CN111999595A - MMC-HVDC power transmission line fault judgment method - Google Patents
MMC-HVDC power transmission line fault judgment method Download PDFInfo
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Abstract
The invention relates to a fault judgment method for an MMC-HVDC power transmission line, which is technically characterized by comprising the following steps of: the invention adopts discrete wavelet analysis to extract the high-frequency voltage effective values of the direct current side and the converter side of the line smoothing reactor and compares the high-frequency voltage effective values so as to distinguish the faults inside and outside the area. And then, acquiring voltage and current data of the single-side protection unit by using a K-means clustering algorithm and a short time window after the direct-current line fault occurs in different fault types and different fault positions, carrying out clustering analysis on the voltage and current data of the single-side protection unit, acquiring the mass center and the threshold of the voltage and current data of the single-side protection unit, and determining corresponding protection criteria through training to realize fault pole selection. The method can quickly and accurately detect the fault of the MMC-HVDC power transmission line without being influenced by the fault position and the transition resistance, and identify the fault type.
Description
Technical Field
The invention belongs to the technical field of power transmission lines, and particularly relates to a fault judgment method for an MMC-HVDC power transmission line.
Background
In recent years, development and utilization of renewable energy sources represented by wind energy and solar energy are accelerated in China, and the proportion of clean energy sources is continuously increased. Compared with the traditional direct-current transmission technology, the flexible direct-current transmission system can independently adjust active power and reactive power, has no problem of commutation failure, and is very suitable for large-scale and long-distance transmission of renewable energy.
The current converter adopted by the flexible direct current system comprises a two-level or three-level voltage source type current converter based on a Pulse Width Modulation (PWM) technology and a modular multilevel current converter (MMC) based on a step wave modulation technology. The two-level or three-level converter has high switching frequency, high switching loss and poor voltage waveform, and is mainly used for low voltage grades. At present, in a flexible direct-current power grid, particularly a direct-current power grid with a higher voltage level, a modular multilevel converter is widely applied.
The fault characteristics of the MMC-HVDC system are closely related to the primary system structure and the control system, and the electrical quantities of the direct current transmission line, such as current and voltage, present different characteristics when different types of systems have faults. At present, an MMC-HVDC system which is put into operation generally adopts a symmetrical monopole main wiring mode, and a single converter forms a natural bipolar system. The grounding mode is divided into AC side grounding and DC side grounding through a clamping resistor.
The MMC-HVDC transmission line adopting the mode of grounding at the direct current side through a clamping resistor is composed of half-bridge sub-modules, as shown in figure 2. The system mainly comprises an MMC rectifier station, an inverter station, a direct-current transmission line and smoothing reactors at two ends of a line, wherein an M side is a rectifier side, an N side is an inverter side, and each bridge arm of the MMC consists of a plurality of sub-modules and a bridge arm reactance. The three-phase MMC topology is shown in fig. 3, and includes 6 bridge arms, and the upper and lower bridge arms of each phase are combined together to form a phase unit.
The working state of the sub-module can be changed by controlling the on and off of the IGBT in the sub-module, and the sub-module has 3 working states and 6 working modes in total through analysis. In actual operation, the MMC needs to keep the voltage of a direct current side constant, and requires that the number of submodules in an input state at each moment in each phase unit is equal and is kept unchanged; three-phase ac voltage is required to be output from the ac side, and is generally realized by a Pulse Width Modulation (PWM) method and a step-wave modulation method. With the increase of the number of the sub-modules of the modular multilevel converter, the recent level approximation modulation mode can output quite ideal alternating current voltage waveform, and the modulation mode is more and more widely applied.
The fault of the MMC-HVDC power transmission line can be divided into an alternating current system fault and a direct current system fault. When an alternating current system fault occurs, the positive sequence voltage of an alternating current power grid drops greatly, and the current of a direct current system drops; if the fault is an asymmetric fault, the direct current voltage and the current are subjected to frequency doubling fluctuation, and the fluctuation can be eliminated and suppressed by improving a control strategy.
