Model predictive control strategy for optimal switching sequence of MMC based on output voltage space vector fitting

Abstract

The present invention provides a model predictive control strategy for an optimal switching sequence of MMC based on output voltage space vector fitting. The strategy calculates the coordinates of each candidate vector in the g-h coordinate system from the vector prediction value according to the discrete prediction model of the output voltage space vector of the three-phase MMC AC side; obtains the optimal switching sequence by screening the redundant switching states of the candidate vectors; constructs a value function of the sum of squared output current errors based on the current change gradient and obtains the optimal action time expression by taking the partial derivative thereof; calculates the optimal duty cycle of the bridge arm and the number of submodules turned on according to the bridge arm unbalanced voltage drop prediction model; and achieves submodule capacitor voltage balance through a sorting algorithm. The benefit of the present invention is that compared with the traditional model predictive control strategy, the strategy has a small computational burden, effectively reduces the output current harmonic content, and has a more concentrated harmonic spectrum distribution. Taking MMC as an example, a general algorithm for screening the optimal switching sequence of a multi-level converter is designed, which can be applied to any level and has a constant computational load.

Description

Technical Field

[0001] The present invention relates to the technical field of power electronic converter model predictive control, and in particular to an MMC optimal switching sequence model predictive control strategy based on output voltage space vector fitting. Background Art

[0002] Modular multilevel converter (MMC) has attracted much attention due to its many advantages such as high degree of modularity, strong scalability, low switching frequency, and excellent harmonic characteristics. It has stood out in the field of medium-high voltage and large-capacity power conversion and has been widely researched and applied.

[0003] The control system of an MMC has multiple control objectives, including output current, circulating current, and submodule capacitor voltage. Traditional control methods generally implement closed-loop control of a single control objective based on proportional-integral control, and then achieve joint control of multiple objectives by cascading various regulators. This control approach not only suffers from complex structure and slow dynamic response, but also affects the overall control effect of the MMC system. Model Predictive Control (MPC) has been widely used in multi-input, multi-output control systems such as MMC due to its advantages such as multi-objective control, high steady-state accuracy, and fast dynamic response. Traditional Finite Control Set Model Predictive Control (FCS-MPC) has a large computational load, difficult weighting factor tuning, and only one optimal switching state is implemented in each control cycle, resulting in unstable switching frequency and large current ripple. To achieve a fixed switching frequency, some researchers have proposed a modulation model predictive control (M2PC) strategy for MMCs. This strategy uses two or more switching states within each control cycle to improve the control accuracy of the MMC's output current. However, the impact of the MMC's different redundant switching states on output current ripple has not been considered. Therefore, further research on M2PC methods for MMCs is essential. Summary of the Invention

[0004] To address the shortcomings and challenges of existing technologies, the present invention provides an MMC Optimal Switching Sequence Model Predictive Control (OSS-MPC) strategy based on output voltage space vector fitting. Compared to traditional FCS-MPC and M2PC, OSS-MPC reduces output current ripple and achieves a more concentrated harmonic spectrum distribution while maintaining a low computational load. Furthermore, the present invention uses MMC as an example to design a general algorithm for selecting the optimal switching sequence for multilevel converters, resolving the difficulty in selecting specific switching states due to the plethora of space vectors in multilevel converters.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] Step 1: Establish a discrete prediction model for the three-phase MMC output voltage space vector; calculate the predicted value of the voltage vector at the next moment based on the prediction model;

[0007] Step 2: coordinate the voltage vector prediction value in the gh coordinate system and calculate the vector coordinates of each vertex of the triangle where the prediction vector is located;

[0008] Step 3: Filter the redundant switch states of the candidate vectors and determine the optimal switch sequence to be put into use at the next moment;

[0009] Step 4: Based on the current change gradient, a value function is constructed for the sum of squared errors between the output current prediction value and the reference value. The partial derivative of the vector action time is then taken to obtain an analytical expression for each action time of the switching sequence, and the optimal action time is then calculated.

