A general pulse allocation method for MMC under optimal PD-PWM modulation

Abstract

The present invention discloses a general pulse distribution method for MMC under optimal PD-PWM modulation, which is specifically as follows: step 1: establishing a switch model of MMC; step 2: calculating the influence of the total number of submodules invested in the MMC on the circulating state; step 3: dividing the target level L into a level that can control the circulating current and a level that cannot control the circulating current; step 4: setting the circulating current target value I cmref Step 5: Set a sub-state candidate group, where the number of sub-states in the sub-state candidate group is K, and the sub-state candidate group is a K*2N matrix; Step 6: Use a pseudo-random function to select a sub-state from the sub-state candidate group to determine the pulse state at the next moment. This invention actively controls the circulating current and minimizes the total number of switching cycles, improving the operating efficiency of the MMC system. It also ensures the self-balancing characteristics of the sub-module capacitor voltage over a large time scale, eliminating the need for active voltage control and saving hardware costs.

Description

Technical Field

[0001] The present invention belongs to the technical field of high-voltage and high-power power electronics in power systems. Background Art

[0002] The modular multilevel converter (MMC) was first proposed by Professor R. Marquardt in a German patent in 2001. Since around 2010, this topology has gradually become a research hotspot. Well-known domestic and international companies such as ABB, Siemens, General Electric, and NARI Relay Protection have developed commercial products with successful applications in high-voltage direct current (HVDC) transmission systems, static VAR compensators (SVCs), and medium-voltage motor drives. Furthermore, MMC is also considered to have significant application potential in emerging fields such as medium-voltage marine propulsion systems, power electronic transformers, distributed energy storage systems, and medium- and low-voltage DC systems.

[0003] In medium-voltage applications, the number of submodules (N) within an MMC bridge arm is generally less than 20. For example, using a 3300V IGBT in a 10kV AC grid, 8-10 submodules per bridge arm can meet voltage requirements. In this application (especially when N is less than 10), pulse width modulation (PWM) is generally considered to offer superior output voltage harmonic performance compared to level approximation modulation methods, making it more suitable.

[0004] Centralized control, exemplified by PD-PWM, is characterized by a "top-down" approach. It prioritizes the converter's overall multi-level output voltage waveform, ensuring its shape strictly matches the designed target waveform. Then, according to specific rules, the pulse distribution process allocates the actual trigger pulses to each submodule. While this ensures the converter's overall output voltage is a PD-PWM waveform with its typical spectral characteristics, the pulse distribution process also determines whether each submodule's actual switching frequency is minimized, switching behavior is uniform, and circulating currents are controlled.

[0005] Traditional PD-PWM modulation applies modulation to the upper and lower bridge arms of the MMC separately, generating either N+1 or 2N+1 voltage outputs at the midpoint of each phase arm, depending on whether the modulation signals are 180° out of phase. The paper "Optimized Phase Disposition (PD) Modulation of a Modular Multilevel Converter" (McGrath BP, Teixeira CA, et al.) rigorously demonstrates that this independent modulation method exhibits the harmonic characteristics of PD-PWM only when the phase arm outputs the N+1 level. When the phase arm outputs the 2N+1 level, its harmonic characteristics are consistent with those of PSC-PWM at the same level, thus losing the advantages of the PD-PWM strategy. Therefore, the paper argues that in order to output a 2N+1 waveform with PD-PWM harmonic characteristics at the midpoint of the MMC's phase arms, the upper and lower arms of the MMC must be treated as a single entity and modulated uniformly. This approach is also known as optimal PD-PWM modulation for the MMC.

[0006] Under optimized PD-PWM modulation, the paper "Design and implementation of finite state machine decoders for phase disposition pulse width modulation of modular multilevel converters" (authors Teixeira CA, Sun YC, et al.) proposes a pulse distribution method based on a finite state machine. This method corrects the circulating current offset caused by the inherent flaws of the PD-PWM strategy by forcing redundant state transitions during level band transitions. However, this method cannot address the inherent low-frequency circulating current caused by the topological characteristics of the MMC itself. Furthermore, traditional stationary coordinate system proportional resonant or rotating coordinate system proportional integral methods based on common-mode signal correction are no longer applicable. Therefore, the paper "Circulating current suppression control of modular multilevel converters under optimized phase disposition (PD) modulation" (authors Sun YC, Lyu D, et al.) proposes a modified state machine that actively suppresses the circulating current of the MMC by forcing redundant state switching. However, the finite state machines in these methods rely on manual path planning and are only suitable for analyzing five-level scenarios (N=2). When N increases further, the number of redundant states of the MMC will increase by hundreds or thousands, and it becomes infeasible to rely on manual advance planning of the complete state path. Summary of the Invention

[0007] Purpose of the invention: In order to solve the problems existing in the above-mentioned prior art, the present invention provides a universal pulse distribution method for MMC under optimal PD-PWM modulation.