For dc system faults, there are a single-pole ground fault and a double-pole short circuit fault. For a single-pole ground fault, due to the presence of the clamping resistor in the dc system, the voltage drop to ground of the faulted pole is zero and the voltage to ground of the non-faulted pole is increased by a factor of two. The bridge arm current rises to some extent, but the overcurrent degree is not large, the direct current can be quickly recovered to be normal, and the direct current voltage fluctuates for a short time due to the charging and discharging processes of the direct current circuit. For bipolar grounding short circuit, the direct current voltage is rapidly reduced to zero, the direct current is rapidly increased, and can be increased to be several times of the rated current, and finally tends to be stable. Therefore, the bipolar grounding short-circuit fault is the most serious fault type, and has great influence on the safe, reliable and stable operation of the power system.
However, aiming at the existing MMC-HVDC transmission line, a method for accurately identifying a fault area and judging the fault type is not found, so that the maintenance and the overhaul of the MMC-HVDC transmission line generate huge problems, and the development of a flexible direct current transmission system is also restricted.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a fault judgment method for an MMC-HVDC power transmission line, which can accurately judge a fault area and judge the type of a fault.
The technical problem to be solved by the invention is realized by adopting the following technical scheme:
a fault judgment method for an MMC-HVDC power transmission line comprises the following steps:
step 1, monitoring the direct-current side high-frequency direct-current voltage change rate of a smoothing reactor of an MMC-HVDC power transmission line in real time, judging whether the direct-current voltage change rate is larger than a direct-current voltage change rate threshold value, if so, performing a step 2, otherwise, repeatedly performing the step 1;
step 2, extracting an effective value of a high-frequency direct-current voltage at the direct-current side of a smoothing reactor of the MMC-HVDC power transmission line and an effective value of a high-frequency direct-current voltage at the converter side through discrete wavelet analysis, carrying out fault judgment according to the extracted effective values, and dividing a judgment result into a direct-current line fault, an external fault or no fault;
step 4, taking the data processing result as a vector X, and calculating the vector X and the optimal mass center n of each faultmAnd judging the selected vector X and the optimal mass center n of each faultmWhether the minimum value of the minimum distance is smaller than or equal to the threshold value of the corresponding fault or not is judged, and if yes, the MMC-HVDC transmission line is judged to be a pairIf the fault is not met, judging that the fault is out of area or no fault.
Moreover, the calculation method for extracting the effective value of the high-frequency direct-current voltage at the direct-current side of the smoothing reactor and the effective value of the high-frequency direct-current voltage at the converter side of the MMC-HVDC power transmission line in the step 2 comprises the following steps:
wherein, URIs the effective value of the direct current voltage, k is the number of sampling points in the sampling time window, utranI is 1, 2.
Moreover, the method for judging the fault in the step 2 comprises the following steps: judging whether the absolute value of the difference value between the effective value of the direct-current side high-frequency direct-current voltage of the MMC-HVDC power transmission line smoothing reactor and the effective value of the converter side high-frequency direct-current voltage is larger than a set threshold value of the difference value of the voltage effective values or not, judging whether the effective value of the direct-current side high-frequency direct-current voltage of the smoothing reactor is larger than the effective value of the converter side high-frequency direct-current voltage or not, if yes, judging that the direct-current line has a fault, and otherwise, judging that the direct-current.
Moreover, the method for performing per unit processing on the data of the positive and negative electrode voltage and current at the rectifying side or the positive and negative electrode voltage and current at the inverting side and summing the data to obtain the data processing result in the step 3 comprises the following steps:
wherein S isiFor the calculation result of the positive and negative electrode voltage and current data on the rectifying side or the inverting side, i is 1,2,3,4, S1As a result of the calculation of the positive voltage on the rectifying side or the inverting side, S2As a result of calculation of the positive current on the rectifying side or the inverting side, S3As a result of calculation of the rectifying-side or inverting-side negative electrode current, S4Calculation result of rectification side or inversion side negative electrode current, Hb,iIs the per unit value H of the voltage and current of the positive and negative electrodes at the rectifying side or the inverting sideb,1Is the per unit value of the positive current on the rectifying side or the inverting side, Hb,2Is the per unit value of the positive voltage on the rectifying side or the inverting side, Hb,3Is the per unit value of the voltage of the rectifier side or the inverter side negative electrode, Hb,4Is the per unit value of the current of the negative pole at the rectifying side or the inverting side, n is the number of sampling points in a time window, Hi,jIs a sampling value H of positive and negative electrode voltage and current of a rectifying side or an inverting side in a time window1,jIs the sampling value of the positive voltage of the rectifying side or the inverting side in the time window, H2,jIs the sampling value H of the positive current of the rectifying side or the inverting side in the time window3,jIs the sampling value H of the negative pole voltage on the rectifying side or the inverting side in the time window4,jThe sampling value of the negative pole current of the rectifying side or the inverting side in the time window is obtained.
