A VSG power decoupling control method and system considering inner loop and line dynamics

Abstract

A VSG power decoupling control method and system considering inner loop and line dynamics is disclosed. In this method, the equivalent output impedance function of the VSG incorporating the dynamic characteristics of the inner loop and the dynamic impedance function of the transmission line are established, and then connected in series to obtain the total equivalent impedance function, thereby establishing a nonlinear dynamic equation for power transmission. This equation is linearized at the steady-state operating point to obtain the small-signal transfer function matrix for power transmission. Based on this matrix, a cross-feedforward decoupling branch is constructed and the decoupling coefficient is calculated, while a reactive power steady-state error compensation coefficient is introduced. The internal potential amplitude and power angle signals are acquired in real time, and the decoupling feedforward signal is obtained through weighted calculation. This signal is then superimposed on the reactive power compensation signal at the output of the corresponding control loop to achieve power decoupling control. This application aims to improve the dynamic accuracy and system stability of virtual synchronous machine power decoupling control under large disturbance conditions in weak power grids.

Description

Technical Field

[0001] This application belongs to the field of power electronic control, and in particular relates to a VSG power decoupling control method and system that takes into account the inner loop and line dynamics. Background Technology

[0002] To address the issues of traditional grid-connected inverters lacking inertia and damping, and being unable to effectively support grid voltage and frequency, virtual synchronous machine (VSM) technology emerged. By simulating the rotor motion equations and excitation characteristics of a synchronous generator, it endows the inverter with external characteristics similar to a rotating electrical machine. However, VSM is essentially a control strategy based on droop characteristics. In weak grid environments such as low-voltage distribution networks where distributed energy resources are typically connected, or at the ends of long-distance transmission lines, the line impedance often exhibits non-negligible resistive characteristics, resulting in inductive and resistive characteristics. This leads to a complex and strong coupling relationship between the active and reactive power output of the VSM; that is, adjusting the active power causes fluctuations in reactive power, and vice versa. This power coupling phenomenon affects the dynamic regulation performance and operational stability of the system.

[0003] Related technologies typically employ power decoupling control methods based on electromagnetic models. This method considers the electromagnetic transients caused by the inductance and resistance of transmission lines when analyzing system characteristics. It calculates decoupling compensation components by introducing a line impedance model, thus canceling power coupling terms in the control loop. When constructing its control model, it usually assumes that "the inner loop bandwidth is much larger than the power loop bandwidth," treating the voltage and current loops as ideal unity-gain elements or simply as delay elements. Therefore, when deriving the decoupling algorithm, the dynamic characteristics of the voltage-current dual-loop control system are directly ignored. It is assumed that the inverter can instantaneously and error-free track the voltage command given by the power loop, thereby simplifying the design complexity of the control system and achieving a certain degree of static decoupling.

[0004] However, under conditions of large disturbances such as grid voltage drops or sudden load changes, when the system encounters disturbances and needs to quickly adjust power, the voltage and current loops in the actual physical system are limited by PI controller parameters, filter characteristics, and switching frequency. Their dynamic response process objectively exists and cannot be ignored. This results in a dynamic deviation in amplitude and phase between the actual output terminal voltage of the inverter and the ideal command. Consequently, the decoupling compensation amount derived based on the ideal inner loop assumption does not match the compensation amount actually required by the system. This mismatch in dynamic characteristics will cause the control signal originally intended to eliminate coupling to fail in the transient process. Not only is it difficult to suppress power fluctuations, but it may also change the equivalent output impedance characteristics of the system, easily inducing continuous power oscillations or even causing the system to disconnect from the grid due to instability. Summary of the Invention

[0005] This application provides a VSG power decoupling control method and system that takes into account the inner loop and line dynamics, in order to improve the dynamic accuracy and system stability of virtual synchronous machine power decoupling control under large disturbance conditions in weak power grids.

[0006] Firstly, this application provides a VSG power decoupling control method that considers both inner loop and line dynamics. Based on the circuit parameters of the virtual synchronizer and the voltage and current dual closed-loop control parameters, an equivalent output impedance function of the virtual synchronizer, incorporating the inner loop dynamic characteristics, is established. Based on the impedance parameters of the transmission line, a dynamic impedance function of the transmission line is established. The equivalent output impedance function of the virtual synchronizer and the dynamic impedance function are superimposed in series to obtain the total equivalent impedance function. Based on the total equivalent impedance function, nonlinear dynamic equations describing the active and reactive power output of the virtual synchronizer are established. The nonlinear dynamic equations are linearized at a preset steady-state operating point to obtain the power transmission small-signal transfer function matrix. A cross-feedforward decoupling branch containing undetermined decoupling coefficients is constructed. Based on the power transmission small-signal transfer function... The function matrix is ​​used to calculate the undetermined decoupling coefficients, with the constraint that the mutual coupling transfer function term between active and reactive power is zero. Based on the attenuation ratio of the open-loop gain of the reactive power control loop after adding the cross-feedforward decoupling branch, the reactive power steady-state error compensation coefficient is calculated. The internal potential amplitude signal and power angle signal of the virtual synchronous machine are acquired in real time. The internal potential amplitude signal and power angle signal are weighted using the decoupling coefficients to obtain the active power decoupling feedforward signal and the reactive power decoupling feedforward signal. The reactive power reference value or reactive power feedback value is corrected using the reactive power steady-state error compensation coefficient to generate the reactive power compensation signal. The active power decoupling feedforward signal is superimposed on the output of the active power control loop of the virtual synchronous machine. The reactive power decoupling feedforward signal and the reactive power compensation signal are superimposed on the output of the reactive power control loop of the virtual synchronous machine.

[0007] By adopting the above technical solution, and establishing the VSG equivalent output impedance function and transmission line dynamic impedance function that include the inner loop dynamic characteristics, the total equivalent impedance function is obtained, enabling the power decoupling control method to more accurately reflect the dynamic characteristics of the system. The nonlinear dynamic equations and power transmission small-signal transfer function matrix established based on this more closely resemble the dynamic response characteristics of the actual system. By constructing cross-feedforward decoupling branches and calculating the decoupling coefficients, the mutual interference between active and reactive power can be reduced. Introducing a reactive power steady-state error compensation coefficient can reduce the reactive power control performance degradation caused by the introduction of decoupling branches. The decoupling feedforward signal obtained by real-time signal acquisition and weighted calculation, superimposed on the corresponding control loop output, can improve the control accuracy of the system during the dynamic process of power output and reduce the overshoot and settling time of power output.

[0008] In conjunction with some implementations of the first aspect, in some implementations, based on the circuit parameters and voltage-current dual closed-loop control parameters of the virtual synchronizer, an equivalent output impedance function of the virtual synchronizer including the inner loop dynamic characteristics is established. Specifically, this includes: using the dynamic phasor method, decomposing the circuit parameters and voltage-current dual closed-loop control parameters of the virtual synchronizer through time-varying Fourier series to obtain the inner loop control model and the original output impedance model; selecting a frequency including the power coupling frequency band as the order reduction frequency threshold; within the order reduction frequency threshold, deleting the high-frequency dynamic components in the inner loop control model and the original output impedance model to obtain the order-reduced inner loop transfer function and the order-reduced output impedance; equating the order-reduced inner loop transfer function to the influence on the voltage source, and determining the order-reduced output impedance as the equivalent output impedance function of the virtual synchronizer, thus forming an equivalent output impedance function of the virtual synchronizer including the inner loop dynamic characteristics.

[0009] By employing the above technical solution, the VSG circuit parameters and control parameters are decomposed using time-varying Fourier series decomposition via the dynamic phasor method, allowing for a more detailed description of the system's inner-loop dynamic characteristics. By selecting a frequency containing the power coupling band as the reduction frequency threshold, and removing high-frequency dynamic components within this threshold, the reduced-order inner-loop transfer function and output impedance retain the frequency components that significantly influence power coupling characteristics while simplifying the complexity of the system's mathematical model. Equivalently representing the reduced-order inner-loop transfer function as an effect on a voltage source allows the equivalent output impedance function to reflect the impact of inner-loop control on the system's impedance characteristics, improving the accuracy of impedance modeling.

[0010] In conjunction with some implementations of the first aspect, in some implementations, nonlinear dynamic equations describing the active and reactive power output of the virtual synchronous machine are established based on the total equivalent impedance function. Specifically, this includes: establishing a complex frequency domain voltage balance equation that includes the internal potential, grid voltage, and total equivalent impedance function in the Thevenin equivalent output model of the virtual synchronous machine, based on Kirchhoff's voltage law; determining the dynamic phasor expression of the output current of the virtual synchronous machine based on the complex frequency domain voltage balance equation; constructing the complex power expression of the virtual synchronous machine output using the dynamic phasor expression and the dynamic phasor expression of the output voltage of the virtual synchronous machine; and separating the complex power expression into real and imaginary parts to obtain nonlinear dynamic equations with the power angle and internal potential amplitude as input variables and active and reactive power as output variables, respectively.

