Model Predictive Control Method for Star-Type Arm-Interphase Coupled MMC Applicable to Low-Frequency Operating Conditions

Abstract

The present invention discloses a model predictive control strategy for a star-bridge-arm inter-phase coupled MMC applicable to low-frequency working conditions, including the following steps: Step 1: Establish discrete predictive models for each sub-arm and the star bridge arm on the main bridge arm, obtain the reference values and sampled values of the control quantities, and thereby predict the optimal arm voltages of the sub-arm and the star bridge arm; Step 2: According to the power balance condition, calculate the reference values of the DC component and the high-frequency circulating current component of the arm current to achieve the balanced control of the capacitor voltage of the phase unit and the capacitor voltage of the arm unit; Step 3: Combine the modulation strategy and the capacitor voltage balance control to determine the switching states of each sub-module. The present invention realizes the control of the capacitor voltage of the sub-arm, the capacitor voltage of the star bridge arm, the AC current, and the output common-mode voltage of the star-bridge-arm inter-phase coupled MMC applicable to low-frequency working conditions, greatly reduces the number of PI regulators in the control loop, simplifies the control structure, and improves the dynamic response ability of the system.

Description

Technical Field

[0001] The invention belongs to the technical field of the application of a modular multilevel converter in a high-voltage high-power AC drive system, and particularly relates to a model predictive control strategy for a star-bridge-arm phase-interleaved modular multilevel converter (MMC) suitable for low-frequency working conditions. Background Art

[0002] The modular multilevel converter (MMC) is a type of multilevel converter. It has a highly modular structure, good redundancy, a low switching frequency and small losses. Compared with traditional multilevel converters, MMC has obvious advantages and a wider application range. At present, MMC has been widely used in many medium-voltage applications, such as the field of motor drive and the field of variable-frequency speed regulation drive, where it can achieve stepless speed regulation, improve the dynamic characteristics of the system, and enhance the efficiency and quality of the motor drive system. When MMC is applied to control motor starting or low-frequency operation, the output voltage will be distorted. Under low-frequency working conditions, the huge pulsation problem of the sub-module capacitor voltage will have an adverse impact on the operation safety and stability of the high-voltage high-power AC drive system. If a suitable low-frequency suppression strategy is adopted to effectively solve this problem, MMC will have good development and application in the field of AC drive. Currently, the commonly used low-frequency suppression strategies include the high-frequency signal injection method and the additional power channel method, both of which can achieve the suppression of the sub-module capacitor voltage fluctuation under low-frequency working conditions.

[0003] However, the traditional high-frequency signal injection method will increase the common-mode voltage on the output side of the converter, which has an adverse impact on the bearings and insulated windings of the motor. In engineering, a front-end transformer can be added to weaken the influence of the common-mode voltage on the motor, but this reduces the advantages of the modular multilevel converter compared with other multilevel converters. For the star-bridge-arm phase-interleaved MMC, by adding a branch at the midpoints of the upper and lower bridge arms of each phase, the output does not contain the additionally injected high-frequency common-mode voltage. The classical control method for the star-bridge-arm phase-interleaved MMC is based on PI closed-loop control, which requires a large number of regulators in the control loop, involves a large amount of calculation, and makes parameter tuning difficult. Summary of the Invention

[0004] Aiming at the control method for the star-bridge-arm phase-interleaved MMC based on PI regulators, which has problems such as a large number of required controllers, complex parameter adjustment, and large amount of calculation. The invention proposes a model predictive control strategy for the star-bridge-arm phase-interleaved MMC, which realizes the control of the sub-module capacitor voltage of the main bridge arm, the sub-module capacitor voltage of the star bridge arm, the output current, and the output common-mode voltage under low-frequency working conditions, simplifies the control loop, and improves the dynamic response ability of the system.

[0005] To achieve the above object, the present invention provides a model predictive control strategy for a star-bridge-arm interphase-coupled MMC applicable to low-frequency operating conditions. By applying the model predictive algorithm to the inner current control loop, the optimal arm voltages of the main bridge arm and the star bridge arm of the star-bridge-arm interphase-coupled MMC are directly predicted, and then combined with the modulation strategy and the capacitor voltage balancing control to determine the control signals of the switching devices in each sub-module, specifically including the following steps:

[0006] S1: Discretize the sub-arm voltage using the forward Euler method to obtain the voltage at the Kth sampling period T s , and the discrete-domain expression of each sub-arm voltage is:

[0007]

[0008] where u j (K) is the output voltage of the jth phase at the Kth sampling period, L is the arm inductance value, i rjx (K) is the arm current of each sub-arm at the Kth sampling period, i rjx (K + 1) is the expected output value of the arm current of each sub-arm at the beginning of the (K + 1)th sampling period, u h (K) is the high-frequency injection voltage at the Kth sampling period, r = p, n (p represents the upper arm, n represents the lower arm), j = a, b, c (representing three phases a, b, c), and x = 1, 2 (representing two sub-arms in each arm).

