Method and system for judging transient synchronization stability of multi-converter series system

Abstract

The invention relates to the technical field of power system stability analysis, in particular to a method and a system for judging transient synchronization stability of a multi-converter series system, and the method comprises the steps: building a converter transient model which retains the dynamic state of a phase-locked loop by considering the condition of a network-following converter; the method comprises the following steps: constructing a system node impedance matrix according to a power grid topology, and obtaining a system stand-alone transient aggregation model according to equivalent decoupling of the node impedance matrix; and based on the transient aggregation model, analyzing the transient synchronization stability of the system under the conditions of different voltage intensities and different voltage drops after an alternating current fault. On the basis of similar transformation of a power grid node impedance matrix, equivalent decoupling of a transient model of a multi-converter series system is achieved, then a single-converter transient aggregation model of the system is obtained, and the calculated amount of synchronous stability analysis of the system is effectively reduced. Based on the obtained single machine aggregation model, a direct method for transient synchronous stability analysis of the multi-converter series system is provided, and the transient synchronous stability of the system can be efficiently judged.

Description

Technical Field

[0001] The present invention relates to the technical field of power system stability analysis, and in particular to a method and system for determining transient synchronous stability of a multi-converter series system. Background Art

[0002] Renewable energy generators are connected to the AC grid via grid-connected inverters. With the rapid growth of renewable energy grid integration, large-scale grid integration has led to an increasing prevalence of converter dynamics dominating grid transients, creating new stability issues. Current mainstream converters use phase-locked loops (PLLs) to track the port voltage phase, enabling synchronous grid connection. Due to their second-order dynamics, similar to the rotor motion equations of traditional synchronous generators, the PLLs are susceptible to instability under AC grid faults, similar to the angle stability of synchronous generators. This phenomenon is commonly referred to as converter-dominated synchronous stability. Loss of synchronization between the converter and the AC grid can easily cause widespread disconnection of renewable energy sources, severely impacting the effective integration of renewable energy and the stable operation of the system. Therefore, transient synchronous stability assessment of converter-connected systems is crucial.

[0003] Existing transient synchronization stability analysis of grid-connected converter systems mostly focuses on single-unit grid-connected systems or systems with parallel converters. By building a converter phase-locked loop model and integrating it with the AC grid model, a single-unit grid-connected system model can be derived. Furthermore, the system's transient synchronization stability can be analyzed using the equal-area rule, energy function, or phase plane method. For systems with multiple converters connected in parallel, when the converter models are identical and symmetrically connected, a single-unit aggregate model can be constructed through multiplication. By analyzing the transient synchronization stability of a single-unit grid-connected system, the stability characteristics of the original system can be understood.

[0004] However, the actual network topology of the grid-connected converter system is complex, usually formed by a complex connection structure of series and parallel connections. The transient synchronous stability analysis method of the single-machine grid-connected system or the multi-machine parallel connection system is difficult to meet the actual system stability determination requirements.

[0005] The information disclosed in this background technology section is only intended to deepen the understanding of the overall background technology of the present disclosure and should not be regarded as an admission or any form of suggestion that the information constitutes the prior art known to those skilled in the art. Summary of the Invention

[0006] The present invention provides a method and system for determining transient synchronous stability of a multi-converter series system, which can effectively solve the problems in the background technology.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is:

[0008] A method for determining transient synchronous stability of a multi-converter series system includes the following steps:

[0009] Build a converter transient model including phase-locked loop dynamics;

[0010] Based on the converter transient model, a series system transient model including N converters is constructed;

[0011] Based on the orthogonal linear transformation of matrix eigendecomposition, the transient model of the series system is reduced in dimension to be equivalent to a single-machine aggregation model;

[0012] Based on the single-machine aggregation model, the equal-area rule is used to determine the transient synchronization stability of the multi-converter series system.

