A method, apparatus, equipment, medium, and product for dynamic gray box modal analysis of grid-connected inverters.

Abstract

This application discloses a method, apparatus, equipment, medium, and product for gray-box modal analysis of grid-connected inverter dynamics, relating to the field of power system dynamic stability. The method includes: decomposing the dynamics of the grid-connected inverter based on admittance decomposition theory, determining the global admittance aligned to the global coordinate system, thereby determining the disturbance quantity, and determining the global participation factor based on the disturbance quantity; normalizing and reducing the global participation factor based on the participation ratio, and then locating the dominant controller; calculating the explicit parameter participation factor based on the dominant controller and the global admittance, and determining the parameter sensitivity; the parameter sensitivity is used to improve the stability of the power system. This application aims to provide a reasonable analysis of the impact of different controllers on stability in a grid-connected inverter, to locate the key control loops and key control parameters affecting the power system, thereby effectively optimizing the tuning of the grid-connected inverter control parameters to improve system stability.

Description

Technical Field

[0001] This application relates to the field of dynamic stability of power systems, and in particular to a method, apparatus, equipment, medium and product for dynamic gray box modal analysis of grid-connected inverters. Background Technology

[0002] The widespread integration of grid-following inverters (GFLs) has profoundly altered the dynamic characteristics of power systems, and the unstable oscillations caused by the interaction of GFLs with the grid have attracted widespread attention. While the oscillation problem of traditional synchronous generators has been thoroughly studied in the past, the various oscillation stability problems of grid-connected systems including grid-following inverters are more complex. Power electronic equipment often requires complex control loops to achieve multiple control objectives, thus exhibiting complex dynamic characteristics. Furthermore, due to the strong coupling between multiple control loops and the numerous and difficult-to-tune control parameters, oscillation problems may arise in practice, dominated by different control loops.

[0003] Modal analysis based on the state-space model (MASS) has attracted much attention due to its ability to assess system stability and response characteristics using linear algebra. MASS quantifies the contribution of each state variable to a specific mode through participation factors (PF), which helps identify key influencing factors and potential improvement measures. MASS requires complete control details of the system; however, inverter-based resources (IBRs) are often only provided with gray-box or even black-box models.

[0004] Impedance models concentrate the dynamic characteristics of all components at their voltage and current ports and analyze system stability through a full-system dynamic matrix. Based on this, modal analysis based on the impedance model (MAI) is used to analyze and evaluate the contribution of system components to system oscillation modes at the component level. MAI focuses on treating IBRs as a whole; therefore, unlike MASS, it cannot pinpoint the main factors affecting system dynamics to the control loop and state variables. The idea of ​​decomposing the inverter's control algorithm into several discrete circuit elements offers the possibility of extending modal analysis methods into the internal components of IBRs, but this requires further feasibility analysis. Summary of the Invention

[0005] The purpose of this application is to provide a method, apparatus, equipment, medium, and product for dynamic gray box modal analysis of grid-connected inverters. This method can reasonably analyze the impact of different controllers on the stability of grid-connected inverters, locate the key control loops and key control parameters affecting the power system, and effectively optimize the control parameters of grid-connected inverters to improve system stability.

[0006] To achieve the above objectives, this application provides the following solution:

[0007] Firstly, this application provides a method for gray-box modal analysis of grid-connected inverter dynamics, including:

[0008] For any grid-connected inverter in a power system connected to a bus, the overall admittance when aligned to the global coordinate system is determined based on split dynamics. The split dynamics are obtained by splitting the dynamics of the grid-connected inverter based on admittance splitting theory. The split dynamics include electromagnetic dynamics dominated by the current control loop and synchronous dynamics dominated by the phase-locked loop. The overall admittance includes a first part admittance, a second part admittance, and a third part admittance characterizing the electromagnetic dynamics and synchronous dynamics. The first part admittance and the third part admittance are each related to the parameters of the current control loop and the phase-locked loop, while the second part admittance is affected by the coupling effect of the parameters of the two control loops, the current control loop and the phase-locked loop.

[0009] For any bus-connected grid-connected inverter in a power system, the disturbance is determined based on the overall admittance, and the overall participation factor is determined based on the disturbance. The overall participation factor includes a participation factor characterizing the degree of electromagnetic dynamics participation and a participation factor characterizing the degree of synchronous dynamics participation. The participation factor characterizing the degree of electromagnetic dynamics participation is jointly caused by the first part admittance and the second part admittance, while the participation factor characterizing the degree of synchronous dynamics participation is jointly caused by the second part admittance and the third part admittance.

[0010] For any grid-connected inverter in the power system, the overall participation factor is normalized and calculated based on the participation ratio, and the dominant controller is located according to the calculated participation ratio value; the dominant controller is the controller that plays a leading role in the stability of the power system.

[0011] For any bus-connected grid-connected inverter in a power system, the explicit parameter participation factor is calculated based on the dominant controller and the overall admittance to determine the parameter sensitivity, which is used to improve the stability of the power system. The parameter sensitivity characterizes the influence of the sensitivity of the parameters in the overall admittance on the dominant characteristic value of the power system dynamics.

[0012] Optionally, the expression for the overall admittance is:

[0013]

[0014] Among them, Y mDQ For overall admittance; The angle deviation matrix determined for the initial power flow; Y medq K represents the overall admittance of the electromagnetic dynamics in the current control loop. mU K is the coefficient matrix related to the steady-state voltage. mI This is the coefficient matrix related to the steady-state current; U mPLL The equivalent voltage caused by the phase-locked loop parameters; Angle deviation matrix determined for the initial power flow Perform the inverse operation; Y meDQ The first admittance characterizing electromagnetic dynamics and synchronicity dynamics; Y mDQ1 The second admittance characterizing electromagnetic dynamics and synchronicity dynamics; Y mDQ2 The third part, admittance, characterizes electromagnetic dynamics and synchronicity dynamics.

