CN107634671B - Asymmetric equivalent circuit model of modular multilevel converter bridge arm - Google Patents

Asymmetric equivalent circuit model of modular multilevel converter bridge arm Download PDF

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CN107634671B
CN107634671B CN201710867476.9A CN201710867476A CN107634671B CN 107634671 B CN107634671 B CN 107634671B CN 201710867476 A CN201710867476 A CN 201710867476A CN 107634671 B CN107634671 B CN 107634671B
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钱峰
伍双喜
杨银国
刘俊磊
罗钢
娄源媛
张子泳
吴国炳
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Electric Power Dispatch Control Center of Guangdong Power Grid Co Ltd
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Abstract

The invention provides a Modular Multilevel Converter (MMC) bridge arm asymmetric equivalent circuit model, because the Modular Multilevel Converter (MMC) bridge arm is easy to generate harmonic waves and circulating currents (mainly direct current components) when being asymmetric, two controlled sources are adopted to replace interference items generated by the asymmetric capacitance of a positive bridge arm module and a negative bridge arm module of the Modular Multilevel Converter (MMC), and the problem of follow-up analysis and problem solution are facilitated. The invention is used for making the relation between the system variables of the modular multilevel converter become clear when the Modular Multilevel Converter (MMC) is applied in the power system, which is very helpful for analyzing the characteristics of the variables and the influence on the system.

Description

Asymmetric equivalent circuit model of modular multilevel converter bridge arm
Technical Field
The invention belongs to the technical field of power electronics, and particularly relates to an asymmetric equivalent circuit model of a bridge arm of a Modular Multilevel Converter (MMC) equivalently replaced by a controlled source.
Background
A Modular Multilevel Converter (MMC) such a structure was originally proposed by r.marquardt at the university of defense army of the federal military in munich, germany, see fig. 1 of the specification, which mainly consists of six arms, typically even number of arms, each phase consisting of two arms, being a positive (upper) arm and a negative (lower) arm. Each bridge arm has the same structure and is formed by connecting N modules and an inductor in series, and each module is formed by a half bridge and a capacitor. The upper and lower tubes of the half-bridge work complementarily, when the upper tube is switched on, the lower tube is cut off, and the capacitor is connected in series to the circuit for charging or discharging; when the upper tube is cut off and the lower tube is opened, the capacitor is bypassed. Obviously, the number of capacitors connected in series in the circuit can be controlled by controlling the on and off of the switching tubes, and if the capacitance of each module capacitor is the same, and the voltage is the same and the average value is equal to Vd/N, the output voltage can be changed by controlling the access number of the capacitors.
The modular multilevel converter is built by power electronic devices, the resistance and the inductance of positive and negative bridge arms are difficult to be completely equal, errors exist inevitably, or when one bridge arm or a plurality of bridge arms in a model have faults in a special time, the number of the positive and negative bridge arms of the model is in an asymmetric state, harmonic waves and bridge arm circulation currents are easy to generate, the output quality is influenced by waveform distortion, the loss of the devices is increased, and the requirements on switching devices are improved.
Disclosure of Invention
In order to solve the problem of the above bridge arm asymmetry, the invention provides an asymmetric equivalent circuit model of a bridge arm of a modular multilevel converter, which is a modular multilevel converter bridge arm asymmetry model adopting a controlled constant current source to replace an interference term generated by asymmetric capacitance of a positive bridge arm module and a negative bridge arm module.
In order to solve the technical problems, the technical scheme of the invention is as follows:
a modularized multi-level converter bridge arm asymmetrical equivalent circuit model is divided into an alternating current circuit part and a direct current circuit part;
the DC circuit part comprises two DC linesCurrent source Vd/2, inductance LdcResistance RdcCapacitor CdcAnd a controlled source Sc2Two DC power supplies V connected in parallel to form a first moduled/2, inductance LdcResistance RdcAnd the first modules are connected in series;
the AC circuit part including a capacitor CacAnd a controlled source Sc1Second module and inductance L formed in parallelacResistance RacAnd a Load, a second module, an inductor LacResistance RacAnd Load series connections;
the AC/DC circuit part passes through the network T1、T2And (6) coupling connection.
