Novel distributed model predictive control method suitable for multi-level converter

Abstract

The invention discloses a novel distributed model predictive control method suitable for a multi-level converter. The method comprises the following steps: step 1, establishing a discrete space state equation of a flying capacitor multi-level converter (FCMC); 2, designing a general continuous set model predictive control (CCS)-MPC controller, and converting controller solution into a general quadratic programming QP problem under the condition of considering constraints; and step 3, decomposing the CCS-MPC control task of the FCMC into a plurality of low-dimensional sub-optimization tasks through a QP problem optimization decomposition algorithm based on Nash equilibrium, thereby effectively reducing the total calculation amount. Compared with a traditional lumped structure FCS-MPC, the strategy not only has more excellent steady-state performance and lower calculation burden, but also increases the calculation amount of the DMPC in an approximately linear manner instead of the exponential increase of the similar FCS-MPC along with the increase of the level number, and is more suitable for a multi-level converter.

Description

Technical Field

[0001] The invention belongs to the technical field of power electronics, and in particular relates to a novel distributed model predictive control method suitable for a multi-level converter. Background Art

[0002] In recent years, multilevel converters have gradually become one of the key technologies for smart grids, green energy and industrial drives due to their high performance and reliability. Flying Capacitor Multilevel Converter (FCMC) has attracted wide attention due to its potential in high-density and high-efficiency power conversion. At present, the traditional control strategies of FCMC are mainly divided into two categories: the first is finite-control-set model predictive control (FCS-MPC), and the second is continuous-control-set model predictive control (CCS-MPC).

[0003] However, the above two traditional control strategies still have significant problems such as the non-fixed switching frequency and the excessively fast growth rate of the computational burden as the number of levels increases. Therefore, for high-level high-frequency power FCMC, the present invention proposes a new distributed model predictive control (DMPC) strategy suitable for multi-level converters, which can greatly reduce redundant calculations. Compared with the traditional FCS-MPC or CCS-MPC controller, this strategy can maintain the excellent control performance of MPC and take into account the characteristics of modular controllers, which is of great research significance. Summary of the invention

[0004] In view of the shortcomings of the existing multi-level converter control strategy, the present invention proposes a new distributed model predictive control method suitable for multi-level converters, which can significantly reduce the output current ripple, alleviate the calculation burden, and has good adaptability in FCMC control.

[0005] In order to solve the above technical problems, the technical solution provided by the present invention is:

[0006] A novel distributed model predictive control method for a multilevel converter comprises the following steps:

[0007] Step 1, establishing the discrete space state equation of the flying capacitor multi-level converter FCMC;

[0008] Step 2: Design a general continuous set model predictive control CCS-MPC controller and transform the controller solution into a general quadratic programming QP problem under the consideration of constraints;

[0009] Step three, through the QP problem optimization decomposition algorithm based on Nash equilibrium, the CCS-MPC control task of FCMC is decomposed into multiple low-dimensional sub-optimization tasks, effectively reducing the total computational complexity.

[0010] In a possible implementation manner, the step 1 specifically includes:

[0011] According to the single-phase N-level gallium nitride GaN FCMC topology circuit under modular design, each switch module in the circuit is composed of two complementary GaNs, with a total of 2 (N-1) GaN switch tubes and N-2 flying capacitors, and multi-level output is achieved through module cascading;

[0012] Assuming the circuit is ideal and the flying capacitor voltage is constant, the blocking voltage v of each GaN is s(m) Depends on the voltage of the adjacent flying capacitor:

[0013] v s(m) =v c(m) -v c(m-1) m∈{1, 2, ..., (N-1)} (1)

[0014] In which, define v c(m) is the voltage across the flying capacitor, v c(0) =0 and v c(N-1) =V DC , m and N are the number of units and levels respectively. Using Kirchhoff’s voltage law, we get the switch node voltage v sw :

[0015]

[0016] Where S m is a switching function, which is 1 when the switch is on and 0 when it is off; V DC is the DC voltage at the input side;

[0017] Obtain the discrete average space state equation:

[0018]

[0019] in:

[0020]

[0021] Among them, O and E N-2 are the zero matrix and the N-2 order identity matrix respectively, A and B are the state matrices, d m (k) is the switching function Sm The average switching cycle, T is the sampling time, R is the resistive load, L is the output inductance, i L is the output current.

