Multi-model LQR control method for grid-connected inverter under weak power grid

Abstract

The invention relates to a multi-model LQR control method for a grid-connected inverter under a weak power grid, and belongs to the technical field of power electronics. A traditional control method is difficult to effectively deal with the problems of broadband harmonic oscillation and stability caused by wide-range change of power grid impedance under a weak power grid. Firstly, a plurality of LQR controllers for different power grid impedance working conditions are designed, and the LQR controllers are stored in a model library. Secondly, according to the impedance change of the power grid, the weight coefficient of each sub-model is calculated, a sub-controller is selected in a weighting mode, and a global control signal is generated; and finally, enabling the global control signal to act on a grid-connected inverter, and achieving the control of the grid-connected current. According to the invention, the appropriate controller can be automatically selected according to the change of the impedance of the power grid, the harmonic oscillation is effectively suppressed, the stability and robustness of the system are improved, and the method is suitable for the grid-connected inverter application scenarios under various weak power grids.

Description

Technical Field

[0001] The invention belongs to the technical field of power electronics and relates to a multi-model LQR control method of a grid-connected inverter under a weak power grid. Background Art

[0002] The rapid development of new energy has led to a large number of grid-connected inverters being connected to the grid, resulting in a weakening of the grid strength. Under weak grid conditions, the grid impedance (short-circuit ratio) varies over a wide range, and the inverter's phase-locked loop, digital control delay, etc. interact with the grid impedance, which will cause stability and harmonic oscillation problems in the system. At the same time, harmonic oscillation has a wide-band characteristic. Therefore, it is necessary to propose a wide-band harmonic oscillation suppression strategy with adaptive capabilities under weak grid conditions.

[0003] In order to effectively suppress the broadband harmonic oscillation of the grid-connected inverter under weak power grid and improve the stability of the system, many harmonic oscillation suppression methods have been proposed in the literature. From the perspective of impedance reshaping, they can be mainly divided into two categories: inverter side impedance reshaping method and grid side impedance reshaping method. The output impedance of the grid-connected inverter can be reshaped by changing the control structure of the inverter or optimizing the control parameters of the inverter. Changing the control structure of the inverter mainly includes changing the controller type, building virtual impedance, and adding active damping. In the inverter control, a grid-connected point voltage feedforward link is added, and an additional grid-connected current feedback path is introduced. Equivalently, a virtual impedance is connected in series and in parallel in the inverter output impedance model, which increases the amplitude and phase angle of the inverter output impedance and improves the stability of the system. Some literatures propose an improved phase compensation resonant controller, which improves the stability of the grid-connected inverter under weak power grid by optimizing the phase compensation angle. Optimizing the control parameters of the inverter can also improve the output impedance of the inverter, but the adjustable range of the control parameters is usually narrow and the robustness of the system is weak. There are also documents that improve the stability of the system by reducing the controller gain of the phase-locked loop and lowering the phase-locked loop bandwidth. However, too small a phase-locked loop bandwidth will reduce the dynamic performance of the system and slow down the tracking speed of the grid-connected current.

[0004] Connecting an active damper (also called an impedance adapter) in parallel on the grid side can reshape the impedance characteristics of the grid and improve the stability of the system. The active damper detects the harmonic oscillation frequency in the grid-connected voltage in real time and controls the converter to be equivalent to a virtual resistor at this frequency, thereby achieving effective damping of the system resonance and improving the stability of the system. One of the difficulties in the design of an active damper is the value of the virtual resistor. Although a virtual resistor value as small as possible can ensure the damping effect, the active damper will absorb larger harmonic currents from the grid and increase power loss. In addition, since this type of method requires the addition of additional hardware equipment, it will increase the cost of the system.

[0005] The harmonic oscillation suppression methods proposed in the literature are mainly designed for specific frequency bands and specific links of the system. It is difficult to achieve a good suppression effect on wide-band harmonic oscillations. Therefore, it is urgent to study adaptive and wide-band harmonic oscillation suppression strategies. Multi-model adaptive control is a control algorithm with strong adaptive ability, which is used to solve complex system problems such as nonlinearity, variable working conditions, strong disturbances, and parameter uncertainty. It mainly includes three links: model library (determined by the parameters and structural uncertainty of the controlled object model), controller library (designed according to different models in the model library), and model matching supervision mechanism (used for system model selection). The main idea of ​​multi-model adaptive control is to use multiple models to approximate the dynamic characteristics of the entire controlled object, and design corresponding controllers for each sub-model respectively, and then reasonably select the controller by switching or weighting, and map a limited number of simple sub-controllers into the final control to act on the controlled object. This method can automatically identify the system characteristics after disturbance without the need for prior knowledge of the system, and automatically adjust the controller to achieve the desired control performance. In order to solve the subsynchronous resonance problem caused by the connection of wind power systems to series compensation lines, some literature has proposed an adaptive auxiliary controller based on a multi-model control method. The proposed auxiliary controller can effectively suppress subsynchronous oscillations under a wide range of operating conditions.

