A virtual voltage vector-based model predictive control method for modulation type MMC

Abstract

The application belongs to the technical field of direct current transmission, and discloses a MMC modulation type model prediction control method based on virtual voltage vectors, which takes the inverter current tracking error on the AC side and the inter-phase circulating current suppression as control targets, introduces multiple virtual levels, uses a small number of virtual voltage vectors to replace a large number of actual voltage vectors for rolling optimization, determines the optimal virtual voltage vector combination and calculates the duty ratio thereof, obtains the optimal actual voltage vector combination and the duty ratio thereof through the spatial relationship between the virtual voltage vector and the actual voltage vector, then calculates the circulating current action required for circulating current suppression and the duty ratio thereof, and finally generates the control signals of each sub-module in the controlled MMC by using the capacitor voltage balancing method and the modulation strategy, so that the controlled MMC can output three control levels in each control period, and thus the actual current output by the controlled MMC in each control period is closer to the corresponding target current.

Description

Technical Field

[0001] This invention belongs to the technical field of DC power transmission, specifically relating to an MMC modulation model predictive control method based on virtual voltage vector. Background Technology

[0002] Due to the uneven distribution of power resources in my country, long-distance power transmission is often required. Flexible DC transmission projects based on Modular Multilevel Converters (MMC) have emerged and have begun to be gradually promoted.

[0003] Modular multilevel converters (MMCs) are widely used in long-distance renewable energy power generation projects due to their excellent scalability, high modularity, and tolerance to DC short-circuit faults. Their main control objectives are AC-side current tracking, circulating current suppression, and equalization control of submodule capacitor voltages. Currently, traditional MMC control strategies require the integration of linear controllers for AC-side current, circulating current suppression, and submodule capacitor voltage balancing. This leads to complex control system design, and the excessive number of linear controllers increases the difficulty of system control parameter tuning and stability analysis. Circulating current suppression typically employs a circulating current suppressor based on second-harmonic negative-sequence coordinate transformation. This controller increases system computational complexity and is only applicable to three-phase systems, making it inflexible for single-phase systems.

[0004] Model Predictive Control (MPC) is suitable for multi-input multi-output nonlinear systems. Compared to classical linear control (PI dual-loop control), it can easily achieve multiple control objectives, has a fast dynamic response, and a simple principle. Its disadvantages include the need for coordination among multiple control objectives through weighting coefficients; improper selection of these coefficients can degrade control performance. Furthermore, it requires calculating all possible submodule switching states within each control cycle and selecting the optimal switching combination to achieve the control objective, resulting in a high computational burden and significantly impacting computation speed. While it reduces processor costs to some extent by eliminating the need for a modulation module, it introduces problems such as inconsistent switching frequencies and dispersed output harmonic spectra, which are detrimental to filter design. Summary of the Invention

[0005] For multi-objective control of MMC, this invention proposes a virtual voltage vector-based MMC modulation model predictive control method. This method uses fewer virtual voltage vectors to replace a larger number of actual voltage vectors for prediction, reducing computational burden. In interphase circulating current control, it eliminates the need for negative-sequence coordinate transformation based on second harmonics, simplifying suppression. In the sub-unit capacitor voltage balancing scheme, it utilizes capacitor voltage balancing methods to achieve balancing while reducing system computational burden. An additional modulation scheme achieves a fixed switching frequency, resolving the spectral dispersion problem caused by model predictive control.

[0006] This invention can be achieved through the following technical solutions:

[0007] A virtual voltage vector-based MMC modulation model predictive control method is proposed. This method targets AC-side inverter current tracking error and interphase circulating current suppression. By introducing multiple virtual voltage levels, a smaller number of virtual voltage vectors are used to replace a larger number of actual voltage vectors for rolling optimization. The optimal combination of virtual voltage vectors is determined, and their duty cycles are calculated. Then, the optimal combination of actual voltage vectors and their duty cycles are obtained through the spatial relationship between virtual and actual voltage vectors. Next, the circulating current action required for circulating current suppression and its duty cycle are calculated. Finally, a capacitor voltage balancing method and modulation strategy are used to generate control signals for each submodule in the controlled MMC, enabling the controlled MMC to output three control levels in each control cycle. This ensures that the actual current output by the controlled MMC in each control cycle more closely approximates the corresponding target current.

[0008] Furthermore, an AC-side predicted current evaluation function and a circulating current prediction model are constructed. Based on the AC-side predicted current evaluation function, multiple virtual levels are rolled for optimization to determine the optimal virtual voltage vector combination and calculate its duty cycle Dv. Then, through the spatial relationship between the virtual voltage vector and the actual voltage vector, the optimal actual voltage vector combination and its duty cycle Da are obtained.

[0009] Then, based on the circulation prediction model, calculate the circulation prediction value and its duty cycle Dz corresponding to the input or output of the sub-module;

[0010] Finally, the modulation signal of each sub-module in the controlled MMC is obtained by using the duty cycle Dz of the circulating current control and the duty cycle Da of the AC side predictive current control, combined with the capacitor voltage balancing method. The signal of the semiconductor switching device is obtained by using the modulation strategy through the modulator.

[0011] Furthermore, based on the equivalence principle of two-port networks, each phase structure in the MMC is equivalent to a three-level converter composed of two semiconductor switches, and four virtual levels are introduced, as follows:

[0012] 1) Virtual Level VI: All submodules of the upper bridge arm are in the active state, and all submodules of the lower bridge arm are in the deactivated state. The equivalent AC neutral point output voltage at this time is: -u p ;

[0013] 2) Virtual Level VII: All submodules of the upper bridge arm are in the off state, and all submodules of the lower bridge arm are in the on state. The equivalent AC neutral point output voltage at this time is: u n ;

[0014] 3) Virtual Level VIII: All submodules of the upper arm and all submodules of the lower arm are in the active state. The equivalent AC neutral point output voltage at this time is: u n -u p ;

[0015] 4) Virtual Level VIV: All submodules of the upper bridge arm are in the cut-off state, and all submodules of the lower bridge arm are in the cut-off state. At this time, the equivalent AC midpoint output voltage is 0.

[0016] Assuming that the capacitor voltages of each submodule in each phase arm of the MMC are approximately equal, i.e., the voltages of the upper and lower arms are approximately equal, then the equivalent AC midpoint output voltages of virtual level VIII and virtual level VIV are both zero. This divides the one-dimensional virtual voltage space into two regions: virtual voltage region 1, which consists of virtual level VI and virtual level VIII; and virtual voltage region 2, which consists of virtual level VII and virtual level VIII.

