Multi-converter grid-connected frequency domain stability analysis method and system based on system admittance matrix dynamic model

Abstract

The invention discloses a multi-converter grid-connected frequency domain stability analysis method and system based on a system admittance matrix dynamic model, and the method comprises the steps: firstly, determining a main circuit structure of a single-inverter grid-connected system and a control strategy of the main circuit structure, and building a small signal model; secondly, carrying out equivalence on an alternating-current power grid accessed by multiple converters, and obtaining a node admittance matrix transfer function of a grid-connected system and system equivalent impedance outside the parallel converter by utilizing a node voltage method; then, solving left and right feature vector matrixes L and T and modal impedance of the total equivalent impedance of the system by using a modal analysis method; and finally, applying the overall impedance stability criterion to each modal impedance, and determining the stability of the grid-connected system by judging that the slope kx of the imaginary part of the corresponding modal impedance is greater than 0 and the real part value is less than 0 in a poor damping oscillation mode. The stability criterion provided by the invention can accurately analyze the influence of multi-converter access on the stability of the alternating-current power grid, and can be widely applied to a large-scale power system to obtain a visual result.

Description

Technical Field

[0001] The invention belongs to the technical field of distributed renewable energy grid-connected power generation, and relates to a multi-converter grid-connected frequency domain stability analysis method based on a system admittance matrix dynamic model. The invention also relates to an analysis system utilizing the method. Background Art

[0002] In the process of renewable energy access and re-electrification on the load side, a large number of new energy, load, energy storage and other equipment with different characteristics are connected through power electronics technology, and the distribution system has shown a clear trend of power electronics. However, the access of multiple converters has also brought new challenges to the safety and stability of distribution network operation, which is reflected in the fact that the converter control system will interact with traditional power system components such as synchronous generators, power transformers and transmission lines to produce resonance problems, especially the interaction between the converter control system and the distribution network. These oscillations will further lead to instability of the distribution network and pose a threat to power quality.

[0003] Common methods for modeling grid-connected converter systems to study oscillation phenomena are state-space and impedance-based modeling methods. The state-space method represents the system as a set of linear equations in the time domain, but it requires detailed control parameter information and has limited application in real-world situations. The impedance-based modeling method represents the system as a transfer function in the s-domain, and methods such as the Quist stability criterion and the overall impedance stability criterion (PND) can be used to study the impact of a single converter control system on the stability of the AC grid in the frequency domain.

[0004] For the stability problem of multiple converters connected to the AC power grid, the commonly used stability judgment methods are the generalized Nyquist criterion (GNC) and modal analysis. The generalized Nyquist criterion uses the node admittance matrix in the s domain to judge the system stability by whether the Nyquist curve of the eigenvalue of the feedback ratio matrix contains the (-1, j0) point. However, GNC may lead to incorrect stability conclusions due to misleading correlations when deriving closed-loop transfer functions. For large networks, stability analysis is also challenging due to the large number of eigenvalue Nyquist curves. For the resonant modal analysis method (RMA), it helps to identify the harmonic resonance mode of the system in the form of the admittance matrix, but no stability standard is proposed. Therefore, for the current stability problem of multiple converters connected to the AC power grid, there is a lack of a simple and effective stability criterion. Summary of the invention

[0005] Technical problem: At present, the stability analysis and judgment methods for multi-converter AC power grids are complex, the application methods are limited, and the analysis results are incomplete. To solve this problem, this paper proposes a multi-converter grid-connected frequency domain stability analysis method based on the system admittance matrix dynamic model, which can reduce the workload of stability analysis and obtain complete stability analysis results.

[0006] Technical solution: The technical solution adopted by the present invention to solve the technical problem is: a method for analyzing the frequency domain stability of a multi-converter grid-connected system based on a system admittance matrix dynamic model is proposed, which includes the following contents:

[0007] A frequency domain stability analysis method for multi-converter grid-connected power supply based on a system admittance matrix dynamic model, characterized by comprising the following steps:

[0008] According to the main circuit structure and control strategy of the single inverter grid-connected system, a small signal model is established;

[0009] According to the small signal model, the AC power grid fed by multiple converters is equivalent, and the node admittance matrix transfer function Y of the grid-connected system is obtained by using the node voltage method. T (s) and the system equivalent impedance Y outside the parallel converter N (s);

[0010] Using the modal analysis method, the diagonal eigenvalue matrix of the equivalent node admittance matrix of the grid-connected system is obtained, and the corresponding modal impedance λ is calculated through the diagonal eigenvalue matrix zi ;

[0011] Determine the slope k of the imaginary part of the corresponding modal impedance in the underdamped oscillation mode x >0 and the real part value is less than 0 under the premise of the stability of the grid-connected system.

[0012] The established small signal model is a small signal model in the dq axis coordinate system based on the main circuit structure and control strategy of the single inverter grid-connected system. The small signal model at the common coupling point used for stability research is:

[0013] u(t)=Δv qd (t)

[0014] y(t)=Cx(t)+Du(t)y(t)=Δi c-qd (t)

[0015] Where x(t), u(t) and y(t) represent the state, input and output variables of the system respectively; A is the system matrix, which represents the connection between the internal states of the system; B is the input matrix, which represents the effect of the input variables on the state variables; C is the output matrix; D is the direct transfer matrix; Δv qd Indicates the dq axis small disturbance of the grid-connected point voltage; Δi c-qd The dq-axis small disturbance quantity representing the converter output current further transforms the small signal model to:

[0016]

[0017] Where Δv qd =[Δv q Δv d ] T ,Δi c-qd =[Δi c-q Δi c-d ] T , Z vsc-qq (s) represents the response of the q-axis current when a voltage is applied to the q-axis, Z vsc-qd (s) represents the response of the q-axis current when a voltage is applied to the d-axis, Z vsc-dq (s) represents the response of the d-axis current when the voltage is applied on the q-axis, Z vsc-dd (s) represents the response of the d-axis current when a voltage is applied on the d-axis.