[0008] Technical Solution: The present invention provides a universal pulse distribution method for MMC under optimal PD-PWM modulation. The single-phase MMC includes upper and lower bridge arms, each of which includes N cascaded submodules. Each submodule includes a pair of two-quadrant switches and an energy storage capacitor. The method specifically includes the following steps:

[0009] Step 1: Establish the switch model of MMC;

[0010] Step 2: The redundant state of MMC is converted into a one-dimensional matrix S with 2N elements = [σ u1 ,σ u2 ,…,σ un ,…,σ uN ,σ l1 ,σ l2 ,…,σ ln ,…,σ lN ] represents, where σ un represents the switching state function of the nth submodule in the upper bridge arm, σ ln represents the switch state function of the nth submodule in the lower bridge arm; σ jn ={0,1}, 0 represents removal, 1 represents input, j = {u, l}, n = {1, 2, ..., N|, calculate the impact of the total number of submodules invested in the MMC on the circulation state;

[0011] Step 3: Divide the target level L into a level that can control the circulating flow type and a level that cannot control the circulating flow type;

[0012] Step 4: Set the circulating current target value I according to the MMC switch model in step 1 cmref ;

[0013] Step 5: According to the impact of the total number of submodules in the MMC on the circulating current state in step 2, the type of the target level L in step 3, and the circulating current target value in step 4, set a sub-state candidate group. The number of sub-states in the sub-state candidate group is K, and the sub-state candidate group is a K*2N matrix;

[0014] Step 6: Use a pseudo-random function to select a group of next states from the next state candidate group to determine the pulse state at the next moment.

[0015] Furthermore, the switch model of the MMC in step 1 is:

[0016]

[0017] Among them, u o is the output voltage at the midpoint of the MMC phase bridge arm, L m is the mutual inductance of the coupled inductors in the MMC, i cm is the common mode current; U dc is the voltage amplitude of the MMC DC side, L k is the MMC leakage inductance, i dm is the differential mode current; σ cm is the common mode component of the submodule switching function, σ dm is the differential mode component of the submodule switching function;

[0018] i cm ,i dm The expression is as follows:

[0019]

[0020] i u 、i l are the currents of the upper and lower bridge arms respectively;

[0021] σ cm The expression is as follows:

[0022]

[0023] Furthermore, the expression of the circulation target value in step 4 is as follows:

[0024]

[0025] Where R(*) means taking a real number, is the output current reference value.

[0026] Furthermore, the influence of the total number of submodules put into the MMC on the circulation state in step 2 is specifically as follows: the total number of submodules put into the upper and lower bridge arms S sum is N, N-1 or N+1; when S sum =N, σ cm =1, the circulation remains unchanged; when S sum =N-1, σ cm <1, the circulation increases; when S sum =N+1, σ cm >1, the circulation decreases, σ cm is the common-mode component of the submodule switching function.

[0027] Furthermore, the step 5 is specifically as follows:

[0028] If L is able to control the circulating current level, then S sum= N, calculate the circulating current size according to the current of the upper and lower bridge arms, and compare it with the target value I cnref If the calculated circulation is less than the target value I cnref , then enter the sub-state region that increases the circulation, specifically: find the columns with N elements that are 1 in the one-dimensional matrix S corresponding to the current state, set the columns with elements that are 1 to 0 in order from left to right, and set only one column with elements that are 1 to 0 at a time, to obtain N one-dimensional matrices; select the one-dimensional matrix that makes the MMC output level L from the N one-dimensional matrices, use the selected one-dimensional matrix as the next-state candidate group, and arrange each matrix in the next-state candidate group from top to bottom in the order of setting 0, to obtain a K*2N two-dimensional matrix;

[0029] If the calculated circulation is greater than or equal to the target value I cnref , then enters the sub-state region where the circulating current is reduced. The step of entering the sub-state region where the circulating current is reduced is as follows: find N columns with N elements being 0 in the one-dimensional matrix S corresponding to the current state, set the columns with N elements being 0 to 1 in order from left to right, and set only one column with an element being 0 to 1 at a time, to obtain N one-dimensional matrices; screen out a one-dimensional matrix that makes the MMC output level L from the N one-dimensional matrices, use the screened one-dimensional matrix as a sub-state candidate group, and arrange each matrix in the sub-state candidate group from top to bottom in the order of setting 0, to obtain a K*2N two-dimensional matrix.

[0030] If L is unable to control the circulating current level, then S sum =N-1 or S sum =N+1; when S sum =N+1, find N+1 columns with 1 elements in the one-dimensional matrix S corresponding to the current state, and set the columns with 1 elements to 0 in order from left to right, setting only one column with 1 elements to 0 at a time, to obtain N+1 one-dimensional matrices; select the one-dimensional matrix that makes the MMC output level L from the N+1 one-dimensional matrices, use the selected one-dimensional matrix as the next-state candidate group, and arrange each matrix in the next-state candidate group from top to bottom in the order of setting 0, to obtain a K*2N two-dimensional matrix;

[0031] When S sum =N-1, find N-1 columns with N-1 elements of 0 in the one-dimensional matrix S corresponding to the current state, set the columns with elements of 0 to 1 in order from left to right, and set only one column with elements of 0 to 1 at a time, to obtain N-1 one-dimensional matrices; filter out the one-dimensional matrix that makes the MMC output level L from the N-1 one-dimensional matrices, use the filtered one-dimensional matrix as the next-state candidate group, and arrange each matrix in the next-state candidate group from top to bottom in the order of setting 1, to obtain a K*2N two-dimensional matrix.