[0015] Optionally, the expression for the disturbance amount is:

[0016]

[0017] Where, ΔY mDQ For overall admittance Y mDQ The disturbance amount; ΔY meDQ The first admittance Y characterizing electromagnetic dynamics and synchronicity dynamics meDQ The disturbance amount; ΔY msDQ1 The second admittance Y, characterizing electromagnetic dynamics and synchronicity dynamics msDQ1 The disturbance amount; ΔY msDQ2 The third admittance Y, characterizing electromagnetic dynamics and synchronicity dynamics msDQ2 The disturbance amount; ΔY medq The global admittance Y of the electromagnetic dynamics in the current control loop medg The disturbance amount; E2 is the second-order identity matrix; ΔK mU The coefficient matrix K related to the steady-state voltage mU The disturbance quantity; ΔK mI The coefficient matrix K related to the steady-state current mI The disturbance quantity; ε me and ε ms Both are scalars representing the degree of disturbance.

[0018] Optionally, the expression for the overall participation factor is:

[0019]

[0020]

[0021] Among them, PF me PF is a participation factor characterizing the degree of involvement in electromagnetic dynamics. ms λ represents the participation factor characterizing the degree of involvement in synchronization dynamics; <, > represents the Frobenius inner product; λ k This is the k-th characteristic value of the power system; For the dynamic node impedance matrix elements Z of the entire power system mm In λ k Take the residue at the specified position; * indicates taking the conjugate transpose of the matrix; Y meDQ (λ k ) is in λ k The first part of the admittance at Y; msDQ1 (λ k ) is in λ k The second admittance at Y; msDQ2 (λ k ) is in λ k The third part of the admittance.

[0022] Optionally, the participation ratio can be calculated using the following formula:

[0023]

[0024] Among them, PR me To characterize the participation ratio of electromagnetic dynamics based on EMAI; PR ms The participation ratio for synchronicity dynamics is characterized based on EMAI; PF me PF is a participation factor based on EMAI to characterize the degree of electromagnetic dynamics involvement. ms PR is a participation factor based on EMAI to characterize the degree of synchronous dynamics participation; m is the bus number in the power system; me′ To characterize the participation ratio of electromagnetic dynamics based on MASS; PR ms′ The participation ratio for characterizing synchronization dynamics based on MASS; PF me′ PF is a participation factor based on MASS to characterize the degree of involvement in electromagnetic dynamics. ms′ PF is a participation factor based on MASS to characterize the degree of participation in synchronization dynamics. mid PF is the participation factor of the integral element of the d-axis PI controller in the current control loop. miq PF is the participation factor of the integral element of the q-axis PI controller in the current control loop. mθ PF is the participation factor for the angle variable of the phase-locked loop. mω This is the participation factor of the PI integral stage controller in the phase-locked loop.

[0025] Optionally, the expression corresponding to the parameter sensitivity of the PI controller in the current control loop is:

[0026]

[0027] in, The sensitivity of the proportional gain parameter of the PI controller; The parameter sensitivity of the integral gain of the PI controller; s is the Laplace operator; G del For the control delay transfer function; Z medq K represents the impedance of the electromagnetic dynamics in the current control loop. pi K represents the proportional gain of the PI controller. ii The integral gain of the PI controller;

[0028] The parameter sensitivity in a phase-locked loop and the equivalent voltage U caused by the phase-locked loop parameters mPLL Related; U mPLL Determined by measurement.

[0029] Secondly, this application provides a grid-connected inverter dynamic gray box modal analysis device, comprising:

[0030] The overall admittance determination module is used to determine the overall admittance of any grid-connected inverter in a power system when aligned to the global coordinate system, based on split dynamics. The split dynamics are obtained by splitting the dynamics of the grid-connected inverter based on admittance splitting theory. The split dynamics include electromagnetic dynamics dominated by the current control loop and synchronous dynamics dominated by the phase-locked loop. The overall admittance includes a first part admittance, a second part admittance, and a third part admittance characterizing the electromagnetic dynamics and synchronous dynamics. The first part admittance and the third part admittance are respectively related to the parameters of the current control loop and the phase-locked loop, while the second part admittance is affected by the coupling of the parameters of the two control loops, the current control loop and the phase-locked loop.

[0031] The overall participation factor determination module is used to determine the disturbance amount based on the overall admittance for any grid-connected inverter in the power system, and to determine the overall participation factor based on the disturbance amount. The overall participation factor includes a participation factor characterizing the degree of electromagnetic dynamics participation and a participation factor characterizing the degree of synchronous dynamics participation. The participation factor characterizing the degree of electromagnetic dynamics participation is jointly caused by the first part admittance and the second part admittance, while the participation factor characterizing the degree of synchronous dynamics participation is jointly caused by the second part admittance and the third part admittance.

[0032] The participation ratio calculation module is used to normalize and convert the overall participation factor based on the participation ratio of any grid-connected inverter connected to any bus in the power system, and to locate the dominant controller based on the calculated participation ratio value; the dominant controller is the controller that plays a leading role in the stability of the power system.

[0033] The parameter sensitivity determination module is used to calculate the explicit parameter participation factor for any bus-connected grid-connected inverter in the power system based on the dominant controller and the overall admittance, and determine the parameter sensitivity to improve the stability of the power system; the parameter sensitivity characterizes the influence of the sensitivity of the parameters in the overall admittance on the dominant characteristic value of the power system dynamics.

[0034] Thirdly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described grid-connected inverter dynamic gray box modal analysis method.

