An extremely low frequency driven mmc topology circuit and a control method thereof

Abstract

The application discloses an extremely low frequency driven MMC topology circuit and a control method thereof, comprising three resonant filter modules, two ends of the resonant filter modules are electrically connected with upper bridge arm circuits and lower bridge arm circuits respectively, the upper bridge arm circuits and the lower bridge arm circuits each comprise N-1 high-capacitance voltage submodules and one low-capacitance voltage submodule; the N-1 high-capacitance voltage submodules are connected in series in turn, and the low-capacitance voltage submodule is connected in series at the end. The application utilizes the resonant circuit to suppress the double frequency component of the submodule capacitance voltage, thereby suppressing the submodule capacitance voltage fluctuation; based on the output waveform performance improvement problem under the extremely low frequency driving condition, the application can suppress the harmonic content by increasing the output level number, and simultaneously realizes the effective tracking of the output current and the submodule capacitance voltage balance by combining the multivariable closed loop control.

Description

Technical Field

[0001] This invention relates to the field of electrical engineering, and in particular to an MMC topology circuit driven at extremely low frequencies and its control method. Background Technology

[0002] The output waveform performance of an MMC can be affected by factors such as capacitor voltage fluctuations, harmonic content, grid-side voltage imbalance, high-power grid-side loads, and circulating current control performance.

[0003] Regarding capacitor voltage fluctuations, some researchers utilize the average value and imbalance of capacitor voltage to set the optimal switching range, thereby reducing losses and unnecessary repeated switching of submodules. Researchers eliminate power imbalance components through current compensation and achieve submodule capacitor voltage balancing in M3C under fault conditions through circulating current control; however, these control methods are relatively complex. Meanwhile, some researchers have proposed a control strategy of separate control for upper and lower bridge arms. This method can achieve submodule capacitor voltage balancing and also charge the battery, but it neglects the second harmonic circulating current component.

[0004] Furthermore, some scholars have proposed a phase-cascaded high-capacity HVDC transformer topology. To address the voltage balancing issue of the high-voltage side submodule capacitors, the voltages of the high- and medium-voltage side submodule capacitors are decoupled and controlled, achieving circulating current suppression and voltage balancing between the high- and medium-voltage sides. To address the issue of large voltage fluctuations in the submodule capacitors under low-frequency conditions, some researchers have introduced a resonant filter circuit between each phase arm of the MMC to suppress the second harmonic component of the capacitor voltage; however, they have not considered improving the output waveform performance of the MMC.

[0005] Regarding harmonic content, some scholars have connected a SiC metal-oxide-semiconductor field-effect transistor (MOSFET) full-bridge sub-module in series on each phase AC side. This method reduces losses while increasing the number of output levels, thereby suppressing harmonic content. However, this method does not consider the improvement of the output waveform performance of MMC under low-frequency conditions.

[0006] Furthermore, regarding grid-side voltage imbalance, some researchers have proposed a frequency-reducing model predictive control (MMDC) strategy suitable for grid voltage imbalance. This method can solve the three-phase current asymmetry problem and reduce the switching frequency; however, it does not consider improvements to the model predictive control strategy itself. Other researchers have improved the speed of the model predictive control strategy by introducing machine learning into it. This method effectively reduces the online computation while ensuring steady-state and dynamic performance. Still others have improved the steady-state performance of the model predictive control strategy by feeding error feedback into the predicted values. This method can suppress harmonic content and improve the steady-state performance of model predictive control.

[0007] Meanwhile, some scholars have improved the current compensation strategy. This method combines passive control and sliding mode control to achieve current compensation, improving both the steady-state and dynamic performance of the compensation strategy. Furthermore, some scholars have studied capacitor voltage balancing under grid voltage imbalance conditions. While avoiding the introduction of negative sequence current, they achieve rapid capacitor voltage balancing through closed-loop control of the bridge arm capacitor voltage and direct power compensation. Addressing the increased control difficulty under grid-side voltage imbalance, some researchers have combined feedback linearization control with sliding mode control. This method has advantages in robustness and dynamic performance, but it is relatively complex. Additionally, for high-power grid-side loads, some researchers use precise converter compensation for negative sequence current and efficient utilization of regenerative braking energy in energy storage as control methods to compensate for grid-side negative sequence current. Regarding circulating current control performance, to address the circulating current control accuracy problem of M3C when converting from low-frequency AC to power-frequency AC, scholars have introduced flat control into the circulating current suppression strategy. This method improves the steady-state performance of circulating current control, but it does not consider the increased fluctuation amplitude of submodule capacitor voltage.