[0009] At the beginning of each sampling period, according to the sampled arm currents of each sub-arm and the reference values of the expected output arm currents of each sub-arm, the voltage of each sub-arm can be calculated, that is, the sum of the output voltages of all the conducting sub-modules on the sub-arm. Thus, the discrete prediction model of the voltage of each sub-arm can be obtained as:

[0010]

[0011] where i pj1_ref and i pj2_ref are respectively the reference values of the currents of the two sub-arms of the upper arm of the jth phase, i nj1_ref and i nj2_ref are respectively the reference values of the currents of the two sub-arms of the lower arm of the jth phase. Similarly, the discrete prediction model of the star bridge arm voltage can be obtained as:

[0012]

[0013] where i hj_ref is the reference value of the high-frequency circulating current component of the arm current of the jth phase, and i hj (K) is the high-frequency circulating current of the jth phase at the Kth sampling period.

[0014] S2: According to the discrete prediction models of the sub-arms and the star bridge arm established in S1, to obtain the optimal arm voltage values at the (K + 1)-th moment, it is necessary to calculate the reference values of the sub-arm currents and the high-frequency circulating current. The expression of the sub-arm current reference value is:

[0015]

[0016] where, i dj_ref and i j_ref are the reference values of the DC component and the fundamental frequency component of the j-phase bridge arm current respectively.

[0017] The reference value of the fundamental frequency component is a three-phase sine signal known by the prediction algorithm. The reference values of the DC component and the high-frequency component need to be calculated according to the power balance condition. The system energy is stored in the sub-module capacitors dispersedly. Ignoring the power loss of the converter, the power balance condition is obtained as:

[0018]

[0019] The phase capacitor voltage balance control makes the average value u Cj_av of the sub-module capacitor voltages of each phase follow the rated value U cap of the capacitor voltage. The theoretical value i dj of the DC current component calculated from the power balance condition, plus the compensation amount Δi dj of the DC current component generated by the phase voltage outer-loop controller, constitutes the DC current reference value i dj_ref ; The bridge arm capacitor voltage balance control is used to achieve the balance of the upper and lower bridge arm capacitor voltages. Combining with the power balance condition, the high-frequency current reference value i hj_ref can be obtained.

[0020] According to the calculated DC shunt reference value, high-frequency component reference value and fundamental frequency component reference value, the reference value expressions of the sub-arm current and the star bridge arm current can be obtained. Substituting them into the discrete prediction expressions of the sub-arm voltage and the star bridge arm voltage, the optimal arm voltage values of the next sampling period can be obtained.

[0021] S3: For the optimal arm voltages of each arm at the (K + 1)-th moment predicted in S2, the optimal working states of each sub-module are obtained through appropriate modulation methods and capacitor voltage equalization control algorithms. The specific methods are as follows:

[0022] For the two sub-arms on each arm in the main bridge arm, there are N / 2 half-bridge sub-modules on each sub-arm. Considering the case of a small N, the outer-phase unit uses carrier phase-shifted modulation, and the inner sub-arm unit uses unified pulse-width modulation, so as to obtain the optimal switching states [N optrj1 , N optrj2 of the two sub-arms respectively:

[0023]

[0024] Among them, u rj1_ref , u rj2_ref are the predicted voltages of the two sub-arms in each bridge arm respectively, U cap is the rated value of the sub-module capacitor voltage, D rj1 , D rj2 are the duty cycles of the sub-modules in the PWM state in the two sub-arms respectively.

[0025] After obtaining the number of conducting sub-modules in each sub-arm, the sorting equalization algorithm is used to balance the capacitor voltages of the sub-arm sub-modules and determine the working states of each sub-module. Define the currents flowing through the two sub-arms in each bridge arm as i rj1 , i rj2 .