[0017] Furthermore, the virtual levels VI and VII are substituted into the AC side current evaluation function for rolling optimization. The virtual level with the minimum evaluation function is taken as the optimal virtual voltage. Then, the virtual space voltage partition is determined, the optimal virtual voltage vector combination is obtained, and its duty cycle Dv is calculated.

[0018] Furthermore, the duty cycle Dv corresponding to the optimal virtual voltage vector combination is calculated using the following equation.

[0019]

[0020] In the formula, The optimal virtual voltage vector V at time k+1 vo1 AC side output current under action, The virtual voltage vector V at time k+1 vo2 That is, the AC side output current under the action of the virtual voltage vector VIII, i ref,x (k+1) is the reference current at time k+1.

[0021] Furthermore, let N be the number of sub-modules in each bridge arm, then the number of sub-modules in each phase is 2N, and the AC side midpoint output voltage has 2N+1 levels. Assuming that the capacitor voltage of each sub-module in each phase bridge arm of the MMC is approximately equal, that is, the voltage of the upper and lower bridge arms is approximately equal and approximately equal to the reference value E = V. dc / N,

[0022] Considering bus voltage balance, the number of sub-modules activated in each phase during each switching cycle must remain constant at N. Therefore, the controlled MMC can output N+1 levels, which is U. a(N+1) =-(N / 2)E,U a(N) =-(N / 2-1)E,…,0,…,U a2 = (N / 2-1)E, U a1 = (N / 2)E, thus forming N actual spatial voltage regions, denoted as actual spatial voltage region 1, 2, 3...N. Among them, virtual spatial voltage region 1 covers actual spatial voltage region 1 to (N / 2), and virtual spatial voltage region 2 covers actual spatial voltage region (N / 2+1) to N. The relationship between the AC side midpoint output voltage and the number of upper and lower bridge arm sub-modules engaged is shown in the table below.

[0023] AC side neutral point output voltage (V) <![CDATA[Number N of sub-modules for lower-bridge-arm input l > <![CDATA[Number N of the upper-bridge-arm input sub-modules u > (N / 2)E N 0 (N / 2+1)E N-1 1 … … … -(N / 2-1)E 1 N-1 -(N / 2)E 0 N

[0024] Furthermore, the optimal actual voltage region S is calculated using the following equation.

[0025] h = round((D v *V vo1 +(1-D v V vo2 ) / (V dc / N))

[0026]

[0027] Here, round() is the floor function;

[0028] Based on the optimal actual voltage region S, the voltage at the endpoint of this region is used as the optimal actual voltage vector to determine the optimal combination of actual voltage vectors. The larger optimal actual voltage vector is denoted as V. ao1 Its control period T s The duration of action within this timeframe is denoted as t. 1,x The smaller optimal actual voltage vector is V. ao2 Its control period T s The duration of action within this timeframe is denoted as t. 2,x ,

[0029] The duty cycle corresponding to the optimal actual voltage region combination

[0030] In the formula, For any one of the three phases, i.e., phase x, in V ao1 The derivative of the predicted AC current under the action, For any one of the three phases, i.e., phase x, in V ao2 The derivative of the predicted AC current under the action, Let be the reference current at time k+1. This represents the actual measured value of the AC side current at time k.

[0031] Furthermore, the action time t 1,x t 2,x This is to obtain the optimal solution where the partial derivative of the AC side predicted current evaluation function corresponding to the optimal actual voltage vector is zero.

[0032] Furthermore, when the circulating current direction is positive, an additional submodule needs to be connected, and the voltage u on the bridge arm side at the next moment... diff,x = (N+1)*V dc / N, calculate the predicted circulation value at this time based on the circulation prediction model, using i diff+ This indicates that when the circulating current direction is negative, a submodule needs to be disconnected, and the voltage u on the bridge arm side at the next moment... diff,x = (N-1)*V dc / N, calculate the predicted circulation value at this time based on the circulation prediction model, using i diff- This indicates that when there is no action, the voltage u on the bridge arm side at the next moment... diff,x =N*V dc / N, calculate the predicted circulation value at this time based on the circulation prediction model, using i diff0 The duty cycle Dz corresponding to the circulating flow control is calculated using the following equation.

[0033]

[0034] Among them, i dc This is the DC side current; Based on the sign of the circulation, i diff,o2 For i diff0 .

[0035] Furthermore, the method for generating control signals for each submodule in the controlled MMC using capacitor voltage balancing and modulation strategies includes the following steps:

[0036] 1) Determine the direction of the current in the bridge arm. If it is positive, arrange the capacitor voltages of the sub-modules in ascending order; if it is negative, arrange the capacitor voltages of the sub-modules in descending order. Then, assign a voltage sequence number to each sub-module in the bridge arm according to the voltage order.

[0037] 2) Based on the relationship between the actual voltage vector and the number of sub-modules connected in the bridge arm, the optimal actual voltage vector V is obtained. ao1 Vao2 The corresponding number of upper and lower bridge arm sub-modules deployed (N) u1 |V ao1 N u2 |V ao2 ) and (N l1 |V ao1 N l2 |V ao2 ), where N u1 N l1 For V ao1 The corresponding number of upper and lower bridge arm sub-modules; N u2 N l2 For V ao2 The corresponding number of sub-modules deployed in the upper and lower bridge arms;

[0038] 3) Calculate the modulation signal of each submodule.

[0039] When the control action for circulating current suppression is to activate an additional submodule, the formula for calculating the modulation signal is:

[0040] D u =1-(D a -0.5D z )

[0041] D l =D a +0.5D z

[0042] When the control action for circulating current suppression is to remove an additional submodule, the formula for calculating the modulation signal is:

[0043] D u =1-(D a +0.5D z )

[0044] D l =D a -0.5D z

[0045] 4) Select the smaller number of element values ​​from the input pairs of the two bridge arm submodules, and let it be n. min Based on the voltage sorting results, voltage numbers less than or equal to n are sorted. min The modulation signal of the submodule is set to 1, which means it is in the fully engaged state, indicating that it is always in the engaged state throughout the entire control cycle.

[0046] The voltage sequence number is equal to n min The modulation signal of the +1 submodule is set to D. u Or D lThis is a semi-engaged state, meaning that the system is only in an engaged state for a certain period of time within the entire control cycle, where D... u The corresponding submodule of the upper bridge arm, D l The submodule corresponding to the lower bridge arm, the submodule engaged at this time is called the half-action submodule;

[0047] The modulation signals of the remaining submodules are set to 0;

[0048] 5) Each phase of the MMC has 2N carrier signals, which correspond to each submodule. The N carrier signals of the upper arm are triangular waves with a frequency equal to the control frequency, and there is no phase difference between the carrier signals. The N carrier signals of the lower arm are triangular waves with a frequency equal to the control frequency and a phase delay of 180° from the upper arm carrier signals, and there is no phase difference between the carrier signals.