Moreover, the time window in step 3 is 1 ms.
Furthermore, the vector X in step 4 is represented as follows:
X＝[S1,S2,S3,S4]
wherein S1As a result of the calculation of the positive voltage on the rectifying side or the inverting side, S2As a result of calculation of the positive current on the rectifying side or the inverting side, S3As a result of calculation of the rectifying-side or inverting-side negative electrode current, S4And calculating the current of the rectifying side or the inverting side cathode.
Further, each failure in the step 4 includes: positive ground faults, negative ground faults and bipolar short faults.
Furthermore, in step 4, vector X and optimal centroid n of each fault are calculatedmAnd judging the selected vector X and the optimal mass center n of each faultmThe calculation method of whether the minimum value of the minimum distance is less than or equal to the threshold value of the corresponding fault comprises the following steps:
wherein n ismFor the best centroid, mu, of each type of fault under each faultmFor thresholds of various faults under each faultThe values m 1,2,3 and m are fault type numbers, 1 is a positive ground fault, 2 is a negative ground fault, 3 is a bipolar short-circuit fault, con (x) 1 indicates the occurrence of a corresponding fault, and con (x) 0 indicates an out-of-range fault or no fault.
Furthermore, the direct current voltage change rate threshold value in the step 1, the set threshold value of the voltage effective value difference value in the step 2, and the optimal mass center n of each fault in the step 3mAnd threshold value mu of each type of fault under each faultmAre determined by means of a data set simulating the MMC-HVDC transmission line.
And the MMC-HVDC transmission line adopts a mode that a direct current side is grounded through a clamping resistor and consists of half-bridge sub-modules.
The invention has the advantages and positive effects that:
the method comprises the steps of extracting high-frequency voltage effective values of a direct current side of a line smoothing reactor and a converter side by adopting discrete wavelet analysis, comparing the high-frequency voltage effective values to judge faults inside and outside a region, then adopting a K-means clustering algorithm, acquiring voltage and current data of a single-side protection unit by utilizing different fault types, different fault positions and a short time window after the direct current line fault occurs, carrying out clustering analysis on the voltage and current data of the single-side protection unit, acquiring the mass center and the threshold of the voltage and current data of the single-side protection unit, and determining corresponding protection criteria by training to realize fault pole selection. The method can quickly and accurately detect the fault of the MMC-HVDC power transmission line without being influenced by the fault position and the transition resistance, and identify the fault type.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a block diagram of an MMC-HVDC system;
FIG. 3 is a MMC-HVDC system topology diagram;
fig. 4 is a bipolar short-circuit fault equivalent circuit diagram.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
A fault judgment method for an MMC-HVDC power transmission line is shown in figure 1 and comprises the following steps:
step 1, monitoring the direct-current side high-frequency direct-current voltage change rate of the smoothing reactor of the MMC-HVDC power transmission line in real time, judging whether the direct-current voltage change rate is larger than a direct-current voltage change rate threshold value, if so, performing step 2, otherwise, repeatedly performing step 1.
And 2, extracting the effective value of the direct-current side high-frequency direct-current voltage of the smoothing reactor of the MMC-HVDC power transmission line and the effective value of the current converter side high-frequency direct-current voltage through discrete wavelet analysis, judging whether the absolute value of the difference value of the effective value of the direct-current side high-frequency direct-current voltage of the smoothing reactor of the MMC-HVDC power transmission line and the effective value of the current converter side high-frequency direct-current voltage is larger than a set threshold value of the difference value of the voltage effective values or not, judging whether the effective value of the direct-current side high-frequency direct-current voltage of the smoothing reactor is larger than the effective value of the current converter side high-frequency direct-current voltage or not if the absolute value of the.
The calculation method for extracting the effective value of the high-frequency direct-current voltage at the direct-current side of the smoothing reactor of the MMC-HVDC power transmission line and the effective value of the high-frequency direct-current voltage at the converter side in the step comprises the following steps:
wherein, URIs the effective value of the direct current voltage, k is the number of sampling points in the sampling time window, utranI is 1, 2.
