A small signal stability analysis method for heterogeneous inverters connected to the power grid

Abstract

The present invention discloses a small signal stability analysis method for heterogeneous inverters connected to a power grid, and relates to the technical field of stability analysis. The method includes constructing a complex vector impedance model of each component in a power system; wherein the components include a grid-following inverter, a grid-building inverter, and passive components; according to the complex vector impedance model of each component and the connection relationship between each node, a complex vector admittance matrix of the power system is established; based on the complex vector admittance matrix, the oscillation mode and characteristic roots of the power system are obtained; if all characteristic roots are located on the left side of the complex plane, the power system is determined to be stable, otherwise the power system is determined to be unstable. The method of establishing a complex vector admittance matrix can reduce the tediousness of subsequent data processing; in addition, the process of establishing a complex vector admittance matrix is ​​simple and clear, which helps to improve the efficiency of stability analysis.

Description

Technical Field

[0001] The present invention relates to the technical field of stability analysis, and in particular to a small signal stability analysis method for heterogeneous inverters connected to a power grid. Background Art

[0002] In the past decade, new energy sources such as wind and solar energy have been connected to the power grid in large quantities through power electronic inverters, and the new energy has become a key technical feature of the new generation of power systems. New energy sources have significant intermittency, volatility and uncertainty, requiring the power system to be able to flexibly adjust both at the power generation and power consumption ends to adapt to the new needs of power balance. At present, the power electronic inverters commonly used in engineering adopt a grid-following control strategy, which controls the active power and reactive power injected into the power grid through vector current. The normal operation of this control method depends on the stable voltage provided by the synchronous generator. However, with the large-scale access of new energy power generation equipment to the power grid through inverters, the proportion of synchronous generators in the power grid has gradually decreased, resulting in a decrease in the overall strength of the power grid, which poses a major challenge to the stable operation of the power system. In order to ensure the stable operation of power systems with a high proportion of new energy penetration, more and more grid-building inverters are connected to the power grid. Unlike grid-following inverters that exhibit current source characteristics, grid-building inverters exhibit voltage source characteristics and can actively support the voltage and frequency of the power grid, becoming a key component in building a new power system dominated by new energy. At present, the new power system shows a mixed state of coexistence of grid-following inverters and grid-building inverters, that is, heterogeneous inverters are connected to the grid.

[0003] When analyzing the stability of power systems, the state space method is often used for small signal modeling. However, the state space model of a large-scale power grid established through small signal modeling has a high order and is difficult to establish, and the matrix is ​​asymmetric, making subsequent data processing more cumbersome. Summary of the invention

[0004] In order to solve the above technical problems existing in the existing problems, the present invention aims to provide a small signal stability analysis method for heterogeneous inverters connected to a power grid.

[0005] Specifically, the technical solution includes the following steps:

[0006] Step S1, constructing a complex vector impedance model of each component in the power system; wherein the components include a grid-following inverter, a grid-building inverter and passive components;

[0007] Step S2, establishing a complex vector admittance matrix of the power system according to the complex vector impedance model of each component and the connection relationship between each node;

[0008] Step S3, calculating the characteristic roots of the power system based on the complex vector admittance matrix, comprising:

[0009] Let the determinant of the complex vector admittance matrix be 0, and the root obtained is the characteristic root of the power system;

[0010] If all characteristic roots are located on the left side of the complex plane, the power system is determined to be stable; if there are characteristic roots on the right side of the complex plane, the power system is determined to be unstable.

[0011] It can be seen that the technical solution provided by the present invention can establish a complex vector admittance matrix with lower order and symmetry, which can reduce the complexity of subsequent data processing; in addition, the process of establishing the complex vector admittance matrix is ​​simple and clear, which helps to improve the efficiency of stability analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 Schematic diagram of a grid-connected inverter system in one embodiment of the present invention.

[0013] Figure 2 The figure is a schematic diagram of the active outer ring structure of a grid-type inverter in one embodiment of the present invention.

[0014] Figure 3 The figure is a schematic diagram of the reactive outer loop structure of a grid-type inverter in one embodiment of the present invention.

[0015] Figure 4 Schematic diagram of the voltage-current dual closed-loop structure of a grid-type inverter in one embodiment of the present invention.

[0016] Figure 5 Schematic diagram of a grid-connected inverter system according to an embodiment of the present invention.

