Analysis Method and Device for Stability and Interaction of Multi-Inverter Parallel System

Abstract

The present invention discloses a method and device for analyzing the stability and interaction of a multi-inverter parallel system. The entire expanded microgrid is divided into a sub-system A where the original inverter is connected to the grid and a sub-system B composed of newly installed inverters. The two sub-systems are connected in parallel at the common connection point and are connected to the grid via the common connection point. Models of the two sub-systems are established, and the transfer functions of the two sub-systems are solved. The interaction between sub-system A and sub-system B is analyzed, and the closed-loop model of the two-inverter grid-connected system is characterized by the block diagrams of the two sub-systems, and the transfer function of the closed-loop system is solved. Based on the transfer functions of the two open-loop sub-systems and the closed-loop system, the eigenvalues of the system are obtained. The differences between the eigenvalues of the closed-loop system and the open-loop sub-systems are compared to quantify the degree of interaction between multiple inverters and its impact on system stability. The present invention can be applied to evaluate the impact of a parameter-asymmetric inverter parallel system on system stability and guide the proposal of methods to enhance system stability.

Description

Technical Field

[0001] The invention relates to a multi-inverter parallel system, in particular to a stability and interaction analysis method and device for the multi-inverter parallel system. Background Art

[0002] Inverters are used as the interface for renewable distributed generation to connect to the grid, and a larger generation capacity can be achieved by connecting to the grid in parallel. Compared with a single grid-connected inverter, the dynamic characteristics of parallel inverters interact with the voltage changes at the common connection point of the grid. In order to predict the stability of parallel inverters, it is necessary to obtain the impact of the interaction of multiple parallel inverters on the damping characteristics and state space model.

[0003] The same inverter parallel system can analyze the influence of inverter interaction on stability through the impedance model. It uses the concept of node admittance matrix to establish an interactive admittance model that can describe the physical grid admittance of the multi-inverter system interaction, which can intuitively explain the resonance and instability of the multi-inverter system. The same inverter parallel system can analyze the influence of inverter interaction on stability through the state space model. Based on the relative gain array principle, it quantitatively analyzes the coupling degree between control channels and obtains the variation of the interaction between control channels with the system operating frequency, LCL filter capacitance value and the number of parallel inverters. According to the impedance model and the state space model, the interaction between the same inverters is summarized as the internal stability and external stability of the stability of the same parallel inverter, and the two stabilities are decoupled. The internal stability is only affected by the inverter parameters, and the external stability is affected by the number of inverters through the multiplication effect.

[0004] For the impact of different line lengths brought by newly installed grid-connected inverters on the overall stability of the system, the root locus of the state space model or the Bode diagram based on the impedance model can be used to qualitatively analyze the impact of newly added lines of different lengths on the stability of a specific multi-inverter system.

[0005] The parameters of the inverters in renewable energy power stations (such as the length of the collection line) are not exactly the same, and the interaction analysis of the same parallel inverters is not sufficient for the stability prediction of the actual multi-inverter system. The system of parallel inverters with differentiated parameters is asymmetric. Asymmetric systems can only be characterized by detailed impedance models or state space models. By drawing the Bode diagram of the detailed impedance model or solving the eigenvalues ​​of the detailed state space model, the dynamic characteristics of the system with specific parameters can be obtained. However, the general law of the influence of interaction on the damping characteristics cannot be extracted from the detailed model of the multi-inverter parallel system.

[0006] In the field of stability analysis of multi-inverter grid-connected systems, the invention patent application "Stability testing method applied to multi-inverter parallel grid-connected systems" (Publication No.: CN106684920A, Publication Date: May 17, 2017) analyzes the stability of the system by establishing an impedance model of the system and using the Nyquist criterion. This invention can test the unstable loops of the system. However, the method in this invention can only test the stability of systems with specific parameters, cannot quantify the interaction between the newly installed inverter and the original system in the inverter expansion system, and also cannot obtain the general law of the influence of this interaction on stability. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a method and device for analyzing the stability and interaction of a multi-inverter parallel system, in view of the deficiencies of the prior art, to evaluate the influence law of the newly installed inverter on the stability of the original system in the inverter expansion scenario, and then guide the installation position and parameter optimization of the new inverter to ensure the stable operation of the expanded system.

