A Wide-Frequency Oscillation Analysis Method, Device and Medium for a Network-Forming Photovoltaic Grid-Connected System

Abstract

The present application discloses a wide - frequency oscillation analysis method, device and medium for a network - forming photovoltaic grid - connected system, which relates to the field of power system stability analysis. The method includes: discretizing the electromagnetic transient continuous - state space models of each component in the network - forming photovoltaic grid - connected system respectively to obtain the electromagnetic transient discrete - state space models, and further determining the electromagnetic transient discrete equivalent circuit; using the adjoint circuit method, according to the electromagnetic transient discrete equivalent circuits and electromagnetic transient discrete - state space models of each component in the system, determining the electromagnetic transient discrete - state space model of the system, and then performing eigenvalue modal analysis to calculate the eigenvalues, modal frequencies, damping ratios and participation factors; the eigenvalues, modal frequencies and damping ratios characterize the stability of the network - forming photovoltaic grid - connected system, and the participation factors are used to locate the characteristic state variables that cause modal instability in the network - forming photovoltaic grid - connected system. The present application can quickly and accurately realize the wide - frequency oscillation analysis of the network - forming photovoltaic grid - connected system.

Description

Technical Field

[0001] The present application relates to the field of power system stability analysis, and in particular, to a method, device, and medium for analyzing broadband oscillations in a network-forming photovoltaic grid-connected system. Background Art

[0002] With the transformation of the energy structure and the large-scale access of new energy sources such as wind power and photovoltaic power, new energy is gradually becoming the main form of energy supply in the future "new power system". The power electronic characteristics of the power system are becoming more and more prominent, and the application of power electronic converters in the power system is becoming increasingly widespread. However, due to the multi-time scale control characteristics of power electronic devices and the uncertainty of new energy itself, the safe and stable operation of the "new power system" faces new threats and challenges. In contrast, the core of the traditional power system is the synchronous generator set, and the oscillation problem mainly focuses on the low-frequency band. The broadband oscillation phenomenon in the "new power system" covers a very wide frequency range, from low frequency to high frequency, and its oscillation form shows rich and diverse characteristics. These broadband oscillations also exhibit significant time-varying and wide-area propagation characteristics, posing complex and severe challenges to the stability of the power system. Summary of the Invention

[0003] The purpose of the present application is to provide a method, device, and medium for analyzing broadband oscillations in a network-forming photovoltaic grid-connected system, which can quickly and accurately analyze the broadband oscillations of the network-forming photovoltaic grid-connected system.

[0004] To achieve the above purpose, the present application provides the following solutions:

[0005] In a first aspect, the present application provides a method for analyzing broadband oscillations in a network-forming photovoltaic grid-connected system, including:

[0006] Construct an electromagnetic transient continuous state space model of each component in the network-forming photovoltaic grid-connected system; the network-forming photovoltaic grid-connected system includes a power supply side component unit and an AC side component unit; both the power supply side component unit and the AC side component unit include multiple components;

[0007] Based on bilinear transformation, discretize the electromagnetic transient continuous state space model of each component to obtain the corresponding electromagnetic transient discrete state space model;

[0008] Based on the electromagnetic transient discrete state space model of each component, determine the corresponding electromagnetic transient discrete equivalent circuit;

[0009] Adopt the adjoint circuit method, and according to the electromagnetic transient discrete equivalent circuit and the electromagnetic transient discrete state space model of each component in the network-forming photovoltaic grid-connected system, determine the electromagnetic transient discrete state space model of the network-forming photovoltaic grid-connected system;

[0010] Perform eigenvalue modal analysis on the electromagnetic transient discrete state space model of the grid-forming PV grid-connected system to calculate eigenvalues, modal frequencies, damping ratios, and participation factors; the eigenvalues, the modal frequencies, and the damping ratios are all used to characterize the stability of the grid-forming PV grid-connected system, and the participation factors are used to locate the characteristic state variables that cause modal instability in the grid-forming PV grid-connected system.

[0011] In a second aspect, the present application provides a computer device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor, where the processor executes the computer program to implement the wide-frequency oscillation analysis method for the grid-forming PV grid-connected system.

[0012] In a third aspect, the present application provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the wide-frequency oscillation analysis method for the grid-forming PV grid-connected system is implemented.

[0013] According to the specific embodiments provided by the present application, the present application has the following technical effects: The present application provides a wide-frequency oscillation analysis method, device, and medium for a grid-forming PV grid-connected system, establishes an electromagnetic transient continuous state space model of each component in the grid-forming PV grid-connected system, then discretizes it based on bilinear transformation to form an electromagnetic transient discrete state space model and an electromagnetic transient discrete equivalent circuit of each component, uses the adjoint circuit method to form an electromagnetic transient discrete state space model of the grid-forming PV grid-connected system, and obtains eigenvalues, modal frequencies, damping ratios, and participation factors in the discrete domain based on this model to analyze the stability of the system and locate the dominant influencing factors of the unstable mode. The above overall process provided by the present application can provide an accurate electromagnetic transient discrete state space model of the grid-forming PV grid-connected system for the wide-frequency oscillation characteristic analysis of the "new power system" with large-scale power electronics, and simplifies the selection process of its state variables, thereby quickly and accurately realizing the wide-frequency oscillation analysis of the grid-forming PV grid-connected system. Description of the Drawings

[0014] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0015] Figure 1 It is a schematic flowchart of a wide-frequency oscillation analysis method for a grid-forming PV grid-connected system provided by an embodiment of the present application.

