CN108767887B - Sub-module capacitor voltage prediction correction method for high-voltage direct-current transmission - Google Patents

Sub-module capacitor voltage prediction correction method for high-voltage direct-current transmission Download PDF

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CN108767887B
CN108767887B CN201810601253.2A CN201810601253A CN108767887B CN 108767887 B CN108767887 B CN 108767887B CN 201810601253 A CN201810601253 A CN 201810601253A CN 108767887 B CN108767887 B CN 108767887B
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CN108767887A (en
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罗安
岳雨霏
郭鹏
徐千鸣
胡家瑜
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Hunan University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/483—Converters with outputs that each can have more than two voltages levels
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/483—Converters with outputs that each can have more than two voltages levels
    • H02M7/4835—Converters with outputs that each can have more than two voltages levels comprising two or more cells, each including a switchable capacitor, the capacitors having a nominal charge voltage which corresponds to a given fraction of the input voltage, and the capacitors being selectively connected in series to determine the instantaneous output voltage
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/53—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M7/537—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters
    • H02M7/5387—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration
    • H02M7/53871—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration with automatic control of output voltage or current
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/60—Arrangements for transfer of electric power between AC networks or generators via a high voltage DC link [HVCD]

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Abstract

The invention discloses a prediction and correction method for capacitor voltage of sub-modules of high-voltage direct-current transmission, which aims at a high-voltage direct-current transmission system adopting a modular multilevel structure, adopts a measurement method of using a voltage sensor for each bridge arm of a modular multilevel converter station, and performs prediction and correction on the capacitor voltage of all sub-modules of each bridge arm in the converter station by measuring the voltage of the bridge arm, thereby realizing virtual measurement of the capacitor voltage of all sub-modules and achieving the aim of controlling the balance of the capacitor voltage. Compared with the traditional measuring method adopting multiple sensors, the method reduces the number of the sensors, greatly reduces the production cost of hardware, and has certain guiding value for the practical engineering application of a direct current power transmission system.

Description

Sub-module capacitor voltage prediction correction method for high-voltage direct-current transmission
Technical Field
The invention relates to the field of high-voltage direct-current transmission, in particular to a submodule capacitor voltage prediction correction method of modular multi-level high-voltage direct-current transmission.
Background
In the field of medium-high voltage dc transmission, modular multilevel structures are becoming more and more popular with their outstanding advantages, including: according to the requirements of different power and voltage grades, the method has the advantages of easy expandability and high modularization degree; high efficiency and high power quality; the direct current bus does not need to be connected with a large capacitor in parallel. However, there are some problems due to the modular multilevel structure, such as: the problems of sub-module capacitor voltage unbalance phenomenon caused by a distributed capacitor layout structure, in-phase upper and lower bridge arm voltage unbalance caused by internal circulation, inter-phase voltage unbalance and the like can generate extra power loss in the modular multilevel converter station, and the safe and stable operation of a direct-current transmission system is not facilitated. In addition, because the medium-high voltage direct current transmission converter station adopts a cascade structure of hundreds of sub-modules, and the capacitance voltage of the hundreds of sub-modules needs to be sampled when voltage balance control is carried out, each sub-module needs to be provided with a voltage sensor to measure the capacitance voltage, so that a hardware measuring system of the converter station has a great burden, and more voltage sensors can possibly reduce the reliability of the operation of the converter station. Therefore, how to reduce the number of voltage sensors is a less considered issue in the research in the field.