[0018] For an AC grid system fed by multiple converters, multiple converters connected to a common coupling point are represented by a Norton equivalent circuit, which consists of an equivalent current source i n =[i n1 i n2 …i nn ] T and its corresponding converter equivalent impedance Z vsc (s) parallel connection;

[0019] If other external components are connected to the common coupling point, such as series resistive inductive components or parallel capacitive components, their impedance model can be expressed as:

[0020]

[0021] Among them, R and L represent the equivalent inductance and resistance of the series-connected resistive and inductive components, and C represents the capacitance of the parallel-connected capacitive component.

[0022] By applying the node voltage method, the admittance Y of each converter is vsc (s) = Z vsc (s) -1 and other external components are added to the node admittance matrix of the system, and the current on the n buses flowing through the common coupling point is expressed as i = [i 1 i 2 … i n ] T The voltage at the common coupling point is expressed as v = [v 1 v 2 … v n ] T The output current of n external components on each bus is represented by i n =[i n1 i n2 … i nn ]T Then the relationship between the voltage and current at the AC grid end, i.e., the common coupling point, is expressed as:

[0023]

[0024] where Y T (s) and Y S (s) are the node admittance matrix transfer function of the grid-connected system and the impedance of the external components;

[0025] Substituting the above equation into the small signal model at the common coupling point, we have:

[0026]

[0027] Among them, A is the system matrix, B is the input matrix, C is the output matrix, D is the direct transfer matrix, I is the identity matrix, and Z T (s)=Y T (s) -1 is the impedance matrix transfer function, expressed as:

[0028]

[0029] Among them, adj(sI-A) is the adjoint matrix of (sI-A), Z Tb (s) is Z T The adjoint matrix of (s), Z T The poles of (s) are the roots of the denominator D(s) = |sI-A|, i.e., the eigenvalues ​​λi of the state space matrix A;

[0030] The voltage and current at the common coupling point can also be rewritten as a unit negative feedback structure:

[0031] v=(I+L(s)) -1 Z N (s)i n L(s)=Z N (s)Y S (s)

[0032] Among them, Z N (s)=(Y N (s)) -1 And I is the n-th order identity matrix, and L(s) represents the open-loop transfer function.

[0033] Using the modal analysis method, the small signal model at the common coupling point is expressed as:

[0034] v=Y T (jω x )i n Y T (jω x )=LΛY T

[0035] Among them, Y T (jω x ) is the frequency ω x The system admittance matrix at v and i n are the node voltage and current injection vectors at the common coupling point; L and T are the left and right eigenvector matrices, respectively; Λ Y is a diagonal eigenvalue matrix:

[0036]

[0037] The Λ Y is the impedance matrix transfer function Z T (jω x ), that is:

[0038] Z T (jω x )=(Y T (jω x )) -1 =LΛ Z T

[0039] Λ Z =[λ z1 λ z2 …λ zn ]I

[0040] where Λ Z The diagonal term of is denoted as modal impedance λ zi , when the modal impedance reaches a maximum value within a certain range, it is called a critical mode. The resonant mode is determined by the modal impedance |λ of the frequency domain curve. zi |The peak value of the amplitude is identified, Z T The poles and modal impedance Λ Z The poles of (s) are the same, that is,

[0041]

[0042] Λ Zb (s) = TZ Tb (s)L=[λ zb1 λ zb2 …λ zbn ]I.

[0043] Diagonal matrix Λ Z The corresponding modal impedance λ zi It is expressed as:

[0044]

[0045] Among them, p0 =σ 0 ±jω 0 is λ zi A pair of complex conjugate poles of corresponds to a certain system oscillation mode and the eigenvalue λ of the state space matrix A 0 Matching, G(jω x ) is a polynomial expression representing the remaining terms,

[0046] When |σ 0 |<<|ω 0 |, the modal impedance will be at ω x ≈ω 0 At this point, G(jω x )≈G(jω 0 )=G r +jG x , where G r and G x is dependent on ω 0 is a constant complex number, so the modal impedance λ zi Further expressed as:

[0047]

[0048] in,

[0049] When resonance occurs, λ zi，x The zero-crossing frequency is:

[0050]

[0051] In the case of a weakly damped oscillation mode, ω x With the oscillation mode ω 0 The frequency of is approximately matched, that is, ω x ≈ω 0 , therefore, in ω x Place zi The real part of is approximately:

[0052]

[0053] Among them, k x is λ z0x In ω x ≈ω 0 The slope at

[0054]

[0055] In the weakly damped oscillation mode, when the modal impedance λ zi Real part λ z0x In ω x ≈ω 0 The slope kx is greater than 0 and the modal impedance λ zi The imaginary part λ zi，r When it is less than 0, the system is considered stable.

[0056] A multi-converter grid-connected frequency domain stability analysis system based on a system admittance matrix dynamic model, comprising:

[0057] Control device: used to establish a small signal model according to the main circuit structure and control strategy of the single inverter grid-connected system;

[0058] Equivalent device: used to perform the equivalent of the AC power grid fed by multiple converters according to the small signal model, and obtain the node admittance matrix transfer function Y of the grid-connected system using the node voltage method T (s) and the system equivalent impedance Y outside the parallel converter N (s);

[0059] Analysis device: used to use the modal analysis method to find the diagonal eigenvalue matrix of the equivalent node admittance matrix of the grid-connected system, and calculate the corresponding modal impedance λ through the diagonal eigenvalue matrix zi ;;

[0060] Determination device: used to determine the slope k of the imaginary part of the corresponding modal impedance in the underdamped oscillation mode x >0 and the real part value is less than 0 under the premise of the stability of the grid-connected system.

[0061] The analysis device controls the L-type three-phase grid-connected inverter containing parasitic resistance in the dq coordinate system, wherein the synchronous reference system phase-locked loop obtains the grid voltage phase θ required for Park coordinate transformation. PLL , the cascade control of the power outer loop and the current inner loop ensures the active and reactive power of the grid, and the small signal model at the common coupling point used for stability research is:

[0062] u(t)=Δv qd (t)

[0063] y(t)=Cx(t)+Du(t)y(t)=Δi c-qd (t)

[0064] Where x(t), u(t) and y(t) represent the state, input and output variables of the system respectively; A is the system matrix, which represents the connection between the internal states of the system; B is the input matrix, which represents the effect of the input variables on the state variables; C is the output matrix; D is the direct transfer matrix; Δv qd Indicates the dq axis small disturbance of the grid-connected point voltage; Δi c-qd The dq-axis small disturbance quantity representing the converter output current further transforms the small signal model to:

[0065]

[0066] Where Δv qd =[Δv q Δv d ] T ,Δi c-qd =[Δi c-q Δi c-d ] T , Z vsc-qq (s) represents the response of the q-axis current when a voltage is applied to the q-axis, Z vsc-qd (s) represents the response of the q-axis current when a voltage is applied to the d-axis, Z vsc-dq (s) represents the response of the d-axis current when the voltage is applied on the q-axis, Z vsc-dd (s) represents the response of the d-axis current when a voltage is applied on the d-axis.