[0016] Figure 2Schematic diagram of the structure of a single-stage network-forming photovoltaic grid-connected system provided by an embodiment of the present application.

[0017] Figure 3 Block diagram of the DC voltage matching control link provided by an embodiment of the present application.

[0018] Figure 4 Block diagram of the droop control link and voltage and current inner loop control link of the network-forming photovoltaic grid-connected system provided by an embodiment of the present application.

[0019] Figure 5 Schematic diagram of the electromagnetic transient discrete equivalent circuit of the photovoltaic power generation unit provided by an embodiment of the present application.

[0020] Figure 6 Schematic diagram of the electromagnetic transient discrete equivalent circuit of the inductor branch provided by an embodiment of the present application.

[0021] Figure 7 Schematic diagram of the electromagnetic transient discrete equivalent circuit of the capacitor branch provided by an embodiment of the present application.

[0022] Figure 8 Schematic diagram of the electromagnetic transient discrete equivalent circuit of the resistor branch provided by an embodiment of the present application.

[0023] Figure 9 Schematic diagram of the electromagnetic transient discrete equivalent circuit of the initial system provided by an embodiment of the present application.

[0024] Figure 10 Schematic diagram of the discrete time-domain eigenvalue stability region provided by an embodiment of the present application.

[0025] Figure 11 Schematic diagram of the structure of a computer device provided by an embodiment of the present application. Detailed implementation manners

[0026] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application.

[0027] The eigenvalue analysis method is a commonly used tool for power system stability assessment. By establishing the state - space model of the system and then calculating the eigenvalues of the state matrix, this method can evaluate the dynamic stability of the power system and identify possible oscillation modes. These eigenvalues reveal the response characteristics of the power system at different frequencies, including the frequency, decay rate, and stability of the oscillation. Moreover, based on modal analysis, the dominant influencing factors related to the oscillation modes can be obtained, providing key information for deeply understanding the dynamic behavior of power system oscillations and designing effective control strategies. Therefore, the "eigenvalue analysis method" can be used for the broadband oscillation analysis of the "new power system".

[0028] In view of the complexity of large - scale "new power systems", a discrete state - space modeling strategy can be introduced. This strategy draws on the core concept of EMTP (Electro - Magnetic Transient Program) modeling, and equivalently transforms system components into a parallel model of conductance and historical current sources. In this framework, the historical current source terms are selected as key state variables, and this selection is based on the linear independence shown among them, fully meeting the strict conditions for state variable selection. The discrete state - space modeling method effectively simplifies the complex process of state variable selection when performing state - space modeling for large - scale systems, providing a more efficient and accurate approach for power system analysis.

[0029] As an important part of the "new power system", it is necessary to establish a discrete state - space model for network - forming photovoltaic power generation. Based on the above analysis, this application provides a broadband oscillation analysis method, device, and medium for a network - forming photovoltaic grid - connected system, constructing an electromagnetic transient discrete state - space model of the network - forming photovoltaic grid - connected system suitable for analyzing the broadband oscillation characteristics of large - scale power - electronic "new power systems". This model can deeply analyze the oscillation characteristics of the network - forming photovoltaic grid - connected system in the broadband range. Through this model, not only can a comprehensive broadband oscillation analysis of the network - forming photovoltaic grid - connected system be carried out, but also the dominant influencing factors affecting system stability can be effectively identified, thus providing an important basis for the stable operation and optimal design of the system.

[0030] To make the above - mentioned objects, features, and advantages of this application more obvious and understandable, the following further details this application in conjunction with the drawings and specific embodiments.

[0031] In an exemplary embodiment, as Figure 1 shown, a broadband oscillation analysis method for a network - forming photovoltaic grid - connected system is provided. This method is executed by a computer device, which can be specifically executed alone by a computer device such as a terminal or a server, or jointly executed by a terminal and a server. In the embodiments of this application, it includes the following steps 101 to 105.

[0032] Step 101, construct an electromagnetic transient continuous state space model for each component in the grid-forming PV grid-connected system; the grid-forming PV grid-connected system includes a power-side component unit and an AC-side component unit; both the power-side component unit and the AC-side component unit include multiple components.

[0033] Specifically, the power-side component unit is a photovoltaic power generation unit, including a photovoltaic array, a DC capacitor, a three-phase single-stage inverter, and an output filter; among them, the control of the three-phase single-stage inverter is jointly realized by a DC voltage matching control link, a reactive power droop control link, and a voltage-current inner loop control link.

[0034] The DC voltage matching control link realizes the self-synchronization function of the inverter and the grid by precisely utilizing the dynamic characteristics of the DC capacitor, ensuring that the inverter can seamlessly connect to the grid. The droop control link provides dynamic voltage support for the inverter through a reactive power-voltage droop control strategy, enabling it to adjust the output voltage according to the grid demand and enhancing the stability and flexibility of the system; the voltage-current inner loop control link, as the core control part, is responsible for quickly and accurately adjusting the output voltage and current of the inverter to achieve precise tracking and response to the grid, further improving the dynamic performance and power quality of the system.

