MMC optimal switch sequence model prediction control strategy based on output voltage space vector fitting

Abstract

The invention provides an MMC optimal switch sequence model prediction control strategy based on output voltage space vector fitting. According to the strategy, coordinates of candidate vectors in a g-h coordinate system are calculated through vector predicted values according to a discrete prediction model of a three-phase MMC alternating current side output voltage space vector; obtaining an optimal switching sequence by screening redundant switching states of the candidate vectors; constructing a value function of an output current error sum of squares based on the current change gradient, and solving a partial derivative of the value function to obtain an optimal action time expression; calculating the optimal duty ratio of the bridge arm and the number of conducted sub-modules according to the bridge arm unbalanced voltage drop prediction model; and capacitor voltage balance of the sub-modules is realized through a sorting algorithm. The method has the advantages that compared with a traditional model prediction control strategy, the strategy is small in operation burden, the harmonic content of output current is effectively reduced, harmonic spectrum distribution is more concentrated, a universal algorithm for screening the optimal switching sequence of the multi-level converter is designed with MMC as an example, the method can be applied to any level, and the operation amount is not changed.

Description

Technical Field

[0001] The 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 MMC has multiple control targets, including output current, circulating current and submodule capacitor voltage. The traditional control method is generally based on proportional integral control to achieve closed-loop control of a single control target, and then realizes joint control of multiple targets by cascading each regulator. This control method not only has defects such as complex structure and slow dynamic response, but also affects the overall control effect of the MMC system. Model Predictive Control (MPC) is widely used in multi-input and multi-output control systems such as MMC because of its advantages such as multi-target control, high steady-state accuracy and fast dynamic response speed. The traditional finite control set model predictive control (FCS-MPC) has a large amount of calculation, difficult weight factor adjustment, and only one optimal switching state is put into each control cycle, resulting in an unstable switching frequency and large current ripple. In order to achieve a fixed switching frequency, some scholars have proposed a modulation model predictive control strategy (M2PC) for MMC, which uses two or more switching states in each control cycle to improve the control accuracy of the MMC output current. However, the impact of different redundant switching states of MMC on the output current ripple has not been considered. Therefore, it is very necessary to further study the model predictive control method applied to MMC. Summary of the invention

[0004] In view of the shortcomings and existing problems of the prior art, the present invention provides an MMC optimal switching sequence model predictive control strategy (OSS-MPC) based on output voltage space vector fitting, which aims to reduce the output current ripple and make the harmonic spectrum distribution more concentrated under the premise of ensuring low computational complexity compared with traditional FCS-MPC and M2PC. At the same time, the present invention takes MMC as an example to design a general algorithm for screening the optimal switching sequence of multi-level converters, which solves the problem that the specific switching state is difficult to select due to too many space vectors of the multi-level converter.

[0005] To achieve the above purpose, 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 according to 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 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 calculated to obtain the analytical expression of each action time of the switching sequence, and then the optimal action time is calculated;

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

[0011] Step 6: Calculate the optimal duty cycle of the upper and lower bridge arms according to the switching sequence action time and the circulating current suppression duty cycle; combine the optimal switching sequence to obtain the number of submodules turned on corresponding to 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 discrete prediction model of the three-phase output voltage space vector is established by discretizing it through forward Euler;

[0014] In the step 2, the voltage vector prediction value is 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 rounded up and down to obtain four candidate vector coordinates, and then the basic vector coordinates of each vertex of the triangle where the prediction vector is located are determined through logical judgment;

[0015] In the step 3, the redundant switch states of the candidate vectors are screened; the same basic voltage vector may correspond to multiple switch states. In order to ensure that the number of switch sequence actions is minimized and the common mode voltage generated is minimized, 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 the step three, the optimal switch sequence to be put into use at the next moment is determined; after determining the redundant switch states of the three vectors, according to the principle of symmetrical seven-segment space vector modulation, the first switch state needs to be selected from the basic vector containing an even number of redundant states; then, according to the principle of the minimum number of switching actions, the second and third switch states with the minimum number of actions compared to the previous segment are selected from the remaining two candidate vectors, and finally the seven-segment optimal switch sequence is obtained symmetrically.