[0008] To solve the above technical problem, the technical solution adopted by the present invention is: a method for analyzing the stability of a multi-inverter parallel system, comprising the following steps:

[0009] S1. Divide the microgrid into the original inverter grid-connected subsystem A and the newly installed inverter subsystem B;

[0010] S2. Obtain the transfer function G A (s) of subsystem A:

[0011] Obtain the transfer function G B (s) of subsystem B: G B (s) = [H 2 (s) - Z line2 (s)] -1 ;

[0012] Calculate the transfer function G(s) of the closed-loop system composed of subsystem A and subsystem B using the following formula: where Y i (s) = [H i (s) - Z linei (s)] -1 , H i (s) represents the transfer function from the x and y axis currents to the x and y axis terminal voltages of the #i inverter, and Z linei (s) represents the transfer function of the equivalent impedance of the collector line of the #i inverter, i = 1, 2; L g and R gare the equivalent inductance and equivalent resistance value of the power grid respectively, ω is the angular frequency of the power grid voltage; Inverter #1 is the inverter in subsystem A, Inverter #2 is the inverter in subsystem A, and s represents the complex frequency in the Laplace transform;

[0013] S3. Calculate the damping ratio of subsystem A, the damping ratio of subsystem B, and the damping ratio of the closed-loop system; among them, the calculation formula of the damping ratio is: λ is the eigenvalue of the transfer function G A (s), or the eigenvalue of the transfer function G B (s), or the eigenvalue of the transfer function G(s);

[0014] If the damping ratio of subsystem A < the damping ratio of the closed-loop system, it is determined that the stability of the closed-loop system is enhanced; otherwise, the stability of the closed-loop system deteriorates;

[0015] If the damping ratio of subsystem B < the damping ratio of the closed-loop system, it is determined that the stability of the closed-loop system is enhanced; otherwise, the stability of the closed-loop system deteriorates.

[0016] The existing technical solution only analyzes the overall stability of the multi-inverter grid-connected system using the impedance model. Compared with the existing technical solution, the present invention represents the expansion system as a closed-loop system interconnected by the open-loop subsystem of the original inverter and the open-loop subsystem of the newly installed inverter, and compares the damping ratios of the eigenvalues of the closed-loop system and the two open-loop subsystems, so as to analyze the influence of the newly installed inverter on the stability of the original system, and further guide the installation position and parameter optimization of the newly installed inverter.

[0017] Furthermore, the method of the present invention further includes:

[0018] Calculate the difference between the eigenvalue of the transfer function G A (s) and the first eigenvalue of the transfer function G(s) to obtain the first difference;

[0019] Calculate the difference between the eigenvalue of the transfer function G B (s) and the second eigenvalue of the transfer function G(s) to obtain the second difference;

[0020] If both the first difference and the second difference are 0, there is no interaction between subsystem A and subsystem B.

[0021] The larger the modulus of the first difference and the second difference, the stronger the interaction between subsystem A and subsystem B.

[0022] By analyzing the degree of interaction between subsystem A and subsystem B, the influence degree of the newly installed inverter on the stability of the original system can be quantified; if there is no interaction between subsystem A and subsystem B, ensuring the stability of subsystem B when operating alone can achieve the stable operation of the system after the expansion of the multi-inverter grid-connected system.

[0023] In the present invention, the transfer function H i (s) from the x- and y-axis line currents of the #i inverter to the x- and y-axis terminal voltages is calculated as follows:

[0024]

[0025] where, Δv fxy represents the vector formed by the x- and y-axis components of the terminal voltage of the #i inverter, and Δi xyi represents the vector formed by the x- and y-axis components of the line current of the #i inverter. I represents the identity matrix. Taking the grid voltage direction as the x-axis, the d-axis of the #i inverter as the output voltage direction of the inverter, and θ as the angle between the d-axis and the x-axis. v fdi0 is the steady-state value of the d-axis component of the terminal voltage of the #i inverter, G pll,i (s) = [0 k pt,i s + k it,i / s 2 , where k pt,i and k it,i respectively represent the proportional parameter and the integral parameter of the phase-locked loop control of the #i inverter. k pi,i and k ii,i respectively represent the proportional parameter and the integral parameter of the current loop control. L fi is the filter inductance value of the #i inverter, and U dci0 represents the steady-state value of the DC voltage of the #i inverter. k pv,i and k iv,i respectively represent the proportional parameter and the integral parameter of the voltage loop control of the #i inverter. C i represents the DC bus capacitor of the microgrid. i di0 is the steady-state value of the d-axis component of the line current of the #i inverter.