[0011] By employing the above technical solution, a complex frequency domain voltage balance equation is established based on Kirchhoff's voltage law, incorporating internal potential, grid voltage, and the total equivalent impedance function. The dynamic phasor expression for the output current is derived, leading to the construction of an output complex power expression. This allows the established nonlinear dynamic equation for power transmission to reflect the system's transient dynamic characteristics. Separating the complex power expression into real and imaginary parts yields a nonlinear dynamic equation with power angle and internal potential amplitude as input variables, and active and reactive power as output variables. This allows for a more accurate description of the influence mechanism of input variables on output power. This dynamic phasor-based modeling method improves the accuracy of describing the dynamic characteristics of power transmission.

[0012] In conjunction with some implementations of the first aspect, in some implementations, based on the power transmission small-signal transfer function matrix, and using the constraint that the mutual coupling transfer function term between active power and reactive power is zero, the undetermined decoupling coefficients are calculated. Specifically, this includes: establishing a system containing intermediate variables. and The decoupling control equation is represented as the product of the decoupling matrix and the input state variables. The decoupling matrix is:

[0013]

[0014] and The decoupling coefficients are to be determined.

[0015] Multiply the decoupling matrix by the power transmission small-signal transfer function matrix to establish the open-loop transfer function matrix equation of the system including the decoupling element. The open-loop transfer function matrix equation of the system is as follows:

[0016]

[0017] and These are the small-signal disturbances for active power and reactive power, respectively. and These are the small-signal disturbances of the power angle and internal potential, respectively. , , and These are the elements in the small-signal transfer function matrix for power transmission; set the off-diagonal elements in the result of the open-loop transfer function matrix equation of the system to zero to calculate the undetermined decoupling coefficients.

[0018] By adopting the above technical solution, a decoupling control equation including intermediate variables is established, and the decoupling matrix is ​​multiplied by the power transmission small-signal transfer function matrix, thus constructing the system open-loop transfer function matrix equation containing the decoupling element. The undetermined decoupling coefficients are solved using the constraint that off-diagonal elements are zero, making the decoupled system transfer function matrix approximately diagonal. This decoupling method based on the transfer function matrix can reduce the impact of active power control on reactive power output, while also reducing the interference of reactive power control on active power output.

[0019] In conjunction with some implementation methods of the first aspect, in some implementation methods, the undetermined decoupling coefficients are calculated, and the resulting calculation expression is:

[0020]

[0021] In the above function, The coupling transfer function characterizing the internal potential to active power. The principal transfer function characterizing the work angle with respect to active power. The coupling transfer function characterizing the power angle with respect to reactive power. The main transfer function characterizing the internal potential to reactive power.

[0022] By adopting the above technical solution, and setting the decoupling coefficient to a specific ratio between the main transfer function and the coupled transfer function, the cross-coupling effect in the power control process can be reduced. When the power angle changes, through... The decoupling effect can reduce the interference of power angle changes on reactive power; when the internal potential amplitude changes, it can be decoupled through... The decoupling effect can reduce the interference of internal potential amplitude changes on active power. This decoupling design method based on transfer function ratio makes the decoupling effect adaptive to system parameters and operating conditions, maintaining a good decoupling effect under different operating conditions.

[0023] In some embodiments, in conjunction with the first aspect, the method further includes: constructing an electromagnetic transient simulation model and configuring the circuit parameters and control parameters of the electromagnetic transient simulation model so that the electromagnetic transient simulation model uses the same parameters as those used when establishing the equivalent output impedance function of the virtual synchronous machine and the dynamic impedance function of the transmission line; establishing a theoretical calculation model based on the power transmission small-signal transfer function matrix; applying a step disturbance of the same active power reference value to the electromagnetic transient simulation model and the theoretical calculation model at the same steady-state operating point; collecting the active power and reactive power output of the electromagnetic transient simulation model as measured response curves, and collecting the active power and reactive power output of the theoretical calculation model as theoretical response curves; calculating the goodness of fit between the measured response curve and the theoretical response curve in the time domain; and determining that the power transmission small-signal transfer function matrix is ​​accurate if the goodness of fit is greater than a preset threshold.

[0024] By adopting the above technical solution, establishing an electromagnetic transient simulation model and a theoretical calculation model, and comparing and verifying them under the same operating conditions, the accuracy of the small-signal transfer function matrix for power transmission can be improved. Applying the same active power reference value step disturbance to both models, and comparing the output power response curves, the ability of the theoretical model to describe the dynamic characteristics of the actual system can be verified. Based on the goodness-of-fit criterion of the time-domain response curve, the accuracy of the theoretical model can be quantitatively evaluated. This verification method comprehensively considers the dynamic response characteristics of the system at various time points, improves the reliability of model verification, and helps to obtain a more accurate description of power transmission characteristics.

[0025] In conjunction with some implementation methods of the first aspect, in some implementation methods, the goodness of fit between the measured response curve and the theoretical response curve in the time domain is calculated. Specifically, this includes: unifying the measured response curve and the theoretical response curve to the same time axis for sampling to obtain the corresponding measured data sequence and theoretical data sequence; calculating the difference between the measured data sequence and the theoretical data sequence at each sampling point, and calculating the norm of the difference as an error statistic; calculating the norm of the deviation of the measured data sequence from its mean as a benchmark statistic; and determining the goodness of fit as the ratio of the error statistic to the benchmark statistic.

[0026] By adopting the above technical solution, sampling the measured and theoretical response curves on a unified time axis, and establishing a goodness-of-fit evaluation index based on norm calculation, the accuracy of model validation is improved. Using the deviation norm of the measured data sequence as a benchmark statistic reduces the influence of data dimensions, making the evaluation results relative and universal. This evaluation method based on mathematical statistics is objective, can more accurately reflect the ability of the theoretical model to describe the characteristics of the actual system, and improves the credibility of model validation.

[0027] In a second aspect, embodiments of this application provide a VSG power decoupling control system that takes into account inner loop and line dynamics. The VSG power decoupling control system includes: one or more processors and a memory; the memory is coupled to one or more processors, the memory is used to store computer program code, the computer program code includes computer instructions, and one or more processors call the computer instructions to cause the system to perform the method described in the first aspect and any possible implementation thereof.

[0028] Thirdly, embodiments of this application provide a computer-readable storage medium including instructions that, when executed on a system, cause the system to perform the method described in the first aspect and any possible implementation thereof.

[0029] Fourthly, embodiments of this application provide a computer program product that, when run on a system, causes the system to execute the method described in any possible implementation of the first aspect.

[0030] One or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages:

[0031] 1. This application provides a VSG power decoupling control method that considers both inner loop and line dynamics. By establishing the VSG equivalent output impedance function and transmission line dynamic impedance function that incorporate the inner loop dynamic characteristics, the total equivalent impedance function is obtained, enabling the power decoupling control method to more accurately reflect the dynamic characteristics of the system. The nonlinear dynamic equations and power transmission small-signal transfer function matrix established based on this method more closely resemble the dynamic response characteristics of the actual system. By constructing cross-feedforward decoupling branches and calculating the decoupling coefficients, the mutual interference between active and reactive power can be reduced. Introducing a reactive power steady-state error compensation coefficient can reduce the reactive power control performance degradation caused by the introduction of decoupling branches. The decoupling feedforward signal obtained by real-time signal acquisition and weighted calculation, superimposed on the corresponding control loop output, can improve the control accuracy of the system during the power output dynamic process and reduce the power output overshoot and settling time.

[0032] 2. This application provides a VSG power decoupling control method that considers both inner-loop and line dynamics. By establishing an electromagnetic transient simulation model and a theoretical calculation model, and comparing and verifying them under the same operating conditions, the accuracy of the small-signal transfer function matrix for power transmission can be improved. Applying the same active power reference value step disturbance to both models and comparing the output power response curves can verify the ability of the theoretical model to describe the dynamic characteristics of the actual system. Based on the goodness-of-fit criterion of the time-domain response curve, the accuracy of the theoretical model can be quantitatively evaluated. This verification method comprehensively considers the dynamic response characteristics of the system at various time points, improves the reliability of model verification, and helps to obtain a more accurate description of power transmission characteristics. Attached Figure Description

[0033] Figure 1 This is a flowchart illustrating a VSG power decoupling control method that takes into account the inner loop and line dynamics in an embodiment of this application.

[0034] Figure 2 This is another schematic flowchart of a VSG power decoupling control method that takes into account the inner loop and line dynamics in an embodiment of this application.

[0035] Figure 3 This is a schematic diagram of the physical device structure of a VSG power decoupling control system that takes into account the inner loop and line dynamics, provided in an embodiment of this application. Detailed Implementation

[0036] The terminology used in the following embodiments of this application is for the purpose of describing particular embodiments only and is not intended to be limiting of this application. As used in the specification and appended claims of this application, the singular expressions “a,” “an,” “the,” “the,” “the,” and “this” are intended to include the plural expressions as well, unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used in this application refers to any or all possible combinations including one or more of the listed items.

