Inverter inertia margin calculation method under VSG control based on state space equation

Abstract

The application discloses a kind of VSG control under inverter inertia margin calculation method based on state space equation, including 1, establish the state space equation of inverter under VSG control strategy, by eigenvalue analysis, obtain the constraint condition of VSG control parameter design under stability requirement;2, based on VSG equivalent inertia constant expression, determine the quantitative relationship between VSG control parameter and inverter inertia under VSG control;3, in combination with VSG control parameter constraint condition and VSG equivalent inertia constant expression, calculate the inverter inertia margin under VSG control.The application determines the adjustable range of VSG control parameter under stability constraint based on state space equation, and quantitatively describes the influence of VSG control parameter on inertia according to equivalent inertia constant, and then accurately and effectively realizes the calculation of inverter inertia margin under VSG control.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of inverter control, and particularly relates to an inertia margin calculation method for an inverter under VSG control. BACKGROUND

[0002] With the increasing proportion of new energy power generation, the strength of the power grid is continuously weakened, and the frequency stability problem is increasingly prominent. Taking the virtual synchronous generator (VSG) control as a representative, the network type control makes the power electronic equipment provide virtual inertia, which becomes an effective way to cope with the frequency stability problem of the new energy power system.

[0003] The inertia capacity of a synchronous machine is determined by its own inherent structure and cannot be adjusted, but under VSG control, the output characteristics of the inverter can be changed by configuring the control parameters, so as to realize the adjustability of the inertia. Some existing researches utilize the adjustability of the VSG inertia to design a VSG inertia optimization strategy to optimize the VSG inertia support capacity and improve the system frequency response characteristics.

[0004] An important prerequisite for realizing the VSG inertia optimization is to determine the inertia margin of the inverter under VSG control. However, the current researches on the inertia margin of the inverter under VSG control still have deficiencies, and the boundary of the VSG inertia adjustability is not clear. Most of the current researches start from the perspective of energy balance and propose the configurable inertia margin of the inverter under different energy storage ratios, ignoring the constraint conditions of the VSG control parameter design under the stability requirements of the inverter grid-connected system. The stability of the inverter grid-connected system under VSG control is closely related to the VSG control parameters, and improper configuration of the VSG control parameters may cause the inverter to fail to operate stably in grid-connected mode. However, there is no effective solution to the above situation in the currently disclosed patents. SUMMARY

[0005] In order to solve the deficiencies of the prior art, the application provides a VSG control under inverter inertia margin calculation method based on state space equation, so as to realize the maximum inertia support capacity of VSG under stability constraints, thereby improving the accuracy and effectiveness of the inverter inertia margin under VSG control.

[0006] The application solves the technical problem by adopting the following technical scheme:

[0007] The VSG control under inverter inertia margin calculation method based on state space equation provided by the application has the characteristics that the method comprises the following steps:

[0008] Step 1: establishing a mathematical model of the inverter under VSG control according to the inverter circuit equation and the VSG control principle;

[0009] Step 2, linearize the mathematical model of the inverter under VSG control, establish the state space equation of the inverter under VSG control, so as to obtain the state matrix ;

[0010] Step 3, change the VSG control parameters, including: the value of VSG inertia coefficient And VSG damping coefficient , and calculate the eigenvalue of the state matrix of the state space equation of the inverter under VSG control, so as to judge the stability of the inverter under different VSG control parameters, so as to determine the value range of the VSG control parameters under the stability constraint condition ;

[0011] Step 4, construct the VSG equivalent inertia constant by formula (8) to determine the quantitative relationship between the VSG control parameters and the inertia of the inverter under VSG control;

[0012] (8)

[0013] In formula (8), represents the typical droop characteristic delay time constant of the power system where the inverter is located, represents the steady-state active coefficient of the inverter;

[0014] Step 5, according to the value range of the VSG control parameters under the stability constraint condition And the VSG equivalent inertia constant , draw the three-dimensional function surface of the VSG control parameters and the equivalent inertia constant in the value range , to obtain the maximum equivalent inertia constant of the inverter under VSG control , so as to quantitatively describe the inertia margin of the inverter under VSG control.