[0010] Step 5: Calculate the duty cycle of circulating current suppression at the next moment based on the bridge arm unbalanced voltage drop prediction model;

[0011] Step 6: Calculate the optimal duty cycle of the upper and lower bridge arms based on the switching sequence action time and the circulating current suppression duty cycle; combine the optimal switching sequence to obtain the number of submodules that are turned on in the upper and lower bridge arms of each phase;

[0012] Step 7: Use the bubble sort algorithm to achieve sub-module capacitor voltage balance and output PWM pulse signal;

[0013] In the step 1, a discrete prediction model of the MMC three-phase voltage synthesis vector is established; a time-domain mathematical model of the MMC system is established according to Kirchhoff's voltage law, and a discretization process is performed on it through forward Euler to establish a discrete prediction model of the three-phase output voltage space vector;

[0014] In the second step, the voltage vector prediction value is coordinate-processed in the gh coordinate system and the vector coordinates of each vertex of the triangle where the prediction vector is located are determined; in the gh coordinate system, the corresponding coordinates of all basic space vectors of the MMC are integers, and the predicted voltage vector is normalized and then rounded up and down to obtain four candidate vector coordinates, and then the base vector coordinates of each vertex of the triangle where the prediction vector is located are determined through logical judgment;

[0015] In step 3, redundant switch states of the candidate vectors are screened; the same basic voltage vector may correspond to multiple switch states. To ensure the minimum number of switching sequence actions and the minimum common-mode voltage generated, the basic vector containing an even number of redundant states needs to retain the middle two switch states, and the basic vector containing an odd number of redundant states needs to retain the middle one switch state;

[0016] In step three, the optimal switching sequence to be put into operation at the next moment is determined. After determining the redundant switching states of the three vectors, according to the principle of symmetrical seven-segment space vector modulation, the first switching state needs to be selected from the basic vector containing an even number of redundant states. Then, according to the principle of minimizing the number of switching operations, the second and third switching states with the smallest number of operations compared to the previous segment are selected from the remaining two candidate vectors, and finally, the seven-segment optimal switching sequence is symmetrically obtained.

[0017] In step 4, a value function of the sum of squares of the errors between the output current prediction value and the reference value is constructed based on the current change gradient. The current prediction value at the next moment under the action of the switching sequence is obtained from the output current change gradient and the action time corresponding to each switching state, and a value function of the sum of squares of the errors between the predicted value and the reference value is constructed. By taking the partial derivative of the action time, an analytical expression for each action time of the switching sequence can be derived, and then the optimal action time of each vector is calculated.

[0018] Compared with the prior art, the present invention has the following advantages:

[0019] 1) The present invention designs a method for screening the optimal switching sequence of a multi-level space vector. The computational complexity of this method is not affected by the number of levels and can be extended to any number of levels without adding additional computational burden. It can realize low-complexity space vector modulation of a multi-level converter.

[0020] 2) Compared with traditional finite control set model predictive control, the present invention does not require weight factor design, improves current tracking accuracy, and can fix the switching frequency. Compared with traditional modulation model predictive control, the present invention obtains the optimal action time of the sequence by taking the partial derivative of the current error square sum function, further reducing the output current ripple, lowering the harmonic content, and improving dynamic performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1The topology diagram of the modular multilevel converter

[0022] Figure 2 The space vector diagram of the voltage source five-level converter in the gh coordinate system

[0023] Figure 3 Example diagram of redundant switch states for screening candidate vectors

[0024] Figure 4 Output current trajectory diagram under the optimal switching sequence

[0025] Figure 5 Comparison diagram of optimal duty cycle and carrier DETAILED DESCRIPTION

[0026] To illustrate the basic principles, technical solutions, and performance advantages of the present invention, the following further describes, with reference to the accompanying drawings, a specific embodiment of the MMC optimal switching sequence model predictive control strategy based on output voltage space vector fitting, according to the present invention. It should be understood that the following description is merely illustrative and is not intended to limit the scope and application of the present invention.