[0026] The transfer function H i (s) of the #i inverter takes into account the dynamics of the DC voltage outer loop, the current inner loop, and the phase-locked loop, and can effectively reflect the dynamic characteristics of the inverter in a wide frequency band.

[0027] The transfer function Z linei (s) of the equivalent impedance of the collector line of the #i inverter is calculated as follows:

[0028]

[0029] where, L linei represents the equivalent inductance of the collector line of the #i inverter, and R linei represents the equivalent resistance of the collector line of the #i inverter.

[0030] Transfer function Z of the collector line linei (s) retains the dynamics of the line equivalent inductance and can more accurately reflect the influence of the line on the stability of the open-loop subsystem and the mid-frequency band of the closed-loop system.

[0031] As an inventive concept, the present invention also provides a method for analyzing the interaction of a multi-inverter parallel system, which includes the following steps:

[0032] S1. Divide the microgrid into the original inverter grid-connected subsystem A and the newly installed inverter subsystem B;

[0033] S2. Obtain the transfer function G A (s):

[0034] Obtain the transfer function G B (s): G B (s) = [H 2 (s) - Z line2 (s)] -1 ;

[0035] Use the following formula to calculate the transfer function G(s) of the closed-loop system composed of subsystem A and subsystem B: where Y i (s) = [H i (s) - Z linei (s)] -1 , H i (s) represents the transfer function from the x and y axis currents of the #i inverter to the x and y axis terminal voltages, and Z linei (s) represents the transfer function of the equivalent impedance of the collector line of the #i inverter, i = 1, 2; L g and R g are respectively the equivalent inductance and equivalent resistance values of the power grid, ω is the angular frequency of the power grid voltage; the #1 inverter is the inverter in subsystem A, the #2 inverter is the inverter in subsystem A, and s represents the complex frequency in the Laplace transform;

[0036] S3. Calculate the difference between the eigenvalues of the transfer function G A (s) and the first eigenvalue of the transfer function G(s) to obtain the first difference;

[0037] Calculate the difference between the eigenvalues of the transfer function G B (s) and the second eigenvalue of the transfer function G(s) to obtain the second difference;

[0038] If both the first difference and the second difference are 0, there is no interaction between subsystem A and subsystem B.

[0039] As an inventive concept, the present invention further provides a terminal device, which includes a processor and a memory; the memory stores computer programs / instructions; the processor executes the computer programs / instructions stored in the memory; the computer programs / instructions are configured to implement the steps of the above method of the present invention.

[0040] As an inventive concept, the present invention further provides a computer-readable storage medium, on which computer programs / instructions are stored; characterized in that when the computer programs / instructions are executed by a processor, the steps of the above method of the present invention are implemented.

[0041] As an inventive concept, the present invention further provides a computer program product, including computer programs / instructions; characterized in that when the computer programs / instructions are executed by a processor, the steps of the above method of the present invention are implemented.

[0042] Compared with the prior art, the beneficial effects of the present invention are as follows: The inverter capacity expansion system of the present invention is a system in which the original system and the newly installed inverter are connected in parallel. The capacity expansion system is represented as a closed-loop system in which the open-loop subsystem of the original inverter and the open-loop subsystem of the newly installed inverter are interconnected. By comparing the eigenvalue differences and damping differences between the two open-loop subsystems and the closed-loop system, the interaction degree of the two open-loop subsystems is quantified, and the impact of capacity expansion on system stability is evaluated. The present invention can evaluate the influence law of the newly installed inverter on the stability of the original system in the inverter capacity expansion scenario, and further guide the installation position and parameter optimization of the new inverter to ensure the stable operation of the system after capacity expansion. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 Schematic diagram of a multi-inverter parallel grid-connected system in the capacity expansion scenario described in the specific embodiment of the present invention;

[0044] Figure 2 Two-inverter parallel system model representing the interconnection of subsystem A and subsystem B described in the specific embodiment of the present invention;

[0045] Figure 3a Schematic diagram of the root locus of the intermediate frequency eigenvalues of open-loop subsystem A, open-loop subsystem B, and the closed-loop system when the length of the collector line varies between 0 and 34 km under ideal grid conditions in an embodiment of the present invention;