[0037] Hereinafter, the terms "first" and "second" are used for descriptive purposes only and should not be construed as implying or suggesting relative importance or implicitly indicating the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature, and in the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more.

[0038] The following example is used in conjunction with Figure 1 This application describes a VSG power decoupling control method that takes into account the inner loop and line dynamics in its embodiments:

[0039] Please see Figure 1This is a flowchart illustrating a VSG power decoupling control method that takes into account the inner loop and line dynamics in an embodiment of this application.

[0040] S101. Based on the circuit parameters of the virtual synchronous machine and the voltage and current dual closed-loop control parameters, establish the equivalent output impedance function of the virtual synchronous machine that includes the inner loop dynamic characteristics.

[0041] The system establishes an equivalent output impedance function of the virtual synchronous machine, incorporating the dynamic characteristics of the inner loop, based on the circuit parameters and voltage-current dual closed-loop control parameters of the virtual synchronous machine. Specifically, this involves: using the dynamic phasor method to decompose the circuit parameters and voltage-current dual closed-loop control parameters of the virtual synchronous machine through time-varying Fourier series decomposition to obtain the inner loop control model and the original output impedance model; selecting a frequency including the power coupling band as the order reduction frequency threshold; within the order reduction frequency threshold, deleting high-frequency dynamic components from the inner loop control model and the original output impedance model to obtain the reduced inner loop transfer function and the reduced output impedance; treating the reduced inner loop transfer function as an equivalent effect on the voltage source, and determining the reduced output impedance as the equivalent output impedance function of the virtual synchronous machine, thus creating an equivalent output impedance function of the virtual synchronous machine that incorporates the dynamic characteristics of the inner loop.

[0042] The circuit parameters of a virtual synchronous machine encompass physical quantities such as the inverter-side filter inductance, filter capacitor, grid-side inductance, and parasitic resistance of the lines. These parameters determine the system's hardware electrical characteristics. The voltage and current dual-loop control parameters involve the proportional coefficient, integral coefficient, and possible resonant controller parameters in the inner-loop control strategy, forming the underlying fast adjustment mechanism of the virtual synchronous machine. The equivalent output impedance function of the virtual synchronous machine is a complex frequency domain function used to describe the dynamic ratio between the port voltage response and the output current response under different frequency disturbances. The inner-loop dynamic characteristics refer to the transient response characteristics of the voltage and current loops as their state variables change over time when subjected to disturbances; this characteristic is particularly significant at high frequencies. The dynamic phasor method is a modeling method based on generalized averaging theory. It captures the envelope dynamics of the system by preserving the dynamic changes of the main coefficients in the Fourier series of the signal. Time-varying Fourier series decomposition is the process of decomposing a time-domain signal into complex Fourier coefficients that vary with time. The order reduction frequency threshold is a preset frequency limit used to distinguish between low-frequency dominant dynamics and high-frequency secondary dynamics. This threshold is typically selected at the upper limit of the frequency band containing significant power coupling effects. The reduced inner-loop transfer function and output impedance refer to simplified mathematical models that retain the main characteristic values ​​of the system after ignoring fast-decaying modes above the order reduction frequency threshold.

[0043] When establishing the equivalent output impedance function of a virtual synchronous machine containing the dynamic characteristics of the inner loop in the specific implementation of the system, various technical means can be adopted. One specific implementation method is dynamic phasor modeling technology based on the state-space averaging method. First, based on the circuit topology and the double-loop control block diagram, the system writes out the full-order state-space differential equations in the stationary or rotating coordinate system. Then, the system applies a dynamic phasor transformation operator to transform the original time-domain differential equations into complex differential equations with dynamic phasors as variables. During this process, the system identifies the low-frequency band where power coupling mainly occurs and sets this range as a reference for the order reduction frequency threshold. Within this threshold range, the system uses singular perturbation methods or residual processing techniques to zero out or algebraize the small time constant terms corresponding to high-frequency parasitic parameters, thereby eliminating the corresponding high-frequency eigenvalues ​​in the state matrix and obtaining the reduced-order inner-loop transfer function. Another implementation method is modeling technology based on frequency domain response fitting. The system can calculate the original wideband output impedance frequency response data by injecting a frequency sweep signal into the simulation or physical model of the virtual synchronizer and measuring the voltage and current responses at the ports. Next, using a system identification algorithm, within a range of interest based on the reduced-order frequency threshold, the system fits a low-order rational fractional transfer function to approximate the original frequency response curve. Finally, the system determines this reduced-order impedance model as the equivalent output impedance function of the virtual synchronizer.

[0044] S102. Based on the impedance parameters of the transmission line, establish the dynamic impedance function of the transmission line.

[0045] The system first clarifies the physical meaning of the impedance parameters of the transmission line and their role in dynamic analysis. The impedance parameters of the transmission line mainly include the series resistance, series inductance, and, in long-distance power transmission or cable transmission, the non-negligible parallel conductance and parallel capacitance. These parameters are not constant and are affected by ambient temperature, skin effect, and proximity effect. The dynamic impedance function of the transmission line differs from the traditional power frequency steady-state impedance; it is a function of complex frequency, describing the voltage and current response of the line under transient processes, frequency shifts, or non-sinusoidal waveform excitation. The purpose of establishing this function is to capture the energy storage and release processes of the line inductance and capacitance during power fluctuations. These dynamic processes introduce additional phase lag and amplitude attenuation, directly affecting the transient characteristics of the virtual synchronous machine's output power. In this step, the "dynamic" aspect that the system needs to handle specifically refers to the manifestation of the line parameters in the complex frequency domain, rather than the parameters themselves changing slowly over time.

[0046] When establishing the dynamic impedance function of a transmission line, the system can employ lumped parameter modeling techniques. For short- or medium-short-distance connections, the system ignores the distributed parameter effects of the line, equating it to a series combination of resistors and inductors or a piconet equivalent circuit including capacitance to ground. In the complex frequency domain, if a resistor-inductor model is used, the system directly constructs the impedance function. If modeling in the context of dynamic phasors is considered, the system replaces complex variables with complex variables containing the fundamental angular frequency, thus obtaining the line impedance matrix or transfer function in a rotating coordinate system or dynamic phasor domain. Another implementation method is to use distributed parameter approximation modeling techniques. For longer cables or transmission lines, the system describes the distribution of voltage and current along the line based on telegraph equations. Since the exact solution in hyperbolic function form is too complex in control design, the system uses Taylor series expansion or Pad approximation to approximate transcendental functions such as the hyperbolic tangent function as finite-order rational polynomial functions. For example, in the low-frequency band of interest, the system can truncate the distributed parameter model and equate it to a cascade of multiple piconet circuits, thereby deriving the input impedance expression of the port. This method can more accurately reflect the characteristics of the circuit at the high-frequency resonant point.

[0047] S103. The equivalent output impedance function of the virtual synchronous machine is superimposed in series with the dynamic impedance function to obtain the total equivalent impedance function;

[0048] The core operation performed by the system in this step is the series superposition of impedances, aiming to construct a mathematical model that characterizes the overall electrical characteristics from the electromotive force source point inside the virtual synchronous machine to the point of common coupling or the infinite grid bus. The equivalent output impedance function of the virtual synchronous machine represents the dynamic characteristics of the source side, including the influence of the generator body and control loop; the dynamic impedance function represents the dynamic characteristics of the transmission channel. The total equivalent impedance function is the mathematical synthesis of these two, physically corresponding to the total internal impedance in the Thevenin equivalent circuit. Series superposition is not a simple scalar addition, but an algebraic operation performed in the complex frequency domain, involving the merging, common denominator, and recalculation of polynomials. This function is the basis for subsequent analysis of the power coupling mechanism, because the impedance-to-inductance ratio of the total impedance directly determines the degree of coupling between active and reactive power. If the total impedance is purely inductive, the power is naturally decoupled; if it is resistive-inductive or capacitive, strong coupling exists.

[0049] When implementing series superposition, the system can employ complex frequency domain algebraic operations. The system adds the reduced-order virtual synchronous machine output impedance (usually a rational fraction about complex frequencies) obtained in step S101 to the line dynamic impedance (also a rational fraction about complex frequencies) obtained in step S102. The system needs to unify the two fractions by finding a common denominator, making the denominator the least common multiple polynomial of the two original denominators, and then perform corresponding multiplication and addition operations on the numerators. Finally, a unified, higher-order rational transfer function is obtained, whose polynomial coefficients in the numerator and denominator are jointly determined by the virtual synchronous machine parameters and the line parameters. Another implementation method is the state-space combination method based on matrix operations. If the previous steps were based on a state-space model, the system possesses the system matrix of the virtual synchronous machine and the system matrix of the line. Since the two are in series, the system can construct a new combined state-space model by expanding the state variables. In this new model, the output equation relates the internal potential of the virtual synchronous machine and the relationship between the grid voltage difference and the total current. The system uses the combined state matrix to derive the total equivalent impedance function through a formula.