[0006] In order to improve the stability of grid-connected inverters under weak power grids, this paper proposes a weighted multi-model LQR adaptive control strategy based on LQR control. First, a discrete LQR controller based on full-state feedback is designed, and the current tracking accuracy and stability of the inverter are comprehensively considered to optimize the state weighting matrix Q; then, considering that the single LQR controller has a limited adaptability to grid impedance changes, the weighted multi-model adaptive control idea is introduced, the corresponding model library and controller library are constructed, and a weighted algorithm is designed to ensure that the weight coefficient can converge quickly when the grid impedance changes over a wide range, thereby ensuring the global stability of the system. Finally, the effectiveness of the control strategy proposed in this paper is verified through MATLAB / Simulink time domain simulation. Summary of the invention

[0007] In view of this, an object of the present invention is to provide a multi-model LQR control method for a grid-connected inverter under a weak power grid.

[0008] In order to achieve the above object, the present invention provides the following technical solutions:

[0009] A multi-model LQR control method for a grid-connected inverter under a weak power grid comprises the following steps:

[0010] Step 1: Establish a discrete state space model of the grid-connected inverter, including state variables such as inverter-side inductance, filter capacitor, grid-side inductance, grid-connected point voltage, grid voltage, inverter output voltage, capacitor voltage, inverter output current, capacitor current and grid-connected current;

[0011] Step 2: For the working condition where the grid impedance is 0mH, a discrete linear quadratic regulator LQR controller based on full state feedback is designed, and the state weighting matrix Q is optimized to make the inverter have a fast and well-damped transient current response and be able to track grid voltage changes;

[0012] Step 3: For the working condition of grid impedance of 6mH, a discrete LQR controller based on full state feedback is designed, and the state weighting matrix Q is optimized to make the inverter have a fast and well-damped transient current response and be able to track grid voltage changes;

[0013] Step 4: Build a model library, including the two sub-models designed in steps 2 and 3 and their corresponding LQR controllers;

[0014] Step 5: According to the change of grid impedance, the weight coefficient of each sub-model is calculated, and the sub-controller is selected in a weighted manner to generate a global control signal;

[0015] Step 6: Apply the global control signal to the grid-connected inverter to control the grid-connected current.

[0016] Furthermore, in step 2 and step 3, the values ​​of the state weight matrix Q are respectively Q=diag(0.07, 0, 0.07, 0, 10 4 , 10 9 ) and Q = diag(0.04, 0, 0.04, 0, 10 4 , 10 9 ).

[0017] Furthermore, in step 5, the weight coefficient is calculated as follows:

[0018]

[0019] In the formula, e i (t) is the error between the ith sub-model and the actual object; α and β are the weights of the current transient error and the error within the memory length, respectively; γ is the forgetting factor, which determines the memory length of the historical information and ensures that J i Convergence of (t), α≥0, β>0, γ>0.

[0020] Further, in step 5, the calculation method of the global control signal is:

[0021]

[0022] A control system for a grid-connected inverter under a weak power grid, comprising:

[0023] Grid-connected inverter;

[0024] Model library, used to store sub-models for different grid impedance conditions and their corresponding LQR controllers;

[0025] A weight coefficient calculation unit, used for calculating the weight coefficient of each sub-model according to the change of the grid impedance;

[0026] A controller selection unit, used for selecting a sub-controller according to a weight coefficient and generating a global control signal;

[0027] The control signal output unit is used to apply the global control signal to the grid-connected inverter.

[0028] Furthermore, the model library includes two sub-models for grid impedances of 0 mH and 6 mH and their corresponding LQR controllers.

[0029] Furthermore, the weight coefficient calculation unit calculates the weight coefficient using the following method:

[0030]

[0031] In the formula, e i (t) is the error between the ith sub-model and the actual object; α and β are the weights of the current transient error and the error within the memory length, respectively; γ is the forgetting factor, which determines the memory length of the historical information and ensures that J i Convergence of (t), α≥0, β>0, γ>0.

[0032] Further, the controller selection unit selects a sub-controller and generates a global control signal using the following method:

[0033]

[0034] A grid-connected inverter under a weak power grid is controlled by adopting the method described.

[0035] The beneficial effects of the present invention are:

[0036] (1) Through multi-model adaptive control, the appropriate controller can be automatically selected according to the change of grid impedance, effectively suppressing wide-band harmonic oscillation, avoiding system instability, and improving system stability.

[0037] (2) Multi-model adaptive control can adapt to a wide range of changes in grid impedance and improve the system's robustness to grid disturbances.

[0038] (3) By optimizing the design of the LQR controller, high-precision current tracking can be achieved and the quality of the grid-connected current can be improved.

[0039] (4) Multi-model adaptive control can reduce the system's sensitivity to grid impedance, allowing the system to maintain good performance under different grid environments.