[0013] Furthermore, expressing the converter transient model by a state space equation includes the following steps:

[0014] The phase-locked loop dynamic equation of the i-th converter is established, which is specifically expressed as:

[0015]

[0016] ω plli =ω0+(x plli +K pi U gqi );

[0017] Where, the subscript i represents the i-th converter, i = 1, 2, ..., N, and there are N converters in total; θ plli and ω plli are the phase-locked loop output phase angle and angular frequency, respectively, plli is the output of the phase-locked loop integral controller, K ii and K pi are the proportional and integral coefficients of the phase-locked loop respectively; U gqi is the q-axis component of the converter terminal voltage;

[0018] The current and voltage in the AC grid public coordinate system are converted to the converter local coordinate system; the state space form of the converter transient model is specifically expressed as:

[0019]

[0020] Among them, X i =[θ plli x plli ] T , Indicates the rated angular frequency of the power grid, U gdqi =[U gdi U gqi ] T , U gdi +jU gqi is the terminal voltage of the i-th converter in the dq coordinate system.

[0021] Furthermore, the converter local coordinate system dq determined based on the phase-locked loop and the AC grid public coordinate system xy have the following relationship:

[0022]

[0023] Among them, I gxi +jI gyi and I gdi +jI gqi are the output current of converter i in xy and dq coordinate systems respectively; U gxi +jU gyi is the voltage at terminal i of the converter in the xy coordinate system;

[0024] The converter output current in the converter local coordinate system dq is the same as the reference value, which can be expressed as:

[0025]

[0026] Among them, I gdi ref and I gqi ref are the d-axis and q-axis current inner loop control reference values ​​of the i-th converter respectively.

[0027] Furthermore, a transient model of a series system consisting of N converters is constructed, which is specifically expressed as follows:

[0028]

[0029] I g =diag[T xyi ]I gdq ;

[0030] U gdq =diag[T dqi ]U g ;

[0031] Among them, diag[M i ] indicates that the diagonal elements are M i The block diagonal matrix of T X2 T …X N T ] T , U g =[U g1 T U g2 T … U gN T ] T , U g1 represents the terminal voltage of converter 1, ..., UgN Indicates the terminal voltage of the converter N, I gdq =[I gdq1 T I gdq2 T … I gdqN T ] T , U gdq =[U gdq1 T U gdq2 T … U gdqN T ] T ;I gi =[I gxi I gyi ] T , I gxi 、jI gyi is the output current of converter i in the xy coordinate system, I gdqi =[I gdi I gqi ] T , I gdi 、jI gqi is the output current of converter i in the dq coordinate system,

[0032]

[0033] The power grid network equation is described by the node impedance matrix, which is specifically expressed as:

[0034] U g =Z g I g +U CM ;

[0035] Among them, Z g is the system node impedance matrix; U CM =[U C T U C T … U C T ] T , U c =[U cx U cy ] T , U cx +jU cy is the voltage of bus C in the xy coordinate system, where C is the node identifier and has nothing to do with the phase difference;

[0036] The series system transient model and the power grid network equation are combined and specifically expressed as follows:

[0037]

[0038] Where A=diag[A i ],b1=[B1T dq1 T B2T dq2 T … B N T dqN T ] T ,b2=diag[B i T dqi ]Z g diag[T xyi ].

[0039] Furthermore, when the line resistance is ignored, the system node impedance matrix Z g Specifically expressed as:

[0040]

[0041] in, hour, x ij =x ji ;x k is the line reactance connecting the kth converter and the (k-1)th converter, x L is the reactance of the transmission line; k = 1, 2,…, N.

[0042] Furthermore, for the matrix X g Perform eigendecomposition on the eigenvalue λ i And the orthogonal eigenvector matrix U, satisfying:

[0043] U T X g U=diag[λ i ];

[0044] Define the coordinate transformation, specifically expressed as:

[0045] U g =U2U y , I g =U2I y ;

[0046] in, E2 is a 2nd order unit matrix, U y =[U y1 T U y2 T … U yN T ]T , I y =[I y1 T I y2 T … I yN T ] T , U yi and I yi are 2-dimensional column vectors, i = 1, 2, ..., N.