When the number of the positive and negative bridge arms of the modular multilevel converter is in an asymmetric state, harmonic waves and bridge arm circulation currents are easy to generate, and the direct current component is mainly used. The equivalent circuit model adopts a controlled source to analyze the circulating current and harmonic waves generated in the asymmetric state of the bridge arm of the modular multilevel converter, so that the relation between system variables of the modular multilevel converter becomes clear, and the equivalent circuit model is very helpful for analyzing the characteristics of the variables and influencing the system.
Preferably, the network T1Is a double-ended network with the same port characteristics as an ideal transformer, the network T1Is a sine function and can transmit AC/DC signals, which is essentially an ideal model of an inverter, and has a transformation ratio of 1Network T2Is a double-ended network with the same port characteristics as an ideal transformer, the network T1Is a sine function and can transmit AC/DC signals, and is essentially an ideal model of the inverter, and the transformation ratio is 1:2Su(ii) a S aboveuIs only represented by a symbol, representing the network T1And T2Represents a function such that the ratio of the final network exhibits a sinusoidal variation.
Preferably, the capacitance Cdc、CacRespectively reflect the voltages ofThe sum and the difference of the capacitance and the voltage of the positive and negative bridge arms.
Preferably, a controlled source Sc1And Sc2The method replaces the interference term generated by the asymmetrical capacitance of the positive and negative bridge arm modules
Compared with the prior art, the technical scheme of the invention has the beneficial effects that: when the number of the positive and negative bridge arms of the modular multilevel converter is in an asymmetric state, harmonic waves and bridge arm circulation currents are easy to generate, and the direct current component is mainly used. The equivalent circuit model adopts a controlled source to analyze the circulating current and harmonic waves generated in the asymmetric state of the bridge arm of the modular multilevel converter, so that the relation between system variables of the modular multilevel converter becomes clear, and the equivalent circuit model is very helpful for analyzing the characteristics of the variables and influencing the system.
Drawings
Fig. 1 is a block diagram of a Modular Multilevel Converter (MMC) topology.
FIG. 2 is an MMC bridge arm asymmetric equivalent circuit diagram.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent; for the purpose of better illustrating the embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product;
it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted. The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
In fig. 1, each sub-module has two switching tubes connected in series, and as with a half-bridge converter, the upper and lower switching tubes work complementarily, when the upper tube is turned on, the lower tube is turned off, and at this time, the module capacitor C is connected to the circuit, and charging or discharging is performed according to the direction of the bridge arm current, for the bridge arm, a capacitor voltage is added, that is, a level, and at this time, the module state can be defined as "on", or "1"; when the upper tube is cut off, the lower tube is switched on, and the module capacitor C is bypassed by the lower tube, for the bridge arm, the capacitor voltage is reduced equivalently, namely, the level is reduced, and the module state can be defined as cut-off or 0; in addition, during the dead zone period or when the system stops working, the upper and lower switching tubes of the module are simultaneously cut off, at this time, the module is in a 'locking' stage, in the 'locking' state, if the direction of the bridge arm current is the same as the reference direction in fig. 1, namely, from top to bottom, the current charges the capacitor through the anti-parallel diode of the upper tube, the module is in an 'on' state, and if the current flows from bottom to top, the current flows through the anti-parallel diode of the lower tube, and the module is in an 'off' state. It can be seen that in the "latched" state, the module is in different operating states depending on the direction of current flow.
When the fluctuation of the capacitor voltage is not considered, each capacitor voltage is one level, the number of the levels of the positive and negative bridge arms which are conducted at a certain time is assumed to be P and Q respectively, and the number of the output levels is LevTable 1 shows all the states of a phase MMC when N ═ 4 (i.e., one leg consists of 4 modules and one inductor connected in series). In table 1, the first column P + Q indicates the sum of positive and negative bridge arm levels, i.e., the number of capacitors connected to the module, the second and third columns indicate the positive and negative bridge arm levels, the fourth column indicates the number of output levels, and the fifth column indicates the difference between the input level and the sum of the positive and negative bridge arm levels, which is indicated as
Figure BDA0001416431520000031
In connection with fig. 1, it is evident that this is the sum of the two inductor voltages.