[0040] (5) The present invention can effectively improve the reliability of the grid-connected inverter, reduce the probability of system failure, and extend the service life of the system.

[0041] (6) The present invention does not require additional hardware equipment, which can reduce the cost of the system.

[0042] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0044] Figure 1 This is the system structure diagram of the single-phase LCL grid-connected inverter;

[0045] Figure 2 It is the root locus variation diagram of the closed-loop system under different weight values; Figure 5 (a) When q1 = 0.01, q5 = 1, q6∈(10 7 ,10 9 ), the root locus changes with q6; Figure 5 (b) When q1 = 0.01, q6 = 1, q5∈(500,100000), the closed-loop root locus changes with the change of q5; Figure 5 (c) shows the situation when q5=1, q6=1, q1, q3∈(0.001,0.2), the root locus changes with the changes of q1 and q3;

[0046] Figure 3 It is the closed-loop pole change diagram when the grid impedance changes under the feedback matrix K0 condition;

[0047] Figure 4 The structure of the weighted multi-model adaptive control system;

[0048] Figure 5 It is the closed-loop pole change diagram when the grid impedance changes under the feedback matrix K6 condition;

[0049] Figure 6 This is the grid-connected simulation result when the grid impedance is 0mH; Figure 6 (a) is the current waveform of the grid-connected voltage; Figure 6 (b) is the FFT analysis of grid-connected current;

[0050] Figure 7 It is the grid-connected simulation waveform when the grid impedance jumps under the state feedback matrix K0;

[0051] Figure 8 This is the grid-connected simulation result when the grid impedance is 6mH; Figure 8 (a) is the current waveform of the grid-connected voltage; Figure 8 (b) is the FFT analysis of grid-connected current;

[0052] Fig. 9 It is the grid-connected simulation waveform when the grid impedance jumps under the state feedback matrix K6; Fig. 9 (a) is the grid-connected voltage and current waveform when the grid impedance jumps from 4mH to 3.8mH at 0.5s when the state feedback matrix K6 is used; Fig. 9 (b) is the grid-connected voltage and current waveform when the grid impedance jumps from 15mH to 16mH at 0.5s when the state feedback matrix K6 is used;

[0053] Fig.10 The grid-connected simulation waveform using multi-model adaptive control when the grid impedance jumps from 6mH to 13mH;

[0054] Fig.11 It is the weight change diagram under multi-model control;

[0055] Fig.12 This is the simulation waveform of multi-model adaptive control when the grid impedance jumps from 1mH to 3mH;

[0056] Fig.13 It is the weight change diagram under multi-model control;

[0057] Fig.14 The simulation waveform of multi-model adaptive control when the grid impedance jumps from 2mH to 12mH;

[0058] Fig.15 It is the weight change diagram under multi-model control;

[0059] Fig.16 This is the simulation waveform of multi-model adaptive control when the grid impedance jumps from 13mH to 1mH;

[0060] Fig.17 It is the weight change diagram under multi-model control;

[0061] Fig.18The simulation waveform of multi-model adaptive control is shown when the grid impedance jumps from 1mH to 2mH and the load jumps from half load to full load.

[0062] Fig.19 It is the weight change diagram of each sub-model under multi-model control;

[0063] Fig. 20 The simulation waveform of multi-model adaptive control is shown when the grid impedance jumps from 1mH to 2mH and the load jumps from half load to full load.

[0064] Fig.21 This is a graph of weight changes under multi-model control. DETAILED DESCRIPTION

[0065] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0066] Among them, the drawings are only used for illustrative explanations, and they only represent schematic diagrams rather than actual pictures, and should not be understood as limitations on the present invention. In order to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0067] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if the terms "upper", "lower", "left", "right", "front", "rear", etc. indicate the orientation or position relationship, they are based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, the terms describing the position relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0068] 1. P.S.

[0069] The LCL type grid-connected inverter using digital control under weak power grid faces challenges, and needs to achieve high-quality grid-connected current, suppress harmonic oscillations, and ensure stable grid connection when the grid impedance fluctuates. The present invention proposes a linear quadratic regulator (LQR) for inverters under weak power grid conditions. By discretizing the continuous state space equation of the system and considering the sampling period delay to establish a discrete model, the design process of selecting the state weighting matrix Q is elaborated in detail to reasonably configure the closed-loop system poles to achieve the desired performance. However, the single LQR controller has a limited range of adaptability to grid impedance changes. In view of this, the present invention adopts a weighted multi-model adaptive control strategy, and designs multiple LQR controllers at different working points so that each of them covers a certain grid impedance range, thereby greatly broadening the adaptability range of the inverter to the grid impedance. Compared with the traditional single model control, this method can flexibly call the adaptive controller according to the actual situation of the grid, ensuring good stable control and dynamic performance under any grid impedance. Finally, through MATLAB / Simulink time domain simulation, the results show that the proposed multi-model adaptive control method is effective under weak power grids, providing an effective solution for the control of grid-connected inverters under weak power grids.