[0035] Figure 2 It is a schematic diagram of a single-stage grid-forming PV grid-connected system. The DC capacitor is connected in parallel with the photovoltaic array. The DC capacitor is used to smooth the direct current generated by the photovoltaic array and then send it to the three-phase single-stage inverter. DC-AC conversion is performed in the three-phase single-stage inverter to convert the direct current into alternating current with the same frequency and phase as the grid. The output end of the three-phase single-stage inverter is connected to the input end of the output filter to suppress harmonics and filter the alternating current output by the three-phase single-stage inverter through an LCL filter to ensure that the power quality meets the grid requirements and finally safely and efficiently connect to the grid; the output end of the output filter is connected to the grid. Figure 2 In it, C dc is the DC capacitor, L C1 , L C2 are divided into the filter inductor on the inverter side and the filter inductor on the grid side, C f is the filter capacitor, R g and L g are respectively the equivalent resistance and inductance of the line; I pv , I dc , i k , i g are divided into the current generated by the photovoltaic array, the current flowing into the inverter, the current flowing out of the inverter, and the grid-connected current; U dc , u k , u cf , u g, u s are the DC voltage, the inverter output voltage, the voltage at the parallel connection point of the filter capacitor, the grid connection point voltage, and the AC grid voltage, respectively.

[0036] (11) When the component is a photovoltaic array, based on the engineering model of the photovoltaic cell, using the four electrical performance parameters (including the short-circuit current I ref = 25 °C, S ref = 1000 W / m 2 ) provided by the manufacturer under standard operating conditions, the U-I characteristic equation of the photovoltaic cell under non-standard conditions is derived: scref , the maximum power point current I mref , the open-circuit voltage U ocref , the maximum power point voltage U mref )

[0037]

[0038]

[0039] The electrical parameters I sc , I m , U oc , U m corresponding to the non-standard cell temperature and light intensity can be derived according to the parameters under standard test conditions through the following formula.

[0040]

[0041] Among them, S is the actual light intensity; T air is the actual air temperature; T ref is the reference value of the air temperature; S ref is the reference value of the light intensity; k is the temperature coefficient, usually taking a value of 0.03 °C·m 2 / W; a, b, c are compensation coefficients, usually taking values of 0.0025 / °C, 0.5, 0.00288 / °C respectively; e is the base of the natural logarithm, usually approximated as 2.71828.

[0042] Let the number of series-connected photovoltaic cells in the photovoltaic array be N s , and the number of parallel-connected cells be N p . Using the engineering model of the photovoltaic cell, the U-I characteristic equation of the photovoltaic array under standard operating conditions is:

[0043]

[0044] After linearizing the U-I characteristic equation of the photovoltaic array and combining Figure 2 the small-signal equation of the photovoltaic array can be obtained, that is, the electromagnetic transient continuous state space model corresponding to the photovoltaic array is:

[0045]

[0046] Among them, I pv is the output current of the photovoltaic array, V pv is the output voltage of the photovoltaic array, Δ represents the change of each variable, ΔI pv , ΔV pv are both algebraic variables. The subscript 0 represents the steady-state value of each variable. Specifically, I sc0 is the short-circuit current of the photovoltaic cell at steady state, V pv0 is the output voltage of the photovoltaic array at steady state, U oc0 is the open-circuit voltage of the photovoltaic cell at steady state. C1 and C2 are intermediate parameters.

[0047] (12) When the component is a DC capacitor, based on KCL, the basic characteristics of the capacitor component and combined with Figure 2 the characteristic equation of the DC capacitor can be deduced:

[0048]

[0049] Considering that the switching loss of the inverter is small, this factor can be ignored during the modeling process. Therefore, the sum of the power increased by the DC capacitor and the power output by the inverter is equal to the power output by the photovoltaic array. From the instantaneous power theory (coordinate transformation uses equal-amplitude transformation), it can be deduced that:

[0050]

[0051] Substitute the formula deduced from the above instantaneous power theory into the characteristic equation of the DC capacitor, and substitute i qg = 0, u qg = 0 to get:

[0052]

[0053] After linearizing the above equation, the small-signal model of the DC-side filter capacitor can be obtained, that is, the electromagnetic transient continuous state space model corresponding to the DC capacitor is:

[0054]

[0055] Among them, ΔV pv = ΔU dc ; C dc is the capacitance value of the DC capacitor, U dc is the DC voltage, u dg is the d-axis component of the grid-connected connection point voltage, i dg is the d-axis component of the grid-connected current.

[0056] (13) When the component is an output filter, based on KCL, KVL, the basic characteristics of capacitors and inductors, and combined with Figure 2 the filter characteristic equation can be deduced as follows:

[0057]

[0058] By performing abc / dq coordinate transformation and linearization on the above equations, the small-signal equations of the output filter in the dq coordinate system can be obtained, that is, the electromagnetic transient continuous state space model corresponding to the output filter is:

[0059]

[0060] where, i dk is the d-axis component of the current flowing out of the three-phase single-stage inverter, i qk is the q-axis component of the current flowing out of the three-phase single-stage inverter, i dg is the d-axis component of the grid-connected current, i qg is the q-axis component of the grid-connected current, u dcf is the d-axis component of the voltage at the parallel point of the filter capacitor, u qcf is the q-axis component of the voltage at the parallel point of the filter capacitor, u dk is the d-axis component of the output voltage of the three-phase single-stage inverter, u qk is the q-axis component of the output voltage of the three-phase single-stage inverter, u dg is the d-axis component of the voltage at the grid connection point, u qg is the q-axis component of the voltage at the grid connection point, ω is the AC side angular frequency of the grid-forming PV grid-connected system, C f is the filter capacitor, L C1 and L C2 are the filter inductors on the inverter side and the grid side respectively.

