Lnj表示第j相下桥臂的桥臂电感。In the formula, N represents the number of sub-modules on each bridge arm, L pj represents the bridge arm inductance of the upper bridge arm of the j-th phase, ω represents the grid angular frequency, C represents the capacitance in the sub-modules, and L nj represents the lower-phase j-th phase. The leg inductance of the bridge leg.
2.根据权利要求1所述的一种MMC桥臂阻抗不对称下的交流侧直流偏置电流预测方法,其特征在于,采用以下步骤得到式(1):2. the AC side DC bias current prediction method under a kind of MMC bridge arm impedance asymmetry according to claim 1, is characterized in that, adopts the following steps to obtain formula (1): 步骤S1:分析MMC稳态下偏置电流特性,得到MMC稳态下交流侧偏置电流的特性表达式;Step S1: analyze the bias current characteristics under the MMC steady state, and obtain the characteristic expression of the AC side bias current under the MMC steady state; 步骤S2:分析桥臂参数不对称下的偏置电流特性,并根据步骤S1得到的MMC稳态下交流侧偏置电流的特性表达式,得到桥臂参数不对称情况下的交流侧直流偏置电流。Step S2: Analyze the bias current characteristics under the condition of the bridge arm parameter asymmetry, and obtain the AC side DC bias under the condition of the bridge arm parameter asymmetry according to the characteristic expression of the AC side bias current under the MMC steady state obtained in step S1 current. 3.根据权利要求2所述的一种MMC桥臂阻抗不对称下的交流侧直流偏置电流预测方法,其特征在于,步骤S1具体包括以下步骤:3. The method for predicting AC side DC bias current under asymmetric impedance of a MMC bridge arm according to claim 2, wherein step S1 specifically comprises the following steps: 步骤S11:根据基尔霍夫电流定律得到,第j相桥臂的电流ivj满足下式:Step S11: Obtained according to Kirchhoff's current law, the current i vj of the j-th phase bridge arm satisfies the following formula: ivj=ipj-inji vj = i pj - i nj ; 式中,ipj表示第j相上桥臂电流,inj表示第j相下桥臂电流;In the formula, i pj represents the current of the upper bridge arm of the jth phase, and inj represents the current of the lower bridge arm of the jth phase; 定义桥臂共模电流为icirj,即表示第j相环流:The common mode current of the bridge arm is defined as i cirj , which means the j-th phase circulating current:
Figure FDA0003020857430000021
Figure FDA0003020857430000021
步骤S12:设桥臂电流表示为以下多种频率成分叠加的形式:Step S12: Let the bridge arm current be expressed in the form of superposition of the following multiple frequency components:
Figure FDA0003020857430000022
Figure FDA0003020857430000022
式中,Ipj_0表示第j相上桥臂电流的直流分量,Inj_0表示第j相下桥臂电流的直流分量,Ipj_h
Figure FDA0003020857430000023
分别表示第j相桥臂电流h次谐波的幅值和初相角;
In the formula, I pj_0 represents the DC component of the upper arm current of the jth phase, I nj_0 represents the DC component of the lower arm current of the jth phase, and I pj_h and
Figure FDA0003020857430000023
respectively represent the amplitude and initial phase angle of the h-th harmonic of the jth-phase bridge arm current;
取平均开关函数:Take the average switching function:
Figure FDA0003020857430000024
Figure FDA0003020857430000024
式中,Spj、Snj分别表示第j相上、下桥臂的开关函数,m为电压调制比,θj为交流系统第j相等效电动势初相角;In the formula, Spj and Snj represent the switching functions of the upper and lower arms of the jth phase, respectively, m is the voltage modulation ratio, and θ j is the initial phase angle of the equivalent electromotive force of the jth phase of the AC system; 令电容电流的集合平均值为桥臂电流与平均开关函数的乘积:Let the collective mean value of the capacitor current be the product of the bridge arm current and the mean switching function:
Figure FDA0003020857430000031
Figure FDA0003020857430000031
式中,ic,pj表示第j相上桥臂子模块电容电流集合平均值,ic,nj表示第j相下桥臂子模块电容电流集合平均值;In the formula , ic,pj represents the average value of the capacitor current set of the j-th upper bridge arm sub-module , and ic,nj represents the j-th phase lower bridge arm sub-module capacitor current set average value; 步骤S13:为了满足稳态运行,令电容电流的直流分量为0,即:Step S13: In order to satisfy the steady-state operation, let the DC component of the capacitor current be 0, that is:
Figure FDA0003020857430000032
Figure FDA0003020857430000032
式中,Ipj_1表示第j相上桥臂电流基频谐波的幅值,Inj_1表示第j相下桥臂电流基频谐波的幅值,
Figure FDA0003020857430000033
表示第j相桥臂电流基频谐波的初相角;
In the formula, I pj_1 represents the amplitude of the fundamental frequency harmonic of the upper arm current of the jth phase, I nj_1 represents the amplitude of the fundamental frequency harmonic of the lower arm current of the jth phase,
Figure FDA0003020857430000033
Represents the initial phase angle of the fundamental frequency harmonic of the jth-phase bridge arm current;
步骤S14:采用下式计算MMC稳态下交流侧偏置电流的特性表达式:Step S14: Use the following formula to calculate the characteristic expression of the AC side bias current in the MMC steady state:
Figure FDA0003020857430000034
Figure FDA0003020857430000034
式中,Icirj_1表示第j相桥臂共模电流的基频分量。In the formula, I cirj_1 represents the fundamental frequency component of the common mode current of the j-th phase bridge arm.