[0026] Determine the switching states of the sub-modules in sub-arm I: If i rj1 > 0, sort the capacitor voltages of N / 2 sub-modules in sub-arm I in ascending order, and select the first N optrj1 sub-modules to be in the "inserted" state to fully charge the capacitor, and the other sub-modules work in the cut-off state; if i rj1 ≤0, sort the capacitor voltages of N / 2 sub-modules in sub-arm I in descending order, and select the first N optrj1 sub-modules to be in the "inserted" state to fully discharge the capacitor, and the other sub-modules work in the cut-off state.

[0027] Determine the switching states of the sub-modules in sub-arm II: If i rj2 > 0, sort the capacitor voltages of N / 2 sub-modules in sub-arm II in ascending order, and select the first N optrj2 sub-modules to be in the "inserted" state to fully charge the capacitor, and the other sub-modules work in the cut-off state; if i rj2 ≤0, sort the capacitor voltages of N / 2 sub-modules in sub-arm II in descending order, and select the first N optrj2 sub-modules to be in the "inserted" state to fully discharge the capacitor, and the other sub-modules work in the cut-off state.

[0028] For the star-shaped bridge arm, there are N / 4 full-bridge sub-modules on each star bypass branch. Considering the case of a small N, carrier phase-shifted modulation is adopted. For the full-bridge sub-modules, the switching devices are divided into two groups, and the modulation signals of the two groups of sub-modules are complementary. The triangular carrier phases of each sub-module in the bridge arm are staggered by π / N angles in turn. When the modulation signal u rsj_ref is greater than the instantaneous value of the triangular carrier, output 1, otherwise output 0, and the trigger signals of the full-bridge sub-modules on the star-shaped bridge arm can be obtained.

[0029] Compared with the prior art, the present invention realizes the balanced control of the capacitor voltages of the arm sub-modules and the suppression of the high-frequency common-mode voltage on the output side, without establishing a cost function and eliminating a large number of variable prediction calculations, making the device switching frequency fixed and obtaining better output characteristics. Compared with the traditional control method based on PI regulators, the dynamic response ability of the system is improved. Brief Description of the Drawings

[0030] Figure 1 is the flow chart of the present invention;

[0031] Figure 2 is the topological structure diagram of the star-arm interphase-coupled MMC which is the research object of the present invention;

[0032] Figure 3 is the single-phase equivalent circuit diagram of the star-arm interphase-coupled MMC;

[0033] Figure 4 is the control principle block diagram of the star-arm interphase-coupled MMC based on the model predictive algorithm of the present invention. Detailed Embodiment

[0034] The present invention will be further described below with reference to the accompanying drawings.

[0035] As Figure 1 shown, the present invention proposes a control method based on the model predictive algorithm for the star-arm interphase-coupled MMC applicable to low-frequency working conditions to simplify the control loop and reduce the control complexity. The model predictive control method of this embodiment is based on the topological structure of the star-arm interphase-coupled MMC. As Figure 2 shown, this topology is composed of three phase units in total. Each phase consists of upper and lower arms containing N sub-modules with the same structure and two bypass branches. Among them, the DC power supply voltage is U dc ; the voltages and currents of the sub-arms of the upper arm are u pjx , i pjx respectively; the voltages and currents of the sub-arms of the lower arm are u njx , i njx respectively; the voltages and currents of the upper and lower star arms are u rsj , i rsj, r = p, n (p represents the upper bridge arm, n represents the lower bridge arm), j = a, b, c (representing three phases a, b, and c), x = 1, 2 (indicating two sub - arms in each bridge arm). The mid - points (p, n) of the upper and lower bridge arms of each phase are respectively connected to a bypass branch composed of N / 4 full - bridge sub - modules. The main bridge arm is the same as the traditional MMC topology. The bypass branches of the three phases form a star connection, so it is called a star - type bridge - arm inter - phase - coupled MMC. The star - type bridge - arm inter - phase - coupled MMC constructs an inter - phase power transmission channel at the mid - points of the three - phase bridge arms to reduce the power fluctuation between phases, achieve energy balance, and at the same time ensure that there is no high - frequency common - mode voltage on the output side.