[0017] In the 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; the current prediction value under the action of the switch sequence at the next moment can be obtained from the output current change gradient and the action time corresponding to each switch state, and a value function of the sum of squares of the error between the current prediction value and the reference value is constructed, and the analytical expression of each action time of the switch sequence can be derived by taking partial derivatives of the action time, 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 the method is not affected by the number of levels, can be extended to any number of levels, does not increase the additional computational burden, and can realize low-complexity multi-level converter space vector modulation;

[0020] 2) Compared with the traditional finite control set model predictive control, the present invention does not require weight factor design, improves the current tracking accuracy, and the switching frequency can be fixed; compared with the 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 reduces the output current ripple, has lower harmonic content, and better dynamic performance; BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1The topological structure diagram of the modular multi-level 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] In order to illustrate the basic principle, technical solution and performance advantages of the present invention, the specific implementation of the MMC optimal switching sequence model predictive control strategy based on output voltage space vector fitting according to the present invention will be further described below in conjunction with the accompanying drawings. It should be understood that the following description is only exemplary and is not intended to limit the protection 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 side bus, three phase units and an AC side load. The MMC DC side is used to connect the DC bus, and the AC side is connected to an AC power supply or a three-phase load. The phase unit can be divided into an upper and a lower bridge arm. 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: L 0 and R 0 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 predicted value of the expected voltage vector 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 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 basic vector coordinates integers, the unit length of the gh coordinate system is defined as the modulus length 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 values, 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 corresponding 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 calculating the vector coordinates of each vertex of the triangle where the prediction vector is located. * 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 They represent the coordinates of the four basic voltage vectors closest to the predicted vector respectively;

[0041] From the geometric relationship, we know that these four basic voltage vectors will form a closed parallelogram, where U cf , U fc Always appears on the diagonal of the parallelogram and can be used as a candidate vector U 1 and U 2The candidate vector U 3 Then you need to use 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 switch states of the candidate vectors. For multi-level converters, each basic voltage vector may correspond to multiple switch states. In order to ensure the minimum number of switch sequence actions and the minimum common-mode voltage generated, the basic vector with an even number of redundant states needs to retain the middle two switch states, and the basic vector with an odd number of redundant states needs to retain the middle one switch state. Therefore, it is necessary to first determine the parity of the number of redundant switch states of the candidate vector. In the gh coordinate system, the number of redundant switch states and the coordinates of the first largest sector have 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 calculate 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 state in the gh coordinate system is shown as follows:

[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 in combination with the above formula, the specific switching state of the candidate vector can be screened out.

[0052] Step 5: Determine the optimal switch sequence to be put into use at the next moment. According to the principle of symmetrical seven-segment space vector modulation, the first switch state should be selected from the basic vector containing an even number of redundant states according to the last switch state of the switch sequence at the previous moment; then, according to the principle of the minimum number of switch actions, the second and third switch states with the minimum number of actions compared to the previous segment are selected from the remaining two candidate vectors, and finally the seven-segment optimal switch 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 candidate vector U 1 and U 2 Coordinates, calculated to obtain the corresponding redundant switch states are all even numbers, so U 1 and U 2 The corresponding four switch states all 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 the four switch states according to the above formula, and select (3, 2, 0) with the smallest Y value as the first switch state S 1 , and select the redundant switch state (4,3,1) corresponding to the first start as the fourth switch state S 4 ; Then, according to the principle of the minimum number of switching actions, the second and third switching states with the minimum number of actions compared to the previous one are selected from the remaining two candidate vectors, and finally the seven-segment optimal switching sequence is obtained symmetrically: (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 by 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] Through the Euler discretization method, the output current gradient can be obtained as:

