CN111581824A - Modeling method for small disturbance stability analysis of modular multilevel converter - Google Patents

Modeling method for small disturbance stability analysis of modular multilevel converter Download PDF

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CN111581824A
CN111581824A CN202010387272.7A CN202010387272A CN111581824A CN 111581824 A CN111581824 A CN 111581824A CN 202010387272 A CN202010387272 A CN 202010387272A CN 111581824 A CN111581824 A CN 111581824A
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mmc
equivalent
voltage
capacitance
modeling method
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CN111581824B (en
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韦甜柳
王一振
李巍巍
李岩
朱琳
许树楷
朱喆
邱逢良
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Tianjin University
Research Institute of Southern Power Grid Co Ltd
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Abstract

The invention relates to a modeling method suitable for stability analysis of a modular multilevel converter, which is characterized in that an MMC is equivalent to a structure that a controllable current source is connected with an equivalent capacitor and an equivalent conductance in parallel, and the modeling method comprises the following steps: measuring direct current voltage, alternating current side transmission power and direct current side power when the MMC is in steady state normal operation; determining the number N of the MMC bridge arm sub-modules and the sub-module capacitance values; calculating the parallel conductance; calculating equivalent capacitance; an equivalent current source; the columns write the differential equation: and obtaining a state space matrix of small disturbance stability.

