A control parameter tuning method for virtual synchronous machine based on hybrid H2 / H∞ performance index

Abstract

The present invention relates to a virtual synchronous machine control parameter setting method based on a hybrid H2 / H∞ performance index, comprising: S1, determining a first open-loop transfer function of an inner-loop current controller and a second open-loop transfer function of an outer-loop voltage controller in a virtual synchronous generator double closed-loop control system; S2, converting the first open-loop transfer function and the second open-loop transfer function into a first state space equation and a second state space equation respectively, and the control parameters to be determined in the first state space equation and the second state space equation are relatively independent of other variables; S3, according to the H2 / H∞ performance index, ∞ The mixed performance index, the first state space equation and the second state space equation are used to determine the linear matrix inequality group; S4, taking the regional pole configuration as a constraint condition, solving the linear matrix inequality group to obtain the value of the unknown control parameter.

Description

Technical Field

[0001] The invention relates to a virtual synchronous machine control parameter setting method based on a mixed H2 / H∞ performance index, and belongs to the field of VSG parameter setting. Background Art

[0002] Virtual synchronous generator (VSG) is a control strategy that allows the inverter to simulate the characteristics of a synchronous generator by introducing virtual inertia and virtual damping. VSG technology can directly combine the rotor motion equation and the reactive excitation controller to provide a reference voltage for the voltage and current double closed-loop control part. Although the double closed-loop cascade control part can easily realize the control of the inverter, its parameter setting needs to analyze and consider factors such as system stability and the interaction between the loops.

[0003] Regarding the setting of PI parameters, actual projects generally use trial and error to determine their specific values. While adjusting one parameter to improve some performance indicators of the controlled object, the trial and error method may also make other performance indicators of the controlled object worse. Therefore, although the trial and error method can provide a way to select PI parameters, it also has problems such as relying on certain experience and skills and lacking theoretical support.

[0004] At present, there are many schemes for parameter tuning of voltage and current dual closed-loop controllers. Classic parameter tuning methods include pole configuration tuning method, cancellation principle method, etc. However, these methods are not only complex, but also require high accuracy of the model. Another type is the intelligent control method that applies neural network control technology to PI parameter tuning. For example, by real-time monitoring of the voltage and current of the grid-connected inverter, the particle swarm algorithm or genetic algorithm can be used to dynamically adjust the PI parameters. However, intelligent control technology itself does not have a perfect theory to prove its convergence, stability and robustness, and due to its randomness, it is easy to fall into the local optimal situation.

[0005] Therefore, a parameter tuning method for a dual closed-loop control system with greater stability is needed.

[0006] The patent "Design Method of State Feedback Controller of Virtual Synchronous Generator System Considering Time Delay" with publication number CN112003326A discloses the following steps: Step 1, establish the state space model of the VSG control inverter grid-connected system; Step 2, consider the time delay and rewrite the state space model; Step 3, derive the time-delay stability conditions through LMI according to the Lyapunov stability theorem; Step 4, add a state feedback controller; Step 5, obtain the new time-delay stability conditions of the system under the action of the state feedback controller; Step 6, obtain the state feedback controller equation according to the stability conditions. This method effectively solves the influence of time delay on VSG control by designing a state feedback controller, so that the VSG system can meet the ideal performance requirements and improve the time-delay stability of the virtual synchronous generator grid-connected system. This patent mainly solves the influence of time delay on VSG control by adding a state feedback controller, and the robustness needs to be further improved. Summary of the invention

[0007] In order to overcome the problems existing in the prior art, the present invention designs a device that meets the H2 performance index, H ∞ A control parameter tuning method based on performance indicators and pole position constraints is proposed, and a group of matrix inequalities for calculating the values ​​of pending control parameters is proposed, so that the double closed-loop control system can meet multiple performance indicators while ensuring stability, robustness, and the desired dynamic response performance.

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

[0009] The control parameter tuning method of a virtual synchronous machine based on a hybrid H2 / H∞ performance index includes the following steps:

[0010] S1, determining a first open-loop transfer function of an inner-loop current controller and a second open-loop transfer function of an outer-loop voltage controller in a dual-closed-loop control system of a virtual synchronous generator;

[0011] S2, converting the first open-loop transfer function and the second open-loop transfer function into a first state space equation and a second state space equation respectively, wherein the undetermined control parameters in the first state space equation and the second state space equation are relatively independent of other variables;

[0012] S3, according to H2 / H ∞ Mixing the performance index, the first state space equation and the second state space equation, determining a linear matrix inequality system;

[0013] S4. Using the regional pole configuration as a constraint, solve the linear matrix inequality group to obtain the value of the unknown control parameter.