[0050] S104. Based on the total equivalent impedance function, establish the nonlinear dynamic equations describing the active and reactive power output of the virtual synchronous machine.

[0051] The system establishes nonlinear dynamic equations describing the active and reactive power output of the virtual synchronous machine based on the total equivalent impedance function. Specifically, this includes: establishing a complex frequency domain voltage balance equation that includes the internal potential, grid voltage, and total equivalent impedance function in the Thevenin equivalent output model of the virtual synchronous machine, based on Kirchhoff's voltage law; determining the dynamic phasor expression of the output current of the virtual synchronous machine based on the complex frequency domain voltage balance equation; constructing the complex power expression of the virtual synchronous machine output using the dynamic phasor expression and the dynamic phasor expression of the output voltage of the virtual synchronous machine; and separating the complex power expression into real and imaginary parts to obtain nonlinear dynamic equations with the power angle and internal potential amplitude as input variables and active and reactive power as output variables.

[0052] This step aims to derive the core mathematical model describing the power output characteristics of the virtual synchronous machine. Nonlinear dynamic equations refer to a set of differential or algebraic equations that reveal the complex interdependencies between the system's state variables (such as power angle and internal potential amplitude) and output variables (active power and reactive power). These equations are inherently nonlinear due to the presence of sine and cosine functions, and the frequency dependence of the impedance function itself. Kirchhoff's voltage law is the physical basis for establishing these equations, stipulating that the algebraic sum of voltage rises and falls in the loop is zero. Thevenin's equivalent output model treats the virtual synchronous machine as a controllable voltage source in series with an equivalent impedance. The complex frequency domain voltage balance equations describe Kirchhoff's voltage law in the Laplace domain or dynamic phasor domain. The dynamic phasor expression is the complex envelope representation of the time-domain signal. The output complex power expression is defined as the product of the voltage phasor and the current conjugate phasor. By separating the real and imaginary parts, the system can clearly define the generation mechanisms of active and reactive power and their analytical relationships with impedance parameters, voltage amplitude, and phase angle difference.

[0053] The system establishes nonlinear dynamic equations through the following steps: First, based on the Thevenin equivalent circuit, the system applies Kirchhoff's voltage law to compose complex frequency domain equations, relating the internal potential dynamic phasor, the grid voltage dynamic phasor, the output current, and the total equivalent impedance. From this, the system parsely derives the dynamic phasor expression for the current. Next, the system constructs a complex power expression, which is the product of the voltage dynamic phasor and the current conjugate dynamic phasor. At this point, the system expands the dynamic phasors into magnitude and phase angle forms. The system uses Euler's formula to expand the exponential terms into trigonometric functions and expresses the total impedance in terms of magnitude and impedance angle. Another implementation method utilizes coordinate transformation techniques. The system projects all variables onto a synchronously rotating coordinate system, establishing voltage balance equations based on direct and quadrature axis components. The system uses the power formula, substituting the current differential equation into the power formula to eliminate the intermediate variable current, directly obtaining a set of power differential equations containing voltage and impedance dynamics. This method avoids complex number operations and directly handles nonlinear relationships in the real number domain.

[0054] S105. Linearize the nonlinear dynamic equation at the preset steady-state operating point to obtain the small-signal transfer function matrix of power transmission.

[0055] The preset steady-state operating point refers to the equilibrium state of a virtual synchronous machine under rated operation or a specific load, typically composed of steady-state power angle, steady-state internal potential, steady-state active power, and steady-state reactive power. Linearization is based on the small-signal assumption, which considers the disturbances experienced by the system to be insignificant relative to the steady-state values, thus ignoring higher-order infinitesimals in the nonlinear equations and retaining only first-order variable components. The power transfer small-signal transfer function matrix is ​​a two-dimensional matrix whose elements describe the linear dynamic relationship between input variables (power angle disturbance, internal potential disturbance) and output variables (active power disturbance, reactive power disturbance). This matrix reveals the local dynamic characteristics of the system near a specific operating point; in particular, the magnitude of the cross-coupling terms (off-diagonal elements of the matrix) directly reflects the strength of the coupling.

[0056] When implementing linearization, the system can employ analytical differentiation. The system first defines the state vector and output vector. Based on the nonlinear equations obtained in step S104, the system calculates the partial derivatives of each term in the function with respect to the power angle and internal potential. Specifically, the system calculates the partial derivatives of active power with respect to the power angle, active power with respect to the internal potential, reactive power with respect to the power angle, and reactive power with respect to the internal potential, and assigns these partial derivatives to values ​​at the steady-state operating point. These partial derivative values ​​constitute the small-signal gain, and combined with the dynamic part of the impedance function, the system constructs the transfer function matrix. Another implementation method is the numerical perturbation method. If the nonlinear equations are too complex to be analytically differentiated, the system can apply a small step perturbation or pulse perturbation to the power angle and internal potential at the steady-state operating point in the simulation environment or the controller's internal algorithm. The system records the output active and reactive power response curves and uses system identification technology to extract the transfer function between the input and output.

[0057] S106. Construct a cross-feedforward decoupling branch containing undetermined decoupling coefficients;

[0058] Undetermined decoupling coefficients refer to the gain or transfer function set in the decoupling branch, whose numerical or functional form is yet to be determined. They are the solution targets for subsequent calculation steps. A cross-feedforward decoupling branch is a specific control structure that is not directly connected in series with the main control loop. Instead, it injects the control signal or state variable of one control loop into the input or output of another control loop after specific processing. In this application, it specifically refers to introducing the signal of the power angle control loop into the internal potential control loop, and simultaneously introducing the signal of the internal potential control loop into the power angle control loop. This cross structure forms a diagonal decoupling network in a multivariable control system, aiming to artificially create a "reverse coupling" to counteract the "forward coupling" inherent in the physical system itself.

[0059] When constructing the cross-feedforward decoupling branch, the system can adopt an input-side feedforward decoupling structure. Specifically, the system introduces a signal branch from the power angle (or frequency) loop at the reference input of the voltage control loop or the output of the regulator; similarly, a signal branch from the voltage loop is introduced at the corresponding position in the power angle (or frequency) loop. Transfer function modules are connected in series on these two branches. The inputs to these two modules are small-signal disturbances (or transformed intermediate variables), and the outputs are compensation signals used to correct the other loop. Another implementation is to use an output-side feedback linear decoupling structure. The system can construct a decoupling matrix module after the feedback measurement stages of active and reactive power. This module receives the measured active and reactive power, performs internal operations on the undetermined coefficient matrix, outputs virtual decoupling power feedback values, and sends these virtual values ​​to the controller of the virtual synchronous machine. This structure attempts to merge the physical object and the decoupling matrix into a new generalized controlled object, making it exhibit decoupling characteristics to the controller.

[0060] S107. Based on the small-signal transfer function matrix of power transmission, and with the constraint that the mutual coupling transfer function term between active power and reactive power is zero, calculate the undetermined decoupling coefficients.

[0061] The system calculates the undetermined decoupling coefficients based on the small-signal transfer function matrix of power transmission, using the constraint that the mutual coupling transfer function term between active and reactive power is zero. Specifically, this includes:

[0062] Establish a system that includes intermediate variables and The decoupling control equation is represented as the product of the decoupling matrix and the input state variables. The decoupling matrix is:

[0063] and The decoupling coefficients are to be determined.

[0064] Multiply the decoupling matrix by the power transmission small-signal transfer function matrix to establish the open-loop transfer function matrix equation of the system including the decoupling element. The open-loop transfer function matrix equation of the system is as follows:

[0065]

[0066] and These are the small-signal disturbances for active power and reactive power, respectively. and These are the small-signal disturbances of the power angle and internal potential, respectively. , , and These are the elements in the small-signal transfer function matrix of power transmission; the off-diagonal elements in the result of the open-loop transfer function matrix equation of the system are set to zero to solve for the undetermined decoupling coefficients, where the calculation expression for solving for the undetermined decoupling coefficients is:

[0067]

[0068] In the above function, The coupling transfer function characterizing the internal potential to active power. The principal transfer function characterizing the work angle with respect to active power. The coupling transfer function characterizing the power angle with respect to reactive power. The main transfer function characterizing the internal potential to reactive power.

[0069] The small-signal transfer function matrix of power transfer describes the coupling characteristics of an undecoupled system. The inter-coupling transfer function term refers to the element on the off-diagonal side of the open-loop transfer function matrix, representing the transfer functions that cause reactive power changes due to power angle changes and active power changes due to internal potential changes. Making the inter-coupling transfer function term zero is a constraint, meaning the system aims to introduce a decoupling matrix to transform the transfer function matrix of the generalized controlled object into a diagonal matrix. A diagonal matrix implies a one-to-one correspondence between inputs and outputs, with no cross-interference. Calculating the undetermined decoupling coefficients is essentially solving a system of algebraic equations. According to the matrix multiplication rule, setting the off-diagonal elements of the resulting matrix to zero allows us to deduce the analytical expression for the decoupling coefficients.