[0017] Figure 6 Schematic diagram of the structure of a grid-following inverter phase-locked loop in one embodiment of the present invention.

[0018] Figure 7 Schematic diagram of a grid-type current loop structure in one embodiment of the present invention.

[0019] Figure 8 Schematic diagram of a three-machine four-node system formed after heterogeneous inverters are connected to the power grid.

[0020] Fig. 9 This is a schematic diagram of the voltage waveform at the grid connection point after the grid-following inverter is connected to the power system.

[0021] Fig.10 Schematic diagram of the voltage waveform at the grid connection point after the grid-connected inverter is connected to the power system.

[0022] Fig.11 Schematic diagram of the key characteristic root loci of the system's complex vector admittance matrix after changing the control parameters of the active outer loop of the grid-connected inverter.

[0023] Fig.12Schematic diagram of the waveform of the system active power after changing the control parameters of the active outer loop of the grid-connected inverter. DETAILED DESCRIPTION

[0024] Hereinafter, the technical solution provided by the present invention will be further elaborated in combination with embodiments and drawings.

[0025] Embodiment 1:

[0026] This embodiment provides a small signal stability analysis method for a new energy heterogeneous inverter connected to a power grid based on a complex vector admittance matrix, the method comprising the following steps:

[0027] Step S1, performing complex vector impedance modeling on all components in the power system, including grid-following inverters, grid-forming inverters, and passive components;

[0028] Step S2, combining the complex vector impedance models of each component established in step S1, and establishing a complex vector admittance matrix of the entire system according to the connection relationship between nodes;

[0029] Step S3, combining the complex vector admittance matrix of the system obtained in step S2, obtaining the oscillation mode and characteristic roots of the system, and obtaining the key characteristic roots thereof by comparing the damping ratio;

[0030] Step S4, combining the key characteristic roots obtained in step S3, by changing the inverter control parameters in the system, observing the running trajectory of the key characteristic roots when the control parameters are changed, and comparing with the system time domain model output obtained by simulation to verify the accuracy of the established model;

[0031] Step S5: Combined with the key characteristic root loci obtained in step S4, a stability analysis is performed on the system, and the influence of the change of the control parameters on the stability of the system is determined by observing the characteristic root loci of the key characteristic roots.

[0032] 1. If Figure 1 As shown, the impedance model of the grid-connected inverter system is constructed according to the grid-connected inverter system.

[0033] Among them, PWM is Pulse Width Modulation, pulse width modulation; v oabc1 is the grid-connected point voltage of the grid-connected inverter, i oabc1 is the grid-connected point current of the grid-connected inverter, i Labc1 is the inductor current of the grid-type inverter, v odq1 The grid-connected point voltage of the grid-connected inverter dq Axis component, i odqc1is the grid-connected point current of the grid-connected inverter dq Axis component, v dqref Output of the power ring of the grid-type inverter dq Axis reference voltage, u s is the grid voltage. Figure 2 , Figure 3 As shown in the figure, the power outer loop of the grid-connected inverter is modeled with small signals, and the mathematical model of the droop control link is obtained as follows:

[0034] ;

[0035] In the formula, is the angular frequency of the active frequency control output, is the rated angular frequency of the power grid, k psc is the active power droop control coefficient, k qsc is the reactive power droop control coefficient, U is the voltage reference value of reactive voltage control output, U ref is the rated voltage of the grid, P ref is the active reference power, Q ref is the reactive reference power, P o To calculate the actual output power after the output active power passes through the low-pass filter, Q o To calculate the actual output power after the output reactive power passes through the low-pass filter.

[0036] Two-phase rotation dq In the coordinate system, the expressions of active power and reactive power output by the inverter after passing through the low-pass filter are as follows:

[0037] ;

[0038] In the formula, G LPF represents the low-pass filter transfer function, v od1 The grid-connected point voltage of the grid-connected inverter d Axis component, v oq1 The grid-connected point voltage of the grid-connected inverter q Axis component, i od1 is the grid-connected point current of the grid-connected inverter d Axis component, i oq1is the grid-connected point current of the grid-connected inverter q Axis component. The small signal model of the power outer loop is obtained:

[0039] ;

[0040] In the formula, s is a Lagrangian operator with ( s ) is s variables in the domain; For small signal input s The angular frequency of the active frequency control output in the domain, Δ v ref ( s ) is a small signal input s The reference value of the grid-connected point voltage of the grid-connected inverter in the domain, Δ i od1 ( s ) is a small signal input s Current at the grid-connected point of grid-connected inverter in the domain d Axis component, Δ i oq1 ( s ) is a small signal input s Current at the grid-connected point of grid-connected inverter in the domain q Axis component, Δ v od1 ( s ) is a small signal input s The voltage of grid-connected inverter in the domain d Axis component, Δ v oq1 ( s ) is a small signal input s The voltage of grid-connected inverter in the domain q Axis component.

