A network-configuration type converter transient power angle nonlinear mathematical analysis modeling method

Abstract

The application discloses a kind of network type converter transient power angle nonlinear mathematical analysis modeling methods, this method is directed to the power system containing network type converter, lack of the mathematical analysis model of its transient power angle characteristic problem and proposes.The specific steps realized by the method are as follows: the system model of network type converter single-machine infinite system is constructed;Transient power angle nonlinear mathematical model of network type converter single-machine infinite system is established;Least square method is applied to fitting nonlinear differential equation;Transient power angle nonlinear differential equation after fitting is solved based on multiscale method.The application deduces the mathematical analysis model of network type converter transient power angle using circuit theorem, least square method and multiscale method, can predict the transient power angle response process of network type converter system in advance, compared with traditional phase diagram method, the mathematical analysis model can be analyzed network type converter transient power angle characteristic under different system parameters in large disturbance process.

Description

Technical Field

[0001] This invention relates to the field of stability assessment of new energy power systems, specifically to a nonlinear mathematical analytical modeling method for transient power angle of grid-type converters. Background Technology

[0002] With the large-scale grid connection of new energy sources such as wind and solar power, which use converters as interfaces, converters have gradually become a key factor affecting the stable operation of the power system. Traditional converters use phase-locked loops (PLLs) as synchronization units, achieving synchronization with the grid at the point of common coupling; hence, they are also called grid-connected converters. However, due to their low inertia and low damping characteristics, the large-scale integration of grid-connected converters reduces the grid's regulation capacity, jeopardizing the grid's stable operation. To address this issue, grid-connected converters have received widespread attention, as they have the ability to provide voltage and frequency support to the grid.

[0003] Currently, there is limited research on the transient synchronization stability of grid-connected converters. This is because in microgrids, converters ensure the safety and stability of the microgrid by actively disconnecting from the grid during transients. However, with the future widespread presence of new energy sources in the power system, research on the transient synchronization stability of these new energy sources becomes particularly crucial.

[0004] Current research methods for the transient stability of converters mainly focus on phase diagram analysis and Lyapunov's method, but these methods are essentially mathematical and can only analyze a single set of system parameters. Therefore, it is necessary to study nonlinear mathematical analytical modeling methods for the transient power angle of grid-type converters. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a nonlinear mathematical analytical modeling method for transient power angle of grid-type converters.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A mathematical analytical modeling method for transient power angle nonlinearity of a grid-type converter includes the following steps:

[0008] Construct a system model for a single-unit infinite bus system of a grid-type converter;

[0009] Establish a transient nonlinear mathematical model of the system model;

[0010] The system model is equivalent to a simplified circuit model, and the grid-type converter is equivalent to a controlled voltage source model. Based on Thevenin's circuit theorem, the output electromagnetic power of the converter is solved. The expression for the output electromagnetic power of the converter and the mathematical model of the control loop are combined to obtain the nonlinear mathematical model of the virtual power angle of the system.

[0011] The least squares method is applied to fit the nonlinear differential equation to obtain the nonlinear differential equation of the work angle;

[0012] The nonlinear differential equation of the transient work angle after fitting is solved based on the multi-scale method.

[0013] Furthermore, the mathematical model of the active power control link of the converter in step 2 can be expressed as:

[0014]

[0015] Where P0 represents the power reference value; ω0 represents the reference angular frequency; and ω represents the converter output angular frequency.

[0016] The virtual power angle δ is the grid voltage vector U g The angle between the inverter terminal voltage vector E and the inverter terminal voltage vector E can be expressed as:

[0017] δ=∫(ω - ω0)dt (24)

[0018] Applying circuit theorems, the output electromagnetic power P of the converter e It can be represented as:

[0019]

[0020] Among them U g X represents the amplitude of the infinite grid voltage, E is the amplitude of the converter output voltage, and X represents the amplitude of the voltage across the grid. g This indicates the line reactance.

[0021] In the control structure of a grid-type converter, the response speed of the virtual synchronous control loop is slower than that of the current loop and voltage loop. Therefore, the dynamic performance of the current loop and voltage loop can be ignored during transients. Combining equations (23)-(25), the nonlinear mathematical model of the transient power angle of the grid-type converter is obtained as follows:

[0022]

[0023] Furthermore, in step 3, the least squares method is applied to fit the sine term in the nonlinear mathematical model, and the fitting result is as follows:

[0024] sinx≈ax 4 +bx 3 +cx 2 +dx+e (27)

[0025] Where a = 0.03713, b = -0.2333, c = 0.0534, d = 0.9834, e = 0.001126.

