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

Abstract

The invention discloses a VSG-controlled inverter inertia margin calculation method based on a state-space equation, and the method comprises the steps: 1, building an inverter state-space equation under a VSG control strategy, and obtaining a constraint condition of VSG control parameter design under a stability requirement through feature value analysis; 2, based on a VSG equivalent inertia constant expression, determining a quantitative relation between a VSG control parameter and an inverter inertia under VSG control; and 3, calculating an inverter inertia margin under VSG control by combining a VSG control parameter constraint condition and a VSG equivalent inertia constant expression. According to the method, the adjustable range of the VSG control parameter under the stability constraint is determined based on the state-space equation, and the influence of the VSG control parameter on the inertia is quantitatively described according to the equivalent inertia constant, so that the calculation of the inverter inertia margin under the VSG control is accurately and effectively realized.

Description

Technical Field

[0001] The invention belongs to the technical field of inverter control, and in particular relates to a method for calculating the inertia margin of an inverter under VSG control. Background Art

[0002] As the proportion of renewable energy power generation continues to increase, the strength of the power grid continues to weaken, and the frequency stability problem becomes increasingly prominent. The grid-type control represented by virtual synchronous generators (VSG) control enables power electronic equipment to provide virtual inertia, which has become an effective way to deal with the frequency stability problem of renewable energy power systems.

[0003] The inertia capacity of the synchronous machine is determined by its inherent structure and cannot be adjusted. However, under VSG control, the inverter output characteristics can be changed by configuring the control parameters, thereby achieving the adjustability of the inertia. Some studies have used the adjustability of VSG inertia to design VSG inertia optimization strategies to optimize the VSG inertia support capacity and improve the system frequency response characteristics.

[0004] An important prerequisite for achieving VSG inertia optimization is to determine the inertia margin of the inverter under VSG control. However, there are still deficiencies in current research on the inertia margin of the inverter under VSG control, and the adjustability boundary of VSG inertia is still unclear. Most current studies start from the perspective of energy balance and propose configurable inertia margins for inverters under different energy storage ratios, ignoring the design constraints of VSG control parameters under the requirements of inverter grid-connected stability. The stability of the inverter grid-connected system under VSG control is closely related to the VSG control parameters. Improper configuration of VSG control parameters may cause the inverter to be unable to stably connect to the grid. However, there is no effective solution to the above situation in the currently disclosed patents. Summary of the invention

[0005] In order to solve the deficiencies of the above-mentioned prior art, the present invention proposes a method for calculating the inertia margin of the inverter under VSG control based on the state space equation, so as to realize the maximum inertia support capacity of the VSG under stability constraints, thereby improving the accuracy and effectiveness of the inertia margin of the inverter under VSG control.

[0006] The present invention solves the technical problem by adopting the following technical solution:

[0007] The invention discloses a method for calculating the inertia margin of an inverter under VSG control based on a state space equation, which comprises the following steps:

[0008] Step 1: Based on the inverter circuit equation and VSG control principle, a mathematical model of the inverter under VSG control is established;

[0009] Step 2: Linearize the mathematical model of the inverter under VSG control, establish the state space equation of the inverter under VSG control, and obtain the state matrix ;

[0010] Step 3: Change VSG control parameters, including: VSG inertia coefficient and VSG damping coefficient The value of VSG control is obtained, and the eigenvalues ​​of the state matrix of the inverter state space equation under VSG control are calculated. The real part of each eigenvalue is less than 0, so as to judge the stability of the inverter under different VSG control parameters and determine the value range of VSG control parameters under stability constraints. ;

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

[0012] (8)

[0013] In formula (8), 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;

[0014] 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.

[0015] The method for calculating the inertia margin of the inverter under VSG control based on the state space equation of the present invention is also characterized in that the step 2 comprises:

[0016] Step 2.1: Linearize the mathematical model of the inverter circuit part, and then use equation (1) to obtain the state space equation of the inverter circuit part:

[0017] (1)

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

[0019] Step 2.2: Linearize the mathematical model of the VSG control part, and use equation (2) to obtain the state space equation of the VSG control part:

[0020] (2)

[0021] In formula (2), A small signal variation representing the measured active power at the inverter output. A small signal variation representing the reactive power measurement at the inverter output. Indicates the small signal change of the active power reference value at the inverter output. The small signal variation of the reactive power reference value at the inverter output. represents the delay constant for power measurement at the inverter output, Indicates the small signal change of the angular frequency control intermediate quantity at the inverter output, Represents the small signal change in the angular frequency at the inverter output, Indicates the rated angular frequency at the inverter output. Indicates the small signal change of the voltage amplitude at the inverter output to control the intermediate quantity, A small signal variation representing the voltage amplitude at the inverter output. represents the VSG inertia coefficient, represents the VSG damping coefficient, Indicates the rated capacity of the inverter. represents the PI controller integral coefficient of the VSG reactive power control loop, represents the PI controller proportional coefficient of the VSG reactive power control loop;

[0022] Step 2.3: Combine the state space equation of the inverter circuit part and the state space equation of the VSG control part, and then use equation (3) to obtain the inverter state space equation under VSG control:

[0023] (3)

[0024] In formula (3), 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:

[0025] (4)

[0026] (5)

[0027] (6)

[0028] (7).