[0067] For an AC power grid system fed by multiple converters, the equivalent device represents multiple converters connected to a common coupling point by a Norton equivalent circuit, wherein the Norton equivalent circuit is composed of an equivalent current source i n =[i n1 i n2 …i nn ] T and its corresponding converter equivalent impedance Z vsc (s) parallel connection;

[0068] If other external components are connected to the common coupling point, such as series resistive inductive components or parallel capacitive components, their impedance model can be expressed as:

[0069]

[0070] Among them, R and L represent the equivalent inductance and resistance of the series-connected resistive and inductive components, and C represents the capacitance of the parallel-connected capacitive component.

[0071] By applying the node voltage method, the admittance Y of each converter is vsc (s) = Z vsc (s) -1 and other external components are added to the node admittance matrix of the system, and the current on the n buses flowing through the common coupling point is expressed as i = [i 1 i 2 … i n ] T The voltage at the common coupling point is expressed as v = [v 1 v 2 … v n ] T The output current of n external components on each bus is represented by i n =[in1 i n2 … i nn ] T Then the relationship between the voltage and current at the AC grid end, i.e., the common coupling point, is expressed as:

[0072]

[0073] where Y T (s) and Y S (s) are the node admittance matrix transfer function of the grid-connected system and the impedance of the external components;

[0074] Substituting the above equation into the small signal model at the common coupling point, we have:

[0075]

[0076] Among them, A is the system matrix, B is the input matrix, C is the output matrix, D is the direct transfer matrix, I is the identity matrix, and Z T (s)=Y T (s) -1 is the impedance matrix transfer function, expressed as:

[0077]

[0078] Among them, adj(sI-A) is the adjoint matrix of (sI-A), Z Tb (s) is Z T The adjoint matrix of (s), Z T The poles of (s) are the roots of the denominator D(s) = |sI-A|, i.e., the eigenvalues ​​λi of the state space matrix A;

[0079] The voltage and current at the common coupling point can also be rewritten as a unit negative feedback structure:

[0080] v=(I+L(s)) -1 Z N (s)i n L(s)=Z N (s)Y S (s)

[0081] Among them, Z N (s)=(Y N (s)) -1 And I is the n-th order identity matrix, and L(s) represents the open-loop transfer function.

[0082] The analysis device uses the modal analysis method to express the small signal model at the common coupling point as:

[0083] v=Y T (jω x)i n Y T (jω x )=LΛ Y T

[0084] Among them, Y T (jω x ) is the frequency ω x The system admittance matrix at v and i n are the node voltage and current injection vectors at the common coupling point; L and T are the left and right eigenvector matrices, respectively; Λ Y is a diagonal eigenvalue matrix:

[0085]

[0086] The Λ Y is the impedance matrix transfer function Z T (jω x ), that is:

[0087] Z T (jω x )=(Y T (jω x )) -1 =LΛ Z T

[0088]

[0089] where Λ Z The diagonal term of is denoted as modal impedance λ zi , when the modal impedance reaches a maximum value within a certain range, it is called a critical mode. The resonant mode is determined by the modal impedance |λ of the frequency domain curve. zi |Amplitude peak to identify, Z T The poles and modal impedance Λ Z The poles of (s) are the same, that is,

[0090]

[0091] Λ Zb (s) = TZ Tb (s)L=[λ zb1 λ zb2 … λ zbn ]I.

[0092] The determination device transforms the diagonal matrix Λ Z The corresponding modal impedance λ zi It is expressed as:

[0093]

[0094] Among them, p0 =σ 0 ±jω 0 is λ zi A pair of complex conjugate poles of corresponds to a certain system oscillation mode and the eigenvalue λ of the state space matrix A 0 Matching, G(jω x ) is a polynomial expression representing the remaining terms,

[0095] When |σ 0 |<<|ω 0 |, the modal impedance will be at ω x ≈ω 0 At this point, G(jω x )≈G(jω 0 )=G r +jG x , where G r and G x is dependent on ω 0 is a constant complex number, so the modal impedance λ zi Further expressed as:

[0096]

[0097] in,

[0098] When resonance occurs, λ zi，x The zero-crossing frequency is:

[0099]

[0100] In the case of a weakly damped oscillation mode, ω x With the oscillation mode ω 0 The frequency of is approximately matched, that is, ω x ≈ω 0 , therefore, in ω x Place zi The real part of is approximately:

[0101]

[0102] Among them, k x is λ z0x In ω x ≈ω 0 The slope at

[0103]

[0104] In the weakly damped oscillation mode, when the modal impedance λ zi Real part λ z0x In ω x ≈ω 0 The slope kx is greater than 0 and the modal impedance λ zi The imaginary part λ zi，r When it is less than 0, the system is considered stable.

[0105] An electronic device comprises one or more processors for storing one or more programs. When the one or more programs are executed by the one or more processors, the one or more processors execute the multi-converter grid-connected frequency domain stability analysis method based on the system admittance matrix dynamic model as described in any one of claims 1 to 5.

[0106] A storage medium having a computer program stored therein, wherein the computer program is configured to execute, when running, the method for analyzing the grid-connected frequency domain stability of a multi-converter based on a system admittance matrix dynamic model as described in any one of claims 1 to 5.

[0107] Beneficial effects: The multi-converter grid-connected frequency domain stability analysis method based on the system admittance matrix dynamic model proposed in this patent can accurately evaluate the stability problems of large networks without detailed system parameters. Compared with traditional stability analysis methods, this method significantly reduces the computational workload and can provide visualization results of the system harmonic oscillation mode. This technical feature makes it possible to more conveniently conduct power system stability assessment and optimization design in actual projects. BRIEF DESCRIPTION OF THE DRAWINGS

[0108] Figure 1 It is a schematic diagram of the control structure of a three-phase L-type inverter.