[0022] In a possible implementation manner, the step 2 specifically includes:

[0023] Define the input vector u(k), output vector x(k) and reference vector w(k+1) respectively:

[0024]

[0025] The optimization problem at time k is expressed as: find the optimal input vector u(k) that makes the output vector x(k+1) of the controlled system as close as possible to the given reference value w(k+1);

[0026] The optimization problem is solved by finding the minimum value of the cost function J(k):

[0027]

[0028] Where Q is a diagonal matrix composed of weight coefficients. By solving the necessary condition dJ(k) / du(k)=0, we can get the stationary point u corresponding to the minimum value of the cost function. M (k):

[0029] u M (k) = B -1 [w(k+1)-Ax(k)] (17)

[0030] Station u M (k) is the optimal solution. Due to physical limitations and safety criteria, the input and output vectors must be limited to a specific range and the constraints of the input and output vectors must be precisely defined. These constraints are uniformly expressed as:

[0031]

[0032] Among them, u min and u max are the minimum input vector and the maximum input vector respectively;

[0033] Its matrix form is:

[0034] Fu M (k) £l(19)

[0035] in

[0036]

[0037] Substituting constraint (9) into equation (5), we can obtain the optimization problem under constraint conditions:

[0038]

[0039] The optimization problem of the above form is called a quadratic programming (QP) problem, which consists of a quadratic performance indicator, a linear equation, and a linear inequality constraint.

[0040] In a possible implementation manner, the step three specifically includes:

[0041] Formula (10) is the QP problem that needs to be solved by the FCMC CCS-MPC online optimization controller;

[0042] In order to reduce the complexity of solving a single QP problem, equation (10) is decomposed into multiple sub-problems. That is, the single controller problem represented by equation (10) is decomposed into a group of problems and assigned to mutually cooperating sub-controllers. The number of controllers is equal to the matrix u M The number of rows, the i-th controller solves u i As the control input, y i As the output single-objective predictive control optimization problem, equation (10) is decomposed into a set of QP problems as follows:

[0043]

[0044] Compared with formula (10), we get:

[0045] 1) In distributed control, the original cost function J(k) is replaced by multiple cost functions J associated with subproblems. i (k) replaced;

[0046] 2) Because the established matrix B contains the correlation between the output of the sub-controller and all the input variables, these sub-optimization problems are coupled with each other;

[0047] The Nash optimal solution is found through iteration. When the iteration ends, the output of each controller meets the set value, the performance index reaches the minimum, and all sub-controllers reach Nash equilibrium, then the entire system is in the Nash optimal state.

[0048] The present invention has at least the following beneficial effects: compared with the traditional lumped structure finite control set model predictive control (FCS-MPC), this strategy not only has better steady-state performance and lower computational burden, but also as the number of levels increases, the computational complexity of DMPC increases approximately linearly rather than exponentially like FCS-MPC, and is more suitable for multi-level converters. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 A flowchart of a novel distributed model predictive control method applicable to a multi-level converter according to an embodiment of the present invention;

[0050] Figure 2 A schematic diagram of a modular design of a GaN-based N-level FCMC in one embodiment of the present invention;

[0051] Figure 3 A control scheme of a five-level FCMC in one embodiment of the present invention;

[0052] Figure 4 FIG. 4 is a flow chart of a DMPC algorithm of an N-level FCMC in an embodiment of the present invention. DETAILED DESCRIPTION

[0053] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0054] See also Figure 1 , which is a flowchart of a novel distributed model predictive control method applicable to a multi-level converter according to an embodiment of the present invention, comprises the following steps:

[0055] Step 1, establishing the discrete space state equation of the flying capacitor multi-level converter FCMC;

[0056] Step 2: Design a general continuous set model predictive control CCS-MPC controller and transform the controller solution into a general quadratic programming QP problem under the consideration of constraints;

[0057] Step three, through the QP problem optimization decomposition algorithm based on Nash equilibrium, the CCS-MPC control task of FCMC is decomposed into multiple low-dimensional sub-optimization tasks, effectively reducing the total computational complexity.