[0046] Figure 3b Schematic diagram of the root locus of the intermediate frequency eigenvalues of open-loop subsystem A, open-loop subsystem B, and the closed-loop system when the collector line varies between 0 and 34 km in an embodiment of the present invention;

[0047] Figure 4a In an embodiment of the present invention, when P in1Schematic diagram of the active power response of Inverter #1 in System I when it is reduced by 5%;

[0048] Figure 4b In one embodiment of the present invention, when P in1 is reduced by 5%, schematic diagram of the active power response of Inverter #1 in System II;

[0049] Figure 4c In one embodiment of the present invention, when P in1 is reduced by 5%, the active power response of Inverter #1 in System III at P in1 when it is reduced by 5%.

[0050] L f ——Filter inductor, C——DC bus capacitor, ω——System frequency, P——Active power output of the inverter, output Z line ——Line equivalent impedance, PCC——Point of common coupling, R g ——Grid equivalent resistance, L g ——Grid equivalent reactance, Z g ——Grid equivalent impedance, v g ——Grid voltage, v f ——Inverter voltage, v g ——Voltage at the point of common coupling. Detailed implementation manners

[0051] The specific steps of the embodiments of the present invention include:

[0052] Step 1, the present invention analyzes that the entire expanded microgrid system is divided into two parts, the original inverter grid-connected subsystem A and the subsystem B composed of the newly installed inverter. The inverter in subsystem A is numbered Inverter #1, and the inverter in subsystem B is numbered #2.

[0053] Step 2, taking the line current Δi xy2 of Inverter #2 and the voltage Δv pxy at the point of common coupling as the input and output variables of subsystem A respectively, establish a block diagram of subsystem A, and solve the transfer function of subsystem A.

[0054] Specifically, the components of the open-loop subsystem A include Inverter #1 and the grid impedance. By establishing the transfer functions of the components in subsystem A, obtaining the physical relationships between the variables of the components, and then obtaining the block diagram of subsystem A, the transfer function of subsystem A is solved:

[0055] The input variable of Inverter #i is the voltage Δv pxy at the point of common coupling, and the output variable is the line current Δi xyi of Inverter #i. According to the circuit structure and control structure of the inverter, establish the transfer function of Inverter #i:

[0056]

[0057] wherein, i xyi = [i xi , i yi T represents the vector formed by the x-axis component i xi and the y-axis component i yi of the line current of the #i inverter, v pxy = [v px , v py T represents the vector formed by the x-axis component v px and the y-axis component v py of the common connection point voltage. The common connection point refers to the connection between the grid-connected inverter and the power grid. H(s) represents the transfer function from the xy-axis line current (including the x-axis line current and the y-axis line current) of the inverter to the xy-axis terminal voltage (x-axis terminal voltage and y-axis terminal voltage), Z line (s) represents the transfer function of the equivalent impedance of the collector line. The symbol Δ represents the small-signal change amount, and the digital subscript represents the inverter number.

[0058] Establish a general model;

[0059]

[0060] I represents the identity matrix;

[0061] Taking the power grid voltage direction as the x-axis, the d-axis of the inverter as the output voltage direction of the inverter, and θ as the angle between the d-axis and the x-axis;

[0062] v fd is the steady-state value of the d-axis component of the inverter terminal voltage;

[0063] G pll (s) = [0 k pt s + k it / s 2 , k pt and k it respectively represent the proportional parameter and the integral parameter of the inverter phase-locked loop control;

[0064] k pi and k ii respectively represent the proportional parameter and the integral parameter of the current loop control. L f is the value of the inverter filter inductor, and U dc0 represents the steady-state value of the DC voltage of the inverter; ​​

[0065] k pv and k iv respectively represent the proportional parameter and integral parameter of the inverter voltage loop control;

[0066] i d is the steady-state value of the d-axis component of the inverter line current;

[0067] The physical relationships among the component variables in subsystem A are described as follows:

[0068] The input variable Δi of subsystem A xy2 and the line current Δi of Inverter #1 xy1 and the grid line current Δi gxy have the following physical relationship:

[0069] Δi xy2 = Δi gxy - Δi xy1 Equation (2)

[0070] where, i gxy = [i gx , i gy T represents the vector formed by the xy components of the grid line current, and the subscripts "1" and "2" represent the serial numbers of the inverters.