[0047] Furthermore, the block diagonal matrix is ​​converted into a unified form through the Kronecker product, and the transient model of the series system is simplified as follows:

[0048]

[0049] I yN =T xy I ydqN ;

[0050] U ydqN =T dq U yN ;

[0051] U yN =λ N EI yN +u sN U C ;

[0052] I c =u sN U C I yN ;

[0053] Among them, for the matrix X g Eigenvalues ​​and eigenvectors of: λ i ≈λ Li ,u i ≈u Li ,λ i is the matrix X g The eigenvalue of λ Li is the approximate eigenvalue of the simplified model, u i is the matrix X g The corresponding eigenvector, u Li is the approximate eigenvector of the simplified model, Y N is the state variable set of the aggregation model, A and B are the coefficient matrices of the system state space model, and U ydqN is the input voltage vector after dq coordinate transformation, I yN is the aggregate output current vector, T xy is the coordinate transformation matrix, I ydqNis the current component in the dq coordinate system, T dq is the dq coordinate transformation matrix, U yN is the output voltage vector, λ N is the equivalent polymerization impedance parameter, E is the equivalent potential source amplitude, u sN is the modulation signal amplitude, U C is the voltage amplitude at the grid connection point, I c is the equivalent output current amplitude.

[0054] Furthermore, the single-machine aggregation model of the multi-converter series system is specifically expressed as follows:

[0055]

[0056] ω′ pll =ω′0+(x′ pll +K p U yNq );

[0057]

[0058] Among them, U cq =-U c sinθ′ pll ,and θ′ pll is the equivalent phase angle of the phase-locked loop output, x′ pll is the state variable of the phase-locked loop integral link, K p , K i is the proportional and integral control coefficient of the phase-locked loop, U yNq is the q-axis output voltage component, ω0′ is the reference angular frequency of the phase-locked loop, ω pll ′ is the angular frequency estimated by the phase-locked loop, I yNd ,I yNq : d-axis and q-axis current components, U yNd ,U yNq : d-axis and q-axis voltage components, U cx ,U cy : The rectangular coordinate component of the grid connection point voltage.

[0059] Furthermore, an equivalent rotor motion equation is constructed based on the single-machine aggregation model, which is specifically expressed as:

[0060]

[0061] in, Indicates mechanical power, u sN K i U c sinθ′p ll +ω′ pll usN K p U c cosθ′ pll It indicates that electromagnetic power can be used to analyze the transient synchronous stability of the system based on the equal area rule.

[0062] Furthermore, the equal-area rule is applied to analyze the acceleration area and deceleration area to determine the transient synchronous stability of the multi-converter series system; if the acceleration area is greater than the deceleration area, the system is determined to be unstable.

[0063] A transient synchronization stability determination system for a multi-converter series system includes the following modules:

[0064] A converter transient modeling module is used to establish a converter transient model including phase-locked loop dynamics. The model is based on the phase-locked loop proportional-integral control parameters, the terminal voltage q-axis component and the grid rated angular frequency and is represented by a state-space equation;

[0065] A series system modeling module is used to construct a series system transient model based on the transient models of N converters. The model integrates the states of each converter through a block diagonal matrix and combines it with the grid node impedance matrix to describe the electrical connection relationship between converters.

[0066] An equivalent decoupling module is used to perform eigenvalue decomposition and coordinate transformation on the transient model of the series system, and to decouple the high-dimensional system into a single-machine aggregate model through Kronecker product. The state variables and matrices of the aggregate model are derived from the eigenvalues ​​and eigenvectors of the original system.

[0067] A stability determination module, based on the single-machine aggregation model, uses the equal area rule to calculate the acceleration area and the deceleration area, and determines the transient synchronization stability of the system by comparing the area sizes;

[0068] The data interaction module is used to obtain the grid fault type, grid connection point voltage amplitude and converter output current reference value in real time, and output the stability judgment result.