The method for judging whether the absolute value of the difference value between the effective value of the direct-current side high-frequency direct-current voltage of the MMC-HVDC power transmission line smoothing reactor and the effective value of the converter side high-frequency direct-current voltage is greater than the set threshold value of the difference value of the effective values of the voltages or not and judging whether the effective value of the direct-current side high-frequency direct-current voltage of the smoothing reactor is greater than the effective value of the converter side high-frequency direct-current voltage comprises the following:
UR.dcfor smoothing reactor DC side high frequencyEffective value of DC voltage, UR.acIs an effective value, U, of high-frequency direct-current voltage at the converter side of the smoothing reactorR.setAnd setting a threshold value for the voltage effective value difference value.
And 3, continuously acquiring the voltage and the current of the positive and negative electrodes of the MMC-HVDC rectification side or the voltage and the current data of the positive and negative electrodes of the inversion side by adopting a time window of 1ms through a K-means clustering algorithm, performing per-unit processing on the voltage and the current of the positive and negative electrodes of the MMC-HVDC rectification side or the voltage and the current data of the positive and negative electrodes of the inversion side, and summing to obtain a data processing result.
In this step, the method for performing per unit processing and summing on the positive and negative voltage and current at the MMC-HVDC rectification side or the positive and negative voltage and current data at the inversion side to obtain the data processing result comprises the following steps:
wherein S isiFor the calculation result of the positive and negative electrode voltage and current data on the rectifying side or the inverting side, i is 1,2,3,4, S1As a result of the calculation of the positive voltage on the rectifying side or the inverting side, S2As a result of calculation of the positive current on the rectifying side or the inverting side, S3As a result of calculation of the rectifying-side or inverting-side negative electrode current, S4Calculation result of rectification side or inversion side negative electrode current, Hb,iIs the per unit value H of the voltage and current of the positive and negative electrodes at the rectifying side or the inverting sideb,1Is the per unit value of the positive current on the rectifying side or the inverting side, Hb,2Is the per unit value of the positive voltage on the rectifying side or the inverting side, Hb,3Is the per unit value of the voltage of the rectifier side or the inverter side negative electrode, Hb,4Is the per unit value of the current of the negative pole at the rectifying side or the inverting side, n is the number of sampling points in a time window, Hi,jIs a sampling value H of positive and negative electrode voltage and current of a rectifying side or an inverting side in a time window1,jIs the sampling value of the positive voltage of the rectifying side or the inverting side in the time window, H2,jIs the sampling value H of the positive current of the rectifying side or the inverting side in the time window3,jIs the sampling value H of the negative pole voltage on the rectifying side or the inverting side in the time window4,jIs a time windowAnd sampling numerical values of negative pole current on the rectifying side or the inverting side in the port.
Step 4, taking the data processing result as a vector X, and calculating the vector X and the optimal mass center n of each faultmAnd judging the selected vector X and the optimal mass center n of each faultmWhether the minimum value of the minimum distance is smaller than or equal to a threshold value of a corresponding fault or not is judged, if yes, the MMC-HVDC transmission line is judged to be the corresponding fault, if not, the MMC-HVDC transmission line is judged to be an out-of-area fault or no fault, and each fault comprises the following steps: positive ground faults, negative ground faults and bipolar short faults.
The vector X in this step is represented as follows:
X＝[S1,S2,S3,S4]。
calculating vector X and optimal mass center n of each faultmAnd judging the selected vector X and the optimal mass center n of each faultmThe calculation method of whether the minimum value of the minimum distance is less than or equal to the threshold value of the corresponding fault comprises the following steps:
wherein n ismFor the best centroid, mu, of each type of fault under each faultmFor the threshold values of each type of fault under each fault, m is 1,2,3, m is the fault type number, 1 is a positive ground fault, 2 is a negative ground fault, 3 is a bipolar short-circuit fault, con (x) 1 is the occurrence of a corresponding fault, and con (x) 0 is an out-of-range fault or no fault.