Disclosure of Invention
The invention aims to solve the technical problem that the prior art is insufficient, and provides a sub-module capacitor voltage prediction correction method for high-voltage direct-current power transmission.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a sub-module capacitor voltage prediction correction method for high-voltage direct-current transmission comprises the following steps:
1) establishing an expression of actual variation (taking the bridge arm as an example) of the bridge arm voltage of the high-voltage direct-current transmission converter station in adjacent control periods, a relational expression of the bridge arm voltage of the high-voltage direct-current transmission converter station and all the sub-module capacitor voltages in the bridge arm in the adjacent control periods and an expression of variation of a switching signal of each sub-module in the bridge arm of the high-voltage direct-current transmission converter station in the adjacent control periods and variation of the sum of the switching signals of all the sub-modules in the bridge arm based on the relationship between the bridge arm voltage and all the sub-module capacitor voltages of the bridge arm in the high-voltage direct-current transmission converter station and according to a kirchhoff's voltage law and a kirchhoff's current law;
wherein, the expression of the actual variation (taking the bridge arm as an example) of the bridge arm voltage of the HVDC converter station in the adjacent control period is
Δupx(k)＝upx(k)-upx(k-1)；
Wherein, Δ upx(k) (x ═ a, b, c) denotes adjacent control periods [ k-2, k-1 [ ]]And [ k-1, k]Actual variation of bridge arm voltage upx(k-1) and upx(k) Respectively representing control periods [ k-2, k-1 ]]And [ k-1, k]Actual measurement of the inner leg voltage.
The relational expression of the bridge arm voltage of the high-voltage direct-current transmission converter station and the capacitor voltages of all sub-modules in the bridge arm in the adjacent control period is as follows:
Figure BDA0001693288940000021
wherein u isdci(k-1) (i ═ 1, 2.. N, N denotes the total number of submodules in the bridge arm) and udci(k) Indicates that the ith sub-module is in the control period [ k-2, k-1 ]]And [ k-1, k]Actual value of capacitor voltage, si(k-1) and si(k) Indicating each submodule is in the control period [ k-2, k-1 ]]And [ k-1, k]The internal switching signal is a signal that is switched,
Figure BDA0001693288940000022
and
Figure BDA0001693288940000023
respectively, in a control period [ k-2, k-1 ]]And [ k-1, k]And the sum of the products of the actual capacitor voltage of each submodule and the corresponding switch signal.
The expression of the variation of the switching signal of each submodule in the bridge arm of the high-voltage direct-current transmission converter station in the adjacent control period and the variation of the sum of the switching signals of all submodules in the bridge arm is as follows:
Figure BDA0001693288940000024
wherein, Δ si(k) Indicating each submodule is in the control period [ k-2, k-1 ]]And [ k-1, k]Amount of change, Δ s, insum(k) Indicating that the sum of the bridge arm switching signals is in a control period k-2, k-1]And [ k-1, k]The amount of change in the amount of change,
Figure BDA0001693288940000031
and
Figure BDA0001693288940000032
respectively, in a control period [ k-2, k-1 ]]And [ k-1, k]Inner bridge arm switching signal summation.
2) The method comprises the steps that a single voltage sensor is adopted to measure the actual bridge arm voltage of each bridge arm of the converter station in an adjacent control period, the actual capacitance voltage of each submodule in the bridge arm in one control period does not need to be measured, and the measured bridge arm voltage is used for predicting and correcting the capacitance voltage of each submodule in each control period;
in the high-voltage direct-current transmission converter station, the capacitance voltage value of each submodule in each bridge arm does not need to be measured through a voltage sensor, the capacitance voltage is predicted and corrected by using the bridge arm voltage variation obtained by single-sensor measurement, and in each control period, firstly, the switching signal variation delta s of the submodule is usedi(k) And in the control period [ k-1, k ]]Internal switching signal si(k) And initially predicting the capacitance voltage of the submodule at the moment k, wherein the prediction expression is as follows:
Figure BDA0001693288940000033
wherein,
Figure BDA0001693288940000034
is a predicted value of the sub-module capacitor voltage at the moment k,
Figure BDA0001693288940000035
is the correction value of the capacitor voltage of the submodule at the moment k-1, T is the control period time interval, C is the submodule capacitor, ipx(k) Bridge arm current at time k.
Then, the actually measured adjacent control periods [ k-2, k-1 ] are used]And [ k-1, k]Bridge arm voltage variation delta upx(k) Predicted value of sub-module capacitance voltage at k moment
Figure BDA0001693288940000036
Making correction, and assuming that the correction quantity of sub-module capacitor voltage is qi(k) Then the predicted correction value for the capacitor voltage is expressed as:
Figure BDA0001693288940000037
wherein,
Figure BDA0001693288940000038
and the correction value of the sub-module capacitor voltage at the time k is closer to the actual capacitor voltage value of the sub-module, so that the sequencing effect basically consistent with the sampling of all the sub-module capacitor voltages is achieved.