[0109] Figure 2 It is the small signal model block diagram of the three-phase L-type inverter.

[0110] Figure 3 It is an equivalent schematic diagram of multiple converters connected to the AC distribution network.

[0111] Figure 4 It is a structural diagram of a case where two converters are connected to an AC distribution network.

[0112] Figure 5 It is a time domain simulation diagram of two converters connected to the AC distribution network.

[0113] Figure 6 It is the eigenvalue analysis diagram of the admittance model for testing the grid-connected system.

[0114] Figure 7 It is the generalized Nyquist curve and local enlarged diagram of the admittance model for testing the grid-connected system.

[0115] Figure 8 This is a stability analysis diagram of the test grid-connected system using the stability criterion proposed in this paper. DETAILED DESCRIPTION

[0116] The present invention will be further described below in conjunction with the accompanying drawings.

[0117] The present invention proposes a frequency domain stability analysis method for multi-converter grid-connected power supply based on a system admittance matrix dynamic model, which is characterized by comprising the following steps:

[0118] S1. Establish the main circuit structure and control strategy of the single inverter grid-connected system and build a small signal model;

[0119] This article takes a three-phase L-type inverter with internal resistance as an example. Figure 1 The control structure diagram of the three-phase L-type inverter is shown in Figure 2. The inverter uses a vector control strategy and a cascade controller with a power outer loop and a current inner loop to control the active and reactive power of the grid. The control is implemented in the dq coordinate system, and a synchronous reference frame phase-locked loop (SRF-PLL) is used to obtain the grid voltage phase θ required for Park coordinate transformation. PLL .like Figure 2 As shown, the small signal model at the point of common coupling (PCC) for stability study can be expressed as:

[0120] u(t)=Δv qd (t)

[0121] y(t)=Cx(t)+Du(t)y(t)=Δi c-qd (t)

[0122] Where x(t), u(t), and y(t) represent the state, input, and output variables of the system, respectively. The transfer function between the input and output variables can be represented by a 2×2 impedance matrix in the s-domain:

[0123]

[0124] Where Δv qd =[Δv q Δv d ] T ,Δi c-qd =[Δi c-q Δi c-d ] T .

[0125] S2. For AC grid systems fed by multiple converters, such as Figure 3 The micro-source converter connected to the common coupling point is represented by a Norton equivalent circuit, which is represented by i n =[i n1 i n2 …i nn ] Tand its corresponding converter equivalent impedance Z vsc (s) in parallel.

[0126] If other external components are connected to the common coupling point, such as series resistance and inductance or parallel capacitance, it can be expressed as

[0127]

[0128] By applying the node voltage method, the admittance Y of each converter is vsc (s) = Z vsc (s) -1 and other external components are added to the node admittance matrix of the system. The current flowing through the common coupling point is expressed as i = [i 1 i 2 …i n ] T The voltage at the common coupling point is expressed as v = [v 1 v 2 …v n ] T The relationship between the voltage and current at the AC grid end (i.e., at the common coupling point) can be expressed as

[0129]

[0130] where Y T (s) and Y S (s) are the node admittance matrix transfer function of the grid-connected system and the impedance of the external components, respectively.

[0131] Substituting the above equation into the small signal model at the common coupling point, we have:

[0132]

[0133] Among them, Z T (s)=Y T (s) -1 is the impedance matrix transfer function, which can be expressed as:

[0134]

[0135] Among them, adj(sI-A) is the adjoint matrix of (sI-A), Z Tb (s) is Z T The adjoint matrix of (s). Z T The poles of (s) are the roots of the denominator D(s) = |sI-A|, that is, the eigenvalues ​​λi of the state space matrix A.

[0136] The voltage and current at the point of common coupling can also be rewritten as:

[0137] v=(I+L(s))-1 Z N (s)i n L(s)=Z N (s)Y S (s)

[0138] Among them, Z N (s)=(Y N (s)) -1 And I is the n-th order identity matrix.

[0139] S3. Using the modal analysis method, the small signal model at the common coupling point can be expressed as:

[0140] v=Y T (jω x )i n Y T (jω x )=LΛ Y T

[0141] Among them, Y T (jω x ) is the frequency ω x The system admittance matrix at v and i n are the node voltage and current injection vectors at the common coupling point; L and T are the left and right eigenvector matrices respectively; Λ Y is a diagonal eigenvalue matrix:

[0142]

[0143] Need to explain Y is the impedance matrix transfer function Z T (jω x ), that is:

[0144] Z T (jω x )=(Y T (jω x )) -1 =LΛ Z T

[0145] Λ Z =[λ z1 λ z2 ... zn ]I

[0146] where Λ Z The diagonal term of is called the modal impedance λ zi When the modal impedance reaches a maximum value within a certain range, it is called a critical mode. The resonant mode can be determined from the modal impedance |λ of the frequency domain curve. zi |The peak value of the amplitude is identified.T The poles and modal impedance Λ Z The poles of (s) are the same,

[0147]

[0148] Λ Zb (s) = TZ Tb (s)L=[λ zb1 λ zb2 … λ zbn ]I

[0149] S4. The stability of the grid-connected system can be expressed by the diagonal matrix Λ Z To evaluate, by transforming each modal impedance λ zi Analyzed independently as a SISO system applying the overall impedance stability criterion, these modal impedances can be expressed as:

[0150]

[0151] Among them, p 0 =σ 0 ±jω 0 is λ zi A pair of complex conjugate poles of corresponds to a certain system oscillation mode and the eigenvalue λ of the state space matrix A 0 Matching, G(jω x ) is the polynomial expression λ representing the remaining terms zi .

[0152] It can be seen that in the weakly damped oscillation mode (i.e. |σ 0 |<<|ω 0 |) the modal impedance will be at the oscillation frequency (i.e. ω x ≈ω 0 ) reaches its peak value. At this time, G(jω x )≈G(jω 0 )=G r +jG x , where G r and G x is dependent on ω 0 Therefore, the modal impedance λ zi It can be further expressed as:

[0153]

[0154] in,

[0155] Resonance occurs at λ zi，x The zero-crossing frequency of zi，x (ω x )=0

[0156]

[0157] Among them, the feasible solution corresponds to the positive zero-crossing frequency value with the largest amplitude.