[0035] Fourthly, this application provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the above-described grid-connected inverter dynamic gray box modal analysis method.

[0036] Fifthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the above-described grid-connected inverter dynamic gray box modal analysis method.

[0037] According to the specific embodiments provided in this application, this application has the following technical effects:

[0038] This application provides a method, apparatus, equipment, medium, and product for gray-box modal analysis of grid-connected inverter dynamics. Based on admittance decomposition theory, the dynamics of the grid-connected inverter are decomposed, and then the global admittance aligned to the global coordinate system is determined, thereby determining the disturbance quantity and the global participation factor based on the disturbance quantity. The global participation factor is normalized and converted based on the participation ratio, and then the dominant controller is located. Based on the dominant controller and the global admittance, the explicit parameter participation factor is calculated to determine the parameter sensitivity; the parameter sensitivity is used to improve the stability of the power system. This application makes a reasonable analysis of the impact of different controllers on stability in the grid-connected inverter to locate the key control loops and key control parameters affecting the power system, thereby effectively optimizing the tuning of the grid-connected inverter control parameters to improve system stability. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0040] Figure 1A flowchart for the gray box modal analysis method of grid-connected inverter dynamics;

[0041] Figure 2 For grid-connected inverter topology diagram;

[0042] Figure 3 The equivalent circuit diagram of the control elements of a grid-connected inverter is shown; among them, Figure 3 (a) is the equivalent circuit diagram of dq sequence control; Figure 3 (b) is the equivalent circuit diagram of positive and negative sequence control; Figure 3 (c) is a schematic diagram of the equivalent circuit components of the control element;

[0043] Figure 4 This is a diagram illustrating synchronous dynamics; where, Figure 4 (a) is a schematic diagram of coordinate system transformation; Figure 4 (b) is a schematic diagram of the synchronous dynamics embedded admittance;

[0044] Figure 5 Schematic diagram for the renovation of the 14 busbar system;

[0045] Figure 6 Simulation waveform diagram of GFL8 for step fault of active load on bus 8;

[0046] Figure 7 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0047] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0048] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0049] Modal analysis based on the state-space model (MASS) requires the system to be a white-box model, thus it is unsuitable for grid-forming inverters (GFLs), which often only provide gray-box or even black-box models. This application addresses the technical problem of gray-box participation evaluation of the dynamics dominated by different controllers within a grid-forming inverter. Specifically, based on the concept of admittance decomposition, the dynamics of the grid-forming inverter are divided into electromagnetic dynamics (ED) dominated by the current control loop (CCL) and synchronous dynamics (SD) dominated by the phase-locked loop (PLL). An overall power factor (PF) characterizing ED and SD is proposed to evaluate the participation degree of different control loops, and an analytical parameter PF is proposed to improve unstable oscillation modes. Gray-box modal analysis of the internal dynamics of the grid-forming inverter is thus achieved. The purpose of this application is to quickly locate the controller inside a grid-connected inverter that plays a dominant role in system stability, and to propose a gray-box modal analysis method for the internal dynamics of a grid-connected inverter.

[0050] In one exemplary embodiment, such as Figure 1 As shown, a gray-box modal analysis method for grid-connected inverter dynamics is provided. This method is executed by a computer device, specifically a terminal or server, or both. In this embodiment, the method is illustrated using a server as an example, and includes the following steps.

[0051] like Figure 1 As shown, the grid-connected inverter dynamic gray box modal analysis method provided in this application includes:

[0052] Step 100: For any grid-connected inverter connected to any bus in the power system, determine the overall admittance when aligned to the global coordinate system based on the split dynamics. The split dynamics are obtained by decomposing the dynamics of the grid-connected inverter based on admittance decomposition theory; the split dynamics include: electromagnetic dynamics dominated by the current control loop and synchronous dynamics dominated by the phase-locked loop. The overall admittance includes a first part admittance, a second part admittance, and a third part admittance characterizing the electromagnetic dynamics and synchronous dynamics; wherein, the first part admittance and the third part admittance are each related to the parameters of the current control loop and the phase-locked loop, while the second part admittance is affected by the coupling influence of the parameters of the two control loops, the current control loop and the phase-locked loop.

[0053] Step 200: For any grid-connected inverter on any bus in the power system, determine the disturbance quantity based on the overall admittance, and determine the overall participation factor based on the disturbance quantity. The overall participation factor includes a participation factor characterizing the degree of electromagnetic dynamics participation and a participation factor characterizing the degree of synchronization dynamics participation; the participation factor characterizing the degree of electromagnetic dynamics participation is jointly caused by the first part of the admittance and the second part of the admittance, while the participation factor characterizing the degree of synchronization dynamics participation is jointly caused by the second part of the admittance and the third part of the admittance.

[0054] Step 300: For any grid-connected inverter in the power system, normalize the overall participation factor based on the participation ratio, and determine the dominant controller based on the calculated participation ratio value. The dominant controller is the controller that plays a leading role in the stability of the power system.

[0055] Step 400: For any bus-connected grid-connected inverter in the power system, calculate the explicit parameter participation factor based on the dominant controller and overall admittance to determine the parameter sensitivity, which is used to improve the stability of the power system. Parameter sensitivity characterizes the influence of the sensitivity of parameters in the overall admittance on the dominant eigenvalue of the power system dynamics.