[0014] Furthermore, the step S1 is specifically as follows:

[0015] Perform dq feedforward decoupling processing on the inductor current state equation, and obtain the first open-loop transfer function according to the first-order inertia link transfer function;

[0016] The capacitor voltage state equation is subjected to dq feedforward decoupling processing, and the second open-loop transfer function is obtained according to the first-order inertia link transfer function.

[0017] Furthermore, the linear matrix inequality group is expressed as:

[0018]

[0019]

[0020] Tr(Q)<γ2

[0021]

[0022]

[0023] Where, the positive definite symmetric matrix P and the matrix M are matrices to be determined; I represents the identity matrix; γ1 is the performance index H ∞ ;γ2 is the performance index H2; Q∈R 1×1 And its trace is less than γ2; F, H, C are matrices, P∈R 3×3 ; M∈R 3 ×1 ; J and N are the parameter matrices of the pole configuration region; K represents the undetermined control parameters.

[0024] Further, according to the first state space equation and the second state space equation, the matrices F, H, and C in the linear matrix inequality group for determining the minimum realization of the double closed-loop control system are determined.

[0025] Furthermore, the step S4 is specifically as follows:

[0026] Select the pole configuration region D to minimize the mixed H2 / H ∞ The performance index and the pole configuration region D are the constraints for solving the linear matrix inequality group. The linear matrix inequality group is solved to obtain the values ​​of the unknown control parameters.

[0027] Furthermore, the solution of the linear matrix inequality system includes the matrix P corresponding to the inner loop current controller i 、M i and the matrix P corresponding to the outer loop voltage controller v 、M v ; The matrix P i 、M i and the matrix P v 、M v Substitute into the formula K=H-1 P -1 M solves the unknown control parameter K.

[0028] Compared with the prior art, the present invention has the following characteristics and beneficial effects:

[0029] The virtual synchronous generator double closed-loop control system of the present invention is designed to meet the H2 performance index, H ∞ A control parameter tuning method based on performance indicators and pole position constraints is proposed, and a group of matrix inequalities for calculating the values ​​of pending control parameters is proposed, so that the double closed-loop control system can meet multiple performance indicators while ensuring stability, robustness, and the desired dynamic response performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a flow chart of the present invention;

[0031] Figure 2 It is a schematic diagram of a three-phase grid-connected inverter of VSC-HVDC;

[0032] Figure 3 It is an inverter controller structure based on VSG;

[0033] Figure 4 is a schematic diagram of the control strategy of the virtual synchronous machine;

[0034] Figure 5 It is the block diagram of the current loop d-axis control structure;

[0035] Figure 6 It is the block diagram of the voltage outer loop d-axis control structure;

[0036] Figure 7 This is the block diagram of the classic PI control structure;

[0037] Figure 8 is the pole configuration region D(α,θ) in the s-plane;

[0038] Fig. 9 It is the unit step response and pulse disturbance response curve of the double closed-loop control system. DETAILED DESCRIPTION

[0039] The present invention is described in more detail below with reference to the embodiments.

[0040] Embodiment 1

[0041] Virtual synchronous generator double closed-loop control system, such as Figure 3As shown, it includes: virtual speed regulation module, virtual excitation module, inertia damping module, voltage and current dual closed-loop control module, and pulse width modulation module (PWM module). Among them, the virtual speed regulation module acts on the receiving-end converter of the flexible DC transmission system, so that the converter has the ability to participate in the frequency regulation of the power grid; the inertia damping module refers to the operating characteristics of the synchronous generator, so that the converter has inertia and damping characteristics, and improves the anti-interference ability of the power grid; the virtual excitation module acts on the receiving-end converter of the flexible DC transmission system, so that the converter has the ability to regulate the voltage of the power grid.

[0042] like Figure 4 As shown, the virtual speed regulation module outputs the corresponding VSG mechanical torque control value to the inertia damping module according to the input frequency command value and the active power command value; the inertia damping module outputs the corresponding converter reference internal potential phase according to the input VSG mechanical torque;

[0043] The virtual excitation module outputs the corresponding reference internal potential amplitude according to the input output voltage command value and reactive power command value; the reference voltage is synthesized for the amplitude and phase of the reference internal potential and input into the voltage-current dual closed-loop control module; the voltage-current dual closed-loop control module generates a DC modulation signal in a dq synchronous rotating coordinate system; the DC modulation signal is subjected to a Park inverse transformation and input into a pulse width modulation module to obtain a switching signal in a three-phase natural coordinate system.

