Photovoltaic power generation system grid-connected model stability analysis method considering photovoltaic permeability

Abstract

The invention relates to a photovoltaic power generation system grid-connected model stability analysis method considering photovoltaic permeability, and belongs to the field of new energy power generation and system stability analysis. The method comprises the steps that a transfer function model of the photovoltaic power generation system is converted into a differential equation, a state-space equation of the photovoltaic power generation system is obtained through Laplace inverse transformation, and the applicability of the state-space equation of the photovoltaic power generation system is preliminarily verified through step response analysis; establishing a photovoltaic power generation system grid-connected model; when stability analysis is carried out on the photovoltaic power generation system, a P matrix required by a Lyapunov function is solved based on a state-space equation of the photovoltaic power generation system, and a photovoltaic permeability threshold value when the photovoltaic power generation system is stable is obtained through analysis according to a Lyapunov stability criterion. The method can be in a stable state in both simple and complex systems in the process that the permeability threshold value of a photovoltaic power generation system mainly based on middle-high voltage power distribution network power supply side local concentrated grid connection reaches 30%, and has practicability and effectiveness.

Description

Technical Field

[0001] The present invention relates to a stability analysis method for a photovoltaic power generation system grid-connected model taking photovoltaic penetration into account, and belongs to the technical field of new energy power generation and system stability analysis. Background Art

[0002] Photovoltaic power generation systems are the most representative clean energy generation systems. The integration of a high proportion of photovoltaic power into the grid transforms traditional power grids into active and proactive systems, impacting the planning, operation, control, and stability analysis of power systems. Solar energy itself is highly random and volatile, and photovoltaic power generation is significantly affected by environmental factors, resulting in a high degree of uncertainty in the power generated by photovoltaic power generation systems. As photovoltaic penetration increases, it faces various challenges across multiple timescales, including transient stability, operation scheduling, and planning and design of power systems. These challenges include transient voltage fluctuations, reduced frequency regulation capabilities, and increased difficulty in assessing the reliability of grid planning. Therefore, for photovoltaic power generation systems primarily connected to the power supply side of medium and high voltage distribution networks, it is important to construct a reasonable and accurate photovoltaic power generation system model, analyze the stability of photovoltaic power generation grid-connected systems, and determine the photovoltaic power generation system penetration threshold for stable system operation.

[0003] In the field of photovoltaic power generation system modeling, hybrid modeling methods are widely used. This method combines mechanism analysis with control strategies to achieve mathematical modeling. Tian Yuguo et al. established an extended nonlinear phase-locked loop model suitable for transient analysis for photovoltaic power generation systems that take into account virtual inertia control and low voltage ride-through, targeting the grid-connected requirements of large-capacity photovoltaic power generation systems. Huang Xin et al. used a real-time digital simulator (RTDS) to construct equivalent models of photovoltaic power generation systems using proportional integral (PI) and proportional resonance (PR) control algorithms, respectively. These models can more efficiently achieve the control objectives of high-power photovoltaic grid-connected systems. Yan Kai et al. established an equivalent model of a photovoltaic power station and a grid-connected inverter and its control model, and used the MPPT algorithm to maximize the photovoltaic array's photoelectric conversion efficiency. Gou Yiyun et al. established an improved control strategy for phase compensation of the phase-locked loop to improve the reactive power withdrawal speed of photovoltaic inverters during the fault recovery phase. The applicability and effectiveness of the established strategy were verified using the RT-Lab semi-physical simulation platform.

[0004] In terms of stability analysis, the traditional method of photovoltaic power generation system transfer function model mainly relies on classic criteria such as Nyquist and Routh. JOHNV et al. calculated the system transfer function model based on the disturbance observation method MPPT control, increased the stability and response rate of the system, and verified the stability of the system model by using Bode diagram observation; Qin Ling et al. established a photovoltaic power generation system model with grid-connected power generation and reactive power compensation robust control, and derived the closed-loop transfer function model of the system on this basis, and decoupled the system power to the system current. The distortion results of the system current were observed by simulation method, and the stability of the established system was verified; Gao Jiayuan et al. proposed a control loop parameter automatic control method based on proportional weights through research and analysis on the stability of grid-connected inverters under weak power grids. Adaptive adjustment method, and the Nyquist stability criterion method was used to verify the stability of the grid-connected inverter (GCI) system to ensure that the GCI has sufficient stability margin under weak power grid; Sun Zhenao et al. analyzed the impact of the grid-connected inverter on the power grid after connection, established an inverter model including grid resistance, and on this basis established a transfer function model of the system's grid-connected current and voltage, and verified the stability of the system by observing the Bode diagram; Yi Guiping et al. used switching functions to establish inverters and LCL filters, and on this basis established a closed-loop transfer function model of the system, and verified the stability of the system in combination with the Hurwitz stability criterion.

[0005] When using transfer functions to analyze a system, only the relationship between the system's input and output signals can be studied; it cannot reflect the relationship between the system's internal variables. Furthermore, classical control theory is not applicable to time-varying systems. Furthermore, stability studies have not primarily analyzed the penetration rate of photovoltaic power generation systems. As the penetration rate increases, it can cause system fluctuations and potentially lead to instability. Summary of the Invention

[0006] The technical problem solved by the present invention is: the present invention provides a stability analysis method for the grid-connected model of a photovoltaic power generation system taking into account the photovoltaic penetration rate, taking into account the photovoltaic penetration rate, constructing a stability analysis method including the penetration rate variable, which is used to achieve a quantitative assessment of the stable operation boundary of the system after a high proportion of photovoltaics is connected to the power grid.

[0007] The technical solution of the present invention is: a method for analyzing the stability of a photovoltaic power generation system grid-connected model taking into account photovoltaic penetration, the method comprising:

[0008] Step 1: Based on the photovoltaic power generation system model, a dynamic equivalent model of the photovoltaic power generation system is established and Parker transformation is performed, based on which the transfer function model of the photovoltaic power generation system is calculated;

[0009] Step 2: Convert the transfer function model of the photovoltaic power generation system to a differential equation, and further obtain the state space equation of the photovoltaic power generation system by Laplace inverse transform. Use step response analysis to preliminarily verify the applicability of the state space equation of the photovoltaic power generation system.

[0010] Step 3. After preliminary verification, the state space equation of the photovoltaic power generation system is optimized by using fractional-order differential equations, and a photovoltaic power generation system grid-connected model is established; taking into account the impact of photovoltaic penetration rate on the grid-connected photovoltaic power generation system, when performing stability analysis on the photovoltaic power generation system, the P matrix required by the Lyapunov function is solved based on the state space equation of the photovoltaic power generation system, and the photovoltaic penetration rate threshold when the photovoltaic power generation system is stable is obtained using the Lyapunov stability criterion analysis.

[0011] Furthermore, the Step 1 includes:

[0012] Step 1.1. Establish a photovoltaic power generation system model; the photovoltaic inverter model is shown in formula (1):

[0013]

[0014] Among them, E a 、E b 、E c Indicates the three-phase AC voltage of the grid-connected busbar; R and L indicate the total resistance and inductance of the filter inductor and step-up transformer connected to the inverter; U a 、U b 、U c Indicates the AC side voltage of the three-phase inverter; I a , I b , I c represents the three-phase current on the AC side of the three-phase inverter; t represents time;

[0015] Step 1.2, establish a photovoltaic power generation penetration rate model; the photovoltaic power generation penetration rate model is shown in formula (2):

[0016]

[0017] Among them, PP represents photovoltaic penetration, P pv Represents the real-time output power of the photovoltaic power generation system, P load Indicates the real-time power demand of the power load in the area. Indicates the maximum value of the ratio of photovoltaic power to load power;

[0018] Step 1.4, establish a dynamic equivalent model of the photovoltaic power generation system; the dynamic equivalent model of the photovoltaic power generation system is shown in formula (3):

[0019]