TABLE 1 level diagram
Figure BDA0001416431520000041
As can be seen from table 1, there are 9(2N +1) levels in total for the MMC, but the levels experienced across the inductor are not the same. In the grey area of the table, the level to which the inductor is subjected is 0, which means that the number of levels of the positive and negative arms is the same as the input voltage at any time, and the system will not generate any voltage as long as the input voltage is unchangedAdditional circulation (circulation in addition to that generated by the system operating mechanisms, in which case the stability of the system is best, these levels, which are 5(N +1) in total, may be referred to as "standard base levels", if the output contains only these levels, then the system modulation is now called "base level" output modulation. The output level at any time when the number of capacitors connected to the positive and negative legs is N, it can also be seen from table 1 that the same state as the "standard base level" exists, these levels may be referred to as "non-standard base levels". when the system is in a "non-standard base level" output state, the system output is at a base level, however, the number of the levels connected into the positive and negative bridge arms is not N, and the difference value of the levels is added to the inductor, so that additional circulating current is generated, and the circulating current is i.addCan be expressed as:
Figure BDA0001416431520000051
in the formula:
DiffLevis the level applied across the inductor, with a value of 0, ± 1 … … ± n;
Vdis the supply voltage;
tonis the execution time;
n is the number of modules in one bridge arm;
l is an inductance value.
It is clear that if no destination is operating in a "non-standard base level" state, it will cause circulating currents outside the expectations to the system, thereby affecting the stability of the system. These "non-standard base levels" provide conditions for circulation control. It can also be seen that the smaller the absolute value of the output level, the greater the number of "non-standard base levels", the greater the range of circulation control, and that circulation loses the possibility of control when the absolute value of the output level is the largest.
In addition to the basic level, there are other N output levels, but in these states the number and input of the positive and negative bridge arm access levels are not equal, not equal to N, and the difference is added across the inductor, thus creating a creditExternal circulation, and expressed by equation (1), if fixed in this state, the system will not be stable. Such levels, which are N in total, are at positions spaced apart by a standard level, and are referred to as "insertion levels", and if the output level contains insertion levels, i.e., output 2N +1 levels, the system output is referred to as "full level". As can be seen from table 1, there are redundant states in which the number of levels applied across the inductor is odd and is symmetric with 0, and it is obvious that if the number of inductor levels is always greater than 0, a large circulating current is brought about, thereby affecting the stability of the system. If DiffLevIf > 0, then iaddIncrease if DiffLevIf < 0, then iaddDecrease, if during the duration of an inserted level, i during the time that the level is maintainedaddIs 0, and the Diff is controlled by the PWM method Lev1 and DiffLevFor-1 effect, if the duty cycle is 50%, i is maintained for one insertion leveladdThe average value is 0, if the PWM frequency is high enough, the quantity of the positive and negative bridge arm access levels is N within a certain time, so that the positive and negative bridge arm access levels are consistent with the standard basic level. This is the theoretical basis for the generation of the 2N +1 level. It is obvious that controlling the duty cycle of PWM controls the magnitude of the circulating current. The generation of 2N +1 level brings high frequency components to the system circulating current, and the peak value is determined by equation (1).
If the state of a module is defined by a switching function, the state of the ith module can be described as:
assuming that the capacitor voltages are balanced, that is, the capacitor voltages of the modules in the same bridge arm are the same at any time, the voltages (sum of the output voltages of the sub-modules) corresponding to the two ends of any sub-module stack have
Figure BDA0001416431520000062
Figure BDA0001416431520000063
In the formula:
vPuand vNuRepresenting the voltage of the u-phase upper and lower bridge arm sub-module stack,
vpcand vNcIs the sub-module capacitor voltage and is,
SPand SNIs the sum of the switching functions of the upper and lower bridge arm submodules.
Is apparent SPAnd SNThe value of (A) varies from 0 to N, which represents the number of open submodules of the upper and lower bridge arms, S is the sine if the modulation signal is the sinePAnd SNIs sinusoidal. Therefore, the upper and lower arms can be regarded as a system in which the number of input capacitances is continuous. Considering the symmetry of the upper and lower arms, one can define:
Figure BDA0001416431520000064
Figure BDA0001416431520000065
then, equations (3) and (4) may be modified respectively as follows:
Figure BDA0001416431520000067
in the formula:
as a switching function of the u phase, SmIs SuThe maximum amplitude of (d);
Figure BDA0001416431520000069
and
Figure BDA00014164315200000610
the sum of the u-phase positive and negative bridge arm module capacitance and voltage is respectively.