[0029] The electronic device of the present invention includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the inverter inertia margin calculation method under VSG control, and the processor is configured to execute the program stored in the memory.

[0030] The present invention provides a computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and the computer program executes the steps of the method for calculating the inertia margin of the inverter under VSG control when the computer program is executed by a processor.

[0031] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0032] 1. When calculating the inertia margin of the inverter under VSG control, the present invention takes into account the constraints on inertia of the inverter grid-connected stability requirements, which is conducive to ensuring the safe and stable operation of the inverter grid-connected system under VSG control;

[0033] 2. The present invention analyzes the grid-connected stability of the inverter under VSG control based on the state space equation. The effectiveness of the theoretical method has been widely verified by academic research and engineering applications, and the analysis results have a high degree of credibility;

[0034] 3. The present invention quantitatively describes the inverter inertia with an equivalent inertia constant, and the final calculated inertia margin is also given in the form of the maximum value of the equivalent inertia constant. 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 present invention can provide an effective reference for the inertia optimization of the power system containing VSG, so that the inverter under VSG control can play a better inertia support effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 The basic structure of the inverter grid-connected system under VSG control in the present invention;

[0037] Figure 2 is the value range of the VSG control parameter under the stability constraint condition in the embodiment of the present invention;

[0038] Figure 3 is a three-dimensional function surface of VSG equivalent inertia constant under stability constraint conditions in an embodiment of the present invention;

[0039] Figure 4a The inverter simulation result when the control parameters are set within the stability constraint value range in the embodiment of the present invention;

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

[0041] Figure 5 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0042] The technical solution of the present invention will be further described in detail below in conjunction with specific implementation methods and drawings:

[0043] Since the adjustment of VSG inertia depends on the configuration of control parameters, considering the design constraints of VSG control parameters of inverter grid-connected stability, the inverter inertia margin will also be subject to certain restrictions. Therefore, in this embodiment, the present invention proposes a quantitative analysis method for the inertia support capacity of a direct-drive wind power generation system under VSG control. The method is based on the state space equation to analyze the constraints of VSG control parameters under stability requirements, and quantitatively describes the relationship between VSG control parameters and inertia capacity through an equivalent inertia constant expression, and obtains the maximum inertia support capacity of VSG, thereby accurately calculating the inertia margin of the inverter under VSG control under the premise of fully considering the stability constraints. Specifically, Figure 5 As shown, the method is performed in the following steps:

[0044] Step 1: Based on the inverter circuit equation and VSG control principle, establish the mathematical model of the inverter under VSG control. The basic structure of the inverter grid-connected system under VSG control is as follows: Figure 1 As shown;

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

[0046] (1)

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

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

[0049] (2)

[0050] In formula (2), Indicates the active power measurement value, Represents the reactive power measurement value, Indicates the active power reference value, Represents the reactive power reference value, represents the delay constant for power measurement, Indicates the intermediate value of the inverter output angular frequency control. Indicates the rated value of the inverter output angular frequency. Indicates the intermediate value of the inverter output voltage amplitude control. Indicates the voltage amplitude at the inverter output. represents the VSG inertia coefficient, represents the VSG damping coefficient, Indicates the rated capacity of the inverter. represents the integral coefficient of the VSG reactive power control loop PI controller, Represents the proportional coefficient of the VSG reactive power control loop PI controller;

[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 obtain the state matrix;

[0052] Step 2.1: Linearize the mathematical model of the inverter circuit part, and use equation (3) to obtain the state space equation of the inverter circuit part:

[0053] (3)

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

[0055] Step 2.2: Linearize the mathematical model of the VSG control part, and use equation (4) to obtain the state space equation of the VSG control part:

[0056] (4)

[0057] In formula (4), A small signal variation representing the measured active power at the inverter output. A small signal variation representing the reactive power measurement at the inverter output. Indicates the small signal change of the active power reference value at the inverter output. The small signal variation of the reactive power reference value at the inverter output. represents the delay constant for power measurement at the inverter output, Indicates the small signal change of the angular frequency control intermediate quantity at the inverter output, Represents the small signal change in the angular frequency at the inverter output, Indicates the rated angular frequency at the inverter output. Indicates the small signal change of the voltage amplitude at the inverter output to control the intermediate quantity, A small signal variation representing the voltage amplitude at the inverter output. represents the VSG inertia coefficient, represents the VSG damping coefficient, Indicates the rated capacity of the inverter. represents the PI controller integral coefficient of the VSG reactive power control loop, represents the PI controller proportional coefficient of the VSG reactive power control loop;

[0058] Step 2.3: Combine the state space equation of the inverter circuit part and the state space equation of the VSG control part, and then use equation (5) to obtain the inverter state space equation 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 , combined with the inverter's physical parameters, and 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 on the computer-readable storage medium, and the computer program executes the steps of the above method when executed by a processor.