[0020] Among them, U id and U iq Indicates the dq axis component of the inverter output voltage, U dc Indicates the inverter DC bus voltage, U gd 、U gq and I d , I q Represents the dq-axis components of the voltage and current at the grid connection point of the photovoltaic power generation system, I pv Represents the photovoltaic array output current, s q and s d represents the dq axis component of the switching quantity under the synchronous coordinate axis, C represents the DC side capacitance of the photovoltaic power generation system, and ω represents the synchronous frequency; among them, the inverter output voltage U i With switch quantity s q and s d The relationship is as follows:

[0021]

[0022] Step 1.5, combine formula (3) and formula (4) to obtain formula (5):

[0023]

[0024] in, and Represents the dq-axis first-order component of the voltage and current at the grid connection point of the photovoltaic power generation system, Represents the dq-axis second-order component of the grid-connected point current of the photovoltaic power generation system;

[0025] Step 1.6. Perform Park transformation on equation (5) to obtain equation (6):

[0026]

[0027] Where s represents the Laplace variable, Δ represents the small signal disturbance, and ΔI d (s), ΔI q (s) is the variation of dq axis voltage and current in the frequency domain, i.e., the Laplace transform form under small signal disturbance; s q and s d is the dq-axis component of the switching vector in the synchronous coordinate system;

[0028]

[0029] Step 1.7, by combining equations (5) and (6), equation (5) can be transformed from the dq axis to the α-β axis;

[0030]

[0031] in, Indicates the change in α-β axis voltage, ΔI α (s), ΔI β (s) represents the change of α-β axis current, θ0 represents the power factor angle;

[0032]

[0033] Ignoring the voltage phase angle, equation (9) can be simplified to:

[0034]

[0035] Among them, ΔI r (s), ΔI j (s) represents the change in the real and imaginary parts of the current of the grid-connected voltage, ΔU g (s) represents the grid connection point voltage of the photovoltaic power generation system in the frequency domain;

[0036] Step 1.8. Obtain the transfer function model of the photovoltaic power generation system through calculation; the transfer function model of the photovoltaic power generation system is shown in formula (11):

[0037]

[0038] in,

[0039]

[0040] Furthermore, the Step 2 includes: using Lyapunov's second method to judge the stability of the photovoltaic power generation system, converting the obtained transfer function model of the photovoltaic power generation system into a differential equation, and further obtaining the state space equation of the photovoltaic power generation system by Laplace inverse transform; when using Lyapunov's second method to judge the stability, it is required to take the state space equation of the photovoltaic power generation system X 1 :X 1 =A0X, if A0 is a non-singular matrix, then Xe=0 is the only equilibrium state of the photovoltaic power generation system.

[0041] Furthermore, Step 2 specifically includes:

[0042] Step 2.1, construct a photovoltaic power generation system based on Lyapunov function;

[0043] According to Lyapunov’s definition, the scalar function V(x) of the photovoltaic power generation system is shown in formula (12):

[0044] V(x)=X T PX(12)

[0045] Where P represents a positive definite real symmetric matrix, which is obtained by the state space equation; X represents the state vector of the photovoltaic power generation system;

[0046] Convert Equation (12) into energy function As shown in formula (13):

[0047]

[0048] Where, Q = -(A T +PA)Q is a pre-given positive definite matrix, i.e., the identity matrix, and P is the symmetric matrix to be determined. If Q>0, then At this time, the system is in X e =0 is the stable state, X e Represents the value of the system's state variables at the equilibrium point;

[0049] The stability of the photovoltaic power generation system is judged by Lyapunov's second method. The symmetric matrix P is solved by Lyapunov equation. If P is positive definite according to Sylvester criterion, the system is stable.

[0050] Step 2.2: Construct the Lyapunov function shown in formula (12), and then transform the photovoltaic power generation system transfer function model shown in formula (11) into a differential equation. The differential equation is shown in formula (14):

[0051]

[0052] In the formula Respectively represent the first-order, second-order, third-order, and fourth-order derivatives of the photovoltaic power generation system voltage; and They represent the first-order, second-order, third-order, and fourth-order derivatives of the current in the α-β stationary coordinate system respectively; where I α , I β represents the current component in the α-β stationary coordinate system, U g Indicates the grid connection point voltage;

[0053] a4=0;

[0054]

[0055] Step 2.3, perform Laplace inverse transformation on equation (14) to obtain the state space equations of the photovoltaic power generation system shown in equations (15) and (16), where equation (15) is the α-axis state space equation and equation (16) is the β-axis state space equation;

[0056]

[0057]

[0058] Among them, Y α Indicates I α ; Y β Indicates I β ;

[0059] x=[x1 x2 x3 x4] T ; μ=U g ;

[0060]

[0061] in, Represents the state vector of the α-β axis, including state variables related to the α and β axes, μ represents the input variable of the photovoltaic power generation system, β1, β2, β3, and β4 represent the coefficients affecting the state of the α axis, γ1, γ2, γ3, and γ4 represent the coefficients affecting the state of the β axis, and x1, x2, x3, and x4 represent the state variables of the photovoltaic power generation system, corresponding to the α-β axis state variables respectively; Matrix A describes the dynamic relationship between the state variables of the photovoltaic power generation system, Matrix B describes how the input variable μ affects the state change of the α axis, and Matrix E describes how the input variable μ affects the state change of the β axis;

[0062] Step 2.4: Use step response analysis to preliminarily verify the applicability of the state space equation of the photovoltaic power generation system. Under the condition that the penetration rate of the photovoltaic power generation system is 0, experimental simulation data verification is carried out to obtain the step response curve of the photovoltaic power generation system.

[0063] Furthermore, Step 3 includes: further improving the state space equation because the step response curve of the photovoltaic power generation system does not converge when the experimental simulation data is verified under the condition that the photovoltaic power generation system penetration rate is 0; the specific steps include:

[0064] Step 3.1: When optimizing the state space equation of the photovoltaic power generation system, the fractional-order differential equation is used to simplify the state space equation. The general form of the fractional-order differential equation is as follows:

[0065] e n D n y(t)+…+e1D 1 y(t)+e0y(t)=u(t) (17)

[0066]

[0067] Where D represents the derivative operator, n represents the fractional order; D n represents the fractional derivative; D 1 y(t) represents the first-order derivative, that is represents the rate of change; D n y(t) represents the nth order derivative, d ny represents the nth-order differential of the dependent variable y, dx n represents the nth-order differential e of the independent variable x n ,e n-1 ,…,e0 is the coefficient of the fractional differential equation, representing the parameters of the system, y(t) represents the output variable of the system, and u(t) represents the input variable of the system

[0068] Convert the fractional-order differential equations (17) and (18) into state-space equations. The converted state-space equations are:

[0069]

[0070] Among them, x i (t)(i=1,...,n) are fractional-order state variables, A′, B′ are matrices of appropriate dimensions, ′ represents only a label, not the transpose in matrix operations, A′, B′ represent the dynamic relationship between the state variables of the system, and matrices A′, B′ represent the influence of inputs x(t) and u(t) on the rate of change of the state variables, respectively. The parameters in matrices A′, B′ are related to the coefficients in the fractional-order differential equations;

[0071] x(t)=[x1(t)x2(t)…x n (t)] T ;

[0072]

[0073] The fractional-order differential equations and state-space equations of the photovoltaic power generation system are improved, and the results after improvement are as follows:

[0074]

[0075] Equation (20) is transformed into the state space equation as follows:

[0076]

[0077] Among them, Y α Indicates I α ; Y β Indicates I β ; The state vector representing the improved α-β axis contains the state variables related to the α and β axes;

[0078] x=[x1 x2 x3 x4] T ; μ=U g ;

[0079]

[0080] For the state space equation of the improved photovoltaic power generation system, its step response curve converges; the improved photovoltaic power generation system is in a stable state, and based on the state space equations (21) and (22), the P matrix required by the Lyapunov function can be solved. Finally, by judging whether the P matrix is ​​positive, it can be judged whether the system is stable and the photovoltaic penetration threshold value when the system is stable at different penetration rates.