Description

Modeling method for small disturbance stability analysis of modular multilevel converter
Technical Field
The invention belongs to the field of flexible direct current systems, and particularly relates to a modeling method suitable for small disturbance stability analysis of a modular multilevel converter.
Background
The flexible direct-current transmission system based on the Voltage Source Converter (VSC) can accurately and quickly control the amplitude and phase of the Voltage at the alternating-current side of the VSC by using full-control power electronic devices such as IGBTs and pulse width modulation technology, so that from the perspective of the alternating-current system, the VSC Converter station can be equivalent to a motor or a generator without rotational inertia, and the independent control of the active power and the reactive power can be realized in the PQ four quadrant almost instantly, which is the basic characteristic of the VSC. Based on this characteristic, VSC does not have reactive compensation problem, can be for the passive system power supply, and area is little, is fit for constituting multiterminal direct current system and urban distribution network interconnection.
Compared with a two-level converter and a three-level converter topological structure, the Modular Multilevel Converter (MMC) has the characteristics of low manufacturing difficulty, low loss, step voltage reduction, good waveform quality and the like, and particularly can solve the problem of voltage imbalance caused by direct series connection of IGBTs. Therefore, the MMC has good application prospect in a direct current transmission and distribution system. For example, the first multi-terminal flexible dc transmission project in operation in the world, south australia three-terminal flexible dc transmission project, is an engineering application based on an MMC topology.
However, the MMC contains a large number of sub-modules, and the switch model is complex to establish and is not suitable for stable analysis and calculation of the flexible direct current system, so that the research on a model suitable for stability analysis of the MMC is particularly important.
Disclosure of Invention
The invention aims to provide a modeling method which can be used for evaluating the stability condition of a whole flexible direct current system and guiding the selection of primary parameters of the flexible direct current system and is suitable for small disturbance stability analysis of a modular multilevel converter, and the technical scheme is as follows:
a modeling method suitable for stability analysis of a modular multilevel converter is characterized in that an MMC is equivalent to a controllable current source IeqAnd equivalent capacitance CeqAnd an equivalent conductance G parallel structure, the method comprises the following steps:
1) direct-current voltage V for measuring steady-state normal operation of MMC (modular multilevel converter)dcnAC side transmission power PacnAnd DC side power Pdcn；
2) Determining the number N of the MMC bridge arm sub-modules and the capacitance C of the sub-modules0；
3) Calculating parallel conductance
Figure BDA0002484258900000011
4) Calculating the equivalent capacitance Ceq＝3C0/N；
5) Equivalent current source Ieq＝Pac/Vdc；
6) With current i through line inductance LLConstant power load equivalent capacitance C2Voltage v ofc2MMC equivalent capacitor C1Voltage v ofc1Differential equations are written for the state variable columns:
Figure BDA0002484258900000021
Figure BDA0002484258900000022
Figure BDA0002484258900000023
obtaining a state space matrix of small disturbance stability:
Figure BDA0002484258900000024
wherein R is line resistance, and P represents work of constant power load CPLRate, PacRepresenting the transmitted power at the AC side of the MMC in steady state, vc10And vc20Representing the initial voltage before the MMC and constant power load disturbances, respectively.
The invention has the technical characteristics that: on the basis of fully considering the control performance of the MMC, the invention provides a modeling method suitable for analyzing the small-disturbance stability of the MMC. According to the method, the complex MMC is equivalent to a structure in which a controllable current source is connected with an equivalent capacitor and an equivalent conductance in parallel, the dimension of the model is greatly reduced, and the method has the advantages of simple form and convenience in stability analysis.
Drawings
FIG. 1 is a schematic diagram of MMC topology
FIG. 2 is a schematic diagram of an MMC converter phase A
FIG. 3 is a model suitable for MMC stability analysis according to the present invention
FIG. 4 is a schematic diagram of a simple DC system for supplying power to a constant power load by an MMC
FIG. 5 shows the effect of MMC submodule capacitance parameters on feature roots
FIG. 6 is a graph of the effect of line inductance parameters on feature roots
Detailed description of the preferred embodiments
The following will describe in detail a modeling method suitable for MMC small disturbance stability analysis proposed by the present invention with reference to the accompanying drawings and specific implementation.
The MMC shown in FIG. 1 comprises 6 three-phase bridge arms, each of which is provided with a bridge arm reactance L0And N sub-modules connected in series, each sub-module having a half-bridge structure composed of fully-controlled power electronic devices (IGBTs), and a capacitor C0Each IGBT device is connected in anti-parallel with a diode for sub-module capacitance.
In order to deeply analyze the MMC characteristics, an analysis is performed below with respect to the MMC converter a phase shown in fig. 2.
Under the condition of normal operation of MMC, the upper bridge arm is put into nuSubmodule, lower bridge arm input nlSub-modules, nu+nlN, the current flowing through the upper arm is iu＝ia/2+idiffCurrent i flowing through the lower arml＝-ia/2+idiffWherein iaIs a component of A AC current idiffIs a direct current component.
Figure BDA0002484258900000031
Figure BDA0002484258900000032
Above bridge arm input submodule voltage VuVoltage V of lower bridge arm voltage input submodulelComponent of A AC current iaAnd a direct current component idiffAs state variables, it can be derived from fig. 2:
Figure BDA0002484258900000033
similarly, the B-phase and C-phase dc voltage differential equations can be expressed as:
Figure BDA0002484258900000034
Figure BDA0002484258900000035
suppose that
Figure BDA0002484258900000036
Can obtain the product
Figure BDA0002484258900000037
From FIG. 1, it can be seen
3idiff＝-Idc(7)
Figure BDA0002484258900000038
Substituting (7) and (8) into (6) can obtain:
Figure BDA0002484258900000041
Figure BDA0002484258900000042
wherein, IdcFor direct current, the direction is from MMC to DC grid, PacThe active power flowing to the direct current power grid for the MMC.
Therefore, from the perspective of the system, an equivalent model of the MMC on the dc side can be obtained, as shown in fig. 3, the MMC exhibits a characteristic of parallel connection of a capacitor and a controllable dc current source on the dc side, wherein G represents the loss of the MMC converter, and is generally small and can be omitted.
For the simple direct current system of the MMC shown in FIG. 4 supplying power to the constant power load, the following measures are taken, wherein R is the line resistance, L is the line inductance, and C is1Representing MMC equivalent capacitance, C2Represents the equivalent capacitance of the constant power load CPL, P represents the power of the constant power load CPL, vc1And vc2Representing the voltage of the MMC and the constant power load, respectively.
1) Direct-current voltage V for measuring steady-state normal operation of MMC (modular multilevel converter)dcnAC side transmission power PacnAnd DC side power Pdcn。
2) Determining the number N of the MMC bridge arm sub-modules and the capacitance C of the sub-modules0。
3) Calculating parallel conductance
Figure BDA0002484258900000043
4) Calculating the equivalent capacitance C1＝3C0/N。
5) Equivalent current source Ieq＝Pac/Vdc。
With current i through line inductance LLConstant power load equivalent capacitance C2Voltage v ofc2MMC equivalent capacitor C1Voltage v ofc1Writing a differential equation for the state variable column yields:
Figure BDA0002484258900000044
Figure BDA0002484258900000045
Figure BDA0002484258900000046
therefore, the state space matrix describing the stability of the small perturbations of the circuit shown in FIG. 4 is
Figure BDA0002484258900000047
Wherein R is line resistance, L is line inductance, C1Representing MMC equivalent capacitance, C2Represents the equivalent capacitance of the constant power load CPL, P represents the power of the constant power load CPL, PacRepresenting the transmitted power at the AC side of the MMC in steady state, vc10And vc20Representing the initial voltage before the MMC and constant power load disturbances, respectively.
The influence of the capacitance parameter of the MMC sub-module on the characteristic root can be obtained through analysis (14) and is shown in figure 5, and the influence of the line inductance parameter on the characteristic root is shown in figure 6.
Therefore, the modeling method suitable for MMC small disturbance stability analysis provided by the invention is completed completely.