[0044] Embodiment 2

[0045] The control parameters (specifically the undetermined PI gain parameters in this embodiment) in the virtual synchronous generator double closed-loop control system are adjusted according to the following method to meet the following design indicators:

[0046] (1) The double closed-loop control system is asymptotically stable;

[0047] (2) ξ is a disturbance signal with finite energy. The transfer function from ξ to the control output is T ξ (s) satisfies H ∞ Performance index γ1>0;

[0048]

[0049] (3) The transfer function T(s) from the reference input to the control output satisfies the H2 performance index γ2>0;

[0050]

[0051] (4) The poles of the double closed-loop control system are located in a given area D on the s-plane.

[0052] like Figure 1 As shown, the specific steps are as follows:

[0053] S1. Determine the first open-loop transfer function H i (s) and the second open-loop transfer function H v (s):

[0054] For the inner loop current PI controller, the first-order inertia link equivalent pulse width modulation module is used to generate the delay effect of the switching signal; the state equation of the inductor current Perform dq feedforward decoupling control processing to obtain the first open-loop transfer function H i (s):

[0055]

[0056] T d ≈0.5T s

[0057] Where R1 is the equivalent parasitic resistance of the filter inductor; L1 is the filter inductor value; e a 、e b 、e c is the output voltage of the three-phase inverter; u oa 、u ob 、u oc is the filter capacitor voltage of the inverter; i a 、i b 、i c is the filter inductor current; k ip is the proportional coefficient of the inner loop current PI controller, k ii is the integral coefficient of the inner loop current PI controller, T d is the equivalent time constant of the delay effect, T s is the switching period, L is the filter inductance value, and r is the equivalent parasitic resistance of the filter inductor.

[0058] The structure diagram of the inner loop current PI controller is as follows: Figure 5 As shown, where i d is the d-axis component of the output current of the modular multilevel converter (MMC), i dref is the voltage outer loop output signal as the reference value of the current loop, ξ i (s) is the unknown disturbance that may occur in the inner loop current PI controller.

[0059] Similarly, for the outer loop voltage PI controller, the first-order inertia link equivalent pulse width modulation module is used to generate the delay effect of the switching signal; the state equation of the capacitor voltage Perform dq feedforward decoupling control processing to obtain the second open-loop transfer function H v (s):

[0060]

[0061] Where, C is the filter capacitor connected in star configuration; k vp is the proportional coefficient of the outer loop voltage PI controller; i oa 、i ob 、i oc is the inverter output current; k vi is the integral coefficient of the outer loop voltage PI controller; T s is the switching period; C is the filter capacitor connected in star configuration.

[0062] The structure diagram of the outer loop voltage PI controller is as follows: Figure 6 As shown, where u d is the d-axis component of the output voltage of the modular multilevel converter, u dref is the output signal of the virtual excitation module as the reference value of the voltage outer loop, ξ v (s) is the unknown disturbance that may occur in the outer loop voltage PI controller.

[0063] S2. Convert the first open-loop transfer function and the second open-loop transfer function into the first state space equation and the second state space equation respectively, so that the undetermined PI gain parameter in the state space equation is relatively independent of other variables (that is, the characteristic of this state space realization is that the undetermined PI gain parameter can be independently formed into a vector):

[0064] S21, for the control process such as Figure 5 The first open-loop transfer function H i (s), and transform it into Figure 7 The classic PI control form shown is:

[0065] Let H i (s) = K i (s)G i (s)

[0066]

[0067]

[0068] Then we have:

[0069]

[0070] and

[0071]

[0072] in

[0073]

[0074]

[0075]

[0076] Thus, the transfer function of the inner loop current PI controller is expressed as:

[0077]

[0078] According to the transfer function, its state space implementation can be directly written in the following form:

[0079]

[0080] i d =C cl x+d 1cl i dref +d 2cl ξ i

[0081] In the formula, I2 is the second-order unit matrix; b 1cl =[θ]=HK; b 2cl =[-θ]=-HK; d 1cl =0;d 2cl =1.