[0158] In the case of a weakly damped oscillation mode, this means that ω x With the oscillation mode ω 0 The frequency of is approximately matched, that is, ω x ≈ω 0 Therefore, in ω x Place zi The real part of can be approximated as:

[0159]

[0160] Among them, k x is λ z0x In ω x ≈ω 0 The slope at

[0161]

[0162] Therefore, by extending the modal analysis method to the overall impedance stability criterion and applying it to each modal impedance λ zi The stability criterion of multi-converter feeding into AC grid is: In the weakly damped oscillation mode, the modal impedance λ zi Real part λ z0x In ω x ≈ω 0 The slope k x is greater than 0 and the modal impedance λ zi The imaginary part λ zi，r Less than 0.

[0163] This article uses the case of two converters connected to the AC distribution network, such as Figure 4 As shown in Figure 1, the equivalent power grid is connected to node 1, and the two converters are connected to nodes 2 and 3 respectively. The network passive components are divided into Y N and external components, which may be connected to the Y S The resonant interaction of the system in the circuit leads to instability (i.e., no open-loop RHP poles). The parameters selected in this case are shown in the following table.

[0164] Table 1 Case grid-connected power generation system parameters

[0165]

[0166] The impedance matrix of external components can be expressed as:

[0167]

[0168] The admittance matrix of the micro-source converter and the power grid can be expressed as:

[0169]

[0170] Among them, Y tl1 , Y tl2 , Y cc1 , Y cc2 , Y vsc1 , Y vsc2 and Y g are 2×2 matrices. The input and output small disturbance variables of the system are Δi n =[Δi ng-q Δi ng-d 0 2×1 0 2×1 ] T and Δv=[Δv tmv-q Δv tmv-d Δv tl1-q Δv tl1-d Δv tl2-q Δv tl2-d ].

[0171] exist Figure 5 In , the stability is evaluated using s-domain and frequency-domain stability criteria. By evaluating the system impedance matrix ZT(s), it can be found that Figure 6 Note that f 0 =1192Hz(ieω 0 =7488=2πf 0 ) is a pair of complex conjugate poles in the RHP. These poles are related to Z T The eigenvalues ​​of the state space representation match. This instability can be seen in Figure 7 This is further confirmed in the paper where L n3 The Nyquist curve surrounds the point (-1, j0) in a clockwise direction. Other Nyquist curves (such as λn6) do not surround (-1, j0).

[0172] The stability evaluation using the PMD stability criterion is as follows Figure 8 The modal impedance amplitude curve λ in the frequency domain z5 There is a peak at 1192Hz, and its actual part is negative, which confirms that Z T instability.

[0173] The present invention also provides a multi-converter grid-connected frequency domain stability analysis system based on a system admittance matrix dynamic model, comprising:

[0174] Control device: used to establish a small signal model according to the main circuit structure and control strategy of the single inverter grid-connected system;

[0175] Equivalent device: used to perform the equivalent of the AC power grid fed by multiple converters according to the small signal model, and obtain the node admittance matrix transfer function Y of the grid-connected system using the node voltage method T (s) and the system equivalent impedance Y outside the parallel converter N (s);

[0176] Analysis device: used to use the modal analysis method to find the diagonal eigenvalue matrix of the equivalent node admittance matrix of the grid-connected system, and calculate the corresponding modal impedance λ through the diagonal eigenvalue matrix zi ;;

[0177] Determination device: used to determine the slope k of the imaginary part of the corresponding modal impedance in the underdamped oscillation mode x >0 and the real part value is less than 0 under the premise of the stability of the grid-connected system.

[0178] The analysis device controls the L-type three-phase grid-connected inverter containing parasitic resistance in the dq coordinate system, wherein the synchronous reference system phase-locked loop obtains the grid voltage phase θ required for Park coordinate transformation. PLL , the cascade control of the power outer loop and the current inner loop ensures the active and reactive power of the grid, and the small signal model at the common coupling point used for stability research is:

[0179] u(t)=Δv qd (t)

[0180] y(t)=Cx(t)+Du(t)y(t)=Δi c-qd (t)

[0181] Where x(t), u(t) and y(t) represent the state, input and output variables of the system respectively; A is the system matrix, which represents the connection between the internal states of the system; B is the input matrix, which represents the effect of the input variables on the state variables; C is the output matrix; D is the direct transfer matrix; Δv qd Indicates the dq axis small disturbance of the grid-connected point voltage; Δi c-qd The dq-axis small disturbance quantity representing the converter output current further transforms the small signal model to:

[0182]

[0183] Where Δv qd =[Δv q Δv d ] T ,Δi c-qd =[Δi c-q Δi c-d ] T , Z vsc-qq(s) represents the response of the q-axis current when a voltage is applied to the q-axis, Z vsc-qd (s) represents the response of the q-axis current when a voltage is applied to the d-axis, Z vsc-dq (s) represents the response of the d-axis current when the voltage is applied on the q-axis, Z vsc-dd (s) represents the response of the d-axis current when a voltage is applied on the d-axis.

[0184] For an AC power grid system fed by multiple converters, the equivalent device represents multiple converters connected to a common coupling point by a Norton equivalent circuit, wherein the Norton equivalent circuit is composed of an equivalent current source i n =[i n1 i n2 …i nn ] T and its corresponding converter equivalent impedance Z vsc (s) parallel connection;

[0185] If other external components are connected to the common coupling point, such as series resistive inductive components or parallel capacitive components, their impedance model can be expressed as:

[0186]

[0187] Among them, R and L represent the equivalent inductance and resistance of the series-connected resistive and inductive components, and C represents the capacitance of the parallel-connected capacitive component.