[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: t 1 ,t 2 ,t 3 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] For the action time t 2 ,t 3 Find the partial derivative, 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] From the above formula, we can know that the reason why MMC generates circulating current is that the sum of the upper and lower bridge arm voltages of the j-phase unit cannot be kept equal to the DC side voltage at all times, and there will be an unbalanced voltage. This unbalanced voltage acts on the inductance and equivalent resistance on the bridge arm to generate 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 basic 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 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 switch state corresponding to the nth segment of the jth phase in the optimal switch 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; sort the sub-module capacitor voltages, where it is stipulated that the direction of the bridge arm current is positive when the sub-module capacitor is in a charging state. If the bridge arm current is positive, the sub-module with lower voltage is prioritized; if the bridge arm current is negative, the sub-module with higher voltage is prioritized.

[0085] The above is a specific implementation of the present invention and its advantages, but the protection scope of the present invention is not limited thereto. For ordinary technicians in the technical field, 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. The MMC optimal switching sequence model predictive control strategy based on output voltage space vector fitting is characterized by: The strategy uses the AC side output voltage space vector discrete prediction model to calculate the nearest candidate vector coordinates of the prediction vector in the gh coordinate system, and determines the optimal switching sequence by screening the redundant switching states of the vector. The value function of the sum of squares of the output current error is constructed based on the current change gradient, and the partial derivative of the vector action time is calculated to obtain the analytical expression of the optimal action time of the sequence. The circulating current suppression duty cycle is calculated through the bridge arm unbalanced voltage drop prediction model, and the optimal bridge arm duty cycle and the number of sub-modules turned on are calculated in combination with the optimal switching sequence; finally, the bubble sort algorithm is used to achieve sub-module capacitor voltage balance and output switch control signals; The specific steps include: Step 1: Establish a discrete prediction model for the three-phase MMC output voltage space vector; calculate the voltage vector prediction value at the next moment according to 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 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 calculated to obtain the analytical expression of each action time of the switching sequence, and then the optimal action time is calculated; Step 5: Calculate the duty cycle of circulating current suppression at the next moment according to the bridge arm unbalanced voltage drop prediction model; Step 6: Calculate the optimal duty cycle of the upper and lower bridge arms according to the switching sequence action time and the circulating current suppression duty cycle; combine the optimal switching sequence to obtain the number of submodules turned on corresponding to 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.

2. According to the method of claim 1, step 1, step 2 and step 3 constitute a general algorithm for screening the optimal switching sequence of a multi-level converter, characterized in that: In step three, the redundant switch states of the candidate vector are screened. In order to minimize the number of switch sequence actions and the generated common-mode voltage, 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. The specific redundant switch state can be screened out according to the parity of the number of redundant states and the correspondence between the coordinates of the candidate vector and the specific switch state.

3. The method according to claim 1, characterized in that In step three, the optimal switching sequence to be put into use at the next moment is determined. Specifically, 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 based on the last switching state of the switching sequence at the previous moment; then, according to the principle of the minimum number of switching actions, the second and third switching states with the minimum number of actions compared to the previous stage are selected from the remaining two candidate vectors, and finally the seven-segment optimal switching sequence is obtained symmetrically.

4. The method according to claim 1, characterized in that: 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 calculated to obtain the analytical expression of each action time of the switching sequence, as follows: The output current gradient can be obtained by the Euler discretization method: 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-segment switching state and the first-segment switching state correspond to the same voltage base vector, so the current change gradients of the two are equal, and the following output current prediction model can be 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 can be 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 can be calculated to minimize the output current tracking error and effectively reduce the output current ripple.

5. The method according to claim 1, characterized in that In step 6, the optimal duty ratio of the upper and lower bridge arms is calculated based on the switching sequence action time and the circulating current suppression duty ratio. Specifically, the optimal action time t of the three basic 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 can be 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 switch state corresponding to the nth segment of the jth phase in the optimal switch 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 can be obtained according to the above formula: pjopt d njopt .

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