[0041] like Figure 4 As shown, the voltage and current double closed loop of the grid-type inverter is modeled with small signals. The voltage outer loop is linearized with small signals and written in matrix form, and the expression of the reference current small signal model output by the voltage outer loop is as follows:

[0042] ;

[0043] In the formula, i dref1 The reference current of the voltage outer loop output of the grid inverter d Axis component, i qref1 The reference current of the voltage outer loop output of the grid inverter q Axis component, v odref1The reference voltage of the grid inverter d Axis component, v oqref1 The reference voltage of the grid inverter q Axis component, v od1 The grid-connected point voltage of the grid-connected inverter d Axis component, v oq1 The grid-connected point voltage of the grid-connected inverter q Axis component, C f1 is the capacitance to ground, K pv_m , K iv_m It is the voltage outer loop control parameter of the grid-type inverter.

[0044] Figure 4 In the equation, PI is the controller parameter in the voltage and current double closed-loop control. v dref Output of the power ring of the grid-type inverter d Axis reference voltage, v qref Output of the power ring of the grid-type inverter q Axis reference voltage.

[0045] The small signal linearization of the current inner loop is performed and written in matrix form, and the duty cycle small signal model of the current inner loop output is obtained as follows:

[0046] ;

[0047] In the formula, d d is the output duty cycle of the inner loop current of the grid-type inverter d Axis component, d q is the output duty cycle of the inner loop current of the grid-type inverter q Axis component, i Ld1 is the inductor current of the grid-type inverter d Axis component, i Lq1 is the inductor current of the grid-connected inverter q Axis component, L f1 is the filter inductor, K pi_m , K ii_m It is the current inner loop control parameter of the grid-type inverter.

[0048] The small signal model of the main circuit link is obtained by linearizing the small signal of the main circuit link and writing it in matrix form:

[0049] ;

[0050] In the formula, V ind is the output voltage of the grid-connected inverter d Axis component, V inq is the output voltage of the grid-connected inverter q Axis component; i od1 is the grid-connected point current of the grid-connected inverter d Axis component, i oq1 is the grid-connected point current of the grid-connected inverter q Axis component.

[0051] The complete equivalent impedance of the power synchronous control grid inverter is obtained through the relationship between the voltage and current output by the inverter. Z GFM ( s ), the expression is as follows:

[0052] ;

[0053] ;

[0054] In the formula, and for dq The voltage and current of the grid-type inverter in the coordinate system, Z GFM ( s ) is the complete equivalent impedance of the grid-connected inverter, Y GFM ( s ) is the complete equivalent admittance of the grid-connected inverter.

[0055] Further, we get a grid-connected inverter dq The small signal input-output relationship in the coordinate system is as follows:

[0056] ;

[0057] In the formula, Y dd1 ( s )、 Y dq1 ( s )、 Y qd1 ( s )and Yqq1 ( s ) are the four elements in the admittance matrix of the grid-type inverter.

[0058] Convert the complex vector impedance model of the grid-connected inverter to αβ coordinate system, and obtain the grid-type inverter αβ Coordinate system small signal input and output relationship:

[0059] ;

[0060] ;

[0061] In the formula, for αβ The output current of the grid-type inverter under the small signal input in the coordinate system, for αβ The output current of the grid inverter after frequency coupling under small signal input in the coordinate system, Y Mc,αβ ( s )for αβ The complex vector impedance model of the grid-type inverter is constructed in the coordinate system. for αβ The output voltage of the grid-type inverter under small signal input in the coordinate system, for αβ The output conjugate voltage of the grid inverter after frequency coupling under small signal input in the coordinate system, T αβ-dq,vec for αβ Coordinate system and dq The transformation matrix between coordinate systems in the form of complex vectors, Y Mc,dq ( s - jω 0 )for αβ Complex vector impedance model of frequency-coupled grid-type inverter in coordinate system.