3) Sequencing the voltage correction values obtained in the step 2), distributing pulse signals of the sub-modules under the operation condition of ensuring low switching frequency, and realizing the balance control of the sub-module capacitor voltage.
Compared with the prior art, the invention has the beneficial effects that: the invention aims at a high-voltage direct-current power transmission system with a modular multilevel structure, and the method adopts a single voltage sensor to measure each bridge arm in a modular multilevel converter station to predict and correct the capacitance voltage of all sub-modules of the bridge arm so as to realize the balance control of the capacitance voltage.
Drawings
Fig. 1 is an equivalent circuit diagram of a modular multi-level hvdc transmission system of the present invention;
FIG. 2 is a block diagram of a capacitance-to-voltage predictive correction control process using a single-sensor measurement method according to an embodiment of the invention;
FIG. 3 is a flow chart of capacitance-voltage balance control using a single-sensor measurement method according to an embodiment of the present invention.
Detailed Description
Fig. 1 is an equivalent circuit diagram of a modular multi-level hvdc transmission system according to the present invention. In the figure, MMC-1 and MMC-2 are high-voltage converter stations which adopt a modular multilevel structure in a high-voltage direct-current power transmission system, Udc1And Udc2Respectively the DC bus voltage, l of the converter stationoFor the length of the DC cable, RoAnd LoRespectively a resistance and an inductance of a power transmission line at the alternating current side of the converter station; u. ofsabc1And usabc2Three-phase grid voltages of an alternating current system 1 and an alternating current system 2 of the converter station respectively, wherein PCC-1 and PCC-2 are common connection points between the alternating current system and the converter station, T is a transformer, u is a voltageg1And ug2Secondary side voltage, P, of the potential transformer1/Q1And P2/Q2Respectively the active power and the reactive power transmitted by the MMC-1 and the MMC-2 of the converter station.
FIG. 2 is a block diagram of a capacitance-to-voltage predictive correction control process using a single-sensor measurement method according to an embodiment of the invention. Fig. 2 is a block diagram of a single-sensor capacitance-voltage prediction correction control process taking an upper bridge arm of a single-phase system of a modular multilevel converter station as an example, and the control process includes: the method comprises the steps of measuring a system, predicting capacitance and voltage of a submodule, judging a level state, and correcting and sequencing the capacitance and voltage of the submodule. In the figure, SM1～SMNN half-bridge submodules cascaded by bridge arms, L and R are bridge arm reactors and parasitic resistors respectively, and each half-bridge submodule is composed of a power switch device T1And T2The sub-modules of each half-bridge are connected in series and connected with a capacitor C in parallel, so that the application occasion of the prediction correction algorithm is closer to the actual engineering application occasionThe capacitor sides are connected with the bleeder resistors in parallel. For high-voltage application occasions, a single sensor is adopted to measure a bridge arm reactor uLpxAnd uLnxAnd an output voltage u on the AC sidecxThe bridge arm voltage is obtained, which is given above as an example:
upx＝Udc/2-uLpx-ucx；
wherein, UdcIs the dc bus voltage. In order to obtain the correction value of the sub-module capacitor voltage at the time k, the control process is divided into five steps as follows:
(1) the measurement system comprises: bridge arm voltage u at moment of measuring k-1px(k-1), bridge arm voltage u at time kpx(k) And bridge arm current ipx(k)；
(2) And (3) prediction: predicting the capacitance voltage of each submodule at the moment k by using the measured quantity to obtain
Figure BDA0001693288940000051
(3) And (3) level judgment: judging the variation delta s of the sum of all sub-module switching signals in the bridge arm of the high-voltage direct-current transmission converter stationsum(k) Selecting a submodule needing to be corrected according to the state;
