Model predictive control algorithm for optimal switching sequence of MMC based on two-dimensional control area

Abstract

The present invention provides a model predictive control algorithm for the optimal switching sequence of MMC based on a two-dimensional control area, which includes the following steps: using the two-dimensional control area to design a switch sequence to be selected; establishing a current discrete prediction model; defining an error function and solving partial derivatives to obtain the optimal action time of each switch state; rolling optimization of the sequence set to be selected to select the switch sequence that minimizes the value function; making the sum of the upper and lower bridge arm voltages follow the expected value to suppress the interphase circulating current; and using the sorting voltage balancing method to complete the switch control of the MMC converter. Compared with traditional model prediction, this strategy eliminates weight factors, expands the number of MMC output levels, improves the degree of freedom of control, and fixes the switching frequency. Harmonics are concentrated near the switching frequency, which reduces the difficulty of designing the output filter, and has a wide range of applications, and is suitable for both three-phase MMC and single-phase and H-bridge MMC.

Description

Technical Field

[0001] The invention relates to the technical field of power electronic converter model predictive control, and in particular to an optimal switching sequence model predictive control algorithm applied to a modular multi-level converter. Background Art

[0002] Modular Multilevel Converter (MMC) has the advantages of high efficiency, low harmonic content and low switching frequency, and is widely used in high-voltage DC transmission systems, high-voltage inverters and active power filters. Due to its highly modular structure, MMC has good scalability and can adapt to various voltage and power level applications.

[0003] The mathematical model of MMC has the characteristics of multiple inputs, multiple outputs and nonlinearity. During its operation, multiple control objectives need to be considered, including output voltage or current control, circulating current suppression, submodule capacitor voltage balance control, etc. Traditional control strategies mostly use closed-loop control, which is complex and difficult to adjust the parameters of proportional integral regulators. In comparison, model predictive control (MPC) is easy to handle multiple system constraints, multiple variables and nonlinear systems, and has the advantages of fast response speed. It has many advantages in the control of MMC. Traditional model predictive control has problems such as large amount of calculation, many times of traversal optimization, and difficulty in adjusting weight factors. In addition, it only selects one optimal switching state in one control cycle, requires a high sampling frequency, and cannot achieve a fixed switching frequency. The harmonic spectrum is widely distributed, making the design of the output filter particularly difficult. In response to this problem, some scholars have proposed the optimal switching sequence (OSS) model predictive control strategy, which can achieve a fixed switching frequency, but still has a high computational burden and is limited in application occasions. Each phase can be controlled independently in the one-dimensional control region, but its redundant switching states are few, which limits the control freedom and the output waveform quality is poor. Therefore, it is necessary to further study the optimal switching sequence model predictive control algorithm applied to MMC. Summary of the invention

[0004] The purpose of the present invention is to expand the concept of OSS on the basis of the optimal switch sequence model predictive control to realize the independent control of each phase of the MMC converter. An MMC optimal switch sequence model predictive control algorithm based on a two-dimensional control area is proposed, which is characterized in that the strategy extends the concept of the optimal switch sequence to the control of a single-phase MMC, uses the two-dimensional control area to design the switch sequence to be selected, establishes a current discrete prediction model, defines the error function and solves the partial derivative, obtains the optimal action time of each switch state, considers the influence of each switch state on the current change, performs rolling optimization on the sequence set to be selected, selects the switch sequence that minimizes the value function, adjusts the number of submodules invested in each bridge arm to suppress the interphase circulation, and finally uses the sorting voltage balancing method to complete the switch control of the MMC converter, which specifically includes the following steps:

[0005] Step 1: Extend the concept of optimal switching sequence to the control of single-phase MMC and design multiple switching sequences to be selected using the two-dimensional control area;

[0006] Step 2: Establish a discrete prediction model for output current, define the error function and solve the partial derivative to obtain the optimal action time of each switch state in the sequence;

[0007] Step 3: Consider the impact of each switch state on current change, perform rolling optimization on the selected sequence set, and select the switch sequence that minimizes the value function;