In FIG. 1, the analysis is performed by taking phase u as an example. Assuming that the module capacitors are voltage-sharing, the voltage-sharing can be obtained according to kirchhoff's law:
Figure BDA0001416431520000072
in the formula (I), the compound is shown in the specification,
iPuand iNuAre the currents flowing through the upper and lower bridge arms respectively,
rdis the equivalent direct current resistance of the bridge arm.
If a voltage is added to the positive and negative bridge arms at the same time, the output is not influenced, but the quantity of the access levels of the positive and negative bridge arms is not equal to N, and the system can generate additional circulation i as shown in the formula (1)addT in control formula (1) by controlling the amount of voltage inserted into the positive and negative armsonAnd DiffLevTo thereby control iaddFinally, the purpose of controlling the circulation is achieved. Since there is no redundant state at the time of outputting the maximum level, the control of the circulating current is limited because the circulating current cannot be controlled.
Any capacitive power of an MMC can be expressed as:
Figure BDA0001416431520000073
in the formula:
vciwhich represents the instantaneous value of the voltage of the capacitor,
Figure BDA0001416431520000074
is the average value of the voltage of the capacitor,
and C is the size value of the capacitor.
Taking u-phase as an example, the sum of all the capacitance powers of the positive and negative bridge arms can be respectively expressed as:
Figure BDA0001416431520000075
Figure BDA0001416431520000076
in the formula:
vPuiand vNuiCapacitance instantaneous voltages (i is 1,2 … … N) of the ith module of the positive and negative bridge arms respectively,
and
Figure BDA0001416431520000078
the sum of instantaneous voltages of all sub-module capacitors of upper and lower bridge arms is obtained, and when the capacitors of the positive and negative bridge arms are not greatly different, the average value is about Vd，
Andrespectively is the sum of the capacitance values of the positive bridge arm module and the negative bridge arm module.
According to the power balance relationship, the sum of the power consumed by each submodule capacitor of the bridge arm is inevitably equal to the product of the voltage of the submodule and the current flowing through the submodule capacitor, namely:
Figure BDA0001416431520000081
Figure BDA0001416431520000082
in the formula iPuAnd iNuRespectively representing the current flowing through the positive and negative bridge arm submodules.
Positive and negative bridge arm module capacitor planeMean values are respectively CPAnd CNThe average value of the capacitance and the voltage of the positive bridge arm module and the negative bridge arm module is respectively
Figure BDA0001416431520000083
And
Figure BDA00014164315200000811
hypothesis CP＝C，CN＝kcC，
Figure BDA0001416431520000084
(where k iscIs an arbitrary coefficient)
By sorting equations (13) to (14) and considering the relationship of the equation in the front, the following expression can be obtained:
Figure BDA0001416431520000085
Figure BDA0001416431520000086
Figure BDA0001416431520000087
in the formula:
iZufor inverter T2The current of (a) is measured,
iufor inverter T1The current of (2).
Let CΣC/N (the physical meaning is that when all the modules of the bridge arm are switched on, the equivalent capacitance of the bridge arm is large, and if the bridge arm is equivalent to a variable capacitance, C is∑Is the minimum value of this capacitance), Cdc＝2CΣ，Cac＝8CΣ，
Figure BDA0001416431520000088
According to the definition, and let Rdc＝2rd，Ldc＝2L，Rac＝rd/2，LacIs L/2, simultaneousThe equation in the front can then yield the following expression:
Figure BDA0001416431520000089
Figure BDA00014164315200000810
according to equations (17) - (21), an equivalent model under the condition of asymmetric positive and negative arms of the modular multilevel converter can be drawn, as shown in fig. 2. Network T in the figure1、T2For an ideal inverter equivalent model, CdcAnd CacThe voltage in (1) respectively reflects the sum and difference of capacitance and voltage of positive and negative bridge arms, Sc1And Sc2The interference terms generated by the asymmetrical capacitance of the positive and negative bridge arm modules are two controlled sources and are determined by an equation (18) and an equation (17).