[0049] The modulation signal of each submodule is compared with the corresponding carrier signal. When the modulation signal is greater than the carrier signal, the modulator outputs a PWM signal of 1, which is a high level state; when the modulation signal is less than the carrier signal, the modulator outputs a PWM signal of 0, which is a low level state. The PWM signal is the switching signal of the semiconductor device.

[0050] For the submodule in a semi-engaged state, the action time of the semi-moving submodule of the upper arm is (1-D). u )T s The action time of the half-motion submodule of the lower bridge arm is D. l T s Their duration of action is all about 0.5T from the center of the control cycle. s Symmetry, meaning the high level of the PWM signal of the half-action submodule in the upper bridge arm starts from 0.5T. s -0.5(1-D u )T s The moment begins at 0.5T s +0.5(1-D u )T s The control cycle ends, and the level remains low for the remainder of the control period.

[0051] The low level of the PWM signal of the lower bridge arm's half-action submodule starts from 0.5T. s -0.5D l T s The moment begins at 0.5T s +0.5D l T s End; the control cycle remains high for the rest of the time.

[0052] The beneficial technical effects of this invention are as follows:

[0053] Compared to traditional control schemes based on second-harmonic negative-sequence coordinate transformation, this method avoids the complex controller design process.

[0054] Compared to the classic model predictive control method, this method does not require adjusting the weighting factor and achieves a fixed switching frequency through an additional modulator.

[0055] (1) Set virtual voltages and use a smaller number of virtual voltage vectors to replace a larger number of actual voltage vectors for rolling optimization, thereby reducing the rolling optimization process and alleviating the processor load.

[0056] (2) An additional modulator is set to modulate the modulation signal and the triangular carrier signal to obtain the final PWM signal used to control the MMC. This can achieve a fixed switching frequency, reduce the problem of spectrum dispersion, and is beneficial to AC side filter design.

[0057] (3) Three control levels can be output in one control cycle. Two of the control levels can be used to synthesize the target voltage signal more accurately, reducing the tracking error of the AC side inverter current. The remaining control level is used to suppress circulating current. There is no need to suppress circulating current based on negative sequence second harmonic ground coordinate transformation, avoiding complex coordinate transformation calculation and decoupling control, and simplifying the design difficulty. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of the control flow of the present invention;

[0059] Figure 2 This is a schematic diagram of the main circuit topology of the four-unit sub-module MMC structure in an embodiment of the present invention;

[0060] Figure 3 This is a schematic diagram of the circulating current equivalent circuit of the four-unit sub-module MMC structure in an embodiment of the present invention;

[0061] Figure 4 This is a diagram showing the relationship between the virtual voltage vector and the spatial voltage vector of this invention;

[0062] Figure 5 This is a schematic diagram of the search and application area of ​​the present invention;

[0063] Figure 6 This is a schematic diagram of the voltage vector principle of the present invention;

[0064] Figure 7 This is a schematic diagram illustrating the modulation method of the present invention;

[0065] Figure 8 The static current tracking simulation waveform during the experiment using the model predictive control of this invention;

[0066] Figure 9The simulation waveform of dynamic current tracking during the experiment using the model predictive control of this invention.

[0067] Figure 10 This is a schematic diagram illustrating the effect of the circulation suppression method of the present invention when the model predictive control of the present invention is used in an experiment.

[0068] Figure 11 A comparison chart of THD before and after adding circulation suppression is provided when conducting experiments using the model predictive control of this invention. Detailed Implementation

[0069] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings and preferred embodiments.

[0070] like Figure 1 As shown, this invention provides a model predictive control method for MMC modulation based on virtual voltage vectors. With AC-side inverter current tracking error and interphase circulating current suppression as control objectives, it introduces multiple virtual voltage levels, using a smaller number of virtual voltage vectors to replace a larger number of actual voltage vectors for rolling optimization. The optimal combination of virtual voltage vectors is determined, and its duty cycle is calculated. Then, through the spatial relationship between virtual and actual voltage vectors, the optimal combination of actual voltage vectors and its duty cycle are obtained. Next, the circulating current combination and its duty cycle required for circulating current suppression are calculated. Finally, a capacitor voltage balancing method and modulation strategy are used to generate control signals for each sub-module in the controlled MMC, enabling the controlled MMC to output three control levels in each control cycle. This ensures that the actual current output by the controlled MMC in each control cycle more closely approximates the corresponding target current. The model predictive control method of this invention can reduce processor computational burden, suppress interphase circulating current, balance sub-module capacitor voltages, maintain bus voltage stability, reduce AC-side output current tracking error, and achieves high control accuracy and wide application range. Details are as follows:

[0071] Step 1: Construct the AC side predicted current evaluation function and circulating current prediction model

[0072] Based on the topology of the MMC and Kirchhoff's voltage law, the dynamic mathematical model of the MMC arm voltage and AC current measurement in the abc coordinate system is as follows:

[0073]

[0074] In the formula, i o,x R is the AC output current of any one of the three phases (a, b, c) in phase x. a L is the equivalent resistance of the bridge arm. a For the bridge arm inductance, L l R is the load inductance. l For load resistance, v g V is the grid voltage.t,x The midpoint output voltage of the MMC is expressed as follows:

[0075] v t,x =u n,x -u p,x

[0076] In the formula, u n,x For the lower bridge arm voltage, u p,x This is the voltage of the upper bridge arm.

[0077] Then, using the trapezoidal numerical integral formula, the AC current measurement dynamic model and the interphase circulating current model are discretized to obtain the predictive mathematical model of the system.

[0078] Integrating the mathematical model of AC output current measurement over one cycle:

[0079]

[0080] The AC output current prediction model is as follows:

[0081]

[0082] In the formula, L e The equivalent inductance is expressed as L. e =L a +2L l R e The equivalent resistance is expressed as R. e =R a +2R l T s To control the cycle.

[0083] The dynamic mathematical model of the circulating loop is as follows:

[0084]

[0085] In the formula, i diff,x For the circulation of phase x, V dc The DC bus voltage, u diff,x The voltage on the bridge arm side is expressed as follows:

[0086] u diff,x =u n,x +u p,x

[0087] Then, by integrating the circulation dynamic equation over one period, we obtain:

[0088]

[0089] The discrete prediction model for the circulation is obtained using the trapezoidal numerical integration formula:

[0090]

[0091] Step 2: Based on the AC side predicted current evaluation function, perform rolling optimization on multiple virtual levels, determine the optimal virtual voltage vector combination and calculate its duty cycle Dv, and then obtain the optimal actual voltage vector combination and its duty cycle Da through the spatial relationship between the virtual voltage vector and the actual voltage vector.