[0032] Furthermore, the method can also calculate the number of MMC redundant states according to the order of the MMC output level and the total number of conductive submodules in the upper and lower bridge arms, and obtain the impact of the output level order on the circulating current. Specifically, the output levels are grouped according to the order of the MMC output level, with the same order forming a group, and a total of 2N+1 groups. The number of redundant states in each group and the impact on the circulating current are obtained according to the following Table 1:

[0033] Table 1:

[0034]

[0035] In the table, ↑ indicates that the circulation increases, → indicates that the circulation remains unchanged, and ↓ indicates that the circulation decreases; Indicates the number of switch state combinations of all submodules in the lower bridge arm when all N submodules in the lower bridge arm are turned on. Indicates the number of redundant states of the lower bridge arm when N-1 of the N sub-modules in the lower bridge arm are turned on, that is, the number of switch state combinations of all sub-modules in the lower bridge arm when N-1 of the N sub-modules in the lower bridge arm are turned on; Indicates the number of redundant states of the upper bridge arm when N-1 sub-modules among the N sub-modules of the upper bridge arm are turned on.

[0036] Furthermore, in step 3, if L+N is an even number, L cannot control the circulating current level; if L+N is an odd number, L can control the circulating current level.

[0037] Furthermore, the step 6 is specifically as follows: using a pseudo-random function f(K) to generate a positive integer k less than or equal to K, and taking the kth row in the K*2N matrix corresponding to the positive integer k as the randomly generated next state S opt ;

[0038] A cache matrix B is set to store p sub-states, and it is determined whether the currently generated sub-state is in the cache matrix B. If not, the currently generated sub-state is used as the pulse of the MMC at the next moment and cached in the cache matrix B, and the first sub-state in the cache matrix B is deleted; otherwise, the currently generated sub-state is deleted, and the pseudo-random function f(K) is re-adopted to generate the sub-state, so that the random function generates different sub-states within one fundamental wave period; if the number of times the sub-state is regenerated exceeds the preset m times, the comparison with the cache matrix B is stopped, and the mth randomly generated sub-state in the regeneration is used as the pulse of the MMC at the next moment and cached in the cache matrix B, and the first sub-state in the cache matrix B is deleted.

[0039] Beneficial effects:

[0040] 1. The present invention takes into account that the level change of the multi-level target waveform is inevitable. In this method, all states in the secondary state group have only one element changed compared with the current state, which ensures that the total number of switching times is minimized and no unnecessary switching actions occur.

[0041] 2. The present invention compares the circulating current with the target value, so that all states in the selected sub-state group make the circulating current close to the target value, actively controlling the circulating current and preventing low-frequency components such as double frequency and quadruple frequency from occurring.

[0042] 3. This invention introduces a pseudorandom function to uniformize switching behavior over a large time scale, enabling each submodule to achieve self-balancing of capacitor voltages. This method eliminates the need for voltage sequencing, active voltage control, or voltage sensors, reducing hardware costs.

[0043] 4. The present invention can not only achieve the three secondary goals of circulating current control, minimization and uniformity of submodule switching actions, but also does not require manual planning of state paths in advance, is applicable to any number of level occasions, and is universal. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a topological diagram of the single-phase MMC of the present invention.

[0045] Figure 2 This is a flow chart of the general pulse distribution method of the present invention.

[0046] Figure 3 The waveforms of circulating current, output current, capacitor voltage of each submodule, average capacitor voltage of upper and lower bridge arms, and output voltage are shown in Figure (a) when N=7. cm Figure (b) is the waveform of the bridge arm current i when N=7. u ,i l and the output current i o Figure (c) shows the waveform of the capacitor voltage u of each submodule when N=7 dcjn Figure (d) shows the waveform of the average sub-module capacitor voltage u of the upper and lower bridge arms when N=7. smave Figure (e) is the waveform of the output voltage u when N=7 o Waveform diagram;

[0047] Figure 4 The waveforms of circulating current, output current, capacitor voltage of each submodule, average capacitor voltage of upper and lower bridge arms, and output voltage are shown in Figure (a) when N=8. cm Figure (b) is the waveform of the bridge arm current i when N=8 u ,i l and the output current i oFigure (c) shows the waveform of the capacitor voltage u of each submodule when N=8 dcjn Figure (d) shows the waveform of the average sub-module capacitor voltage u of the upper and lower bridge arms when N=8. smave Figure (e) is the waveform of the output voltage u when N=8 o Waveform diagram;

[0048] Figure 5 The figures are comparison diagrams of the five-level MMC using the finite state machine method and the method proposed in this article, wherein Figure (a) is the output voltage and circulation diagram of the five-level MMC when the method proposed in this article is adopted; Figure (b) is the output voltage and circulation diagram of the five-level MMC when the finite state machine method is adopted; Figure (c) is the normalized weighted total harmonic content diagram of the output voltage of the five-level MMC when the method proposed in this article is adopted; Figure (d) is the normalized weighted total harmonic content diagram of the output voltage of the five-level MMC when the finite state machine method is adopted.

