CN110688778A - AC side DC bias current prediction method under MMC bridge arm impedance asymmetry - Google Patents
AC side DC bias current prediction method under MMC bridge arm impedance asymmetry Download PDFInfo
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Abstract
The invention relates to a method for predicting direct current bias current on an alternating current side under the condition of asymmetric bridge arm impedance of an MMC (modular multilevel converter). firstly, main loop parameters of a system to be predicted are determined; then analyzing the bias current characteristic of the MMC in the steady state to obtain a characteristic expression of the bias current of the alternating current side of the MMC in the steady state; and finally, analyzing the characteristic of the bias current under the condition of asymmetric bridge arm parameters to obtain the direct-current bias current on the alternating-current side under the condition of asymmetric bridge arm parameters. The invention can effectively predict the direct current on the alternating current side.
Description
Technical Field
The invention relates to the technical field of direct current transmission, in particular to a method for predicting direct current bias current on an alternating current side under asymmetric bridge arm impedance of an MMC (modular multilevel converter).
Background
The direct current transmission technology is widely applied and brings huge economic benefits, and meanwhile, certain technical and management new problems are generated, and new challenges are brought to the operation of an alternating current and direct current system. Among them, dc magnetic biasing is a new problem in the development of the current power system. By dc bias, it is meant that dc components occurring for some reason cause dc magnetization of the ferromagnetic material until saturation. Therefore, in a power system, such as a power transformer, a current transformer, and the like, which are designed based on the principle of electromagnetic induction, power equipment having an iron core that constitutes a main magnetic flux is affected by the problem of dc magnetic bias.
The topology structure adopted by the VSC-HVDC project which is actually put into operation mainly comprises a two-level topology structure, a three-level topology structure and a modular multi-level topology structure. The Modular Multilevel Converter (MMC) can better solve the inherent defects of the two-level Converter and the three-level Converter, and has the advantages of low loss, small harmonic of output voltage and the like, thereby being concerned by the industry. However, the existing bias model aims at two bias sources of magnetic storm generated by single-pole earth loop operation and solar blackson motion in the traditional power transmission engineering. In practical engineering, due to numerous factors such as manufacturing process, manufacturing materials and operation conditions, parameters of an upper bridge arm and a lower bridge arm of the MMC have the problem of incomplete symmetry, and direct current bias of alternating current side current is caused, so that direct current bias of the transformer is caused. With the increase of the operation life of the system, the change degree of the bridge arm parameters is increased, so that the magnetic bias problem under the condition is long-term and can be more serious along with the time, however, an effective direct current bias current prediction method is not provided in the prior art for the condition that the bridge arm parameters of the MMC-HVDC system are asymmetric.
Disclosure of Invention
In view of this, the present invention provides a method for predicting an ac-side dc bias current under asymmetric bridge arm impedance of an MMC bridge, which can effectively predict a dc current on an ac side.
The invention is realized by adopting the following scheme: a method for predicting direct current bias current on an alternating current side under asymmetric bridge arm impedance of an MMC (modular multilevel converter) comprises the following steps:
determining main loop parameters of a system to be predicted;
according to main loop parameters of a system to be predicted, calculating the direct current bias current on the alternating current side under the condition of asymmetric bridge arm parameters by adopting a formula (1):
in the formula Ivj_0Representing j-phase alternating-current side direct-current bias current under the condition of asymmetric bridge arm parameters; u shapedcRepresenting the DC side voltage, RpjRepresents the equivalent resistance of the j-th phase upper arm, RnjRepresenting the equivalent resistance of a j-th phase lower bridge arm; wherein the content of the first and second substances,
in the formula, N represents the number of sub-modules on each bridge arm, LpjRepresenting bridge arm inductance of a j-th phase upper bridge arm, omega representing power grid angular frequency, C representing capacitance in the sub-module, LnjAnd the bridge arm inductance of the j-th phase lower bridge arm is shown.
Further, the following procedure was employed to obtain formula (1):
step S1: analyzing the bias current characteristic of the MMC in a steady state to obtain a characteristic expression of the alternating-current side bias current of the MMC in the steady state;
step S2: and analyzing the characteristic of the bias current under the condition of asymmetric bridge arm parameters, and obtaining the direct-current bias current on the alternating-current side under the condition of asymmetric bridge arm parameters according to the characteristic expression of the bias current on the alternating-current side under the stable state of the MMC obtained in the step S1.