[0092] S21, according to the equivalence principle of two-port networks, the MMC can be equivalently represented externally as a converter that can output four corresponding virtual levels through virtual switch state control via the AC side neutral point and ground point. This is similar to a three-level converter whose structure consists of two semiconductor switches per phase. The four virtual levels introduced are as follows:

[0093] 1) Virtual Level VI: All submodules of the upper bridge arm are in the active state, and all submodules of the lower bridge arm are in the deactivated state. The virtual switch state of the bridge arm is represented by [1,0]. At this time, the equivalent AC neutral point output voltage is: -u p ;

[0094] 2) Virtual Level VII: All submodules of the upper bridge arm are in the off state, and all submodules of the lower bridge arm are in the on state. The virtual switch state of the bridge arm is represented by [0,1]. At this time, the equivalent AC midpoint output voltage is: u n ;

[0095] 3) Virtual Level VIII: All submodules of the upper bridge arm and all submodules of the lower bridge arm are in the active state. The virtual switch state of the bridge arm is represented by [1,1]. At this time, the equivalent AC neutral point output voltage is: u n -u p ;

[0096] 4) Virtual Level VIV: All submodules of the upper arm are in the cut-off state, and all submodules of the lower arm are in the cut-off state. The virtual switch state of the arm is represented by [0,0]. At this time, the equivalent AC midpoint output voltage is 0.

[0097] Assuming good voltage balance control in each phase arm of the MMC, meaning the capacitor voltages of each submodule are approximately equal, the voltages of the upper and lower arms can be considered approximately equal. Therefore, the equivalent AC midpoint output voltage of both virtual level VIII and virtual level VIV is 0, and their impact on AC current control is almost identical. Thus, only one needs to be chosen. Considering bus voltage balance, virtual level VIII is selected to achieve an equivalent zero level. Using this virtual level, the one-dimensional voltage region can be divided into two partitions, and the virtual voltage vector V can be obtained. v1 V v2 V v3 Vv3 The zero vector, as shown in the attached figure. Figure 4 As shown by the red arrow, virtual space voltage region 1 is determined by V. v1 and V v3 Composition, and virtual space voltage region 2, by V v2 and V v3 The reference voltage falls within any virtual voltage region and can be linearly represented by the two virtual voltage vectors constituting the ends of that virtual voltage region. Since there are only two virtual voltage regions, the virtual space vector combination (V...) can be used... v1 V v3 ) or (V v2 V v3 The reference voltage can then be synthesized.

[0098] S22. Construct an evaluation function for the AC side current, and use virtual voltage vectors for rolling optimization to obtain the optimal combination of virtual voltage vectors and its duty cycle Dv. The specific steps are as follows:

[0099] 221) Construct an evaluation function based on the variance between the predicted current and the reference current.

[0100] g = (i o,x (k+1)-i ref,x (k+1)) 2

[0101] In the formula, i ref,x (k+1) is the reference current of phase x at time k+1, i o,x (k+1) represents the predicted current at time k+1 of phase x.

[0102] 222) Substitute a virtual voltage vector into the AC side output current prediction model to obtain the predicted current, and then substitute it into the evaluation function. Since the determination of the virtual voltage vector combination is independent of the zero vector, it is only necessary to substitute V. v1 or V v2 That's all.

[0103] 223) Repeat step 222) until all virtual levels have been evaluated. The virtual voltage vector that minimizes the evaluation function is the optimal virtual voltage vector. This process is called rolling optimization. Traditional MPC uses actual levels or voltage vectors for rolling optimization, which causes the rolling optimization time to increase with the number of output levels, resulting in a very large amount of computation, which is not conducive to practical engineering applications. However, since rolling optimization is performed using virtual voltage vectors, the number of rolling optimizations is always 2, regardless of the actual number of output levels of MPC, which can greatly reduce the amount of computation and improve the calculation speed.

[0104] 224) Determine the virtual voltage partition where the reference voltage is located from the optimal virtual voltage vector, and calculate the duty cycle Dv of the optimal virtual voltage vector.

[0105]

[0106] In the formula, V at time k+1 vo1 Predicted AC side current under action, V vo1 To find the optimal virtual voltage vector that minimizes the evaluation function, V at time k+1 vo2 Predicted AC side current under action, V vo2 For virtual voltage vector V v3 .

[0107] Compared to the traditional MPC method that outputs only one control level in one control cycle, this scheme can effectively reduce current tracking error and achieve a fixed switching frequency by synthesizing a reference voltage vector from two voltage vectors obtained by the algorithm of this invention and by using a modulation module.

[0108] S23. Define the relationship between the actual MMC voltage level and the number of conducting submodules, establish the actual one-dimensional voltage partitioning, and derive the correspondence between the actual voltage partitioning and the virtual voltage partitioning. The specific steps are as follows:

[0109] 231) Based on the MMC submodule input principle, establish the relationship between the actual output level and the input submodules of the upper and lower bridge arms.

[0110] Under proper control, the capacitor voltages of all MMC submodules are equal and all within the reference value E=V. dc Near / N, where N is the number of sub-modules in each bridge arm, the number of sub-modules per phase is 2N. The output voltage at the midpoint of the MMC is the difference between the voltages of the lower and upper bridge arms, therefore a maximum of 2N+1 voltage levels can be output. Considering bus voltage balance, the number of sub-modules engaged in each phase of the MMC during each switching cycle must remain constant at N. Therefore, the MMC can output voltage levels of N+1, i.e., U. a(N+1) =-(N / 2)E,U a(N) =-(N / 2+1)E,…,0,…,U a2 = (N / 2-1)E, U a1 = (N / 2)E, as shown in the table below.

[0111] Table 1. Relationship between AC side midpoint output voltage and the number of bridge arm submodules deployed.

[0112] AC side neutral point output voltage (V) <![CDATA[Number N of sub-modules put into the lower bridge arm l > <![CDATA[Number N of sub-modules in the upper bridge arm u > (N / 2)E N 0 (N / 2+1)E N-1 1 … … … -(N / 2-1)E 1 N-1 -(N / 2)E 0 N

[0113] 232) Establishing a practical one-dimensional spatial voltage partition

[0114] Based on the actual number of output voltages of the MMC, the actual spatial voltage vector region of the MMC can be divided into N regions, namely, actual spatial voltage region 1 to actual spatial voltage region N. Virtual spatial voltage region 1 covers actual spatial voltage region 1 to (N / 2); virtual spatial voltage region 2 covers actual spatial voltage region (N / 2+1) to N. When N=4, the actual voltage partitioning is as shown in the attached figure. Figure 4 As shown, V a1 V a2 V a3 V a4 V a5 The one-dimensional real-space voltage vector is represented by a blue arrow. Figure 5 This indicates the relationship between the number of upper and lower bridge arm sub-modules and the actual voltage vector. In this way, the reference voltage synthesized using the virtual space voltage vector can be further represented by the actual space voltage vector.

