CN111697864A - Spherical decoding algorithm-based predictive control method for three-phase inverter - Google Patents

Abstract

The invention relates to an inverter model prediction control strategy based on a spherical decoding algorithm in the technical field of power electronics. The control strategy reconstructs the optimization problem of the controller model in a vector form on the basis of direct model prediction control and expresses the optimization problem as an integer quadratic programming. The integer search space is reduced due to the limited number of three-phase inverter voltage levels. On the basis of preliminary optimization, the number of solutions is further reduced by improving a sphere decoding algorithm based on a branch-and-bound technology, and finally, the optimization problem is solved to find an optimal switching sequence. The invention can effectively improve the steady-state performance of the inverter; the problem that the calculation complexity is exponentially increased due to multi-step length prediction can be solved; switching losses can be reduced; the working efficiency of the inverter is improved.

Description

Spherical decoding algorithm-based predictive control method for three-phase inverter

Technical Field

The invention relates to a power electronic system, in particular to a three-phase inverter model prediction control method based on a spherical decoding algorithm.

Background

Existing three-phase inverter controls include:

one, traditional control method

One of the most studied problems in inverter control methods is current control. In the past decades, two traditional control methods, namely hysteresis control and PWM-based linear control, have been extensively studied, and the results of the two control methods are summarized as follows:

1) the basic idea of hysteresis current control is as follows: the switching state of the power converter may be changed each time the current reaches a boundary condition to ensure that the current is inside the hysteresis band. The method is simple in concept, does not need a complex circuit structure or a processor when being implemented, but has very good performance and very fast dynamic response. But the disadvantage is that the switching frequency varies with the hysteresis width, load parameters and operating conditions. This is also one of the main drawbacks of hysteresis control, since varying switching frequencies can cause resonance problems. In addition, the switching loss also limits the application range of the hysteresis control method in the low-power field.

2) The most common selection scheme is usually the use of proportional-integral (PI) controllers, based on linear control of pulse width modulation or space vector modulation. By this method, a constant switching frequency can be obtained by a fixed carrier signal. The performance of such a control scheme depends on the design parameters of the controller and the reference current frequency. Although the PI controller may ensure that the steady state error of the continuous reference signal is 0, there is a significant error when applied to a sinusoidal reference signal. As the frequency of the reference current increases, the error increases and cannot even meet the requirements of some application fields.

II, direct model prediction control:

in the field of power electronics, the most straightforward and efficient predictive controller, while easy to apply, uses a single step prediction to adjust a plurality of variables to track their respective reference values. This predictive control concept is very simple and versatile. The method mainly comprises three parts, namely a cost function, a controller model and an enumeration-based solving algorithm. It has the disadvantage or disadvantage that the optimization problem tracking of direct Model Predictive Control (MPC) reference tracking is based on integer decision variables. This means that the number of possible solutions is multiplied when the prediction length is extended. On the one hand, integer decision variables help enumerate all the possible solutions for common methods. On the other hand, exhaustive enumeration quickly becomes difficult to compute as predicted step sizes are increased. Therefore, direct model prediction control is difficult to be directly applied to multi-step prediction.

Disclosure of Invention

The invention aims to provide a spherical decoding algorithm-based three-phase inverter prediction control method, which is used for solving the problems of large tracking error, complex parameters and resonance caused by switching frequency change of the traditional control method.

The technical solution of the invention is as follows:

a three-phase inverter prediction control method based on a sphere decoding algorithm is characterized by comprising the following steps:

step 1, reconstructing the optimization problem of the controller model in a vector form, and expressing the problem as an integer quadratic programming, wherein the formula is as follows:

J＝(U(k))^THU(k)+2(Θ(k))^TU(k)+θ(k) (12)

wherein, U (k) represents a switching sequence, H is a function formed by a system matrix, a penalty matrix and the like, and theta (k) are functions of a state vector of a time step k;

step 2, determining a switching sequence U (k): shifting the optimal switching sequence by a time step and repeating the switching position by considering the constraint condition (22c) to obtain the switching sequence U_ini(k) And further determining the initial value ρ (k) of the radius needed by the sphere decoding algorithm to be used in the time step k, wherein the formula is as follows:

wherein, I₃Representing a third order identity matrix, U_opt(k-1) represents a switching sequence of a previous cycle; the initial value given by the spherical radius ρ (k) is set to