Further, step S1 specifically includes the following steps:
step S11: the current i of the j-th phase bridge arm is obtained according to kirchhoff current lawvjSatisfies the following formula:
ivj＝ipj-inj；
in the formula ipjRepresenting the upper arm current of the j-th phase, injIs shown asj-phase lower bridge arm current;
defining bridge arm common mode current as icirjI.e. represents the j-th phase circulation:
step S12: let the bridge arm current be represented in the form of a superposition of the following frequency components:
in the formula Ipj_0Representing the direct component of the bridge arm current in the j-th phase, Inj_0Representing the direct component of the j-th lower arm current, Ipj_hAnd
respectively representing the amplitude and the initial phase angle of h harmonic of the j-th phase bridge arm current;
averaging the switching function:
in the formula, Spj、SnjRespectively representing the switching functions of the upper and lower bridge arms of the j phase, m is the voltage modulation ratio, thetajThe phase angle is the jth equivalent electromotive force initial phase angle of the alternating current system;
let the collective average value of the capacitance currents be the product of the bridge arm current and the average switching function:
in the formula ic,pjRepresenting the mean value of the capacitor current set of the sub-modules of the upper bridge arm of the j phasec,njRepresenting the average value of the capacitance and current set of the jth lower bridge arm submodule;
step S13: to satisfy steady state operation, let the dc component of the capacitor current be 0, i.e.:
in the formula Ipj_1Representing the amplitude, I, of the fundamental frequency harmonic of the bridge arm current in the j-th phasenj_1Showing the amplitude of the fundamental frequency harmonic of the j-th lower bridge arm current,
representing an initial phase angle of a current fundamental frequency harmonic of a j-th phase bridge arm;
step S13: calculating a characteristic expression of the alternating-current side bias current under the MMC steady state by adopting the following formula:
in the formula Icirj_1And the fundamental frequency component of the common-mode current of the j-th phase bridge arm is represented.
Further, step S2 specifically includes the following steps:
step S21: only considering the direct current 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 (I), the compound is shown in the specification,
the fundamental frequency component representing the voltage increment of the j-th upper leg,
fundamental frequency component, I, representing voltage increment of the j-th lower legpj_0Representing the direct component of the bridge arm current in the j-th phase, Inj_0Representing a direct current component of a j-th phase lower bridge arm current;
step S22: setting the fundamental frequency quantity of j alternating current output voltage as follows:
in the formula (I), the compound is shown in the specification,
a fundamental frequency component representing a j-th alternating current output voltage; u represents the amplitude of the fundamental frequency voltage of the j-th alternating current output voltage;
the impedances of the upper bridge arm and the lower bridge arm are distinguished, and the fundamental frequency fluctuation of the bridge arm voltage meets the following conditions:
in the formula (I), the compound is shown in the specification,the fundamental frequency component of the voltage of the upper bridge arm of the j-th phase is shown,representing voltage fundamental frequency component of j-th lower bridge arm
Step S23: considering step S21-step S22 comprehensively, for the upper arm there are:
in the formula Ipj_1Representing the fundamental frequency component of the bridge arm current on the j phase;
the calculation of the fundamental frequency quantity of the upper bridge arm current adopts the following formula:
wherein the content of the first and second substances,
then, the dc component of the upper arm current in the asymmetric case is:
similarly, the direct current component of the lower bridge arm under the asymmetric condition is as follows:
wherein the content of the first and second substances,
step S23: obtaining an expression of the DC bias current at the AC side under the condition of asymmetric bridge arm parameters as follows:
compared with the prior art, the invention has the following beneficial effects:
1. according to the invention, the direct current bias current characteristic of the alternating current side under the MMC-HVDC steady state is obtained based on the sub-module capacitance current characteristic, the mutual conversion of the circulation fundamental frequency quantity and the alternating current direct current quantity is realized, and the method is suitable for any scene that direct current appears on the alternating current side due to the existence of circulation fundamental frequency.
2. The invention provides an alternating-current side direct-current bias current equivalent method expressed by system parameters by considering the condition that the parameters of a bridge arm of the modular multilevel converter are asymmetric, and no additional monitoring equipment is needed, so that the simplification of a system valve side is realized when the direct-current bias problem of a transformer is researched in the scene. For the direct current transmission project to be built, when system parameters are determined, the method can be used for determining angle auxiliary parameters for reducing the influence of direct current magnetic biasing; for the direct current transmission project which is put into operation, the method can be used for evaluating the direct current magnetic biasing influence of the transformer under the condition of asymmetric bridge arm parameters and judging the necessity of magnetic biasing suppression.
Drawings
FIG. 1 is a schematic flow chart of a method according to an embodiment of the present invention.
FIG. 2 is a three-phase MMC typical topology.