[0015] The VSG control under the inverter inertia margin calculation method based on the state space equation of the application has the characteristics that the step 2 comprises:

[0016] Step 2.1, linearize the mathematical model of the inverter circuit part, so as to obtain the state space equation of the inverter circuit part by formula (1):

[0017] (1)

[0018] In formula (1), represents the small signal change of the d-axis current at the output end of the inverter, represents the initial value of the d-axis current at the output end of the inverter, a small signal variation of the q-axis current at the output of the inverter, an initial value of the q-axis current at the output of the inverter, a small signal variation of the d-axis current at the output of the filter, an initial value of the d-axis current at the output of the filter, a small signal variation of the q-axis current at the output of the filter, an initial value of the q-axis current at the output of the filter, a small signal variation of the d-axis voltage at the output of the inverter, a small signal variation of the q-axis voltage at the output of the inverter, a small signal variation of the d-axis voltage at the output of the filter, an initial value of the d-axis voltage at the output of the filter, a small signal variation of the q-axis voltage at the output of the filter, an initial value of the q-axis voltage at the output of the filter, a small signal variation of the d-axis voltage of the equivalent grid, a small signal variation of the q-axis voltage of the equivalent grid, a small signal variation of the angular frequency at the output of the inverter, an initial value of the angular frequency at the output of the inverter, an inductance value of the filter, an inductance value of the grid side, a capacitance value of the filter;

[0019] Step 2.2, linearize the mathematical model of the VSG control part, so as to obtain the state space equation of the VSG control part by using formula (2):

[0020] (2)

[0021] In formula (2), a small signal variation of the active power measurement value at the output of the inverter, a small signal variation of the reactive power measurement value at the output of the inverter, a small signal variation of the active power reference value at the output of the inverter, a small signal variation of the reactive power reference value at the output of the inverter, a time delay constant of the power measurement at the output of the inverter, a small signal variation of the angular frequency control intermediate quantity at the output of the inverter, a small signal variation of the angular frequency at the output of the inverter, ωr represents an angular frequency rating of an inverter output end, Δω represents a small signal variation of an intermediate quantity of voltage amplitude control of an inverter output end, ΔV represents a small signal variation of voltage amplitude of an inverter output end, J represents a VSG inertia coefficient, D represents a VSG damping coefficient, P represents a rated capacity of an inverter, K represents an integral coefficient of a PI controller of a VSG reactive power control loop, K represents a proportional coefficient of a PI controller of a VSG reactive power control loop.

[0022] Step 2.3, the state space equation of the inverter circuit part and the state space equation of the VSG control part are solved to obtain the state space equation of the inverter under VSG control by using formula (3):

[0023] (3)

[0024] In formula (3), X(t) represents a state variable at time t, U(t) represents an input variable at time t, Y(t) represents an output variable at time t, A represents a state matrix, B represents an input matrix, C represents an output matrix; and

[0025] (4)

[0026] (5)

[0027] (6)

[0028] (7).

[0029] The electronic device comprises a memory and a processor, and the memory is used for storing a program supporting the processor to execute the VSG control under inverter inertia margin calculation method, and the processor is configured to execute the program stored in the memory.

[0030] The computer readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the VSG control under inverter inertia margin calculation method are executed.

[0031] Compared with the prior art, the present application has the following beneficial effects:

[0032] 1. The application considers the constraint of the inertia of the inverter grid-connected stability requirement when calculating the inertia margin of the inverter under VSG control, which is beneficial to guarantee the safe and stable operation of the inverter grid-connected system under VSG control.

[0033] 2. The application analyzes the inverter grid-connected stability under VSG control based on the state space equation, and the effectiveness of the theoretical method has been widely verified by academic research and engineering application, and the analysis result has high reliability.

[0034] 3. The application quantitatively describes the inverter inertia with equivalent inertia constant, and the finally calculated inertia margin is also given in the form of the maximum value of the equivalent inertia constant, so that the calculation result of the inertia margin is more intuitive and compatible with the existing synchronous machine inertia system.

[0035] 4. The inertia margin of the inverter under VSG control obtained by the application can provide effective reference for the inertia optimization of the VSG power system, so that the inverter under VSG control can play a better inertia support effect. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 The figure is the basic structure of the inverter grid-connected system under VSG control in the application.

[0037] Figure 2 The figure is the value range of the VSG control parameter under the stability constraint condition in the embodiment of the application.

[0038] Figure 3 The figure is the three-dimensional function surface of the VSG equivalent inertia constant under the stability constraint condition in the embodiment of the application.

[0039] Figure 4a The figure is the inverter simulation result when the control parameter is set within the stability constraint value range in the embodiment of the application.