[0115] S24. Based on the correspondence between virtual voltage partitions and actual voltage partitions, determine the optimal actual voltage partition and the optimal actual voltage vector combination, and calculate its duty cycle Da.

[0116] The optimal actual voltage region S can be determined by the following formula:

[0117] h = round((D v *V vo1 +(1-D v V vo2 ) / (V dc / N))

[0118]

[0119] Here, round() is the function for rounding down.

[0120] Based on the optimal actual voltage region S, and using the voltage at the endpoint of this region as the optimal actual voltage vector, the optimal combination of actual voltage vectors is determined. The larger actual voltage vector is denoted as V. ao1 Its control period T s The duration of action within this timeframe is denoted as t. 1,x The smaller actual voltage vector is V ao2 Its control period T s The duration of action within this timeframe is denoted as t. 2,x The duty cycle corresponding to the optimal actual voltage region combination is...

[0121] In the formula, The specific calculation process is described below. For x phase in V ao1 The derivative of the predicted AC current under the action, For x phase in V ao2 The derivative of the predicted AC current under the action, i ref,x (k+1) is the reference current at time k+1. This represents the actual measured value of the AC side current at time k.

[0122] The above-mentioned action time t 1,x t 2,x The solution process is as follows:

[0123] First, calculate the current slope based on the optimal actual voltage vector corresponding to the actual spatial voltage region:

[0124]

[0125] In the formula, σ 1,x For x phase in V ao1 The derivative of the predicted AC output current under the action, σ 2,x For x phase in V ao2 The derivative of the predicted AC output current under the action.

[0126] Secondly, the calculation is performed using two optimal actual voltage vectors V. ao1 V ao2 The predicted current under one control cycle, according to the differential principle, is expressed as follows:

[0127] The evaluation function can then be rewritten as: g = (i ref,x -i o,x (k)-σ 1,x t 1,x -σ 2,x t 2,x ) 2

[0128] According to optimal control theory, the system takes the optimal solution when the partial derivative of the evaluation function is zero. Therefore:

[0129]

[0130] Therefore, the duty cycle of the actual space voltage vector is:

[0131] Step 3: Based on the circulation prediction model, calculate the predicted circulation value corresponding to the deployment or removal of the sub-module and its duty cycle Dz for the deployment or removal time. The specific steps are as follows:

[0132] 31) Determine the sign of the circulating current. When the circulating current is positive, an additional submodule needs to be added; when the circulating current is negative, an additional submodule needs to be removed. Because an additional submodule needs to be added or removed, the total number of submodules added within a control cycle is not always N. Therefore, the application range (i.e., the range of actual submodules added) is larger than the search range (i.e., the range of submodules corresponding to the voltage vector in rolling optimization), as shown in the appendix. Figure 5 As shown.

[0133] 32) Calculate the predicted circulation value at the next moment based on the state of input or output.

[0134] When an additional submodule is added, the bridge arm side voltage u at the next moment diff,x = (N+1)*V dc / N, calculate the predicted circulation value at this time based on the circulation prediction model, using i diff+ express;

[0135] When a submodule is removed, the bridge arm voltage u at the next moment diff,x = (N-1)*V dc / N, calculate the predicted circulation value at this time based on the circulation prediction model, using i diff- express;

[0136] When there is no action, the voltage u on the bridge arm side at the next moment diff,x = (N)*V dc / N, calculate the predicted circulation value at this time based on the circulation prediction model, using i diff0 Indicates. That is.

[0137]

[0138] 33) Calculate the duty cycle D for adding or removing an additional module. z :

[0139]

[0140] In the formula, i dc This is the DC-side current, which is equally divided among the three phase bridge arms; i diff,o1 Based on the positive or negative sign of the circulation, i diff,o2 For i diff0 .

[0141] Step 4: Using the duty cycle Dz of the circulating current control and the duty cycle Da of the AC side predictive current control, combined with the capacitor voltage balancing method, the modulation signal of each sub-module in the controlled MMC is obtained. The modulation strategy is then used to obtain the signal of the semiconductor switching device through the modulator. The specific steps are as follows:

[0142] 41) Determine the direction of the current in the bridge arm. If it is positive, arrange the capacitor voltages of the sub-modules in ascending order; if it is negative, arrange the capacitor voltages of the sub-modules in descending order, and assign a voltage sequence number to each sub-module in the bridge arm according to the voltage order.

[0143] For example, in an MMC structure with N=4, the upper arm sub-modules are numbered from top to bottom as SMP1, SMP2, SMP3, and SMP4, with voltages of 101V, 99V, 100V, and 102V respectively. When the arm current is in the positive direction, the voltage numbers of each sub-module are 3, 1, 2, and 4 respectively; when the arm current is in the negative direction, the voltage numbers of each sub-module are 2, 4, 3, and 1 respectively.

[0144] 42) Based on the relationship between the actual voltage vector and the number of sub-modules connected to the bridge arm, the optimal actual voltage vector V is obtained. ao1 V ao2 The corresponding number of upper and lower bridge arm sub-modules deployed (N) u1 |V ao1 N u2 |V ao2 ) and (N l1 |V ao1 N l2 |V ao2 ), where N u1 N l1 These are the optimal actual voltage vectors V ao1 The corresponding number of upper and lower bridge arm sub-modules; N u2 N l2 For another optimal actual voltage vector V ao2 The corresponding number of sub-modules deployed in the upper and lower bridge arms.

[0145] 43) Calculate the modulation signal of each submodule.