Fig. 3 is a schematic diagram illustrating a relationship between the number of MMC sub-modules and the bias current according to an embodiment of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, 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, the present embodiment provides a method for predicting an ac-side dc bias current under an asymmetric bridge arm impedance of an MMC, where a typical topology of a typical three-phase MMC is shown in fig. 2. In the figure, the submodules adopt a half-bridge structure, and each bridge arm consists of N identical Submodules (SM) and bridge arm inductors L0And an equivalent resistance R0Are connected in series. The positive direction of each electrical quantity is defined as shown in the figure. Points O and O' respectively represent zero potential reference points on the direct current side and the alternating current side, and v represents an alternating current outlet of the MMC. Ideal voltage source u for AC systemsjEquivalence is performed (j ═ a, b, and c, and represents three ac phases). AC system via coupling reactor LacIs connected to the MMC alternating current outlet. u. ofvjRepresenting the voltage at j AC outlet, ivjRepresenting the j cross-current side current. i.e. irjIndicates the bridge arm current (r ═ p indicates the upper bridge arm, r ═ n indicates the lower bridge arm), u indicates the bridge arm currentrjRepresenting the sum of the voltages of all sub-modules on a certain bridge arm. U shapedcDenotes the DC side voltage, IdcRepresenting the dc transmission current.
The embodiment specifically comprises the following steps:
determining main loop parameters (including the voltage modulation ratio of the system, the system voltage of an alternating current side, bridge arm impedance, capacitor parameters, the number of sub-modules and the like) of the system to be predicted;
according to main loop parameters of a system to be predicted, calculating the direct current bias current on the alternating current side under the condition of asymmetric bridge arm parameters by adopting a formula (1):
in the formula Ivj_0Representing j-phase alternating-current side direct-current bias current under the condition of asymmetric bridge arm parameters; u shapedcRepresenting the DC side voltage, RpjRepresents the equivalent resistance of the j-th phase upper arm, RnjRepresenting the equivalent resistance of a j-th phase lower bridge arm; wherein the content of the first and second substances,
in the formula, N represents the number of sub-modules on each bridge arm, LpjRepresenting bridge arm inductance of a j-th phase upper bridge arm, omega representing power grid angular frequency, C representing capacitance in the sub-module, LnjAnd the bridge arm inductance of the j-th phase lower bridge arm is shown.
In this example, the following procedure was used to obtain formula (1):
step S1: analyzing the bias current characteristic of the MMC in a steady state to obtain a characteristic expression of the alternating-current side bias current of the MMC in the steady state;
step S2: and analyzing the characteristic of the bias current under the condition of asymmetric bridge arm parameters, and obtaining the direct-current bias current on the alternating-current side under the condition of asymmetric bridge arm parameters according to the characteristic expression of the bias current on the alternating-current side under the stable state of the MMC obtained in the step S1.
In this embodiment, step S1 specifically includes the following steps:
step S11: the current i of the j-th phase bridge arm is obtained according to kirchhoff current lawvjSatisfies the following formula:
ivj＝ipj-inj；
in the formula ipjRepresenting the upper arm current of the j-th phase, injRepresenting the j-th phase lower bridge arm current;
defining bridge arm common mode current as icirjI.e. represents the j-th phase circulation:
step S12: let the bridge arm current be represented in the form of a superposition of the following frequency components:
in the formula Ipj_0Representing the direct component of the bridge arm current in the j-th phase, Inj_0Representing the direct component of the j-th lower arm current, Ipj_hAnd
respectively representing the amplitude and the initial phase angle of h harmonic of the j-th phase bridge arm current;
averaging the switching function:
in the formula, Spj、SnjRespectively representing the switching functions of the upper and lower bridge arms of the j phase, m is the voltage modulation ratio, thetajThe phase angle is the jth equivalent electromotive force initial phase angle of the alternating current system;
let the collective average value of the capacitance currents be the product of the bridge arm current and the average switching function:
in the formula ic,pjRepresenting the mean value of the capacitor current set of the sub-modules of the upper bridge arm of the j phasec,njRepresenting the average value of the capacitance and current set of the jth lower bridge arm submodule;
step S13: to satisfy steady state operation, let the dc component of the capacitor current be 0, i.e.:
in the formula Ipj_1Representing the amplitude, I, of the fundamental frequency harmonic of the bridge arm current in the j-th phasenj_1Showing the amplitude of the fundamental frequency harmonic of the j-th lower bridge arm current,
representing an initial phase angle of a current fundamental frequency harmonic of a j-th phase bridge arm;
step S13: calculating a characteristic expression of the alternating-current side bias current under the MMC steady state by adopting the following formula:
in the formula Icirj_1And the fundamental frequency component of the common-mode current of the j-th phase bridge arm is represented.