[0070] 2. Modeling of grid-connected inverters under weak power grid

[0071] The system structure of the single-phase LCL grid-connected inverter is as follows: Figure 1 As shown, the LCL filter consists of the inverter side inductor L1, filter capacitor C and grid side inductor L2, U dc is the DC bus voltage, u r ,u c ,u pcc and u g are the inverter output voltage, capacitor voltage, grid connection point voltage and grid voltage, i1, i c and i2 are the inverter output current, capacitor current and grid current. g is the grid impedance (the present invention considers the worst case and regards it as a pure inductive impedance, i.e., Z g =sL g ). The phase-locked loop outputs the synchronous signal sinθ of the grid voltage, G c is the current controller, k d is the active damping coefficient of the capacitor current.

[0072] Generally, the bandwidth of the phase-locked loop is much lower than the bandwidth of the current inner loop. In the present invention, the bandwidth of the phase-locked loop is designed to be relatively low, so the influence of the phase-locked loop on the system stability can be ignored.

[0073] 3. Design of discrete LQR controller for grid-connected inverter

[0074] 3.1 Inverter discrete state space model

[0075] The state space model of the LCL filter after discretization is:

[0076]

[0077] The state vector is x p =[i1 u c i2], the output is y p =[i2],A p ′,B p ′,B p ' g The expression is as follows:

[0078]

[0079]

[0080] Where T s is the sampling period, ω r is the resonant frequency of the LCL filter, which is expressed as

[0081]

[0082] When modeling the grid-connected inverter, a delay of one sampling period is considered. The control signal u is delayed to form the modulation signal u M Therefore, u and u M The relationship between

[0083] u M (k+1)=u(k) (6)

[0084] The current controller is selected as a resonant controller, and its continuous transfer function G c2 (s) can be expressed as:

[0085]

[0086] Where ω1 is the fundamental frequency of the power grid, e is the error signal, and e=i ref -i2,y c Represents the output of the current controller. In order to rewrite the current controller into state space form, x c1 and x c2 The two variables are defined as:

[0087]

[0088] Similarly, the discrete state space model of the current controller is

[0089]

[0090] The coefficient matrix in formula (18) can be derived as

[0091]

[0092]

[0093] According to the above model, by expanding the state space equations of equations (9), (13) and (19), we can get the following state space model:

[0094]

[0095] The state vector is the vector x=[x p u M x c ] T , and the coefficient matrix expression in formula (22) is as follows:

[0096]

[0097] 3.2 LQR controller design

[0098] Assume a discrete linear time-invariant system whose state space equation is

[0099] x(k+1)=Ax(k)+Bu(k) (15)

[0100] Where A and B are constant matrices with constant elements

[0101] The corresponding performance indicator function is:

[0102]

[0103] Where Q is a semi-positive definite real symmetric matrix; R is a positive definite real symmetric matrix. Q and R are weight matrices of x(k) and u(k) respectively.

[0104] In the inverter system control, the linear quadratic optimal control objective can be equivalent to the minimum error (best control tracking performance) and the minimum transient power consumption. Therefore, the key to the optimization control problem is to use the minimization principle and the optimal control law: u = -Kx. Obtain the minimum value of the performance index function J within a certain range, where K is the optimal feedback gain matrix, and the matrix K can be expressed as

[0105] K=(R+B T PB)B T PA (17)

[0106] Where P is the Riccati matrix, which can be obtained from the Riccati differential equation

[0107] PA+A T P-PBR-1 B T P+Q=0 (18)

[0108] For the grid-connected inverter using digital control in weak power grid, the next step is to design the weight matrices Q and R.

[0109] Assume Q = diag[q1, q2, q3, q4, q5, q6], where q i The weight value of the i-th state is determined. q6 is the weight of the current tracking error. q5 is the weight of the tracking error derivative. q4 reflects the influence of calculation delay in digital control. q1, q2, and q3 are the state weight values ​​of the three states of the controlled object. The following will give q according to the empirical rule. i Some practical value design guidelines.

[0110] (1) The design of the weight value q1 should focus on the inverter measured current i1 to ensure a fast and well-damped transient current response.

[0111] (2) Since the capacitor impedance of the LCL filter is high, the fundamental current shunted by the capacitor is small, resulting in similar characteristics of i1 and i2. Therefore, they should have similar associated weights, that is, q1 = q3.

[0112] (3) To avoid inverter saturation, the capacitor voltage should be allowed to follow u c The power grid changes, so the state weight needs to be set to low weight or zero weight, that is, q2=0.

[0113] (4) The weight q4 is related to the computational delay under digital control, and the state quantity u M The corresponding weight q4 should initially be close to or equal to 0, that is, q4=0.

[0114] (5) Weights q5 and q6 directly affect the current tracking error and its inverse. In order to minimize the low-frequency and high-frequency components of the current tracking error, higher weights should be assigned to q5 and q6.