[0081] Step 3.2, the photovoltaic power generation system is connected to the grid through the inverter to form a photovoltaic power generation system grid-connected model; the connection between the grid AC side and the PV DC side is expressed by formula (23);

[0082]

[0083] Among them, I d , I q Represents the dq axis components of the grid-connected current of the photovoltaic power generation system; R, L represent the AC resistance and inductance; E d 、E q Indicates the three-phase AC measurement of the busbar at the grid connection point E a 、E b 、E c The dq-axis component of the voltage; U dc Indicates the inverter DC bus voltage, s q and s d Indicates the dq axis components of the switching quantity under the synchronous coordinate axis;

[0084] Convert Equation (23) into the state space equations of the photovoltaic power generation system as shown in Equations (24) and (25):

[0085]

[0086] Among them, Y d Indicates I d ; Y q Indicates I q ; x′ represents the grid-connected state variable of the photovoltaic power generation system;

[0087]

[0088] The present invention provides a photovoltaic power generation system grid-connected model stability analysis system taking photovoltaic penetration rate into account, the system comprising: a module for executing the photovoltaic power generation system grid-connected model stability analysis method taking photovoltaic penetration rate into account.

[0089] The present invention provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, a stability analysis method for a grid-connected model of a photovoltaic power generation system taking photovoltaic penetration into account is implemented.

[0090] The present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the method for analyzing the stability of a photovoltaic power generation system grid-connected model taking into account photovoltaic penetration rate is implemented.

[0091] The present invention provides a computer program product, comprising a computer program, which, when executed by a processor, implements a method for analyzing the stability of a photovoltaic power generation system grid-connected model taking photovoltaic penetration into account.

[0092] The beneficial effects of the present invention are:

[0093] (1) Based on the dynamic model of photovoltaic power generation system, the present invention establishes a state space model of photovoltaic power generation system, uses fractional-order differential equations to optimize the system state space equations, and verifies its feasibility;

[0094] (2) The present invention takes into account the photovoltaic penetration rate variable. When the penetration rate is set to increase from zero to 0.021MW (penetration rate is 1%) to 0.84 (penetration rate is 40%), the stability value of the system shows a downward trend as the penetration rate increases. When the system stability value is less than zero, the system is in an unstable state.

[0095] (3) When analyzing the stability of the photovoltaic system, the Lyapunov stability criterion analysis shows that when the photovoltaic power generation system penetration threshold reaches 30%, it can be in a stable state in both simple and complex systems, which can improve the practicality and effectiveness of the proposed method. The analysis results of the Nyquist plot are consistent with the analysis results of the Lyapunov first method, which can provide conservative support for the Lyapunov first method.

[0096] (4) In the photovoltaic power generation system of the present invention, which is mainly based on local centralized grid connection on the power supply side of the medium and high voltage distribution network, when the penetration rate of the photovoltaic power generation system exceeds 30%, the unit step response of the system AC measurement does not converge. At this time, the system is in an unstable operating state. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] Figure 1 is the dynamic equivalent model of the photovoltaic power generation system in the present invention;

[0098] Figure 2 These are the three stable forms defined by Lyapunov in this invention;

[0099] Figure 3 is the system step response curve under the condition that the penetration rate of the photovoltaic power generation system in the present invention is 0;

[0100] Figure 4 The optimized system step response curve is obtained under the condition that the penetration rate of the photovoltaic power generation system is 0 in the present invention;

[0101] Figure 5 This is a topological diagram of the voltage-type inverter in the present invention;

[0102] Figure 6 The photovoltaic power generation system of the present invention is incorporated into the IEEE14 node topology diagram;

[0103] Figure 7 The photovoltaic power generation system of the present invention is incorporated into the IEEE33 node topology diagram;

[0104] Figure 8 The eigenvalue distribution diagram of the system P matrix under different penetration rates of the photovoltaic power generation system in the present invention; Figure 8 (a) is the eigenvalue distribution diagram of the P matrix of the IEEE14-node system with a penetration rate of 31% in the present invention; Figure 8 (b) is the eigenvalue distribution diagram of the P matrix of the IEEE33-node system under the penetration rate of 31% in the present invention; Figure 8 (c) is the eigenvalue distribution diagram of the P matrix of the IEEE14-node system under the penetration rate of 30.0625% in the present invention; Figure 8 (d) is the eigenvalue distribution diagram of the P matrix of the IEEE33-node system under the penetration rate of 30.0625% in the present invention; Figure 8 (e) is the eigenvalue distribution diagram of the P matrix of the IEEE 14-node system with a penetration rate of 30% in the present invention; Figure 8 (f) is the eigenvalue distribution diagram of the P matrix of the IEEE33-node system under the penetration rate of 30% in the present invention;

[0105] Figure 9 is the step response curve of the system at different permeabilities based on the state space equation in the present invention; Figure 9 (a) is the step response curve of the IEEE 14-bus system based on the state space equation at a penetration rate of 31% in the present invention; Figure 9 (b) is the step response curve of the IEEE33-node system based on the state space equation at a penetration rate of 31% in the present invention; Figure 9 (c) is the step response curve of the IEEE 14-node system based on the state space equation at a penetration rate of 30.0625% in the present invention; Figure 9 (d) is the step response curve of the IEEE 33-node system based on the state space equation at a penetration rate of 30.0625% in the present invention; Figure 9 (e) is the step response curve of the IEEE 14-node system based on the state space equation at a penetration rate of 30% in the present invention; Figure 9 (f) is the step response curve of the IEEE 33-node system based on the state space equation at a penetration rate of 30% in the present invention;

[0106] Figure 10This is a diagram showing changes in system stability values ​​at different permeabilities in the present invention; Figure 10 (a) is a three-dimensional mapping diagram of the system stability value at different permeabilities in the present invention; Figure 10 (b) is the contour distribution diagram of the system stability value at different permeabilities in the present invention;

[0107] Figure 11 is the system step response curve at different permeabilities based on the optimized state space equation in the present invention; Figure 11 (a) is the step response curve of the IEEE 14-node system based on the optimized state space equation at a penetration rate of 30% in the present invention; Figure 11 (b) is the step response curve of the IEEE33-node system based on the optimized state space equation at a penetration rate of 30% in the present invention; Figure 11 (c) is the step response curve of the IEEE 14-node system based on the optimized state space equation at a penetration rate of 30.0625% in the present invention; Figure 11 (d) is the step response curve of the IEEE 33-node system based on the optimized state space equation at a penetration rate of 30.0625% in the present invention; Figure 11 (e) is the step response curve of the IEEE 14-node system based on the optimized state space equation at a penetration rate of 31% in the present invention; Figure 11 (f) is the step response curve of the IEEE33-node system based on the optimized state space equation at a penetration rate of 31% in the present invention;

[0108] Figure 12 This is a graph showing changes in active power at the grid connection point under different penetration rates in the present invention;

[0109] Figure 13 This is the Nyquist curve of the grid connection point under different permeabilities in the present invention. Figure 13 (a) is the Nyquist curve of the photovoltaic power generation grid-connected system with a penetration rate of 31% in the present invention; Figure 13 (b) is the Nyquist curve of the photovoltaic power generation grid-connected system with a penetration rate of 30% in the present invention. DETAILED DESCRIPTION

[0110] Example 1: Figures 1-13 As shown, a stability analysis method for a photovoltaic power generation system grid-connected model taking into account photovoltaic penetration rate is provided, the method comprising:

[0111] Step 1: Based on the photovoltaic power generation system model, a dynamic equivalent model of the photovoltaic power generation system is established and Parker transformation is performed, based on which the transfer function model of the photovoltaic power generation system is calculated;

[0112] Furthermore, the Step 1 includes:

[0113] Step 1.1. Establish a photovoltaic power generation system model; the photovoltaic inverter model is shown in formula (1):

[0114]