[0146] Based on the voltage sorting results, the modulation signals of each submodule differ. Since three control levels need to be output within one control cycle, some submodules may not only be in an active or inactive state within a single control cycle, but rather active for a certain period and in an inactive state for the rest of the cycle. When a submodule needs to be active for the entire control cycle, its modulation signal is 1, referred to as the fully active state; when a submodule needs to be inactive, its modulation signal is 0; when a submodule is active for only part of the control cycle, its modulation signal is D. u Or D l This is called the half-engaged state, and the corresponding submodule is the half-action submodule. The corresponding modulation signal is calculated as follows:

[0147] When the control action for circulating current suppression is to activate an additional submodule, the formula for calculating the modulation signal is:

[0148] D u =1-(D a -0.5D z )

[0149] D l =D a +0.5D z

[0150] When the control action for circulating current suppression is to remove an additional submodule, the formula for calculating the modulation signal is:

[0151] D u =1-(D a +0.5D z )

[0152] D l =D a -0.5D z

[0153] 44) Select the smaller number of element values ​​from the two pairs of input numbers of the two bridge arm submodules, and let it be n. min Based on the voltage sorting results of the submodules, voltage numbers less than or equal to n are sorted. min Set the modulation signal of the submodule to 1, and set the voltage sequence number to n. min The modulation signal of the +1 submodule is set to control the duty cycle D. u Or D l .

[0154] For example, in an MMC structure with four sub-modules (N=4), the actual output voltage vector is (E,0), the number of input pairs in the lower arm is (3,2), and the number of input pairs in the upper arm is (1,2). Then, in the lower arm, the sub-modules with voltage indices less than or equal to 2 are set to 1, and the sub-modules with voltage indices equal to 3 are set to a duty cycle of D. u Set all other submodules to 0; set the submodules with voltage sequence number less than or equal to 1 in the upper bridge arm to 1, and set the duty cycle D for the submodules with voltage sequence number equal to 2. l The remaining submodules are set to 0, and the principle is as follows (see attached diagram). Figure 7 As shown.

[0155] 45) Each phase of the MMC has 2N carrier signals, corresponding to each submodule. The N carrier signals of the upper arm are triangular waves with a frequency equal to the control frequency, and there is no phase difference between the carrier signals. The N carrier signals of the lower arm are triangular waves with a frequency equal to the control frequency and a 180° phase delay from the upper arm carrier signals, and there is no phase difference between the carrier signals. Since N... u1 Total less than N u2 And N l1 Total and N l2Therefore, the upper arm half-action submodule should first be in the cut-off state and then switch to the engaged state, while the lower arm half-action submodule should first be in the engaged state and then switch to the cut-off state. Thus, the carrier signals of the upper and lower arms need to be delayed by 180° phase.

[0156] The modulation signal of each submodule is compared with the corresponding carrier signal. When the modulation signal is greater than the carrier signal, the modulator outputs a PWM signal of 1 (high level); when the modulation signal is less than the carrier signal, the modulator outputs a PWM signal of 0 (low level). The PWM signal is the switching signal of the semiconductor device.

[0157] For the submodule in a semi-engaged state, the action time of the semi-moving submodule of the upper arm is (1-D). u )T s The action time of the half-motion submodule of the lower bridge arm is D. l T s Their duration of action is all about 0.5T from the center of the control cycle. s Symmetry, meaning the high level of the PWM signal of the half-action submodule in the upper bridge arm starts from 0.5T. s -0.5(1-D u )T s The moment begins at 0.5T s +0.5(1-D u )T s The control cycle ends, and the level remains low for the remainder of the control period.

[0158] The low level of the PWM signal of the lower bridge arm's half-action submodule starts from 0.5T. s -0.5D l T s The moment begins at 0.5T s +0.5D l T s End; the control cycle remains high for the rest of the time.

[0159] The PWM signal of a submodule in the fully engaged state is high throughout the entire control cycle; the PWM signal of a submodule in the fully disengaged state is low throughout the entire control cycle.

[0160] Thus, in the MMC driven by the PWM signal calculated above, the PWM signals of the submodules in the upper and lower bridge arms that are in a half-operation state have a pulse width difference determined by the circulating current suppression duty cycle due to the addition of circulating current suppression. Therefore, the pulse width of the upper bridge arm half-operation state submodule transitioning from low to high level and the pulse width of the lower bridge arm half-operation state submodule transitioning from high to low level are not completely symmetrical, resulting in an additional control level. Combined with V ao2 Corresponding level, V ao1Corresponding to the level, three control levels are output within one control cycle. The modulation principle and the correspondence principle of the output level are shown in the appendix. Figure 7 As shown, the output levels of the MMC operate in the following order: V ao2 Corresponding level - Additional level - V ao1 Corresponding level - Additional level - V ao2 Corresponding level, where V ao2 The duration of the corresponding voltage level is T. s -D a T s -0.5D z T s From time zero to 0.5(1-D) a T s -0.5D z T s The time ends at 0.5(Ts+DaT) s +0.5D z T s ) Start to T s End; the duration of the additional level is D. z T s From 0.5(Ts-DaTs-0.5D) z T s From time 0.5(1-D) a T s +0.5D z T s The time ends at 0.5(1+D) a T s -0.5D z T s From time 0.5 (T) s +D a T s +0.5D z T s (Time ends; V) ao1 The duration of the corresponding voltage level is D. a T s -0.5D z T s From 0.5(T) s -D a T s +0.5DzT s From time 0.5 (T) s +D a T s -0.5D z T s The time ends, and its working principle is as follows: Figure 6As shown. Three control levels are output within one control cycle, two of which are voltages V. ao1 With V ao2 A more accurate synthesized reference voltage can effectively reduce inverter current tracking error, and additional control levels are used to suppress circulating current and reduce harmonics in the output waveform.

[0161] To verify the feasibility of the model predictive control method of this invention, we use a four-unit sub-modular multilevel converter as an example for experimental illustration. The specific structure of the four-unit sub-modular multilevel converter is as follows: Figure 2 As shown, this submodule has a half-bridge structure. By replacing the bridge arm voltages with controllable voltage sources, its circulating current equivalent circuit is obtained, as follows: Figure 3 As shown.

[0162] Therefore, it can be seen that within one control cycle, each phase of the MMC requires four sub-modules to be engaged, which can generate five voltages, namely U1 = -2E, -E, 0, E, 2E. The relationship between the output voltage and the number of bridge arm sub-modules engaged is as follows: Figure 5 As shown.

[0163] Based on the relationship between the MMC midpoint output voltage and the submodule capacitor voltage, we can conclude that: when the midpoint output voltage is -2E, 0 submodules are connected to the upper bridge arm and 4 submodules are connected to the lower bridge arm; when the midpoint output voltage is -E, 1 submodule is connected to the upper bridge arm and 3 submodules are connected to the lower bridge arm; and so on. When the midpoint output voltage is E, 3 submodules are connected to the upper bridge arm and 1 submodule is connected to the lower bridge arm; when the midpoint output voltage is 2E, 4 submodules are connected to the upper bridge arm and 0 submodules are connected to the lower bridge arm.