[0056] The expression for the overall admittance is:

[0057]

[0058] Among them, Y mDQ For overall admittance; The angle deviation matrix determined for the initial power flow; Y medq K represents the overall admittance of the electromagnetic dynamics in the current control loop. mU K is the coefficient matrix related to the steady-state voltage. mI This is the coefficient matrix related to the steady-state current; U mPLL The equivalent voltage caused by the phase-locked loop parameters; Angle deviation matrix determined for the initial power flow Perform the inverse operation; Y meDQ The first admittance characterizing electromagnetic dynamics and synchronicity dynamics; Y msDQ1 The second admittance characterizing electromagnetic dynamics and synchronicity dynamics; Y msDQ2 The third part, admittance, characterizes electromagnetic dynamics and synchronicity dynamics.

[0059] The expression for the disturbance is:

[0060]

[0061] Where, ΔY mDQ For overall admittance Y mDQ The disturbance amount; ΔYmeDQ The first admittance Y characterizing electromagnetic dynamics and synchronicity dynamics meDQ The disturbance amount; ΔY msDQ1 The second admittance Y, characterizing electromagnetic dynamics and synchronicity dynamics msDQ1 The disturbance amount; ΔY msDQ2 The third admittance Y, characterizing electromagnetic dynamics and synchronicity dynamics msDQ2 The disturbance amount; ΔY medq The global admittance Y of the electromagnetic dynamics in the current control loop medq The disturbance amount; E2 is the second-order identity matrix; ΔK mU The coefficient matrix K related to the steady-state voltage mU The disturbance quantity; ΔK mI The coefficient matrix K related to the steady-state current mI The disturbance quantity; ε me and ε ms Both are scalars representing the degree of disturbance.

[0062] The expression for the overall participation factor is:

[0063]

[0064]

[0065] Among them, PF me PF is a participation factor characterizing the degree of involvement in electromagnetic dynamics. ms λ represents the participation factor characterizing the degree of involvement in synchronization dynamics; <, > represents the Frobenius inner product; λ k This is the k-th characteristic value of the power system; For the dynamic node impedance matrix elements Z of the entire power system mm In λ k Take the residue at the specified position; * indicates taking the conjugate transpose of the matrix; Y meDQ (λ k ) is in λ k The first part of the admittance at Y; msDQ1 (λ k ) is in λ k The second admittance at Y; msDQ2 (λ k ) is in λ k The third part of the admittance.

[0066] The formula for calculating the participation ratio is:

[0067]

[0068] Among them, PR me To characterize the participation ratio of electromagnetic dynamics based on EMAI; PR msThe participation ratio for synchronicity dynamics is characterized based on EMAI; PF me PF is a participation factor based on EMAI to characterize the degree of electromagnetic dynamics involvement. ms PR is a participation factor based on EMAI to characterize the degree of synchronous dynamics participation; m is the bus number in the power system; me′ To characterize the participation ratio of electromagnetic dynamics based on MASS; PR ms′ The participation ratio for characterizing synchronization dynamics based on MASS; PF me′ PF is a participation factor based on MASS to characterize the degree of involvement in electromagnetic dynamics. ms′ PF is a participation factor based on MASS to characterize the degree of participation in synchronization dynamics. mid PF is the participation factor of the integral element of the d-axis PI controller in the current control loop. miq PF is the participation factor of the integral element of the q-axis PI controller in the current control loop. mθ PF is the participation factor for the angle variable of the phase-locked loop. mω This is the participation factor of the PI integral stage controller in the phase-locked loop.

[0069] The expression corresponding to the parameter sensitivity of the PI controller in the current control loop is:

[0070]

[0071] in, The sensitivity of the proportional gain parameter of the PI controller; The parameter sensitivity of the integral gain of the PI controller; s is the Laplace operator; G del For the control delay transfer function; Z medq K represents the impedance of the electromagnetic dynamics in the current control loop. pi K represents the proportional gain of the PI controller. ii This is the integral gain of the PI controller.

[0072] The parameter sensitivity in a phase-locked loop and the equivalent voltage U caused by the phase-locked loop parameters mPLL Related; U mPLL Determined by measurement.

[0073] The technical solution of this application includes admittance decomposition of the grid-connected inverter, calculation of the overall participation factor of the dynamics characterized by different controllers of the grid-connected converter, identification of the controller of the grid-connected converter that plays a dominant role in system stability, and calculation of explicit parameter participation factors to enhance system damping and improve system stability. The solution steps are as follows, and the following steps are performed sequentially:

[0074] Step 1: Decompose the admittance of the grid inverter.

[0075] Based on the concept of admittance decomposition, the dynamics of the grid converter are divided into electromagnetic dynamics (ED) dominated by the current control loop (CCL) and synchronous dynamics (SD) dominated by the phase-locked loop (PLL).

[0076] In all variable subscripts, m is connected to the GFL of the m-th bus in the system. m Related. Figure 4 (a) ω b It is the angular velocity of the system reference power supply, θ m θ m0 and Δθ m It is GFL m The angle relative to the reference power source, the steady-state angle, and the angle deviation. When the PLL does not provide additional dynamics, i.e., Δθ... m =0, which indicates Figure 4 (a) The rocking coordinate system and the stable coordinate system coincide. At this time, the global admittance of ED in CCL is expressed as Y. medq This section focuses on the overall admittance Y when considering the PLL. mDQ The splitting process.

[0077] The small-signal transfer function of the PLL is shown in equation (1).

[0078]

[0079] Where K mpP K miP and H mv They represent GFL respectively m The proportional gain, integral gain, and voltage-to-angle transfer function of the PLL. ΔU md ΔU mq and ΔU mdq They represent GFL respectively m The d-axis voltage, q-axis voltage, and dq-axis voltage are given. s is the Laplace operator.