[0062] 2. If Figure 5 As shown in the figure, the impedance model of the grid-connected inverter system is constructed according to the grid-connected inverter system. Among them, PLL (Phase-Locked Loop) is a phase-locked loop. C f2 is the capacitance to ground, is the phase angle of the phase-locked loop output, i odq2 The grid-connected current of the grid-following inverter dq Axis component, i dqref2 Grid-following inverter dq Shaft current reference value.

[0063] like Figure 6 As shown, the small signal modeling of the phase-locked loop of the grid-following inverter is carried out, and the small signal model of the phase-locked loop is as follows:

[0064] ;

[0065] ;

[0066] In the formula, is the angular frequency of the grid-type phase-locked loop output, v od2 The grid-connected point voltage of the grid-following inverter d Axis component, v oq2 The grid-connected point voltage of the grid-following inverter q Axis component, K p_pll , K i_pll is the phase-locked loop control parameter. Figure 6 middle, v oabc2 It is the grid connection point voltage of the grid-following inverter.

[0067] like Figure 7 As shown in the figure, the current loop of the grid-following inverter is linearized and written in matrix form, and the small signal model of the current loop is obtained as follows:

[0068] ;

[0069] In the formula, v dref The reference voltage for the inner loop output of the grid-following inverter d Axis component, v qref The reference voltage for the inner loop output of the grid-following inverter q Axis component, i od2 The grid-connected current of the grid-following inverter d Axis component, i oq2 The grid-connected current of the grid-following inverter q Axis component, K pi_L , K ii_L It is the current inner loop control parameter of the grid-following inverter. Figure 7 middle, i dref1 and i dref2 They are the reference voltages of the current inner loop output of the grid-building inverter and the grid-following inverter. d Axis component, vdqref2 Grid-following inverter dq Shaft voltage reference value.

[0070] Through the relationship between the voltage and current output by the inverter, the complete equivalent impedance of the grid-connected inverter is obtained. Z GLF ( s ), the formula is as follows:

[0071] ;

[0072] ;

[0073] In the formula, and for dq The voltage and current of the grid-following inverter in the coordinate system, Z GFL ( s ) is the complete equivalent impedance of the grid-connected inverter, Y GFL ( s ) is the complete equivalent admittance of the grid-type inverter.

[0074] Grid-connected inverter dq The small signal input-output relationship in the coordinate system is as follows:

[0075] ;

[0076] In the formula, Y dd2 ( s )、 Y dq2 ( s )、 Y qd2 ( s )and Y qq2 ( s ) are the four elements in the admittance matrix of the grid-following inverter.

[0077] Since both the grid-connected inverter and the grid-following inverter are grid-connected inverters, the output impedance in different coordinate systems has different forms, so the inverter needs to be converted. αβ In the coordinate system, calculate αβ The complex vector in the coordinate system is given by the following formula:

[0078] ;

[0079] In the formula, X αβ ( s ) represents a complex vector, represents the conjugate of a complex vector. Specifically, X α ( s ) is a complex vector α Axis component, X β ( s ) is a complex vector β Axis component.

[0080] Will s Replace with s - jω 0 , and substitute the above formula into the Laplace transform in the scalar impedance model calculation, the formula is as follows:

[0081] ;

[0082] ;

[0083] In the formula, and After frequency coupling under small signal input dq Coordinate system d Axis components and q Axis component, T αβ-dq,vec for αβ Coordinate system and dq Conversion matrices in the form of complex vectors between coordinate systems; is the initial phase of the inverter.

[0084] In summary, the small signal input-output relationship of the grid-connected inverter in the αβ coordinate system is:

[0085] ;

[0086] ;

[0087] In the formula, for αβ The output current of the grid-connected inverter under small signal input in the coordinate system, for αβ The output current of the grid-connected inverter after frequency coupling under small signal input in the coordinate system, Y c,αβ ( s )for αβ Complex vector impedance model in coordinate system, Y c,αβ ( s ) reveals the mechanism of frequency coupling effect, that is, the frequency is ω 0 After the complex vector input impedance model is constructed, the frequencies of the output complex vectors will be ω and s - j 2 ω 0 ; for αβ The output voltage of the grid-connected inverter under small signal input in the coordinate system, for αβ The output voltage of the grid-connected inverter after frequency coupling under small signal input in the coordinate system; Y c,dq ( s - jω 0 )for αβ Complex vector impedance model of grid-connected inverter with frequency coupling in coordinate system.