And 3, starting from the first component of the switching candidate sequence set U, constructing a switching sequence U (k) component by considering the allowed single-phase switching positions in the set U. If the associated squared distance is less than the current p²(k) Value, then continue with the nextComponents, once the last component is reached, u (k) is full-dimensional, i.e., a candidate solution; if U (k) satisfies the handover constraint (22c) and the distance is less than the current optimum value, the existing optimal solution U is updated_opt(k) And a radius ρ (k); otherwise, the optimal solution and the radius keep the original values unchanged. In the process, the spherical radius is continuously reduced, the sphere is continuously tightened, the candidate sequences are made to be as small as possible, and finally the switching sequence which satisfies the formula (12), namely the optimal switching sequence, is found in the candidate sequences;

and 4, acting the signal representing the optimal switching sequence on three groups of bridge arms of the three-phase inverter to enable the bridge arms of the three-phase inverter to act according to the switch positions given by the optimal switching sequence to realize the inversion function.

The optimization problem of the controller model is reconstructed in a vector form and expressed as an integer quadratic programming on the basis of the controller model based on direct prediction control. The integer search space is reduced due to the limited number of three-phase inverter voltage levels.

On the basis of preliminary optimization, the control method further reduces the number of solutions by improving a sphere decoding algorithm based on a branch-and-bound technology, and finally solves the optimization problem to find the optimal switching sequence.

Compared with the prior art, the invention has the beneficial effects that: by carrying out multi-step prediction control on the three-phase inverter, the working efficiency and stability of the three-phase inverter are greatly improved, and the three-phase inverter is specially used in a power electronic system containing the three-phase inverter.

Drawings

FIG. 1 is a three-phase three-level voltage source type inverter for driving an induction motor

FIG. 2 is a control schematic

FIG. 3 is an algorithm flow chart

Fig. 4 is a flow chart of the predictive control method of the three-phase inverter based on the sphere decoding algorithm.

Detailed Description

The invention is further described with reference to the following drawings and specific examples, which are not intended to be limiting.

1. The controller target:

as shown in fig. 1, the three-level three-phase inverter for a cage-type asynchronous motor has a medium potential fixed to zero for simplicity. The voltage generated by each phase inverter is

0 and

corresponding to switch position u_a、u_bAnd u_c∈ { -1, 0, 1 }. Total DC bus Voltage v_dcAre shown and assumed to be constant. u ═ u_au_bu_c]^TRepresenting three-phase switch positions. The voltages applied to the motor in the orthogonal coordinate system are:

in the formula, v_s＝[v_sαv_sβ]^T，

The motor model adopts a static αβ reference coordinate system model, stator current i_sα、i_sβAnd rotor flux linkage psi_rα、ψ_rβAs state variables. The angular velocity of the rotor is considered as a (relatively slowly varying) variable.

The aim of the current controller is to regulate the stator current by manipulating the switch position to a time-varying reference value i_s ^*＝[i_sα ^*i_sβ ^*]^TBut may vary. While minimizing switching stresses. Switching is disabled between 1 and-1. The basic control principle to achieve this goal is shown in fig. 2.

2. A controller model:

the derivation of the prediction model can conveniently introduce the state vector:

x＝[i_sαi_sβψ_rαψ_rβ]^T(2)

stator current as system output vector, i.e.

y＝i_s＝[i_sαi_sβ]^T(3)

The three-phase switch position u forms an input vector and is provided by the controller;

using the state vector x to derive a continuous-time prediction model in state space form:

y(t)＝Cx(t) (5)

in the formula (I), the compound is shown in the specification,

the model parameters are respectively stator resistance R_sAnd rotor resistance R_rFurther, the stator, the rotor and the mutual inductive reactance are X, respectively_ls、X_lrAnd X_mAnd X_s＝X_ls+X_m，X_r＝X_lr+X_m，D＝X_sX_r-X_m ²From t ═ kT by integration (4)_sTo T ═ k +1) T_sFrom the observation that u (t) is constant over a time interval, so that when u (t) equals u (k), the resulting discrete representation:

x(k+1)＝Ax(k)+Bu(k) (6)

y(k)＝Cx(k) (7)

wherein k is equal to N

3. The cost function is:

the problem of finite length MPC control can be solved, typically by minimization of a cost function:

the first term of equation (9) is the tracking error for the prediction, i.e., the time-varying output reference y^*The penalty for the difference between the tracking error and the output vector y is the future time step k +1, k +2, k + N_p. The second term is the suppression of the switching variation, parameter λ_μ> 0 is an adjustable parameter for adjusting the trade-off between tracking accuracy (which refers to the deviation of the output) and switching.