[0008] In summary, research on capacitor voltage fluctuations still suffers from limitations such as complex control methods, neglect of second harmonic components, and lack of consideration for improving output waveform performance. Resonant filter circuits can be introduced to suppress the second harmonic component of the capacitor voltage. A topology using different sub-modules in series on each bridge arm can suppress harmonic content, but improvements to output waveform performance under low-frequency conditions still need to be considered. Meanwhile, research on grid-side voltage imbalance conditions still faces challenges such as complex control and room for improvement in steady-state and dynamic performance. Research on circulating current control performance still needs to address the issue of increased capacitor voltage fluctuation amplitude.

[0009] Definitions:

[0010] NLM: Nearest Level Modulation Summary of the Invention

[0011] To address the aforementioned technical problems, this invention proposes an ultra-low frequency driven MMC topology circuit and its control method.

[0012] The objective of this invention is achieved through the following technical solution:

[0013] A very low frequency driven MMC topology circuit includes three resonant filter modules. The two ends of each resonant filter module are electrically connected to an upper bridge arm circuit and a lower bridge arm circuit, respectively. Each upper and lower bridge arm circuit includes N-1 high-capacitor-voltage sub-modules and one low-capacitor-voltage sub-module. The N-1 high-capacitor-voltage sub-modules are connected in series, with the low-capacitor-voltage sub-module connected in series at the end. The ratio of the capacitor voltage of the high-capacitor-voltage sub-module to the low-capacitor-voltage sub-module is 2:1. The low-capacitor-voltage sub-module is individually controlled by a single-phase PWM rectifier connected in parallel. Both the high-capacitor-voltage and low-capacitor-voltage sub-modules are half-bridge structures, each half-bridge structure including two IGBTs, diodes connected in anti-parallel across the IGBTs, and a capacitor. The upper and lower bridge arms are electrically connected to the resonant filter modules.

[0014] In a further improvement, the resonant filter module includes a first filter capacitor C. f The first filter capacitor C f The two ends are electrically connected to one end of the first filter inductor Lf, and the other ends of the two first filter inductors Lf are electrically connected to each other and then to the output terminal; the first filter capacitor C f The two ends of the circuit are respectively connected to the N sub-modules of each bridge arm circuit through the second filter inductor L.

[0015] Further improvements include the first filter capacitor C. f The capacitance is C f If the inductance of the first filter inductor Lf is Lf', then:

[0016] 8w o L f 'C f '=1

[0017] Among them, w o This is the AC output frequency.

[0018] In a further improvement, the half-bridge structure includes a first IGBT VT1 and a second IGBT VT2; the collector of the first IGBT VT1 is electrically connected to the negative terminal of the first diode VD1 and one end of the capacitor, the emitter of the first IGBT VT1 is electrically connected to the positive terminal of the first diode VD1, the collector of the second IGBT VT2 and the negative terminal of the second diode VD2; the emitter of the second IGBT VT2 is electrically connected to the positive terminal of the second diode VD2 and the other end of the capacitor.

[0019] Further improvements are made, N≥2.

[0020] A control method for an ultra-low frequency driven MMC topology circuit, as shown above, specifically includes the following steps:

[0021] Step 1: Obtain the equivalent number N of submodules for each upper bridge arm circuit. px_oneq The number of equivalent submodules N of the lower bridge arm circuit nx_oneq :

[0022] N px_oneq =round(N eq u prx )

[0023] N nx_oneq =round(N eq u nrx )

[0024] Where, N eq =2N-1, u prx This is the normalized upper arm voltage modulation waveform; u nrx This is the normalized lower bridge arm voltage modulation waveform; round() indicates rounding.

[0025] Step 2: Obtain the number N of high-capacitor-voltage submodules in each bridge arm circuit. on :N on =floor(Z / 2), where floor() rounds down to the nearest integer; Z is N. px_oneq or N nx_oneq ;

[0026] Step 3: Determine the number of sub-modules with high capacitor voltage in each bridge arm circuit. n If the number is odd, the switching signal of the corresponding low capacitor voltage submodule is 1; otherwise, the switching signal of the corresponding low capacitor voltage submodule is 0. A switching signal of 1 indicates that the low capacitor voltage submodule is engaged, and a switching signal of 0 indicates that the low capacitor voltage submodule is engaged.