(4) and (3) correction: according to the level judgment result, correcting the predicted value of the sub-module capacitance voltage to obtain
Figure BDA0001693288940000052
(5) Sorting: will be provided with
Figure BDA0001693288940000053
Sending the signals into a sequencing algorithm, and distributing the switching signals s of each submodule by adopting the sequencing algorithm with low switching frequency1～sN。
FIG. 3 is a flow chart of capacitance-voltage balance control using a single-sensor measurement method according to an embodiment of the present invention. Firstly, 4 switching signal modes, s, of the submodule are definedi(k-1) and si(k) Respectively representing control periods [ k-2, k-1]And [ k-1, k]Internal switching signals, the 4 modes are represented as follows:
M1：si(k-1)＝0，si(k)＝0；
M2：si(k-1)＝0，si(k)＝1；
M3：si(k-1)＝1，si(k)＝1；
M4：si(k-1)＝1，si(k)＝0。
for convenience of description, the following is provided with M1～M4The quantity of symbols represents the sub-module corresponding to the respective mode. First, M is initialized2～M4Number n of submodules of modeM2～nM4To be 0, the control flow chart related to the present invention specifically includes 8 steps as follows:
(1) measurement: obtaining the actual variation delta u of the bridge arm voltagepx(k)。
(2) And (3) prediction: according to M2～M4Correction values for sub-modules of a pattern at time k-1
Figure BDA0001693288940000054
Predicting the capacitor voltage at the k moment to obtain
Figure BDA0001693288940000055
Is represented as follows:
①M1：
Figure BDA0001693288940000056
②M2：
Figure BDA0001693288940000057
③M3：
Figure BDA0001693288940000058
④M4：
Figure BDA0001693288940000059
wherein, Δ uincre(k)＝(T/C)ipx(k)si(k) Is M3Submodule capacitor voltage increments of a pattern.
(3) Counting the number of modules: statistics M2～M4The number of submodules of the mode is respectively stored in a variable nM2～nM4In (1).
(4) And (3) summing predicted values: to M2～M4Modular submodule capacitor voltage prediction value
Figure BDA0001693288940000061
Sums, respectively stored in the variables Sum _ M2(k)～Sum_M4(k) In (1).
(5) And (3) level judgment: judgment of Δ ssum(k) Status.
(6) Number of correction modules: according to step (5), from nM2～nM4The number of modules needing to be corrected is selected, and the total number is recorded as nCorrection of。
(7) Correcting errors: selecting sub-modules according to the step (6), selecting corresponding sub-module capacitance voltage sums from the step (4), and recording the Sum as Sum _ M (k), for example: n isCorrection of＝nM2+nM4The Sum is Sum _ M (k) Sum _ M2(k)+Sum_M4(k) (ii) a The correction error can be made by Δ upx(k) And Sum _ M (k) to calculate:
Q(k)＝Δupx(k)-Sum_M(k)；
(8) and (3) correction: averagely distributing the correction error obtained in the step (7) to each submodule needing to be corrected, and correcting the predicted value of the capacitor voltage as follows:
Figure BDA0001693288940000062

Claims (4)

1. a sub-module capacitor voltage prediction correction method for high-voltage direct-current transmission is characterized by comprising the following steps:
1) establishing an expression of actual variation of bridge arm voltage of the high-voltage direct-current transmission converter station in adjacent control periods, a relational expression of bridge arm voltage of the high-voltage direct-current transmission converter station and capacitor voltage of all sub-modules in the bridge arm in adjacent control periods, and an expression of variation of switching signal of each sub-module in the bridge arm of the high-voltage direct-current transmission converter station in adjacent control periods and variation of sum of switching signals of all sub-modules in the bridge arm based on the relationship between bridge arm voltage and capacitor voltage of all sub-modules in the bridge arm, a sub-module switching signal and bridge arm current in the high-voltage direct-current transmission converter station, according to kirchhoff's voltage law and switching value signals;
2) measuring the actual bridge arm voltage of each bridge arm of the converter station in adjacent control periods by adopting a single voltage sensor, and predicting and correcting the capacitance voltage of each submodule in each control period by using the measured actual bridge arm voltage;