[0080] Transforming the voltage variable from the dq axis of the rocking coordinate system to the DQ axis of the global coordinate system yields:

[0081]

[0082] U m0 u mq0 u md0 and Tθ m0 These represent the initial voltage values, the initial voltage values ​​along the q-axis, the initial voltage values ​​along the d-axis, and the angle deviation matrix determined by the initial power flow, respectively. ΔumD , Δu mQ and Δu mDQ They represent GFL respectively m The D-axis voltage, Q-axis voltage, and DQ-axis voltage.

[0083] The current also satisfies a similar relationship to that in equation (2). Figure 4 (b) and equation (3) give the GFL m Admittance Y when aligned to global coordinate system mDQ Transformation block diagram and expression.

[0084]

[0085] Among them, E2 and I m0 These represent the second-order identity matrix and the initial current value, respectively. The superscript -1 indicates the inverse operation.

[0086] H mv U m0 It is a scalar. For equation (3), (E² + U) m0 H mv ) -1 Using the matrix inversion lemma, Y can be... mDQ Decomposed into the three parts of admittance Y in equation (4) that characterize ED and SD meDQ Y msDQ1 and Y msDQ2 Y meDQ and Y msDQ2 Each is related to the CCL and PLL parameters, while Y msDQ1 It is affected by the coupling of parameters in two control loops.

[0087]

[0088] Where K mU and K mI These are the coefficient matrices related to steady-state voltage and current, respectively. mPLL This represents the equivalent voltage caused by the PLL parameters.

[0089]

[0090] U mPLL =u md0 +s 2 / (K miP +sK mpP )

[0091] Where i mq0 and i md0 These are the initial values ​​of the q-axis and d-axis currents, respectively.

[0092] The initial values ​​of voltage and current are shown in equation (6).

[0093] u md0 =U m u mq0 =0, i md0 =P m / U m i mq0 =-Q m / U m (6)

[0094] U m P m and Q m They are GFL m The voltage amplitude, output active power and reactive power.

[0095] Y meDQ Y msDQ1 and Y msDQ2 These can be obtained through measurement and fitting. The PLL control loop is cut off, i.e., the PLL gain is set to 0. Y mDQ It can then be divided into Y meDQ and Y msDQ1 +Y msDQ2 Y msDQ1 +Y msDQ2 Only U in the middle mPLL It is the variable to be determined, and only K is available. miP and K mpP Unknown. K mU and K mI Since both have two non-zero values, K can be solved by writing two equations at a suitable frequency point. miP and K mpP Thus far, Y mDQ It can be divided into three parts in equation (4).

[0096] Step 2: Calculate the overall participation factor of the dynamics represented by different controllers of the grid converter.

[0097] Evaluate GFL m The overall power factor (PF) of overall participation is defined as PF. m .

[0098]

[0099] in, For the dynamic node impedance matrix elements Z of the entire power system mm In λ k The remainder is taken at the specified position; * represents the conjugate transpose of the matrix. <, > represent the Frobenius inner product. λ k Let Δλ be the k-th characteristic value of the power system. k and ΔY mDQ They represent λ respectively kand Y mDQ The disturbance quantity ε m It represents ΔY mDQ A scalar measure of the degree of disturbance.

[0100] Taking the disturbance amount from equation (4), we can obtain:

[0101]

[0102] Where ε me and ε ms Both are scalars representing the degree of disturbance; they respectively represent ΔY meDQ and Δ(1 / U mPLL The degree of disturbance.

[0103] To further pinpoint the main loops affecting the system, GFL is defined by analogy to equation (9). m PF, which characterizes the level of involvement of ED and SD. me and PF ms .

[0104]

[0105] PF me It is Y meDQ and Y msDQ1 Caused by both, and PF ms It is Y msDQ1 and Y msDQ2 This was caused by both factors. This also reflects Y's... msDQ1 It is affected by the coupling of parameters in two control loops. PF me and PF ms These reflect the characteristics of CCL and PLL, respectively.

[0106] Step 3: Locate the controller of the grid converter that plays a leading role in system stability.

[0107] Based on MASS, calculate the state variable PF for all GFLs.

[0108] PF mid PF miq PF mθ and PF mω They represent GFL respectively m The power factor (PF) of the dq-axis PI controller integral element in the CCL, the PF of the angle variable in the PLL, and the PF of the PI integral element controller in the PLL are calculated. To normalize the PF values ​​for the EMAI and MASS methods, the participation ratio (PR) is defined to evaluate the ED and SD participation levels of different GFLs.

[0109]

[0110] Where || represents the absolute value. The subscript ' indicates that the ED and SD characteristics are represented from the state variable. PR me and PR me’ This indicates that PR is characterized by EMAI and MASS respectively, while PR ms and PR ms’ This indicates that the PR values ​​for SD are characterized by EMI and MASS, respectively. The PR values ​​are based on the characteristics of ED and SD for different grid-connected converters in the system. me and PR ms The numerical values ​​were used to pinpoint the dominant controller corresponding to the key dynamics affecting system stability. By narrowing down the factors influencing system stability to specific controllers, the control parameters of these key controllers could be further optimized to effectively improve system stability.

[0111] Step 4: Calculate the explicit parameter participation factor to enhance system damping and improve system stability.

[0112] In addition, the sensitivity of admittance to a certain parameter ρ can be used as a reference. The dominant factors affecting system dynamics are located in the parameters.

[0113] The parameter PF is defined as in equation (11), however It is difficult to parse and obtain.

[0114]

[0115] Based on the admittance decomposition results, the sensitivity of different parameters is given. The analysis results.

[0116] First, consider the parameters of ED. At this point, ΔY mDQ It can be represented as:

[0117]

[0118] Solving for admittance perturbations by converting them into impedance perturbations.

[0119]

[0120] Depend on Figure 3 The equivalent result of impedance splitting in CCL can be obtained directly.