Furthermore, the direct current voltage change rate threshold value in the step 1, the set threshold value of the voltage effective value difference value in the step 2, and the optimal mass center n of each fault in the step 3mAnd threshold value mu of each type of fault under each faultmThe method comprises the steps that a data set for simulating the MMC-HVDC power transmission line is determined, and the MMC-HVDC power transmission line is grounded through a clamping resistor at a direct current side and is composed of half-bridge sub-modules.
The invention is derived by the following derivation process:
when a bipolar short-circuit fault occurs on the outlet side of a direct-current line of a converter at one end of an MMC-HVDC transmission line, after the fault occurs and before the converter is not locked, the sub-module capacitor is rapidly discharged, and the fault equivalent circuit at the moment is shown in figure 4.
Where n denotes the number of submodules per bridge arm, C0Representing the sub-module capacitance, R0Representing bridge arm equivalent resistance, L0Representing bridge arm equivalent inductance, LdA smoothing reactor provided on the outlet side of the dc line is shown, and O represents a zero potential reference point. According to the average value model of MMC, a three-phase ac system can be equivalent to a circuit configuration as shown on the right side of fig. 4, and uf is an equivalent additional voltage of a fault point.
At this time, the DC voltage u across the smoothing reactor installed on the outlet side of the DC lined_dcAnd ud_acThe ratio relation of the two in the frequency domain can be obtained:
as the frequency increases, the ratio will be much greater than 1. Then, when the dc line fails, the amplitude of the high-frequency dc voltage on the dc side of the smoothing reactor is much larger than that of the high-frequency dc voltage on the inverter side.
According to the MMC-HVDC power transmission line fault judgment method, simulation detection is carried out on a certain MMC-HVDC power transmission line fault simulation system, and a simulation result of PSCAD/EMTDC shows that the method is not affected by fault positions and transition resistance, and can be used for rapidly and accurately detecting the fault of the MMC-HVDC power transmission line and identifying the fault type.
It should be emphasized that the embodiments described herein are illustrative rather than restrictive, and thus the present invention is not limited to the embodiments described in the detailed description, but also includes other embodiments that can be derived from the technical solutions of the present invention by those skilled in the art.
Claims (10)
1. A fault judgment method for an MMC-HVDC power transmission line is characterized by comprising the following steps: the method comprises the following steps:
step 1, monitoring the direct-current side high-frequency direct-current voltage change rate of a smoothing reactor of an MMC-HVDC power transmission line in real time, judging whether the direct-current voltage change rate is larger than a direct-current voltage change rate threshold value, if so, performing a step 2, otherwise, repeatedly performing the step 1;
step 2, extracting an effective value of a high-frequency direct-current voltage at the direct-current side of a smoothing reactor of the MMC-HVDC power transmission line and an effective value of a high-frequency direct-current voltage at the converter side through discrete wavelet analysis, carrying out fault judgment according to the extracted effective values, and dividing a judgment result into a direct-current line fault, an external fault or no fault;
step 3, continuously acquiring positive and negative electrode voltage and current of the MMC-HVDC rectification side or positive and negative electrode voltage and current data of the inversion side by adopting a time window through a K-means clustering algorithm, performing per-unit processing on the positive and negative electrode voltage and current of the MMC-HVDC rectification side or the positive and negative electrode voltage and current data of the inversion side, and summing to obtain a data processing result;
step 4, taking the data processing result as a vector X, and calculating the vector X and the optimal mass center n of each faultmAnd judging the selected vector X and the optimal mass center n of each faultmAnd whether the minimum value of the minimum distance is smaller than or equal to a threshold value of the corresponding fault or not is judged, if yes, the MMC-HVDC transmission line is judged to be the corresponding fault, and if not, the MMC-HVDC transmission line is judged to be an out-of-area fault or no fault.
2. The MMC-HVDC transmission line fault judgment method of claim 1, characterized in that: the calculation method for extracting the effective value of the high-frequency direct-current voltage at the direct-current side of the smoothing reactor and the effective value of the high-frequency direct-current voltage at the converter side of the MMC-HVDC power transmission line in the step 2 comprises the following steps:
wherein, URIs the effective value of the direct current voltage, k is the number of sampling points in the sampling time window, utranRepresenting high frequency band of dc voltageSample values i 1, 2.