[0026] Replacing the sine function in equation (26) with the fitted polynomial function, we obtain the fitted nonlinear differential equation as follows:

[0027]

[0028] The polynomial coefficients can be expressed as follows:

[0029]

[0030] Furthermore, in step 4, equation (28) is transformed into a nonlinear vibration equation with a small perturbation parameter ε:

[0031]

[0032] in:

[0033]

[0034] Take two time scales, t0 and t1:

[0035] t n =ε n t (32)

[0036] Let the solution take the form of:

[0037] δ(t,ε)=δ0(t)+εδ1(t)+o(ε 2 (33)

[0038] The differential operator can be expressed as:

[0039]

[0040] Substitute equations (33) and (34) into equation (30), and ignore o(ε) 2 From this, we can obtain:

[0041]

[0042] By comparing the coefficients of ε to the same power in equation (35), a series of perturbation equations can be obtained:

[0043]

[0044] From ε 0 The general solution to the corresponding perturbation equation can be obtained as follows:

[0045]

[0046] Where A(t1) are the undetermined coefficients of the first approximate solution. Let be the complex conjugate coefficient of A(t1).

[0047] The steady-state solution of equation (37) can be corrected to the steady-state value after the actual system failure and calculated as follows:

[0048]

[0049] Therefore, the first-order approximate solution of the fitted nonlinear differential equation can be written in the following form:

[0050]

[0051] Substituting the first-order approximate solution into ε 1 From the corresponding perturbation equation, we get:

[0052]

[0053] Where cc is the complex conjugate of the preceding expression.

[0054] To eliminate the long-term term, e in equation (40) iω 0 t 0 and e -iω 0 t The coefficient of 0 is 0, that is

[0055]

[0056] Let the complex coefficient A(t1) be of the following form:

[0057]

[0058] Where a and It is a real function that varies with the time scale t1.

[0059] Substituting equation (42) into equation (41) and separating the real and imaginary parts, we can obtain:

[0060]

[0061] Where a0 and These are the constant coefficients to be determined in the complex coefficients. Based on the initial values ​​of the differential equation: δ(0) = δ0, δ(0) = 0, the constant coefficients a0 and a0 can be obtained.

[0062] By combining equations (39), (42), and (43), we can obtain the first-order approximate analytical solution of the nonlinear differential equation after the transient work angle fitting:

[0063]

[0064] Equation (44) consists of an vibration term and a constant term. The vibration term is a sinusoidal function whose amplitude decays with time and whose frequency increases with time. The constant term is the power angle value corresponding to the new equilibrium point of the system after the disturbance. Equation (44) can be used as an analytical tool to characterize the change of power angle in the transient process of the system when a disturbance occurs.

[0065] The beneficial effects of this invention are:

[0066] 1. The nonlinear mathematical analytical modeling method for transient power angle of grid converter proposed in this invention solves the problem of lack of effective mathematical analytical models for transient synchronous stability analysis of grid converter in the prior art. Based on the established mathematical analytical model, the synchronous stability characteristics of grid converter system in transient process can be quantitatively analyzed.

[0067] 2. The transient power angle nonlinear mathematical analytical modeling method for grid-type converters proposed in this invention, compared with the traditional phase diagram analysis method, can perform mathematical analytical analysis for different system parameters, and has the advantage of versatility, not limited to a single set of system parameters. Attached Figure Description

[0068] The invention will now be further described with reference to the accompanying drawings.

[0069] Figure 1 This is the control block diagram of a single-unit infinite bus system for a grid-type converter to which this invention applies;

[0070] Figure 2 This is a simplified circuit diagram of a single-unit infinite bus system of a grid-type converter to which this invention applies;

[0071] Figure 3 This is a comparison graph of the sine function and the fitted polynomial function;

[0072] Figure 4 This is a comparison diagram of the phase diagram method results and the proposed mathematical analytical model results for the transient power angle characteristics of a grid-type converter. Detailed Implementation

[0073] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0074] This invention proposes a transient modeling method for power systems that include grid-connected and grid-linked converters, applicable to power systems that include both grid-connected and grid-linked converters.