[0070] In the specific implementation of the calculation, the system first writes out the open-loop transfer function matrix equation containing the decoupling matrix. According to the structure of step S106, the system establishes the decoupling matrix. The system multiplies this matrix with the original system matrix. According to matrix multiplication, the off-diagonal elements of the resulting matrix are composed of the original matrix elements and the decoupling coefficients. The system sets these two off-diagonal elements to zero, thus establishing a system of equations. Solving this system of equations, the system obtains the expression for the decoupling coefficients, which is usually expressed as the ratio of the coupling term to the main channel term in the original transfer function matrix. This is a direct analytical calculation method. Another implementation method is a numerical optimization method based on frequency domain characteristics. If the order of the transfer function obtained by analytical division is too high or physically unrealizable, the system can set an optimization objective in the frequency domain to find the parameters of a standard low-order transfer function, so that its frequency response characteristics approximate the theoretical analytical solution to the greatest extent possible in the key frequency band. This method sacrifices complete theoretical decoupling across the entire frequency band in exchange for a simpler and easier-to-implement controller structure.

[0071] S108. Calculate the reactive power steady-state error compensation coefficient based on the attenuation ratio of the open-loop gain of the reactive power control loop after adding the cross-feedforward decoupling branch.

[0072] In this step, the system addresses the side effects caused by the introduction of decoupling control. While adding a cross-feedforward decoupling branch eliminates coupling, according to feedback control theory, the equivalent main channel gain of the control loop changes. Specifically, the introduction of the decoupling matrix alters the transfer function characteristics on the original system's main diagonal, typically manifesting as a decrease or amplification of low-frequency gain. The attenuation ratio of the open-loop gain of the reactive power control loop refers to the ratio of the gain of the equivalent reactive power main transfer function after decoupling in the DC or low-frequency range to the gain of the original transfer function before decoupling. If this ratio is less than one, it means the loop gain decreases, which weakens the system's ability to track reactive power commands and increases steady-state error. The reactive power steady-state error compensation coefficient is a scalar gain factor used to connect an amplification stage in series in the control loop to restore the original loop gain and eliminate the steady-state accuracy loss caused by decoupling.

[0073] In the specific implementation calculations, the final value theorem analysis method can be used. First, the closed-loop or open-loop transfer function expression of the reactive power channel after decoupling is written, and the complex variables are allowed to approach zero to calculate their DC gain value. Simultaneously, the DC gain of the original system without the decoupling branch is calculated. The attenuation ratio is the ratio of the old and new gains. The compensation coefficient is calculated as the reciprocal of this ratio. This method is suitable for situations where the system's DC gain exists and is finite. Another implementation method is the frequency domain analysis method based on Bode plots. The system plots the Bode plot of the open-loop transfer function of the reactive power loop before and after decoupling, observing the difference in the vertical axis of the amplitude-frequency characteristic curve in the low-frequency band. The required gain compensation is calculated based on the difference. This method intuitively reflects the gain change across the entire frequency band and can be used not only to compensate for steady-state errors but also to adjust the system's crossover frequency, ensuring that the dynamic response speed does not slow down due to decoupling.

[0074] S109. Real-time acquisition of the internal potential amplitude signal and power angle signal of the virtual synchronizer;

[0075] In this step, the system performs sensing and measurement tasks, providing the necessary input variables for decoupling control. Real-time acquisition means that data acquisition must have extremely low time delay and a sufficiently high sampling rate to meet the bandwidth requirements of the control system. The internal electromotive force amplitude signal of the virtual synchronous machine is a state variable within the control algorithm, typically corresponding to the output of the excitation control loop or the output of the reactive power voltage droop control. The power angle signal is the difference between the position angle of the virtual rotor of the virtual synchronous machine and the angle of the grid voltage vector. These two signals are independent variables of the nonlinear equation established in step S104 and are also the input sources of the decoupling branch in step S106. Accurate acquisition of these two signals is a prerequisite for achieving precise decoupling.

[0076] In the specific implementation of data acquisition, the system typically uses a direct software variable reading method for internal potential amplitude signals. Since the virtual synchronizer is a control algorithm implemented based on a digital processor, the internal potential itself is a register value within the algorithm. The system only needs to directly call this variable during each control interruption cycle, without requiring external sensors. For power angle signals, the system typically uses a phase-locked loop (PLL) assisted calculation method. The system uses a software PLL to track the phase of the grid voltage at the point of common coupling in real time, while simultaneously reading the virtual phase generated internally by the virtual synchronizer algorithm. The power angle is obtained by calculating the difference between the virtual phase and the grid phase. Another implementation method is an estimation method based on a state observer. If the grid voltage contains a large number of harmonics or imbalances, direct PLL may experience jitter. The system can construct an observer based on a generalized integrator or Kalman filter to extract the phase information of the fundamental positive-sequence component from contaminated voltage and current measurements, and combine this with the internal mechanical equations to estimate a smoothed power angle signal.

[0077] S110. The internal potential amplitude signal and the power angle signal are weighted and calculated using the decoupling coefficient to obtain the active decoupling feedforward signal and the reactive decoupling feedforward signal.

[0078] In this step, the system performs specific signal processing operations, converting the acquired physical quantities into control compensation quantities. Weighted calculation refers to the process of performing time-domain convolution or frequency-domain multiplication on the input signal and the decoupling coefficients (transfer functions) calculated in step S107. In digital control systems, this is typically manifested as iterative calculation of difference equations. The active power decoupling feedforward signal is a compensation quantity designed to eliminate the impact of internal potential fluctuations on active power; it originates from the internal potential signal processed by relevant decoupling coefficients. The reactive power decoupling feedforward signal is a compensation quantity designed to eliminate the impact of power angle fluctuations on reactive power; it originates from the power angle signal processed by relevant decoupling coefficients. These two signals are ultimately injected into the control loop as correction terms.

[0079] In implementing the weighted calculation, the system primarily employs digital filter technology. First, the continuous-domain transfer function obtained in step S107 is discretized into a Z-domain impulse transfer function using bilinear transformation, zero-pole matching, or backward difference. Next, these Z-domain functions are transformed into difference equations. Within the processor's interrupt service routine, the system calculates the current output in real-time using the current input and historical input / output data. Another implementation method is the state-space implementation. The system transforms the high-order decoupled transfer function into a discrete state-space model. In each control cycle, the system performs matrix-vector multiplication to update the internal state and calculate the output. This method offers better numerical stability when dealing with high-order controllers and facilitates limiting the internal state to prevent computational overflow.

[0080] S111. Use the reactive power steady-state error compensation coefficient to correct the reactive power reference value or reactive power feedback value and generate a reactive power compensation signal.

[0081] In this step, the system applies the compensation coefficient calculated in step S108 to perform gain correction on the reactive power control loop. The reactive power reference value is the reactive power target given by the upper-level scheduling of the virtual synchronous machine, and the reactive power feedback value is the actual measured reactive power. Correction refers to changing the magnitude of these values ​​using mathematical operations. The reactive power compensation signal is the result of the correction operation and will be sent to subsequent comparators or regulators. The purpose of this step is to ensure that, after introducing the decoupling branch, the final reactive power output of the system can track the given value without steady-state error.

[0082] In practical implementation, the system can employ a reference value pre-gain correction method. The system multiplies the reactive power reference value by a compensation coefficient to obtain the corrected reference value. Then, the corrected reference value is compared with the actual reactive power feedback value, generating an error signal that is sent to the regulator. This method effectively raises the system's setpoint to compensate for the output deficiency caused by the decrease in loop gain. Another implementation method is the feedback channel gain correction method. The system can also choose to divide the feedback channel by the compensation coefficient (or multiply by its reciprocal). Then, the original reference value is compared with the corrected feedback value. From a control theory perspective, these two methods are equivalent in steady-state effect, both aiming to adjust the DC gain of the closed-loop system to unit 1. However, in practical engineering, it is generally preferred to correct the reference value because the signal on the feedback channel contains noise, and division operations or amplification factors may amplify the noise.

[0083] S112. Superimpose the active decoupling feedforward signal onto the active control loop output of the virtual synchronous machine; superimpose the reactive decoupling feedforward signal and the reactive compensation signal onto the reactive control loop output of the virtual synchronous machine.