[0069] The beneficial effects of the present invention are:

[0070] In the present invention, based on the similarity transformation of the grid node impedance matrix, the equivalent decoupling of the transient model of the multi-converter series system is achieved, and then the transient aggregation model of the system single machine is obtained, which effectively reduces the computational complexity of the system synchronous stability analysis.

[0071] The single-machine aggregate model retains key dynamic characteristics of the original system (such as phase-locked loop dynamics and impedance characteristics) while significantly reducing the dimensionality of state variables, significantly improving simulation and analysis efficiency. It is suitable for real-time or large-scale system stability assessment. Based on the resulting single-machine aggregate model, a direct method for transient synchronous stability analysis of multi-converter series systems is proposed, which enables efficient determination of system transient synchronous stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments recorded in the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0073] Figure 1 This is a flow chart of the method for determining transient synchronous stability of a multi-converter series system in the present invention. DETAILED DESCRIPTION

[0074] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0075] It should be noted that when an element is referred to as being "fixed to" another element, it may be directly attached to the other element or there may be an intermediate element. When an element is referred to as being "connected to" another element, it may be directly connected to the other element or there may be an intermediate element. The terms "vertical," "horizontal," "left," "right," and similar expressions used herein are for illustrative purposes only and do not represent the only implementation methods.

[0076] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which this invention pertains. The terms used in this specification of the present invention are for the purpose of describing specific embodiments only and are not intended to limit the present invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0077] The purpose of this invention is to achieve a fast and effective determination of transient synchronous stability of a system with multiple converters connected in series, especially to locate high-risk operating conditions and fault types. A direct method for transient synchronous stability analysis is given, such as Figure 1 shown.

[0078] To achieve the above object, the present invention specifically discloses a method for determining transient synchronous stability of a multi-converter series system, comprising the following steps:

[0079] A converter transient model including phase-locked loop dynamics is established; based on the converter transient model, a series system transient model including N converters is constructed; based on the orthogonal linear transformation of matrix eigendecomposition, the series system transient model is reduced in dimension to be equivalent to a single-machine aggregate model; based on the single-machine aggregate model, the equal-area rule is used to determine the transient synchronization stability of the multi-converter series system.

[0080] In the scheme of the present invention, a transient model of the system with converters connected in series is first derived, which retains the dynamics of the phase-locked loop. Then, the model is organized into a state space representation, and the equivalent decoupling of the transient model of the multi-machine system is achieved by similar diagonalizing the state space matrix. Finally, based on the decoupling results, a single-machine transient aggregation model of the system with converters connected in series is established, and on this basis, a direct analysis method for the transient synchronous stability of the system is proposed. This method can effectively reduce the computational complexity of the transient synchronous stability analysis of the system with multiple converters connected in series, and provide analytical analysis results.

[0081] In this embodiment, the grid-following converter uses a phase-locked loop (PLL) to track the grid connection point voltage phase to achieve synchronous grid connection. Transient synchronization stability is closely related to the performance of the PLL. When a short-circuit fault occurs in the grid, the grid connection point voltage drops, causing the converter to enter a low-voltage ride-through state. The outer control loop then exits operation, and the inner current loop reference value is determined by the fault ride-through control strategy. Given that the inner current loop responds much faster than the PLL, when analyzing PLL synchronization stability, the converter output current can be assumed to be equal to the inner current loop input reference value in the dq coordinate system.

[0082] In the transient synchronous stability analysis of a system with N series converters, the converter transient model is represented by a state-space equation, including the following steps:

[0083] The phase-locked loop dynamic equation of the i-th converter is established, which is specifically expressed as:

[0084]

[0085] ω plli =ω0+(x plli +K pi U gqi );

[0086] Where, the subscript i represents the i-th converter, i = 1, 2, ..., N, and there are N converters in total; θ plli and ω plli are the phase-locked loop output phase angle and angular frequency, respectively, plli is the output of the phase-locked loop integral controller, K iiand K pi are the proportional and integral coefficients of the phase-locked loop respectively; U gqi is the q-axis component of the converter terminal voltage.