[0036] Figure 3 The single - phase equivalent circuit diagram of the star - type bridge - arm inter - phase - coupled MMC is given. The star - type bypass branch divides the upper and lower bridge arms of each phase into two parts, which are called sub - bridge arms. That is, each phase unit consists of two upper sub - arms, two lower sub - arms, and two star - type bypasses, a total of 6 bridge arms. For the convenience of analysis, each bridge arm can be equivalent to a controllable voltage source. Half - bridge sub - modules are used on the sub - arms, so it is equivalent to a unipolar controllable voltage source; full - bridge sub - modules are used on the star - type bridge arms, so it is equivalent to a bipolar controllable voltage source. The voltage expressions of the upper and lower bridge arms are:

[0037]

[0038] Among them, L is the bridge - arm inductor, u j is the output voltage of phase j, i pj1 , i pj2 are the currents flowing through the two sub - arms of the upper bridge arm respectively, and i nj1 , i nj2 are the currents flowing through the two sub - arms of the lower bridge arm respectively. This topology is used to solve the problem of the increase in the common - mode voltage on the output side caused by the traditional high - frequency signal injection method. Therefore, the current flowing through each branch contains a fundamental - frequency component, a high - frequency component, and a DC component. The expressions of each component are:

[0039]

[0040] To avoid high - frequency signals from appearing in the common - mode voltage, high - frequency voltage signals of equal magnitude and opposite directions are injected into the two sub - arms belonging to the same bridge arm. At this time, the voltage expressions of each sub - arm are:

[0041]

[0042] The current expressions of each sub - arm are:

[0043]

[0044] The star - type bypass is used to exchange the power fluctuation between the three phases. The voltages of the upper and lower star - type bridge arms of each phase are:

[0045]

[0046] The upper and lower star-bridge arm currents of each phase are as follows:

[0047]

[0048] To reduce the fluctuations of the sub-module capacitor voltage under low-frequency conditions, a high-frequency voltage signal is injected into the voltage of each sub-arm. According to the relationship between the output voltage amplitude and the DC voltage, the expression of the high-frequency voltage is obtained as:

[0049]

[0050] where m is the converter modulation ratio, and S h represents the switching function, which can be in the form of a sine wave or a square wave.

[0051] The control principle block diagram of the star-bridge arm interphase-coupled MMC based on the model predictive algorithm is as shown in Figure 4 Figure [Figure number not provided in the original]. This control strategy applies the model predictive algorithm to the inner current control loop. First, it directly predicts the optimal bridge arm voltages of the main bridge arm and the star-bridge arm of the star-bridge arm interphase-coupled MMC, and then combines the modulation strategy and the voltage equalization control to generate the control signals for the switching devices of each sub-module.

[0052] Specifically, it includes the following steps:

[0053] S1: Discretize the sub-arm voltage using the forward Euler method to obtain the discrete-domain expression of the sub-arm voltage at the Kth sampling period T s , as follows:

[0054]

[0055] In the formula, u j (K) is the output voltage of the jth phase at the Kth sampling period, L is the bridge arm inductance value, i rjx (K) is the bridge arm current of each sub-arm at the Kth sampling period, i rjx (K + 1) is the expected output value of the bridge arm current of each sub-arm at the beginning of the (K + 1)th sampling period, u h (K) is the high-frequency injection voltage at the Kth sampling period, r = p, n (p represents the upper bridge arm, n represents the lower bridge arm), j = a, b, c (representing the three phases of a, b, and c), and x = 1, 2 (representing the two sub-arms in each bridge arm).

[0056] At the beginning of each sampling period, according to the sampled bridge arm currents of each sub-arm and the reference values of the expected output bridge arm currents of each sub-arm, the voltage of each sub-arm can be calculated, that is, the sum of the output voltages of all the conducting sub-modules on the sub-arm. Thus, the discrete prediction model of the voltage of each sub-arm can be obtained as:

[0057]

[0058] Among them, \(i\) pj1_ref and \(i\) pj2_ref are respectively the reference values of the currents of the two sub-arms of the upper bridge arm of phase \(j\), and \(i\) nj1_ref and \(i\) nj2_ref are respectively the reference values of the currents of the two sub-arms of the lower bridge arm of phase \(j\). Similarly, the discrete prediction model of the star bridge arm voltage can be obtained as follows:

[0059]

[0060] Among them, \(i\) hj_ref is the reference value of the high-frequency circulating current component of the phase \(j\) bridge arm current, and \(i\) hj (K) is the high-frequency circulating current in the \(K\)th sampling period of phase \(j\).

[0061] S2: According to the discrete prediction models of the sub-arms and the star bridge arm established in S1, to obtain the optimal values of the voltages of each bridge arm at the \(K + 1\) moment, it is necessary to find the reference values of the currents of each sub-arm and the reference value of the high-frequency circulating current. The expression of the reference value of the sub-arm current is:

[0062]

[0063] Among them, \(i\) dj_ref and \(i\) j_ref are respectively the reference values of the DC component and the fundamental frequency component of the phase \(j\) bridge arm current.

