CN111581824B - Modeling method for small disturbance stability analysis of modularized multi-level converter - Google Patents
Modeling method for small disturbance stability analysis of modularized multi-level converter Download PDFInfo
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Abstract
The invention relates to a modeling method suitable for stability analysis of a modularized multi-level converter, which is characterized in that MMC is equivalent to a structure of parallel connection of a controllable current source, an equivalent capacitor and an equivalent conductivity, 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 stably and normally operates; determining the number N of the sub-modules of the MMC bridge arm and the capacitance value of the sub-modules; calculating parallel conductance; calculating an equivalent capacitance; an equivalent current source; column written differential equation: and obtaining a state space matrix with small disturbance stability.
Description
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 modularized multi-level converter.
Background
The flexible direct current transmission system based on the voltage source type converter (Voltage Source Converter, VSC) can accurately and rapidly control the voltage amplitude and the phase of the alternating current side of the VSC by utilizing full-control power electronic devices such as IGBT and a 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 independent control of active power and reactive power can be realized in PQ four quadrants almost instantaneously, which is the basic characteristic of the VSC. Based on the characteristics, the VSC has no reactive compensation problem, can supply power for a passive system, has small occupied area, and is suitable for forming interconnection between a multi-terminal direct current system and an urban power distribution network.
Compared with a topological structure of a two-level converter and a three-level converter, the modularized multi-level converter (ModularMultilevelConverter, MMC) has the characteristics of low manufacturing difficulty, small loss, reduced step voltage, good waveform quality and the like, and particularly can solve the problem of unbalanced voltage caused by direct series connection of IGBT. Therefore, the MMC has good application prospect in a direct current power transmission and distribution system. For example, the first multi-terminal flexible direct current transmission project put into operation in the world, namely, the south Australian three-terminal flexible direct current transmission project, is the project application based on MMC topological structure.
However, the MMC contains a large number of sub-modules, and the switch model is complicated to build and is not suitable for stability analysis and calculation of the flexible direct current system, so that the research on the model suitable for the 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 modularized multi-level converter, and the technical scheme is as follows:
a modeling method suitable for stability analysis of a modularized multi-level converter is characterized in that MMC is equivalent to a controllable current source I eq And equivalent capacitance C eq And an equivalent conductance G parallel structure, the method comprising the steps of:
1) MeasuringDC voltage V during steady state normal operation of MMC dcn Ac side transmission power P acn And DC side power P dcn ；
2) Determining the number N of the submodules of the MMC bridge arm and the capacitance value C of the submodules 0 ；
3) Calculating parallel conductance
4) Calculating equivalent capacitance C eq ＝3C 0 /N；
5) Equivalent current source I eq ＝P ac /V dc ；
6) With current i through line inductance L L Constant power load equivalent capacitor C 2 Voltage v of (2) c2 MMC equivalent capacitance C 1 Voltage v of (2) c1 Writing differential equations for the state variable columns:
obtaining a state space matrix with small disturbance stability:
wherein R is line resistance, P represents power of constant power load CPL, P ac Represents MMC AC side transmission power at steady state, v c10 And v c20 Representing the initial voltage before MMC and constant power load disturbance, respectively.
The invention has the technical characteristics that: on the basis of fully considering MMC control performance, the invention provides a modeling method suitable for MMC small disturbance stability analysis. The method has the advantages that the complex MMC is equivalent to a structure that a controllable current source is connected with an equivalent capacitor and an equivalent conductivity in parallel, the dimension of a model is greatly reduced, the form is simple, and the stability analysis is convenient.
Drawings
FIG. 1 is a schematic diagram of MMC topology
Fig. 2 is a phase diagram of an MMC converter
FIG. 3 shows a model for MMC stability analysis according to the present invention
FIG. 4 is a schematic diagram of a simple DC system for supplying MMC to a constant power load
FIG. 5 shows the influence of MMC submodule capacitance parameters on feature roots
FIG. 6 is a graph showing 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 according to the present invention with reference to the accompanying drawings and specific embodiments.