[0061] (14) When the component is a three-phase single-stage inverter, as Figure 3 shown, it is the control block diagram of the DC voltage matching control link. Among them, the following equations can be written according to the block diagram of the DC voltage matching control link:

[0062]

[0063] ω = x1 + ω0.

[0064] By linearizing the above two equations and substituting ΔU dcref = 0, the small-signal equations of the DC voltage matching control link can be obtained as:

[0065]

[0066] As Figure 4As shown, the block diagram of the droop control link and the voltage and current inner loop control link of the grid-forming PV grid-connected system. The following equations can be written based on the block diagram of the droop control link and the voltage and current inner loop control link:

[0067]

[0068]

[0069] Linearize the above two equations and substitute ΔU g = 0, ΔQ ref = 0, u qgref = 0, Q = 1.5×(u qg i dg -u dg i qg ), i qg0 = 0, u qg0 = 0. Then the small-signal equations of the droop control link and the voltage and current inner loop control link can be obtained as:

[0070]

[0071]

[0072] Among them, x1, x2, x3, x4, x5, θ P are state variables, u dk , u qk are algebraic variables; M Q is the droop coefficient of Q-V reactive power droop control, M T is the tracking coefficient of the DC voltage, M D is the damping coefficient equivalent to inertial synchronization, M J is the inertia coefficient equivalent to inertial synchronization, Q is the reactive power generated by the inverter, Q ref is the reference value of the reactive power generated by the inverter, U gref is the reference value of the grid-connected point voltage amplitude, U dc is the DC voltage, U dcref is the reference value of the DC voltage, k pud is the PI proportional coefficient of the d-axis voltage inner loop, k iud is the PI integral coefficient of the d-axis voltage inner loop, k puq is the PI proportional coefficient of the q-axis voltage inner loop, k iuq is the PI integral coefficient of the q-axis voltage inner loop, k pid is the proportional coefficient of the d-axis current inner loop, k iid is the integral coefficient of the d-axis current inner loop, k piq is the proportional coefficient of the q-axis current inner loop, k iiq is the integral coefficient of the q-axis current inner loop.

[0073] The small signal differential equations and algebraic equations of each component of the photovoltaic power generation unit are arranged into the following matrix form:

[0074]

[0075] Among them, A1, B1, C1, A2, B2, C2 are all coefficient matrices, x pv is the state variable column vector; u inter is the intermediate variable column vector, u gdq is the terminal voltage column vector of the photovoltaic power generation unit.

[0076] x pv =[U dc ,i dk ,i qk ,i dg ,i qg ,u dcf ,u qcf ,x1,x2,x3,x4,x5,θ P ].

[0077] u inter =[I pv ,ω,u dk ,u qk ].

[0078] u gdq =[u dg ,u qg ].

[0079] Substitute the algebraic equations of each component of the photovoltaic power generation unit into the small signal differential equation and eliminate the intermediate variable u inter The following equation can be obtained:

[0080]

[0081] Among them, the expressions of the state matrix and input matrix are:

[0082]

[0083] The current expression of the photovoltaic power generation unit output to the network is:

[0084] i gdq =C pv x pv .

[0085] Among them, C pv is the coefficient matrix, i gdq =[i dg ,i qg ], eliminating the intermediate variable u interAfter obtaining the equations and the current expression of the photovoltaic power generation unit output to the network, the electromagnetic transient continuous state space model corresponding to the power supply side component unit can be obtained as follows:

[0086]

[0087] Among them, A pv and B pv are both coefficient matrices; i gdq is the current output by the photovoltaic power generation unit to the network.

[0088] In an application example, the AC side component unit includes an inductor branch, a capacitor branch, and a resistor branch, and all are connected to the power grid. Specifically, common components on the AC side (such as transformers, transmission lines, etc.) can usually be simulated and represented by three-phase R-L-C parallel or series branches. Given the wide application and fundamental status of the electromagnetic transient continuous state space models of the inductor, capacitor, and resistor branches in the power system, the detailed construction process will not be repeated here.

[0089] Step 102: Based on the bilinear transformation, discretize the electromagnetic transient continuous state space model of each component to obtain the corresponding electromagnetic transient discrete state space model.

[0090] Specifically, the electromagnetic transient discrete state space expressions of the photovoltaic power generation unit, the inductor branch, and the capacitor branch are respectively expressed as follows:

[0091]

[0092]

[0093] Among them, h pv 、h L 、h C are the historical current terms of the photovoltaic power generation unit, the inductor branch, and the capacitor branch respectively; i gdq 、i Ldq 、i Cdq are the terminal current of the photovoltaic power generation unit, the inductor branch current, and the capacitor branch current in the dq coordinate system respectively; u gdq 、u Ldq 、u Cdq are the terminal voltage of the photovoltaic power generation unit, the inductor branch voltage, and the capacitor branch voltage in the dq coordinate system respectively; the rest are coefficient matrices.

