An MMC low-frequency operation control method based on improved bridge arm current prediction

Abstract

The application discloses a kind of MMC low-frequency operation control methods based on improved bridge arm current prediction, belong to the control method field when power electronic equipment low-frequency operation.This method will replace the prediction of bridge arm current in the discrete model of traditional MPC algorithm with optimal reference value, so as to directly obtain the reference value of bridge arm voltage, thus omitting the establishment of objective function and rolling optimization process, greatly reducing the amount of calculation.On this basis, high-frequency circulating current is injected by using the improved bridge arm current prediction method, which not only takes into account the realization of multiple control objectives of the system, but also improves the control accuracy with reduced number of system controllers (i.e., avoids the traditional bridge arm current controller), achieves zero tracking error, and at the same time, significantly suppresses the low-frequency fluctuation of capacitor voltage, which is better than the traditional high-frequency injection method.

Description

Technical Field

[0001] This invention relates to the field of control methods for low-frequency operation of power electronic equipment, and specifically to a low-frequency operation control method based on improved bridge arm current prediction (MMC). Background Technology

[0002] With the development of power electronics technology, flexible DC transmission technology based on fully controlled voltage source inverters has been widely used in high-voltage, high-power applications. However, most inverters have complex structures and are not easily expandable. In 2001, Marquardt et al. in Germany proposed a novel modular multilevel converter (MMC). This converter has advantages such as modularity, strong scalability, good output voltage quality, and no need for bulky transformers. It is considered by scholars to be one of the most promising power electronic topologies for flexible DC transmission.

[0003] MMCs typically output sinusoidal voltage and current through DC-AC conversion, resulting in fundamental and second harmonic components in the output power. Based on the principle of power conservation between input and output, it can be deduced that power ripple exists in the bridge arms, affecting the sub-modules and causing their capacitor voltages to fluctuate around the reference voltage. This phenomenon restricts the application of MMCs in medium- and high-voltage motors, where frequency conversion control is commonly used, exacerbating capacitor voltage fluctuations. The resulting increases in capacitor capacity, converter cost, and size are significant problems. Current methods for suppressing capacitor voltage fluctuations include low-frequency circulating current injection and high-frequency injection.

[0004] Low-frequency circulating current injection can suppress voltage fluctuations, but this method essentially suppresses the common-mode component of the voltage fluctuations in the upper and lower bridge arm capacitors by injecting a low-frequency circulating current. However, the differential-mode component, which is the most significant component of the capacitor voltage fluctuations, is not suppressed, thus its ability to suppress fluctuations is very limited. High-frequency injection (patent application number 201911030745) establishes a power transmission channel by injecting a high-frequency zero-sequence voltage on the output side and a high-frequency circulating current of the same frequency into the bridge arm, which can effectively suppress capacitor voltage fluctuations. However, in the high-frequency injection method, the high-frequency circulating current injection section requires control using PI regulation, resulting in complex parameter design. Furthermore, when the injected waveform is not a standard sine wave, such as a trapezoidal wave, tracking errors will exist, affecting the voltage fluctuation suppression effect.

[0005] MMCs inherently possess multiple control objectives, including output current control, circulating current control, and submodule capacitor voltage balancing. Furthermore, given that MMCs are complex nonlinear systems, researchers have proposed using Model Predictive Control (MPC) for multi-objective control. Studies have shown that applying MPC algorithms to MMC control not only avoids traditional PI and PR controllers but also enables the simultaneous regulation of multiple objectives, thus simplifying control system design. However, the traditional MPC algorithm inherently requires establishing an objective function and performing rolling optimization, inevitably increasing the computational load. Summary of the Invention

[0006] Based on the above background, this invention provides a low-frequency operation control method for MMC based on improved arm current prediction. This method replaces the predicted arm current in the discrete model of the traditional MPC algorithm with the optimal reference value, thus directly deriving the reference value of the arm voltage. Therefore, it omits the establishment of the objective function and the rolling optimization process, significantly reducing the computational load. Furthermore, by injecting a high-frequency circulating current using the improved arm current prediction method, it not only achieves multiple control objectives of the system but also improves control accuracy while reducing the number of system controllers (i.e., avoiding the traditional arm current controller), achieving the goal of zero tracking error. Simultaneously, it significantly suppresses low-frequency fluctuations in capacitor voltage, demonstrating better performance than the traditional high-frequency injection method.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A low-frequency operation control method for MMC based on improved arm current prediction includes the following steps:

[0009] (1) Based on Kirchhoff's laws, establish a continuous domain mathematical model of the three-phase MMC topology;

[0010] (2) The continuous domain mathematical model of the three-phase MMC topology is discretized using Euler's forward formula to obtain the discrete domain mathematical model of the arm current.