[0008] Step 4: Calculate the expected value and predicted value of the sum of the upper and lower bridge arm voltages at time k+1, and adjust the number of submodules put into each bridge arm to eliminate the error between the expected value and the predicted value of the bridge arm voltage, thereby suppressing the circulating current;

[0009] Step 5: Use the sorting method to balance the submodule capacitor voltage and send out control pulses;

[0010] Furthermore, the MMC optimal switch sequence model predictive control algorithm based on the two-dimensional control region is characterized by: using the two-dimensional control region to design the switch sequence to be selected;

[0011] In an MMC converter with N bridge arm submodules, each bridge arm has N+1 possible switch states. The vertical axis represents the switch state of the upper bridge arm, and the horizontal axis represents the switch state of the lower bridge arm, forming a two-dimensional control area. In order to maintain the balance between the DC side voltage and the bridge arm voltage and reduce the number of rolling optimizations, only the sequences near the diagonal of the two-dimensional control area are selected. Each sequence consists of three switch states, including a switch state S located on the diagonal. j2 and the two switch states S closest to it j1 , S j3 , there are 2N sequences to be selected in each phase;

[0012] The two-dimensional control area can expand the number of MMC output levels, reduce the harmonic content, and improve the degree of freedom of control; this method can realize independent control of each phase, which is suitable for three-phase MMC as well as single-phase and H-bridge MMC.

[0013] Furthermore, the MMC optimal switch sequence model predictive control algorithm based on the two-dimensional control area is characterized by: establishing a current discrete prediction model, defining an error function and solving partial derivatives, and obtaining the optimal action time t of each switch state. j1 ,t j2 ,t j3

[0014] The current discrete prediction model of the MMC inverter is as follows:

[0015]

[0016] Where: i j (k+1),u pj (k+1) and u nj (k+1) are the j-phase current, j-phase upper bridge arm voltage and lower bridge arm voltage measured at time k+1; L and R are the reactance and resistance of the AC side respectively; L o and R o are the bridge arm reactance and resistance respectively; T s is the sampling time;

[0017] Since the sampling time T s Very small. To simplify the calculation, when predicting the current after each switch state is applied, the initial current is approximated by the sampling value at time k. Due to the use of the voltage balancing algorithm, the average value of the capacitor voltage of the bridge arm submodule can be approximated by the sampling value of any submodule, as shown in the following formula:

[0018]

[0019] Where: m ranges from 1 to 3; i j,m is the predicted current value after the mth switch state in the sequence; t j,m is the action time of the mth switch state; S nj,m , S pj,m is the number of upper and lower bridge arm conducting submodules of phase j corresponding to the mth switch state; U nj (k) U pj (k) are the average values ​​of the capacitor voltages of the upper and lower bridge arm submodules of phase j at time k;

[0020] In order to maintain the balance between the DC side voltage and the bridge arm voltage, the number of equivalent sub-modules put into operation in each phase bridge arm in one switching cycle should be N, so the action time of the first switching state is the same as that of the third switching state, that is, t j,1 =tj,3 , then t j,2 =T s -2t j,1 ;

[0021] Considering the current error under the action of each voltage basis vector, the cost function is established as follows:

[0022]

[0023] Where: is the j-phase reference current at time k;

[0024] Find the partial derivative of the cost function:

[0025]

[0026] Solving the above equation can obtain the optimal action time of each switch state in the sequence.

[0027] Compared with the prior art, the present invention has the following advantages: no weight factor is required, and the control method is simple; the number of MMC output levels is expanded, the harmonic content is reduced, and the degree of freedom of control is improved; the switching frequency is fixed, and the harmonics are concentrated near the switching frequency, which reduces the difficulty of designing the output filter; OSS is applied to the independent control of each phase of the MMC, and the application occasions are wide, which is suitable for both three-phase MMC and single-phase and H-bridge MMC. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is the topology diagram of modular multi-level inverter;

[0029] Figure 2 is a two-dimensional control area diagram in one embodiment;

[0030] Figure 3 is a diagram of a switch sequence to be selected in an embodiment;

[0031] Figure 4 This is a carrier comparison chart. DETAILED DESCRIPTION

[0032] In order to illustrate the basic principle, technical solution and performance advantages of the present invention, an embodiment of the present invention will be further described below in conjunction with the accompanying drawings. It should be noted that the present invention can be implemented in a variety of different ways covered by the claims.