[0082] So from the reference input i dref To control output i d The transfer function is

[0083] T i (s) = C cl (sI-A cl ) -1 b 1cl +d 1cl

[0084] From the disturbance input ξ i To control output i d The transfer function is

[0085] T ξi (s) = C cl (sI-A cl ) -1 b 2cl +d 2cl

[0086] S22, Similarly, for the control process such as Figure 6 The second open-loop transfer function is also transformed into Figure 7 The classic PI control form shown is finally expressed as:

[0087]

[0088] Its state space implementation is as follows:

[0089]

[0090] u d =C clv x+d 1clv u dref +d 2clv ξ v

[0091] In the formula,

[0092] θ v =H v K v ;

[0093] I2 is the second-order unit matrix; b 1clv =[θ v ]=H v K v ; b 2clv =[-θ v ]=-H v K v ; d 1clv =0;d 2clv =1.

[0094] S3. According to the design index, a linear matrix inequality group is proposed as follows:

[0095]

[0096]

[0097] Tr(Q)<γ2

[0098]

[0099]

[0100] In the formula, the positive definite symmetric matrix P and the matrix M are matrices to be determined; Q∈R 1×1 And its trace is less than γ2; F, H, C are the correlation matrices that determine the minimum realization of the double closed-loop control system, P∈R 3×3 ; M∈R 3×1 ; J and N are pole configuration areas The parameter matrix of the PI gain parameter to be determined is represented by K = H -1 P -1 M.

[0101] For the inner loop current PI controller:

[0102]

[0103] For the outer loop voltage PI controller:

[0104]

[0105] S4. Select the desired pole configuration area D of the s-plane, expressed as:

[0106]

[0107] like Figure 8 As shown, the pole configuration area is selected as the overlapping part of the left area of ​​the s-plane straight line -α and the conical area with the origin as the vertex and an angle of 2θ.

[0108] Thus we get

[0109] J1=2α,N1=1

[0110] J2=0,

[0111] Next, select the optimal H2 / H mixture according to actual requirements. ∞ Performance Indicators

[0112] min[w1*γ1+w2*trace(Q)]

[0113] That is, minimize the mixed H2 / H ∞ performance index, and takes it as the constraint condition for solving the linear matrix inequality group, where w1 and w2 are H ∞ The weight values ​​of the performance index γ1 and the H2 performance index γ2 are w1+w2=1, and their values ​​are selected according to actual requirements.

[0114] Substitute the matrices F, H, C, J, N and weights w1 and w2 corresponding to the inner loop current PI controller into the linear matrix inequality group and solve to obtain the corresponding positive definite symmetric matrix P i and the matrix M i ,

[0115] Substitute the matrices F, H, C, J, N and weights w1 and w2 corresponding to the outer loop voltage PI controller into the linear matrix inequality group and solve to obtain the corresponding positive definite symmetric matrix P v and the matrix M v ;

[0116] According to the formula K=H -1 P -1 M, and obtain the undetermined PI gain parameters of the double closed-loop control system.

[0117] Embodiment 3

[0118] Consider the inverter filter inductor L = 1.5mH, filter capacitor C = 9.9μF, equivalent resistance r = 0.01Ω, switching frequency f s =20kHz. Then the open-loop transfer function of the inner-loop current PI controller is:

[0119]

[0120] The open-loop transfer function of the outer loop voltage PI controller is:

[0121]

[0122] The implementation form of the dual closed-loop control system is shown in step 2, where the minimum implementation correlation matrix corresponding to the inner loop current PI controller is:

[0123]

[0124]

[0125]

[0126] The minimum implementation correlation matrix corresponding to the outer loop voltage PI controller is:

[0127]

[0128]

[0129]

[0130] Select as Figure 8 The area on the left half plane of s shown in FIG. 1 is used as the area for configuring poles, that is, the undetermined PI gain parameters should satisfy the poles of the double closed-loop control system. Figure 8 The area on the left side of the solid line is shown. This area is actually the intersection of two areas, namely the area on the left side of the straight line -α and the overlapping part of the cone area with the origin as the vertex and an angle of 2θ. The representation of this area is as described in step S4.

[0131] 1) Select α = 5, θ = 60°. If the H2 performance index of the double closed-loop control system is more important, w1 = 0.2, w2 = 0.8, that is, by optimizing the mixed H2 / H ∞ The performance index min0.2*γ1+0.8*trace(Q) is used to solve the linear matrix inequality group and obtain the optimization result k p =0.0075, k i =0.0500, at this time the pole of the inner loop current PI controller is

[0132] s1=-39994.994

[0133] s2=-6.667

[0134] s3=-5.002

[0135] For the outer loop voltage PI controller, k p =0.000099, k i =0.000495, the extreme point is

[0136] s1=-19989.995

[0137] s2=-5.003+4.999i

[0138] s3=-5.003-4.999i

[0139] It can be seen that the poles are in the desired region.