[0011] (3) Replace the predicted value of the bridge arm current in the discrete domain mathematical model with the optimal reference value to obtain the calculation formula for the MMC bridge arm voltage reference;

[0012] (4) Introduce the high-frequency zero-sequence voltage into the discrete domain mathematical model of the bridge arm current, and obtain the calculation formula of the bridge arm voltage reference after injecting high-frequency voltage based on the calculation formula of the MMC bridge arm voltage reference described in step (3).

[0013] (5) By the output current, DC side current and circulating current reference value and the relationship between each current quantity, the optimal reference value of the arm current is obtained. Substitute it into the calculation formula of the arm voltage reference after injecting high frequency voltage obtained in step (4) to obtain the arm voltage reference value. Inject the arm voltage reference value into the three-phase MMC topology and realize the low-frequency operation control of MMC after appropriate modulation method.

[0014] Compared with the prior art, the present invention has the following beneficial effects:

[0015] (1) The present invention adopts the method of directly predicting the optimal bridge arm current, which makes full use of the current information in the bridge arm. Compared with the traditional model predictive control, it omits the complex process of selecting the objective function and rolling optimization. The amount of calculation is independent of the number of sub-modules, which greatly reduces the amount of calculation.

[0016] (2) The present invention uses the method of predicting the bridge arm current to inject circulating current, which does not require the complex structure of traditional PI and PR controllers, and can achieve good tracking effect.

[0017] (3) The present invention adopts a control strategy based on bridge arm current prediction, and on this basis, high frequency injection is realized, which can achieve better fluctuation suppression effect than traditional injection. Attached Figure Description

[0018] Figure 1 This is a three-phase MMC circuit topology;

[0019] Figure 2 This is the overall block diagram for predictive control of bridge arm current;

[0020] Figure 3 The capacitor voltage waveform when the frequency abruptly changes from 50Hz to 10Hz (without high frequency injection);

[0021] Figure 4 for Figure 3 Output current waveform under operating conditions;

[0022] Figure 5 for Figure 3 Bridge arm current tracking waveform under operating conditions;

[0023] Figure 6 The voltage waveform of the submodule after high-frequency injection at an operating frequency of 10Hz;

[0024] Figure 7 The voltage waveform of the submodule injected at high frequency under the condition of gradual frequency change;

[0025] Figure 8 for Figure 6 Output current waveform under operating conditions. Detailed Implementation

[0026] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0027] Figure 1 The diagram shows the main topology of a three-phase MMC. The three-phase MMC has six arms, and each arm contains N submodules. The DC bus voltage is U. dc The DC side current is i dc The upper arm voltage and the lower arm voltage are u, respectively. pj and u nj (j=a,b,c), the upper arm current and the lower arm current are respectively i pj and i nj The AC component of the bridge arm circulation is i zj The output phase voltage is u j The output phase current is i j The bridge arm inductance is L0, and the bridge arm resistance is R0.

[0028] Figure 2 The diagram shows a block diagram of the MMC low-frequency operation control method based on improved arm current prediction proposed in this invention. This control method comprises four parts: power outer loop control, overall energy control, arm current prediction control, and submodule voltage balance control. The power outer loop control uses the dq coordinate system and instantaneous power theory, comparing the commanded power value with the real-time calculated value. The difference is passed through a PI controller to obtain the active and reactive current components. The overall energy control... dc Using / N as a reference value, the average capacitor voltage of all three-phase submodules is used as a real-time sample value, and the difference between the values ​​is sent to the PI regulator to obtain the DC side reference current. The current is then evenly distributed to each phase to obtain the DC-side reference current for each phase. Predictive control of the bridge arm current is the core of the entire control system. It integrates the obtained output current, circulating current, and DC current, and uses discrete model prediction formulas to calculate the corresponding bridge arm voltage reference value. Submodule voltage balance control is used to ensure voltage balance of the submodule capacitors within the bridge arm during low-frequency operation. This requires real-time monitoring of the voltage u of each submodule. c (i) The reference value is the average voltage of the submodules in one phase arm. After subtraction, the voltage balance signal u is determined by combining the polarity of the bridge arm currents. bal_ref (i).