[0075] Figure 1The mathematical analytical modeling method for the transient power angle nonlinearity of the grid-type converter shown consists of the following six steps:

[0076] Step 1: Construct a system model of a single-unit infinite bus system for a grid-type converter;

[0077] like Figure 1 As shown, the single-unit infinite bus system model of the grid-type converter consists of the grid-type converter passing through an LC filter, and then through the line reactance L. g It is connected to an infinite power grid. The active power control loop in the grid-type converter control structure adopts a virtual synchronous control strategy, and the reactive power loop adopts a droop control strategy. The active and reactive power control loops generate phase and amplitude commands for the voltage reference value; after passing through the voltage and current loop, they generate drive signals, which are fed into the PWM generator to realize the control function.

[0078] A grid-type converter single-unit infinite voltage system contains an infinite grid-side voltage vector U. g Converter terminal voltage vector E, filter inductor L f Line impedance L g I g P represents the output current of the converter after filtering. e and Q e These represent the instantaneous output active power and reactive power, respectively; P0 is the power reference value set by the converter; in the active power control loop, D is a virtual damping parameter to realize the frequency regulation function; J is a virtual inertia parameter to simulate inertial characteristics; the reactive power control loop adopts droop control mode.

[0079] Step 2: Establish a transient nonlinear mathematical model of the single-unit infinite bus system of the grid-type converter;

[0080] based on Figure 1 The control structure with an active power loop in the converter can be represented mathematically as follows:

[0081]

[0082] Where J is the virtual inertia parameter; D is the virtual damping parameter; ω0 represents the reference angular frequency; ω represents the converter output angular frequency; t represents time; P0 represents the power reference value; P e This refers to the instantaneous output of active power.

[0083] Define the difference between the grid voltage phase angle and the converter output voltage phase angle as the virtual power angle δ, i.e., the grid voltage vector U. g The angle between the inverter terminal voltage vector E and the inverter terminal voltage vector E can be expressed as:

[0084] δ=∫(ω - ω0)dt (46)

[0085] The system model in step 1 is equivalent to a simplified circuit model, as follows: Figure 2 As shown, the grid-type converter is equivalent to a controlled voltage source model. Based on Thevenin's circuit theorem, the converter output electromagnetic power P e It can be represented as:

[0086]

[0087] Among them U g X represents the amplitude of the infinite grid voltage, E is the amplitude of the converter output voltage, and X represents the amplitude of the voltage across the grid. g This indicates the line reactance.

[0088] In the control structure of a grid-type converter, the response speed of the virtual synchronous control loop is slower than that of the current loop and voltage loop. Therefore, the dynamic performance of the current loop and voltage loop can be ignored during transients. By combining the expression for the output electromagnetic power of the converter with the mathematical model of the control loop, we obtain the nonlinear mathematical model of the system power angle, i.e., by combining equations (45)-(47), we obtain the nonlinear mathematical model of the transient power angle of the grid-type converter as follows:

[0089]

[0090] Step 3: Apply the least squares method to fit the nonlinear differential equation;

[0091] The least squares method is applied to fit the sine term in the nonlinear mathematical model to obtain the fitted polynomial function, and the curves before and after fitting are compared as follows: Figure 3 As shown, the fitting result is as follows:

[0092] sinx≈ax 4 +bx 3 +cx 2 +dx+e (49)

[0093] Where a = 0.03713, b = -0.2333, c = 0.0534, d = 0.9834, e = 0.001126.

[0094] Substituting the polynomial function with a sine function into the nonlinear differential equation of the work angle, we obtain the fitted nonlinear differential equation of the work angle. That is, replacing the sine function in equation (48) with the fitted polynomial function, we obtain the fitted nonlinear differential equation as follows:

[0095]

[0096] The polynomial coefficients A, B, and C can be expressed as:

[0097]

[0098] In the polynomial parametric expression, P0 is the power reference value; J is the virtual inertia parameter; D is the virtual damping parameter; U g X represents the amplitude of the infinite grid voltage; E is the amplitude of the converter output voltage; g This indicates the line reactance.

[0099] Step 4: Solve the fitted transient nonlinear differential equation of work angle based on the multi-scale method;

[0100] The fitted nonlinear differential equation (50) of the work angle obtained in step 3 is transformed into a nonlinear vibration equation with a small perturbation parameter ε:

[0101]

[0102] Where β, γ, θ, and Δ represent the new polynomial coefficients, which are expressed by the polynomial coefficients A, B, and C, the small perturbation parameter ε, and the fitted curve values ​​a, b, c, and d.