[0088] Specifically, for the grid-following inverter: the complex vector impedance model of the grid-following inverter is converted to the αβ coordinate system, and the αβ coordinate system small signal input and output relationship of the grid-building inverter is obtained:

[0089] ;

[0090] ;

[0091] In the formula, for αβ The output current of the grid-type inverter under small signal input in the coordinate system, for αβ The output current of the grid inverter after frequency coupling under the small signal input in the coordinate system, for αβ The complex vector impedance model of the grid-following inverter in the coordinate system, for αβ The output voltage of the grid-type inverter under small signal input in the coordinate system, for αβ The output conjugate voltage of the grid inverter after frequency coupling under the small signal input in the coordinate system is: Y Lc,dq ( s - jω 0 )for αβ Complex vector impedance model of frequency-coupled grid-following inverter in coordinate system.

[0092] 3. Complex vector modeling of passive components.

[0093] The main passive element in the power system can be established as line inductance L , Line resistance R Capacitance to ground CSince the impedance of the resistor is a constant and does not change with frequency, the complex vector admittance model is mainly obtained from the line inductance and the capacitance to ground. The formula is as follows:

[0094] ;

[0095] ;

[0096] In the formula, L g is the line equivalent inductance, C f is the line equivalent capacitance, Y Lg ( s )for αβ The complex vector impedance model of the inductor in the coordinate system, Y cf ( s )for αβ Complex vector impedance model of a capacitor in coordinate system.

[0097] In summary, the complex vector impedance model of passive components can be expressed as:

[0098] ;

[0099] ;

[0100] In the formula, Y LCαβ(m,n) ( s )for αβ Complex vector admittance model of passive components in the coordinate system, Y m,n ( s )for αβ Nodes in the coordinate system m and nodes n The line inductance and capacitance to ground between Y m,n ( s - j 2 ω 0 )for αβ Nodes after frequency coupling in the coordinate system m and nodes n The line inductance and capacitance to ground.

[0101] Fourth, in step S2, the complex vector impedance model of each component established in step S1 is combined to establish a complex vector admittance matrix of the entire system.

[0102] According to the complex vector impedance model of each element established in step S1 and the connection relationship between each node in the power system, a complex vector admittance matrix is ​​constructed.

[0103] It should be noted that there is only one node between any two elements. The input and output ends of the power system are also nodes. There is a node at each end of the transmission line (which has impedance and can be regarded as an impedance element).

[0104] Specifically, the process of constructing the complex vector admittance matrix includes:

[0105] For each node, establish the Kirchhoff equation of the node, use the Kirchhoff equation to represent the connection relationship between nodes, and αβ Substitute the complex vector impedance model of the passive element in the coordinate system, and solve the equation to obtain the mutual admittance between the node and other nodes. Further, calculate the sum of all mutual admittances, add the mutual admittance between the node and the grounding point to the sum, and obtain the self-admittance of the node. Substitute the complex vector impedance model of the passive element into the calculation process of the self-admittance, and you will get the complex vector node voltage equation of all passive element networks in the power system. When a node is connected to a grid-following inverter or a grid-forming inverter (considered as a new connection), the complex vector impedance model of the passive element in the complex vector node voltage equation of the passive element network is replaced with the complex vector impedance model of the grid-following inverter or the grid-forming inverter.

[0106] Based on the above construction steps, l The power system of nodes is constructed at an order of 2 l The complex vector admittance matrix of .

[0107] The complex vector admittance matrix is ​​divided into four parts: upper left, lower left, upper right and lower right. l × l part; the main diagonal elements of the upper left part are the self-admittance of each node, and the non-diagonal elements are the mutual admittance between each node; the main diagonal elements of the lower right part are the self-admittance of each node after frequency coupling, and the non-diagonal elements are the mutual admittance between each node after frequency coupling; the elements of the lower left part and the upper right part are all 0.