[0058] First, in step one, Figure 2 As shown, the mathematical model of N-level FCMC is established, as shown in equations (1), (2), and (3). According to the single-phase N-level gallium nitride GaN FCMC topology circuit under modular design, each switch module in the circuit is composed of two complementary GaNs, with a total of 2 (N-1) GaN switch tubes and N-2 flying capacitors, and multi-level output is achieved through module cascading;

[0059] Assuming the circuit is ideal and the flying capacitor voltage is constant, the blocking voltage v of each GaN is s(m) Depends on the voltage of the adjacent flying capacitor:

[0060] Assuming the circuit is ideal and the capacitor voltage is constant, the blocking voltage of each switch is v s(m)Depends on the voltage of the adjacent capacitor:

[0061] v s(m) =v c(m) -v c(m-1) m∈{1, 2, ..., (N-1)} (1)

[0062] Define v c(0) =0 and v c(N-1) =V DC , m and N are the number of units and levels respectively. Using Kirchhoff’s voltage law, we get the switch node voltage v sw :

[0063]

[0064] Where S m is a switching function, which is 1 when the switch is on and 0 when it is off; V DC is the DC voltage at the input side;

[0065] Obtain the discrete average space state equation:

[0066]

[0067] in:

[0068]

[0069]

[0070] Among them, O and E N-2 are the zero matrix and the N-2 order identity matrix respectively, A and B are the state matrices, d m (k) is the switching function S m The average switching cycle, T is the sampling time, R is the resistive load, L is the output inductance, i L is the output current.

[0071] Furthermore, in step 2, the controller solution is transformed into a general QP (quadratic programming) problem under the constraint condition, and the optimization problem under the constraint condition is obtained as shown in formula (10):

[0072] Define the input vector u(k), output vector x(k) and reference vector w(k+1) respectively:

[0073]

[0074] The optimization problem at time k can be expressed as: find the optimal input vector u(k) that makes the output vector x(k+1) of the controlled system as close as possible to the given reference value w(k+1).

[0075] The optimization problem can be solved by finding the minimum value of the cost function J(k):

[0076]

[0077] Where Q is a diagonal matrix composed of weight coefficients. By solving the necessary condition dJ(k) / du(k)=0, we can get the stationary point u corresponding to the minimum value of the cost function. M (k):

[0078] u M (k) = B -1 [w(k+1)-Ax(k)] (28)

[0079] Station u M (k) is the optimal solution. Due to physical limitations and safety criteria, the input and output vectors must be limited to a specific range, such as the voltage across the flying capacitor and the output current. Therefore, it is necessary to accurately define the constraints of the input and output vectors. These constraints can be uniformly expressed as:

[0080]

[0081] Among them, u min and u max are the minimum input vector and the maximum input vector respectively.

[0082] Its matrix form is:

[0083] Fu M (k) £l(30)

[0084] in

[0085]

[0086] Substituting constraint (9) into equation (5), we can obtain the optimization problem under constraint conditions:

[0087]

[0088] The optimization problem of the above form is called a quadratic programming (QP) problem, which consists of a quadratic performance indicator, a linear equation, and a linear inequality constraint.

[0089] Then, a new online optimization decomposition algorithm is further proposed, which effectively reduces the total computational complexity by decomposing the online optimization task of the overall high-dimensional multivariable system into multiple low-dimensional sub-optimization tasks.

[0090] Formula (10) is the QP problem that needs to be solved by the FCMC CCS-MPC online optimization controller.

[0091] In order to reduce the complexity of solving a single QP problem, equation (10) can be decomposed into multiple sub-problems. That is, the single controller problem represented by equation (10) is decomposed into a group of problems and assigned to mutually cooperating sub-controllers. The number of controllers is equal to the matrix u M The number of rows, the i-th controller solves u i As the control input, y i As the output single-objective predictive control optimization problem, equation (10) is decomposed into a set of QP problems as follows:

[0092]

[0093] Compared with formula (10), we get:

[0094] 1) In distributed control, the original cost function J(k) is replaced by multiple cost functions J associated with subproblems. i However, due to the lack of a coordinated controller with global information, distributed control is essentially a multi-controller and multi-objective optimization problem.

[0095] 2) Because the established matrix B contains the correlations between the outputs of the sub-controllers and all the input variables, these sub-optimization problems are coupled to each other.