Step S2 specifically includes the following steps:
step S21: to calculate the alternating-current side offset current under the asymmetric MMC parameters, the fundamental frequency quantity of the current needs to be obtained first. To simplify the analysis, only the dc component and the fundamental frequency component in the bridge arm current are considered, and the fundamental frequency increment of the bridge arm voltage is expressed as:
in the formula (I), the compound is shown in the specification,
the fundamental frequency component representing the voltage increment of the j-th upper leg,
fundamental frequency component, I, representing voltage increment of the j-th lower legpj_0Representing the direct component of the bridge arm current in the j-th phase, Inj_0Representing a direct current component of a j-th phase lower bridge arm current;
step S22: setting the fundamental frequency quantity of j alternating current output voltage as follows:
in the formula (I), the compound is shown in the specification,
a fundamental frequency component representing a j-th alternating current output voltage; u represents the amplitude of the fundamental frequency voltage of the j-th alternating current output voltage;
the impedances of the upper bridge arm and the lower bridge arm are distinguished, and the fundamental frequency fluctuation of the bridge arm voltage meets the following conditions:
in the formula (I), the compound is shown in the specification,
the fundamental frequency component of the voltage of the upper bridge arm of the j-th phase is shown,
representing a voltage fundamental frequency component of a j-th phase lower bridge arm;
step S23: considering step S21-step S22 comprehensively, for the upper arm there are:
in the formula Ipj_1Representing the fundamental frequency component of the bridge arm current on the j phase;
the calculation of the fundamental frequency quantity of the upper bridge arm current adopts the following formula:
wherein the content of the first and second substances,
then, the dc component of the upper arm current in the asymmetric case is:
similarly, the direct current component of the lower bridge arm under the asymmetric condition is as follows:
wherein the content of the first and second substances,
step S23: obtaining an expression of the DC bias current at the AC side under the condition of asymmetric bridge arm parameters as follows:
specifically, in order to verify the effectiveness of the embodiment, the embodiment builds a true dual-stage MMC direct-current power transmission system electromagnetic transient model based on the PSCAD/EMTDC, and the parameters of a main loop of the model are shown in table 1. Changing parameters of the bridge arm reactor on the phase A, keeping the other bridge arm parameters as reference values, performing multiple sets of simulation, recording direct current components of output current on an alternating current side, comparing the recorded simulation values of the bias current with the calculated values obtained by the method of the embodiment, and as shown in table 2, the error is only 0.03%, so that the accuracy of the equivalent model of the direct current bias current on the alternating current side under the condition of asymmetric bridge arm parameters provided by the embodiment is proved.
TABLE 1 model major Loop parameters
| Parameter name | Parameter value |
| Rated voltage/kV at AC side | 220 |
| Rated voltage of DC side/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 sub-modules | 20 |
| Rated modulation ratio | 0.85 |
TABLE 2 partial results of comparison of AC side DC bias current analytic calculation value with simulated value
When designing the direct current transmission project parameters to be built, the method of the embodiment is used to assist the determination of the number of the sub-modules as an example. Considering the possible asymmetric condition of the bridge arm parameters that the reactance value of the upper bridge arm is higher than the reference value by 10 percent, the number of the submodules is taken as a variable in the method, and other parameters are unchanged. The variation of the MMC AC side bias current is obtained as shown in figure 3. When the number of the sub-modules is less than 150, the bias current increases with the increase of the number of the sub-modules, and particularly when 120 < N < 150, the increase speed of the bias current is increased. Therefore, considering the magnetic biasing problem caused by the asymmetric condition of the bridge arm parameters, which can occur after the engineering investment, the number of the sub-modules is not more, and the better.
The foregoing is directed to preferred embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention.
Claims (4)
1. A method for predicting DC bias current at AC side under asymmetric bridge arm impedance of MMC is characterized in that,
determining main loop parameters of a system to be predicted;
according to main loop parameters of a system to be predicted, calculating the direct current bias current on the alternating current side under the condition of asymmetric bridge arm parameters by adopting a formula (1):
in the formula Ivj_0Representing j-phase alternating-current side direct-current bias current under the condition of asymmetric bridge arm parameters; u shapedcRepresenting the DC side voltage, RpjRepresents the equivalent resistance of the j-th phase upper arm, RnjRepresenting the equivalent resistance of a j-th phase lower bridge arm; wherein the content of the first and second substances,
in the formula, N represents the number of sub-modules on each bridge arm, LpjRepresenting bridge arm inductance of a j-th phase upper bridge arm, omega representing power grid angular frequency, C representing capacitance in the sub-module, LnjAnd the bridge arm inductance of the j-th phase lower bridge arm is shown.