[0108] Specifically, with l Node Power System 2 l The order complex vector admittance matrix is ​​shown below:

[0109] ;

[0110] In the formula, Y kk ( s ) is the k The self-admittance of the node, Y kh ( s )and Y hk ( s) is the k Nodes and h The mutual admittance between nodes is Y kk ( s - j 2 ω 0 ) is the k The self-admittance of the nodes after frequency coupling. Among them, k =1,2,..., l , h =1,2,..., l .

[0111] When the inverter is connected to a new node in the power system, the number of system nodes changes, and the system admittance matrix is ​​modified as follows:

[0112] ;

[0113] When the inverter in the system is connected to a new node, the number of nodes in the system increases to l +1, the complex vector admittance matrix of the overall system is changed from the original 2 l The matrix order becomes 2 l +2nd order matrix. Modify the self-admittance and mutual-admittance elements in the matrix in the rows and columns corresponding to the nodes, which is the new admittance matrix after the system is modified. Y l+1,k ( s )( k =1,2,…, l ) are nodes l +1 with the rest l The line admittance between nodes.

[0114] Adding a new node l +1 self-admittance Y l+1,l+1 ( s )for:

[0115] .

[0116] Similarly, when a node in the system is disconnected, the nodes in the system become l -1, the complex vector admittance matrix of the overall system is changed from the original 2 l The matrix order becomes 2 l -2 order matrix. Modify the self-admittance and mutual-admittance elements in the matrix in the rows and columns corresponding to the nodes respectively, which is the modified new admittance matrix of the system. Substitute the data required for system operation into the established admittance matrix and calculate the eigenvalue of the matrix to obtain the small signal stability of the established system.

[0117] In step 3, combined with the system complex vector admittance matrix obtained in step S2, the determinant of the complex vector admittance matrix of the system is r ( s )=0, the root of the equation is the characteristic root of the system. If all the characteristic roots of the system are on the left side of the complex plane, it means that the system is running stably; if there are characteristic roots on the right side of the complex plane, it means that the system is unstable. Select the characteristic root with the smallest damping ratio as the key characteristic root of the system, and observe the running trajectory of the key characteristic root when changing the system parameters (such as voltage and current PI controller parameters, line inductance, capacitance and other component parameters), and analyze the impact of each parameter change on the stability of the system.

[0118] The correctness of the above implementation method is verified through specific experimental cases below. Figure 8 It is a three-machine four-node system formed after heterogeneous inverters are connected to the grid. Among them, GFL is a grid-following inverter, GFM is a grid-building inverter, L fL is the equivalent inductance of the grid-connected inverter, L fM is the equivalent inductance of the grid-type inverter, L 12 , L 13 and L g They are all line inductances. Bus1, Bus2, Bus3 and Bus4 are four bus bars. Fig. 9 This is a schematic diagram of the voltage waveform at the grid connection point after the grid-following inverter is connected to the system. Fig.10 The waveform diagram of the grid-connected point voltage after the grid-connected inverter is connected to the above system. V pcc It can be seen that after the grid-connected inverter is connected to the system, the waveform returns to normal, the system returns to stability, and the system stability is enhanced.

[0119] Taking the grid-connected inverter as an example, Fig.11 The diagram is a schematic diagram of the key characteristic root trajectory of the complex vector admittance matrix of the system after changing the control parameters of the active outer loop of the grid-type inverter. It can be seen that as the control parameters of the active outer loop of the grid-type inverter gradually increase from 0.005 to 0.008, the modal stability of the system weakens, the modal frequency gradually increases, and the dominant characteristic root moves to the right side of the complex plane, at which time the system becomes unstable.

[0120] Fig.12 The waveform diagram of the system active power after changing the control parameters of the active outer loop of the grid-type inverter. It can be seen that as the control parameters of the active outer loop of the grid-type inverter gradually increase, the system becomes unstable and the oscillation becomes more serious, which is consistent with the conclusion of the eigenvalue root locus analysis.

[0121] Based on the above experimental principles, it is easy to deduce that the control parameters of the power system will change at different times, and the corresponding characteristic roots will also change.