[0094] Step 103: Based on the electromagnetic transient discrete state space model of each component, determine the corresponding electromagnetic transient discrete equivalent circuit; specifically, integrate the photovoltaic power generation unit into a single-port component, and integrate the inductor branch, capacitor branch, and resistor branch into a two-port component. The electromagnetic transient discrete equivalent circuits of the photovoltaic power generation unit, inductor branch, capacitor branch, and resistor branch are respectively as followsFigures 5 - 8 as shown, where g pv = D pv and g L = D L and g C = D C and g R = 1 / R.

[0095] Step 104: Using the adjoint circuit method, determine the electromagnetic transient discrete state space model of the network-forming PV grid-connected system according to the electromagnetic transient discrete equivalent circuits and electromagnetic transient discrete state space models of the components in the network-forming PV grid-connected system.

[0096] Specifically, Step 104 includes:

[0097] (41) Determine the system topology according to the network-forming PV grid-connected system, and at this time, the main circuit of the network-forming PV grid-connected system can be obtained.

[0098] (42) Using the adjoint circuit method, determine the initial system electromagnetic transient discrete equivalent circuit according to the system topology and the electromagnetic transient discrete equivalent circuits of the components, as Figure 9 shown.

[0099] (43) According to the initial system electromagnetic transient discrete equivalent circuit, determine the branch-node incidence matrix and conductance matrix; among them, the branch-node incidence matrix L is:

[0100]

[0101] The conductance matrix G is:

[0102]

[0103] (44) Using the adjoint circuit method, determine the electromagnetic transient discrete state space model of the network-forming PV grid-connected system according to the branch-node incidence matrix, the conductance matrix and the electromagnetic transient discrete state space models of the components. According to this model, the oscillation characteristics and stability of the system can be deeply analyzed, and an accurate model basis can be provided for the oscillation characteristic analysis of the large-scale power electronic "new power system", and the process of selecting state variables can be simplified.

[0104] First, organize the historical current source iterative formula and output current expression of each component in the network-forming PV grid-connected system to obtain:

[0105]

[0106] Based on the relationships between branch currents and voltages and node currents and voltages, combined with the branch-node incidence matrix and the conductance matrix, by eliminating the intermediate variables in the historical current source iterative formula in the above equations, the electromagnetic transient discrete state space model of the grid-forming PV grid-connected system can be obtained as follows:

[0107]

[0108] where, I 2×2 is a 2×2 identity matrix, g pv is the conductance corresponding to the power source side component unit in the initial system electromagnetic transient discrete equivalent circuit, g line-L is the conductance corresponding to the line inductance in the initial system electromagnetic transient discrete equivalent circuit, is the conductance corresponding to the line resistance in the initial system electromagnetic transient discrete equivalent circuit, h sys (t) is the current source at time t, A dsys is the electromagnetic transient discrete state matrix, h sys (t - Δt) is the current source at time t - Δt, A sys , B sys , C sys are all coefficient matrices, () T represents the transpose of the matrix.

[0109] Step 105: Perform eigenvalue modal analysis on the electromagnetic transient discrete state space model of the grid-forming PV grid-connected system to calculate eigenvalues, modal frequencies, damping ratios, and participation factors; the eigenvalues, the modal frequencies, and the damping ratios are all used to characterize the stability of the grid-forming PV grid-connected system, and the participation factors are used to locate the characteristic state variables that cause modal instability in the grid-forming PV grid-connected system.

[0110] Among them, performing eigenvalue modal analysis on the electromagnetic transient discrete state space model of the grid-forming PV grid-connected system includes:

[0111] (51) Solve the electromagnetic transient discrete state matrix according to the electromagnetic transient discrete state space model of the grid-forming PV grid-connected system; the electromagnetic transient discrete state matrix contains multiple discrete eigenvalues z i (i = 1, 2... n); as Figure 10 shown, the stability of the grid-forming PV grid-connected system is determined by the positions of the discrete eigenvalues in the z-plane. When the magnitudes of all discrete eigenvalues in the polar coordinate system are less than 1, the grid-forming PV grid-connected system is in a stable state; otherwise, it is unstable.

[0112] (52) Calculate the modal frequency and damping ratio according to the eigenvalues in the electromagnetic transient discrete state matrix. In the discrete domain, the modal frequency can be expressed as the ratio of the phase angle of the discrete eigenvalue to the discrete step size, while the damping ratio is used to describe the distance of the discrete eigenvalue from the stable boundary (i.e., the unit circle) in the z-plane. Based on this, the calculation formulas for the modal frequency and the damping ratio are as follows:

[0113]

[0114] where f d represents the frequency of the mode, α d is the damping ratio, is the phase angle of the discrete eigenvalue in the polar coordinate system, |λ d | represents the magnitude of the discrete eigenvalue, Δt d represents the discrete step size, X d is the abscissa of the discrete eigenvalue in the polar coordinate system, and Y d is the ordinate of the discrete eigenvalue in the polar coordinate system.