[0121] Equation (14) gives the parameter sensitivity of the proportional and integral gain of the PI controller in CCL.

[0122]

[0123] Among them G del =e -1.5TsLet T represent the control delay transfer function, and let T represent the sampling period.

[0124] The sensitivity of the PLL's relevant parameters is only related to the scalar U in equation (15). mPLL Related. U mPLL It can be obtained directly through measurement.

[0125]

[0126] This has enabled the identification of the dominant factors affecting system dynamics into parameters.

[0127] In the key controller, i.e., the dominant controller, the value of the participation factor (PF) for each control parameter indicates the direction in which increasing the corresponding control parameter will change the dominant eigenvalue of the system. A decrease in the real part of the system eigenvalue indicates an increase in system damping; therefore, the control parameter with the largest absolute value of the real part of the participation factor PF is selected for adjustment. If the real part of the PF value is positive, the corresponding control parameter value is decreased; conversely, if the real part of the PF value is negative, the corresponding control parameter value is increased. This achieves the goal of increasing system damping and improving system stability.

[0128] This application decomposes the admittance of a grid-connected inverter and proposes an equivalent overall participation factor to evaluate the participation degree of the electromagnetic dynamics dominated by different current controllers and the synchronization dynamics dominated by the phase-locked loop. This effectively identifies the fundamental reasons why different controllers within the grid-connected inverter affect system stability. The theoretical analysis is verified through numerical calculations and simulation results. The research results have certain guiding significance for the gray-box modal analysis of the internal dynamics of grid-connected inverters.

[0129] The overall topology of the grid inverter and filter inductor is as follows: Figure 2 As shown. Figure 2 In this context, PWM represents inverter switching modulation, and abc-dq represents Parker conversion. The equivalent circuit of the current loop control element in a grid-type inverter is as follows: Figure 3 As shown in (a). Where K pi K ii R iv X iv F v L f and G del =e -1.5Ts These are the proportional and integral gains of the PI controller, the virtual resistance and inductance, the voltage feedforward gain, the filter inductance, and the control delay. The variables are converted from dq order to positive and negative order to facilitate decoupling and simplify analysis from the control structure perspective. Figure 3 As shown in (b). The final equivalent current element of the control element is as follows. Figure 3As shown in (c). Each control element and its equivalent circuit element are marked with different colors, and equation (2) gives the specific expression of the equivalent circuit element. In all variable subscripts, m is connected to the GFL of the m-th bus in the system. m Related. PLL does not provide additional dynamics, which indicates Figure 4 (a) The rocking coordinate system and the stable coordinate system are aligned, i.e., Δθ m =0. All power admittances need to be aligned to the global coordinate system before analysis. Figure 4 (a) ω b It is the angular velocity of the system reference power supply, θ m θ m0 and Δθ m It is GFL m The angle relative to the reference power source, the steady-state angle, and the angle deviation. Figure 4 (b) is a schematic diagram of the synchronous dynamics embedded admittance.

[0130] analyze Figure 5 The system was modified to use a 14-bus system. Bus 1 is an infinite bus. Buses 2, 3, 6, and 8 are connected to GFLs. All GFLs have the same control parameters. The proportional and integral gains of the PI controller in the PLL are 62.83 and 986.96, respectively. The proportional and integral gains of the PI controller in the CCL are 0.18 and 84.82, respectively. The filter impedance is 0.01 + j0.03 p.u. The voltage feedforward and virtual impedance are set to 0. The system exhibits a weakly damped mode 2π(-1.04 + j18.41). Due to the weak grid instability of the GFLs and the fact that GFL8 is farthest from the infinite bus, this may mean that GFL8 has the greatest impact on this mode.

[0131] The participation evaluation results for EMAI and MASS are shown in Table 1. Columns 2 and 4 represent the ED participation evaluation for both methods, and columns 3 and 5 represent the SD participation evaluation for both methods. The evaluation results for the two methods are very close, which effectively demonstrates that EMAI can achieve the same evaluation results as MASS.

[0132] Table 1. Evaluation Results of Two Modal Analysis Methods

[0133]

[0134] Table 1 shows that GFL8 is the dominant component affecting system stability, while PF... meThe highest value indicates that the ED of GFL8 plays a dominant role, therefore the CCL parameters need to be readjusted to improve system stability. According to the analysis, the parameters PF of the CCL proportional gain and integral gain of GFL8 are -68.56-j18.37 and -0.125+j0.601, respectively. From the real part of parameter PF, it can be seen that increasing the CCL proportional gain is the most effective measure to increase the damping of this mode, and this will also reduce the oscillation frequency of this mode. Increasing the CCL proportional gain to 0.3 changes the mode to 2π(-2.32+j18.11). A step fault with an active load of 0.1 pu was set on bus 8 before and after parameter adjustment. Simulation results are as follows: Figure 6 As shown, the reduction in the peak value of the oscillation waveform after parameter adjustment demonstrates the effectiveness of the improvement measures.

[0135] The method described in this application considers the influence of interactions between different controllers within a grid-connected inverter, effectively solving the problem of assessing the gray-box participation level in the dominant dynamics of different controllers within the grid-connected inverter. This method is applicable to power systems containing a high proportion of grid-connected inverters, and can effectively improve system stability based on explicit participation sensitivity factors in different controllers of the grid-connected inverter. The proposed method is computationally simple and has good practical engineering application value, enabling rapid and convenient assessment of the root causes affecting system stability within the grid-connected inverter.

[0136] Based on the same inventive concept, this application also provides a grid-connected inverter dynamic gray box modal analysis device for implementing the above-mentioned grid-connected inverter dynamic gray box modal analysis method. The solution provided by this device is similar to the solution described in the above method. Therefore, the specific limitations of one or more embodiments of the grid-connected inverter dynamic gray box modal analysis device provided below can be found in the limitations of the grid-connected inverter dynamic gray box modal analysis method described above, and will not be repeated here.