[0033] The topology of modular multilevel inverter is as follows Figure 1 As shown, it can be divided into three levels: phase unit, bridge arm unit and submodule unit. The submodule can be any structure such as full bridge, half bridge, etc., which is connected to the main circuit after being connected in parallel with the DC capacitor. The DC side of the three-phase MMC can be connected to the DC bus of the power grid and output a constant DC voltage U dcThe AC side can be connected to an AC power source or a three-phase load to output three-phase sinusoidal AC power.

[0034] Taking a five-level MMC inverter as an example, the implementation of its control method includes the following steps:

[0035] Step 1: Design the switch sequence to be selected using the two-dimensional control area.

[0036] In an MMC inverter with 4 bridge arm submodules, each bridge arm has 5 possible switching states, and there are 25 combinations of the upper and lower bridge arm switching states of each phase, forming a two-dimensional control area as shown in Figure 2 As shown in the figure, S pj Indicates the number of submodules with the upper bridge arm of phase j turned on, S nj Indicates the number of submodules with the lower bridge arm of phase j turned on, U sm Indicates the submodule capacitor voltage rating, u j Indicates the output level of the MMC inverter;

[0037] In order to maintain the balance between the DC side voltage and the bridge arm voltage and reduce the number of rolling optimizations, all sequences are selected near the diagonal line from the upper left to the lower right. Figure 2 The coordinates represent the switch states in the sequence, and the candidate sequences are shown in Table 1:

[0038] Table 1 Switch sequence to be selected

[0039]

[0040] The switch sequence and its area in the table are as follows Figure 3 As shown, arrows indicate the paths of the selected sequences.

[0041] Step 2: Establish a current discrete prediction model, define the error function and solve the partial derivative to obtain the optimal action time of each switch state in the selected sequence.

[0042] The current discrete prediction model of the MMC inverter is as follows:

[0043]

[0044] Where: i j (k+1),u pj (k+1) and u nj (k+1) are the j-phase current, j-phase upper bridge arm voltage and lower bridge arm voltage measured at time k+1; L and R are the reactance and resistance of the AC side respectively; L o and R o are the bridge arm reactance and resistance respectively; T s is the sampling time;

[0045] Since the sampling time T sVery small. To simplify the calculation, when predicting the current after each switch state is applied, the initial current is approximated by the sampling value at time k. Due to the use of the voltage balancing algorithm, the average value of the capacitor voltage of the bridge arm submodule can be approximated by the sampling value of any submodule, as shown in the following formula:

[0046]

[0047] Where: m ranges from 1 to 3; i j,m is the predicted current value after the mth switch state in the sequence; t j,m is the action time of the mth switch state; S nj,m , S pj,m is the number of upper and lower bridge arm conducting submodules of phase j corresponding to the mth switch state; U nj (k) U pj (k) are the average values ​​of the capacitor voltages of the upper and lower bridge arm submodules of phase j at time k;

[0048] In order to maintain the balance between the DC side voltage and the bridge arm voltage, the number of equivalent sub-modules put into operation in each phase bridge arm in one switching cycle should be 4, so the action time of the first switching state is the same as that of the third switching state, that is, t j,1 =t j,3 , then t j,2 =T s -2t j,1 ;

[0049] Considering the current error under the action of each voltage basis vector, the cost function is established as follows:

[0050]

[0051] Where: is the j-phase reference current at time k;

[0052] Find the partial derivative of the cost function:

[0053]

[0054] Solving the above equation can obtain the optimal action time of each switch state in the sequence.

[0055] Step 3: Perform rolling optimization on the eight candidate sequences and select the switch sequence that minimizes the value function as the action sequence.