[0071] The grid impedance voltage drop Δv dxy and the grid-connected current Δi gxy satisfy the following relationship:

[0072] Δv dxy = Z g (s)·Δi gxy Equation (3)

[0073] where, the transfer function of the grid impedance is: L g and R g are respectively the equivalent inductance and equivalent resistance values of the grid, and ω is the grid voltage angular frequency.

[0074] The output variable Δv of subsystem A pxy and the grid impedance voltage drop Δv pxy and the grid voltage Δv gxy have the following relationship:

[0075] Δv pxy = Δv dxy + Δv gxy Equation (4)

[0076] When the grid voltage is constant, i.e., Δv gxy = 0, Δv pxy ​= Δv dxy Therefore, the forward path of the open-loop model of subsystem A is described as the line current Δi of the #2 inverter xy2 and the line current Δi of the #1 inverter xy1 After superimposition, the grid current Δi is obtained gxy , passing through the grid impedance Z g (s), the grid impedance voltage Δv is obtained dxy , the grid voltage Δv gxy As the disturbance variable of subsystem A, it is superimposed with the grid impedance voltage Δv dxy to obtain the output variable Δv of subsystem A pxy ; The feedback path is described as the common connection point voltage Δv pxy passing through the dynamic model Y 1 (s) of the #1 inverter to obtain the line current Δi of the #1 inverter xy1 .

[0077] Solve the transfer function of subsystem A according to the transfer functions of the components in subsystem A and the physical relationships between the variables of the components

[0078]

[0079] Step 3, taking the voltage Δv at the common connection point pxy and the line current Δi of the #2 inverter xy2 as the input and output variables of subsystem B respectively, establish the block diagram of subsystem B, and solve the transfer function of subsystem B

[0080] Subsystem B only contains the #2 inverter. After the input signal passes through the #2 inverter, it is directly output. Therefore, the transfer function of the #2 inverter is the transfer function of subsystem B

[0081] G B (s) = Y 2 (s) = [H 2 (s) - Z line2 (s)] -1 Equation (6)

[0082] where the specific expressions of H 2 (s) and Z line2 (s) can be referred to in step S2

[0083] Step 4, taking the grid voltage Δv gxy and the line current Δi of the #2 inverter xy2 as the input and output variables of the parallel system of the two inverters respectively, and characterizing the closed-loop model of the grid-connected system of the two inverters with the block diagrams of the two subsystems. The components of the closed-loop model include the grid impedance, the #1 inverter, and the #2 inverter. The line current Δi of the #2 inverter in subsystem Bxy2 changes occur, and the grid current Δi gxy changes occur, resulting in a change in the voltage Δv at the common connection point of the output variables of subsystem A pxy changes occur, further affecting the dynamics of subsystem A. The voltage Δv at the common connection point pxy can change the output current Δi of inverter #2 xy2 , that is, the dynamics of system A can affect the dynamics of subsystem B. There is an interactive influence between subsystem A and subsystem B. Therefore, by connecting the output of the open-loop subsystem A to the input of the open-loop subsystem B, and connecting the output of the open-loop subsystem B to the input of the open-loop subsystem A, a closed-loop model of the two-inverter grid-connected system can be established.

[0084] According to the transfer functions and physical relationships between the components in the closed-loop model, solve the transfer function of the closed-loop system;

[0085]

[0086] Step 5, the eigenvalues of each system can be obtained from the transfer function established in step S4.

[0087] The eigenvalue λ of the open-loop subsystem A Ai is the root of the equation det G A (s)=0. The symbol det represents the determinant of the matrix.

[0088] Similarly, the eigenvalue λ of the open-loop subsystem B Bi is the root of the equation det G B (s)=0.

[0089] The eigenvalues of the closed-loop system are the roots of the equation det G(s)=0, where represent the eigenvalues corresponding to the open-loop subsystem A and the open-loop subsystem B respectively.

[0090] Step 6, quantify the interaction between the two open-loop subsystems by the difference between the eigenvalues of the closed-loop system and the eigenvalues of the open-loop subsystems:

[0091]

[0092]

[0093] where Δλ Ai is used to quantify the influence of subsystem B on subsystem A. The larger its value, the greater the influence of subsystem B on subsystem A; Δλ Bi is used to quantify the influence of subsystem A on subsystem B. The larger its value, the greater the influence of subsystem A on subsystem B; if Δλ Ai =0 and Δλ Bi= 0 indicates that there is no interaction between the two open-loop subsystems.