[0115] At the same time, the R matrix is ​​used as a control weighting matrix. In the design, in order to match the initial setting of q4 and simplify the design process, R = [1].

[0116] According to the above guidelines, only three weights need to be selected in the weight matrix Q, namely, q1 or q3, q5 and q6. The present invention adopts the root locus method to determine these three weight values. By changing the weight values ​​and observing the change trajectory of the poles of the closed-loop system, the appropriate weight value range is determined to meet the requirements of stable and high-performance operation of the inverter.

[0117] Figure 2 Given that L g= 0. One of the weight values ​​changes, and the other two weight values ​​are fixed at smaller values ​​to observe the changes in the closed-loop root locus. The black arrow in the figure represents the direction of increase of the q value.

[0118] Figure 2 (a) shows the results when q1 = 0.01, q5 = 1, q6∈(10 7 ,10 9 ), the root locus changes with q6. From the figure, it can be seen that only one pair of conjugate poles will change significantly with the change of q6. The damping ratio associated with these poles remains basically unchanged, while the corresponding frequency increases with the increase of q6. Therefore, in order to obtain a faster system dynamic response, a larger q6 should be selected as much as possible.

[0119] Figure 2 (b) shows how the closed-loop root locus changes with the change of q5 when q1=0.01,q6=1,q5∈(500,100000). Similarly, the change of q5 only changes a pair of poles. And as q5 increases, the damping ratio first increases to 1, and then one of the poles will gradually move out of the unit circle. Therefore, it is necessary to choose a suitable q5, which should not be too large, so as not to reduce the stability of the system.

[0120] Figure 2 (c) shows that when q5=1, q6=1, q1, q3∈(0.001, 0.2), the root locus changes with q1 and q3. It can be seen from the figure that when q1 and q3 change, the three poles corresponding to the LCL filter will also change accordingly. And the damping ratio of the dominant pole increases with the increase of q1 and q3, but when q1 and q3 increase to a certain extent, the damping ratio changes slowly and the corresponding frequency is also low.

[0121] 3.3 Stability analysis of grid-connected inverter based on LQR control

[0122] According to the above analysis, the weight matrix Q = diag (0.07, 0, 0.07, 0, 10 4 , 10 9 ), from which we can get the feedback gain matrix K0 = [0.10665, -0.000282, 0.1196, 1.402, -764.89, -4080] corresponding to the grid impedance of 0mH under strong power grid.

[0123] When the inverter adopts LQR control, Figure 3The closed-loop root locus diagram and local enlarged diagram of the system under the condition of grid impedance change are given. At this time, the grid impedance gradually increases from 0mH to 7mH. As the grid impedance increases, the closed-loop pole gradually moves out of the unit circle, indicating that the inverter system is unstable. It is thus obtained that the adaptation range of the feedback gain matrix K0 to the short-circuit ratio is 0-5.2mH. Compared with the traditional control method, the grid-connected inverter based on LQR control under weak power grid proposed in the present invention has been expanded to adapt to the grid impedance, and the stability under weak power grid is enhanced, but when the grid impedance increases further, the system will still be unstable.

[0124] 4 LQR-based weighted multi-model adaptive control

[0125] In a weak grid environment, changes in grid impedance will significantly affect the performance of the grid-connected inverter. Although a LQR controller with certain robustness has been designed in the previous article, its adaptability to grid impedance changes is still limited. When the grid impedance exceeds the adaptation range, the system stability will be difficult to guarantee. To this end, this section will propose a weighted multi-model adaptive control strategy based on LQR to further enhance the stability of the system under weak grid conditions.

[0126] 4.1 Multi-model adaptive control theory

[0127] The structure of weighted multi-model adaptive control is as follows: Figure 4 The basic principle is as follows: First, by constructing a model M covering n typical working conditions i (where i = 1, 2, ..., n) model library, so as to achieve comprehensive coverage of the dynamic characteristics of the entire operating range of the entire controlled object. Then, for each sub-model M i , complete the corresponding controller C in the offline state i (same i = 1, 2, ..., n) design. Then, according to a certain performance index J corresponding to the error between each sub-model output and the actual output i (i=1,2,…,n), and evaluate the matching degree between each sub-model and the controlled object.

[0128] According to the formation mechanism of the control signal, it can be divided into: switching multi-model control and weighted multi-model control. The switching strategy refers to selecting a local controller that is closest to the current working point of the system from multiple controllers as the controller of the controlled object at that moment. The weighted combination strategy gives a certain weight to the corresponding local controller according to the degree of matching between the controlled object and each local model. The global controller is composed of each local controller through probability weighting. Due to the sudden changes in the switching control signal, the system response often has jitters, which affects the transient response of the system. Therefore, weighted multi-model control has gradually become popular.