[0087] The converter local coordinate system dq determined by the phase-locked loop and the AC grid public coordinate system xy have the following relationship:

[0088]

[0089] Among them, I gxi +jI gyi and I gdi +jI gqi are the output current of converter i in xy and dq coordinate systems respectively; U gxi +jU gyi is the voltage at terminal i of the converter in the xy coordinate system, i = 1, 2, …, N.

[0090] Considering that the current inner loop regulation speed is much faster than the phase-locked loop, when analyzing the stability of the phase-locked loop, it can be assumed that the converter output current in the converter local coordinate system dq is the same as the reference value, which can be specifically expressed as:

[0091]

[0092] Among them, I gdi ref and I gqi ref are the d-axis and q-axis current inner loop control reference values ​​of the i-th converter respectively.

[0093] The current and voltage in the AC grid public coordinate system are converted to the converter local coordinate system; the state space form of the converter transient model is specifically expressed as:

[0094]

[0095] Among them, X i =[θ plli x plli ] T , Indicates the rated angular frequency of the power grid, U gdqi =[U gdi U gqi ] T , U gdi +jU gqi is the terminal voltage of the i-th converter in the dq coordinate system, i = 1, 2, …, N.

[0096] In this embodiment, modeling of a series converter system is performed, including:

[0097] Construct a transient model of a series system consisting of N converters, which can be expressed as follows:

[0098]

[0099] I g =diag[T xyi ]I gdq ;

[0100] U gdq =diag[T dqi ]U g ;

[0101] Among them, diag[M i ] indicates that the diagonal elements are M i The block diagonal matrix of T X2 T … X N T ] T , U g =[U g1 T U g2 T … U gN T ] T , U g1 represents the terminal voltage of converter 1, ..., U gN Indicates the terminal voltage of the converter N, I gdq =[I gdq1 T I gdq2 T … I gdqN T ] T , U gdq =[U gdq1 T U gdq2 T … U gdqN T ] T ;I gi =[I gxi I gyi ] T , I gxi 、jI gyi is the output current of converter i in the xy coordinate system, I gdqi =[I gdi I gqi ] T , I gdi 、jI gqi is the output current of converter i in the dq coordinate system,

[0102] The power grid network equation is described by the node impedance matrix, which is specifically expressed as:

[0103] U g =Z g I g +U CM ;

[0104] Among them, Z g is the system node impedance matrix; U CM =[U C T U C T … U C T ] T , U c =[U cx U cy ] T , U cx +jU cy is the voltage of bus C in the xy coordinate system, where C is the node identifier and is independent of the phase difference.

[0105] According to circuit principles, when the line resistance is ignored, the system node impedance matrix Z g Specifically expressed as:

[0106]

[0107] in, hour, x ij =x ji ;x k is the line reactance connecting the kth converter and the (k-1)th converter, x L is the reactance of the transmission line; k=1,2,…,N.

[0108] The series system transient model and the power grid network equation are combined and specifically expressed as follows:

[0109]

[0110] Where A=diag[A i ],b1=[B1T dq1 T B2T dq2 T … B N T dqN T ] T ,b2=diag[B i T dqi]Z g diag[T xyi ].

[0111] Representing a series converter system model by combining the series system transient model with the grid network equations can be used for transient synchronous stability analysis. However, due to the large number of converters and the high dimensionality of the system model, direct analytical analysis of the system's transient synchronous stability is difficult. Electromagnetic transient simulation is required, which is computationally intensive and inefficient. Therefore, a direct method for transient synchronous stability analysis of multi-converter series systems is proposed.

[0112] In this embodiment, the series system transient model is equivalent to a single-machine aggregation model through mathematical transformation, and u i =[u 1i u 2i Ku Ni ] T and λ i Represents the system node impedance matrix Z g The matrix X g The eigenvectors and corresponding eigenvalues ​​(i = 1, 2, ..., N) of the matrix X g Perform eigendecomposition on the eigenvalue λ i And the orthogonal eigenvector matrix U, satisfying:

[0113] U T X g U=diag[λ i ];

[0114] Define the coordinate transformation, specifically expressed as:

[0115] U g =U2U y , I g =U2I y ;

[0116] in, E2 is a 2nd order unit matrix, U y =[U y1 T U y2 T … U yN T ] T , I y =[I y1 T I y2 T …I yN T ] T , U yi and I yiare 2-dimensional column vectors, i = 1, 2, ..., N.