[0188] By applying the node voltage method, the admittance Y of each converter is vsc (s) = Z vsc (s) -1 and other external components are added to the node admittance matrix of the system, and the current on the n buses flowing through the common coupling point is expressed as i = [i 1 i 2 … i n ] T The voltage at the common coupling point is expressed as v = [v 1 v 2 … v n ] T The output current of n external components on each bus is represented by i n =[i n1 i n2 … i nn ] T Then the relationship between the voltage and current at the AC grid end, i.e., the common coupling point, is expressed as:

[0189]

[0190] where Y T (s) and Y S(s) are the node admittance matrix transfer function of the grid-connected system and the impedance of the external components;

[0191] Substituting the above equation into the small signal model at the common coupling point, we have:

[0192]

[0193] Among them, A is the system matrix, B is the input matrix, C is the output matrix, D is the direct transfer matrix, I is the identity matrix, and Z T (s)=Y T (s) -1 is the impedance matrix transfer function, expressed as:

[0194]

[0195] Among them, adj(sI-A) is the adjoint matrix of (sI-A), Z Tb (s) is Z T The adjoint matrix of (s), Z T The poles of (s) are the roots of the denominator D(s) = |sI-A|, i.e., the eigenvalues ​​λi of the state space matrix A;

[0196] The voltage and current at the common coupling point can also be rewritten as a unit negative feedback structure:

[0197] v=(I+L(s)) -1 Z N (s)i n L(s)=Z N (s)Y S (s)

[0198] Among them, Z N (s)=(Y N (s)) -1 And I is the n-th order identity matrix, and L(s) represents the open-loop transfer function.

[0199] The analysis device uses the modal analysis method to express the small signal model at the common coupling point as:

[0200] v=Y T (jω x )i n Y T (jω x )=LΛ Y T

[0201] Among them, Y T (jω x ) is the frequency ω x The system admittance matrix at v and i nare the node voltage and current injection vectors at the common coupling point; L and T are the left and right eigenvector matrices, respectively; Λ Y is a diagonal eigenvalue matrix:

[0202]

[0203] The Λ Y is the impedance matrix transfer function Z T (jω x ), that is:

[0204] Z T (jω x )=(Y T (jω x )) -1 =LΛ Z T

[0205] Λ Z =[λ z1 λ z2 …λ zn ]I

[0206] where Λ Z The diagonal term of is denoted as modal impedance λ zi , when the modal impedance reaches a maximum value within a certain range, it is called a critical mode. The resonant mode is determined by the modal impedance |λ of the frequency domain curve. zi |Amplitude peak to identify, Z T The poles and modal impedance Λ Z The poles of (s) are the same, that is,

[0207]

[0208] Λ Zb (s) = TZ Tb (s)L=[λ zb1 λ zb2 …λ zbn ]I.

[0209] The determination device transforms the diagonal matrix Λ Z The corresponding modal impedance λ zi It is expressed as:

[0210]

[0211] Among them, p 0 =σ 0 ±jω 0 is λ zi A pair of complex conjugate poles of corresponds to a certain system oscillation mode and the eigenvalue λ of the state space matrix A 0Matching, G(jω x ) is a polynomial expression representing the remaining terms,

[0212] When |σ 0 |<<|ω 0 |, the modal impedance will be at ω x ≈ω 0 At this point, G(jω x )≈G(jω 0 )=G r +jG x , where G r and G x is dependent on ω 0 is a constant complex number, so the modal impedance λ zi Further expressed as:

[0213]

[0214] in,

[0215] When resonance occurs, λ zi，x The zero-crossing frequency is:

[0216]

[0217] In the case of a weakly damped oscillation mode, ω x With the oscillation mode ω 0 The frequency of is approximately matched, that is, ω x ≈ω 0 , therefore, in ω x Place zi The real part of is approximately:

[0218]

[0219] Among them, k x is λ z0x In ω x ≈ω 0 The slope at

[0220]

[0221] In the weakly damped oscillation mode, when the modal impedance λ zi Real part λ z0x In ω x ≈ω 0 The slope k x When is greater than 0 and the imaginary part λzi,r of the modal impedance λzi is less than 0, the system is determined to be stable.

[0222] The present invention also relates to an electronic device, comprising one or more processors for storing one or more programs. When the one or more programs are executed by the one or more processors, the one or more processors execute the aforementioned multi-converter grid-connected frequency domain stability analysis method based on the system admittance matrix dynamic model.

[0223] The present invention also relates to a storage medium, in which a computer program is stored, wherein the computer program is configured to execute the aforementioned multi-converter grid-connected frequency domain stability analysis method based on the system admittance matrix dynamic model when running. Although the present invention has been described above with a preferred embodiment, it is not intended to limit the present invention. A person with ordinary knowledge in the technical field to which the present invention belongs can make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be based on that defined in the claims.

Claims

1. A frequency domain stability analysis method for multi-converter grid-connected power systems based on a system admittance matrix dynamic model, characterized in that: The steps include: According to the main circuit structure and control strategy of the single inverter grid-connected system, a small signal model is established; According to the small signal model, the AC power grid fed by multiple converters is equivalent, and the node admittance matrix transfer function Y of the grid-connected system is obtained by using the node voltage method. T (s) and the system equivalent impedance Y outside the parallel converter N (s); Using the modal analysis method, the diagonal eigenvalue matrix of the equivalent node admittance matrix of the grid-connected system is obtained, and the corresponding modal impedance λ is calculated through the diagonal eigenvalue matrix zi ; Determine the slope k of the imaginary part of the corresponding modal impedance in the underdamped oscillation mode x >0 and the real part value is less than 0 under the premise of the stability of the grid-connected system.

2. The method for analyzing the frequency domain stability of multi-converter grid-connected power supply based on the system admittance matrix dynamic model according to claim 1 is characterized in that: The established small signal model is a small signal model in the dq axis coordinate system based on the main circuit structure and control strategy of the single inverter grid-connected system. The small signal model at the common coupling point used for stability research is: u(t)=Δv qd (t) y(t)=Cx(t)+Du(t)y(t)=Δi c-qd (t) Where x(t), u(t) and y(t) represent the state, input and output variables of the system respectively; A is the system matrix, which represents the connection between the internal states of the system; B is the input matrix, which represents the effect of the input variables on the state variables; C is the output matrix; D is the direct transfer matrix; Δv qd Indicates the dq axis small disturbance of the grid-connected point voltage; Δi c-qd The dq-axis small disturbance quantity representing the converter output current further transforms the small signal model to: Where Δv qd =[Δv q Δv d ] T ,Δi c-qd =[Δi c-q Δi c-d ] T , Z vsc-qq (s) represents the response of the q-axis current when a voltage is applied to the q-axis, Z vsc-qd (s) represents the response of the q-axis current when a voltage is applied to the d-axis, Z vsc-dq (s) represents the response of the d-axis current when the voltage is applied on the q-axis, Z vsc-dd (s) represents the response of the d-axis current when a voltage is applied on the d-axis.