[0115] As Figure 10 shown, when α d > 0, the discrete eigenvalue is inside the unit circle in the z-plane, and the system is stable at this time; when α d < 0, the discrete eigenvalue is outside the unit circle in the z-plane, and the system is unstable at this time. By calculating the modal frequency and damping ratio in the discrete domain, the broadband oscillation stability of the network-forming photovoltaic grid-connected system can be quantitatively analyzed.

[0116] (53) According to matrix theory, diagonalize the electromagnetic transient discrete state matrix to obtain the left eigenvector matrix and the right eigenvector matrix.

[0117] Specifically, in the characteristic mode analysis of the discrete domain, a participation factor concept similar to that in the continuous domain analysis is adopted to quantify the influence degree of the system characteristic variables on the characteristic modes. The mathematical principles of these two analysis methods are the same and are both based on the modal decomposition principle of the state matrix. Based on this, in the process of diagonalizing the electromagnetic transient discrete state matrix according to matrix theory in this application, the formula used is:

[0118] P T A dsys Q = Λ dsys .

[0119] where A dsys is the electromagnetic transient discrete state matrix, P is the left eigenvector matrix, Q is the right eigenvector matrix, P T Q = I, and I is the identity matrix; Λ dsysis a diagonal matrix, and the elements in the diagonal matrix are all the eigenvalues of the electromagnetic transient discrete state matrix.

[0120] Perform the following linear transformation to obtain several new state variables Z sys (t), and these variables are called modal quantities.

[0121] h sys (t) = QZ sys (t).

[0122] Substitute the equations of the above modal quantities and the formula of diagonalization decomposition into the electromagnetic transient discrete state space model of the network-forming photovoltaic grid-connected system, then the electromagnetic transient discrete state space equation based on modal quantities can be obtained as follows:

[0123] Z sys (t) = Λ dsys Z sys (t - Δt).

[0124] In view of the diagonal property of the Λ dsys matrix, in the electromagnetic transient discrete state space of the system constructed by using modal quantities, the decoupling of characteristic modes can be achieved. On this basis, when performing modal analysis on the system, it can be carried out separately for each different eigenvalue.

[0125] (54) Determine the participation matrix based on the left eigenvector matrix and the right eigenvector matrix; the participation matrix includes multiple participation factors; the participation factors are used to quantify the influence degree of the characteristic state variables on the characteristic modes, and further locate the characteristic state variables that cause modal instability in the network-forming photovoltaic grid-connected system.

[0126] Similar to the method of continuous characteristic mode analysis, the right eigenvector matrix in the formula of diagonalization decomposition reveals the contribution of n independent modes in the network-forming photovoltaic grid-connected system to the dynamic behavior of discrete state variables, while the left eigenvector matrix reveals the controllability degree of discrete state variables to each mode. In order to more deeply reveal the internal connection between state variables and modal quantities, the concept of participation matrix is introduced, where the determination formula of the participation factor is:

[0127] C (m,n) = P (m,n) Q (m,n) .

[0128] Among them, the subscript (m, n) is the element value of the m-th row and the n-th column in the matrix; C is the participation matrix, C (m,,n)As a participation factor, it is a dimensionless constant used to measure the degree of association between the nth eigenmode and the mth eigenstate variable. By analyzing the magnitude of the participation factor, the state variable most closely associated with the dominant instability mode can be effectively identified, that is, the larger the absolute value of the participation factor, the closer the corresponding state variable is to the dominant instability eigenmode. Further, by examining the physical location or control link where the state variable is located, the key factors causing modal instability can be located, thus providing valuable reference for revealing the occurrence mechanism of system oscillation.

[0129] In an exemplary embodiment, a computer device is provided. The computer device can be a server or a terminal, and its internal structure diagram can be as Figure 11 shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O), and a communication interface. Among them, the processor, the memory, and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The input / output interface of the computer device is used to exchange information between the processor and external devices. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, it realizes the broadband oscillation analysis method for a networked photovoltaic grid-connected system.

[0130] Those skilled in the art can understand that Figure 11 the structure shown in

[0131] is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine some components, or have different component arrangements. In an exemplary embodiment, a computer device is provided, including a memory and a processor. A computer program is stored in the memory, and when the processor executes the computer program, the steps in the above method embodiments are realized.

[0132] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, and when the computer program is executed by the processor, the steps in the above method embodiments are realized.

[0133] 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 for analysis, stored data, displayed data, 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 relevant data need to comply with relevant regulations.

[0134] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, database, or other medium used in the embodiments provided in this application can include at least one of non-volatile and volatile memories. 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), magnetoresistive 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 be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0135] The databases involved in the embodiments provided in this application can include at least one of relational databases and non-relational databases. Non-relational databases can include distributed databases based on blockchain, etc., without limitation. The processors involved in the embodiments provided in this application can be general-purpose processors, central processors, graphics processors, digital signal processors, programmable logic devices, data processing logics based on quantum computing, etc., without limitation.

[0136] The technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, 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, it should be considered to be within the scope described in this specification.

[0137] In this article, specific examples are used to elaborate on the principles and implementation manners of this application. The descriptions of the above embodiments are only used to help understand the method and its core idea of this application. At the same time, for those of ordinary skill in the art, according to the idea of this application, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to this application.