[0084] In this step, the system completes the final synthesis and injection of control signals, which is the final stage of implementing the entire decoupling control strategy. Superposition refers to the algebraic summation of multiple control signals. The output of the active power control loop typically refers to the node that generates frequency or power angle reference values, or directly generates active current reference values. The output of the reactive power control loop typically refers to the node that generates voltage amplitude reference values. The superposition of active power decoupling feedforward signals aims to correct the operation of the active power loop, making it unaffected by changes in internal potential; the superposition of reactive power decoupling feedforward signals and reactive power compensation signals aims to correct the operation of the reactive power loop, making it unaffected by changes in power angle and maintaining steady-state accuracy.

[0085] In practical implementation, for the active power loop, the system superimposes the active power decoupling feedforward signal calculated in step S110 onto the torque input of the virtual mechanical equation, or onto the power angle reference value output by the frequency regulator. This depends on whether the decoupling design is based on the power level or the angle level. In the context of this application, it is typically superimposed on the input side of the virtual mechanical equation as an additional virtual mechanical torque to offset torque fluctuations caused by electrical coupling. For the reactive power loop, the system superimposes the reactive power decoupling feedforward signal and the reactive power compensation signal generated in step S111 together onto the input of the excitation controller, or directly onto the voltage reference value. This means that the final voltage amplitude command sent to the modulator is a synthesis of the base droop control output, the decoupling feedforward quantity, and the steady-state compensation quantity.

[0086] In the above embodiments, by establishing the VSG equivalent output impedance function and the transmission line dynamic impedance function that include the inner loop dynamic characteristics, the total equivalent impedance function is obtained, enabling the power decoupling control method to more accurately reflect the dynamic characteristics of the system. The nonlinear dynamic equations and power transmission small-signal transfer function matrix established based on this are closer to the dynamic response characteristics of the actual system. By constructing cross-feedforward decoupling branches and calculating the decoupling coefficients, the mutual interference between active and reactive power can be reduced. Introducing a reactive power steady-state error compensation coefficient can reduce the reactive power control performance degradation caused by the introduction of decoupling branches. The decoupling feedforward signal obtained by real-time signal acquisition and weighted calculation, superimposed on the corresponding control loop output, can improve the control accuracy of the system during the power output dynamic process and reduce the power output overshoot and settling time.

[0087] In the first embodiment described above, a system model was established considering the inner loop and line dynamic characteristics, and a power decoupling control method was designed based on this model. To verify the accuracy of the established power transmission small-signal transfer function matrix, another VSG power decoupling control method considering the inner loop and line dynamics was further proposed. This method can evaluate the accuracy of the theoretical model by comparing the dynamic response characteristics of the electromagnetic transient simulation model and the theoretical calculation model under the same operating conditions. The following section combines... Figure 2 Another VSG power decoupling control method considering inner loop and line dynamics is described in the embodiments of this application:

[0088] Please see Figure 2 This is another flowchart illustrating a VSG power decoupling control method that takes into account the inner loop and line dynamics in an embodiment of this application.

[0089] S201. Construct an electromagnetic transient simulation model and configure the circuit parameters and control parameters of the electromagnetic transient simulation model so that the electromagnetic transient simulation model uses the same parameters as those used when establishing the equivalent output impedance function of the virtual synchronous machine and the dynamic impedance function of the transmission line.

[0090] Electromagnetic transient simulation models are mathematical models that use computer software to simulate the time-varying behavior of physical quantities such as voltage and current in a power system during electromagnetic transient processes. These models accurately reflect the system's nonlinearity, switching characteristics, and high-frequency dynamics. Circuit parameters typically include, but are not limited to, physical properties such as resistance, inductance, capacitance, line length, and transformer turns ratio. Control parameters encompass adjustment variables in the virtual synchronous machine control strategy, such as inertia coefficient, damping coefficient, proportional-integral coefficients of the voltage and current loops, and virtual impedance parameters. Establishing the equivalent output impedance function of the virtual synchronous machine and the dynamic impedance function of the transmission line refers to the mathematical analytical expressions constructed in the preceding steps to derive the power transmission characteristics; these expressions depend on specific system parameter settings. Parameter consistency means that the values ​​set in the simulation environment must be strictly consistent with the values ​​input in the theoretical derivation to ensure the effectiveness of the comparison and verification. The system first builds a complete circuit topology in the simulation platform, including components such as DC source, inverter bridge arm, filter, transmission line and power grid. Then, it inputs the predetermined physical component values ​​into the circuit model and configures the various gains and time constants in the control algorithm into the simulation control module to ensure that the simulation environment completely reproduces the physical scenario on which the theoretical derivation is based.

[0091] One approach to constructing an electromagnetic transient simulation model is using power system simulation software with a graphical interface. The system retrieves standard component modules from the software library, such as insulated-gate bipolar transistors, inductors, capacitors, and three-phase power supplies, and connects them according to the actual topology of the virtual synchronous machine connected to the power grid to construct the main circuit. Subsequently, a control loop is built using a signal processing module, including a power calculation module, a virtual synchronous machine algorithm module, a voltage-current dual closed-loop control module, and a space vector pulse width modulation module. Another approach is to use code-based numerical calculation software for modeling. The system describes the circuit's differential equations using a scripting language, represents the system's dynamic behavior using the state-space method, and solves for the system's state variables using numerical integration algorithms (such as the Runge-Kutta method). Global variables are defined in the code to store circuit and control parameters, ensuring parameter consistency during main program calls. Function modules are written to implement the virtual synchronous machine's control logic, simulating the inverter's switching actions and their impact on the circuit.

[0092] S202. Establish a theoretical calculation model based on the small-signal transfer function matrix of power transmission;

[0093] The small-signal transfer function matrix for power transfer is a mathematical matrix that describes the dynamic relationship between a system near its steady-state operating point and small input disturbances (such as changes in the active power reference value) and output responses (such as changes in actual active and reactive power). Its internal elements consist of transfer functions in the Laplace transform domain. The theoretical calculation model is a numerical model built based on this transfer function matrix using mathematical computational tools, capable of directly calculating the system's input and output responses. It does not involve simulating specific circuit switching actions but directly solves the linearized differential-algebraic equations. The modeling process involves discretizing or directly defining the transfer function matrix, which includes the inner loop and line dynamic characteristics, derived in previous steps, in the continuous domain, enabling it to perform calculations on the input signal and output results. Based on the derived analytical expressions, the system defines the matrix structure in the numerical computation environment, substituting specific system parameters into the coefficient expressions of the matrix elements, thus forming a linear system model with clearly defined input and output ports. This model can quickly calculate the theoretical dynamic trajectory under a given input.

[0094] One specific method for establishing a theoretical calculation model is the transfer function module connection method based on control system design software. The system creates multiple transfer function modules within the software, each corresponding to an element in the matrix (e.g., active-to-active transfer function, active-to-reactive coupled transfer function, etc.). Input signals are distributed to the corresponding modules using adders and splitters, and the outputs of each module are linearly superimposed to construct a complete MIMO (Multiple-Input Multiple-Output) system model. Another method is the state-space equation construction method based on scripting languages. The system first transforms the transfer function matrix into a state-space expression (A, B, C, D matrix form), where state matrix A describes the internal dynamics, input matrix B describes the input effects, output matrix C describes the observation equations, and direct transfer matrix D describes the feedforward action. The numerical values ​​of these matrices are defined by writing scripts, and the model is instantiated using built-in linear system simulation functions (such as the `step` or `lsim` functions), enabling it to accept time-series inputs and calculate the corresponding state responses.

[0095] S203. At the same steady-state operating point, apply a step disturbance of the active power reference value with the same amplitude to the electromagnetic transient simulation model and the theoretical calculation model respectively.

[0096] The steady-state operating point refers to the equilibrium state of a system before being disturbed, typically defined by the specific values ​​of output voltage amplitude, phase, active power, and reactive power. The same steady-state operating point means that the initial conditions of the two models at t=0 must be completely identical to eliminate the influence of initial deviations on dynamic comparison. A step disturbance to the active power reference value refers to a sudden change in the target active power setpoint of the control system from one value to another within a very short time. This signal form contains rich frequency components, which can fully excite the dynamic characteristics of the system. The same amplitude means that the step change amount (i.e., the difference between the target value and the initial value) set in the two models must be equal. The system first runs the electromagnetic transient simulation model to a steady state, recording the various operating parameters at this point, and then uses these parameters as the initial state of the theoretical calculation model. Next, the system simultaneously sends a step signal to the control input terminals of both models. This signal indicates that the active power reference value increases or decreases instantaneously by a fixed percentage or a specific value, ensuring that the two models are subjected to completely identical external excitation at the same moment.