[0029] Specifically, a low-frequency operation control method for MMC based on improved bridge arm current prediction includes the following steps:

[0030] (1) Define the relevant system parameter physical quantities in the three-phase MMC topology, and establish a continuous domain mathematical model of the three-phase MMC topology based on Kirchhoff's laws.

[0031] (2) For the continuous domain mathematical model of MMC, since it includes the differential of the arm current, Euler's forward formula is used to discretize it, and a discrete domain mathematical model of the arm current is obtained.

[0032] (3) Replace the predicted value of the arm current (value at time k+1) in the discrete domain mathematical model with the optimal reference value to obtain the calculation formula for the MMC arm voltage reference. In this way, the arm voltage can be controlled to track its demand value by using an appropriate modulation method, thereby obtaining the optimal reference value of the arm current;

[0033] (4) Combining the high-frequency injection method, inject high-frequency zero-sequence voltage and high-frequency circulating current. Introduce the high-frequency zero-sequence voltage into the discrete domain mathematical model of the bridge arm current, and obtain the calculation formula for the bridge arm voltage reference after injecting high-frequency voltage based on the calculation formula for the MMC bridge arm voltage reference described in step (3);

[0034] (5) The optimal reference value of the bridge arm current is obtained by using the reference values ​​of the output current, DC side current and circulating current and the relationship between the current quantities. Substitute these values ​​into the calculation formula of the bridge arm voltage reference obtained in step (4) after injecting high frequency voltage, and obtain the bridge arm voltage reference value. Finally, the MMC low frequency operation control is realized by using an appropriate modulation method.

[0035] In step (1), the physical quantities are defined as follows:

[0036] Let the DC bus voltage be U. dc The DC side current is i dc The upper arm voltage and the lower arm voltage are u pj and u nj (j=a,b,c), the upper arm current and the lower arm current are respectively i pj and i nj The AC component of the bridge arm circulation is i zj The output phase voltage is u j The output phase current is i j The bridge arm inductance is L0, and the bridge arm resistance is R0.

[0037] Based on Kirchhoff's laws, establish the mathematical model of MMC:

[0038]

[0039]

[0040] The relationship between the output current, bridge arm current, and DC current is as follows:

[0041] i j =i pj -i nj (3)

[0042]

[0043] The bridge arm current can be derived from the current relationship:

[0044]

[0045] In step (2), in order to obtain the discrete mathematical model of MMC, Euler's forward formula needs to be used:

[0046]

[0047] In the formula, x represents the control variable, k and k+1 represent the sampling time in the discrete model, and T s This indicates the control step size.

[0048] Therefore, the discrete model for the bridge arm current can be derived as follows:

[0049]

[0050]

[0051] In the formula, i pj (k+1) and i nj (k+1) represents the predicted value of the current in the upper and lower arms of phase j at time k+1, U dc (k) and u j (k) represents the measured voltage on the DC side and the AC side of phase j at time k, respectively. pj (k) and u nj (k) represents the voltage of the upper and lower bridge arms at time k, respectively, i pj (k) and i nj (k) represents the current of the upper and lower bridge arms of phase j at time k, respectively, i cj The current is circulating in the bridge arm of phase j.

[0052] In step (3), by replacing the predicted value of the bridge arm current with the optimal reference value, the calculation formula for the bridge arm voltage reference is obtained:

[0053]

[0054]

[0055] As can be seen from the above, the method of handling discrete models in this invention differs from traditional Model Predictive Control (MPC). Traditional MPC requires designing an objective function for the control variables, forward predicting the states of each control variable through the discrete model, and selecting the optimal switching state at each sampling time to issue corresponding pulse commands to the switching transistors—a rolling optimization process. This invention, by replacing the predicted values ​​with reference values, can directly calculate the bridge arm voltage reference value without needing to use an objective function to judge all switching states to obtain the optimal bridge arm voltage. After obtaining the bridge arm voltage reference, the corresponding switching state can be obtained through a suitable modulation method.