[0056] Predict the current of each switching sequence at the optimal action time, as shown in the following formula:

[0057]

[0058] Where: q ranges from 1 to 3; i j,qis the predicted current value after the qth switch state in the sequence, i j,0 is the sampling current i j (k);

[0059] The value function is established as follows:

[0060]

[0061] The best switching sequence can be selected by rolling optimization.

[0062] Step 4: Obtain the expected value of each phase bridge arm voltage at time k+1 from the circulating current prediction model. The discrete prediction model of the j-phase circulating current of the MMC inverter is shown as follows:

[0063]

[0064] Where: U dc is the DC side voltage; i dj (k+1) is the internal circulation of phase j of the MMC at time k+1;

[0065] It can be seen from the above formula that the circulating current is mainly caused by the inequality between the DC bus voltage and the sum of the upper and lower bridge arm voltages of the phase unit. When the difference between them is greater than zero, the circulating current tends to increase, and when the difference is less than zero, the circulating current decreases.

[0066] In order to eliminate the AC component in the circulating current, the following relationship must be satisfied:

[0067]

[0068] Where: I dc is the DC side current;

[0069] It should be pointed out that for a single-phase MMC system, the right side of the equal sign in the above equation should be I dc ;

[0070] From the above relationship, the expected value of the sum of the upper and lower bridge arm voltages of each phase at time k+1 can be obtained:

[0071]

[0072] Step 5: Based on the discrete prediction model of the submodule capacitor voltage, the bridge arm is regarded as a whole to calculate the predicted value of the bridge arm voltage of each phase. Due to the use of the voltage balancing algorithm, the capacitor voltages of each submodule in the same bridge arm are approximately equal, and the bridge arm can be regarded as a whole for voltage prediction, thereby obtaining the average value of the capacitor voltage of the submodule in each bridge arm at time k+1, as shown in the following formula:

[0073]

[0074] Where: u rj,ave(k+1) represents the average value of the capacitor voltage of the j-phase bridge arm unit r (r=p,n) submodule at time k+1; i rj (k) represents the bridge arm current of the bridge arm unit r of phase j; S rji Indicates the number of conducting submodules of the j-phase r-bridge arm when the i-th switching state in the sequence is in effect; t i represents the action time of the i-th switch state in the sequence; N represents the number of bridge arm submodules;

[0075] The predicted value u of the sum of the upper and lower bridge arm voltages of phase j at time k+1 rj (k+1) is:

[0076] u rj (k+1)=S rj7 u rj,ave (k+1)

[0077] Where: S rj7 It indicates the number of conducting submodules of the j-phase r-bridge arm when the seventh switching state in the sequence is in effect.

[0078] Step 6: Appropriately increase or decrease the number of submodules in each bridge arm to suppress the circulation. The number of submodules that should be increased or decreased in each bridge arm within a sampling period is Δn rj,eq Can be obtained by the following formula:

[0079]

[0080] In the above formula, the upper and lower bridge arms of each phase bear half of the error between the expected value and the predicted value of the bridge arm voltage respectively. This method can effectively suppress the circulating current without affecting the AC output.

[0081] Δn rj,eq It is usually a non-integer, and its fractional part is compared with the carrier, such as Figure 4 As shown, an equivalent control effect can be obtained. In the figure, cmp is Δn rj,eq The decimal part of the number of sub-modules that should be inserted into each bridge arm is Δn rj for:

[0082]

[0083] Step 7: Use the sorting method to balance the submodule capacitor voltage and send out control pulses. According to the real-time sorting results of the capacitor voltages of all submodules in the bridge arm, when the bridge arm current is a charging characteristic, the submodule with a lower capacitor voltage is put into operation, and when the bridge arm current is a discharging characteristic, the submodule with a higher capacitor voltage is put into operation.

[0084] The above is a specific implementation of the present invention, but the protection scope of the present invention is not limited thereto. For those skilled in the art, changes and modifications can be made to the above embodiment without departing from the technical spirit and principle described in the present invention, and these changes and modifications should also be regarded as the protection scope of the present invention.