[0129] 4.2 Weighted Multi-Model Adaptive Control Design

[0130] (1) Model Collection

[0131] First, as described in Section 3 above, the grid-connected inverter with a grid impedance of 0mH is modeled to obtain a corresponding sub-model M1, and the corresponding discrete LQR controller is designed as the controller C1 of the sub-model. Since the maximum adaptability of controller C1 to the grid impedance is 5.2mH, based on this, and considering that the LQR controller itself has a certain robustness, this section takes the grid-connected inverter with a grid impedance of 6mH as the sub-model M2, and constructs the model set Ω={M i |i=1,2}.

[0132] When constructing a model set for a system, in order to ensure the completeness of the model set, it is usually hoped that the model set has as many models as possible. However, due to the limitation of computing power, the number of models in the actual model set is limited. In addition, since the LQR controller itself has a certain robustness, it is unnecessary to increase the number of models in the model set too much. Therefore, the number of models in the model set constructed in this section is 2.

[0133] (2) Control Set

[0134] Multi-model control is only a strategy framework. For the sub-controllers, other control methods need to be used to complete the controller design. In fact, the local sub-controllers in multi-model adaptive control can adopt any feasible control strategy with certain robustness. The present invention selects LQR controller as the sub-controller of multi-model adaptive control.

[0135] For sub-model M2, refer to the design process in Section 3 of the present invention and select the weight matrix Q=diag(0.04, 0, 0.04, 0, 10 4 , 10 9 ), we can get the feedback gain matrix K6 = [-0.1014, -0.000251, 0.3013, 1.3282, -1257.5877, -6186.0965] corresponding to the grid impedance of 6mH, that is, we get the controller C2 corresponding to the sub-model M2. When the grid-connected inverter adopts the controller C2, Figure 5 The following are the distribution diagrams and local magnification diagrams of the closed-loop poles of the system under different grid impedances. At this time, the grid impedance gradually increases from 3mH to 18mH. As the grid impedance increases, the closed-loop poles gradually move out of the unit circle, indicating that the system is unstable. The adaptive range of the feedback gain matrix K6 to the grid impedance is 4-15.7mH.

[0136] So far, the corresponding controller set C = {C i|i=1,2}. The selected model set and controller set can effectively cover the case of SCR=2, ensuring the global stability of the grid-connected inverter under a wide range of grid impedance changes.

[0137] (3) Weighted algorithm

[0138] Weighted multi-model adaptive control is to iteratively calculate the current weight value based on the error index function between each local sub-model and the real object, and calculate the global control signal u of the system through online weighting to control the actual controlled object. The error index function is used to measure the performance of each local sub-model in real time.

[0139] For the selection of performance indicators for weighted multi-model control, it is expected that the system can quickly and accurately switch to the controller corresponding to the model that best fits the controlled object, and effectively avoid the oscillation phenomenon caused by switch switching. The present invention adopts an integral performance indicator, which uses the current status of the error and historical related information to evaluate the degree of match between the model and the actual situation. As long as the relevant parameters can be reasonably selected, satisfactory switching results can be achieved. Its weighted performance indicator can be specifically expressed as:

[0140]

[0141] In the formula, e i (t) is the error between the ith sub-model and the actual object; α and β are the weights of the current transient error and the error within the memory length, respectively, focusing on the real-time and long-term matching procedures of performance indicators; γ is the forgetting factor, which determines the memory length of historical information and ensures that J i Convergence of (t), α≥0, β>0, γ>0.

[0142] The weight coefficient of each sub-model can be obtained by normalizing the performance index.

[0143]

[0144] By weighting the output ui of each sub-controller, the final control signal of the system is obtained as follows:

[0145]

[0146] 5 Simulation Verification

[0147] In order to verify the correctness of the theoretical analysis and the effectiveness of the proposed control strategy, a system simulation model was built in MATLAB / Simulink. The parameters of the single-phase grid-connected inverter are shown in Table 1.

[0148] Table 1

[0149] parameter Numeric <![CDATA[DC-side voltage V dc > 400 <![CDATA[Grid voltage U g / V]]> 220 Output power P / kW 5 Grid frequency f / Hz 50 <![CDATA[Sampling frequency f s / Hz]]> 10 <![CDATA[Inductance of inverter L1 / mH]]> 3 Filter capacitor C / uF 3 <![CDATA[Grid-side filtering inductor L2 / mH]]> 2

[0150] 5.2 Simulation under discrete LQR controller

[0151] In order to evaluate the performance of the digitally controlled grid-connected inverter proposed in the present invention using an LQR controller under strong and weak power grids, the present invention performs time domain simulation with a grid impedance of 0 mH under a strong power grid and 6 mH under a weak power grid.

[0152] Figure 6 This is the grid-connected simulation result when the grid impedance is 0mH. The state feedback matrix used in the simulation is K0. When the grid impedance is 0mH, due to the stable design of the closed-loop system, the grid-connected voltage and current waveforms are good, and the grid-connected current distortion rate is 2.46%.