[0094] By comparing the eigenvalue damping ratios of the closed-loop system and the open-loop subsystems, analyze the influence of the interaction on the stability of the closed-loop system.

[0095] For an eigenvalue λ, its real part is denoted as Re(λ) and its imaginary part is denoted as Im(λ), then the damping ratio of the eigenvalue λ is:

[0096]

[0097] Substitute the eigenvalue λ of the open-loop subsystem A Ai and the eigenvalue of the closed-loop system into the above formula respectively to obtain the damping ratio ξ of the open-loop subsystem A Ai and the damping ratio of the corresponding eigenvalue of the closed-loop system If it indicates that under the influence of the open-loop subsystem B, compared with the open-loop subsystem A, the stability of the closed-loop system is enhanced. Conversely, the stability of the closed-loop system deteriorates.

[0098] Substitute the eigenvalue λ of the open-loop subsystem B Bi and the eigenvalue of the closed-loop system into the above formula respectively to obtain the damping ratio ξ of the open-loop subsystem B Bi and the damping ratio of the corresponding eigenvalue of the closed-loop system If it indicates that under the influence of the open-loop subsystem A, compared with the open-loop subsystem B, the stability of the closed-loop system is enhanced. Conversely, the stability of the closed-loop system deteriorates.

[0099] The verification process of the method of the present invention is as follows:

[0100] 1) Similar to steps 2 - 5, establish the transfer functions of the open-loop subsystems of the multi-inverter parallel model and the transfer function of the closed-loop system, and solve the eigenvalues of the system. The specific steps are as follows:

[0101] 1.1) Substitute the actual parameters of the #1 inverter in the entire expanded microgrid system and the actual parameters of the power grid into the transfer function equation of the open-loop subsystem A to establish the transfer function of the subsystem A in the actual expanded microgrid.

[0102] 1.2) Substitute the actual parameters of the #2 inverter in the entire expanded microgrid system into the transfer function equation of the open-loop subsystem B to establish the transfer function of the subsystem B in the actual expanded microgrid.

[0103] 1.3) Use the block diagrams of the two subsystems to represent the closed-loop model of the two-inverter grid-connected system, and solve the transfer function of the closed-loop system.

[0104] 1.4) Solve for the eigenvalues of the system according to the transfer functions of the two open-loop subsystems and the closed-loop system.

[0105] 2) Compare the differences between the eigenvalues of the closed-loop system and those of the open-loop subsystems, and quantify the interaction degree among multiple inverters and its impact on system stability.

[0106] In general, the parallel inverters are produced by the same manufacturer. Therefore, in practical applications, the circuit parameters and control parameters of the parallel inverters are usually the same. However, the lengths of the collection lines may vary. Thus, the eigenvalues of the closed-loop system and the open-loop subsystems are compared when the length of the new line changes. The circuit and control parameters of the two parallel inverters are the same, as shown in Table 1:

[0107] Table 1 Parameters of the two inverters in the system

[0108]

[0109] The rated power of each inverter is 1.5 MW, the transformation ratio is 690 V / 10.5 kV, and the equivalent impedance of the inverter is 0.045 p.u. The cable impedance connecting the inverter and the transformer is R line +jX line = 0.46 + j0.4 Ω / km. The non-ideal power grid is represented by an ideal voltage source of 10.5 kV and the equivalent impedance of the power grid, and X g / R g is 10.

[0110] The line length of the inverter in the atomic system A remains unchanged. With the circuit and control parameters of the two parallel inverters being the same, the eigenvalues of the closed-loop system and the open-loop subsystems are compared when the line length of the newly installed inverter changes, where l A and l B represent the line lengths connected to Inverter #1 and Inverter #2 respectively, l A is fixed at 10 km, and l B varies from 0 to 34 km in steps of 2 km. According to Figure 3a and Figure 3b , "×" and "+" represent the eigenvalues of the open-loop subsystem A and subsystem B respectively, the circles represent the eigenvalues of the closed-loop system, and the arrow direction represents the movement direction.