[0027] Figure 1 It is a modular multi-level converter topology. The main circuit consists of a DC bus, three phase units, and an AC load. The MMC DC side is used to connect to the DC bus, and the AC side is connected to the AC power supply or three-phase load. The phase unit can be divided into upper and lower bridge arms. Each bridge arm is composed of N sub-modules and a bridge arm inductor cascaded.

[0028] Taking the MMC five-level inverter as an example, the specific implementation steps of the control strategy involved in the present invention are as follows:

[0029] Step 1: Establish a discrete prediction model for the three-phase MMC output voltage space vector and calculate the predicted value of the voltage vector at the next moment:

[0030]

[0031] Where: L0 and R0 are the bridge arm inductance and bridge arm equivalent resistance respectively, L and R are the load inductance and resistance respectively, i(k+1), i * (k+1),u * (k+1) is the three-phase composite vector, where i(k) is the actual value of the output current at time k, i * (k+1) is the predicted value of the reference current at time k+1, u * (k+1) represents the expected voltage vector prediction value at time k+1;

[0032] Step 2: Coordinate the voltage vector prediction value in the gh coordinate system. The five-level space vector in the gh coordinate system is as follows: Figure 2 As shown, all the basic vectors of MMC are converted to integers, the g-axis coincides with the α-axis in the α-β coordinate system, and the angle between the h-axis and the g-axis is 60 degrees. In order to make all the basic vector coordinates integers, the unit length of the gh coordinate system is defined as the modulus of the minimum basic vector voltage, that is:

[0033]

[0034] Where: U dc is the DC bus voltage, N is the number of bridge arm submodules, and in this example, N is 4.

[0035] From step 1, we can get the u*(k+1) vector in the α-β coordinate system α and u β Component value, from the geometric relationship, we can get the coordinates of u*(k+1) in the gh coordinate system (U * g ,U * h ) can be expressed as:

[0036]

[0037] Step 3: Calculate the vector coordinates of each vertex of the triangle where the prediction vector is located. Since the coordinates of the basic voltage vector are all integers, we can calculate the vector coordinates of each vertex of the triangle where the prediction vector is located by * g ,U * h ) are rounded up and down to get the four basic voltage vectors closest to the predicted vector, which can be expressed as:

[0038]

[0039]

[0040] Where: ceil(x) and floor(x) represent the upward and downward rounding functions of the variable respectively, U cf 、U fc 、U cc 、U ff Respectively represent the coordinates of the four basic voltage vectors closest to the predicted vector;

[0041] From the geometric relationship, we know that these four basic voltage vectors will form a closed parallelogram, where U cf 、U fc It always appears on the diagonal line of the parallelogram and can be used as candidate vectors U1 and U2. Candidate vector U3 needs to be based on U * g +U * h-(ceil(U g )+floor(U h )) is determined by its sign. If it is positive, then U cc is the third candidate vector; if it is negative, then U ff is the third candidate vector.

[0042] Step 4: Screen the redundant switching states of the candidate vectors. For multilevel converters, each basic voltage vector may correspond to multiple switching states. To minimize the number of switching sequence actions and the generated common-mode voltage, basic vectors with an even number of redundant states must retain the middle two switching states, while basic vectors with an odd number of redundant states must retain the middle one switching state. Therefore, it is necessary to first determine the parity of the number of redundant switching states in the candidate vector. In the gh coordinate system, the relationship between the number of redundant switching states and the coordinates of the first largest sector has the following relationship:

[0043] X=N-|U g +U h |

[0044] Where X represents the number of redundant switch states of the basis vector, (U g ,U h ) is a point of a basis vector in the first largest sector.