3. The method for analyzing the frequency domain stability of multi-converter grid-connected power supply based on the system admittance matrix dynamic model according to claim 2 is characterized in that: For an AC grid system fed by multiple converters, multiple converters connected to a common coupling point are represented by a Norton equivalent circuit, which consists of an equivalent current source i n =[i n1 i n2 …i nn ] T and its corresponding converter equivalent impedance Z vsc (s) parallel connection; If other external components are connected to the common coupling point, such as series resistive inductive components or parallel capacitive components, their impedance model can be expressed as: Among them, R and L represent the equivalent inductance and resistance of the series-connected resistive and inductive components, and C represents the capacitance of the parallel-connected capacitive component. By applying the node voltage method, the admittance Y of each converter is vsc (s) = Z vsc (s) -1 and other external components are added to the node admittance matrix of the system, and the current on the n buses flowing through the common coupling point is expressed as i = [i1 i2…i n ] T The voltage at the common coupling point is expressed as v = [v1 v2…v n ] T The output current of n external components on each bus is represented by i n =[i n1 i n2 …i nn ] T Then the relationship between the voltage and current at the AC grid end, i.e., the common coupling point, is expressed as: where Y T (s) and Y S (s) are the node admittance matrix transfer function of the grid-connected system and the impedance of the external components; Substituting the above equation into the small signal model at the common coupling point, we have: Among them, A is the system matrix, B is the input matrix, C is the output matrix, D is the direct transfer matrix, I is the identity matrix, and Z T (s)=Y T (s) -1 is the impedance matrix transfer function, expressed as: Among them, adj(sI-A) is the adjoint matrix of (sI-A), Z Tb (s) is Z T The adjoint matrix of (s), Z T The poles of (s) are the roots of the denominator D(s) = |sI-A|, i.e., the eigenvalues ​​λi of the state space matrix A; The voltage and current at the common coupling point can also be rewritten as a unit negative feedback structure: v=(I+L(s)) -1 Z N (s)i n L(s)=Z N (s)Y S (s) Among them, Z N (s)=(Y N (s)) -1 And I is the n-th order identity matrix, and L(s) represents the open-loop transfer function.

4. The method for analyzing the frequency domain stability of multi-converter grid-connected power supply based on the system admittance matrix dynamic model according to claim 2 is characterized in that: Using the modal analysis method, the small signal model at the common coupling point is expressed as: v=Y T (jω x )i n Y T (jω x )=LΛ Y T Among them, Y T (jω x ) is the frequency ω x The system admittance matrix at v and i n are the node voltage and current injection vectors at the common coupling point; L and T are the left and right eigenvector matrices, respectively; Λ Y is a diagonal eigenvalue matrix: The Λ Y is the impedance matrix transfer function Z T (jω x ), that is: Z T (jω x )=(Y T (jω x )) -1 =LΛ Z T where Λ Z The diagonal term of is denoted as modal impedance λ zi , when the modal impedance reaches a maximum value within a certain range, it is called a critical mode. The resonant mode is determined by the modal impedance |λ of the frequency domain curve. zi |The peak value of the amplitude is identified, Z T The poles and modal impedance Λ Z The poles of (s) are the same, that is, L Zb (s)=TZ Tb (s)L=[λ zb1 l zb2 …l zbn ]I.

5. The method for analyzing the frequency domain stability of multi-converter grid-connected power supply based on the system admittance matrix dynamic model according to claim 4 is characterized in that: Diagonal matrix Λ Z The corresponding modal impedance λ zi It is expressed as: Among them, p0=σ0±jω0 is λ zi A pair of complex conjugate poles of the system corresponds to a certain system oscillation mode and matches the eigenvalue λ0 of the state space matrix A. x ) is a polynomial expression representing the remaining terms. When |σ0|<<|ω0|, the modal impedance will be at ω x ≈ω0 reaches its peak value, at this time, G(jω x )≈G(jω0)=G r +jG x , where G r and G x is a constant complex number that depends on ω0, so the modal impedance λ zi Further expressed as: in, When resonance occurs, λ zi，x The zero-crossing frequency is: In the case of a weakly damped oscillation mode, ω x Approximately matches the frequency of the oscillation mode ω0, that is, ω x ≈ω0, so at ω x Place zi The real part of is approximately: Among them, k x is λ z0x In ω x ≈ω0, that is In the weakly damped oscillation mode, when the modal impedance λ zi Real part λ z0x In ω x The slope k at ≈ω0 x is greater than 0 and the modal impedance λ zi The imaginary part λ zi，r When it is less than 0, the system is considered stable.

6. A multi-converter grid-connected frequency domain stability analysis system based on a system admittance matrix dynamic model, characterized in that: include: Control device: used to establish a small signal model according to the main circuit structure and control strategy of the single inverter grid-connected system; Equivalent device: used to perform the equivalent of the AC power grid fed by multiple converters according to the small signal model, and obtain the node admittance matrix transfer function Y of the grid-connected system using the node voltage method T (s) and the system equivalent impedance Y outside the parallel converter N (s); Analysis device: used to use the modal analysis method to find the diagonal eigenvalue matrix of the equivalent node admittance matrix of the grid-connected system, and calculate the corresponding modal impedance λ through the diagonal eigenvalue matrix zi ;; Determination device: used to determine the slope k of the imaginary part of the corresponding modal impedance in the underdamped oscillation mode x >0 and the real part value is less than 0 under the premise of the stability of the grid-connected system.