[0097] Applying step disturbances to the model can be achieved by setting simulation time events. In electromagnetic transient simulation software, a step signal generator module is configured, with its "step time" set to a specific moment (e.g., 1 second), "initial value" to steady-state power, and "final value" to target power. The output of this signal generator is directly connected to the active power input port of the virtual synchronous machine controller. For the theoretical calculation model, the system constructs a time vector and an input vector in the numerical calculation script. All elements of the input vector before the corresponding step time are assigned the steady-state initial value, and all elements after the step time are assigned the target value, forming a discretized step sequence. This sequence is then passed as input parameters to the linear system simulation function. Another approach is to control the simulation process through programming. The system writes a master control script, first allowing the model to run for a preset time to reach steady state, and then forcibly modifying the values ​​of control variables in the code. For example, during the loop calculation, the value of variable P_ref is directly changed through conditional statements (e.g., if time > step_time), and this variable is passed to the calculation kernels of the two models in real time, thereby achieving synchronous step disturbance input.

[0098] S204. Collect the active power and reactive power output from the electromagnetic transient simulation model as the measured response curve, and collect the active power and reactive power output from the theoretical calculation model as the theoretical response curve.

[0099] Data acquisition refers to the process of extracting a data sequence of specific variables changing over time from a simulation or calculation process. The measured response curve specifically refers to the data trajectory obtained from an electromagnetic transient simulation model, as this model most closely approximates the characteristics of the actual physical circuit; therefore, its output is considered "measured" or benchmark data. Theoretical response curves, on the other hand, refer to the data trajectory derived from theoretical calculations based on a small-signal model. Active power and reactive power are two key indicators for measuring energy transmission in a power system, representing the energy flow rate of actual work done and the energy flow rate of electromagnetic field exchange, respectively. During simulation operation, a data logger or oscilloscope module is set up to read the instantaneous voltage and current values ​​at the inverter output port in real time at a fixed sampling frequency. The time series of active and reactive power are obtained through power calculation algorithms (such as instantaneous power theory or moving average filtering). Simultaneously, the system directly extracts the corresponding power value sequence from the output vector of the theoretical calculation model. These two sequences are labeled and stored, forming curve data for subsequent comparative analysis.

[0100] The specific method for acquiring response curves can utilize the built-in waveform recording function of the simulation software. The system places a "To Workspace" or "Data Export" module in the electromagnetic transient simulation model, connects it to the output of the power calculation unit, configures the save format as a time series structure or array, and sets the sampling step size (e.g., 50 microseconds). After the simulation ends, the data is automatically saved to the workspace. For theoretical calculation models, after executing the linear system response function (such as lsim), the function directly returns the output matrix and time vector. The system extracts the first column of the output matrix as the theoretical active power data and the second column as the theoretical reactive power data, and saves them as data files of the same type. Another method is to acquire data through a real-time data stream interface. The system uses the APIs (Application Programming Interfaces) provided by various simulation platforms to write an external listening program. During simulation stepping, the listening program reads the memory address values ​​of specified variables in real time and writes the read power values ​​along with the current simulation timestamp to a CSV (comma-separated value) file or database. This method enables cross-platform synchronous data acquisition, facilitating subsequent unified processing.

[0101] S205. Calculate the goodness of fit between the measured response curve and the theoretical response curve in the time domain;

[0102] The system calculates the goodness of fit between the measured and theoretical response curves in the time domain. Specifically, this includes: unifying the measured and theoretical response curves to the same time axis for sampling, obtaining corresponding measured and theoretical data sequences; calculating the difference between the measured and theoretical data sequences at each sampling point, and calculating the norm of the difference as an error statistic; calculating the norm of the deviation of the measured data sequence relative to its mean as a baseline statistic; and determining the goodness of fit as the ratio of the error statistic to the baseline statistic. Goodness of fit is a quantitative indicator used to measure the similarity between two data sequences in shape, amplitude, and trend. The value is usually between 0 and 1 or expressed as a percentage; a higher value indicates a closer similarity. The time domain refers to the analysis domain with time as the independent variable, focusing on the waveform characteristics of the signal changing over time. The measured and theoretical data sequences refer to the discrete sets of values ​​after being resampled along a unified time axis. The error statistic reflects the total difference between the two sets of data, usually expressed using the norm of the difference (such as the Euclidean norm or L2 norm). The baseline statistic is a reference value used to normalize the error, typically the norm of deviation of the measured data relative to its mean, representing the fluctuation energy of the data. The system first preprocesses the two acquired curves to ensure they have the same time length and number of sampling points. Then, it calculates the difference between the two curves point by point and calculates the error statistic based on these differences. Next, it calculates the norm of deviation of the measured data as a baseline. Finally, using a specific mathematical formula (such as 1 minus the ratio of the error statistic to the baseline statistic), it calculates the final goodness-of-fit value, which intuitively reflects the theoretical model's ability to reproduce the dynamics of the actual system.

[0103] The specific method for calculating the goodness of fit can employ a variant of the Normalized Root Mean Square Error (NRMSE) algorithm. The system first resamples the theoretical data sequence using an interpolation algorithm (such as linear interpolation or spline interpolation) to ensure its timestamps are perfectly aligned with the measured data sequence. Next, it calculates the square of the difference between the measured and theoretical values ​​at each time point, sums them, takes the average, and then takes the square root to obtain the root mean square error (RMSE). Then, it calculates the range (maximum minus minimum) or standard deviation of the measured data as a normalization factor. Finally, the goodness of fit is calculated as: 1 - (RMSE / normalization factor). Alternatively, the coefficient of determination (R-squared) algorithm can be used. The system calculates the sum of squares of the differences between the measured and theoretical data (residual sum of squares SS_res), and the sum of squares of the differences between the measured data and its mean (total sum of squares SS_tot). The goodness of fit is defined as R² = 1 - (SS_res / SS_tot). This method directly reflects the proportion of variation in measured data explained by the theoretical model. The closer R² is to 1, the more perfectly the theoretical model can reproduce the dynamic changes of the measured curve.

[0104] S206. If the fit is greater than the preset threshold, the power transmission small signal transfer function matrix is ​​determined to be accurate.

[0105] A preset threshold is a predefined numerical standard used by the system to distinguish whether a model is "accurate enough." This threshold is usually set according to actual engineering needs, such as 0.90 (i.e., 90%) or 0.95, indicating that the theoretical model should explain at least 90% or 95% of the actual dynamic changes. Judgment refers to the logical decision-making process based on the comparison results. Accuracy of the power transfer small-signal transfer function matrix means that the mathematical model can realistically describe the physical characteristics of the actual system within an acceptable error range and can be reliably used for subsequent controller design or stability analysis. The system compares the goodness-of-fit value calculated in the previous step with the preset threshold stored in memory. If the calculated goodness-of-fit is strictly greater than the threshold, the logical judgment result is true, and the system outputs a confirmation signal, indicating that the established small-signal model has passed verification; conversely, if the goodness-of-fit is less than or equal to the threshold, the model is judged to be inaccurate, and it may be necessary to re-examine the parameters or the derivation process.

[0106] The accuracy can be determined through conditional branching statements in automated test scripts. After calculating the fit, the system executes code logic similar to "if fitness_score > threshold". If the condition is met, the script outputs "Model Verified: Accuracy Acceptable" to the console and sets the verification pass flag to True, allowing the process to proceed to the next step (such as controller parameter optimization). If the condition is not met, the script outputs a warning message and automatically generates a difference report listing the fit value and the threshold. Another approach is interactive determination using a visual interface. The system displays a comparison graph of the measured curve and the theoretical curve on the graphical user interface (GUI), along with the calculated fit value and a status indicator. When the fit is greater than the threshold, the indicator light turns green, and a "Verification Passed" dialog box pops up on the screen; when the fit is insufficient, the indicator light turns red, indicating to the user that the model has a bias.

[0107] In the above embodiments, by establishing an electromagnetic transient simulation model and a theoretical calculation model, and comparing and verifying them under the same operating conditions, the accuracy of the small-signal transfer function matrix for power transmission can be improved. Applying the same active power reference value step disturbance to both models, and comparing the output power response curves, the ability of the theoretical model to describe the dynamic characteristics of the actual system can be verified. Based on the goodness-of-fit criterion of the time-domain response curve, the accuracy of the theoretical model can be quantitatively evaluated. This verification method comprehensively considers the dynamic response characteristics of the system at various time points, improves the reliability of model verification, and helps to obtain a more accurate description of power transmission characteristics.

[0108] The system in the embodiments of this invention is described below from the perspective of hardware processing. Please refer to [link / reference needed]. Figure 3 This is a schematic diagram of the physical device structure of a VSG power decoupling control system that takes into account the inner loop and line dynamics, provided in an embodiment of this application.

[0109] It should be noted that, Figure 3 The structure of the system shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of the present invention.

[0110] like Figure 3 As shown, the system includes a Central Processing Unit (CPU) 301, which can perform various appropriate actions and processes based on a program stored in Read-Only Memory (ROM) 302 or a program loaded from storage portion 308 into Random Access Memory (RAM) 303, such as executing the methods described in the above embodiments. The RAM 303 also stores various programs and data required for system operation. The CPU 301, ROM 302, and RAM 303 are interconnected via a bus 304. An Input / Output (I / O) interface 305 is also connected to the bus 304.