[0153] Figure 7 When the state feedback matrix K0 is used, and the grid impedance jumps from 5mH to 5.4mH at 0.5s, before 0.5s, the closed-loop system is stable and the voltage and current waveforms are good, but after 0.5s, the grid impedance is 5.4mH. At this time, a pair of closed-loop poles move out of the unit circle, and this change directly leads to serious instability of the grid voltage and current, and the grid current cannot track the given value. It can be concluded that the state feedback matrix K0 designed with the grid impedance of 0 as the static working point has a certain range of adaptability to the grid impedance. Once the impedance range is exceeded, the system will immediately become unstable.

[0154] Figure 8 This is the grid-connected simulation result when the grid impedance is 6mH. The state feedback matrix used in the simulation is K6. At this time, when the grid impedance is 6mH, due to the stable design of the closed-loop system, the grid-connected voltage and current waveforms remain good, and the grid-connected current distortion rate is 1.37%. Figure 8 (a) is the grid-connected voltage and current waveform; Figure 8 (b) is the FFT analysis of grid-connected current.

[0155] Fig. 9 (a) and Fig. 9 (b) The grid-connected voltage and current waveforms are shown when the grid impedance jumps from 4mH to 3.8mH and from 15mH to 16mH at 0.5s when the state feedback matrix K6 is used. Before the grid impedance jumps, the grid-connected voltage and current waveforms remain good, but once the grid impedance jumps to a value beyond the limit that the state feedback matrix K6 can control, the grid-connected voltage and current waveforms will be greatly distorted, and the grid-connected power cannot accurately track the given value. This is because in both cases, a pair of closed-loop poles will move out of the unit circle, causing the closed-loop system to become unstable, resulting in grid-connected failure. This is consistent with Figure 5 The theoretical analysis results are consistent.

[0156] 5.3 Simulation of weighted multi-model adaptive control based on LQR

[0157] For the LQR-based weighted multi-model adaptive control designed by the present invention, the parameters α, β and γ in the weighted algorithm are optimized and the simulation results of the system under weak power grid are as follows.

[0158] When the grid impedance jumps within the range of 4-15.3mH, Fig.10 The grid-connected simulation waveforms before and after the grid impedance jump are given. At this time, the current waveform can remain stable. At 0.5 seconds, the grid impedance jumps from 6mH to 13mH. Since the inverter models of 6mH and 13mH can be stably controlled by the controller 2 corresponding to model 2 in the model library, the weight corresponding to model 2 remains at 1 at this time, and the weight corresponding to model 1 converges to 0. The weight change diagram is shown in the figure. Fig.11 shown.

[0159] When the grid impedance jumps within the range of 0-5.3mH, Fig.12 The grid-connected simulation waveforms before and after the grid impedance jump are given. At this time, the voltage and current waveforms can remain stable. At time 0.5, the grid impedance jumps from 1mH to 3mH. Since the inverter models of 1mH and 3mH can be stably controlled by controller 1 corresponding to model 1 in the model library, the weight corresponding to model 1 converges to 1, and the weight corresponding to model 2 converges to 0. The weight change diagram is shown in the figure below. Fig.13 shown.

[0160] When the grid impedance changes arbitrarily within the range of 0-15.5, Fig.14 The grid-connected simulation waveforms before and after the grid impedance jump are given. At this time, the voltage and current waveforms can remain stable. At 0.5s, the grid impedance jumps from 2mH to 12mH. Before 0.5s, the grid impedance is 2mH, and the impedance adaptation range of controller 1 corresponding to model 1 in the model library is within the impedance adaptation range. At this time, the inverter model can be stably controlled by controller 1. After 0.5s, the grid impedance jumps to 12mH. At this time, it will adaptively converge to controller 2 corresponding to model 2 in the model library, and will be controlled by controller 2. The weight change before and after the grid impedance jump is given by Fig.15 shown.

[0161] Fig.16The grid-connected simulation waveform is given when the grid impedance jumps from 13mH to 1mH at 0.5s. At this time, the voltage and current waveforms can remain stable. At 0.5s, the grid impedance jumps from 13mH to 1mH. Before 0.5s, the grid impedance is 13mH, and the impedance adaptation range of controller 2 corresponding to model 2 in the model library is within the impedance adaptation range. At this time, the inverter model can be stably controlled by controller 2. After 0.5s, the grid impedance jumps to 1mH. At this time, it will adaptively converge to controller 1 corresponding to model 1 in the model library, and will be controlled by controller 1. The weight change before and after the grid impedance jump is given by Fig.17 shown.

[0162] Fig.18 The dynamic simulation waveform is given when the grid impedance jumps from 1mH to 2mH and the load jumps from half load to full load at 0.5s. At this time, the voltage and current waveforms can remain stable, and the grid-connected inverter still has good dynamic performance during the jump process. The weight change before and after the jump is given by Fig.19 As shown, it can be seen that the corresponding controller weights can converge quickly to 1.