[0140] 2) Select α = 10, θ remains unchanged, and optimize the mixture H2 / H ∞ The performance index min0.2*γ1+0.8*trace(Q) is used to solve the linear matrix inequality group and obtain the optimization result k p =0.02, k i =0.2, at this time the pole of the inner loop current PI controller is

[0141] s1=-39986.660

[0142] s2=-10.003+5.772i

[0143] s3=-10.003-5.772i

[0144] For the outer loop voltage PI controller, k p =0.0002, k i =0.0019, the extreme point is

[0145] s1=-19979.979

[0146] s2=-10.010+9.999i

[0147] s3=-10.010+9.999i

[0148] Obviously, after changing the desired pole position area, the re-solved controller can readjust the system closed-loop poles to the desired area.

[0149] Two sets of controller parameters are used for simulation. Under 20% impulse disturbance, the unit step response curve is as follows: Fig. 9As shown in the figure, the dotted line y1 is the response curve when the first set of parameters is used for control, and the solid line y2 is the response curve when the second set of parameters is used for control.

[0150] In summary, by using the method of the present invention, multi-objective PI control parameters that meet the desired requirements can be adjusted.

[0151] Obviously, the described embodiments are only some embodiments of the present invention, not all 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.

Claims

1. A virtual synchronous machine control parameter setting method based on a hybrid H2 / H∞ performance index, characterized in that: The steps include: S1, determining a first open-loop transfer function of an inner-loop current controller and a second open-loop transfer function of an outer-loop voltage controller in a dual-closed-loop control system of a virtual synchronous generator; S2, converting the first open-loop transfer function and the second open-loop transfer function into a first state space equation and a second state space equation respectively, wherein the undetermined control parameters in the first state space equation and the second state space equation are relatively independent of other variables; S3, according to H2 / H ∞ The hybrid performance index, the first state space equation, and the second state space equation determine a set of linear matrix inequalities, where: The linear matrix inequality system is expressed as: Tr(Q)<γ2; Where, the positive definite symmetric matrix P and the matrix M are matrices to be determined; I represents the identity matrix; γ1 is the performance index H ∞ ;γ2 is the performance index H2; Q∈R 1×1 And its trace is less than γ2; F, H, C are matrices, P∈R 3×3 ; M∈R 3×1 ; J and N are the parameter matrices of the pole configuration region; K represents the undetermined control parameter; S4. Using the regional pole configuration as a constraint, solve the linear matrix inequality group to obtain the value of the unknown control parameter.

2. The method for setting control parameters of a virtual synchronous machine based on a hybrid H2 / H∞ performance index according to claim 1, characterized in that: The step S1 is specifically as follows: Perform dq feedforward decoupling processing on the inductor current state equation, and obtain the first open-loop transfer function according to the first-order inertia link transfer function; The capacitor voltage state equation is subjected to dq feedforward decoupling processing, and the second open-loop transfer function is obtained according to the first-order inertia link transfer function.

3. The method for setting control parameters of a virtual synchronous machine based on a hybrid H2 / H∞ performance index according to claim 1, characterized in that: According to the first state space equation and the second state space equation, matrices F, H and C in the linear matrix inequality group for determining the minimum realization of the double closed-loop control system are determined.

4. The method for setting control parameters of a virtual synchronous machine based on a hybrid H2 / H∞ performance index according to claim 3, characterized in that: Step S4 is specifically as follows: Select the pole configuration region D to minimize the mixed H2 / H ∞ The performance index and the pole configuration region D are the constraints for solving the linear matrix inequality group. The linear matrix inequality group is solved to obtain the values ​​of the unknown control parameters.

5. The method for setting control parameters of a virtual synchronous machine based on a hybrid H2 / H∞ performance index according to claim 4, characterized in that: The solution to the linear matrix inequality system includes the matrix P corresponding to the inner loop current controller i 、M i and the matrix P corresponding to the outer loop voltage controller v 、M v ; The matrix P i 、M i and the matrix P v 、M v Substitute into the formula K=H -1 P -1 M solves the unknown control parameter K.

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