Claims

1. A wide - frequency oscillation analysis method for a network - forming photovoltaic grid - connected system, characterized in that, The wide - frequency oscillation analysis method for the network - forming photovoltaic grid - connected system includes: Constructing an electromagnetic transient continuous - state space model for each component in the network - forming photovoltaic grid - connected system; the network - forming photovoltaic grid - connected system includes a power - side component unit and an AC - side component unit; both the power - side component unit and the AC - side component unit include multiple components; Based on bilinear transformation, discretizing the electromagnetic transient continuous - state space model of each component respectively to obtain the corresponding electromagnetic transient discrete - state space model; Based on the electromagnetic transient discrete - state space model of each component, determining the corresponding electromagnetic transient discrete equivalent circuit; Using the adjoint - circuit method, according to the electromagnetic transient discrete equivalent circuits and electromagnetic transient discrete - state space models of each component in the network - forming photovoltaic grid - connected system, determining the electromagnetic transient discrete - state space model of the network - forming photovoltaic grid - connected system; Performing eigenvalue modal analysis on the electromagnetic transient discrete - state space model of the network - forming photovoltaic grid - connected system to calculate eigenvalues, modal frequencies, damping ratios, and participation factors; the eigenvalues, the modal frequencies, and the damping ratios are all used to characterize the stability of the network - forming photovoltaic grid - connected system, and the participation factors are used to locate the characteristic state variables that cause modal instability in the network - forming photovoltaic grid - connected system.

2. The broadband oscillation analysis method for the network-forming type photovoltaic grid-connected system according to claim 1, characterized in that The power - side component unit is a photovoltaic power generation unit, including a photovoltaic array, a DC capacitor, a three - phase single - stage inverter, and an output filter; among them, the control of the three - phase single - stage inverter is jointly realized by a DC voltage matching control link, a reactive power droop control link, and a voltage - current inner - loop control link; The DC capacitor is connected in parallel with the photovoltaic array, and the DC capacitor is used to smooth the direct current generated by the photovoltaic array and then send it to the three - phase single - stage inverter; the output end of the three - phase single - stage inverter is connected to the input end of the output filter; the output end of the output filter is connected to the power grid; The AC - side component unit includes an inductor branch, a capacitor branch, and a resistor branch.

3. The broadband oscillation analysis method for the network-forming type photovoltaic grid-connected system according to claim 1, wherein Using the adjoint - circuit method, according to the electromagnetic transient discrete equivalent circuits and electromagnetic transient discrete - state space models of each component in the network - forming photovoltaic grid - connected system, determining the electromagnetic transient discrete - state space model of the network - forming photovoltaic grid - connected system includes: Determining the system topology according to the network - forming photovoltaic grid - connected system; Using the adjoint - circuit method, according to the system topology and the electromagnetic transient discrete equivalent circuits of each component, determining the initial system electromagnetic transient discrete equivalent circuit; According to the initial system electromagnetic transient discrete equivalent circuit, determining the branch - node incidence matrix and the conductance matrix; Using the adjoint - circuit method, according to the branch - node incidence matrix, the conductance matrix, and the electromagnetic transient discrete - state space models of each component, determining the electromagnetic transient discrete - state space model of the network - forming photovoltaic grid - connected system.

4. The broadband oscillation analysis method for the network-forming type photovoltaic grid-connected system according to claim 1, wherein Performing eigenvalue modal analysis on the electromagnetic transient discrete - state space model of the network - forming photovoltaic grid - connected system includes: According to the electromagnetic transient discrete state space model of the grid-forming PV grid-connected system, solve the electromagnetic transient discrete state matrix; the electromagnetic transient discrete state matrix contains multiple discrete eigenvalues; when the magnitudes of all discrete eigenvalues in the polar coordinate system are less than 1, the grid-forming PV grid-connected system is in a stable state; Calculate the modal frequency and damping ratio according to the eigenvalues in the electromagnetic transient discrete state matrix; According to matrix theory, perform diagonalization decomposition on the electromagnetic transient discrete state matrix to obtain the left eigenvector matrix and the right eigenvector matrix; Based on the left eigenvector matrix and the right eigenvector matrix, determine the participation matrix; the participation matrix includes multiple participation factors; the participation factors are used to quantify the influence degree of the characteristic state variables on the characteristic modes, and further locate the characteristic state variables that cause modal instability in the grid-forming PV grid-connected system.

5. The broadband oscillation analysis method for a network-forming type photovoltaic grid-connected system according to claim 4, wherein The calculation formulas for the modal frequency and the damping ratio are: Among them, f d represents the modal frequency, α d is the damping ratio, is the phase angle of the discrete eigenvalue in the polar coordinate system, |λ d | represents the magnitude of the discrete eigenvalue, Δt d represents the discrete step size, X d is the horizontal axis coordinate of the discrete eigenvalue in the polar coordinate system, Y d is the vertical axis coordinate of the discrete eigenvalue in the polar coordinate system; According to matrix theory, the formula used in the process of performing diagonalization decomposition on the electromagnetic transient discrete state matrix is: P T A dsys Q = Λ dsys ; Among them, A dsys is the electromagnetic transient discrete state matrix, P is the left eigenvector matrix, Q is the right eigenvector matrix, and P T Q = I, where I is the identity matrix; Λ dsys is a diagonal matrix, and the elements in the diagonal matrix are all the eigenvalues of the electromagnetic transient discrete state matrix; The determination formula for the participation factor is: C (m,n) = P (m,n) Q (m,n) ; where the subscript (m,n) represents the element value in the m-th row and n-th column of the matrix; C is the participation matrix, and C (m,,n) is a participation factor.