[0111] See Figure 3a , when the two inverters are connected to an ideal power grid, regardless of how l B changes, the eigenvalues of the closed-loop system of the two parallel inverters are consistent with those of the two subsystems. This is because the grid impedance of the ideal power grid is 0 and the voltage at the point of common coupling is equal to the grid voltage. Therefore, the dynamics of subsystem A and subsystem B are decoupled, and there is no interaction between subsystem A and subsystem B, that is, Δλ Ai= 0 and Δλ Bi = 0. In an ideal power grid, l B has a monotonic effect on the damping of the dual-inverter parallel system, and an increase in l B has an adverse effect on the damping in the intermediate frequency range.

[0112] See Figure 3b , the eigenvalues of the closed-loop system and the open-loop subsystem when the inverter is connected to a non-ideal power grid with a short-circuit ratio (SCR) of 9. In most cases, there are differences between the closed-loop and open-loop eigenvalues. It should be noted that when l B is 10 km, that is, l B = l A , Δλ B is 0. At this time, the parameters of the two parallel inverters are the same, the grid current Δi gxy is 0, and therefore, Δv pxy can also be 0. According to Appendix Figure 2 , Δv pxy = 0, that is, the output signal of subsystem A is 0. In the two-inverter parallel system, the dynamics of subsystem A have no effect on subsystem B. At this time Δλ B = 0. However, in any case and λ A will not have overlapping points because in the two-inverter parallel inverter system, Δi xy2 will not be equal to 0 in any case, and subsystem B always has an impact on the dynamics of subsystem A. As can be seen from Figure 3b , when the collector line lengths of the two inverters are equal, the eigenvalues of the closed-loop system have the minimum damping, indicating that the interaction reduces the stability of the closed-loop system under this condition.

[0113] To apply the method proposed in the present invention to a generalized multi-inverter parallel system, a comparative simulation of a two-inverter parallel system under different grid conditions is carried out to verify the analysis results of the above interaction.

[0114] The collector line lengths of the three systems are shown in Table 2, and the inverter parameters and collector line parameters are the same as those listed in Table 1.

[0115] Table 2 Collector line lengths of three actual systems

[0116]

[0117]

[0118] Under the condition of a non-ideal grid short-circuit ratio of 9, at 6.0 s, the input power of the DC link of the #1 inverter drops by 5%, and the active power response reference Figures 4a to 4c。Reference Figure 4a , the stabilization time of System I is about 1 s; Reference Figure 4b , System II recovers to the steady state after 3 s of perturbation, and there are small fluctuations in the steady-state active power of Inverter #1; Reference Figure 4c , the transition time of System III is about 35 s, which is much longer than that of the first and second systems.

[0119] According to the above analysis, it is found that a multi-inverter system with at least two collector lines of the same length has weaker damping characteristics than a system with completely different collector line lengths.

Claims

1. A method for analyzing the stability of a multi-inverter parallel system, characterized in that, it includes the following steps: S1. Divide the microgrid into the original inverter grid-connected subsystem A and the newly installed inverter subsystem B; S2. Obtain the transfer function G of subsystem A A (s): Obtain the transfer function G of subsystem B B (s): G B (s) = [H 2 (s) - Z line2 (s)] -1 ; The transfer function G(s) of the closed-loop system composed of subsystem A and subsystem B is calculated using the following formula: where Y i (s) = [H i (s) - Z linei (s)] -1 , H i (s) represents the transfer function from the x- and y-axis currents of the #i inverter to the x- and y-axis terminal voltages, Z linei (s) represents the transfer function of the equivalent impedance of the collector line of the #i inverter, i = 1, 2; L g and R g are the equivalent inductance and equivalent resistance values of the power grid respectively, ω is the angular frequency of the power grid voltage; the #1 inverter is the inverter in subsystem A, the #2 inverter is the inverter in subsystem A, and s represents the complex frequency in the Laplace transform; S3. Calculate the damping ratio of subsystem A, the damping ratio of subsystem B, and the damping ratio of the closed-loop system. The calculation formula for the damping ratio is as follows: λ is the eigenvalue of the transfer function G A (s), or the eigenvalue of the transfer function G B (s), or the eigenvalue of the transfer function G(s); If the damping ratio of subsystem A < the damping ratio of the closed-loop system, it is determined that the stability of the closed-loop system is enhanced; otherwise, the stability of the closed-loop system deteriorates; If the damping ratio of subsystem B < the damping ratio of the closed-loop system, it is determined that the stability of the closed-loop system is enhanced; otherwise, the stability of the closed-loop system deteriorates.