[0122] Therefore, the characteristic roots of the power system at different times can be obtained, and each pair of characteristic complex roots in the characteristic roots at each time can be calculated. λ Damping ratio ζ , the formula is as follows:

[0123] ;

[0124] ;

[0125] Among them, each pair of characteristic complex roots λ Corresponding to one oscillation mode, σ is the characteristic complex root λ The real part of represents the decay rate of the corresponding oscillation mode, ω is the characteristic complex root λ The imaginary coefficient of represents the resonant frequency of the corresponding oscillation mode;

[0126] The characteristic root with the smallest damping ratio at each moment is selected as the key characteristic root, and the operation trajectory of the key characteristic root is drawn according to the time series relationship. According to the operation trajectory, the changing state of the power system stability can be observed.

[0127] Therefore, when the complex vector admittance matrix of the system is obtained, when the control parameters of the heterogeneous inverter connected to the power grid system change, the influence of the control parameters on the system stability can be analyzed according to the operating trajectory of the key characteristic roots, which verifies the correctness of the theoretical analysis.

[0128] In summary, the present invention applies the complex vector impedance modeling method to establish the complex vector admittance matrix of the power system. The modeling method is simple and clear, and the obtained complex vector admittance matrix has symmetry, which can reduce the complexity of subsequent data processing and improve the efficiency of stability analysis. When the network structure changes, it is only necessary to modify the self-admittance and mutual admittance between nodes to update the operation model of the power system, which can be generally applied to the small signal stability analysis of the power system and help improve the efficiency of stability analysis. In addition, by observing the operating trajectory formed by the key characteristic roots of the power system at different times, the fluctuation state of the stability of the power system in the corresponding period can be judged, which is intuitive and conducive to improving the efficiency of stability analysis.

Claims

1. A small signal stability analysis method for heterogeneous inverters connected to a power grid, characterized in that: The following steps are involved: Step S1, constructing a complex vector impedance model of each component in the power system; wherein the components include a grid-following inverter, a grid-building inverter and passive components; Step S2, establishing a complex vector admittance matrix of the power system according to the complex vector impedance model of each component and the connection relationship between each node; Step S3, calculating the characteristic roots of the power system based on the complex vector admittance matrix, comprising: Let the determinant of the complex vector admittance matrix be 0, and the root obtained is the characteristic root of the power system; If all characteristic roots are on the left side of the complex plane, the power system is considered stable; if there are characteristic roots on the right side of the complex plane, the power system is considered unstable. Step S1 includes: constructing a complex vector impedance model of a grid-type inverter under power synchronization control, and the formula is as follows: Where s is the Lagrangian operator, Δi od1 (s) is the d-axis component of the grid-connected point current of the grid-connected inverter in the s-domain under small signal input, Δi oq1 (s) is the q-axis component of the grid-connected point current of the grid-connected inverter in the s-domain under small signal input, Y GFM (s) is the complete equivalent admittance of the grid-type inverter in the s domain, Δv od1 (s) is the d-axis component of the grid-connected point voltage of the grid-connected inverter in the s-domain under small signal input, Δv oq1 (s) is the q-axis component of the grid-connected point voltage of the grid-connected inverter in the s-domain under small signal input, Z GFM (s) is the complete equivalent impedance of the grid-type inverter in the s domain; The complex vector impedance model of the grid-type inverter is converted to the αβ coordinate system, and the αβ coordinate system small signal input and output relationship of the grid-type inverter is obtained, and the formula is as follows: In the formula, ΔI Mαβ (s) is the output current of the grid-type inverter under small signal input in the αβ coordinate system, is the output current of the grid inverter after frequency coupling under small signal input in the αβ coordinate system, Y Mc,αβ (s) is the complex vector impedance model of the grid-type inverter in the αβ coordinate system, ΔU Mαβ (s) is the output voltage of the grid-type inverter under small signal input in the αβ coordinate system, is the output conjugate voltage of the grid inverter after frequency coupling under small signal input in the αβ coordinate system, T αβ-dq,vec is the transformation matrix in complex vector form between the αβ coordinate system and the dq coordinate system, Y Mc,dq (s-jω0) is the complex vector impedance model of the grid-type inverter after frequency coupling in the αβ coordinate system.