[0064] The reference value of the fundamental frequency component is a three-phase sine signal known to the prediction algorithm. The reference values of the DC component and the high-frequency component need to be calculated according to the power balance condition. The system energy is stored dispersedly in the sub-module capacitors. Ignoring the power loss of the converter, the power balance condition is obtained as follows:

[0065]

[0066] The phase capacitor voltage balance control makes the average value \(u\) Cj_av of the sub-module capacitor voltages of each phase follow the rated value \(U\) cap of the capacitor voltage. The theoretical value \(i\) dj of the DC current component calculated from the power balance condition, plus the compensation amount \(\Delta i\) dj of the DC current component generated by the phase voltage outer loop controller, constitutes the reference value \(i\) dj_ref of the DC current; the bridge arm capacitor voltage balance control is used to achieve the balance of the upper and lower bridge arm capacitor voltages. Combining the power balance condition, the reference value \(i\) hj_ref of the high-frequency current can be obtained.

[0067] According to the calculated DC shunt reference value, high-frequency component reference value, and fundamental frequency component reference value, the reference value expressions of the sub-arm current and star-bridge arm current can be obtained. Substituting them into the discrete prediction expressions of each sub-arm voltage and star-bridge arm voltage, the optimal arm voltages of each bridge in the next sampling period can be obtained.

[0068] S3: For the optimal arm voltages of each bridge at the (K + 1)-th moment predicted in S2, the optimal operating states of each sub-module are obtained through appropriate modulation methods and capacitor voltage balancing control algorithms. The specific method is as follows:

[0069] For the two sub-arms on each bridge in the main bridge arm, there are N / 2 half-bridge sub-modules on each sub-arm. Considering the case where N is small, the outer phase unit uses carrier phase-shifted modulation, and the inner sub-arm unit uses unified pulse-width modulation to obtain the optimal switching states of the two sub-arms optrj1 , N optrj2 :

[0070]

[0071] where u rj1_ref , u rj2_ref are the predicted voltages of the two sub-arms in each bridge arm respectively, U cap is the rated value of the sub-module capacitor voltage, D rj1 , D rj2 are the duty cycles of the sub-modules in the PWM state in the two sub-arms respectively.

[0072] After obtaining the number of conducting sub-modules in each sub-arm, the sorting equalization algorithm is used to balance the capacitor voltages of the sub-arm sub-modules and determine the operating states of each sub-module. Define the currents flowing through the two sub-arms in each bridge arm as i rj1 , i rj2 .

[0073] Determine the switching states of the sub-modules in sub-arm I: If i rj1 > 0, sort the capacitor voltages of the N / 2 sub-modules in sub-arm I in ascending order, and select the first N optrj1 sub-modules to be in the "connected" state to fully charge the capacitor, and the other sub-modules work in the disconnected state; if i rj1 ≤ 0, sort the capacitor voltages of the N / 2 sub-modules in sub-arm I in descending order, and select the first N optrj1 sub-modules to be in the "connected" state to fully discharge the capacitor, and the other sub-modules work in the disconnected state.

[0074] Determine the switching states of the sub-modules in sub-arm II: If i rj2 > 0, sort the capacitor voltages of the N / 2 sub-modules in sub-arm II in ascending order, and select the first N optrj2The sub-module is in the "input" state to fully charge the capacitor, and other sub-modules work in the cut-off state; if i rj2 ≤ 0, the capacitor voltages of N / 2 sub-modules in the second sub-arm are sorted in descending order, and the first N optrj2 sub-modules are in the "input" state to fully discharge the capacitor, and other sub-modules work in the cut-off state.

[0075] For the star-shaped arm, there are N / 4 full-bridge sub-modules on each star bypass branch. Considering the case where N is small, carrier phase-shifted modulation is adopted. For the full-bridge sub-module, the switching devices are divided into two groups, and the modulation signals of the two groups of sub-modules are complementary. The triangular carrier phases of each sub-module in the arm are staggered by π / N angles in turn. When the modulation signal u rsj_ref is greater than the instantaneous value of the triangular carrier, output 1; otherwise, output 0, and the trigger signals of the full-bridge sub-modules on the star-shaped arm can be obtained.