[0040] Figure 4b The figure is the inverter simulation result when the control parameter is set outside the stability constraint value range in the embodiment of the application.

[0041] Figure 5 The figure is the flow chart of the method of the application. DETAILED DESCRIPTION

[0042] The technical solutions of the application will be further specifically explained in combination with the specific embodiments and the drawings:

[0043] Since the adjustment of VSG inertia depends on the configuration of control parameters, considering the design constraints of VSG control parameters on the stability of inverter grid-connected, the inverter inertia margin will also be limited to a certain extent, therefore, in the embodiment, the application proposes a quantitative analysis method for inertia support capability of direct-drive wind power generation system under VSG control, which is based on the analysis of VSG control parameter constraint conditions under stability requirements through state space equation, and quantitatively describes the relationship between VSG control parameters and inertia capability through equivalent inertia constant expression, and obtains the maximum inertia support capability of VSG, so as to accurately calculate the inverter inertia margin under VSG control on the premise of fully considering the stability constraint conditions, specifically, as shown in Figure 5 The method is performed according to the following steps:

[0044] Step 1, according to the inverter circuit equation and VSG control principle, the mathematical model of the inverter under VSG control is established, and the basic structure of the inverter grid-connected system under VSG control is as shown in Figure 1

[0045] Step 1.1, in the dq axis coordinate system, according to Kirchhoff's voltage law and Kirchhoff's current law, the circuit equation is written, and the mathematical model of the inverter circuit part is obtained as shown in formula (1):

[0046] (1)

[0047] In formula (1), represents the differential calculation symbol, represents the d-axis current at the output end of the inverter, represents the q-axis current at the output end of the inverter, represents the d-axis current at the output end of the filter, represents the q-axis current at the output end of the filter, represents the d-axis voltage at the output end of the inverter, represents the q-axis voltage at the output end of the inverter, represents the d-axis voltage at the output end of the filter, represents the q-axis voltage at the output end of the filter, represents the equivalent grid d-axis voltage, represents the equivalent grid q-axis voltage, represents the angular frequency at the output end of the inverter, represents the filter inductance value, represents the grid-side inductance value, represents the filter capacitance value;

[0048] Step 1.2, according to the control principle of active power control loop and reactive power control loop of VSG, the mathematical model of VSG control part is obtained as shown in formula (2):

[0049] ​ (2)

[0050] In formula (2), represents an active power measurement value, represents a reactive power measurement value, represents an active power reference value, represents a reactive power reference value, represents a time delay constant of power measurement, represents an inverter output end angular frequency control intermediate quantity, represents an inverter output end angular frequency rated value, represents an inverter output end voltage amplitude control intermediate quantity, represents an inverter output end voltage amplitude, represents a VSG inertia coefficient, represents a VSG damping coefficient, represents an inverter rated capacity, represents a VSG reactive power control loop PI controller integral coefficient, represents a VSG reactive power control loop PI controller proportional coefficient.

[0051] Step 2, linearize the mathematical model of the inverter under VSG control, establish the state space equation of the inverter under VSG control, and thus obtain the state matrix;

[0052] Step 2.1, linearize the mathematical model of the inverter circuit part, and thus obtain the state space equation of the inverter circuit part by using formula (3):

[0053] (3)

[0054] In formula (3), represents a small signal change of the d-axis current at the inverter output end, represents an initial value of the d-axis current at the inverter output end, represents a small signal change of the q-axis current at the inverter output end, represents an initial value of the q-axis current at the inverter output end, represents a small signal change of the d-axis current at the filter output end, represents an initial value of the d-axis current at the filter output end, represents a small signal change of the q-axis current at the filter output end, represents an initial value of the q-axis current at the filter output end, represents a small signal change of the d-axis voltage at the inverter output end, represents a small signal change of the q-axis voltage at the inverter output end, small signal variation of the d-axis voltage at the output of the filter, initial value of the d-axis voltage at the output of the filter, small signal variation of the q-axis voltage at the output of the filter, initial value of the q-axis voltage at the output of the filter, small signal variation of the d-axis voltage of the equivalent grid, small signal variation of the q-axis voltage of the equivalent grid, small signal variation of the angular frequency at the output of the inverter, initial value of the angular frequency at the output of the inverter, inductance value of the filter, inductance value at the grid side, capacitance value of the filter;

[0055] Step 2.2, linearize the mathematical model of the VSG control part, so as to obtain the state space equation of the VSG control part by using formula (4):

[0056] (4)