[0049] Figure 6 The waveforms of the upper and lower bridge arm currents, circulating currents, and submodule capacitor voltages before and after switching from the finite state machine method to the method proposed in the present invention are shown. DETAILED DESCRIPTION

[0050] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0051] This invention primarily applies to a universal pulse distribution method for MMCs under optimal PD-PWM modulation. By introducing a pseudorandom function, it aims to uniformize switching behavior over a large time scale, enabling self-balancing of capacitor voltages within each submodule. By comparing the circulating current with a target value, all states in the selected sub-state group are aligned to the target value, actively controlling the circulating current and preventing the generation of low-frequency components such as doubled and quadrupled frequencies.

[0052] like Figure 1 As shown, the single-phase MMC consists of two bridge arms, upper and lower, each bridge arm is composed of N submodules cascaded. The submodule of MMC is usually a half-bridge structure, which includes a pair of two-quadrant switch tubes and an energy storage capacitor. jn It represents the nth submodule of the jth bridge arm (j={u,l},n={1,2,...,N}) where u is the upper bridge arm and l is the lower bridge arm. In steady state, the design target value of the submodule capacitor voltage is 2U dc / N(U dcThe external total DC voltage is also the output voltage of the MMC DC side. A coupling inductor is configured at the connection between the two bridge arms to limit the short-circuit current (circulating current) caused by the mismatch between the external total DC voltage and the total voltage of the phase bridge arm conduction submodule. L0 and R0 represent the AC side load inductance and load resistance.

[0053] like Figure 2 Figure 2 shows a flow chart of a general pulse allocation method based on finite state machine principles. This method consists of three main steps: determining the nature of the target level, determining the sub-state group, and determining the sub-state based on a pseudo-random function. This allocation method introduces three constraints into the custom rules for sub-state selection: circulating current control, minimizing the number of switching operations, and ensuring uniformity in the number of switching operations.

[0054] Through Figure 1 Establishing equations for the two mesh loops of a single-phase MMC and determining the MMC switching model mainly involves the following sub-steps:

[0055] (S11) Kirchhoff voltage equations are established for the two mesh circuits of the single-phase MMC, and we can obtain:

[0056]

[0057] Corresponding to loop ①.

[0058]

[0059] Corresponding to loop ②.

[0060] Among them, i u 、i l are the upper and lower arm currents, u o is the output voltage at the midpoint of the MMC phase bridge arm; L m , L s 、R s are the mutual inductance, self-inductance and equivalent resistance of the coupled inductors respectively; u acjn represents the AC side voltage of the nth submodule in the jth bridge arm;

[0061] (S12) Define the common mode current (i.e., circulating current) i according to the following equations (3) and (4): cm , differential mode current i dm , and substitute it into equations (1) and (2) to obtain the system-level common-mode and differential-mode mathematical models of MMC as equations (5) and (6); where:

[0062]

[0063]

[0064] u acunIndicates the AC side voltage of the nth submodule in the upper bridge arm, u aclun Indicates the AC side voltage of the nth submodule in the lower bridge arm.

[0065] (S13) Define the submodule switch function σ jn ={1, 0} respectively, where 1 indicates that the submodule is put into operation and 0 indicates that the submodule is removed. Therefore, the common mode σ of the switching function can be listed by referring to (3) and (4). cm and differential mode σ dm form;

[0066]

[0067] where σ cm is the common mode component of the switching function, σ dm is the differential mode component of the switching function. un represents the switching state function of the nth submodule in the upper bridge arm, σ ln Indicates the switch status of the nth submodule in the lower bridge arm.

[0068] (S14) Substitute (7)(8) into (5)(6), and approximate the upper and lower bridge arm submodule capacitances to steady-state values. Ignore the bridge arm internal resistance and then sort out:

[0069]

[0070] Among them L k To express leakage inductance, the above two equations are the switching models of MMC.

[0071] In the general pulse distribution method based on the finite state machine principle, the redundant states are first classified and the properties of the target level are determined. The main sub-steps are as follows:

[0072] (S21) Define the redundant switch state of MMC as a one-dimensional matrix S with 2N elements = [σ u1 ,σ u2 ,…,σ un ,…,σ uN ,σ l1 ,σ l2 ,…,σ ln ,…,σ lN ], the 1st to Nth columns are the switching functions of the upper bridge arm submodule, the N+1st to 2Nth columns are the switching functions of the lower bridge arm submodule, and the total number of conducting submodules in each bridge arm is S sum Generally, there are three cases: N, N-1 and N+1, so the number of S is S 总 species; among them:

[0073]

[0074] Indicates the total number of combinations in which N submodules among the 2N submodules are in the input state. Indicates the total number of combinations in which N-1 submodules are in the input state among the 2N submodules. Indicates the total number of combinations in which N+1 submodules are in the activated state among the 2N submodules.

[0075] (S22) According to equations (7) and (9), and considering the different effects of different total number of conducting submodules on the circulating current, the redundant state is divided into three categories; specifically:

[0076] 1)S sum =N, σ cm =1, the circulation remains unchanged (indicated by →);

[0077] 2)S sum =N-1, σ cm <1, the circulation increases (indicated by ↑);

[0078] 3)S sum =N+1, σ cm >1, the circulation decreases (indicated by ↓).