[0056] In step (4), based on the idea of ​​high-frequency injection, a power exchange channel is established between the upper and lower bridge arms, allowing their energy fluctuations to cancel each other out, thus significantly reducing capacitor voltage fluctuations. Let the injected high-frequency voltage be u. z =U z sin(2πf h t), U z f is the amplitude of the high-frequency voltage. h If the frequency is a high-frequency voltage, then according to equations (1)-(2) and (7)-(10), the calculation formulas for the bridge arm voltage after the high-frequency voltage is injected are listed:

[0057]

[0058]

[0059] In order to establish a power channel between the bridge arms, a corresponding high-frequency circulating current needs to be injected. According to equation (5), the bridge arm current contains various components such as DC current, output current and circulating current. Therefore, a high-frequency circulating current can be introduced by setting a reference value for the bridge arm current.

[0060] Step (5) includes the following steps:

[0061] Step 1: As the above analysis shows, calculating the reference value of the arm current, which includes various current components, is the key to the entire control strategy. The expression for the arm current reference is obtained from equation (5):

[0062]

[0063] The asterisk (*) indicates a reference value for the variable.

[0064] Step 2: For output current control, from the perspective of overall control of the outer layer of MMC, select the active power and reactive power on the AC side to obtain the reference value of AC current, that is, outer loop power control, which requires the use of the common dq rotating coordinate system.

[0065] Based on instantaneous power theory, the instantaneous active power and reactive power injected into the AC system are:

[0066]

[0067] In the formula p s q s For active and reactive power, u d u q Let i be the phase voltage in the dq coordinate system. d i q Let be the current in the dq coordinate system.

[0068] Since, under steady-state conditions, the d-axis component of the voltage in a typical AC system is the phase voltage amplitude, and the q-axis component is 0, substituting into equation (14) yields:

[0069]

[0070] Let the given active power be P. * The reactive power is Q * The reference value of AC current in the dq coordinate system is obtained:

[0071]

[0072] Step 3: The reference values ​​for the DC current of each phase can be obtained through overall energy balance control. Overall energy balance aims to stabilize the average voltage of all submodules in the three phases of the MMC near the reference value of the capacitor voltage. The overall energy balance of the MMC can be controlled by adjusting the DC-side current, let the DC-side current be i. dc Since it is a DC flow, it can be directly adjusted using a simple PI controller. The calculation formula is as follows:

[0073]

[0074] In the formula, N represents the number of sub-modules in a bridge arm, and U c_avg k represents the average capacitor voltage of the MMC three-phase submodule. p k represents the proportional coefficient in PI regulation. i This represents the integral coefficient in PI control.

[0075] Since the three-phase MMC is a completely symmetrical structure, theoretically the DC current of the three-phase arms should be equal. Therefore, the reference value for the DC component of the arm is... in This represents the reference value for the DC component of the j-phase bridge arm.

[0076] Step 4: The circulating current reference value is usually set to 0 at normal operating frequency. However, in order to suppress the voltage fluctuation of the submodule capacitor under low frequency conditions, the circulating current reference value needs to be set to the injected high-frequency circulating current. Thus, based on the characteristics of the bridge arm current, the injection method of high-frequency circulating current is introduced.

[0077] The circulating current reference value is calculated based on the high-frequency injection method, derived from the components of the bridge arm power. From the MMC voltage relationship, it can be seen that:

[0078]

[0079] Combining equations (3) and (4), we obtain the instantaneous power expressions for the upper and lower bridge arms:

[0080]

[0081] Assuming the circulating current in the bridge arm contains only the DC component I dc Furthermore, the output phase voltage is a standard sine wave, and the current lags the phase angle. The power of the upper and lower bridge arms can be obtained:

[0082]

[0083] In the formula, U j I represents the amplitude of the output phase voltage of phase j. j This represents the amplitude of the output current of phase j.

[0084] As can be seen from equation (21), the first two terms represent the fundamental frequency fluctuation of the bridge arm power. To suppress the fundamental frequency energy, the exchange power between the upper and lower bridge arms using the high-frequency injection method is:

[0085]

[0086] The expression for the injected high-frequency zero-sequence voltage has been set in step (4). Substituting this expression into equation (22) and performing simple processing, we obtain the circulating current expression:

[0087]

[0088] In the formula, u z ω represents the injected zero-sequence voltage. h It represents the angular frequency of the zero-sequence voltage.