the expression for correcting the capacitor voltage of each submodule is:
Figure FDA0003213070560000011
wherein,
Figure FDA0003213070560000012
correcting the capacitor voltage of the submodule at the moment k; q. q.si(k) For the correction of the sub-module capacitor voltage, qi(k)＝Q(k)/nCorrection of，Q(k)＝Δupx(k)-Sum_M(k)，Δupx(k) The actual variation of the bridge arm voltage is obtained; n isCorrection ofDenotes from nM2～nM4The number of selected modules to be corrected, nM2～nM4Are respectively used for storing M2～M4The number of submodules of the mode; m2：si(k-1)＝0，si(k)＝1；M3：si(k-1)＝1，si(k)＝1；M4：si(k-1)＝1，si(k)＝0；si(k-1) and si(k) Indicating each submodule is in the control period [ k-2, k-1 ]]And [ k-1, k]An internal switching signal; to M2～M4Modular submodule capacitor voltage prediction value
Figure FDA0003213070560000013
Sums, respectively stored in the variables Sum _ M2(k)～Sum_M4(k) In (m), Sum _ M (k) is nCorrection ofThe sum of the predicted values of the capacitor voltage of the corresponding sub-modules; i is 1,2,. N, N represents the total number of sub-modules of the bridge arm;
3) and (4) performing loss reduction sequencing on the sub-module capacitor voltage values subjected to prediction correction, distributing pulse signals of the sub-modules, and ensuring that the system operates under the working condition of low switching frequency to realize balance control on the sub-module capacitor voltage.
2. The method for predicting and correcting the capacitor voltage of the sub-module of the HVDC transmission according to claim 1, wherein in step 1), the actual variation Δ u of the bridge arm voltage of the HVDC transmission converter station in the adjacent control periodpx(k) The expression is as follows: Δ upx(k)＝upx(k)-upx(k-1)；
The relational expression of the bridge arm voltage of the high-voltage direct-current transmission converter station and the capacitor voltages of all sub-modules in the bridge arm in the adjacent control period is as follows:
Figure FDA0003213070560000021
wherein u ispx(k-1) and upx(k) Respectively representing control periods [ k-2, k-1 ]]And [ k-1, k]Actual measurement values of the bridge arm voltages in the bridge; x is a, b, c; u. ofdci(k-1) indicates the control period [ k-2, k-1 ] for each sub-module]Actual value of the capacitor voltage udci(k) Indicating each submodule is in the control period k-1, k]Actual value of capacitor voltage, si(k-1) and si(k) Indicating each submodule is in the control period [ k-2, k-1 ]]And [ k-1, k]The internal switching signal is a signal that is switched,
Figure FDA0003213070560000022
and
Figure FDA0003213070560000023
respectively, in a control period [ k-2, k-1 ]]And [ k-1, k]And the sum of the products of the actual capacitor voltage of each submodule and the corresponding switch signal.
3. The method for predicting and correcting the capacitance and the voltage of the sub-modules in the HVDC transmission according to claim 2, wherein the expressions of the variation of the switching signal of each sub-module in the bridge arm of the HVDC transmission converter station in the adjacent control period and the variation of the sum of the switching signals of all the sub-modules in the bridge arm are as follows:
Figure FDA0003213070560000024
wherein, Δ si(k) Indicating each submodule is in the control period [ k-2, k-1 ]]And [ k-1, k]Amount of change, Δ s, insum(k) Indicating that the sum of the bridge arm switching signals is in a control period k-2, k-1]And [ k-1, k]The amount of change in the amount of change,
Figure FDA0003213070560000025
and
Figure FDA0003213070560000026
respectively, in a control period [ k-2, k-1 ]]And [ k-1, k]Inner bridge arm switching signal summation.
4. The sub-module capacitance voltage prediction correction method for high-voltage direct current transmission according to claim 3, characterized in that in step 2), the expression for predicting the capacitance voltage of each sub-module is as follows:
Figure FDA0003213070560000031
wherein,
Figure FDA0003213070560000032
is a predicted value of the sub-module capacitor voltage at the moment k,
Figure FDA0003213070560000033
is the correction value of the capacitor voltage of the submodule at the moment k-1, T is the control period time interval, C is the submodule capacitor, ipx(k) Bridge arm current at time k.
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