[0079] (S23) The AC voltage level output by the MMC is divided into basic groups, and within each basic group, the basic group is subdivided according to the impact of the output AC voltage level on the circulating current. That is, all conduction combinations are divided into those that affect the control of the circulating current (increase or decrease) and those that cannot control the circulating current. The impact of the 2N+1 level MMC redundancy state on the circulating current and its amount can be obtained; specifically:

[0080] The 2N+1 level MMC output voltage has 2N+1 steps, so it can naturally be divided into 2N+1 groups, with the same number of steps as one group; as shown in Table 1 below, for example, when the output level is N-1, it can be divided into two situations: the upper bridge arm is turned on 0, the lower bridge arm is turned on N-1 (circulating current ↑) and the upper bridge arm is turned on 1, the lower bridge arm is turned on N (circulating current ↓), representing S sum =0+N-1=N-1 and S sum =1+N two circulation change conditions, S sum =N-1 when the circulation increases. sum =N+1, the circulating current decreases. It is worth noting that at this output level, due to S sum It cannot be equal to N, so the circulation can only increase or decrease, not remain unchanged.

[0081]

[0082]

[0083] In the table, ↑ indicates that the circulation increases, → indicates that the circulation remains unchanged, and ↓ indicates that the circulation decreases; Indicates the number of switch state combinations of all submodules in the lower bridge arm when all N submodules in the lower bridge arm are turned on (no matter how much N is, the number of this combination is 1). Indicates the number of redundant states of the lower bridge arm when N-1 of the N submodules in the lower bridge arm are turned on, that is, the number of switch state combinations of all submodules in the lower bridge arm when N-1 of the N submodules in the lower bridge arm are turned on; Indicates the number of redundant states of the upper bridge arm when N-1 sub-modules among the N sub-modules in the upper bridge arm are turned on.

[0084] As shown in Table 1, the target level of MMC can be divided into two types: controllable circulating current and uncontrollable circulating current. Under the controllable circulating current level, the sum of the upper and lower bridge arm submodules turned on S sum ∈{N+1,N-1}, when S sum =N-1, the circulation increases; when S sum =N+1, the circulating current decreases. At the level of uncontrollable circulating current, the sum of the upper and lower bridge arm submodules conducting S sum = N, the circulating current remains unchanged. Since N can be odd or even, and a target level of N always corresponds to a constant circulating current, determining whether the circulating current has changed cannot be determined by determining whether the target level is odd or even. However, determining whether the target level L is at a controllable circulating current level can be determined by determining the odd or even sum of the target level L and N. When L + N is odd, L is a controllable circulating current level; when L + N is even, L is an uncontrollable circulating current level.

[0085] (S24) Figure 2 As shown, when L+N is an odd number, S sum = N, the current of the upper and lower bridge arms after sampling is updated, and the circulating current size is calculated and compared with the target value I cmref If the comparison is smaller than the target value, the system enters a sub-state region where the circulating current increases. Therefore, a sub-module that is turned on in the current state should be turned off, and the system enters a sub-state region where the circulating current increases. Specifically, the following steps are performed: in the one-dimensional matrix S corresponding to the current state, the columns with N elements that are 1 are set to 0 in order from left to right, and only one column with an element that is 1 is set to 0 at a time, to obtain N one-dimensional matrices; from the N one-dimensional matrices, a one-dimensional matrix that makes the MMC output level L is selected, and the selected one-dimensional matrix is ​​used as a next-state candidate group. Each matrix in the next-state candidate group is arranged from top to bottom in the order of setting 0, to obtain a K*2N matrix, where K is the number of one-dimensional matrices in the next-state candidate group.

[0086]

[0087] The expression of the circulation target value is as follows:

[0088]

[0089] Where R(*) means taking a real number, is the output current reference value.

[0090] If it is greater than or equal to the target value, then enter the sub-state area where the circulation current is reduced. The specific steps of entering the sub-state area where the circulation current is reduced are as follows: find N columns with N elements of 0 in the one-dimensional matrix S corresponding to the current state, set the columns with elements of 0 to 1 in order from left to right, and set only one column with elements of 0 to 1 at a time to obtain N one-dimensional matrices; filter out the one-dimensional matrix that makes the MMC output level L from the N one-dimensional matrices, use the filtered one-dimensional matrix as the sub-state candidate group, and arrange each matrix in the sub-state candidate group from top to bottom in the order of setting 0 to obtain a K*2N two-dimensional matrix, where K is the number of one-dimensional matrices in the sub-state candidate group.

[0091] When L+N is an even number, similar to when L+N is an odd number, S sum =N-1 or S sum =N+1; when S sum =N+1, find N+1 columns with 1 elements in the one-dimensional matrix S corresponding to the current state, set the columns with 1 elements to 0 in order from left to right, and set only one column with 1 elements to 0 at a time, to obtain N+1 one-dimensional matrices; select the one-dimensional matrix that makes the MMC output level L from the N+1 one-dimensional matrices, use the selected one-dimensional matrix as the next-state candidate group, and arrange each matrix in the next-state candidate group from top to bottom in the order of setting 0, to obtain a K*2N two-dimensional matrix, where K is the number of one-dimensional matrices in the next-state candidate group.

[0092] When S sum =N-1, find N-1 columns with N-1 elements of 0 in the one-dimensional matrix S corresponding to the current state, set the columns with elements of 0 to 1 in order from left to right, and set only one column with elements of 0 to 1 at a time, to obtain N-1 one-dimensional matrices; screen out the one-dimensional matrix that makes the MMC output level L from the N-1 one-dimensional matrices, use the screened one-dimensional matrix as the next-state candidate group, and arrange each matrix in the next-state candidate group from top to bottom in the order of setting 1, to obtain a K*2N two-dimensional matrix, where K is the number of one-dimensional matrices in the next-state candidate group.