2. The MMC bridge arm impedance asymmetry based AC-side DC bias current prediction method of claim 1, wherein the following steps are adopted to obtain formula (1):
step S1: analyzing the bias current characteristic of the MMC in a steady state to obtain a characteristic expression of the alternating-current side bias current of the MMC in the steady state;
step S2: and analyzing the characteristic of the bias current under the condition of asymmetric bridge arm parameters, and obtaining the direct-current bias current on the alternating-current side under the condition of asymmetric bridge arm parameters according to the characteristic expression of the bias current on the alternating-current side under the stable state of the MMC obtained in the step S1.
3. The MMC bridge arm impedance asymmetric alternating-current side direct-current bias current prediction method according to claim 2, wherein step S1 specifically includes the following steps:
step S11: the current i of the j-th phase bridge arm is obtained according to kirchhoff current lawvjSatisfies the following formula:
ivj＝ipj-inj；
in the formula ipjRepresenting the upper arm current of the j-th phase, injRepresenting the j-th phase lower bridge arm current;
defining bridge arm common mode current as icirjI.e. represents the j-th phase circulation:
step S12: let the bridge arm current be represented in the form of a superposition of the following frequency components:
in the formula Ipj_0Representing the upper arm of the j-th phaseDirect component of the current, Inj_0Representing the direct component of the j-th lower arm current, Ipj_hAnd
respectively representing the amplitude and the initial phase angle of h harmonic of the j-th phase bridge arm current;
averaging the switching function:
in the formula, Spj、SnjRespectively representing the switching functions of the upper and lower bridge arms of the j phase, m is the voltage modulation ratio, thetajThe phase angle is the jth equivalent electromotive force initial phase angle of the alternating current system;
let the collective average value of the capacitance currents be the product of the bridge arm current and the average switching function:
in the formula ic,pjRepresenting the mean value of the capacitor current set of the sub-modules of the upper bridge arm of the j phasec,njRepresenting the average value of the capacitance and current set of the jth lower bridge arm submodule;
step S13: to satisfy steady state operation, let the dc component of the capacitor current be 0, i.e.:
in the formula Ipj_1Representing the amplitude, I, of the fundamental frequency harmonic of the bridge arm current in the j-th phasenj_1Showing the amplitude of the fundamental frequency harmonic of the j-th lower bridge arm current,
representing an initial phase angle of a current fundamental frequency harmonic of a j-th phase bridge arm;
step S13: calculating a characteristic expression of the alternating-current side bias current under the MMC steady state by adopting the following formula:
in the formula Icirj_1And the fundamental frequency component of the common-mode current of the j-th phase bridge arm is represented.
4. The MMC bridge arm impedance asymmetric alternating-current side direct-current bias current prediction method according to claim 2, wherein step S2 specifically includes the following steps:
step S21: only considering the direct current 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 (I), the compound is shown in the specification,
the fundamental frequency component representing the voltage increment of the j-th upper leg,
fundamental frequency component, I, representing voltage increment of the j-th lower legpj_0Representing the direct component of the bridge arm current in the j-th phase, Inj_0Representing a direct current component of a j-th phase lower bridge arm current;
step S22: setting the fundamental frequency quantity of j alternating current output voltage as follows:
in the formula (I), the compound is shown in the specification,
a fundamental frequency component representing a j-th alternating current output voltage; u represents the amplitude of the fundamental frequency voltage of the j-th alternating current output voltage;
the impedances of the upper bridge arm and the lower bridge arm are distinguished, and the fundamental frequency fluctuation of the bridge arm voltage meets the following conditions:
in the formula (I), the compound is shown in the specification,the fundamental frequency component of the voltage of the upper bridge arm of the j-th phase is shown,
representing a voltage fundamental frequency component of a j-th phase lower bridge arm;
step S23: considering step S21-step S22 comprehensively, for the upper arm there are:
in the formula Ipj_1Representing the fundamental frequency component of the bridge arm current on the j phase;
the calculation of the fundamental frequency quantity of the upper bridge arm current adopts the following formula:
wherein the content of the first and second substances,
then, the dc component of the upper arm current in the asymmetric case is:
similarly, the direct current component of the lower bridge arm under the asymmetric condition is as follows:
wherein the content of the first and second substances,
step S23: obtaining an expression of the DC bias current at the AC side under the condition of asymmetric bridge arm parameters as follows:
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