The invention adopts a power electronic circuit model to simplify the asymmetric condition of a Modular Multilevel Converter (MMC) bridge arm, and is an equivalent circuit model which is built by adopting power electronic devices and meets the mathematical relationship through strict derivation. Harmonic waves and circulation currents (mainly direct current components) are easily generated when bridge arms of the Modular Multilevel Converter (MMC) are asymmetric, an equivalent circuit model is simplified by utilizing power electronic elements, and interference items generated by the asymmetric capacitance of positive and negative bridge arm modules of the Modular Multilevel Converter (MMC) are replaced by two controlled sources, so that the problem of follow-up analysis and the problem of solution are facilitated. The invention is used for making the relation between the system variables of the Modular Multilevel Converter (MMC) become clear when the Modular Multilevel Converter (MMC) is applied in the power system, which is very helpful for analyzing the characteristics of the variables and the influence on the system.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (4)

1. A modularized multi-level converter bridge arm asymmetrical equivalent circuit model is characterized in that the equivalent model is divided into an alternating current circuit part and a direct current circuit part;
the DC circuit part comprises two DC power supplies Vd/2, inductance LdcResistance RdcCapacitor CdcAnd a controlled source Sc2Two DC power supplies V connected in parallel to form a first moduled/2, inductance LdcResistance RdcAnd the first modules are connected in series;
the AC circuit part including a capacitor CacAnd a controlled source Sc1Second module and inductance L formed in parallelacResistance RacAnd a Load, a second module, an inductor LacResistance RacAnd Load series connections;
the AC/DC circuit part passes through the network T1、T2Coupling connection;
the physical meanings of the direct current power supply, the inductor, the resistor, the capacitor and the controlled source or the relation between the direct current power supply, the inductor, the resistor, the capacitor and the MMC actual circuit are as follows:
inductor Ldc：Ldc2L, L being the inductance value of MMC;
resistance Rdc：Rdc＝2rd，rdIs the equivalent direct current resistance of the bridge arm;
capacitor Cdc，Cdc＝2CΣ，C∑The physical meaning is that when all the modules of the bridge arm are switched on, the equivalent capacitance of the bridge arm is large, if the bridge arm is equivalent to a variable capacitance, C is∑Is the minimum value of this capacitance;
capacitor Cac：Cac＝8CΣ；
Inductor Lac：Lac＝L/2；
Resistance Rac：Rac＝rd/2；
Controlled source Sc2, controlled source Sc 1: the interference term generated by the asymmetry of the positive bridge arm module capacitor and the negative bridge arm module capacitor is determined by the following formula:
Figure FDA0002190750770000011
Figure FDA0002190750770000012
in the formula (I), the compound is shown in the specification,
Figure FDA0002190750770000021
Figure FDA0002190750770000022
and
Figure FDA0002190750770000023
the sum of instantaneous voltages of all sub-module capacitors of upper and lower bridge arms is respectively obtained;
iZuis an inverter T in MCC2Current of (i)uFor inverter T1The current of (a);
Figure FDA0002190750770000024
kcis an arbitrary coefficient, SuAs a switching function of the u phase, iNThe maximum circulating current which can be generated when the MMC positive and negative bridge arms are connected with zero level.
2. The modular multilevel converter bridge arm asymmetric equivalent circuit model according to claim 1, wherein the network T is1Is a double-ended network with the same port characteristics as an ideal transformer, the network T1Is a sine function and can transmit AC/DC signals, and the transformation ratio is
Figure FDA0002190750770000025
Network T2Is a portDouble-ended network with characteristics identical to an ideal transformer, the network T2The transformation ratio of (1: 2S) is a sine function and can transmit alternating current and direct current signalsu。
3. The modular multilevel converter bridge arm asymmetric equivalent circuit model according to claim 1, wherein the capacitor Cdc、CacThe voltages of the positive and negative bridge arms respectively reflect the sum and the difference of the capacitance voltages of the positive and negative bridge arms.
4. The modular multilevel converter bridge arm asymmetric equivalent circuit model according to claim 1, characterized in that a controlled source Sc1And Sc2The method replaces the interference term generated by the asymmetrical capacitance of the positive and negative bridge arm modules.
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