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

Abstract

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.

Description

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

technical field

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.

Background technique

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.

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.

SUMMARY OF THE INVENTION

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.

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:

Determine the main loop parameters of the system to be predicted;

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:

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,

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.

Further, adopt the following steps to obtain formula (1):

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;

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.

Further, step S1 specifically includes the following steps:

Step S11: Obtained according to Kirchhoff's current law, the current i _vj of the j-th phase bridge arm satisfies the following formula:

i _vj = i _pj - i _nj ;

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;

The common mode current of the bridge arm is defined as i _cirj , which means the j-th phase circulating current:

Step S12: Let the bridge arm current be expressed in the form of superposition of the following multiple frequency components:

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

respectively represent the amplitude and initial phase angle of the h-th harmonic of the jth-phase bridge arm current;

Take the average switching function:

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;

Let the collective mean value of the capacitor current be the product of the bridge arm current and the mean switching function:

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;

Step S13: In order to satisfy the steady-state operation, let the DC component of the capacitor current be 0, that is:

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,

Represents the initial phase angle of the fundamental frequency harmonic of the jth-phase bridge arm current;

Step S13: Use the following formula to calculate the characteristic expression of the AC side bias current in the MMC steady state:

In the formula, I _{cirj_1} represents the fundamental frequency component of the common mode current of the j-th phase bridge arm.

Further, step S2 specifically includes the following steps:

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:

表示第j相上桥臂的电压增量的基频分量，

表示第j相下桥臂的电压增量的基频分量，I_{pj_0}表示第j相上桥臂电流的直流分量，I_{nj_0}表示第j相下桥臂电流的直流分量；In the formula,

represents the fundamental frequency component of the voltage increment of the upper arm of the j-th phase,

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;

Step S22: Set the fundamental frequency of the j-phase AC output voltage as:

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,

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;

Distinguish the impedance of the upper and lower bridge arms, and the fundamental frequency fluctuation of the bridge arm voltage satisfies:

表示第j相上桥臂的电压基频分量，

表示第j相下桥臂的电压基频分量In the formula,

represents the voltage fundamental frequency component of the upper arm of the j-th phase,

Represents the voltage fundamental frequency component of the lower arm of the jth phase

Step S23: Considering step S21-step S22 comprehensively, for the upper bridge arm:

In the formula, I _{pj_1} represents the fundamental frequency component of the upper arm current of the j-th phase;

Then the calculation of the fundamental frequency of the upper arm current adopts the following formula:

in,

Then, the DC component of the upper arm current in the case of asymmetry is:

In the same way, the DC component of the lower bridge arm in the case of asymmetry is:

in,

Step S23: Obtain the expression of the DC bias current of the AC side under the condition of asymmetric parameters of the bridge arm:

Compared with the prior art, the present invention has the following beneficial effects:

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. 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.

Description of drawings

FIG. 1 is a schematic flowchart of a method according to an embodiment of the present invention.

Figure 2 shows a typical topology of a three-phase MMC.

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.

Detailed ways

The present invention will be further described below with reference to the accompanying drawings and embodiments.

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.

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.

This embodiment specifically includes the following steps:

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.);

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:

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,

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.

In the present embodiment, the following steps are adopted to obtain formula (1):

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;

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.

In this embodiment, step S1 specifically includes the following steps:

Step S11: Obtained according to Kirchhoff's current law, the current i _vj of the j-th phase bridge arm satisfies the following formula:

i _vj = i _pj - i _nj ;

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;

The common mode current of the bridge arm is defined as i _cirj , which means the j-th phase circulating current:

Step S12: Let the bridge arm current be expressed in the form of superposition of the following multiple frequency components:

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

respectively represent the amplitude and initial phase angle of the h-th harmonic of the jth-phase bridge arm current;

Take the average switching function:

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;

Let the collective mean value of the capacitor current be the product of the bridge arm current and the mean switching function:

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;

Step S13: In order to satisfy the steady-state operation, let the DC component of the capacitor current be 0, that is:

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,

Represents the initial phase angle of the fundamental frequency harmonic of the jth-phase bridge arm current;

Step S13: Use the following formula to calculate the characteristic expression of the AC side bias current in the MMC steady state:

In the formula, I _{cirj_1} represents the fundamental frequency component of the common mode current of the j-th phase bridge arm.