[0027] Step 4: Sort the sub-modules with high capacitor voltage in each bridge arm circuit according to the capacitor voltage from smallest to largest, and determine whether the bridge arm current is ≥0.

[0028] Step 5: If yes, assign switch signal 1 to the first N. on One high-capacitor-voltage submodule assigns switch signal 0 to the other high-capacitor-voltage submodules;

[0029] Otherwise, assign switch signal 0 to the first N. on A high-capacitor voltage submodule is assigned a switch signal 1 to the high-capacitor voltage submodule.

[0030] The beneficial effects of this invention are as follows:

[0031] This invention utilizes a resonant circuit to suppress the second harmonic component of the submodule capacitor voltage, thereby suppressing submodule capacitor voltage fluctuations. Based on the problem of improving output waveform performance under extremely low frequency driving conditions, this invention can suppress harmonic content by increasing the number of output levels, and at the same time combine multivariable closed-loop control to achieve effective tracking of output current and balance of submodule capacitor voltage. Attached Figure Description

[0032] The invention will be further illustrated with reference to the accompanying drawings, but the contents of the drawings do not constitute any limitation on the invention.

[0033] Figure 1 This is a schematic diagram of the overall structure of the MMC topology circuit of the present invention;

[0034] Figure 2 This is a flowchart illustrating the switching signal generation process of the MMC topology circuit of this invention.

[0035] Figure 3 The MMC topology modulation flowchart of this invention;

[0036] Figure 4 This is a flowchart of the closed-loop control of the MMC topology circuit of the present invention;

[0037] Figure 5a This is the output tracking diagram of the MMC topology circuit of the present invention;

[0038] Figure 5b This is the output tracing diagram for a traditional MMC.

[0039] Figure 6a This is a diagram of the bridge arm voltages of the MMC topology circuit of the present invention;

[0040] Figure 6b This is a diagram of the bridge arm voltages in a traditional MMC circuit.

[0041] Figure 7a This is a capacitor voltage diagram of the MMC topology circuit of the present invention;

[0042] Figure 7b This is a capacitor-voltage diagram for a traditional MMC circuit.

[0043] Figure 8 This is the circuit diagram for the submodule;

[0044] Figure 9 This is a diagram of a traditional MMC topology.

[0045] Example 1

[0046] This invention designs a novel MMC topology for application under extremely low frequency driving conditions, as shown in the attached figure. Figure 1As shown, each bridge arm consists of N-1 submodules with higher capacitor voltages and one submodule with lower capacitor voltages, with a capacitor voltage ratio of 2:1. By changing the capacitor voltage of the last submodule in the bridge arm, a new voltage level can be generated by superimposing it onto each of the original voltage levels, thus eliminating the need to increase the number of output levels by increasing the number of submodules. The capacitor voltage of the last submodule in the bridge arm is controlled individually by a single-phase PWM rectifier connected in parallel. Simultaneously, a filter capacitor is connected in series between the upper and lower bridge arms of each phase, and two filter inductors are connected in parallel across the filter capacitor. This resonant circuit can suppress the second harmonic component in the submodule capacitor voltage, thereby reducing the voltage fluctuation amplitude of the submodule capacitors.

[0047] This invention uses Thevein's theorem to simplify the cascaded branches of the first N-1 submodules in each arm of a hybrid MMC. Each arm's N submodules employ a half-bridge structure, comprising two IGBTs, anti-parallel diodes at their ends, and one capacitor. The capacitor branch can be equivalently represented as a resistor R. C Voltage source E in the associated direction C Serial processing. The simulation step size is set to h, and discretization is performed using the trapezoidal rule, as shown in the following equation:

[0048]

[0049] Where C is the capacitance value, u n Let i be the branch voltage before a step size. n This represents the branch current before a step size.

[0050] The IGBT and its anti-parallel diodes can be considered as a variable resistor controlled by a switching signal, represented by R1 and R2. The first N-1 sub-modules are equivalent to resistor R. arm With voltage source E arm (th) are connected in series, determined by the following formula:

[0051]

[0052] Based on the above formula derivation, the equivalent circuit of the first N-1 sub-module cascaded branches of each bridge arm can be solved, and then the voltage u across the first N-1 sub-module cascaded branches can be calculated. xN-1 This allows the first N-1 cascaded branches of the submodules to be replaced with a controlled voltage source.