[0115] Among them, E a 、E b 、E c Indicates the three-phase AC voltage of the grid-connected busbar; R and L indicate the total resistance and inductance of the filter inductor and step-up transformer connected to the inverter; U a 、U b 、U c Indicates the AC side voltage of the three-phase inverter; I a , I b , I c represents the three-phase current on the AC side of the three-phase inverter; t represents time;

[0116] Step 1.2, establish a photovoltaic power generation penetration model;

[0117] The PV penetration rate reflects the amount of photovoltaic capacity connected to the system. It can be divided into capacity penetration rate, energy penetration rate, and power penetration rate (PP) by definition. The capacity penetration rate reflects the saturation level of the photovoltaic installed capacity in the system; the energy penetration rate reflects the distribution network's ability to absorb the total power generated by the photovoltaic power generation system; and the PP reflects the optimal matching degree between photovoltaic power generation and load at a certain time throughout the year. In other words, the maximum support capacity of photovoltaic power for load throughout the year is the photovoltaic penetration rate PP. The power penetration rate refers to the maximum ratio of the power generated by the photovoltaic power generation system to the load in the area at the same time in the power grid. The photovoltaic power generation penetration rate model is shown in formula (2):

[0118]

[0119] Among them, PP represents photovoltaic penetration, P pv Represents the real-time output power of the photovoltaic power generation system, P load Indicates the real-time power demand of the power load in the area. Indicates the maximum value of the ratio of photovoltaic power to load power;

[0120] Step 1.4: To describe the characteristics of the photovoltaic power generation system, a dynamic equivalent model of the photovoltaic power generation system is established. The dynamic equivalent model of the photovoltaic power generation system is shown in formula (3):

[0121]

[0122] Among them, U id and U iq Indicates the dq axis component of the inverter output voltage, U dcIndicates the inverter DC bus voltage, U gd 、U gq and I d , I q Represents the dq-axis components of the voltage and current at the grid connection point of the photovoltaic power generation system, I pv Represents the photovoltaic array output current, s q and s d represents the dq axis component of the switching quantity under the synchronous coordinate axis, C represents the DC side capacitance of the photovoltaic power generation system, and ω represents the synchronous frequency; among them, the inverter output voltage U i With switch quantity s q and s d The relationship is as follows:

[0123]

[0124] Step 1.5, combine formula (3) and formula (4) to obtain formula (5):

[0125]

[0126] in, and Represents the dq-axis first-order component of the voltage and current at the grid connection point of the photovoltaic power generation system, Represents the dq-axis second-order component of the grid-connected point current of the photovoltaic power generation system;

[0127] Step 1.6. Perform Park transformation on equation (5) to obtain equation (6):

[0128]

[0129] Where s represents the Laplace variable, Δ represents the small signal disturbance, and ΔI d (s), ΔI q (s) is the variation of dq axis voltage and current in the frequency domain, i.e., the Laplace transform form under small signal disturbance; s q and s d is the dq-axis component of the switching vector in the synchronous coordinate system;

[0130]

[0131] Step 1.7, by combining equations (5) and (6), equation (5) can be transformed from the dq axis to the α-β axis;

[0132]

[0133] in, Indicates the change in α-β axis voltage, ΔI α(s), ΔI β (s) represents the change of α-β axis current, θ0 represents the power factor angle;

[0134]

[0135] Ignoring the voltage phase angle, equation (9) can be simplified to:

[0136]

[0137] Among them, ΔI r (s), ΔI j (s) represents the change in the real and imaginary parts of the current of the grid-connected voltage, ΔU g (s) represents the grid connection point voltage of the photovoltaic power generation system in the frequency domain;

[0138] Step 1.8. Obtain the transfer function model of the photovoltaic power generation system through calculation; the transfer function model of the photovoltaic power generation system is shown in formula (11):

[0139]

[0140] in,

[0141]

[0142] Step 2: Convert the transfer function model of the photovoltaic power generation system to a differential equation, and further obtain the state space equation of the photovoltaic power generation system by Laplace inverse transform. Use step response analysis to preliminarily verify the applicability of the state space equation of the photovoltaic power generation system.

[0143] Furthermore, the Step 2 includes: using Lyapunov's second method to judge the stability of the photovoltaic power generation system, converting the obtained transfer function model of the photovoltaic power generation system into a differential equation, and further obtaining the state space equation of the photovoltaic power generation system by Laplace inverse transform; when using Lyapunov's second method to judge the stability, it is required to take the state space equation of the photovoltaic power generation system X 1 :X 1 =A0X, if A0 is a non-singular matrix, then Xe=0 is the only equilibrium state of the photovoltaic power generation system.

[0144] Matrix A0 is a square matrix, known as the system's state matrix. It describes the dynamic relationships between the system's state variables, that is, how they change over time. Matrix A0 determines the system's free dynamic behavior when there is no external input. Its eigenvalues ​​determine the system's stability, oscillation characteristics, and other characteristics.

[0145] Furthermore, Step 2 specifically includes:

[0146] Step 2.1, construct a photovoltaic power generation system based on Lyapunov function;

[0147] Lyapunov proposed the Lyapunov direct method. According to Lyapunov's definition of stability, the stability of a dynamic system is divided into three main forms: stability, asymptotic stability and large-scale asymptotic stability. Figure 2 These are the three stability forms defined by Lyapunov. Lyapunov's first method requires solving the eigenvalues ​​of the linearized system to determine stability, while Lyapunov's second method can directly perform stability analysis on nonlinear systems.

[0148] According to Lyapunov’s definition, the scalar function V(x) of the photovoltaic power generation system is shown in formula (12):

[0149] V(x)=X T PX(12)

[0150] Where P represents a positive definite real symmetric matrix, which is obtained by the state space equation; X represents the state vector of the photovoltaic power generation system;

[0151] Convert Equation (12) into energy function As shown in formula (13):

[0152]

[0153] Where, Q = -(A T +PA)Q is a pre-given positive definite matrix, i.e., the identity matrix, and P is the symmetric matrix to be determined. If Q>0, then At this time, the system is in X e =0 is the stable state, X e Represents the value of the system's state variables at the equilibrium point;

[0154] In practical applications, Lyapunov's second method is used to assess the stability of photovoltaic power generation systems. The symmetric matrix P is solved using the Lyapunov equation. If P is positive definite according to the Sylvester criterion, the system is stable. However, Lyapunov's second method only provides sufficient conditions for system stability, not necessary ones. If the selected Lyapunov function satisfies the stability analysis criteria, the system is stable. If it does not, the system is considered unstable, but it may still be stable.

[0155] Step 2.2: Use Lyapunov's second method to judge the stability of the system, construct the Lyapunov function shown in formula (12), and then transform the photovoltaic power generation system transfer function model shown in formula (11) into a differential equation. The differential equation is shown in formula (14):

[0156]

[0157] In the formula Respectively represent the first-order, second-order, third-order, and fourth-order derivatives of the photovoltaic power generation system voltage; and They represent the first-order, second-order, third-order, and fourth-order derivatives of the current in the α-β stationary coordinate system respectively; where I α , I β represents the current component in the α-β stationary coordinate system, U g Indicates the grid connection point voltage;

[0158] a4=0;

[0159]

[0160] Step 2.3, perform Laplace inverse transformation on equation (14) to obtain the state space equations of the photovoltaic power generation system shown in equations (15) and (16), where equation (15) is the α-axis state space equation and equation (16) is the β-axis state space equation;

[0161]

[0162] Among them, Y α Indicates I α ; Y β Indicates I β ;

[0163] x=[x1 x2 x3 x4] T ; μ=U g ;

[0164]

[0165] in, Represents the state vector of the α-β axis, including state variables related to the α and β axes, μ represents the input variable of the photovoltaic power generation system, β1, β2, β3, and β4 represent the coefficients affecting the state of the α axis, γ1, γ2, γ3, and γ4 represent the coefficients affecting the state of the β axis, and x1, x2, x3, and x4 represent the state variables of the photovoltaic power generation system, corresponding to the α-β axis state variables respectively; Matrix A describes the dynamic relationship between the state variables of the photovoltaic power generation system, Matrix B describes how the input variable μ affects the state change of the α axis, and Matrix E describes how the input variable μ affects the state change of the β axis;

[0166] Step 2.4: Use step response analysis to preliminarily verify the applicability of the state space equation of the photovoltaic power generation system. Under the condition that the penetration rate of the photovoltaic power generation system is 0, experimental simulation data verification is carried out to obtain the step response curve of the photovoltaic power generation system.