[0096] Consider a system with N-1 decision variables u1 to u N-1 The multi-objective QP problem. Let the decision variable of the i-th decision maker be u i , define the minimum objective cost function J i (u1,...,u N-1 ). The optimal Nash equilibrium solution u*=(u1*,...,u N-1 *) is a decision set that satisfies the following conditions:

[0097]

[0098] When the optimal Nash equilibrium solution is reached, that is, the local optimal goal that can be achieved under the current conditions is met, the decision maker will no longer try to update the decision variable u i , because for u i Any additional modification of the cost function J will not make i (u1,...,u N-1 ) is further reduced. The Nash equilibrium optimal solution can reconcile the needs of individual decision makers and provide an acceptable solution for all relevant parties. It reflects the equilibrium state achieved by each decision maker when pursuing their own optimal solution, and embodies the essence of the Nash equilibrium optimal solution. According to formula (24), by solving the following QP problem:

[0099]

[0100] The Nash optimal solution of each controller can be obtained, where represents the Nash equilibrium optimal solution provided by the remaining sub-controllers. The solution to the above optimization problem is:

[0101]

[0102] From the above formula, we can see that if we want to obtain the Nash optimal u of the i-th controller * i,M (k), the Nash optimal solutions of all other sub-controllers must be obtained in advance To solve this coupled dynamic decision-making problem, each controller can use the communication estimation method to find the Nash optimal solution through iteration. Send to other controllers. When the i-th controller receives the Nash optimal solution of other controllers, it can

[0103]

[0104] The optimal solution is updated accordingly and passed to other sub-controllers. The interaction of all controllers will continue until the iteration ends.

[0105]

[0106] is satisfied. The initial solution of the iteration can be given arbitrarily or all set to 0. If the error accuracy ε is not satisfied during the iteration, it means that the converter has not reached Nash equilibrium, and further iterations are needed to adjust the input and improve local performance. When the output of each controller meets the set value at the end of the iteration, the performance index reaches the minimum, and all sub-controllers reach Nash equilibrium, the entire system is in the Nash optimal state, and further changes in the input will not improve the performance of the converter.

[0107] In a specific application example, in order to further verify the practicality of the proposed DMPC strategy, a GaN-based five-level flying capacitor converter prototype was designed and built, and the design process of the distributed controller was proposed. In the five-level FCMC, according to the distributed control principle, the total number of controllers is equal to the matrix u M The number of rows is four. Its controller set includes three flying capacitor voltage controllers and one current controller. The specific optimization problem is:

[0108] 1) Current sub-controller:

[0109]

[0110] 2)v c(m) Sub-controller, m=1,2,3:

[0111]

[0112] Define the initial conditions of the algorithm:

[0113] i(0)=0,

[0114] d1(0)=d2(0)=d3(0)=d4(0),

[0115] v s(4) (0) = V dc ,v s(3) (0) = v s(2) (0) = v s(1) (0) = 0

[0116] The formula (12) at the initial moment can be simplified as:

[0117]

[0118] Substituting the initial conditions and solving the above equation, we can get

[0119]

[0120] The Nash optimal solution under the constraints is:

[0121]

[0122] according to Figure 3 The iterative process shown in the figure converts the Nash optimal solution d of the current controller into 4,M (0)Send to v c(3) The voltage controller then iterates to the next controller in turn, updates the solution and determines whether the iteration end condition is met. If not, the iteration continues. If it is met, it means that all sub-controllers have reached Nash equilibrium, and the entire system is in the Nash optimal state. Further changes in the input will not improve the performance of the converter.

[0123] Therefore, the subsequent Nash optimal solutions d can be obtained in sequence i,M (0)(i=1,2,3):

[0124]

[0125] The voltage sub-controller is responsible for adjusting the corresponding flying capacitor voltage to the reference value. The current controller is responsible for processing the initial conditions, updating the optimal solution, and determining whether the iteration is completed. The algorithm flow is as follows Figure 4 As shown, the specific process is as follows.

[0126] After obtaining the sampled value and the reference at the sampling time, the error factor e1(k)-e is calculated. N-2(k), then each voltage controller reduces the input variable by a corresponding factor e i (k) as the output. Since e i (k) is a fixed error factor, so adding the increment Δd(k) to the input and output at the same time does not affect the voltage control effect. The increment Δd(k) satisfies the following formula:

[0127]

[0128] When k = 0, we have

[0129]

[0130] Updating the duty cycle by increasing Δd(k) can ensure that the current controller achieves deadbeat control. 4,M (0) is passed to the voltage controller to start the next iteration until the iteration stop condition is met

[0131] |Dd(k)|￡ε

[0132] At this point, all four controllers have reached the Nash equilibrium state, and all Nash equilibrium optimal solutions are obtained. The iterative formula is given by (20)-(23):

[0133]

[0134] It should be understood that the exemplary embodiments described herein are illustrative rather than restrictive. Although one or more embodiments of the present invention have been described in conjunction with the accompanying drawings, it should be understood by those skilled in the art that various changes in form and detail may be made without departing from the spirit and scope of the present invention as defined by the appended claims.