2. A small signal stability analysis method for heterogeneous inverters connected to a power grid as claimed in claim 1, characterized in that: Step S1 includes: constructing a complex vector impedance model of a grid-following inverter under power synchronization control, and the formula is as follows: In the formula, Δi od2 (s) is the d-axis component of the grid-connected point current of the grid-connected inverter in the s-domain under small signal input, Δi oq2 (s) is the q-axis component of the grid-connected point current of the grid-connected inverter in the s-domain under small signal input, Y GFL (s) is the equivalent admittance of the complete grid-connected inverter in the s domain, Δv od2 (s) is the d-axis component of the grid-connected point voltage of the grid-connected inverter in the s-domain under small signal input, Δv oq2 (s) is the q-axis component of the grid-connected point voltage of the grid-connected inverter in the s-domain under small signal input, Z GFL (s) is the complete equivalent impedance of the grid-connected inverter in the s domain; The complex vector impedance model of the grid-following inverter is converted to the αβ coordinate system, and the small signal input-output relationship of the grid-building inverter in the αβ coordinate system is obtained. The formula is as follows: In the formula, ΔI Lαβ (s) is the output current of the grid-following inverter under small signal input in the αβ coordinate system, is the output current of the grid-type inverter after frequency coupling under small signal input in the αβ coordinate system, Y Lc，αβ (s) is the complex vector impedance model of the grid-following inverter in the αβ coordinate system, ΔU Lαβ (s) is the output voltage of the grid-type inverter under small signal input in the αβ coordinate system, is the output conjugate voltage of the grid-type inverter after frequency coupling under small signal input in the αβ coordinate system, Y Lc,dq (s-jω0) is the complex vector impedance model of the grid-connected inverter after frequency coupling in the αβ coordinate system.

3. The small signal stability analysis method for heterogeneous inverters connected to a power grid as claimed in claim 1, characterized in that: Step S1 includes: constructing a complex vector impedance model of passive components under power synchronization control, the formula is as follows: In the formula, m and n both represent nodes, I αβ(m，n) (s) is the current between node m and node n in the αβ coordinate system, is the conjugate current between node m and node n after frequency coupling in the αβ coordinate system, YLCαβ(m,n)(s) is the complex vector admittance model of the passive element in the αβ coordinate system, ΔU αβ (m, n)(s) is the voltage between node m and node n in the αβ coordinate system, is the conjugate voltage between node m and node n after frequency coupling in the αβ coordinate system, Y m，n (s) is the line inductance between node m and node n in the αβ coordinate system, Y m，n (s-j2ω0) is the line inductance between node m and node n after frequency coupling in the αβ coordinate system.

4. The small signal stability analysis method for heterogeneous inverters connected to a power grid as claimed in claim 1, characterized in that: Step S2 specifically includes: For each node, the complex vector impedance model of the adjacent elements is substituted into the Kirchhoff equation of the node to calculate the mutual admittance between the node and other nodes; For each node, calculate the sum of the mutual admittances between the node and other nodes, then add the admittance between the node and the ground point to the sum to obtain the self-admittance of the node; Based on the number of nodes l, a complex vector admittance matrix of order 2l is constructed; where The complex vector admittance matrix includes four l×l parts: upper left, lower left, upper right and lower right; The main diagonal elements in the upper left part are the self-admittance of each node, and the off-diagonal elements are the mutual admittance between nodes; The main diagonal elements in the lower right part are the self-admittance of each node after frequency coupling, and the non-diagonal elements are the mutual admittance between nodes after frequency coupling; The elements in the lower left and upper right parts are all 0.

5. A small signal stability analysis method for heterogeneous inverters connected to a power grid as claimed in claim 4, characterized in that: After establishing the complex vector admittance matrix of the power system, it also includes: after connecting the new element, calculating the self-admittance Y of the newly added node l+1，l+1 (s), the formula is as follows: Where k is the node number, k = 1, 2, ..., l, Y l+1,k (s) is the line admittance between the kth node and the newly added node.

6. The small signal stability analysis method for heterogeneous inverters connected to a power grid as claimed in claim 1, characterized in that: After step S3, the method further includes: obtaining characteristic roots of the power system at different times according to steps S1 to S3; Calculate the damping ratio ζ of each pair of characteristic complex roots λ in the characteristic roots at each moment, the formula is as follows: λ=σ+jω; Among them, each pair of characteristic complex roots λ corresponds to an oscillation mode, σ represents the attenuation rate of the corresponding oscillation mode, and ω represents the resonant frequency of the corresponding oscillation mode; The characteristic root with the smallest damping ratio at each moment is selected as the key characteristic root, and the running trajectory of the key characteristic root is plotted according to the time series relationship.

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