[0167] Step 3. After preliminary verification, the state space equation of the photovoltaic power generation system is optimized by using fractional-order differential equations, and a photovoltaic power generation system grid-connected model is established; taking into account the impact of photovoltaic penetration rate on the grid-connected photovoltaic power generation system, when performing stability analysis on the photovoltaic power generation system, the P matrix required by the Lyapunov function is solved based on the state space equation of the photovoltaic power generation system, and the photovoltaic penetration rate threshold when the photovoltaic power generation system is stable is obtained using the Lyapunov stability criterion analysis.

[0168] Furthermore, the Step 3 includes: due to the experimental simulation data verification under the condition that the photovoltaic power generation system penetration rate is 0, it is obtained Figure 3 The step response curve of the system; the step response curve of the photovoltaic power generation system does not converge, and the state space equation is further improved;

[0169] The system step response curve does not converge in the end, and the system is in an unstable state. Therefore, the state space equation shown in Equation (18) cannot meet the stability requirements, and the space state equation needs to be optimized.

[0170] Table 1 State space equation parameters

[0171]

[0172] The specific steps include:

[0173] Step 3.1: When optimizing the state space equation of the photovoltaic power generation system, the fractional-order differential equation is used to simplify the state space equation. The general form of the fractional-order differential equation is as follows:

[0174] e n D n y(t)+…+e1D 1 y(t)+e0y(t)=u(t) (17)

[0175]

[0176] Where D represents the derivative operator, n represents the fractional order; D n represents the fractional derivative; D 1 y(t) represents the first-order derivative, that is represents the rate of change; D n y(t) represents the nth order derivative, d n y represents the nth-order differential of the dependent variable y, dx n represents the nth-order differential e of the independent variable x n ,e n-1 ,…,e0 is the coefficient of the fractional differential equation, representing the parameters of the system, y(t) represents the output variable of the system, and u(t) represents the input variable of the system

[0177] Convert the fractional-order differential equations (17) and (18) into state-space equations. The converted state-space equations are:

[0178]

[0179] Among them, x i (t)(i=1,...,n) are fractional-order state variables, A′, B′ are matrices of appropriate dimensions, ′ represents only a label, not the transpose in matrix operations, A′, B′ represent the dynamic relationship between the state variables of the system, and matrices A′, B′ represent the influence of inputs x(t) and u(t) on the rate of change of the state variables, respectively. The parameters in matrices A′, B′ are related to the coefficients in the fractional-order differential equations;

[0180] x(t)=[x1(t)x2(t)…x n (t)] T ;

[0181]

[0182] The fractional-order differential equations and state-space equations of the photovoltaic power generation system are improved, and the results after improvement are as follows:

[0183]

[0184] Equation (20) is transformed into the state space equation as follows:

[0185]

[0186] Among them, Y α Indicates I α ; Y β Indicates I β ; The state vector representing the improved α-β axis contains the state variables related to the α and β axes;

[0187] x=[x1 x2 x3 x4] T ; μ=U g ;

[0188]

[0189] Under the condition that the penetration rate of photovoltaic power generation system is 0, the experimental simulation data shown in Table 2 are used for verification and the results are obtained. Figure 4 The step response curve of the system;

[0190] For the state space equation of the improved photovoltaic power generation system, its step response curve converges; the improved photovoltaic power generation system is in a stable state, and based on the state space equations (21) and (22), the P matrix required by the Lyapunov function can be solved. Finally, by judging whether the P matrix is ​​positive, it can be judged whether the system is stable and the photovoltaic penetration threshold value when the system is stable at different penetration rates.

[0191] Table 2 State space equation parameters

[0192]

[0193] Step 3.2, the voltage source inverter topology is as follows Figure 5 As shown, the photovoltaic power generation system is connected to the grid through an inverter to form a photovoltaic power generation system grid-connected model; the connection between the grid AC side and the PV DC side is expressed by formula (23);

[0194]

[0195] Among them, I d , I q Represents the dq axis components of the grid-connected current of the photovoltaic power generation system; R, L represent the AC resistance and inductance; E d 、E q Indicates the three-phase AC measurement of the busbar at the grid connection point E a 、E b 、E c The dq-axis component of the voltage; U dc Indicates the inverter DC bus voltage, s q and s d Indicates the dq axis components of the switching quantity under the synchronous coordinate axis;

[0196] Convert Equation (23) into the state space equations of the photovoltaic power generation system as shown in Equations (24) and (25):

[0197]

[0198] Among them, Y d Indicates I d ; Y q Indicates I q ; x′ represents the grid-connected state variable of the photovoltaic power generation system;

[0199]

[0200] The present invention provides a photovoltaic power generation system grid-connected model stability analysis system taking photovoltaic penetration rate into account, the system comprising: a module for executing the photovoltaic power generation system grid-connected model stability analysis method taking photovoltaic penetration rate into account.

[0201] The present invention provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, a stability analysis method for a grid-connected model of a photovoltaic power generation system taking photovoltaic penetration into account is implemented.

[0202] The present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the method for analyzing the stability of a photovoltaic power generation system grid-connected model taking into account photovoltaic penetration rate is implemented.

[0203] The present invention provides a computer program product, comprising a computer program, which, when executed by a processor, implements a method for analyzing the stability of a photovoltaic power generation system grid-connected model taking photovoltaic penetration into account.

[0204] As a further solution of the present invention, the present invention further includes step 4: example analysis and verification. The specific steps of step 4 are:

[0205] Step 4.1, build based on MATLAB / Simulink Figure 6 and Figure 7 The transmission and distribution system model containing a photovoltaic power generation system is shown in the figure. It is simulated under different photovoltaic penetration rates. The transmission system is an IEEE14-node system model, and the photovoltaic power generation system is connected through a two-winding transformer T4. To verify that the proposed method can be used in complex systems, an IEEE33-node system model is also set under the same conditions.

[0206] Step 4.1.1, the specific settings in the simulation are as follows:

[0207] (1) Transmission system parameter settings:

[0208] In the IEEE14 node, the reference voltage is set to 10 kV, the system frequency is 50 Hz, and the system uses a series RL as the impedance, with a resistance of 0.4 Ω and an inductance of 0.618 H. In the IEEE33 node, the reference voltage is set to 10 kV, the system frequency is 50 Hz, and the system also uses a series RL as the impedance, with a resistance of 0.87 Ω and an inductance of 0.303 H.

[0209] (2) Photovoltaic power generation system parameter settings:

[0210] The photovoltaic power generation system uses an LC filter with an L value of 0.17mH and a capacitor C of 0.168F. The dual-winding step-up transformer T4 has a transformation ratio of 0.7kV / 10kV. Simulations were conducted at different photovoltaic penetration rates under standard and ideal conditions (ignoring losses such as battery heat transfer and hot spots). The photovoltaic power generation system uses dq-axis coordinate vector control, with a pulse width modulation model generated through a phase-locked loop (PLL) for PWM modulation. The photovoltaic parameters are shown in Table 3.

[0211] Table 3 shows the photovoltaic parameters

[0212]

[0213]

[0214] (3) Simulation content:

[0215] In order to study the penetration threshold of the photovoltaic power generation system, the following settings are made in the simulation system:

[0216] 1) Set different penetration rates for the photovoltaic power generation system, starting from zero and increasing the photovoltaic output power by 0.021MW (penetration rate of 1%). Measure the active power and reactive power at the grid connection point, as well as the grid connection point voltage, and also measure the voltage output by the inverter.