[0103]

[0104] Take two time scales, t0 and t1:

[0105]

[0106] Assume the first-order analytical solution has the following form:

[0107] δ(t,ε)=δ0(t)+εδ1(t)+o(ε 2 (55)

[0108] The differential operator can be expressed as:

[0109]

[0110] Where D0, D1, and D2 represent the partial derivatives with respect to t0, t1, and t2, respectively.

[0111] Substitute equations (55) and (56) into equation (52), and ignore o(ε). 2 From this, we can obtain:

[0112]

[0113] By comparing the coefficients of ε to the same power in equation (57), a series of perturbation equations can be obtained:

[0114]

[0115] From ε 0 The general solution to the corresponding perturbation equation can be obtained as follows:

[0116]

[0117] Where A(t1) are the undetermined coefficients of the first approximate solution. Let be the complex conjugate coefficient of A(t1).

[0118] The steady-state solution of equation (59) can be modified to obtain the steady-state value after the actual system failure, and can be calculated as follows:

[0119]

[0120] Therefore, the first-order approximate solution of the fitted nonlinear differential equation can be written in the following form:

[0121]

[0122] Substituting the first-order approximate solution into ε 1 From the corresponding perturbation equation, we get:

[0123]

[0124] Where cc is the complex conjugate of the preceding expression.

[0125] Eliminating the long-term terms in the perturbation equation yields a first-order approximate mathematical analytical model of the work angle; to eliminate the long-term terms, e in equation (62) iω 0 t 0 and e -iω 0 t The coefficient of 0 is 0, that is

[0126]

[0127] Let the complex coefficient A(t1) be of the following form:

[0128]

[0129] Where α and Let be a real function that varies with time scale t1; i represents a complex number.

[0130] Substituting equation (64) into equation (63) and separating the real and imaginary parts, we can obtain:

[0131]

[0132] Where α0 and These are the constant coefficients to be determined in the complex coefficients. Based on the initial values ​​of the differential equation: δ(0) = δ0, δ(0) = 0, the constant coefficients α0 and α0 can be obtained.

[0133] By combining equations (59), (64), and (65), we can obtain the first-order approximate analytical solution of the nonlinear differential equation after the transient work angle fitting:

[0134]

[0135] Equation (66) consists of an vibration term and a constant term. The vibration term is a sinusoidal function whose amplitude decays with time and whose frequency increases with time. The constant term is the power angle value corresponding to the new equilibrium point of the system after the disturbance. Equation (66) can be used as an analytical tool to characterize the change of power angle during the transient process of a system when a disturbance occurs.

[0136] Verify the accuracy of the approximate analytical model as follows: Figure 4 As shown, the proposed mathematical analytical model results are basically consistent with the phase diagram results for the transient response of the grid-type converter.

[0137] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0138] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A mathematical analytical modeling method for transient power angle nonlinearity of a grid-type converter, characterized in that, Includes the following steps: Construct a system model for a single-unit infinite bus system of a grid-type converter; The system model is equivalent to a simplified circuit model, and the grid converter is equivalent to a controlled voltage source model. Based on Thevenin's circuit theorem, the output electromagnetic power of the grid converter is solved. The expression for the output electromagnetic power of the grid converter and the mathematical model of the active power control link of the control loop are combined to obtain the nonlinear mathematical model of the virtual power angle of the system. The least squares method is applied to fit the nonlinear differential equation to obtain the nonlinear differential equation of the work angle; Solving the fitted transient work angle nonlinear differential equation based on the multi-scale method; The method for constructing the nonlinear mathematical model of the system's virtual power angle includes the following steps: Mathematical model of the active power control loop of the converter: （1） Where J is the virtual inertia parameter; D is the virtual damping parameter; ω 0 Indicates the reference angular frequency; ω Indicates the output angular frequency of the converter; t represents time; P 0 Indicates a power reference value; P e For instantaneous output active power The virtual power angle δ is the grid voltage vector. U g and inverter terminal voltage vector E The included angle is expressed as: （2） Converter output electromagnetic power P e Represented as: （3） in U g This represents the voltage amplitude of an infinitely large power grid. E The output voltage amplitude of the converter. X g Indicates the line reactance; Combining equations (1)-(3), the nonlinear mathematical model of the virtual power angle of the grid-type converter system is obtained as follows: （4）。 2. The nonlinear mathematical analytical modeling method for transient power angle of a grid-type converter according to claim 1, characterized in that, The active power control loop in the grid-type converter control structure adopts a virtual synchronous control strategy, and the reactive power loop adopts a droop control strategy. The active and reactive power control loops generate phase and amplitude commands for voltage reference values. After passing through the voltage and current loops, they generate drive signals, which are fed into the PWM generator to realize the control function.