[0137] In one exemplary embodiment, a grid-connected inverter dynamic gray box modal analysis device is provided, comprising:

[0138] The overall admittance determination module is used to determine the overall admittance of any grid-connected inverter connected to any bus in a power system when aligned to the global coordinate system, based on split dynamics. Split dynamics are obtained by splitting the dynamics of the grid-connected inverter based on admittance splitting theory. Split dynamics include electromagnetic dynamics dominated by the current control loop and synchronous dynamics dominated by the phase-locked loop. The overall admittance includes a first part admittance, a second part admittance, and a third part admittance that characterize the electromagnetic dynamics and synchronous dynamics. The first part admittance and the third part admittance are each related to the parameters of the current control loop and the phase-locked loop, while the second part admittance is affected by the coupling effect of the parameters of the two control loops, the current control loop and the phase-locked loop.

[0139] The overall participation factor determination module is used to determine the disturbance amount based on the overall admittance for any bus-connected grid-connected inverter in the power system, and to determine the overall participation factor based on the disturbance amount. The overall participation factor includes a participation factor characterizing the degree of electromagnetic dynamics participation and a participation factor characterizing the degree of synchronous dynamics participation. The participation factor characterizing the degree of electromagnetic dynamics participation is jointly caused by the first part admittance and the second part admittance, while the participation factor characterizing the degree of synchronous dynamics participation is jointly caused by the second part admittance and the third part admittance.

[0140] The participation ratio calculation module is used to normalize and convert the overall participation factor based on the participation ratio of any grid-connected inverter in the power system, and to locate the dominant controller based on the calculated participation ratio value; the dominant controller is the controller that plays a leading role in the stability of the power system.

[0141] The parameter sensitivity determination module is used to calculate the explicit parameter participation factor for any bus-connected grid-connected inverter in a power system based on the dominant controller and overall admittance, and determine the parameter sensitivity to improve the stability of the power system. The parameter sensitivity characterizes the influence of the sensitivity of the parameters in the overall admittance on the dominant characteristic value of the power system dynamics.

[0142] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 7 As shown, the computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operating system and computer programs in the non-volatile storage media to run. The database is used for gray-box modal analysis data of grid-connected inverter dynamics. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a gray-box modal analysis method for grid-connected inverter dynamics.

[0143] Those skilled in the art will understand that Figure 7The structures shown are merely block diagrams of some structures related to the present application and do not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than shown in the figures, or combine certain components, or have different component arrangements. In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0144] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0145] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0146] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0147] 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. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0148] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0149] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0150] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for dynamic gray-box modal analysis of a grid-connected inverter, characterized in that, The grid-connected inverter dynamic gray box modal analysis method includes: For any grid-connected inverter in a power system connected to a bus, the overall admittance when aligned to the global coordinate system is determined based on split dynamics. The split dynamics are obtained by splitting the dynamics of the grid-connected inverter based on admittance splitting theory. The split dynamics include electromagnetic dynamics dominated by the current control loop and synchronous dynamics dominated by the phase-locked loop. The overall admittance includes a first part admittance, a second part admittance, and a third part admittance characterizing the electromagnetic dynamics and synchronous dynamics. The first part admittance and the third part admittance are each related to the parameters of the current control loop and the phase-locked loop, while the second part admittance is affected by the coupling effect of the parameters of the two control loops, the current control loop and the phase-locked loop. For any bus-connected grid-connected inverter in a power system, the disturbance is determined based on the overall admittance, and the overall participation factor is determined based on the disturbance. The overall participation factor includes a participation factor characterizing the degree of electromagnetic dynamics participation and a participation factor characterizing the degree of synchronous dynamics participation. The participation factor characterizing the degree of electromagnetic dynamics participation is jointly caused by the first part admittance and the second part admittance, while the participation factor characterizing the degree of synchronous dynamics participation is jointly caused by the second part admittance and the third part admittance. For any grid-connected inverter in the power system, the overall participation factor is normalized and calculated based on the participation ratio, and the dominant controller is located according to the calculated participation ratio value; the dominant controller is the controller that plays a leading role in the stability of the power system. For any bus-connected grid-connected inverter in a power system, the explicit parameter participation factor is calculated based on the dominant controller and the overall admittance to determine the parameter sensitivity, which is used to improve the stability of the power system. The parameter sensitivity characterizes the influence of the sensitivity of the parameters in the overall admittance on the dominant characteristic value of the power system dynamics.

2. The method for dynamic gray-box modal analysis of grid-connected inverters according to claim 1, characterized in that, The expression for the overall admittance is: Among them, Y mDQ For overall admittance; The angle deviation matrix determined for the initial power flow; Y medq K represents the overall admittance of the electromagnetic dynamics in the current control loop. mU K is the coefficient matrix related to steady-state voltage. mI This is the coefficient matrix related to the steady-state current; U mPLL The equivalent voltage caused by the phase-locked loop parameters; Angle deviation matrix determined for the initial power flow Perform the inverse operation; Y meDQ The first admittance characterizing electromagnetic dynamics and synchronicity dynamics; Y msDQ1 The second admittance characterizing electromagnetic dynamics and synchronicity dynamics; Y msDQ2 The third part, admittance, characterizes electromagnetic dynamics and synchronicity dynamics.