[0217] 2) Convert the measured data into the system's state space equation, and then perform stability analysis based on the Yapunov stability criterion to determine whether the system is in a stable state and determine the photovoltaic penetration threshold that can keep the system stable.

[0218] 3) In order to improve the conservatism of Lyapunov's first method, the Nyquist curve of the system is simulated and analyzed under the same conditions. Figure 13 At the same time, in order to improve the versatility of the model, the operation results in IEEE14-node and IEEE33-node systems were simulated and analyzed comparatively.

[0219] Step 4.2: Verify the effectiveness of the algorithm

[0220] A simulation environment was set up to verify the system's stability at different PV penetration rates. First, based on the system's state-space equation, the symmetric matrix P and its eigenvalues ​​were calculated for different PV penetration rates. Second, the step response curves of the system's state-space equation at different PV penetration rates were analyzed. Finally, the changes in the system's active power and frequency at different PV penetration rates were measured.

[0221] (1) The symmetric matrix P is solved by the state space equation. The simulation results show that when the penetration rate of the photovoltaic power generation system increases to 31%, the system begins to be unstable. At this time, the real symmetric matrix P is non-positive definite. The simulation results of the IEEE14-node system are shown in Equation (26), and the simulation results of the IEEE33-node system are shown in Equation (27).

[0222]

[0223] A bisection method was used to analyze the penetration threshold that allows the system to maintain stability under varying PV penetration rates. When the PV penetration rate exceeds 30.0625%, the system becomes unstable, while below this penetration rate, the system remains stable. At a penetration rate of 30.0625%, the P matrix obtained by solving the state-space equations for the IEEE 14-bus system simulation is positive definite, as shown in Equation (28). However, the P matrix obtained by solving the state-space equations for the IEEE 33-bus system simulation is non-positive definite, as shown in Equation (29).

[0224]

[0225]

[0226] When the PV penetration rate is lower than 30.0625%, the system can remain stable. When the penetration rate is 30%, the P matrix obtained by solving the state-space equations in the IEEE 14-bus system simulation is positive definite, as shown in Equation (30). The P matrix obtained by solving the state-space equations in the IEEE 33-bus system simulation is also positive definite, as shown in Equation (31).

[0227]

[0228] Under the same conditions, based on the state space equation of the system, at three values ​​of photovoltaic penetration of 31%, 30.0625% and 30%, the eigenvalue distribution diagram of the matrix is ​​calculated according to equations (26), (27), (28), (29), (30) and (31). Figure 8 shown.

[0229] When the penetration rate of the photovoltaic power generation system is 31%, 30.0625%, and 30%, the P matrix eigenvalue distribution diagrams obtained by IEEE14-node system simulation are as follows: Figure 8 (a), 8(c), and 8(e), the P matrix eigenvalue distribution obtained by IEEE 33-node system simulation is shown in Figure 8 As shown in (b), 8(d), and 8(f).

[0230] Table 4 shows the P matrix eigenvalues ​​under different penetration rates of the IEEE 14-node system

[0231] 31％ 30.0625％ 30％ 10.93315 -2.60349 -2.65722 10.93315 -0.91362E-4 -0.91107E-4 -14.18002 -0.13761E-7 -0.13451E-7 -0.00025 -0.30551E-8 -0.30708E-8

[0232] Table 5 shows the P matrix eigenvalues ​​under different penetration rates of the IEEE 33-node system

[0233] 31％ 30.0625％ 30％ 0 -2.37764 -9.74231 -6.05136 0.67222007E-7 -0.640754E-8 -1.22717E-10 0.00263E-10 -0.00032E-10 0 -0.00238E-10 -0.00032E-10

[0234] Combine Figure 8 It can be seen from Tables 4 and 5 that when the penetration rate of the photovoltaic power generation system is 31%, there are positive numbers in the real part of the eigenvalues ​​of the P matrix obtained in the two different simulation systems, which does not meet the requirement that the real part of the matrix eigenvalue must be kept less than zero.

[0235] When the PV system penetration rate is 30.0625%, the real parts of the eigenvalues ​​of the P matrix obtained in the IEEE 14-node simulation system and in two different simulation systems are both negative, which meets the requirement that the real parts of the matrix eigenvalues ​​must remain less than zero. However, in the IEEE 33-node simulation system, the real parts of the eigenvalues ​​of the P matrix obtained in two different simulation systems are positive, which does not meet the requirement that the real parts of the matrix eigenvalues ​​must remain less than zero.

[0236] When the penetration rate of the photovoltaic power generation system is 30%, the real part of the eigenvalues ​​of the P matrix obtained in the two different simulation systems is negative, which meets the requirement that the real part of the matrix eigenvalue must be kept less than zero.

[0237] (2) Under the same simulation conditions, the state space equations (15) and (16) based on the system are verified at three values ​​of photovoltaic penetration of 31%, 30.0625% and 30% respectively. The unit step response curves are as follows: Figure 9 shown.

[0238] When the penetration rate of the photovoltaic power generation system is 31%, 30.0625%, and 30%, the step response curves of the system obtained by IEEE14-bus system simulation are as follows: Figure 9 (a), 9(c), and 9(e), the step response curves of the system obtained by IEEE 33-node system simulation are shown in Figure 9 (b), 9(d), and 9(f).

[0239] Depend on Figure 9 It can be seen from (a) and (b) that when the penetration rate of the photovoltaic power generation system is 31%, the step response curve of the system in the two different simulation systems is finally in a non-convergent state, and the system cannot maintain stable operation at this time.

[0240] Depend on Figure 9It can be seen from (c) and (d) that when the penetration rate of the photovoltaic power generation system is 30.0625%, the step response curve of the system in the IEEE14-node simulation system is finally in a convergent state, and the system can maintain stable operation at this time. However, in the IEEE33-node simulation system, the step response curve of the system is finally in a non-convergent state, and the system cannot maintain stable operation at this time.

[0241] Depend on Figure 9 As shown in (e) and (f), when the penetration rate of the photovoltaic power generation system is 30%, the step response curves of the system in the two different simulation systems are finally in a convergent state, and the system can maintain stable operation.

[0242] The stable value of the system in the range of permeability increasing from zero to 40% is solved through simulation data, such as Figure 10 shown.

[0243] The three-dimensional mapping diagram shows the spatial distribution of the stability value of the photovoltaic power generation system as the penetration rate changes. Figure 10 As can be seen in (a), with the increase of permeability, the stability value shows a clear downward trend, indicating that the stability of the system is decreasing. Figure 10 (b) The contour distribution diagram connects points with the same stability value using contour lines, clearly demarcating stable and unstable areas of the photovoltaic power generation system. The denser the contour lines, the more sensitive the system stability is to changes in permeability. The contour lines become denser around a permeability of approximately 0.3, indicating that the system stability changes rapidly at this point, marking a critical point in system stability. Figure 10 (b) shows that in the lower permeability region, below 0.3, the stability value is high and changes relatively slowly, indicating that the system is relatively stable in this range and is insensitive to permeability changes. In the higher permeability region, above 0.3, the stability value drops rapidly and even becomes negative, indicating that the system is unstable.

[0244] (3) Under the same simulation conditions, the optimized state space equations (24) and (25) are verified at three values ​​of photovoltaic penetration of 30%, 30.0625% and 31% respectively. The unit step response curve of the AC system is shown as follows: Figure 11 shown.

[0245] When the penetration rate of the photovoltaic power generation system is 31%, 30.0625%, and 30%, the step response curve of the system obtained by IEEE14-bus system simulation is as follows: Figure 11 (a), 11(c), and 11(e), the step response curves of the system obtained by IEEE 33-node system simulation are shown in Figure 11 (b), 11(d), and 11(f).

[0246] Under the same conditions, the active power of the photovoltaic power generation system grid connection point was measured at three values ​​of photovoltaic penetration: 31%, 30.0625% and 30%. Figure 12 shown.