7. The multi-converter grid-connected frequency domain stability analysis system based on the system admittance matrix dynamic model according to claim 6 is characterized by: The analysis device controls the L-type three-phase grid-connected inverter containing parasitic resistance in the dq coordinate system, wherein the synchronous reference system phase-locked loop obtains the grid voltage phase θ required for Park coordinate transformation. PLL , the cascade control of the power outer loop and the current inner loop ensures the active and reactive power of the grid, and the small signal model at the common coupling point used for stability research is: u(t)=Δv qd (t) y(t)=Cx(t)+Du(t)y(t)=Δi c-qd (t) Where x(t), u(t) and y(t) represent the state, input and output variables of the system respectively; A is the system matrix, which represents the connection between the internal states of the system; B is the input matrix, which represents the effect of the input variables on the state variables; C is the output matrix; D is the direct transfer matrix; Δv qd Indicates the dq axis small disturbance of the grid-connected point voltage; Δi c-qd The dq-axis small disturbance quantity representing the converter output current further transforms the small signal model to: Where Δv qd =[Δv q Δv d ] T ,Δi c-qd =[Δi c-q Δi c-d ] T , Z vsc-qq (s) represents the response of the q-axis current when a voltage is applied to the q-axis, Z vsc-qd (s) represents the response of the q-axis current when a voltage is applied to the d-axis, Z vsc-dq (s) represents the response of the d-axis current when the voltage is applied on the q-axis, Z vsc-dd (s) represents the response of the d-axis current when a voltage is applied on the d-axis.

8. The multi-converter grid-connected frequency domain stability analysis system based on the system admittance matrix dynamic model according to claim 6 is characterized by: For an AC power grid system fed by multiple converters, the equivalent device represents multiple converters connected to a common coupling point by a Norton equivalent circuit, wherein the Norton equivalent circuit is composed of an equivalent current source i n =[i n1 i n2 …i nn ] T and its corresponding converter equivalent impedance Z vsc (s) parallel connection; If other external components are connected to the common coupling point, such as series resistive inductive components or parallel capacitive components, their impedance model can be expressed as: Among them, R and L represent the equivalent inductance and resistance of the series-connected resistive and inductive components, and C represents the capacitance of the parallel-connected capacitive component. By applying the node voltage method, the admittance Y of each converter is vsc (s) = Z vsc (s) -1 and other external components are added to the node admittance matrix of the system, and the current on the n buses flowing through the common coupling point is expressed as i = [i1 i2 … i n ] T The voltage at the common coupling point is expressed as v = [v1 v2 … v n ] T The output current of n external components on each bus is represented by i n =[i n1 i n2 … i nn ] T Then the relationship between the voltage and current at the AC grid end, i.e., the common coupling point, is expressed as: where Y T (s) and Y S (s) are the node admittance matrix transfer function of the grid-connected system and the impedance of the external components; Substituting the above equation into the small signal model at the common coupling point, we have: Among them, A is the system matrix, B is the input matrix, C is the output matrix, D is the direct transfer matrix, I is the identity matrix, and Z T (s)=Y T (s) -1 is the impedance matrix transfer function, expressed as: Among them, adj(sI-A) is the adjoint matrix of (sI-A), Z Tb (s) is Z T The adjoint matrix of (s), Z T The poles of (s) are the roots of the denominator D(s) = |sI-A|, i.e., the eigenvalues ​​λi of the state space matrix A; The voltage and current at the common coupling point can also be rewritten as a unit negative feedback structure: v=(I+L(s)) -1 Z N (s)i n L(s)=Z N (s)Y S (s) Among them, Z N (s)=(Y N (s)) -1 And I is the n-th order identity matrix, and L(s) represents the open-loop transfer function.

9. The multi-converter grid-connected frequency domain stability analysis system based on system admittance matrix dynamic model according to claim 6, characterized in that: The analysis device uses the modal analysis method to express the small signal model at the common coupling point as: v=Y T (jω x )i n Y T (jω x )=LΛ Y T Among them, Y T (jω x ) is the frequency ω x The system admittance matrix at v and i n are the node voltage and current injection vectors at the common coupling point; L and T are the left and right eigenvector matrices, respectively; Λ Y is a diagonal eigenvalue matrix: The Λ Y is the impedance matrix transfer function Z T (jω x ), that is: Z T (jω x )=(Y T (jω x )) -1 =LΛ Z T where Λ Z The diagonal term of is denoted as modal impedance λ zi , when the modal impedance reaches a maximum value within a certain range, it is called a critical mode. The resonant mode is determined by the modal impedance |λ of the frequency domain curve. zi |The peak value of the amplitude is identified, Z T The poles and modal impedance Λ Z The poles of (s) are the same, that is, L Zb (s)=TZ Tb (s)L=[λ zb1 l zb2 … l zbn ]I.

10. The multi-converter grid-connected frequency domain stability analysis system based on the system admittance matrix dynamic model according to claim 6, characterized in that: The determination device transforms the diagonal matrix Λ Z The corresponding modal impedance λ zi It is expressed as: Among them, p0=σ0±jω0 is λ zi A pair of complex conjugate poles of the system corresponds to a certain system oscillation mode and matches the eigenvalue λ0 of the state space matrix A. x ) is a polynomial expression representing the remaining terms, When |σ0|<<|ω0|, the modal impedance will be at ω x ≈ω0 reaches its peak value, at this time, G(jω x )≈G(jω0)=G r +jG x , where G r and G x is a constant complex number that depends on ω0, so the modal impedance λ zi Further expressed as: in, When resonance occurs, λ zi，x The zero-crossing frequency is: In the case of a weakly damped oscillation mode, ω x Approximately matches the frequency of the oscillation mode ω0, that is, ω x ≈ω0, so at ω x Place zi The real part of is approximately: Among them, k x is λ z0x In ω x ≈ω0, that is In the weakly damped oscillation mode, when the modal impedance λ zi Real part λ z0x In ω x The slope k at ≈ω0 x is greater than 0 and the modal impedance λ zi The imaginary part λ zi，r When it is less than 0, the system is considered stable.

11. An electronic device, characterized in that: It includes one or more processors for storing one or more programs. When the one or more programs are executed by the one or more processors, the one or more processors execute the multi-converter grid-connected frequency domain stability analysis method based on the system admittance matrix dynamic model as described in any one of claims 1 to 5.

12. A storage medium storing a computer program, wherein: in, The computer program is configured to execute the frequency domain stability analysis method for multi-converter grid-connected system based on a system admittance matrix dynamic model as described in any one of claims 1 to 5 when running.

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