4. Problem of optimization

Defining:

U(k)＝[u^T(k)u^T(k+1)…u^T(k+N_p-1)](10)

which represents the sequence of inverter switch positions that the controller must determine.

The optimization problem of direct MPC based on reference tracking can be described as:

U_opt(k)＝arg minimize J (11a)

subject to x (l +1) ═ ax (l) + Bu (l) (11b)

y(l+1)＝Cx(l+1) (11c)

Δu(l)＝u(l)-u(l-1) (11d)

U(k)∈U (11e)

The cost function J depends on the state vector x (k), the previously selected switch position U (k-1) and the switch sequence U (k) in equation (11e) U-U × … × U is N_pThe cartesian product of the multiple u sets, u representing the set of discrete three-phase switch positions.

Following the principle of the rolling temporal control, there is only the first element that is optimal.Switching sequence U_opt(k) Is applied to the semiconductor switch at time k. At time k +1, new information for x (k +1) and the output reference value are considered and optimized again to provide the optimal switch position for time k + 1. This optimization process is repeated on-line and continuously cycled.

1) Integer quadratic programming

The optimization problem (11) is reconstructed in vector form and represented as an integer quadratic program. The integer search space is reduced due to the limited number of inverter voltage levels.

Vector description of optimization problem:

the dynamic evolution (11b) and (11c) of the prediction model can be factored into the cost function (9). After lengthy algebraic operations, the cost function can be written in a compact form as equation (12).

J＝(U(k))^THU(k)+2(Θ(k))^TU(k)+θ(k) (12)

In the formula (I), the compound is shown in the specification,

the matrix Y,

S and E are defined as follows:

wherein, I₃Representing a third order identity matrix, Y^*(k) A diagonal penalty matrix representing the output reference trajectory and tracking error is defined as

The cost function (12) is composed of three terms. The first term is quadratic in the switching sequence u (k). The Hessian matrix H is the system matrix A, B and C, and the penalty matrix

Penalty lambda on switch jump transition_uAnd a function of the matrix S. Assuming that the system parameters are time-invariant, the Hessian is also time-invariant. Since Q is required to be a positive half-stator, STS in equation (13a) is a positive definite integral, and

is a positive fixed half stator, so Hessian is a symmetric positive fixed integral. For lambda_μEqual to 0, Hessian will be the positive half parameter.

In the switching sequence u (k), the second term in equation (12) is linear. The time-varying vector theta (k) is a function of the state vector of the time step k, and a reference track Y is output^*(k) And the previously selected switch position u (k-1). The third term in equation (12) is time-varying. The scalar has the same parameters, such as Θ (k).

By way of formulation, equation (12) can be rewritten as:

J＝(U(k)+H^-1Θ(k))^TH(U(k)+H^-1Θ(k))+const(k) (14)

the constant term in equation (14) is independent of U (, k,) and therefore does not affect the optimal solution. This allows us to omit the constant term in the cost function and describe the re-optimization problem as:

U_opt＝arg minimize(U(k)+H^-1Θ(K))^TH(U(k)+H^-1Θ(K)) (15a)

subject to U (k) e U (15b)

Unconstrained minimization solution

Unconstrained optimization (15) is by minimizing, ignoring constraints (15b) and (15 c). Since H is positive, it can be directly seen from equation (15a) that the unconstrained solution at time step k is unique

U_unc(k)＝-H^-1Θ(K) (16)

First element U as unconstrained switching sequence_unc(k) The constraints (15b) (15c) are not satisfied and it cannot directly act as a gate signal for the semiconductor switch. However, U_unc(k) Can be used to solve the constraint optimization problem (15), including constraints (15b) and (15c), as shown below. By taking (16), the cost function (15a) available is:

J＝(U(k)-U_unc(k))^TH(U(k)-U_unc(k)) (17)

when lambda is_μ> 0, since H (by definition) is symmetrically positive, there is a unique invertible lower triangular matrix

Satisfy the requirement of

V^TV＝H (18)

The matrix V is the generated matrix. Notice its inverse V^-1Is also a lower triangle and consists of^-1The oholsky decomposition of (a) was calculated:

V^-1V^-T＝H^-1(19)

the algebraic function in equation (17) can be written as:

the optimization problem (15) of direct MPC with output reference tracking can now be described as integer quadratic programming. Optimal switching sequence, U_opt(k) Is determined by a minimized cost function (21); constraints are obtained with equations (15b) and (15c), i.e.

Subject to U (k) e U (22b)

2) Solving an optimization problem by a spherical decoding algorithm:

the basic idea of the algorithm is to iteratively consider candidate sequences, namely U (k) ∈ U, belonging to a spherical radius ρ (k) > 0, focusing on

Satisfy the switch constraint (22c)

One key feature for sphere decoding, since V is triangular, it is very simple to identify candidate sequences that satisfy equation (23). Since V is the lower triangle, equation (23) can be rewritten as:

means that

The ith element of (1), u_i(k) Is the i element of u (k), v_(i，j)Refers to the i, j term of V. Thus, the solution set of equation (23) can be found in the following manner. Proceeding in a sequential manner like gaussian elimination, in the sense that only one-dimensional problem needs to be solved per step.

To determine u (k), the algorithm requires that the initial value of the radius used in time step k be set to p (k). On the one hand, the radius ρ (k) should be as small as possible, so that we can eliminate as many candidate handover sequences as possible. On the other hand, ρ (k) cannot be too small to ensure that the solution set is not empty. The initial radius should be chosen as a basis.

Guessed switching sequence U_ini(k) Obtained by shifting the previous optimal switching sequence by one time step and repeating the last switching position. This is consistent with the back-off paradigm used in MPC. Since the optimal switching sequence of the previous time step satisfies both constraints (22b) and (22c), the shifted sequence also automatically satisfies these constraints. This statement is true in all cases, including transients. Thus, U_ini(k) Is a viable candidate solution (22) to the optimization problem. Given equation (25), the initial value given by ρ (k) is set to

At each time step k, the controller first uses the current state x (k), the reference value Y^*(k) Previous switch position U (k-1) and previous U_opt(k-1) calculation of U_ini(k) Rho (k) and

see formulas (25) and (26).

The flow chart of the algorithm is shown in fig. 3. As can be seen from the flow chartThe proposed sphere decoder works in a recursive manner. Starting from the first component, the switching sequence U (k) is constructed component by taking into account the allowed single-term switching positions in the set U. If the associated squared distance is less than the current p²(k) Value, then continue with the next component. Upon reaching the last component

Meaning that U (k) is full-dimensional, then U (k) is a candidate solution. If U (k) satisfies the handover constraint (22c) and the distance is less than the current optimum value, the existing optimal solution U is updated_opt(k) And a radius ρ (k).

The invention has the following technical effects:

the method solves the problems of complex parameter adjustment and large resonance and switching loss of the traditional control method, and solves the problem of exponential increase of calculation complexity caused by multi-step prediction of a direct model prediction control method.

According to the invention, through the research on the discrete characteristics of the three-phase inverter, the fact that the three-phase inverter only generates a limited number of switching states is considered, and finally, a system model is used for predicting the variable change characteristic corresponding to each switching state. And by defining a cost function, the most appropriate switching state is selected, so that the tracking error is reduced, and the resonance problem is solved.

(3) The direct model prediction control cannot solve the problem that the number of solutions is multiplied due to multi-step prediction, and further the calculation is difficult. According to the method, the optimization problem is described again in a vector form through integer quadratic programming, the candidate sequence is screened by using an improved spherical decoding algorithm, the operand is reduced to a great extent, the optimization problem is solved, and the candidate sequence is obtained.