[0089] Multiplying the injected circulating current by the high-frequency voltage and ignoring the second harmonic power pulsation, yields the required fundamental frequency power. Furthermore, by performing product-sum-difference operations on equation (23), it can be seen that the injected circulating current essentially contains two frequency components, namely f h ±f. It should also be noted that the injected three-phase circulating current has a phase difference of 120° between each other, so that the circulating current will not affect the DC side and will only flow between the three phases.

[0090] To verify the effectiveness of the control strategy proposed in this invention in suppressing capacitor voltage fluctuations at low frequencies, a system was built as follows: Figure 1 The MMC simulation model shown is as follows. The main simulation parameters are: number of bridge arm sub-modules N = 6, bridge arm resistance = 0.5Ω, bridge arm inductance = 8mH, DC bus voltage = 3kV, sub-module capacitance = 2mF, sub-module reference voltage = 500V, load resistance = 10Ω, load inductance = 5mH, and injected high-frequency voltage frequency = 150Hz.

[0091] Figure 3 The figure shows the voltage waveform of the submodule capacitor when the operating frequency suddenly changes from 50Hz to 10Hz in 0.5s without the injection of high-frequency components. As can be seen from the figure, the peak-to-peak value of the capacitor voltage fluctuation increases from about 38V to 193V, causing a huge pulsation in the submodule voltage. Figure 4 The waveform of the output current under dynamic process is shown, and the THD of the three-phase current is about 0.5%. Figure 5 These are the actual and reference values ​​of the bridge arm current waveform. It can be observed that the waveforms basically overlap, and the tracking effect is good.

[0092] Figure 6 The image shows the voltage waveform of the submodule capacitor at a frequency of 10Hz after the injection of high-frequency components. The voltage fluctuation of the submodule has decreased from 193V to 38V, and the percentage of fluctuation amplitude has decreased from 38.6% to 7.6%, which is the same as the effect at a frequency of 50Hz.

[0093] To verify the dynamic characteristics of the control strategy, Figure 7 The waveform shown depicts the capacitor voltage as the fundamental frequency gradually changes from 2Hz to 10Hz (with a tolerance of 2Hz, changing every 0.5s). At 2Hz, the peak-to-peak value is approximately 97V, decreasing sequentially to 66V, 46V, 39V, and 36V as the frequency increases. Even at a frequency as low as 2Hz, the fluctuation value remains around 20% of the submodule voltage reference value, after which the submodule voltage fluctuation significantly decreases. Furthermore, this waveform represents the voltages of all submodules within a single bridge arm, showing almost complete overlap, indicating good voltage balancing within the submodules. Figure 8 The output current waveform during this dynamic process is shown. Due to the injection of high-frequency components and the relatively low fundamental frequency, the THD is around 2.5%.