[0247] Depend on Figure 11 From (a) and (b), we can see that when the penetration rate of the photovoltaic power generation system is 30%, the step response curve of the system in the two different simulation systems is finally in a convergent state, and the system can maintain stable operation. Figure 11 From (c) and (d), we can see that when the penetration rate of the photovoltaic power generation system is 30.0625%, the step response curve of the system in the IEEE14-node simulation system is finally in a convergent state, at which point the system can maintain stable operation, while the step response curve of the system in the IEEE33-node simulation system is finally in a non-convergent state, at which point the system cannot maintain stable operation. Figure 11 From (e) and (f), we can see that when the penetration rate of the photovoltaic power generation system is 31%, the step response curve of the system in the two different simulation systems is finally in a non-convergent state, and the system cannot maintain stable operation at this time. Figure 12 It was observed that when the penetration rate of the photovoltaic power generation system was 31%, the active power of the grid-connected point dropped to 15.94kW. When the penetration rate exceeded 30%, the active power of the system could not provide effective support, causing the frequency to drop, which in turn led to system instability.

[0248] The following conclusions can be drawn from the example analysis:

[0249] 1) Using state-space equations to analyze the stability of photovoltaic power generation systems, the P matrix can be solved using its internal structural parameters and the overall step response of the system can be observed. However, when using traditional stability analysis methods to analyze transfer functions, only the overall stability of the system can be observed, not its internal stability state. The analysis method proposed in this invention is applicable to both simple and complex systems.

[0250] 2) According to the P matrix and eigenvalue distribution diagram of the photovoltaic power generation system state space equation, when the penetration rate is 31%, the system's P matrix is ​​negative definite in the two simulation systems and there are positive eigenvalues; when the penetration rate is 30.0625%, the system's P matrix positive definite results are inconsistent in the two simulation systems; when the penetration rate is 30%, the P matrix is ​​positive definite in both simulation systems and the eigenvalues ​​are negative;

[0251] 3) Pass Figure 9It can be seen that when the penetration rate of the photovoltaic power generation system is 31%, the step response curve of the system does not converge in the two simulation systems, and the system is unstable at this time; when the penetration rate is 30.0625%, the step response curve of the system shows different convergence states in the two simulation systems. When the penetration rate is 30%, the step response curve of the system can maintain convergence in both simulation systems, and the system is stable at this time;

[0252] 4) By Figure 10 It can be seen that when the penetration rate of the photovoltaic power generation system increases from zero to 0.021MW (penetration rate is 1%), the stability value of the system shows a downward trend. When the system stability value is less than zero, the system is in an unstable state.

[0253] 5) Pass Figure 11 It can be observed that when the penetration rate of the photovoltaic power generation system is 30%, the unit step response of the system including the AC side can maintain stable operation in both IEEE14-node and IEEE30-node systems.

[0254] 6) Pass Figure 13 It can be seen that when the photovoltaic power generation system penetration rate is 31%, the photovoltaic power generation grid-connected system is unstable according to the Nyquist curve, and when the photovoltaic power generation system penetration rate is 30%, the photovoltaic power generation grid-connected system is stable according to the Nyquist curve. The analysis results of the Nyquist diagram are consistent with the analysis results of Lyapunov's first method, which can provide conservative support for Lyapunov's first method.

[0255] In summary, when analyzing the stability of a photovoltaic system, taking into account the photovoltaic penetration variable, as the penetration rate increases from zero, the system's stability value shows a downward trend. When the system stability value is less than zero, the system is unstable. Combined with the Lyapunov stability criterion, the results show that when the photovoltaic power generation system penetration threshold reaches 30%, both simple and complex systems are stable. The Nyquist plot analysis results are consistent with those of Lyapunov's first method, supporting the conservative nature of Lyapunov's first method.

[0256] This paper provides a stability analysis method for a photovoltaic power generation system grid-connected model that takes photovoltaic penetration into account, and establishes a stability analysis framework that takes penetration into account. First, a state-space mathematical model of the photovoltaic power generation system is established, taking into account the impact of photovoltaic penetration on the photovoltaic power generation grid-connected system. Second, the state-space mathematical model of the photovoltaic power generation system is optimized using fractional differential equations, and the validity of the state-space model is verified using a step response method. Finally, photovoltaic power generation grid-connected models are constructed based on IEEE 14-node and IEEE 33-node systems, and the photovoltaic penetration threshold at which the system is stable is determined using the Lyapunov stability criterion.

[0257] The specific embodiments of the present invention are described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the knowledge of ordinary technicians in this field without departing from the scope of the present invention.

Claims

1. A stability analysis method for a photovoltaic power generation system grid-connected model taking into account photovoltaic penetration, characterized by: The method comprises: Step 1: Based on the photovoltaic power generation system model, a dynamic equivalent model of the photovoltaic power generation system is established and Parker transformation is performed, based on which the transfer function model of the photovoltaic power generation system is calculated; Step 2: Convert the transfer function model of the photovoltaic power generation system to a differential equation, and further obtain the state space equation of the photovoltaic power generation system by Laplace inverse transform. Use step response analysis to preliminarily verify the applicability of the state space equation of the photovoltaic power generation system. Step 3. After preliminary verification, the state space equation of the photovoltaic power generation system is optimized by using fractional-order differential equations, and a photovoltaic power generation system grid-connected model is established; taking into account the impact of photovoltaic penetration rate on the grid-connected photovoltaic power generation system, when performing stability analysis on the photovoltaic power generation system, the P matrix required by the Lyapunov function is solved based on the state space equation of the photovoltaic power generation system, and the photovoltaic penetration rate threshold when the photovoltaic power generation system is stable is obtained using the Lyapunov stability criterion analysis.

2. The method for analyzing the stability of a photovoltaic power generation system grid-connected model taking into account photovoltaic penetration according to claim 1, characterized in that: Step 1 includes: Step 1.

1. Establish a photovoltaic power generation system model; the photovoltaic inverter model is shown in formula (1): Among them, E a 、E b 、E c Indicates the three-phase AC voltage of the grid-connected busbar; R and L indicate the total resistance and inductance of the filter inductor and step-up transformer connected to the inverter; U a 、U b 、U c Indicates the AC side voltage of the three-phase inverter; I a , I b , I c represents the three-phase current on the AC side of the three-phase inverter; t represents time; Step 1.2, establish a photovoltaic power generation penetration rate model; the photovoltaic power generation penetration rate model is shown in formula (2): Among them, PP represents photovoltaic penetration, P pv Represents the real-time output power of the photovoltaic power generation system, P load Indicates the real-time power demand of the power load in the area. Indicates the maximum value of the ratio of photovoltaic power to load power; Step 1.4, establish a dynamic equivalent model of the photovoltaic power generation system; the dynamic equivalent model of the photovoltaic power generation system is shown in formula (3): Among them, U id and U iq Indicates the dq axis component of the inverter output voltage, U dc Indicates the inverter DC bus voltage, U gd 、U gq and I d , I q Represents the dq-axis components of the voltage and current at the grid connection point of the photovoltaic power generation system, I pv Represents the photovoltaic array output current, s q and s d represents the dq axis component of the switching quantity under the synchronous coordinate axis, C represents the DC side capacitance of the photovoltaic power generation system, and ω represents the synchronous frequency; among them, the inverter output voltage U i With switch quantity s q and s d The relationship is as follows: Step 1.5, combine formula (3) and formula (4) to obtain formula (5): in, and Represents the dq-axis first-order component of the voltage and current at the grid connection point of the photovoltaic power generation system, Represents the dq-axis second-order component of the grid-connected point current of the photovoltaic power generation system; Step 1.

6. Perform Park transformation on equation (5) to obtain equation (6): Where s represents the Laplace variable, Δ represents the small signal disturbance, and ΔI d (s), ΔI q (s) is the variation of dq axis voltage and current in the frequency domain, i.e., the Laplace transform form under small signal disturbance; s q and s d is the dq-axis component of the switching vector in the synchronous coordinate system; Step 1.7, by combining equations (5) and (6), equation (5) can be transformed from the dq axis to the α-β axis; in, Indicates the change in α-β axis voltage, ΔI α (s), ΔI β (s) represents the change of α-β axis current, θ0 represents the power factor angle; Ignoring the voltage phase angle, equation (9) can be simplified to: Among them, ΔI r (s), ΔI j (s) represents the change in the real and imaginary parts of the current of the grid-connected voltage, ΔU g (s) represents the grid connection point voltage of the photovoltaic power generation system in the frequency domain; Step 1.