[0093] At this time, the expression of K is as follows

[0094]

[0095] In a specific embodiment, the generation of the next state group when N=2 and L+N is an odd number or an even number is taken as an example. Assume that the current state S is [1 0 0 1], and the target level increases by i cm Less than reference value Icmref , since L+N is an odd number at this time, according to step (S24), the candidate group should be set to 0 in sequence. Thus, the candidate groups are [0 0 0 1] and [1 0 0 0]. Since only [0 0 0 1] meets the target level, it is selected as the sub-state group. At this time, K=1, which is consistent with the calculation of formula (12). If the current state S is [1 1 0 1], since S sum =N+1, and after setting the elements that are 1 in S to 0 in sequence, the candidate groups are [0 1 0 1], [10 0 1], and [1 1 0 0]. From these, the combination that meets the output level equal to L is selected to obtain the next state group. In this case, K=2, which is consistent with the calculation of formula (14).

[0096] In the general pulse distribution method based on the finite state machine principle, the actual on-state switch combination is selected from the candidate switch combinations through a pseudo-random function to determine the next state. The method mainly includes the following sub-steps:

[0097] (S31) The next state is determined by a random function f(K), where f(K) is a random function that can randomly generate a positive integer less than or equal to K, and the kth row in the K*2N two-dimensional matrix corresponding to the positive integer k is used as the randomly generated next state S opt , then f(K) can randomly generate a next state S in the next state group opt

[0098] f(K)=k (15)

[0099] (S32) Introduce the state cache matrix B to store the history of the recent p states and make the current randomly generated S opt It is not in the cache matrix B, ensuring that the random function will not generate the same state within a fundamental wave period;

[0100] (S33) Setting a loop-out mechanism, i.e. reselecting a positive integer no more than m times, once it exceeds m, then jumping out of the comparison link with B and directly generating the next state S randomly opt .

[0101] In a specific implementation, the same sub-state group S X The final states selected at different time points are evenly distributed in probability. All states will be selected on a large time scale, driving the submodule capacitor voltage to self-balance. However, in reality, when the carrier frequency is constant, the larger the number N, the longer the cycle of traversing all states will be, and the time scale for achieving self-balance is too large. Therefore, this method introduces a state cache matrix B to store the historical records of the past p times S. Its purpose is to make the current randomly generated S optNot in the cache matrix B. Considering that under optimal PD-PWM modulation, the number of back-and-forth changes between adjacent levels is related to the carrier frequency, the dimension of the cache matrix B should cover this number to ensure that the random function does not generate the same state within a cycle. This method can also be called a pseudo-random method, which shortens the time required for self-balancing to a certain extent.

[0102] Figure 3 As shown in Figure 1, it is the characteristic variable steady-state simulation waveform of MMC under the proposed method when N=7. Figure 3 As shown in (a), by selecting the appropriate redundant state at the controllable level, the circulating current always moves towards the target value, and the circulating current i cm Active suppression is achieved, and the circulating current ripple is controlled at around ±20%. Figure 3 As shown in (b), since the circulating current is effectively controlled, its main component is the DC component, and the MMC bridge arm current i u 、i l And the output current i o , showing a relatively ideal sinusoidal AC form. Figure 3 As shown in (c), since this method selects the next state S by pseudo-random function opt , so that its switch combination distribution is balanced, the submodule capacitor voltage can maintain balance within a large time scale, and its sideband value does not exceed ±10% of the target value. Figure 3 As shown in (d), the average voltage of the upper and lower bridge arm submodule capacitors is consistent with the MMC waveform under PSC-PWM modulation, mainly containing primary and secondary power pulsation components, and the upper and lower bridge arms are balanced. Figure 3 As shown in (e), the AC side output voltage of the 2N+1 type MMC is 15 levels when N=7, which proves the versatility of the proposed method.

[0103] Figure 4 As shown in Figure 1, it is the characteristic variable steady-state simulation waveform of MMC under the proposed method when N=8. Figure 4 As shown in (a), by selecting the appropriate redundant state at the controllable level, the circulating current always moves towards the target value, and the circulating current i cm Active suppression is achieved, and the circulating current ripple is controlled at around +20%. Figure 4 As shown in (b), since the circulating current is effectively controlled, its main component is the DC component, and the MMC bridge arm current i u 、i l And the output current i o , showing a relatively ideal sinusoidal AC form. Figure 4 As shown in (c), since this method selects the next state S by pseudo-random function opt, so that its switch combination distribution is balanced, the submodule capacitor voltage can maintain balance within a large time scale range, and its sideband value does not exceed ±10% of the target value. Furthermore, if Figure 4 As shown in (d), the average voltage of the upper and lower bridge arm submodule capacitors is consistent with the MMC waveform under PSC-PWM modulation, mainly containing primary and secondary power pulsation components, and the upper and lower bridge arms are balanced. Figure 4 As shown in (e), the AC side output voltage of the 2N+1 type MMC is 17 levels when N=8, which proves the versatility of the proposed method.