[0053] Resonant filter module

[0054] The resonant filter module includes a filter capacitor connected in series between the upper and lower bridge arms of each phase, and two filter inductors connected in parallel across their ends. The filter capacitor can be equivalent to two capacitors with twice the capacitance; therefore, the circulating current in one phase can be expressed as:

[0055]

[0056] Among them, i zx For a single-phase circulation, U dc U is the DC-side voltage source value. px with U nx These are the voltages of the upper and lower arms of a single phase, respectively, and Z is the impedance of the arm, which can be expressed as R + jw. o L, Z fc The capacitive reactance of the filter capacitor can be expressed as 1 / jw. o C f Z fl The inductive reactance of the filter inductor can be expressed as jw o L f .

[0057] Then the phase impedance Z brodge It can be represented as:

[0058]

[0059] Where n is the number of high-frequency occurrences, w o Let be the AC output frequency. From equation (6), it can be seen that as long as is satisfied... At that time, Z bridge It becomes infinite. That is, when the following formula holds, the resonant filter module resonates in parallel, and the second harmonic circulating current component can be suppressed.

[0060]

[0061] Level Increment Module

[0062] The level increment module comprises a submodule with a lower capacitor voltage in each bridge arm. By changing the capacitor voltage of this submodule in the bridge arm, a new voltage level can be generated by superimposing it onto each existing voltage level, thus eliminating the need to increase the number of output levels by adding more submodules. The capacitor voltage of this submodule is individually controlled by a single-phase PWM rectifier connected in parallel.

[0063] The novel MMC designed in this invention consists of N-1 sub-modules with higher capacitor voltages and one sub-module with lower capacitor voltage in each bridge arm, with a capacitor voltage ratio of 2:1. Let U be the rated capacitor voltage of the first N-1 sub-modules in each bridge arm. C The rated capacitor voltage U of the Nth submodule C / 2, and the voltage of each submodule capacitor stabilizes to its rated capacitor voltage. Then the bridge arm voltage can be expressed as:

[0064]

[0065] Among them, S i S is the switching function for the i-th submodule in the bridge arm. NThis is the switching function for the Nth submodule of the bridge arm.

[0066] The first N-1 submodules generate N output voltage levels during stable operation, namely 0, u C ,2u C ,…,(N-2)u C (N-1)u C From equation (8), it can be seen that after the output voltage level of the Nth submodule is superimposed on the N output voltage levels of the first N-1 submodules, there are two cases: when the output voltage of the Nth submodule is u C When / 2, it will increase the N output voltage levels of the first N-1 sub-modules by u. C / 2, thus generating N new voltage levels; when the output voltage of the Nth submodule is 0, the original N voltage levels remain unchanged. Therefore, the bridge arm voltage of each bridge arm can be represented as a 2N level waveform, namely 0, u C / 2,u C ,…,(N-1)u C ,(2N-1)u C / 2.

[0067] Modulation and control strategies

[0068] This invention employs Nearest Level Modulation (NLM) to modulate the proposed novel MMC. Under the same number of output levels, the modulation result of the proposed novel MMC can be equivalent to a traditional MMC composed of Neq sub-modules, the expression for which is as follows:

[0069] N eq =2N-1#(9)

[0070] Where N represents the number of submodules in a bridge arm, and Neq represents the equivalent number of submodules. Therefore, the NLM modulation of a hybrid MMC with N bridge arm submodules can be equivalent to the NLM modulation of a traditional MMC with Neq bridge arm submodules. The equivalent number of submodules in the upper and lower bridge arms is:

[0071] N px_oneq =round(N eq u prx )#(10)

[0072] N nx_oneq =round(N eq u nrx )#(11)

[0073] Where, N px_oneq With N nx_oneq u is the equivalent number of operational submodules for the upper and lower bridge arms. prx with unrx The above is the normalized voltage modulation waveform of the upper and lower bridge arms.

[0074] To address the capacitor voltage balancing problem in half-bridge submodules, this invention obtains the number of submodules G deployed in the first N-1 submodules based on the equivalent number of operational submodules deployed in each bridge arm. N-1 Number and the switch state s of the Nth submodule xN The switching signals for the submodules are allocated based on the order of their capacitor voltages and the bridge arm currents. A flowchart illustrating the specific switching signal generation and modulation process is attached. Figure 2 and attached Figure 3 As shown.