8. Obtain the transfer function model of the photovoltaic power generation system through calculation; the transfer function model of the photovoltaic power generation system is shown in formula (11): in, 3. The method for analyzing the stability of a photovoltaic power generation system grid-connected model taking into account photovoltaic penetration according to claim 1, characterized in that: The step 2 includes: using Lyapunov's second method to judge the stability of the photovoltaic power generation system, converting the obtained transfer function model of the photovoltaic power generation system into a differential equation, and further obtaining the state space equation of the photovoltaic power generation system by Laplace inverse transform; when using Lyapunov's second method to judge the stability, it is required to take the state space equation of the photovoltaic power generation system X 1 :X 1 =A0X, if A0 is a non-singular matrix, then Xe=0 is the only equilibrium state of the photovoltaic power generation system.

4. The method for analyzing the stability of a photovoltaic power generation system grid-connected model taking into account photovoltaic penetration according to claim 1, characterized in that: Step 2 includes: Step 2.1, construct a photovoltaic power generation system based on Lyapunov function; According to Lyapunov’s definition, the scalar function V(x) of the photovoltaic power generation system is shown in formula (12): V(x)=X T PX(12) Where P represents a positive definite real symmetric matrix, which is obtained by the state space equation; X represents the state vector of the photovoltaic power generation system; Convert Equation (12) into energy function As shown in formula (13): Where, Q = -(A T +PA)Q is a pre-given positive definite matrix, i.e., the identity matrix, and P is the symmetric matrix to be determined. If Q>0, then At this time, the system is in X e =0 is the stable state, X e Represents the value of the system's state variables at the equilibrium point; The stability of the photovoltaic power generation system is judged by Lyapunov's second method. The symmetric matrix P is solved by Lyapunov equation. If P is positive definite according to Sylvester criterion, the system is stable. Step 2.2: Construct the Lyapunov function shown in formula (12), and then transform the photovoltaic power generation system transfer function model shown in formula (11) into a differential equation. The differential equation is shown in formula (14): In the formula Respectively represent the first-order, second-order, third-order, and fourth-order derivatives of the photovoltaic power generation system voltage; and They represent the first-order, second-order, third-order, and fourth-order derivatives of the current in the α-β stationary coordinate system respectively; where I α , I β represents the current component in the α-β stationary coordinate system, U g Indicates the grid connection point voltage; a4＝0； Step 2.3, perform Laplace inverse transformation on equation (14) to obtain the state space equations of the photovoltaic power generation system shown in equations (15) and (16), where equation (15) is the α-axis state space equation and equation (16) is the β-axis state space equation; Among them, Y α Indicates I α ; Y β Indicates I β ; x=[x1 x2 x3 x4] T ;μ=U g ; in, Represents the state vector of the α-β axis, including state variables related to the α and β axes, μ represents the input variable of the photovoltaic power generation system, β1, β2, β3, and β4 represent the coefficients affecting the state of the α axis, γ1, γ2, γ3, and γ4 represent the coefficients affecting the state of the β axis, and x1, x2, x3, and x4 represent the state variables of the photovoltaic power generation system, corresponding to the α-β axis state variables respectively; Matrix A describes the dynamic relationship between the state variables of the photovoltaic power generation system, Matrix B describes how the input variable μ affects the state change of the α axis, and Matrix E describes how the input variable μ affects the state change of the β axis; Step 2.4: Use step response analysis to preliminarily verify the applicability of the state space equation of the photovoltaic power generation system. Under the condition that the penetration rate of the photovoltaic power generation system is 0, experimental simulation data verification is carried out to obtain the step response curve of the photovoltaic power generation system.

5. The method for analyzing the stability of a photovoltaic power generation system grid-connected model taking into account photovoltaic penetration rate according to claim 1, characterized in that: Step 3 includes: further improving the state space equation because the step response curve of the photovoltaic power generation system does not converge when the experimental simulation data is verified under the condition that the photovoltaic power generation system penetration rate is 0; the specific steps include: Step 3.1: When optimizing the state space equation of the photovoltaic power generation system, the fractional-order differential equation is used to simplify the state space equation. The general form of the fractional-order differential equation is as follows: e n D n y(t)+…+e1D 1 y(t)+e0y(t)=u(t) (17) Where D represents the derivative operator, n represents the fractional order; D n represents the fractional derivative; D 1 y(t) represents the first-order derivative, that is represents the rate of change; D n y(t) represents the nth order derivative, d n y represents the nth-order differential of the dependent variable y, dx n represents the nth-order differential e of the independent variable x n ,e n-1 ,…,e0 is the coefficient of the fractional differential equation, representing the parameters of the system, y(t) represents the output variable of the system, and u(t) represents the input variable of the system Convert the fractional-order differential equations (17) and (18) into state-space equations. The converted state-space equations are: Among them, x i (t)(i=1,...,n) are fractional-order state variables, A', B' are matrices of appropriate dimensions, ' represents only a label, not the transpose in matrix operations, A', B' represent the dynamic relationship between the state variables of the system, and matrices A', B' represent the influence of inputs x(t) and u(t) on the rate of change of the state variables, respectively. The parameters in matrices A', B' are related to the coefficients in the fractional-order differential equations; x(t)=[x1(t)x2(t)…x n (t)] T ; The fractional-order differential equations and state-space equations of the photovoltaic power generation system are improved, and the results after improvement are as follows: Equation (20) is transformed into the state space equation as follows: Among them, Y α Indicates I α ; Y β Indicates I β ; The state vector representing the improved α-β axis contains the state variables related to the α and β axes; x=[x1 x2 x3 x4] T ;μ=U g ; For the state space equation of the improved photovoltaic power generation system, its step response curve converges; the improved photovoltaic power generation system is in a stable state, and based on the state space equations (21) and (22), the P matrix required by the Lyapunov function can be solved. Finally, by judging whether the P matrix is ​​positive, it can be judged whether the system is stable and the photovoltaic penetration threshold value when the system is stable at different penetration rates. Step 3.2, the photovoltaic power generation system is connected to the grid through the inverter to form a photovoltaic power generation system grid-connected model; the connection between the grid AC side and the PV DC side is expressed by formula (23); Among them, I d , I q Represents the dq axis components of the grid-connected current of the photovoltaic power generation system; R, L represent the AC resistance and inductance; E d 、E q Indicates the three-phase AC measurement of the busbar at the grid connection point E a 、E b 、E c The dq-axis component of the voltage; U dc Indicates the inverter DC bus voltage, s q and s d Indicates the dq axis components of the switching quantity under the synchronous coordinate axis; Convert Equation (23) into the state space equations of the photovoltaic power generation system as shown in Equations (24) and (25): Among them, Y d Indicates I d ; Y q Indicates I q ; x′ represents the grid-connected state variable of the photovoltaic power generation system; 6. A photovoltaic power generation system grid-connected model stability analysis system taking into account photovoltaic penetration rate, characterized in that: The system includes: a module for executing the method for analyzing the stability of a photovoltaic power generation system grid-connected model taking into account photovoltaic penetration rate according to any one of claims 1 to 5.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method for analyzing the stability of a grid-connected model of a photovoltaic power generation system taking into account photovoltaic penetration rate as described in any one of claims 1 to 5 is implemented.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for analyzing the stability of a photovoltaic power generation system grid-connected model taking into account photovoltaic penetration rate as described in any one of claims 1 to 5 is implemented.

9. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the method for analyzing the stability of a photovoltaic power generation system grid-connected model taking into account photovoltaic penetration rate as described in any one of claims 1 to 5 is implemented.

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