Step S2 specifically includes the following steps:

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:

表示第j相上桥臂的电压增量的基频分量，

表示第j相下桥臂的电压增量的基频分量，I_{pj_0}表示第j相上桥臂电流的直流分量，I_{nj_0}表示第j相下桥臂电流的直流分量；In the formula,

represents the fundamental frequency component of the voltage increment of the upper arm of the j-th phase,

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;

Step S22: Set the fundamental frequency of the j-phase AC output voltage as:

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,

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;

Distinguish the impedance of the upper and lower bridge arms, and the fundamental frequency fluctuation of the bridge arm voltage satisfies:

表示第j相上桥臂的电压基频分量，

表示第j相下桥臂的电压基频分量；In the formula,

represents the voltage fundamental frequency component of the upper arm of the j-th phase,

represents the voltage fundamental frequency component of the lower arm of the jth phase;

Step S23: Considering step S21-step S22 comprehensively, for the upper bridge arm:

In the formula, I _{pj_1} represents the fundamental frequency component of the upper arm current of the j-th phase;

Then the calculation of the fundamental frequency of the upper arm current adopts the following formula:

in,

Then, the DC component of the upper arm current in the case of asymmetry is:

In the same way, the DC component of the lower bridge arm in the case of asymmetry is:

in,

Step S23: Obtain the expression of the DC bias current of the AC side under the condition of asymmetric parameters of the bridge arm:

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.

Table 1 Model main circuit parameters

parameter name parameter value AC side rated voltage/kV 220 DC side rated voltage/kV ±320 Submodule capacitance/mF 10 Bridge arm reactor/mH 50 Smoothing reactor/mH 50 Bridge arm equivalent resistance/R 0.1 Number of bridge arm submodules 20 Nominal modulation ratio 0.85

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

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.

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. an AC side DC bias current prediction method under asymmetric impedance of MMC bridge arm, is characterized in that, Determine the main loop parameters of the system to be predicted; 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:

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,

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. 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): 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; 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. 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: Step S11: Obtained according to Kirchhoff's current law, the current i _vj of the j-th phase bridge arm satisfies the following formula: i _vj = i _pj - i _nj ; 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; The common mode current of the bridge arm is defined as i _cirj , which means the j-th phase circulating current:

Step S12: Let the bridge arm current be expressed in the form of superposition of the following multiple frequency components:

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

respectively represent the amplitude and initial phase angle of the h-th harmonic of the jth-phase bridge arm current; Take the average switching function:

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; Let the collective mean value of the capacitor current be the product of the bridge arm current and the mean switching function:

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; Step S13: In order to satisfy the steady-state operation, let the DC component of the capacitor current be 0, that is:

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,

Represents the initial phase angle of the fundamental frequency harmonic of the jth-phase bridge arm current; Step S14: Use the following formula to calculate the characteristic expression of the AC side bias current in the MMC steady state:

In the formula, I _{cirj_1} represents the fundamental frequency component of the common mode current of the j-th phase bridge arm. 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: 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:

In the formula,

represents the fundamental frequency component of the voltage increment of the upper arm of the j-th phase,

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,

Represents the initial phase angle of the fundamental frequency harmonic of the jth-phase bridge arm current; Step S22: Set the fundamental frequency of the j-phase AC output voltage as:

In the formula,

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; Distinguish the impedance of the upper and lower bridge arms, and the fundamental frequency fluctuation of the bridge arm voltage satisfies:

In the formula,

represents the voltage fundamental frequency component of the upper arm of the j-th phase,

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; Step S23: Considering step S21-step S22 comprehensively, for the upper bridge arm:

In the formula, I _{pj_1} represents the fundamental frequency component of the upper arm current of the j-th phase; Then the calculation of the fundamental frequency of the upper arm current adopts the following formula:

in,

Then, the DC component of the upper arm current in the case of asymmetry is:

In the same way, the DC component of the lower bridge arm in the case of asymmetry is:

in,

Step S24: Obtain the expression of the DC bias current of the AC side under the condition of asymmetric parameters of the bridge arm:

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