[0094] The embodiments described above provide a detailed explanation of the technical solutions and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A low-frequency operation control method for MMC based on improved bridge arm current prediction, characterized in that, Includes the following steps: (1) Based on Kirchhoff's laws, establish a continuous domain mathematical model of the three-phase MMC topology; (2) The continuous domain mathematical model of the three-phase MMC topology is discretized using Euler's forward formula to obtain the discrete domain mathematical model of the arm current. (3) Replace the predicted value of the bridge arm current in the discrete domain mathematical model with the optimal reference value to obtain the calculation formula for the MMC bridge arm voltage reference; (4) Introduce the high-frequency zero-sequence voltage into the discrete domain mathematical model of the bridge arm current, and obtain the calculation formula for the bridge arm voltage reference after injecting high-frequency voltage based on the calculation formula for the MMC bridge arm voltage reference in step (3). (5) By the relationship between the output current, DC side current and circulating current reference value and each current quantity, the optimal reference value of the bridge arm current is obtained. Substitute it into the calculation formula of the bridge arm voltage reference after injecting high frequency voltage obtained in step (4) to obtain the bridge arm voltage reference value. After modulation, the MMC low frequency operation control is realized. Step (5) includes the following steps: Step (5.1): Based on the formula for calculating the arm current, the reference expression for the arm current is obtained as follows: ； in, express Reference values ​​for the current of the upper and lower bridge arms of each phase. express Phase output phase current reference value, express Reference values ​​for the AC component of the phase bridge arm circulation. express The DC side currents of the three phases are represented by j = a, b, and c, respectively. Step (5.2): By using outer-loop power control, select the active and reactive power on the AC side to obtain the AC current reference value; based on instantaneous power theory, the instantaneous active and reactive power injected into the AC side are: ； In the formula, , These are active power and reactive power, respectively. , These are the phase voltages in the dq coordinate system, respectively. , These are the currents in the dq coordinate system, respectively; Under steady-state conditions, the d-axis component of the AC voltage is the phase voltage amplitude, and the q-axis component is 0. Therefore: ； Further, the reference value of the AC current in the dq coordinate system is obtained: ； ； In the formula, Given the active power, Given reactive power; The reference values ​​of the AC current in the dq coordinate system are obtained by coordinate transformation to obtain the reference values ​​of the current in each phase. ; Step (5.3): Obtain the reference values ​​of DC current for each phase through overall energy control. The calculation formula is as follows: ； In the formula, N represents the number of submodules in one arm of the MMC topology. This represents the average capacitor voltage of the three-phase submodule in the MMC topology. This is the DC bus voltage. This represents the proportional gain in PI regulation. This represents the integral coefficient in PI control; Since the three-phase MMC is a completely symmetrical structure, the DC current of the three-phase bridge arms should be equal. Therefore, the reference value for the DC component of the bridge arm is... ,in express The reference values ​​for the DC component of the phase bridge arm, j = a, b, c represent the three phases respectively; Step (5.4): Set the reference value of the circulating current to the injected high-frequency circulating current. First, obtain the instantaneous power expressions for the upper and lower bridge arms from the MMC voltage and current relationships: ； Assuming the circulating current in the bridge arm contains only DC components Furthermore, the output phase voltage is a standard sine wave, and the current lags the phase angle. ,get: ； In the formula, express Instantaneous power of the upper and lower bridge arms, This represents the amplitude of the output phase voltage of phase j. This represents the amplitude of the output current in phase j. Angular frequency, For phase, For time, for Phase output phase current, For the j-phase bridge arm circulation; Based on the instantaneous power expressions of the upper and lower bridge arms, the exchange power between the upper and lower bridge arms using the high-frequency injection method is derived as follows: ； Circulation expression: ； In the formula, This represents the injected zero-sequence voltage. The angular frequency representing the zero-sequence voltage. This represents the amplitude of the high-frequency voltage.

2. The MMC low-frequency operation control method based on improved bridge arm current prediction according to claim 1, characterized in that, In step (1), the continuous domain mathematical model of the three-phase MMC topology is as follows: ； ； The relationship between the output current, bridge arm current, and DC current is as follows: ； ； Using the current relationship formula, the bridge arm current is obtained as follows: ； In the formula, For bridge arm inductance, For the bridge arm resistance, and They represent Phase upper and lower bridge arm voltages, and They represent Phase upper and lower bridge arm currents for Phase output phase voltage, for The alternating current component of the phase bridge arm circulation, for Phase DC current.

3. The MMC low-frequency operation control method based on improved bridge arm current prediction according to claim 2, characterized in that, In step (2), the discrete-domain mathematical model is: ； ； In the formula, and Represents time k+1 Predicted values ​​of current in the upper and lower bridge arms of the phase. and These are the DC side at time k and Measurement voltage on the phase AC side, and They represent time k respectively Phase upper and lower bridge arm voltages, and They represent time k respectively Phase upper and lower bridge arm currents This indicates the control step size.

4. The MMC low-frequency operation control method based on improved bridge arm current prediction according to claim 1, characterized in that, In step (3), the calculation formula for the MMC bridge arm voltage reference is as follows: ； ； In the formula, and Represents time k+1 Reference values ​​for the current of the upper and lower bridge arms of each phase. and These are the DC side at time k and Measurement voltage on the phase AC side, and They represent time k respectively Reference values ​​for the upper and lower bridge arm voltages. and They represent time k respectively Phase upper and lower bridge arm currents Indicates the control step size. For bridge arm inductance, This is the resistance of the bridge arm.

5. The MMC low-frequency operation control method based on improved bridge arm current prediction according to claim 4, characterized in that, In step (4), the calculation formula for the bridge arm voltage reference after the injection of high-frequency voltage is as follows: ； ； In the formula, This represents the high-frequency voltage injected at time k. The expression is: ； In the formula, This refers to the amplitude of the high-frequency voltage. It is the frequency of high-frequency voltage.

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