Claims

1. MMC optimal switching sequence model predictive control algorithm based on two-dimensional control area, characterized by The specific steps include: Step 1: Design multiple switch sequences to be selected using a two-dimensional control region; wherein the two-dimensional control region is a two-dimensional coordinate system region formed by the vertical axis representing the number of submodules in which the upper bridge arm is turned on and the horizontal axis representing the number of submodules in which the lower bridge arm is turned on; in order to maintain the balance between the DC side voltage and the bridge arm voltage, select a switch sequence near the diagonal of the region, each sequence consisting of three switch states, including a switch state S located on the diagonal j2 and two adjacent switch states S j1 , S j3 ; Step 2: Establish an output current discrete prediction model, define the error function and solve the partial derivative to obtain the optimal action time of each switch state in the selected sequence; Step 3: Consider the impact of each switch state on current change, perform rolling optimization on multiple candidate sequences, and select the switch sequence that minimizes the value function as the action sequence; Step 4: Calculate the expected value and predicted value of the sum of the upper and lower bridge arm voltages at time k+1, and adjust the number of submodules put into each bridge arm to eliminate the error between the expected value and the predicted value of the bridge arm voltage, thereby suppressing the circulating current; Step 5: Use the sorting method to balance the submodule capacitor voltage and send out control pulses.

2. The MMC optimal switching sequence model predictive control algorithm based on two-dimensional control area according to claim 1, characterized in that: The switch sequence to be selected is designed using the two-dimensional control region, as follows: In an MMC converter with N bridge arm submodules, each bridge arm has N+1 possible switch states. The vertical axis represents the switch state of the upper bridge arm, and the horizontal axis represents the switch state of the lower bridge arm, forming a two-dimensional control area. In order to maintain the balance between the DC side voltage and the bridge arm voltage and reduce the number of rolling optimizations, only the sequences near the diagonal of the two-dimensional control area are selected. Each sequence consists of three switch states, including a switch state S located on the diagonal. j2 and the two switch states S closest to it j1 , S j3 , there are 2N sequences to be selected in each phase; Selecting the switch sequence in the two-dimensional control area can expand the number of MMC output levels, reduce the harmonic content, improve the degree of freedom of control, and achieve independent control of each phase. It is applicable to three-phase MMC as well as single-phase and H-bridge MMC.

3. The MMC optimal switching sequence model predictive control algorithm based on two-dimensional control area according to claim 1, characterized in that: A current discrete prediction model is established, the error function is defined and the partial derivative is solved to obtain the optimal action time of each switch state, as follows: The current discrete prediction model of the MMC inverter is: Where: i j (k+1),u pj (k+1) and u nj (k+1) are the j-phase current, j-phase upper bridge arm voltage and lower bridge arm voltage measured at time k+1; L and R are the reactance and resistance of the AC side respectively; L o and R o are the bridge arm reactance and resistance respectively; T s is the sampling time; Since the sampling time T s Very small. To simplify the calculation, when predicting the current after each switch state is applied, the initial current is approximated by the sampling value at time k. Due to the use of the voltage balancing algorithm, the average value of the capacitor voltage of the bridge arm submodule can be approximated by the sampling value of any submodule, as shown in the following formula: Where: m ranges from 1 to 3; i j,m is the predicted current value after the mth switch state in the sequence; t j,m is the action time of the mth switch state; S nj,m , S pj,m is the number of upper and lower bridge arm conducting submodules of phase j corresponding to the mth switch state; U nj (k) U pj (k) are the average values ​​of the capacitor voltages of the upper and lower bridge arm submodules of phase j at time k; In order to maintain the balance between the DC side voltage and the bridge arm voltage, the number of equivalent sub-modules put into operation in each phase bridge arm in one switching cycle should be N, so the action time of the first switching state is the same as that of the third switching state, that is, t j,1 =t j,3 , then t j,2 =T s -2t j,1 ; Considering the current error under the action of each voltage basis vector, the cost function is established as follows: Where: is the j-phase reference current at time k; Find the partial derivative of the cost function: Solving the above equation can obtain the optimal action time of each switch state in the sequence.

Images