[0072] Example:

[0073] Take the calculation of the inertia margin of the inverter under VSG control with 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 primary frequency modulation related standards. 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 use the real part of each eigenvalue to be less than 0 as the judgment basis to judge the grid-connected system of the inverter under different VSG control parameters, and determine the value range of VSG control parameters under stability constraints. The value range results are plotted as follows Figure 2 shown.

[0077] 2. In In the range, substitute each parameter into formula (7), calculate the corresponding equivalent inertia constant value, and draw Three-dimensional function surface 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 calculation results of the inertia margin. and inertia coefficient Set in and The simulation results are as follows: Figure 4a and Figure 4b As shown in Figure 2, VSG control parameters are designed in When the inverter is connected to the grid, the VSG control parameters are designed to ensure stable grid-connected operation. If the inverter is out of stability, the inverter will become unstable. VSG control parameter value range 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 inertia margin of an inverter under VSG control based on a state space equation, characterized in that: The steps include: Step 1: Based on the inverter circuit equation and 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, and obtain the state matrix ; Step 3: Change VSG control parameters, including: VSG inertia coefficient and VSG damping coefficient The value of VSG control is obtained, and the eigenvalues ​​of the state matrix of the inverter state space equation under VSG control are calculated. The real part of each eigenvalue is less than 0, so as to judge the stability of the inverter under different VSG control parameters and determine the value range of VSG control parameters under stability constraints. ; Step 4: Use formula (8) to construct the VSG equivalent inertia constant , to determine the quantitative relationship between VSG control parameters and inverter inertia under VSG control; (8) In formula (8), 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; 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.

2. The method for calculating the inertia margin of the inverter under VSG control based on the state space equation according to claim 1 is characterized in that: The step 2 comprises: Step 2.1: Linearize the mathematical model of the inverter circuit part, and then use equation (1) to obtain the state space equation of the inverter circuit part: (1) In formula (1), Represents the small signal change of the d-axis current at the inverter output, represents the initial value of the d-axis current at the inverter output, Represents the small signal change of the q-axis current at the inverter output, represents the initial value of the q-axis current at the inverter output, Represents the small signal change of the d-axis current at the output of the filter, represents the initial value of the d-axis current at the filter output, Represents the small signal change of the q-axis current at the output of the filter, represents the initial value of the q-axis current at the filter output, Represents the small signal change of the d-axis voltage at the inverter output, Represents the small signal change of the q-axis voltage at the inverter output, Represents the small signal change of the d-axis voltage at the output of the filter, represents the initial value of the d-axis voltage at the filter output, Represents the small signal change of the q-axis voltage at the output of the filter, represents the initial value of the q-axis voltage at the filter output, Indicates the small signal change of the equivalent grid d-axis voltage, Represents the small signal change of the equivalent grid q-axis voltage, Represents the small signal change in the angular frequency at the inverter output, represents the initial value of the angular frequency at the inverter output, represents the inductance value of the filter, Indicates the inductance value on the grid side, Indicates the capacitance value of the filter; Step 2.2: Linearize the mathematical model of the VSG control part, and use equation (2) to obtain the state space equation of the VSG control part: (2) In formula (2), A small signal variation representing the measured active power at the inverter output. A small signal variation representing the reactive power measurement at the inverter output. Indicates the small signal change of the active power reference value at the inverter output. The small signal variation of the reactive power reference value at the inverter output. represents the delay constant for power measurement at the inverter output, Indicates the small signal change of the angular frequency control intermediate quantity at the inverter output, Represents the small signal change in the angular frequency at the inverter output, Indicates the rated angular frequency at the inverter output. Indicates the small signal change of the voltage amplitude at the inverter output to control the intermediate quantity, A small signal variation representing the voltage amplitude at the inverter output. represents the VSG inertia coefficient, represents the VSG damping coefficient, Indicates the rated capacity of the inverter. represents the PI controller integral coefficient of the VSG reactive power control loop, represents the PI controller proportional coefficient of the VSG reactive power control loop; Step 2.3: Combine the state space equation of the inverter circuit part and the state space equation of the VSG control part, and then use equation (3) to obtain the inverter state space equation under VSG control: (3) In formula (3), 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: (4) (5) (6) (7)。 3. An electronic device, comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the inverter inertia margin calculation method under VSG control as described in claim 1 or 2, and the processor is configured to execute the program stored in the memory.

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

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