[0117] According to the properties of the Kronecker product, the coordinate transformation formula is substituted into the power grid network equation to obtain:

[0118] U y =diag[λ i E]I y +U YCM ;

[0119] Among them, U YCM =U2 T U CM =[u s1 U C T u s2 U C T Ku sN U C T ] T ,

[0120] Considering that the converters in the new energy station come from the same manufacturer and are of the same model, the phase-locked loop parameters of each converter are set to the same. In addition, since the internal collection network of the new energy station is mainly used for power collection, the collection line impedance is much smaller than the new energy transmission line, so the steady-state voltage amplitude and phase difference at the converter machine end are not much different. Therefore, it can be assumed that the phase-locked loop models in the series system transient model are the same, and the subscript i representing different unit models can be ignored. The following variable transformation is further defined:

[0121] U gdq =U2U ydq , I gdq =U2I ydq , X=U2Y.

[0122] According to the properties of Kronecker product, U2 -1 =U2 T , bringing the variable transformation formula into the series system transient model, we can get:

[0123]

[0124] I y =U2 T diag[T xy ]U2I ydq ;

[0125] U ydq =U2 T diag[T dq ]U2U y ;

[0126] Further sorting can be obtained:

[0127]

[0128] I y =diag[T xy ]I yaq ;

[0129] U ydq =diag[T dq ]U y ;

[0130] Among them, ω yM0 =U2 T ω M0 =[u s1 ω0 T u s2 ω0 T Ku sN ω0 T ] T .

[0131] Considering that the power network of the converter connected in series consists of two parts: the collection system and the transmission system, the system node impedance matrix Z g X in g It can be further expressed as:

[0132] X g =X n +X L ;

[0133] in, x nij is the reactance of the collection network line, x L is the reactance of the transmission line; i,j=1,2,…,N.

[0134] Since the transmission line impedance is usually much larger than the outbound line impedance, the Xg in the system node impedance matrix Zg is dominated by the XL part. The eigenvalues ​​and eigenvectors of the matrix XL are expressed as:

[0135] λ Lj =0,λ L =Nx L ,u sLj =0,

[0136]

[0137] Among them, λ Li and u Li =[u L1i u L2iKu LNi ] T The matrix X L The eigenvalues ​​and eigenvectors of

[0138] The output current of the converter is expressed as:

[0139]

[0140] Among them, I c Inject the external system current column vector into the converter.

[0141] The block diagonal matrix is ​​converted into a unified form by Kronecker product, and the transient model of the series system is simplified as follows:

[0142]

[0143] I yN =T Xy I ydqN ;

[0144] U ydqN =T dq U yN ;

[0145] U yN =λ N EI yN +u sN U C ;

[0146] I c =u sN U C I yN ;

[0147] Among them, for the matrix X g Eigenvalues ​​and eigenvectors of: λ i ≈λ Li ,u i ≈u Li ,λ i is the matrix X g The eigenvalue of Li is the approximate eigenvalue of the simplified model, u i is the matrix X g The corresponding eigenvector, u Li is the approximate eigenvector of the simplified model, Y N is the state variable set of the aggregation model, A and B are the coefficient matrices of the system state space model, and U ydqN is the input voltage vector after dq coordinate transformation, I yN is the aggregate output current vector, T xyis the coordinate transformation matrix, I ydqN is the current component in the dq coordinate system, T dq is the dq coordinate transformation matrix, U yN is the output voltage vector, λ N is the equivalent polymerization impedance parameter, E is the equivalent potential source amplitude, u sN is the modulation signal amplitude, U C is the voltage amplitude at the grid connection point, I c is the equivalent output current amplitude.