[0045] In order to facilitate the calculation of the number of redundant switch states of the basic voltage vector of other large sectors, the coordinates can be mapped to the first sector and then the redundant number can be determined by the above formula. The mapping relationship is shown in the following table:

[0046] Table 1 Coordinate mapping relationship between other sectors and the first sector

[0047]

[0048] The corresponding relationship between the coordinates and the specific switch states in the gh coordinate system is shown in the following formula:

[0049]

[0050] Where: i ranges from 1 to N, and in this example, N is 4; U g and U h is the coordinate of the voltage basis vector in the gh coordinate system;

[0051] According to the parity of the number of redundant states and combined with the above formula, the specific switching state of the candidate vector can be screened out.

[0052] Step 5: Determine the optimal switching sequence for the next moment. According to the principle of symmetrical seven-segment space vector modulation, the first switching state must be selected from the basic vector containing an even number of redundant states based on the last switching state of the switching sequence at the previous moment. Then, based on the principle of minimum number of switching actions, the second and third switching states with the minimum number of actions compared to the previous segment are selected from the remaining two candidate vectors. Finally, the optimal seven-segment switching sequence is obtained symmetrically.

[0053] Define the switch state at the end of the k-time sequence as (S ak ,S bk ,S ck ), the initial switch state at time k+1 is (S ak1 ,S bk1 ,S ck1 ), the switch action times value Y can be expressed as:

[0054] Y=|S ak1 -S ak |+|S bk1 -S bk |+|S ck1 -S ck |

[0055] by Figure 3 For example, according to the coordinates of candidate vectors U1 and U2, it is calculated that the corresponding redundant switch states are all even numbers. Therefore, the four switch states corresponding to U1 and U2 have a probability of becoming the first switch state. The first switch state needs to be determined based on the switch state at the end of the switch sequence at time k. Assuming that the switch state at the end of the sequence at time k is (3,1,0), first calculate the Y values ​​of these four switch states according to the above formula, and select the one with the smallest Y value (3,2,0) as the first switch state S1. At the same time, select the redundant switch state (4,3,1) corresponding to the first switch state as the fourth switch state S4; then, according to the principle of the minimum number of switching operations, select the second and third switch states with the minimum number of operations compared to the previous segment from the remaining two candidate vectors, respectively. Finally, the seven-segment optimal switching sequence is symmetrically obtained: (3,2,0)→(3,3,0)→(4,3,0)→(4,3,1)→(4,3,0)→(3,3,0)→(3,2,0). Other sequences can be deduced based on this method to obtain the optimal switching sequence corresponding to any voltage vector prediction value.

[0056] Step 6: Based on the current change gradient, a value function of the sum of squares of the error between the output current prediction value and the reference value is constructed, and the partial derivative of the vector action time is taken to obtain the analytical expression of each action time of the switching sequence, and then the optimal action time is calculated.

[0057] The output current gradient can be obtained by the Euler discretization method:

[0058]

[0059] Where: u αn and u βn Indicates the output voltage vector corresponding to the nth switching state, where n ranges from 1 to 4;

[0060] According to the seven-segment space vector modulation principle, the fourth switching state and the first switching state correspond to the same voltage base vector, so the current change gradients of the two are equal. Under the action of the optimal switching sequence within a sampling period, the output current trajectory is as follows: Figure 4 As shown. The following output current prediction model can be established:

[0061]

[0062] Where: t1, t2, t3 are the action time of each vector corresponding to the switch state;

[0063] Combined with the above formula, the sum of squares of the error between the output current prediction value and the current reference value at time k+1 can be expressed as:

[0064]

[0065] Calculate the partial derivatives of the action time t2 and t3 respectively, that is:

[0066]

[0067] From the above formula, we can get the optimal action time t of the three vectors: 1opt , t 2opt , t 3opt The analytical expression is as follows:

[0068]

[0069] According to the analytical expression of the optimal action time, the action time of each section of the optimal switching sequence can be calculated to minimize the output current tracking error and effectively reduce the output current ripple.