3. The nonlinear mathematical analytical modeling method for transient power angle of a grid-type converter according to claim 1, characterized in that, In the system model described, the inverter is connected to a filter inductor, which outputs the filtered current of the converter; the filtered current of the converter is then output to the power grid after passing through the line impedance.

4. The nonlinear mathematical analytical modeling method for transient power angle of a grid-type converter according to claim 2, characterized in that, The active power control loop includes virtual damping parameters and virtual inertia parameters; the virtual damping parameters are used to implement frequency regulation; and the virtual inertia parameters are used to simulate inertial characteristics.

5. The nonlinear mathematical analytical modeling method for transient power angle of a grid-type converter according to claim 1, characterized in that, The application of the least squares method to fit the nonlinear differential equation yields the following fitting result: （5） Where a=0.03713, b=-0.2333, c=0.0534, d=0.9834, e=0.001126. Replacing the sine function in equation (4) with the fitted polynomial function, we obtain the fitted nonlinear differential equation as follows: （6） The polynomial coefficients are respectively represented as: （7）。 6. The nonlinear mathematical analytical modeling method for transient power angle of a grid-type converter according to claim 1, characterized in that, Equation (6) is transformed into a nonlinear vibration equation with a small perturbation parameter ε: （8） in: （9） Where β, γ, θ, and Δ represent the new polynomial coefficients, which are expressed by the polynomial coefficients A, B, and C, the small perturbation parameter ε, and the fitted curve values ​​a, b, c, and d. Take two time scales, t0 and t1: （10） Let the solution take the form of: （11） The differential operator can be expressed as: （12） D 0 , D 1 and D 2 They represent respectively to t 0 , t 1 and t 2 Find the partial derivatives; Substitute equations (11) and (12) into equation (8), and ignore o(ε). 2 From this, we can obtain: （13） Comparing the coefficients of ε to the same power in equation (13), we obtain the perturbation equation: （14） From ε 0 The corresponding perturbation equation, the general solution of which is: （15） Where A(t1) are the undetermined coefficients of the first approximate solution. Let be the complex conjugate coefficient of A(t1).

7. The nonlinear mathematical analytical modeling method for transient power angle of a grid-type converter according to claim 6, characterized in that, The steady-state solution of equation (15) is modified to the steady-state value after the actual system fault, and is calculated as follows: （16） Therefore, the first-order approximate solution of the fitted nonlinear differential equation can be written in the following form: （17） Substituting the first-order approximate solution into ε 1 From the corresponding perturbation equation, we get: （18） Where cc is the complex conjugate of the preceding expression; In formula (18) The coefficient is 0, that is （19） Let the complex coefficient A(t1) be of the following form: （20） in φ and φ are real functions that vary with the time scale t1; Substituting equation (20) into equation (19) and separating the real and imaginary parts, we get: （21） in φ and φ0 are the constant coefficients to be determined in the complex coefficients; based on the initial values ​​of the differential equation: The constant coefficients can be obtained. and φ0; By combining equations (15), (20), and (21), we can obtain the first-order approximate analytical solution of the fitted transient nonlinear differential equation of work angle: （22） Equation (22) consists of a vibration term and a constant term. The vibration term is a sine function whose amplitude decays with time and whose frequency increases with time. The constant term is the power angle value corresponding to the new equilibrium point position of the system after the disturbance. Equation (22) serves as an analytical tool to characterize the change of power angle in the transient process when the system is disturbed.

8. A computer-readable storage medium storing computer instructions, characterized in that, When the instructions are executed by a computer, they implement the method described in any one of claims 1 to 7.

9. The application of the method according to any one of claims 1 to 7 in the transient synchronous stability assessment of grid-type converters.

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