6. Advantageous effects

1) High steady state performance

When evaluating the steady state performance of an inverter, there are two key indicators: total current demand distortion (TDD) and switching value. It is generally believed that optimizing the pulse mode (OPP) at a given switching frequency produces the lowest current TDD. In a three-level inverter induction motor driving system, under the same switching frequency, compared with single-step prediction, the direct MPC with the prediction step size of 10 steps can reduce the current TDD by 20 percent and is very close to the OPP. And therefore possess high steady state performance.

2) Computational complexity reduction

For three-level inverters, the computational complexity grows in the worst case, i.e. exponentially in large technology. However, since the sphere decoding algorithm limits the search range of the optimal switching sequence to the sphere centered on the non-limiting solution, the average calculation amount of the control strategy provided by the invention is independent of the inverter level number, so that the calculation complexity is reduced.

3) Reducing switching losses

By applying a weight factor lambda in the cost function_uThe phase with larger instantaneous phase current corresponds to a larger weight coefficient, and the phase with smaller instantaneous current corresponds to a smaller weight coefficient, so that the switch is switched from the phase with larger current to the phase with smaller current, and the average switching loss is reduced.

The invention adopts a sphere decoding algorithm based on branch-and-bound technology, and depends on the concepts of branches and boundaries. Completing a branch by a set of single-phase switch positions; the boundary is determined by considering only the solution within a sphere of a certain radius. In the optimization process, whenever a better existing solution is found, the radius is reduced, and the sphere is also reduced and tightened, so that the candidate sequence set is as small as possible but not empty.

The method adopts a model prediction control strategy, reconstructs an optimization problem in a vector form, and expresses the optimization problem as an integer quadratic programming, and the integer search space is reduced because the number of voltage levels of an inverter is limited. To solve the computational difficulties caused by multi-step prediction.

The invention realizes the multi-step prediction control strategy of the inverter, and compared with single-step prediction, the direct MPC with the prediction step length of 10 steps can reduce 20% current TDD and is very close to OPP in a three-level inverter induction motor driving system under the same switching frequency, thereby greatly improving the steady state performance of the inverter and improving the working efficiency of the inverter; the calculation complexity is reduced through the algorithm, and due to the superior performance of the model predictive control algorithm, the switching loss is greatly reduced, and the working efficiency of the inverter is improved.

While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention.

Claims (1)

1. A three-phase inverter prediction control method based on a sphere decoding algorithm is characterized by comprising the following steps:

step 1, reconstructing the optimization problem of the controller model in a vector form, and expressing the problem as an integer quadratic programming, wherein the formula is as follows:

J＝(U(k))^THU(k)+2(Θ(k))^TU(k)+θ(k) (12)

wherein, U (k) represents a switching sequence, H is a function formed by a system matrix, a penalty matrix and the like, and theta (k) are functions of a state vector of a time step k;

step 2, determining a switching sequence U (k): shifting the optimal switching sequence by a time step and repeating the switching position by considering the constraint condition (22c) to obtain the switching sequence U_ini(k) And further determining the initial value ρ (k) of the radius needed by the sphere decoding algorithm to be used in the time step k, wherein the formula is as follows:

wherein, I₃Representing a third order identity matrix, U_opt(k-1) represents a switching sequence of a previous cycle; the initial value given by the spherical radius ρ (k) is set to

Step 3, from the switch candidate sequence setThe first component of U starts with constructing the switching sequence U (k) component by taking into account the allowed single-phase switching positions in the set U. If the associated squared distance is less than the current p²(k) Value, then continue with the next component, once the last component is reached, then u (k) is full-dimensional, i.e., a candidate solution; if U (k) satisfies the handover constraint (22c) and the distance is less than the current optimum value, the existing optimal solution U is updated_opt(k) And a radius ρ (k); otherwise, the optimal solution and the radius keep the original values unchanged. In the process, the spherical radius is continuously reduced, the sphere is continuously tightened, the candidate sequences are made to be as small as possible, and finally the switching sequence which satisfies the formula (12), namely the optimal switching sequence, is found in the candidate sequences;

and 4, acting the signal representing the optimal switching sequence on three groups of bridge arms of the three-phase inverter to enable the bridge arms of the three-phase inverter to act according to the switch positions given by the optimal switching sequence to realize the inversion function.

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