3. The MMC-HVDC transmission line fault judgment method of claim 1, characterized in that: the method for judging the fault in the step 2 comprises the following steps: judging whether the absolute value of the difference value between the effective value of the direct-current side high-frequency direct-current voltage of the MMC-HVDC power transmission line smoothing reactor and the effective value of the converter side high-frequency direct-current voltage is larger than a set threshold value of the difference value of the voltage effective values or not, judging whether the effective value of the direct-current side high-frequency direct-current voltage of the smoothing reactor is larger than the effective value of the converter side high-frequency direct-current voltage or not, if yes, judging that the direct-current line has a fault, and otherwise, judging that the direct-current.
4. The MMC-HVDC transmission line fault judgment method of claim 1, characterized in that: the method for performing per unit processing and summing on the positive and negative electrode voltage and current of the MMC-HVDC rectification side or the positive and negative electrode voltage and current data of the inversion side in the step 3 to obtain a data processing result comprises the following steps:
wherein S isiFor the calculation result of the positive and negative electrode voltage and current data on the rectifying side or the inverting side, i is 1,2,3,4, S1As a result of the calculation of the positive voltage on the rectifying side or the inverting side, S2As a result of calculation of the positive current on the rectifying side or the inverting side, S3As a result of calculation of the rectifying-side or inverting-side negative electrode current, S4Calculation result of rectification side or inversion side negative electrode current, Hb,iIs the per unit value H of the voltage and current of the positive and negative electrodes at the rectifying side or the inverting sideb,1Is the per unit value of the positive current on the rectifying side or the inverting side, Hb,2Is the per unit value of the positive voltage on the rectifying side or the inverting side, Hb,3Is the per unit value of the voltage of the rectifier side or the inverter side negative electrode, Hb,4Is the per unit value of the current of the negative pole at the rectifying side or the inverting side, n is the number of sampling points in a time window, Hi,jPositive and negative poles at rectifying side or inversion side in time windowSampled values of voltage and current, H1,jIs the sampling value of the positive voltage of the rectifying side or the inverting side in the time window, H2,jIs the sampling value H of the positive current of the rectifying side or the inverting side in the time window3,jIs the sampling value H of the negative pole voltage on the rectifying side or the inverting side in the time window4,jThe sampling value of the negative pole current of the rectifying side or the inverting side in the time window is obtained.
5. The MMC-HVDC transmission line fault judgment method of claim 1, characterized in that: the time window in step 3 is 1 ms.
6. The MMC-HVDC transmission line fault judgment method of claim 1, characterized in that: the vector X in step 4 is represented as follows:
X＝[S1,S2,S3,S4]
wherein S1As a result of the calculation of the positive voltage on the rectifying side or the inverting side, S2As a result of calculation of the positive current on the rectifying side or the inverting side, S3As a result of calculation of the rectifying-side or inverting-side negative electrode current, S4And calculating the current of the rectifying side or the inverting side cathode.
7. The MMC-HVDC transmission line fault judgment method of claim 1, characterized in that: each fault in the step 4 comprises: positive ground faults, negative ground faults and bipolar short faults.
8. The MMC-HVDC transmission line fault judgment method of claim 1, characterized in that: in the step 4, the vector X and the optimal centroid n of each fault are calculatedmAnd judging the selected vector X and the optimal mass center n of each faultmThe calculation method of whether the minimum value of the minimum distance is less than or equal to the threshold value of the corresponding fault comprises the following steps:
wherein n ismFor the best centroid, mu, of each type of fault under each faultmFor the threshold values of each type of fault under each fault, m is 1,2,3, m is the fault type number, 1 is a positive ground fault, 2 is a negative ground fault, 3 is a bipolar short-circuit fault, con (x) 1 is the occurrence of a corresponding fault, and con (x) 0 is an out-of-range fault or no fault.
9. The MMC-HVDC transmission line fault judgment method of claim 8, characterized in that: the direct current voltage change rate threshold value in the step 1, the set threshold value of the voltage effective value difference value in the step 2 and the optimal mass center n of each fault in the step 3mAnd threshold value mu of each type of fault under each faultmAre determined by means of a data set simulating the MMC-HVDC transmission line.
10. The MMC-HVDC transmission line fault judgment method of claim 1, characterized in that: the MMC-HVDC transmission line adopts a mode that a direct current side is grounded through a clamping resistor and is composed of half-bridge sub-modules.
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