4.根据权利要求2所述的一种MMC桥臂阻抗不对称下的交流侧直流偏置电流预测方法,其特征在于,步骤S2具体包括以下步骤:4. The method for predicting AC side DC bias current under asymmetric impedance of a MMC bridge arm according to claim 2, wherein step S2 specifically comprises the following steps: 步骤S21:仅考虑桥臂电流中的直流量与基频分量,将桥臂电压的基频增量表示为:Step S21: Considering only the DC quantity and the fundamental frequency component in the bridge arm current, the fundamental frequency increment of the bridge arm voltage is expressed as:
Figure FDA0003020857430000035
Figure FDA0003020857430000035
式中,
Figure FDA0003020857430000041
表示第j相上桥臂的电压增量的基频分量,
Figure FDA0003020857430000042
表示第j相下桥臂的电压增量的基频分量,Ipj_0表示第j相上桥臂电流的直流分量,Inj_0表示第j相下桥臂电流的直流分量,θj为交流系统第j相等效电动势初相角,Ipj_1表示第j相上桥臂电流基频谐波的幅值,Inj_1表示第j相下桥臂电流基频谐波的幅值,
Figure FDA0003020857430000043
表示第j相桥臂电流基频谐波的初相角;
In the formula,
Figure FDA0003020857430000041
represents the fundamental frequency component of the voltage increment of the upper arm of the j-th phase,
Figure FDA0003020857430000042
Represents the fundamental frequency component of the voltage increment of the jth phase lower arm, I pj_0 represents the DC component of the jth phase upper arm current, I nj_0 represents the jth phase lower arm current DC component, θ j is the AC system The initial phase angle of the j-phase equivalent electromotive force, I pj_1 represents the amplitude of the fundamental frequency harmonic of the upper arm current of the jth phase, I nj_1 represents the amplitude of the fundamental frequency harmonic of the jth phase lower arm current,
Figure FDA0003020857430000043
Represents the initial phase angle of the fundamental frequency harmonic of the jth-phase bridge arm current;
步骤S22:设j相交流输出电压基频量为:Step S22: Set the fundamental frequency of the j-phase AC output voltage as:
Figure FDA0003020857430000044
Figure FDA0003020857430000044
式中,
Figure FDA0003020857430000045
表示第j相交流输出电压的基频分量;U表示第j相交流输出电压的基频电压的幅值;
In the formula,
Figure FDA0003020857430000045
Represents the fundamental frequency component of the jth phase AC output voltage; U represents the amplitude of the fundamental frequency voltage of the jth phase AC output voltage;
对上、下桥臂阻抗进行区分,桥臂电压的基频波动满足:Distinguish the impedance of the upper and lower bridge arms, and the fundamental frequency fluctuation of the bridge arm voltage satisfies:
Figure FDA0003020857430000046
Figure FDA0003020857430000046
式中,
Figure FDA0003020857430000047
表示第j相上桥臂的电压基频分量,
Figure FDA0003020857430000048
表示第j相下桥臂的电压基频分量,ipj表示第j相上桥臂电流,inj表示第j相下桥臂电流;
In the formula,
Figure FDA0003020857430000047
represents the voltage fundamental frequency component of the upper arm of the j-th phase,
Figure FDA0003020857430000048
represents the voltage fundamental frequency component of the lower arm of the jth phase, i pj represents the current of the upper arm of the jth phase, and inj represents the current of the lower arm of the jth phase;
步骤S23:综合考虑步骤S21-步骤S22,对于上桥臂有:Step S23: Considering step S21-step S22 comprehensively, for the upper bridge arm:
Figure FDA0003020857430000049
Figure FDA0003020857430000049
式中,Ipj_1表示第j相上桥臂电流的基频分量;In the formula, I pj_1 represents the fundamental frequency component of the upper arm current of the j-th phase; 则上桥臂电流基频量的计算采用下式:Then the calculation of the fundamental frequency of the upper arm current adopts the following formula:
Figure FDA0003020857430000051
Figure FDA0003020857430000051
其中,in,
Figure FDA0003020857430000052
Figure FDA0003020857430000052
则,不对称情况下的上桥臂电流的直流分量为:Then, the DC component of the upper arm current in the case of asymmetry is:
Figure FDA0003020857430000053
Figure FDA0003020857430000053
同理,不对称情况下的下桥臂直流分量为:In the same way, the DC component of the lower bridge arm in the case of asymmetry is:
Figure FDA0003020857430000054
Figure FDA0003020857430000054
其中,in,
Figure FDA0003020857430000055
Figure FDA0003020857430000055
步骤S24:得到桥臂参数不对称情况下的交流侧直流偏置电流表达式为:Step S24: Obtain the expression of the DC bias current of the AC side under the condition of asymmetric parameters of the bridge arm:
Figure FDA0003020857430000056
Figure FDA0003020857430000056
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