[0104] Figure 5 As shown in Figure 3, the output voltage and circulating current of the five-level MMC are compared under the finite state machine method and the method proposed in this paper. Figure 5 Figures (a) and (b) show the output voltage and circulating current waveforms obtained using the finite state machine method and the general allocation method proposed in this paper, respectively. Because the finite state machine does not control the circulating current component and also suffers from circulating current offset due to inherent defects in PD-PWM modulation, the circulating current amplitude fluctuates and the envelope exhibits low-frequency fluctuations. In contrast, the method described in this paper actively controls the circulating current component, keeping it fluctuating around its target value, effectively eliminating the low-frequency harmonic components in the circulating current. Figure 5 (c) Figure 5 Figure (d) shows the FFT analysis of the output voltage using the two methods. As can be seen, after the circulating current harmonics are suppressed, the weighted total harmonic content of the output AC voltage drops from 1.56% to 0.94%, making the multi-level level smoother than before the circulating current harmonics are suppressed.

[0105] Figure 6As shown in the figure, the experimental waveforms before and after the finite state machine method is switched to the method proposed in this article. The waveforms measured in the figure are the upper and lower bridge arm currents, the circulating currents, and the four sub-module capacitor voltages (the upper three are the upper and lower bridge arm current waveforms, the circulating current waveforms, and the four sub-module capacitor voltage waveforms of the finite state machine method, and the lower three are the upper and lower bridge arm current waveforms, the circulating current waveforms, and the four sub-module capacitor voltage waveforms of the method proposed in this embodiment). The measured waveforms in the figure are the upper and lower bridge arm currents, the circulating currents, and the four sub-module capacitor voltages. As can be seen from the figure, since the circulating current is actively controlled to a DC form, the bridge arm current is in a relatively ideal sinusoidal AC form, and its peak-to-peak value is reduced from the original 42A to about 28A. In addition, since the redundant states corresponding to each level are at most 4 when N=2, setting the number of rows p of the cache matrix B to 3 can ensure the traversal conduction of the sub-module. It is worth noting that since K is very small here and there are few redundant states, the selection of p does not need to consider the size of the carrier frequency, which is also the main difference from the N=8 working condition. As can be seen from the figure, the finite state machine is able to maintain real-time balance among the submodule capacitor voltages before and after switching. However, after switching, while the submodule capacitor voltages cannot be balanced in real time, the capacitor voltages of all submodules in the phase bridge arm are constrained within a voltage band near the target value, and the capacitor voltage of each submodule exhibits large-scale balance. The main reason for this difference is that the finite state machine method ensures that the switching times of each submodule are essentially equal within each power frequency cycle, while the proposed method can only ensure that the switching times are consistent at several base frequencies.

Claims

1. A general pulse distribution method for MMC under optimal PD-PWM modulation, wherein a single-phase MMC includes upper and lower bridge arms, each of which includes N cascaded submodules, each of which includes a pair of two-quadrant switching tubes and an energy storage capacitor; characterized in that: The method specifically comprises the following steps: Step 1: Establish the switch model of MMC; Step 2: The redundant state of MMC is converted into a one-dimensional matrix S with 2N elements = [σ u1 ,σ u2 ,…,σ un ,…,σ uN ,σ l1 ,σ l2 ,…,σ ln ,…,σ lN ] represents, where σ un represents the switching state function of the nth submodule in the upper bridge arm, σ ln represents the switch state function of the nth submodule in the lower bridge arm; σ jn = {0, 1}, 0 represents removal, 1 represents input, j = {u, l}, n = {1, 2, ..., N}, calculate the impact of the total number of submodules invested in the MMC on the circulation state; Step 3: Divide the target level L into a level that can control the circulating flow type and a level that cannot control the circulating flow type; Step 4: Set the circulating current target value I according to the MMC switch model in step 1 cmref ; Step 5: According to the impact of the total number of submodules in the MMC on the circulating current state in step 2, the type of the target level L in step 3, and the circulating current target value in step 4, set a sub-state candidate group. The number of sub-states in the sub-state candidate group is K, and the sub-state candidate group is a K*2N matrix; Step 6: Use a pseudo-random function to select a group of next states from the next state candidate group to determine the pulse state at the next moment; The influence of the total number of submodules put into operation in the MMC on the circulation state in step 2 is specifically as follows: the total number of submodules put into operation in the upper and lower bridge arms S sum is N, N-1 or N+1; when S sum =N, σ cm =1, the circulation remains unchanged; when S sum =N-1, σ cm <1, the circulation increases; when S sum =N+1, σ cm >1, the circulation decreases, σ cm is the common mode component of the submodule switching function; The step 5 is specifically as follows: If L is able to control the circulating level, then S sum = N, calculate the circulating current size according to the current of the upper and lower bridge arms, and compare it with the target value I cnref If the calculated circulation is less than the target value I cnref , then enter the secondary state region that increases the circulation. Specifically, find the N columns with 1 elements in the one-dimensional matrix S corresponding to the current state, and set the columns with 1 elements to 0 in order from left to right, setting only one column with 1 elements to 0 at a time, and obtain N one-dimensional matrices; A one-dimensional matrix that makes the MMC output level L is selected from N one-dimensional matrices, and the selected one-dimensional matrix is ​​used as a next-state candidate group. Each matrix in the next-state candidate group is arranged from top to bottom in the order of setting 0 to obtain a K*2N two-dimensional matrix; If the calculated circulation is greater than or equal to the target value I cnref , then enter the secondary state region where the circulation is reduced. The specific method of entering the secondary state region where the circulation is reduced is as follows: find N columns with zero elements in the one-dimensional matrix S corresponding to the current state, and set the columns with zero elements to 1 in order from left to right, setting only one column with zero elements to 1 at a time, to obtain N one-dimensional matrices; A one-dimensional matrix that makes the MMC output level L is selected from N one-dimensional matrices, and the selected one-dimensional matrix is ​​used as a next-state candidate group. Each matrix in the next-state candidate group is arranged from top to bottom in the order of setting 0 to obtain a K*2N two-dimensional matrix; If L is unable to control the circulating current level, then S sum =N-1 or S sum =N+1; when S sum =N+1, find the N+1 columns with 1 elements in the one-dimensional matrix S corresponding to the current state, and set the columns with 1 elements to 0 in order from left to right, setting only one column with 1 elements to 0 at a time, and obtain N+1 one-dimensional matrices; A one-dimensional matrix that makes the MMC output level L is selected from N+1 one-dimensional matrices, and the selected one-dimensional matrix is ​​used as a next-state candidate group. Each matrix in the next-state candidate group is arranged from top to bottom in the order of setting 0 to obtain a K*2N two-dimensional matrix; When S sum =N-1, find the N-1 columns of the one-dimensional matrix S corresponding to the current state with N-1 elements of 0, and set the columns of 0 elements to 1 in order from left to right, setting only one column of 0 elements to 1 at a time, and obtain N-1 one-dimensional matrices; A one-dimensional matrix that makes the MMC output level L is screened out from N-1 one-dimensional matrices, and the screened one-dimensional matrix is ​​used as a next-state candidate group. Each matrix in the next-state candidate group is arranged from top to bottom in the order of setting 1 to obtain a K*2N two-dimensional matrix.