Claims (1)

1. A modeling method suitable for stability analysis of a modular multilevel converter is characterized in that an MMC is equivalent to a controllable current source IeqAnd equivalent capacitance CeqAnd the equivalent conductance G is connected in parallel. The method comprises the following steps:
1) direct-current voltage V for measuring steady-state normal operation of MMC (modular multilevel converter)dcnAC side transmission power PacnAnd DC side power Pdcn；
2) Determining the number N of the MMC bridge arm sub-modules and the capacitance C of the sub-modules0；
3) Computing andelectric connector
Figure FDA0002484258890000011
4) Calculating the equivalent capacitance Ceq＝3C0/N；
5) Equivalent current source Ieq＝Pac/Vdc；
6) With current i through line inductance LLConstant power load equivalent capacitance C2Voltage v ofc2MMC equivalent capacitor C1Voltage v ofc1Differential equations are written for the state variable columns:
Figure FDA0002484258890000012
Figure FDA0002484258890000013
Figure FDA0002484258890000014
obtaining a state space matrix of small disturbance stability:
Figure FDA0002484258890000015
wherein R is line resistance, P represents power of constant power load CPL, and P isacRepresenting the transmitted power at the AC side of the MMC in steady state, vc10And vc20Representing the initial voltage before the MMC and constant power load disturbances, respectively.
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CN102882383A (en) * 2012-09-28 2013-01-16 无锡清源电气科技有限公司 Direct power control method of modular multilevel wind power converter
CN106909702A (en) * 2015-12-23 2017-06-30 加拿大欧泊实时技术有限公司北京代表处 A kind of modular multilevel rectifier and transformer station, Modeling and simulation platform, method
CN107453633A (en) * 2017-08-03 2017-12-08 华中科技大学 A kind of MMC DC voltages outer ring controller and generation method
CN108336751A (en) * 2018-03-16 2018-07-27 云南电网有限责任公司 A kind of electromechanical transient modeling method of LCC-MMC mixed DCs power grid
CN109428340A (en) * 2017-08-30 2019-03-05 中国电力科学研究院 A kind of emulation mode and system of flexible DC transmission device
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CN106909702A (en) * 2015-12-23 2017-06-30 加拿大欧泊实时技术有限公司北京代表处 A kind of modular multilevel rectifier and transformer station, Modeling and simulation platform, method
CN107453633A (en) * 2017-08-03 2017-12-08 华中科技大学 A kind of MMC DC voltages outer ring controller and generation method
CN109428340A (en) * 2017-08-30 2019-03-05 中国电力科学研究院 A kind of emulation mode and system of flexible DC transmission device
CN108336751A (en) * 2018-03-16 2018-07-27 云南电网有限责任公司 A kind of electromechanical transient modeling method of LCC-MMC mixed DCs power grid
CN109446653A (en) * 2018-10-30 2019-03-08 华中科技大学 Mixed type MMC state space, stable state parse and the modeling method of small-signal model

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