Claims

1. A novel distributed model predictive control method for multi-level converters, characterized in that: The following steps are involved: Step 1, establishing the discrete space state equation of the flying capacitor multi-level converter FCMC; Step 2: Design a general continuous set model predictive control CCS-MPC controller and transform the controller solution into a general quadratic programming QP problem under the consideration of constraints; Step three, through the QP problem optimization decomposition algorithm based on Nash equilibrium, the CCS-MPC control task of FCMC is decomposed into multiple low-dimensional sub-optimization tasks, effectively reducing the total computational complexity.

2. The novel distributed model predictive control method for multi-level converters according to claim 1, characterized in that: The step 1 specifically includes: According to the single-phase N-level gallium nitride GaN FCMC topology circuit under modular design, each switch module in the circuit is composed of two complementary GaNs, with a total of 2 (N-1) GaN switch tubes and N-2 flying capacitors, and multi-level output is achieved through module cascading; Assuming the circuit is ideal and the flying capacitor voltage is constant, the blocking voltage v of each GaN is s(m) Depends on the voltage of the adjacent flying capacitor: v s(m) =v c(m) -v c(m-1) m∈{1,2,...,(N-1)} (1) In which, define v c(m) is the voltage across the flying capacitor, v c(0) =0 and v c(N-1) =V DC , m and N are the number of units and levels respectively. Using Kirchhoff’s voltage law, we get the switch node voltage v sw : Where S m is a switching function, which is 1 when the switch is on and 0 when it is off; V DC is the DC voltage at the input side; Obtain the discrete average space state equation: in: Among them, O and E N-2 are the zero matrix and the N-2 order identity matrix respectively, A and B are the state matrices, d m (k) is the switching function S m The average switching cycle, T is the sampling time, R is the resistive load, L is the output inductance, i L is the output current.

3. The novel distributed model predictive control method for multi-level converters according to claim 1, characterized in that: The step 2 specifically includes: Define the input vector u(k), output vector x(k) and reference vector w(k+1) respectively: The optimization problem at time k is expressed as: find the optimal input vector u(k) that makes the output vector x(k+1) of the controlled system as close as possible to the given reference value w(k+1); The optimization problem is solved by finding the minimum value of the cost function J(k): Where Q is a diagonal matrix composed of weight coefficients. By solving the necessary condition dJ(k) / du(k)=0, we can get the stationary point u corresponding to the minimum value of the cost function. M (k): u M (k)=B -1 [w(k+1)-Ax(k)] (6) Station u M (k) is the optimal solution. Due to physical limitations and safety criteria, the input and output vectors must be limited to a specific range and the constraints of the input and output vectors must be precisely defined. These constraints are uniformly expressed as: Among them, u min and u max are the minimum input vector and the maximum input vector respectively; Its matrix form is: Fu M (k)￡l(8) in Substituting constraint (9) into equation (5), we can obtain the optimization problem under constraint conditions: The optimization problem of the above form is called a quadratic programming (QP) problem, which consists of a quadratic performance indicator, a linear equation, and a linear inequality constraint.

4. The novel distributed model predictive control method for multi-level converters according to claim 1, characterized in that: The step three specifically includes: Formula (10) is the QP problem that needs to be solved by the FCMC CCS-MPC online optimization controller; In order to reduce the complexity of solving a single QP problem, equation (10) is decomposed into multiple sub-problems. That is, the single controller problem represented by equation (10) is decomposed into a group of problems and assigned to mutually cooperating sub-controllers. The number of controllers is equal to the matrix u M The number of rows, the i-th controller solves u i As the control input, y i As the output single-objective predictive control optimization problem, equation (10) is decomposed into a set of QP problems as follows: Compared with formula (10), we get: 1) In distributed control, the original cost function J(k) is replaced by multiple cost functions J associated with subproblems. i (k) replaced; 2) Because the established matrix B contains the correlation between the output of the sub-controller and all the input variables, these sub-optimization problems are coupled with each other; The Nash optimal solution is found through iteration. When the iteration ends, the output of each controller meets the set value, the performance index reaches the minimum, and all sub-controllers reach Nash equilibrium, then the entire system is in the Nash optimal state.

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