[0070] Step 7: Calculate the circulating current suppression duty cycle at the next moment using the bridge arm unbalanced voltage drop prediction model; the MMC internal circulating current discrete prediction model can be expressed as:

[0071]

[0072] Where: U dc is the DC bus voltage; u pj (k+1) and u nj (k+1) are the voltage values ​​of the upper and lower bridge arms of phase j (j=a, b, c) at time k+1;

[0073] As can be seen from the above formula, the reason why the MMC generates circulating current is that the sum of the upper and lower bridge arm voltages of the j-phase unit cannot always be equal to the DC side voltage, resulting in an unbalanced voltage. This unbalanced voltage acts on the inductance and equivalent resistance on the bridge arm, thereby generating an internal circulating current. In order to eliminate the AC component in the circulating current, the bridge arm unbalanced voltage drop prediction model can be expressed as:

[0074]

[0075] Where: i * zj (k+1) is the reference value of the j-phase circulating current at time k+1, which is usually I dc / 3;u * zj (k+1) is the predicted value of the unbalanced voltage drop of the j-phase bridge arm at time k+1;

[0076] Therefore, the circulating current suppression duty ratio d acting on the upper and lower bridge arms of each phase at time k+1 is pzj d nzj It can be expressed as:

[0077]

[0078] Step 8: According to the switching sequence action time and the circulating current suppression duty cycle, the optimal duty cycle of the upper and lower bridge arms is calculated; in order to facilitate digital implementation, the optimal action time t of the three basis vectors is 1opt , t 2opt , t 3opt It can be equivalent to the duty cycle of the switch tube; the duty cycle of each phase d can be derived from the change relationship of the sequence switch state aopt d bopt d copt They are:

[0079]

[0080] Where: S jn (j=a,b,c,n=1,2,3,4) represents the switching state corresponding to the nth segment of phase j in the optimal switching sequence;

[0081] Combined with the circulating current suppression duty cycle obtained in step 7, the optimal duty cycle d of the upper and lower bridge arms of phase j can be obtained. pjopt d njopt for:

[0082]

[0083] Figure 5 This is the comparison diagram of the optimal duty cycle and carrier. The calculated duty cycle and carrier are compared and combined with the optimal switching sequence to change the number of sub-modules put into the upper and lower bridge arms of each phase.

[0084] Step 9: Use the bubble sort algorithm to achieve sub-module capacitor voltage balance and output PWM pulse signals; by sorting the sub-module capacitor voltages, it is stipulated here that the direction of the bridge arm current is positive when the sub-module capacitor is in the charging state. If the bridge arm current is positive, the sub-module with lower voltage is put into operation first; if the bridge arm current is negative, the sub-module with higher voltage is put into operation first.

[0085] The above is a specific embodiment of the present invention and its advantages, but the scope of protection of the present invention is not limited thereto. Those skilled in the art may make changes and modifications to the above embodiment without departing from the technical spirit and principles described in the present invention, and such changes and modifications should also be considered within the scope of protection of the present invention.