[0075] To achieve effective tracking of output current and circulating current, and balance of submodule capacitor voltage, this invention selects output current, circulating current, and submodule capacitor voltage as control variables (this is an existing method, therefore only briefly described). The multivariable closed-loop control flowchart is attached. Figure 4 As shown. Output current reference value i oxref With circulation reference value i zxref Determined by the following formula:

[0076]

[0077] Among them, U dc Here, M represents the DC-side voltage source value, and R represents the modulation index. o This represents the resistance value of a single-phase load. The output current tracking error, after proportional control, participates in the bridge arm voltage modulation waveform u. prx u nrx The solution is needed.

[0078] The actual value of the circulating current per phase, i zx :

[0079]

[0080] Where i px For the upper arm current of each phase, i nx i represents the current in each lower bridge arm of the phase. zx The DC component is extracted by a low-pass filter. Meanwhile, the reference value for the submodule capacitor voltage balance control is U. dc The actual value u ave The DC component is extracted by a low-pass filter, as determined by the following formula. The tracking error of the submodule capacitor voltage balance control is transformed into an input variable dif for circulating current control after passing through a PI controller. 2x .

[0081]

[0082] in The sum of the capacitor voltages of the N-1 high-capacitor submodules of the upper bridge arm, U is the sum of the capacitor voltages of the N-1 high-capacitor submodules in the lower bridge arm. C Here are the rated capacitor voltages for N-1 high-capacitor-voltage submodules. Let be the capacitor voltage of the i-th high-capacitor-voltage submodule in the upper bridge arm. Let i be the capacitor voltage of the i-th high-capacitor-voltage submodule in the lower bridge arm; i zxref With dif 2x Summing and then ANDing with i zx The difference is used to obtain the circulating current tracking error. This tracking error, after passing through a PI controller, participates in the bridge arm voltage modulation waveform u. prx u nrx Calculation; modulate the bridge arm voltage wave u prx with u nrx After inputting into NLM, the N of each phase is obtained. px_oneq With N nx_oneq N px_oneq With N nx_oneq The equivalent controlled voltage source for the first N-1 submodules of each bridge arm is used to solve for i: Finally, the Simulink solver is run to obtain i ox i px i nx This constitutes a multivariable closed-loop control; ox i px i nx These are the output current per phase, the upper bridge arm current per phase, and the lower bridge arm current per phase, respectively.

[0083] Simulation verification

[0084] To verify the feasibility of this invention, a simulation model was built on MATLAB / Simulink. As shown in Figure 5, under extremely low frequency driving conditions, the proposed novel MMC exhibits good output waveform performance, with a lower Total Harmonic Distortion (THD) compared to the conventional MMC. Furthermore, as shown in Figure 6, compared to the conventional MMC, the proposed novel MMC increases the number of bridge arm voltage output levels by 81.82%. After adopting the level increment module, the THD of the upper bridge arm voltage is reduced by 59.73%, and the THD of the lower bridge arm voltage is reduced by 63.16%. This demonstrates that the level increment module can increase the number of output levels and effectively suppress harmonic content. Furthermore, as shown in Figure 7, under extremely low frequency driving conditions, with the rated capacitor voltage set at 200V, the proposed novel MMC capacitor voltage can be stabilized at around 200V, and its capacitor voltage fluctuation rate is 5.60%, while the traditional MMC capacitor voltage fluctuation rate is 15.55%. Moreover, compared to the traditional MMC, the proposed novel MMC, after adopting a resonant filter module, shows a 63.99% reduction in capacitor voltage fluctuation rate. Therefore, the proposed novel MMC can achieve capacitor voltage balance, and the resonant filter module can suppress the second harmonic component in the capacitor voltage, thereby reducing the voltage fluctuation amplitude of the submodule capacitor.

[0085] Simulation verification

[0086] To verify the feasibility of this invention, a simulation model was built on MATLAB / Simulink. As shown in Figure 5, under extremely low frequency driving conditions, the proposed novel MMC exhibits good output waveform performance, with a lower Total Harmonic Distortion (THD) compared to the conventional MMC. Furthermore, as shown in Figure 6, compared to the conventional MMC, the proposed novel MMC increases the number of bridge arm voltage output levels by 81.82%. After adopting the level increment module, the THD of the upper bridge arm voltage is reduced by 59.73%, and the THD of the lower bridge arm voltage is reduced by 63.16%. This demonstrates that the level increment module can increase the number of output levels and effectively suppress harmonic content. Furthermore, as shown in Figure 7, under extremely low frequency driving conditions, with the rated capacitor voltage set at 200V, the proposed novel MMC capacitor voltage can be stabilized at around 200V, and its capacitor voltage fluctuation rate is 5.60%, while the traditional MMC capacitor voltage fluctuation rate is 15.55%. Moreover, compared to the traditional MMC, the proposed novel MMC, after adopting a resonant filter module, shows a 63.99% reduction in capacitor voltage fluctuation rate. Therefore, the proposed novel MMC can achieve capacitor voltage balance, and the resonant filter module can suppress the second harmonic component in the capacitor voltage, thereby reducing the voltage fluctuation amplitude of the submodule capacitor.