[0163] Fig. 20 The dynamic simulation waveforms are given when the grid impedance jumps from 6mH to 8mH and the load jumps from half load to full load at 0.5s. The grid-connected voltage and current waveforms remain stable. The grid-connected inverter using multi-model control maintains good dynamic performance during the jump process. The weight change before and after the jump is given by Fig.21 As shown, the weights quickly converge to the corresponding controller.

[0164] 6. Conclusion

[0165] Aiming at the broadband harmonic oscillation and stability problems that may be caused by LCL grid-connected inverters under weak power grids, this paper proposes a weighted multi-model adaptive control method to improve the stability and robustness of the system. The following conclusions are obtained:

[0166] 1) By optimizing the weighted matrix Q and flexibly configuring the closed-loop system poles, the designed LQR control can be stable under different grid strengths and achieve high-precision current tracking, further expanding the adaptability range of grid impedance.

[0167] 2) In order to solve the problem that a single LQR controller has a limited adaptability to grid impedance changes, a weighted multi-model adaptive control method is introduced. A complete model library covering sub-models and their corresponding controllers under different grid impedance conditions is constructed, and a weighted algorithm is designed to significantly improve the system's adaptability to grid impedance. The simulation results prove the correctness of the theoretical analysis.

[0168] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A multi-model LQR control method for a grid-connected inverter under a weak power grid, characterized in that: The following steps are involved: Step 1: Establish a discrete state space model of the grid-connected inverter, including state variables such as inverter-side inductance, filter capacitor, grid-side inductance, grid-connected point voltage, grid voltage, inverter output voltage, capacitor voltage, inverter output current, capacitor current and grid-connected current; Step 2: For the working condition where the grid impedance is 0mH, a discrete linear quadratic regulator LQR controller based on full state feedback is designed, and the state weighting matrix Q is optimized to make the inverter have a fast and well-damped transient current response and be able to track grid voltage changes; Step 3: For the working condition of grid impedance of 6mH, a discrete LQR controller based on full state feedback is designed, and the state weighting matrix Q is optimized to make the inverter have a fast and well-damped transient current response and be able to track grid voltage changes; Step 4: Build a model library, including the two sub-models designed in steps 2 and 3 and their corresponding LQR controllers; Step 5: According to the change of grid impedance, the weight coefficient of each sub-model is calculated, and the sub-controller is selected in a weighted manner to generate a global control signal; Step 6: Apply the global control signal to the grid-connected inverter to control the grid-connected current.

2. The multi-model LQR control method for a grid-connected inverter under a weak power grid according to claim 1, characterized in that: In step 2 and step 3, the values ​​of the state weight matrix Q are respectively Q=diag(0.07, 0, 0.07, 0, 10 4 , 10 9 ) and Q = diag(0.04, 0, 0.04, 0, 10 4 , 10 9 ), diag means Q is a diagonal matrix.

3. The multi-model LQR control method for a grid-connected inverter under a weak power grid according to claim 1, characterized in that: In step 5, the weight coefficient is calculated as follows: In the formula, e i (t) is the error between the ith sub-model and the actual object; α and β are the weights of the current transient error and the error within the memory length, respectively; γ is the forgetting factor, which determines the memory length of the historical information and ensures that J i (t), and α≥0, β>0, γ>0, t represents time, and τ represents the integral variable.

4. The multi-model LQR control method for a grid-connected inverter in a weak power grid according to claim 1, characterized in that: In step 5, the calculation method of the global control signal is: Where m represents the mth model, P n represents the nth weight, C n Represents the nth controller.

5. A control system for a grid-connected inverter under a weak power grid, characterized in that: include: Grid-connected inverter; Model library, used to store sub-models for different grid impedance conditions and their corresponding LQR controllers; A weight coefficient calculation unit, used for calculating the weight coefficient of each sub-model according to the change of the grid impedance; A controller selection unit, used for selecting a sub-controller according to a weight coefficient and generating a global control signal; The control signal output unit is used to apply the global control signal to the grid-connected inverter.

6. The control system of the grid-connected inverter under weak power grid according to claim 5, characterized in that: The model library includes two sub-models for grid impedances of 0 mH and 6 mH and their corresponding LQR controllers.

7. The control system of the grid-connected inverter under weak power grid according to claim 5, characterized in that: The weight coefficient calculation unit calculates the weight coefficient using the following method: In the formula, e i (t) is the error between the ith sub-model and the actual object; α and β are the weights of the current transient error and the error within the memory length, respectively; γ is the forgetting factor, which determines the memory length of the historical information and ensures that J i (t), α≥0, β>0, γ>0, t represents time, τ represents the integral variable.

8. The control system of the grid-connected inverter under weak power grid according to claim 5, characterized in that: The controller selection unit selects a sub-controller and generates a global control signal using the following method: Where m represents the mth model, P n represents the nth weight, C n Represents the nth controller.

9. A grid-connected inverter under a weak power grid, characterized in that: The control is performed by the method according to any one of claims 1 to 4.

Images