[0111] The following components are connected to I / O interface 305: input section 306 including a camera, infrared sensor, etc.; output section 307 including a liquid crystal display (LCD) and speakers, etc.; storage section 308 including a hard disk, etc.; and communication section 309 including a network interface card such as a LAN (Local Area Network) card and a modem, etc. Communication section 309 performs communication processing via a network such as the Internet. Drive 310 is also connected to I / O interface 305 as needed. Removable media 311, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., are installed on drive 310 as needed so that computer programs read from them can be installed into storage section 308 as needed.

[0112] In particular, according to embodiments of the present invention, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of the present invention include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing computer programs for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via communication section 309, and / or installed from removable medium 311. When the computer program is executed by central processing unit (CPU) 301, it performs the various functions defined in the present invention.

[0113] It should be noted that the computer-readable medium shown in the embodiments of the present invention can be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. A computer-readable storage medium can be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), flash memory, optical fiber, portable compact disc read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In the present invention, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. In the present invention, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, wherein a computer-readable computer program is carried. The transmitted data signal can take many forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof.

[0114] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. Each block in a flowchart or block diagram may represent a module, segment, or portion of code, which contains one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0115] In another aspect, the present invention also provides a computer-readable storage medium, which may be included in the system described in the above embodiments; or it may exist independently and not assembled into the system. The storage medium carries one or more computer programs that, when executed by a processor of a system, cause the system to implement the methods provided in the above embodiments.

[0116] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit it. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

[0117] As used in the above embodiments, depending on the context, the term "when..." can be interpreted as "if...", "after...", "in response to determining...", or "in response to detecting...". Similarly, depending on the context, the phrase "when determining..." or "if (the stated condition or event) is interpreted as "if determining...", "in response to determining...", "when (the stated condition or event) is detected", or "in response to detecting (the stated condition or event)".

[0118] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state drive), etc.

[0119] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. This program can be stored in a computer-readable storage medium, and when executed, it can include the processes described in the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as ROM or random access memory (RAM), magnetic disks, or optical disks.

Claims

1. A VSG power decoupling control method considering inner loop and line dynamics, characterized in that, include: Based on the circuit parameters and voltage and current dual closed-loop control parameters of the virtual synchronous machine, an equivalent output impedance function of the virtual synchronous machine including the inner loop dynamic characteristics is established. Based on the impedance parameters of the transmission line, establish the dynamic impedance function of the transmission line; The equivalent output impedance function of the virtual synchronous machine is superimposed in series with the dynamic impedance function to obtain the total equivalent impedance function; Based on the total equivalent impedance function, a nonlinear dynamic equation describing the active and reactive power output of the virtual synchronous machine is established. The nonlinear dynamic equation is linearized at a preset steady-state operating point to obtain the power transmission small-signal transfer function matrix. Construct a cross-feedforward decoupling branch containing undetermined decoupling coefficients; Based on the power transmission small-signal transfer function matrix, and with the constraint that the mutual coupling transfer function term between active power and reactive power is zero, the undetermined decoupling coefficient is calculated. The reactive power steady-state error compensation coefficient is calculated based on the attenuation ratio of the open-loop gain of the reactive power control loop after adding the aforementioned cross-feedforward decoupling branch. The internal potential amplitude signal and power angle signal of the virtual synchronous machine are acquired in real time. The internal potential amplitude signal and the power angle signal are weighted and calculated using the decoupling coefficient to obtain the active decoupling feedforward signal and the reactive decoupling feedforward signal. The reactive power steady-state error compensation coefficient is used to correct the reactive power reference value or reactive power feedback value to generate a reactive power compensation signal; The active decoupling feedforward signal is superimposed on the active control loop output of the virtual synchronous machine; The reactive power decoupling feedforward signal and the reactive power compensation signal are superimposed on the reactive power control loop output of the virtual synchronous machine.

2. The method according to claim 1, characterized in that, The process of establishing the equivalent output impedance function of the virtual synchronizer, including the inner loop dynamic characteristics, based on the circuit parameters and voltage / current dual closed-loop control parameters of the virtual synchronizer, specifically includes: Using the dynamic phasor method, the circuit parameters and voltage and current dual closed-loop control parameters of the virtual synchronous machine are decomposed by time-varying Fourier series to obtain the inner loop control model and the original output impedance model. The frequency that includes the power coupling band is selected as the frequency threshold for order reduction. Within the reduced frequency threshold, high-frequency dynamic components in the inner loop control model and the original output impedance model are deleted to obtain the reduced inner loop transfer function and the reduced output impedance. The reduced inner loop transfer function is equivalent to the effect on the voltage source, and the reduced output impedance is determined as the equivalent output impedance function of the virtual synchronous machine, which includes the dynamic characteristics of the inner loop.

3. The method according to claim 1, characterized in that, The step of establishing nonlinear dynamic equations describing the active and reactive power output of the virtual synchronous machine based on the total equivalent impedance function specifically includes: Based on Kirchhoff's voltage law, a complex frequency domain voltage balance equation is established, which includes the internal potential, grid voltage, and total equivalent impedance function in the Thevenin equivalent output model of the virtual synchronous machine. Based on the complex frequency domain voltage balance equation, determine the dynamic phasor expression of the output current of the virtual synchronous machine; Using the dynamic phasor expression and the dynamic phasor expression of the output voltage of the virtual synchronous machine, a complex power expression for the output of the virtual synchronous machine is constructed. The output complex power expression is separated into real and imaginary parts, resulting in nonlinear dynamic equations with power angle and internal potential amplitude as input variables and active power and reactive power as output variables.

4. The method according to claim 1, characterized in that, The calculation of the undetermined decoupling coefficients based on the power transmission small-signal transfer function matrix, with the constraint that the mutual coupling transfer function term between active power and reactive power is zero, specifically includes: Establish a system that includes intermediate variables and The decoupling control equation is represented as the product of the decoupling matrix and the input state variables, wherein the decoupling matrix is: The and stated The undetermined decoupling coefficients; Multiply the decoupling matrix by the power transmission small-signal transfer function matrix to establish the system open-loop transfer function matrix equation containing the decoupling element. The system open-loop transfer function matrix equation is as follows: The and stated These are the small-signal disturbances for active power and reactive power, respectively. and stated Small-signal disturbances, namely the power angle and the internal potential, are respectively. The above The above and the aforementioned These are elements in the power transmission small-signal transfer function matrix; Set the off-diagonal elements in the result of the open-loop transfer function matrix equation of the system to zero in order to calculate the undetermined decoupling coefficients.

5. The method according to claim 4, characterized in that, The calculation expression obtained by solving for the undetermined decoupling coefficients is as follows: In the above function, the The coupling transfer function characterizing the internal potential to active power, the The principal transfer function characterizing the power angle with respect to active power, the The coupling transfer function characterizing the power angle with respect to reactive power, the The main transfer function characterizing the internal potential to reactive power.

6. The method according to claim 1, characterized in that, The method further includes: Construct an electromagnetic transient simulation model and configure the circuit parameters and control parameters of the electromagnetic transient simulation model so that the electromagnetic transient simulation model has the same parameters as those used when establishing the equivalent output impedance function of the virtual synchronous machine and the dynamic impedance function of the transmission line. A theoretical calculation model is established based on the power transmission small-signal transfer function matrix. At the same steady-state operating point, the electromagnetic transient simulation model and the theoretical calculation model are respectively subjected to a step disturbance of the active power reference value with the same amplitude; The active power and reactive power output by the electromagnetic transient simulation model are collected as measured response curves, and the active power and reactive power output by the theoretical calculation model are collected as theoretical response curves. Calculate the goodness of fit between the measured response curve and the theoretical response curve in the time domain; If the fit is determined to be greater than a preset threshold, the power transmission small signal transfer function matrix is ​​determined to be accurate.

7. The method according to claim 6, characterized in that, The calculation of the goodness of fit between the measured response curve and the theoretical response curve in the time domain specifically includes: The measured response curve and the theoretical response curve are sampled along the same time axis to obtain the corresponding measured data sequence and theoretical data sequence. Calculate the difference between the measured data sequence and the theoretical data sequence at each sampling point, and calculate the norm of the difference as an error statistic; The norm of the measured data sequence relative to its mean is calculated as a baseline statistic. The ratio of the error statistic to the benchmark statistic is determined as the goodness of fit.

8. A VSG power decoupling control system considering inner loop and line dynamics, characterized in that, The system includes: One or more processors and a memory; the memory is coupled to the one or more processors, the memory being used to store computer program code, the computer program code including computer instructions, the one or more processors invoking the computer instructions to cause the system to perform the method as described in any one of claims 1-7.

9. A computer-readable storage medium comprising instructions, characterized in that, When the instructions are executed on the system, the system performs the method as described in any one of claims 1-7.

10. A computer program product, characterized in that, When the computer program product is run on the system, the system performs the method as described in any one of claims 1-7.

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