6. The broadband oscillation analysis method for a network-forming type photovoltaic grid-connected system according to claim 3, wherein The branch-node incidence matrix L is: The conductance matrix G is: The electromagnetic transient discrete state space model of the grid-forming PV grid-connected system is: Among them, I 2×2 is a 2×2 identity matrix, g pv is the conductance corresponding to the power source side component unit in the initial system electromagnetic transient discrete equivalent circuit, g line-L is the conductance corresponding to the line inductance in the initial system electromagnetic transient discrete equivalent circuit, is the conductance corresponding to the line resistance in the initial system electromagnetic transient discrete equivalent circuit, h sys (t) is a current source at time t, A dsys is the electromagnetic transient discrete state matrix, h sys (t - Δt) is a current source at time t - Δt, A sys , B sys , C sys are all coefficient matrices, () T represents the transpose of the matrix.

7. The broadband oscillation analysis method for the network-forming type photovoltaic grid-connected system according to claim 2, wherein When the component is a PV array, the corresponding electromagnetic transient continuous state space model is: Among them, I pv is the output current of the photovoltaic array, V pv is the output voltage of the photovoltaic array, and Δ represents the change in each variable; N p is the number of parallel-connected photovoltaic cells in the photovoltaic array, N s is the number of series-connected photovoltaic cells in the photovoltaic array, C1 and C2 are intermediate parameters, and e is the base of the natural logarithm; the subscript 0 represents the steady-state value of each variable, I sc0 is the short-circuit current of the photovoltaic cell at steady state, U oc0 is the open-circuit voltage of the photovoltaic cell at steady state; I mref is the maximum power point current of the photovoltaic cell under standard conditions, I scref is the short-circuit current of the photovoltaic cell under standard conditions, U mref is the maximum power point voltage of the photovoltaic cell under standard conditions, U ocref is the open-circuit voltage of the photovoltaic cell under standard conditions; When the component is a DC capacitor, the corresponding electromagnetic transient continuous state space model is: where, ΔV pv = ΔU dc ; C dc is the capacitance value of the DC capacitor, U dc is the DC voltage, u dg is the d-axis component of the grid connection point voltage, i dg is the d-axis component of the grid current; When the component is an output filter, the corresponding electromagnetic transient continuous state space model is: where, i dk is the d-axis component of the current flowing out of the three-phase single-stage inverter, i qk is the q-axis component of the current flowing out of the three-phase single-stage inverter, i dg is the d-axis component of the grid-connected current, i qg is the q-axis component of the grid-connected current, u dcf is the d-axis component of the voltage at the parallel connection point of the filter capacitor, u qcf is the q-axis component of the voltage at the parallel connection point of the filter capacitor, u dk is the d-axis component of the output voltage of the three-phase single-stage inverter, u qk is the q-axis component of the output voltage of the three-phase single-stage inverter, u dg is the d-axis component of the voltage at the grid connection point, u qg is the q-axis component of the voltage at the grid connection point, ω is the AC-side angular frequency of the grid-forming PV grid-connected system, C f is the filter capacitor, L C1 、L C2 are respectively the filter inductor on the inverter side and the filter inductor on the grid side; When the component is a three-phase single-stage inverter, the corresponding electromagnetic transient continuous state space model includes: The small-signal equation of the DC voltage matching control link is: Δω = Δx1; The small-signal equations of the reactive power droop control link and the voltage-current inner loop control link are respectively: where x1, x2, x3, x4, x5, θ P are state variables; M Q is the droop coefficient of reactive power droop control, M T is the tracking coefficient of DC voltage, M D is the damping coefficient of inertial synchronization equivalent, M J is the inertia coefficient of inertial synchronization equivalent, k pud is the PI proportional coefficient of the inner d-axis voltage loop, k iud is the PI integral coefficient of the inner d-axis voltage loop, k puq is the PI proportional coefficient of the inner q-axis voltage loop, k iuq is the PI integral coefficient of the inner q-axis voltage loop, k pid is the proportional coefficient of the inner d-axis current loop, k iid is the integral coefficient of the inner d-axis current loop, k piq is the proportional coefficient of the inner q-axis current loop, k iiq is the integral coefficient of the inner q-axis current loop.

8. The broadband oscillation analysis method for a network-forming photovoltaic grid-connected system according to claim 7, characterized in that The electromagnetic transient continuous state space model corresponding to the power source side component unit is: x pv = [U dc , i dk , i qk , i dg , i qg , u dcf , u qcf , x1, x2, x3, x4, x5, θ P ; u gdq = [u dg , u qg ; where, x pv is the state variable column vector, u gdq is the terminal voltage column vector of the photovoltaic power generation unit, A pv , B pv , C pv are all coefficient matrices; i gdq is the current output by the photovoltaic power generation unit to the network.

9. A computer device, comprising: A memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the computer program to implement the grid-forming PV grid-connected system broadband oscillation analysis method according to any one of claims 1-8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the grid-forming PV grid-connected system broadband oscillation analysis method according to any one of claims 1-8.

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