As shown in FIG. 1, the MMC comprises three-phase 6 bridge arms, each bridge arm is composed of a bridge arm reactance L 0 And N sub-modules are connected in series, each sub-module is a half-bridge structure composed of all-control power electronic devices (IGBT), and the capacitor C 0 For submodule capacitance, each IGBT device is connected in anti-parallel with a diode.
In order to analyze the MMC characteristics deeply, the following analysis is performed 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 n u Sub-module, lower bridge arm input n l Sub-modules, n u +n l =n, the current through the upper arm is i u ＝i a /2+i diff Current i flowing through lower bridge arm l ＝-i a /2+i diff Wherein i is a For AC component, i diff Is a direct current component.
The voltage V of the upper bridge arm input submodule u Lower bridge arm voltage input submodule voltage V l A alternating current component i a And a direct current component i diff As state variables, it is possible to obtain from fig. 2:
similarly, the phase B and phase C dc voltage differential equations can be expressed as:
assume that
Is available in the form of
From FIG. 1, it can be derived
3i diff ＝-I dc (7)
Substituting (7) and (8) into (6) can obtain:
wherein I is dc The direction of the direct current is from MMC to direct current network, P ac Active power flowing to the direct current power grid for the MMC.
Therefore, an MMC DC side equivalent model can be obtained from the system angle, as shown in fig. 3, the MMC is characterized in that a capacitor and a controllable DC current source are connected in parallel at the DC side, wherein G represents the loss of the MMC converter, is generally smaller and can be omitted.
For the simple direct current system for supplying power to the constant power load by the MMC shown in FIG. 4, measures are taken, wherein R is the line resistance, L is the line inductance, and C 1 Represents MMC equivalent capacitance, C 2 Represents the equivalent capacitance of the constant power load CPL, P represents the power of the constant power load CPL, v c1 And v c2 Representing the voltage of the MMC and constant power load, respectively.
1) DC voltage V during MMC steady-state normal operation dcn Ac side transmission power P acn And DC side power P dcn 。
2) Determining the number N of the submodules of the MMC bridge arm and the capacitance value C of the submodules 0 。
3) Calculating parallel conductance
4) Calculating equivalent capacitance C 1 ＝3C 0 /N。
5) Equivalent current source I eq ＝P ac /V dc 。
With current i through line inductance L L Constant power load equivalent capacitor C 2 Voltage v of (2) c2 MMC equivalent capacitance C 1 Voltage v of (2) c1 Writing differential equations for the state variable columns can result in:
therefore, the state space matrix describing the stability of the small perturbation shown in FIG. 4 is
Wherein R is line resistance, L is line inductance, C 1 Represents MMC equivalent capacitance, C 2 Represents the equivalent capacitance of the constant power load CPL, P represents the power of the constant power load CPL, and P ac Represents MMC AC side transmission power at steady state, v c10 And v c20 Representing the initial voltage before MMC and constant power load disturbance, respectively.
The influence of the capacitance parameters of the MMC submodule on the characteristic root can be obtained through analysis (14) and is shown in fig. 5, and the influence of the line inductance parameters on the characteristic root is shown in fig. 6.
The modeling method suitable for MMC small disturbance stability analysis provided by the invention has the advantage that the tasks are all completed.
Claims (1)
1. A modeling method suitable for stability analysis of a modularized multi-level converter is characterized in that MMC is equivalent to a controllable current source I eq And equivalent capacitance C eq And an equivalent conductance G parallel structure, comprising the following steps:
1) DC voltage V during MMC steady-state normal operation dcn Ac side transmission power P acn And DC side power P dcn ；
2) Determining the number N of the submodules of the MMC bridge arm and the capacitance value C of the submodules 0 ；
3) Calculating parallel conductance
4) Calculating equivalent capacitance C eq ＝3C 0 /N；
5) Equivalent current source I eq ＝P ac /V dc ；
6) With current i through line inductance L L Constant power load equivalent capacitor C 2 Voltage v of (2) c2 MMC equivalent capacitance C 1 Voltage v of (2) c1 Writing differential equations for the state variable columns:
obtaining a state space matrix with small disturbance stability:
wherein R is line resistance, P represents power of constant power load CPL, P ac Represents MMC AC side transmission power at steady state, v c10 And v c20 Representing the initial voltage before MMC and constant power load disturbance, respectively.
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