3. The method for dynamic gray-box modal analysis of grid-connected inverters according to claim 2, characterized in that, The expression for the disturbance is: Where, ΔY mDQ For overall admittance Y mDQ The disturbance amount; ΔY meDQ The first admittance Y characterizing electromagnetic dynamics and synchronicity dynamics meDQ The disturbance amount; ΔY msDQ1 The second admittance Y, characterizing electromagnetic dynamics and synchronicity dynamics msDQ1 The disturbance amount; ΔY msDQ2 The third admittance Y, characterizing electromagnetic dynamics and synchronicity dynamics msDQ2 The disturbance amount; ΔY medq The global admittance Y of the electromagnetic dynamics in the current control loop medq The disturbance amount; E2 is the second-order identity matrix; ΔK mU The coefficient matrix K related to the steady-state voltage mU The disturbance quantity; ΔK mI The coefficient matrix K related to the steady-state current mI The disturbance quantity; ε me and ε ms Both are scalars representing the degree of disturbance.

4. The method for dynamic gray-box modal analysis of grid-connected inverters according to claim 1, characterized in that, The expression for the overall participation factor is: Among them, PF me PF is a participation factor characterizing the degree of involvement in electromagnetic dynamics. ms λ is the participation factor characterizing the degree of involvement in synchronization dynamics; <,> is the Frobenius inner product; λ k This is the k-th characteristic value of the power system; For the dynamic node impedance matrix elements Z of the entire power system mm In λ k Take the residue at the specified position; * indicates taking the conjugate transpose of the matrix; Y meDQ (λ k ) is in λ k The first part of the admittance at Y; msDQ1 (λ k ) is in λ k The second admittance at Y; msDQ2 (λ k ) is in λ k The third part of the admittance.

5. The method for dynamic gray-box modal analysis of grid-connected inverters according to claim 1, characterized in that, The formula for calculating the participation ratio is: |PF me' |=|PF mid |+|PF miq | |PF ms' |=|PF mθ |+|PF mω | Among them, PR me To characterize the participation ratio of electromagnetic dynamics based on EMAI; PR ms The participation ratio for synchronicity dynamics is characterized based on EMAI; PF me PF is a participation factor based on EMAI to characterize the degree of electromagnetic dynamics involvement. ms PP is a participation factor based on EMAI to characterize the degree of synchronous dynamics participation; m is the bus number in the power system; me , representing the participation ratio of electromagnetic dynamics based on MASS characterization; PR ms , representing the participation ratio based on MASS characterization of synchronization dynamics; PF me , is a participation factor based on MASS to characterize the degree of electromagnetic dynamics involvement; PF ms , is a participation factor based on MASS to characterize the degree of participation in synchronization dynamics; PR mid PF is the participation factor of the integral element of the d-axis PI controller in the current control loop. miq PF is the participation factor of the integral element of the q-axis PI controller in the current control loop. mθ PF is the participation factor for the angle variable of the phase-locked loop. mω This is the participation factor of the PI integral stage controller in the phase-locked loop.

6. The method for dynamic gray-box modal analysis of grid-connected inverters according to claim 1, characterized in that, The expression corresponding to the parameter sensitivity of the PI controller in the current control loop is: in, The sensitivity of the proportional gain parameter of the PI controller; The parameter sensitivity of the integral gain of the PI controller; s is the Laplace operator; G del For the control delay transfer function; Z medq K represents the impedance of the electromagnetic dynamics in the current control loop. pi K represents the proportional gain of the PI controller. ii The integral gain of the PI controller; The parameter sensitivity in a phase-locked loop and the equivalent voltage U caused by the phase-locked loop parameters mPLL Related; U mPLL Determined by measurement.

7. A grid-connected inverter dynamic gray box modal analysis device, characterized in that, The grid-connected inverter dynamic gray box modal analysis device includes: The overall admittance determination module is used to determine the overall admittance of any grid-connected inverter in a power system when aligned to the global coordinate system, based on split dynamics. The split dynamics are obtained by splitting the dynamics of the grid-connected inverter based on admittance splitting theory. The split dynamics include electromagnetic dynamics dominated by the current control loop and synchronous dynamics dominated by the phase-locked loop. The overall admittance includes a first part admittance, a second part admittance, and a third part admittance characterizing the electromagnetic dynamics and synchronous dynamics. The first part admittance and the third part admittance are respectively related to the parameters of the current control loop and the phase-locked loop, while the second part admittance is affected by the coupling of the parameters of the two control loops, the current control loop and the phase-locked loop. The overall participation factor determination module is used to determine the disturbance amount based on the overall admittance for any grid-connected inverter in the power system, and to determine the overall participation factor based on the disturbance amount. The overall participation factor includes a participation factor characterizing the degree of electromagnetic dynamics participation and a participation factor characterizing the degree of synchronous dynamics participation. The participation factor characterizing the degree of electromagnetic dynamics participation is jointly caused by the first part admittance and the second part admittance, while the participation factor characterizing the degree of synchronous dynamics participation is jointly caused by the second part admittance and the third part admittance. The participation ratio calculation module is used to normalize and convert the overall participation factor based on the participation ratio of any grid-connected inverter connected to any bus in the power system, and to locate the dominant controller based on the calculated participation ratio value; the dominant controller is the controller that plays a leading role in the stability of the power system. The parameter sensitivity determination module is used to calculate the explicit parameter participation factor for any bus-connected grid-connected inverter in the power system based on the dominant controller and the overall admittance, and determine the parameter sensitivity to improve the stability of the power system; the parameter sensitivity characterizes the influence of the sensitivity of the parameters in the overall admittance on the dominant characteristic value of the power system dynamics.

8. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the grid-connected inverter dynamic gray box modal analysis method according to any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the gray box modal analysis method for grid-connected inverters as described in any one of claims 1-6.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the gray box modal analysis method for grid-connected inverters as described in any one of claims 1-6.

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