Claims

1. The MMC optimal switching sequence model predictive control strategy based on output voltage space vector fitting is characterized by: This strategy uses a discrete prediction model of the AC side output voltage space vector to calculate the nearest candidate vector coordinates in the gh coordinate system. It then determines the optimal switching sequence by screening the redundant switching states of the vector. A value function for the sum of squared output current errors is constructed based on the current gradient, and the partial derivative of the vector action time is taken to obtain an analytical expression for the optimal action time of the sequence. The circulating current suppression duty cycle is calculated using the bridge arm unbalanced voltage drop prediction model, and combined with the optimal switching sequence, the final bridge arm optimal duty cycle and the number of sub-modules turned on are calculated. Finally, the bubble sort algorithm is used to achieve sub-module capacitor voltage balance and output the switch control signal. The specific steps include: Step 1: Establish a discrete prediction model for the three-phase MMC output voltage space vector; calculate the predicted value of the voltage vector at the next moment based on the prediction model; Step 2: coordinate the voltage vector prediction value in the gh coordinate system and calculate the vector coordinates of each vertex of the triangle where the prediction vector is located; Step 3: Filter the redundant switch states of the candidate vectors and determine the optimal switch sequence to be put into use at the next moment; Step 4: Based on the current change gradient, a value function is constructed for the sum of squared errors between the output current prediction value and the reference value. The partial derivative of the vector action time is then taken to obtain an analytical expression for each action time of the switching sequence, and the optimal action time is then calculated. Step 5: Calculate the duty cycle of circulating current suppression at the next moment based on the bridge arm unbalanced voltage drop prediction model; Step 6: Calculate the optimal duty cycle of the upper and lower bridge arms based on the switching sequence action time and the circulating current suppression duty cycle; combine the optimal switching sequence to obtain the number of submodules that are turned on in the upper and lower bridge arms of each phase; Step 7: Use the bubble sort algorithm to achieve sub-module capacitor voltage balance and output PWM pulse signal; In step three, the redundant switch states of the candidate vector are screened. To minimize the number of switching sequence actions and the generated common-mode voltage, the basic vector with an even number of redundant states must retain the middle two switch states, and the basic vector with an odd number of redundant states must retain the middle one switch state. The specific redundant switch state is screened based on the parity of the number of redundant states and the correspondence between the coordinates of the candidate vector and the specific switch state. In step three, the optimal switching sequence to be put into operation at the next moment is determined. Specifically, according to the principle of symmetrical seven-segment space vector modulation, the first switching state is selected from the basic vector containing an even number of redundant states based on the last switching state of the switching sequence at the previous moment. Then, based on the principle of minimizing the number of switching operations, the second and third switching states with the smallest number of operations compared to the previous segment are selected from the remaining two candidate vectors. Finally, the optimal seven-segment switching sequence is obtained symmetrically. In step 4, a value function of the sum of squares of the error between the output current prediction value and the reference value is constructed based on the current change gradient, and the partial derivative of the vector action time is taken to obtain the analytical expression of each action time of the switching sequence, as follows: The output current gradient obtained by the Euler discretization method is: Where: u α,n and u β,n Indicates the output voltage vector corresponding to the nth switching state, where n ranges from 1 to 4; According to the seven-segment space vector modulation principle, the fourth switching state and the first switching state correspond to the same voltage base vector, so the current change gradients of the two are equal. The following output current prediction model is established: Where: t1, t2, t3 are the action time of each vector corresponding to the switch state; Combined with the above formula, the sum of squares of the error between the output current prediction value and the current reference value at time k+1 is expressed as: Calculate the partial derivatives of the action time t2 and t3 respectively, that is: From the above formula, we can get the optimal action time t of the three vectors: 1opt , t 2opt , t 3opt The analytical expression is as follows: According to the analytical expression of the optimal action time, the action time of each section of the optimal switching sequence is calculated to minimize the output current tracking error and effectively reduce the output current ripple.

2. The control strategy according to claim 1, characterized in that: In step 6, the optimal duty cycle of the upper and lower bridge arms is calculated based on the switching sequence action time and the circulating current suppression duty cycle. Specifically, the optimal action time t of the three basis vectors is 1opt , t 2opt , t 3opt Equivalent to the duty cycle of the switch tube, the duty cycle of each phase d is derived from the change relationship of the sequence switch state aopt d bopt d copt They are: Where: S jn (j=a,b,c,n=1,2,3,4) represents the switching state corresponding to the nth segment of phase j in the optimal switching sequence; Combined with the circulating current suppression duty cycle obtained in step 5, the optimal duty cycle d of the upper and lower bridge arms of phase j is obtained according to the above formula pjopt d njopt .

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