[0164] Based on the actual number of output voltages of the MMC, the space voltage vector region of the MMC can be divided into four areas: actual space voltage region 1 to actual space voltage region 4. Virtual space voltage region 1 covers actual space voltage regions 1 to 2; virtual space voltage region 2 covers actual space voltage regions 3 to 4. Their relationship is as follows: Figure 4 As shown.

[0165] Using virtual voltage vectors for rolling optimization and deploying four sub-modules in each control cycle, the search area for the optimal actual voltage vector is as follows: Figure 5 The small area shown.

[0166] like Figure 7 The diagram shows a schematic of the modulation principle when the optimal actual voltage vector is [E,0].

[0167] To verify the feasibility of this invention, a simulation was also built based on Matlab / Simulink, and the specific simulation parameters are shown in Table 2.

[0168] Table 2 Specific parameters for simulation verification

[0169]

[0170] The simulation verification aims to achieve the following objectives: 1) Ensure stable operation of the MMC under grid-connected conditions and verify steady-state current tracking performance; 2) Ensure stable operation of the MMC under grid-connected conditions and verify dynamic current tracking performance; 3) Effectively reduce circulating current and improve the quality of AC output current after the addition of circulating current suppression.

[0171] like Figure 8 As shown, the AC side voltage waveform is at level 9, which is consistent with the previous analysis. Figure 5 Within the application area, the current tracking effect is good, the circulating current fluctuates near zero, the bus voltage fluctuates little, and the submodule capacitor voltage is balanced.

[0172] like Figure 9 As shown, at t = 0.05s, the reference current suddenly changes from 8A to 2A. The current waveform has good dynamic performance, the voltage waveform has no overshoot, the bus voltage is stable, the circulating current is near zero, and the control effect is good.

[0173] like Figure 10 As shown, before t = 0.05s, the system had no circulating current suppression applied, and the output voltage was at level 5, which is consistent with the previous analysis. Figure 5 The search area is within range, but the circulating current fluctuates around zero; after adding circulating current suppression, the AC voltage waveform is at level 9, which is consistent with the previous analysis. Figure 5 The application area is limited, and the bus voltage fluctuation is reduced, with the circulating current near zero.

[0174] like Figure 11 As shown, without circulating current suppression, the THD of the output current is relatively large due to the influence of circulating current; when circulating current suppression is added, the THD is significantly reduced, effectively improving the quality of the output current.

[0175] While specific embodiments of the present invention have been described above, those skilled in the art should understand that these are merely illustrative examples. Various changes or modifications can be made to these embodiments without departing from the principles and essence of the present invention. Therefore, the scope of protection of the present invention is defined by the appended claims.

Claims

1. A virtual voltage vector-based MMC modulation model predictive control method, characterized in that: With AC-side inverter current tracking error and interphase circulating current suppression as control objectives, multiple virtual voltage levels are introduced. A smaller number of virtual voltage levels are used to replace a larger number of actual voltage vectors for rolling optimization. The optimal combination of virtual voltage vectors is determined and its duty cycle is calculated. Then, through the spatial relationship between virtual voltage vectors and actual voltage vectors, the optimal combination of actual voltage vectors and its duty cycle are obtained. Next, the circulating current control required for circulating current suppression and its duty cycle are calculated. Finally, the capacitor voltage balancing method and modulation strategy are used to generate control signals for each sub-module in the controlled MMC, so that the controlled MMC can output three control levels in each control cycle. Thus, the actual current output by the controlled MMC in each control cycle is closer to the corresponding target current.

2. The MMC modulation model predictive control method based on virtual voltage vector according to claim 1, characterized in that: An AC-side predicted current evaluation function and a circulating current prediction model are constructed. Based on the AC-side predicted current evaluation function, multiple virtual levels are rolled for optimization to determine the optimal virtual voltage vector combination and calculate its duty cycle Dv. Then, through the spatial relationship between the virtual voltage vector and the actual voltage vector, the optimal actual voltage vector combination and its duty cycle Da are obtained. Then, based on the circulation prediction model, the circulation control and its duty cycle Dz corresponding to the input or output of the sub-module are calculated; Finally, the modulation signal of each sub-module in the controlled MMC is obtained by using the duty cycle Dz of the circulating current control and the duty cycle Da of the optimal actual voltage vector combination, combined with the capacitor voltage balancing method. The signal of the semiconductor switching device is obtained by using the modulation strategy through the modulator.

3. The MMC modulation model predictive control method based on virtual voltage vector according to claim 2, characterized in that: Based on the equivalence principle of two-port networks, each phase structure in MMC is equivalent to a three-level converter composed of two semiconductor switches, one above and one below, introducing four virtual levels as follows: 1) Virtual Level VI: All submodules of the upper bridge arm are in the active state, and all submodules of the lower bridge arm are in the deactivated state. The equivalent AC neutral point output voltage at this time is: -u p ; 2) Virtual Level VII: All submodules of the upper bridge arm are in the off state, and all submodules of the lower bridge arm are in the on state. The equivalent AC neutral point output voltage at this time is: u n ; 3) Virtual Level VIII: All submodules of the upper arm and all submodules of the lower arm are in the active state. The equivalent AC neutral point output voltage at this time is: u n -u p ; 4) Virtual Level VIV: All submodules of the upper bridge arm are in the cut-off state, and all submodules of the lower bridge arm are in the cut-off state. At this time, the equivalent AC midpoint output voltage is 0. Assuming that the capacitor voltages of each submodule in each phase arm of the MMC are approximately equal, i.e., the voltages of the upper and lower arms are approximately equal, then the equivalent AC side midpoint output voltages of virtual level VIII and virtual level VIV are both zero, thus dividing the one-dimensional virtual voltage space into two partitions, namely virtual space voltage region 1, which is composed of virtual level VI and virtual level VIII. And virtual space voltage region 2, which consists of virtual level VII and virtual level VIII.

4. The MMC modulation model predictive control method based on virtual voltage vector according to claim 3, characterized in that: The virtual levels VI and VII are substituted into the AC side current evaluation function for rolling optimization. The virtual level with the minimum evaluation function is taken as the optimal virtual voltage. Then, the virtual space voltage partition is determined, the optimal virtual voltage vector combination is obtained, and its duty cycle Dv is calculated.

5. The MMC modulation model predictive control method based on virtual voltage vector according to claim 4, characterized in that: Calculate the duty cycle Dv corresponding to the optimal virtual voltage vector combination using the following equation. In the formula, The optimal virtual voltage vector V at time k+1 vo1 AC side output current under action, The virtual voltage vector V at time k+1 vo2 AC side output current under action, Let be the reference current at time k+1.