2. The universal pulse distribution method for MMC under optimal PD-PWM modulation according to claim 1, characterized in that: The switch model of the MMC in step 1 is: Among them, u o is the output voltage at the midpoint of the MMC phase bridge arm, L m is the mutual inductance of the coupled inductors in the MMC, i cm is the common mode current; U dc is the voltage amplitude of the MMC DC side, L k is the MMC leakage inductance, i dm is the differential mode current; σ cm is the common mode component of the submodule switching function, σ dm is the differential mode component of the submodule switching function; i cm ,i dm The expression is as follows: i u 、i l are the currents of the upper and lower bridge arms respectively; σ cm The expression is as follows:

3. The universal pulse distribution method for MMC under optimal PD-PWM modulation according to claim 2, characterized in that: The expression of the circulation target value in step 4 is as follows: Where R(*) means taking a real number, is the output current reference value.

4. The universal pulse distribution method for MMC under optimal PD-PWM modulation according to claim 1, characterized in that: This method can also calculate the number of MMC redundant states according to the order of the MMC output level and the total number of conductive submodules in the upper and lower bridge arms, and obtain the impact of the output level order on the circulating current. Specifically, the output levels are grouped according to the order of the MMC output level, with the same order forming a group, for a total of 2N+1 groups. The number of redundant states in each group and the impact on the circulating current are obtained according to the following Table 1: Table 1: In the table, ↑ indicates that the circulation increases, → indicates that the circulation remains unchanged, and ↓ indicates that the circulation decreases; Indicates the number of switch state combinations of all submodules in the lower bridge arm when all N submodules in the lower bridge arm are turned on. Indicates the number of redundant states of the lower bridge arm when N-1 of the N sub-modules in the lower bridge arm are turned on, that is, the number of switch state combinations of all sub-modules in the lower bridge arm when N-1 of the N sub-modules in the lower bridge arm are turned on; Indicates the number of redundant states of the upper bridge arm when N-1 sub-modules among the N sub-modules of the upper bridge arm are turned on.

5. The universal pulse distribution method for MMC under optimal PD-PWM modulation according to claim 1, characterized in that: In step 3, if L+N is an even number, L cannot control the circulating current level; if L+N is an odd number, L can control the circulating current level.

6. The universal pulse distribution method for MMC under optimal PD-PWM modulation according to claim 1, characterized in that: The step 6 is specifically as follows: using a pseudo-random function f(K) to generate a positive integer k less than or equal to K, and taking the kth row in the K*2N matrix corresponding to the positive integer k as the randomly generated next state S opt ; Set up a cache matrix B to store p sub-states. Determine whether the currently generated sub-state is in cache matrix B. If not, cache the currently generated sub-state as the pulse of the MMC at the next moment in cache matrix B, and delete the first sub-state in cache matrix B. Otherwise, the currently generated sub-state is deleted, and the pseudo-random function f(K) is used again to generate the sub-state, so that the random function generates different sub-states within one fundamental wave period; If the number of times the sub-state is regenerated exceeds the preset m times, the comparison with the cache matrix B is stopped, and the mth randomly generated sub-state in the regeneration is used as the pulse of the MMC at the next moment and cached to the cache matrix B. At the same time, the first sub-state in the cache matrix B is deleted.

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