2. The method for analyzing the stability of a multi-inverter parallel system according to claim 1, characterized in that, it further includes: Calculate the transfer function G A Obtain a first difference by taking the difference between the eigenvalues of (s) and the first eigenvalue of the transfer function G(s); Calculate the transfer function G B Subtract the eigenvalue of (s) from the second eigenvalue of the transfer function G(s) to obtain a second difference; If both the first difference and the second difference are 0, there is no interaction between subsystem A and subsystem B.

3. The method for analyzing the stability of a multi-inverter parallel system according to claim 1, characterized in that, #i Transfer function H of the inverter x- and y-axis currents to the x- and y-axis terminal voltages i (s) is calculated as follows: where, Δv fxy represents the vector formed by the x - and y - axis components of the terminal voltage of the #i inverter, Δi xyi represents the vector formed by the x - and y - axis components of the line current of the #i inverter, I represents the identity matrix, with the grid voltage direction as the x - axis, the d - axis of the #i inverter as the output voltage direction of the inverter, and θ as the angle between the d - axis and the x - axis, v fdi0 is the steady - state value of the d - axis component of the terminal voltage of the #i inverter, G pll,i (s)=[0 k pt,i s + k it,i / s 2 , k pt,i and k it,i respectively represent the proportional parameter and integral parameter of the phase - locked loop control of the #i inverter, k pi,i and k ii,i respectively represent the proportional parameter and integral parameter of the current - loop control, L fi is the filter inductance value of the #i inverter, U dci0 represents the steady - state value of the DC voltage of the #i inverter, k pv,i and k iv,i respectively represent the proportional parameter and integral parameter of the voltage - loop control of the #i inverter, C i represents the DC bus capacitor of the micro - grid, i di0 is the steady - state value of the d - axis component of the line current of the #i inverter.

4. The method for analyzing the stability of a multi-inverter parallel system according to claim 1, characterized in that, #i Transfer function Z of the equivalent impedance of the inverter collector line linei (s) is calculated as follows: Among them, L linei represents the equivalent inductance of the #i inverter collector line, and R linei represents the equivalent resistance of the #i inverter collector line.

5. A method for analyzing the interaction of a multi-inverter parallel system, characterized in that, it includes the following steps: S1. Divide the microgrid into the original inverter grid-connected subsystem A and the newly installed inverter subsystem B; S2. Obtain the transfer function G of subsystem A A (s): Obtain the transfer function G of subsystem B B (s): G B (s) = [H 2 (s) - Z line2 (s)] -1 ; Calculate the transfer function \(G(s)\) of the closed-loop system composed of subsystem A and subsystem B using the following formula: where \(Y\) i (s)=[H i (s)-Z linei (s)] -1 , \(H\) i (s) represents the transfer function from the x- and y-axis currents of the #i inverter to the x- and y-axis terminal voltages, \(Z\) linei (s) represents the transfer function of the equivalent impedance of the collector line of the #i inverter, \(i = 1, 2\); \(L\) g and \(R\) g are the equivalent inductance and equivalent resistance values of the power grid respectively, \(\omega\) is the angular frequency of the power grid voltage; the #1 inverter is the inverter in subsystem A, the #2 inverter is the inverter in subsystem A, and \(s\) represents the complex frequency in the Laplace transform; S3. Calculate the difference between the eigenvalue of G A (s) and the first eigenvalue of the transfer function G(s) to obtain a first difference value; Calculate the transfer function G B Obtain a second difference by taking the difference between the eigenvalue of (s) and the second eigenvalue of the transfer function G(s); If both the first difference and the second difference are 0, there is no interaction between subsystem A and subsystem B.

6. A terminal device, characterized in that, it includes a processor and a memory; the memory stores computer programs / instructions; the processor executes the computer programs / instructions stored in the memory; the computer programs / instructions are configured to implement the steps of the method according to any one of claims 1 to 5.

7. A computer-readable storage medium, on which computer programs / instructions are stored; characterized in that, when the computer programs / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

8. A computer program product, including computer programs / instructions; characterized in that, when the computer programs / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

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