6. The MMC modulation model predictive control method based on virtual voltage vector according to claim 3, characterized in that: Let N be the number of sub-modules in each bridge arm, then the number of sub-modules in each phase is 2N, and the AC side neutral point output voltage has 2N+1 levels. Assume that the capacitor voltage of each sub-module in each phase bridge arm of the MMC is approximately equal, i.e., the voltages of the upper and lower bridge arms are approximately equal and approximately equal to the reference value E=V. dc / N, Considering bus voltage balance, the number of sub-modules activated in each phase during each switching cycle must remain constant at N. Therefore, the controlled MMC can output N+1 levels, which is U. a(N+1) =-(N / 2)E,U a(N) =-(N / 2-1)E,…,0,…,U a2 =(N / 2-1)E,U a1 =(N / 2)E, thus forming N actual spatial voltage regions, denoted as actual spatial voltage region 1, 2, 3...N. Among them, virtual spatial voltage region 1 covers actual spatial voltage region 1 to (N / 2), and virtual spatial voltage region 2 covers actual spatial voltage region (N / 2+1) to N. The relationship between the AC side midpoint output voltage and the number of upper and lower bridge arm sub-modules engaged is shown in the table below. 。 7. The MMC modulation model predictive control method based on virtual voltage vector according to claim 6, characterized in that: The optimal actual spatial voltage region S is calculated using the following equation; Here, round() is the floor function; Based on the optimal actual spatial voltage region S, the voltage at the endpoint of this region is used as the optimal actual voltage vector to determine the optimal combination of actual voltage vectors. The larger optimal actual voltage vector is denoted as V. ao1 Its control period T s The duration of action within this timeframe is denoted as t. 1,x The smaller optimal actual voltage vector is V. ao2 Its control period T s The duration of action within this timeframe is denoted as t. 2,x , The duty cycle corresponding to the optimal actual voltage vector combination , In the formula, , For any one of the three phases, i.e., phase x, in V ao1 The derivative of the predicted AC current under the action, For any one of the three phases, i.e., phase x, in V ao2 The derivative of the predicted AC current under the action, Let be the reference current at time k+1. This represents the actual measured value of the AC side current at time k.

8. The MMC modulation model predictive control method based on virtual voltage vector according to claim 7, characterized in that: The action time t 1,x t 2,x This is to obtain the optimal solution where the partial derivative of the AC side predicted current evaluation function corresponding to the optimal actual voltage vector is zero.

9. The MMC modulation model predictive control method based on virtual voltage vector according to claim 7, characterized in that: When the circulating current direction is positive, an additional submodule needs to be connected, and the voltage on the bridge arm side at the next moment... u diff,x =(N+1)* V dc / N, calculate the predicted circulation value at this time based on the circulation prediction model, using i diff+ This indicates that when the circulating current direction is negative, a submodule needs to be disconnected, and the voltage on the bridge arm side will change at the next moment. u diff,x =(N-1)* V dc / N, calculate the predicted circulation value at this time based on the circulation prediction model, using i diff- This indicates that when there is no action, the voltage on the bridge arm side at the next moment... u diff,x =N* V dc / N, calculate the predicted circulation value at this time based on the circulation prediction model, using i diff0 The duty cycle Dz corresponding to the circulating flow control is calculated using the following equation. in, This is the DC side current; The sign of the circulation determines the direction. for i diff0 .

10. The MMC modulation model predictive control method based on virtual voltage vector according to claim 9, characterized in that... The method for generating control signals for each submodule in a controlled MMC using capacitor voltage balancing and modulation strategies includes the following steps: 1) Determine the direction of the current in the bridge arm. If it is positive, arrange the capacitor voltages of the sub-modules in ascending order; if it is negative, arrange the capacitor voltages of the sub-modules in descending order. Then, assign a voltage sequence number to each sub-module in the bridge arm according to the voltage order. 2) Based on the relationship between the actual voltage vector and the number of sub-modules connected in the bridge arm, the optimal actual voltage vector V is obtained. ao1 V ao2 The corresponding number of upper and lower bridge arm sub-modules deployed (N) u1 |V ao1 N u2 |V ao2 ) and (N l1 |V ao1 N l2 |V ao2 ), where N u1 N l1 For V ao1 The corresponding number of upper and lower bridge arm sub-modules; N u2 N l2 For V ao2 The corresponding number of sub-modules deployed in the upper and lower bridge arms; 3) Calculate the modulation signal of each submodule. When the control action for circulating current suppression is to activate an additional submodule, the formula for calculating the modulation signal is: When the control action for circulating current suppression is to remove an additional submodule, the formula for calculating the modulation signal is: 4) Select the smaller number of element values ​​from the input pairs of the two bridge arm submodules, and let it be n. min Based on the voltage sorting results, voltage numbers less than or equal to n are sorted. min The modulation signal of the submodule is set to 1, which means it is in the fully engaged state, indicating that it is always in the engaged state throughout the entire control cycle. The voltage sequence number is equal to n min The modulation signal of the +1 submodule is set to D. u Or D l This is a semi-engaged state, meaning that the system is only in an engaged state for a certain period of time within the entire control cycle, where D... u The corresponding submodule of the upper bridge arm, D l The submodule corresponding to the lower bridge arm, the submodule engaged at this time is called the half-action submodule; The modulation signals of the remaining submodules are set to 0; 5) Each phase of the MMC has 2N carrier signals, corresponding to each submodule. The N carrier signals of the upper arm are triangular waves with a frequency equal to the control frequency, and there is no phase difference between the carrier signals. The N carrier signals of the lower arm are carrier signals with a frequency equal to the control frequency and delayed by 180° from the upper arm carrier signals. 。 A triangular wave with no phase difference between each carrier signal; The modulation signal of each submodule is compared with the corresponding carrier signal. When the modulation signal is greater than the carrier signal, the modulator outputs a PWM signal of 1, i.e., a high level state; when the modulation signal is less than the carrier signal, the modulator outputs a PWM signal of 0, i.e., a low level state. The PWM signal is the switching signal of the semiconductor device. For the submodule in a semi-engaged state, the action time of the semi-moving submodule of the upper arm is (1-D). u )T s The action time of the half-motion submodule of the lower bridge arm is D. l T s Their duration of action is all about 0.5T from the center of the control cycle. s Symmetry, meaning the high level of the PWM signal of the half-action submodule in the upper bridge arm starts from 0.5T. s -0.5(1-D u )T s The moment begins at 0.5T s +0.5(1-D u )T s The control cycle ends, and the level remains low for the remainder of the control period. The low level of the PWM signal of the lower bridge arm's half-action submodule starts from 0.5T. s -0.5D l T s The moment begins at 0.5T s +0.5D l T s End; the control cycle remains high for the rest of the time.

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