Claims

1. A model predictive control strategy for a star-bridge-arm interphase coupling type MMC applicable to low-frequency operating conditions, characterized in that, Apply the model prediction algorithm to the inner current control loop. First, directly predict the optimal arm voltages of the main arm and the star arm of the star-connected arm-interphase-coupled MMC, and then, combined with an appropriate modulation strategy and voltage equalization control, determine the control signals of the switching devices in each sub-module; The specific steps are as follows: S1: Discretize the sub-arm voltage using the forward Euler method. Based on the sampled sub-arm currents and the reference values of the sub-arm currents expected to be output, obtain the sub-arm voltage discrete prediction model at the (K + 1)-th sampling period T s , as follows: Where U dc is the DC-side voltage, u h (K) is the high-frequency injection voltage in the Kth sampling period, L is the arm inductance value, u j (K) is the output voltage of the jth phase in the Kth sampling period, i rjx (K) is the arm current of each sub-arm in the rth arm of the jth phase in the Kth sampling period, i rjx_ref is the expected output value of the arm current of each sub-arm in the rth arm of the jth phase at the start of the (K + 1)th sampling period, where r = p, n, p represents the upper arm, n represents the lower arm, j = a, b, c, a, b, c represent three phases, x = 1, 2, 1, 2 represent two sub-arms in each arm. Similarly, the discrete prediction model of the star arm voltage can be obtained as follows: where i hj_ref is the reference value of the high-frequency circulating current component of the j-phase bridge arm, and i hj (K) is the high-frequency circulating current in the K-th sampling period of the j-phase; S2: According to the discrete prediction models of the sub-arm and the star arm established in S1, to obtain the optimal arm voltage values of each arm at the (K + 1)-th moment, it is necessary to find the reference values of the sub-arm current and the high-frequency circulating current. The expression of the sub-arm current reference value is: wherein, i dj_ref and i j_ref are respectively the reference values of the DC component and the fundamental frequency component of the j-phase bridge arm current; The reference value of the fundamental frequency component is the three-phase sine signal known to the prediction algorithm. The reference values of the DC component and the high-frequency component need to be calculated according to the power balance condition. The system energy is stored in the sub-module capacitors in a decentralized manner. Ignoring the power loss of the converter, the power balance condition is obtained as: where, u j is the output voltage of phase j, i j is the output current of phase j, U h is the amplitude of the high-frequency injection voltage, I hj is the amplitude of the high-frequency circulating current component of the bridge arm current of phase j. The phase capacitor voltage balance control makes the average value u Cj_av of the sub-module capacitor voltages of each phase follow the rated value U cap of the capacitor voltage. The theoretical value i dj of the DC current component calculated from the power balance condition, plus the compensation amount Δi dj of the DC current component generated by the phase voltage outer-loop controller, constitutes the DC current reference value i dj_ref ; The bridge arm capacitor voltage balance control is used to achieve the balance of the upper and lower bridge arm capacitor voltages. Combining with the power balance condition, the high-frequency current reference value i hj_ref can be obtained; According to the calculated reference values of the DC shunt, the high-frequency component, and the fundamental frequency component, the reference value expressions of the sub-arm current and the star arm current can be obtained. Substitute them into the discrete prediction expressions of the sub-arm voltage and the star arm voltage, and the optimal arm voltage values of each arm in the next sampling period can be obtained; S3: For the optimal arm voltages of each arm at the (K + 1)-th moment predicted in S2, use the modulation strategy and the voltage equalization algorithm to determine the working states of each sub-module.

2. The model predictive control strategy of the star-bridge-arm inter-phase coupling type MMC applicable to low-frequency operating conditions according to claim 1, characterized in that, The specific method for equalizing the capacitor voltages of the sub-modules and determining the optimal working states of each sub-module in S3 is as follows: Adopt an appropriate modulation method and a capacitor voltage equalization control algorithm to determine the switching conditions of each sub-module. The specific method is as follows: For the two sub - arms on each arm in the main bridge arm, there are N / 2 half - bridge sub - modules on each sub - arm. The outer - layer phase unit uses carrier phase - shifted modulation, and the inner - layer sub - arm unit uses unified pulse - width modulation, so as to obtain the number of sub - modules N invested in each sub - arm respectively. optrjx , according to the direction of the sub - arm current being i rjx , the sorting voltage - equalizing algorithm is used to balance the capacitor voltages of the sub - modules in the sub - arm, so as to obtain the control signals of the half - bridge sub - modules in the main arm; For the star arm, there are N / 4 full-bridge sub-modules on each star bypass branch. Adopt carrier phase-shifted modulation to obtain the trigger signals of the full-bridge sub-modules on the star arm.

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