[0087] In summary, under extremely low frequency driving conditions, the capacitive reactance of the MMC submodule increases, and the voltage fluctuation of the traditional MMC capacitor is relatively large.

Claims

1. An MMC topology circuit driven by extremely low frequency, characterized in that, It includes three resonant filter modules, with each end of the resonant filter module electrically connected to the upper bridge arm circuit and the lower bridge arm circuit, respectively. Both the upper and lower bridge arm circuits include... N -1 high capacitor voltage submodule and one low capacitor voltage submodule; N - One high-capacitor-voltage submodule is connected in series, and a low-capacitor-voltage submodule is connected in series at the end; the ratio of the capacitor voltage of the high-capacitor-voltage submodule to that of the low-capacitor-voltage submodule is 2:1; the low-capacitor-voltage submodule is controlled independently by a single-phase PWM rectifier connected in parallel; both the high-capacitor-voltage and low-capacitor-voltage submodules are half-bridge structures, and the half-bridge structure includes two IGBTs and diodes and one capacitor connected in anti-parallel across the IGBTs.

2. The ultra-low frequency driven MMC topology circuit as described in claim 1, characterized in that, The resonant filtering module includes a first filtering capacitor ( C f ), first filter capacitor ( C f The two ends are respectively electrically connected to the first filter inductor ( Lf At one end of the first filter inductor, two first filter inductors ( Lf The other end of the filter capacitor (C) is electrically connected to the output terminal; f The two ends of the filter are respectively connected to the second filter inductor ( L The circuit connects N sub-modules of each bridge arm.

3. The ultra-low frequency driven MMC topology circuit as described in claim 2, characterized in that, The first filter capacitor (C) f The capacitance of ) is C f ', First filter inductor ( Lf The sensitivity value of ) Lf', This makes: ； in, w o This is the AC output frequency.

4. The ultra-low frequency driven MMC topology circuit as described in claim 2, characterized in that, The half-bridge structure includes a first IGBT (VT1) and a second IGBT (VT2); the collector of the first IGBT (VT1) is electrically connected to the negative terminal of the first diode (VD1) and one end of the capacitor, and the emitter of the first IGBT (VT1) is electrically connected to the positive terminal of the first diode (VD1), the collector of the second IGBT (VT2), and the negative terminal of the second diode (VD2); the emitter of the second IGBT (VT2) is electrically connected to the positive terminal of the second diode (VD2) and the other end of the capacitor.

5. The ultra-low frequency driven MMC topology circuit as described in claim 2, characterized in that, N≥2。 6. A control method for an ultra-low frequency driven MMC topology circuit, characterized in that, The ultra-low frequency driven MMC topology circuit, as described in any one of claims 1-5, specifically includes the following steps: Step 1: Obtain the equivalent number of submodules for each upper bridge arm circuit. The number of equivalent submodules of the lower bridge arm circuit : ； ； in, , This is the normalized upper arm voltage modulation wave; This is the normalized lower bridge arm voltage modulation waveform; round() indicates rounding. Step 2: Obtain the number of sub-modules with high capacitor voltage in each bridge arm circuit. N on : floor() indicates rounding down to the nearest integer; Z is or ; Step 3: Determine the number of sub-modules with high capacitor voltage in each bridge arm circuit. N on If the number is odd, the switch signal of the corresponding low capacitor voltage submodule is 1; otherwise, the switch signal of the corresponding low capacitor voltage submodule is 0. A switch signal of 1 indicates that the low capacitor voltage submodule is engaged, and a switch signal of 0 indicates that the low capacitor voltage submodule is not engaged. Step 4: Sort the sub-modules with high capacitor voltage in each bridge arm circuit according to the capacitor voltage from smallest to largest, and determine whether the bridge arm current is ≥0. Step 5: If yes, then assign switch signal 1 to the previous... N on One high-capacitor-voltage submodule assigns switch signal 0 to the other high-capacitor-voltage submodules; Otherwise, assign switch signal 0 to the previous one. N on One high-capacitor-voltage submodule assigns switch signal 1 to the other high-capacitor-voltage submodules.

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