[0057] in formula (4), small signal variation of the active power measurement value at the output of the inverter, small signal variation of the reactive power measurement value at the output of the inverter, small signal variation of the active power reference value at the output of the inverter, small signal variation of the reactive power reference value at the output of the inverter, time constant of the power measurement at the output of the inverter, small signal variation of the angular frequency control intermediate quantity at the output of the inverter, small signal variation of the angular frequency at the output of the inverter, rated value of the angular frequency at the output of the inverter, small signal variation of the voltage amplitude control intermediate quantity at the output of the inverter, small signal variation of the voltage amplitude at the output of the inverter, inertia coefficient of the VSG, damping coefficient of the VSG, rated capacity of the inverter, integral coefficient of the PI controller of the VSG reactive power control loop, proportional coefficient of the PI controller of the VSG reactive power control loop;

[0058] Step 2.3: Combine the state space equations of the inverter circuit part and the state space equations of the VSG control part, and use equation (5) to obtain the state space equation of the inverter under VSG control:

[0059] (5)

[0060] In formula (5), represents the state variable at time t, represents the input variable at time t, represents the output variable at time t, represents the state matrix, represents the input matrix, represents the output matrix; and:

[0061] (6)

[0062] (7)

[0063] (8)

[0064] (9)

[0065] Step 3: Change VSG control parameters, including: VSG inertia coefficient and VSG damping coefficient The value of , combined with the physical parameters of the inverter, is substituted into , , , , , , in which a complete state space equation of the inverter under VSG control is formed, the eigenvalues ​​of the state matrix of the state space equation of the inverter under VSG control are calculated, and the stability of the inverter under different VSG control parameters is judged based on the fact that the real part of each eigenvalue is less than 0, so as to determine the value range of the VSG control parameters under the stability constraint condition. ;

[0066] Step 4: Use formula (10) to construct the VSG equivalent inertia constant , to determine the quantitative relationship between VSG control parameters and inverter inertia under VSG control;

[0067] (10)

[0068] In formula (10), Indicates the typical droop characteristic delay time constant of the power system where the inverter is located, Indicates the steady-state active power coefficient of the inverter;

[0069] Step 5: According to the value range of VSG control parameters under stability constraints and VSG equivalent inertia constant , draw the value range VSG control parameters and equivalent inertia constants The three-dimensional function surface is used to obtain the maximum equivalent inertia constant of the inverter under VSG control. ,by Quantitatively describe the inertia margin of the inverter under VSG control.

[0070] In this embodiment, an electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the above method, and the processor is configured to execute the program stored in the memory.

[0071] In this embodiment, a computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the above method are executed.

[0072] Example:

[0073] Take the calculation of the inertia margin of the inverter under VSG control using the parameters shown in Table 1 as an example:

[0074] Table 1

[0075]

[0076] 1. Substitute various basic parameters and write the state matrix of the inverter state space equation under VSG control. Considering the VSG damping coefficient Equivalent to the droop coefficient, the value range is limited by the relevant standards of primary frequency modulation. Set it between 8-20, select several groups of values, and change the VSG damping coefficient multiple times and inertia coefficient , respectively solve the eigenvalues ​​of the inverter state matrix under VSG control, and judge the grid-connected system of the inverter under different VSG control parameters based on the real part of each eigenvalue being less than 0, and determine the value range of the VSG control parameters under stability constraints. The value range results are plotted as follows Figure 2 shown.

[0077] 2. In Within the range, substitute each parameter into formula (7), calculate the corresponding equivalent inertia constant value, and draw Three-dimensional function surface such as Figure 3 As shown, it is calculated that when When the inverter inertia margin under VSG control is .

[0078] 3. In the PSModel electromagnetic transient simulation software, according to the parameters shown in Table 1, a time domain simulation model of the inverter grid-connected system under VSG control is built to verify the inertia margin calculation results. and inertia coefficient Set in and , the simulation results are as follows Figure 4a and Figure 4b As shown. It can be seen that the VSG control parameter design is When the inverter is connected to the grid, the VSG control parameters are designed to ensure stable grid operation. When the inverter is out of stability, the inverter will become unstable. The range of VSG control parameters under stability constraints The maximum value of the equivalent inertia constant within can effectively describe the inertia margin of the inverter under VSG control.

Claims

1. A method for calculating the inverter inertia margin under the VSG control based on the state space equation, characterized in that, The method comprises the following steps: Step 1, according to the inverter circuit equation and the VSG control principle, a mathematical model of the inverter under VSG control is established; Step 2, linearize the mathematical model of the inverter under VSG control, establish the state space equation of the inverter under VSG control, so as to obtain the state matrix ; Step 3, changing the VSG control parameters, including: the values of VSG inertia coefficient and VSG damping coefficient , and calculating the eigenvalues of the state matrix of the state space equation of the inverter under VSG control, taking the real part of each eigenvalue being less than 0 as the judgment basis, thereby judging the stability of the inverter under different VSG control parameters, and determining the value range of the VSG control parameters under the stability constraint condition . Step 4, constructing VSG equivalent inertia constant with formula (8) to determine the quantitative relationship between VSG control parameters and the inertia of the inverter under VSG control. (8) In formula (8), represents a typical droop characteristic delay time constant of the power system in which the inverter is located, represents a steady-state active coefficient of the inverter; Step 5: According to the value range of VSG control parameters under stability constraints and VSG equivalent inertia constant , draw the value range VSG control parameters and equivalent inertia constants The three-dimensional function surface of is used to obtain the maximum equivalent inertia constant of the inverter under VSG control ,by Quantitatively describe the inertia margin of the inverter under VSG control.

2. The method of claim 1, wherein the state-space equation-based VSG control inverse converter inertia margin calculation method is characterized by, The step 2 comprises: Step 2.1, the mathematical model of the inverter circuit part is linearized, so that the state space equation of the inverter circuit part is obtained by using formula (1): (1) in formula (1), represents a small signal change amount of the d-axis current at the inverter output end, represents an initial value of the d-axis current at the inverter output end, represents a small signal change amount of the q-axis current at the inverter output end, represents an initial value of the q-axis current at the inverter output end, represents a small signal change amount of the d-axis current at the filter output end, represents an initial value of the d-axis current at the filter output end, represents a small signal change amount of the q-axis current at the filter output end, represents an initial value of the q-axis current at the filter output end, represents a small signal change amount of the d-axis voltage at the inverter output end, represents a small signal change amount of the q-axis voltage at the inverter output end, represents a small signal change amount of the d-axis voltage at the filter output end, represents an initial value of the d-axis voltage at the filter output end, represents a small signal change amount of the q-axis voltage at the filter output end, represents an initial value of the q-axis voltage at the filter output end, represents a small signal change amount of the d-axis voltage of the equivalent grid, represents a small signal change amount of the q-axis voltage of the equivalent grid, represents a small signal change amount of the angular frequency at the inverter output end, represents an initial value of the angular frequency at the inverter output end, represents an inductance value of the filter, represents an inductance value at the grid side, represents a capacitance value of the filter; Step 2.2, the mathematical model of the VSG control part is linearized, so that the state space equation of the VSG control part is obtained by using formula (2): (2) in formula (2), a small signal variation of the active power measurement value of the inverter output end, a small signal variation of the reactive power measurement value of the inverter output end, a small signal variation of the active power reference value of the inverter output end, a small signal variation of the reactive power reference value of the inverter output end, a time constant of the power measurement of the inverter output end, a small signal variation of the angular frequency control intermediate quantity of the inverter output end, a small signal variation of the angular frequency of the inverter output end, an angular frequency rated value of the inverter output end, a small signal variation of the voltage amplitude control intermediate quantity of the inverter output end, a small signal variation of the voltage amplitude of the inverter output end, a VSG inertia coefficient, a VSG damping coefficient, a rated capacity of the inverter, a PI controller integral coefficient of the VSG reactive power control loop, a PI controller proportional coefficient of the VSG reactive power control loop; Step 2.3, the state space equation of the inverter circuit part and the state space equation of the VSG control part are combined, so that the state space equation of the inverter under VSG control is obtained by using formula (3): (3) in formula (3), denotes the state variable at time t, denotes the input variable at time t, denotes the output variable at time t, denotes the state matrix, denotes the input matrix, denotes the output matrix; and (4) (5) (6) (7)。 3. An electronic device comprising a memory and a processor, characterized in that The memory is used for storing a program supporting the processor to execute the inverter inertia margin calculation method under VSG control according to claim 1 or 2, and the processor is configured to execute the program stored in the memory.

4. A computer-readable storage medium having stored thereon a computer program, characterized in that The computer program is executed by the processor to execute the steps of the inverter inertia margin calculation method under VSG control according to claim 1 or 2.

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