[0148] In this embodiment, the single-machine aggregation model of the multi-converter series system is specifically expressed as follows:

[0149]

[0150] ω′ pll =ω′0+(x′ pll +K p U yNq );

[0151]

[0152]

[0153] Among them, U ca =-U c sinθ′ pll ,and θ′ pll is the equivalent phase angle of the phase-locked loop output, x′ pll is the state variable of the phase-locked loop integral link, K p , K i is the proportional and integral control coefficient of the phase-locked loop, U yNq is the q-axis output voltage component, ω0′ is the reference angular frequency of the phase-locked loop, ω pll ′ is the angular frequency estimated by the phase-locked loop, I yNd ,I yNq : d-axis and q-axis current components, U yNd ,U yNq : d-axis and q-axis voltage components, U cx ,U cy : The rectangular coordinate component of the grid connection point voltage.

[0154] Through further arrangement, it can be obtained that the equivalent rotor motion equation is constructed based on the single-machine aggregation model, which is specifically expressed as:

[0155]

[0156] in, Indicates mechanical power, u sN Ki U c sinθ′ pll +ω′ pll u sN K p U c cosθ′ pll It indicates that electromagnetic power can be used to analyze the transient synchronous stability of the system based on the equal area rule.

[0157] When the external power grid fails, the voltage amplitude U c The electromagnetic power changes, and the corresponding converter provides reactive power support for the system, resulting in active current output I yNd This constitutes the acceleration and deceleration areas, and whether the system has a risk of transient synchronous instability can be determined based on whether the acceleration area is greater than the maximum deceleration area.

[0158] Specifically, the equal-area rule is applied to analyze the acceleration area and deceleration area to determine the transient synchronous stability of the multi-converter series system; if the acceleration area is greater than the deceleration area, the system is determined to be unstable.

[0159] The present invention further discloses a system for determining transient synchronous stability of a multi-converter series system, comprising the following modules:

[0160] A converter transient modeling module is used to establish a converter transient model including phase-locked loop dynamics. The model is based on the phase-locked loop proportional-integral control parameters, the terminal voltage q-axis component and the grid rated angular frequency and is represented by a state-space equation;

[0161] A series system modeling module is used to construct a series system transient model based on the transient models of N converters. The model integrates the states of each converter through a block diagonal matrix and combines it with the grid node impedance matrix to describe the electrical connection relationship between converters.

[0162] An equivalent decoupling module is used to perform eigenvalue decomposition and coordinate transformation on the transient model of the series system, and to decouple the high-dimensional system into a single-machine aggregate model through Kronecker product. The state variables and matrices of the aggregate model are derived from the eigenvalues ​​and eigenvectors of the original system.

[0163] A stability determination module, based on the single-machine aggregation model, uses the equal area rule to calculate the acceleration area and the deceleration area, and determines the transient synchronization stability of the system by comparing the area sizes;

[0164] The data interaction module is used to obtain the grid fault type, grid connection point voltage amplitude and converter output current reference value in real time, and output the stability judgment result.

[0165] Those skilled in the art will appreciate that the present invention is not limited to the foregoing embodiments. The foregoing embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for determining transient synchronous stability of a multi-converter series system, characterized in that: The following steps are involved: Build a converter transient model including phase-locked loop dynamics; Based on the converter transient model, a series system transient model including N converters is constructed; Based on the orthogonal linear transformation of matrix eigendecomposition, the transient model of the series system is reduced in dimension to be equivalent to a single-machine aggregation model; Based on the single-machine aggregation model, the equal-area rule is used to determine the transient synchronization stability of the multi-converter series system.

2. The method for determining transient synchronous stability of a multi-converter series system according to claim 1, characterized in that: The converter transient model is represented by a state space equation, comprising the following steps: The phase-locked loop dynamic equation of the i-th converter is established, which is specifically expressed as: ωp11i=ω0+(xp11i+KpiUgpi); Where, the subscript i represents the i-th converter, i = 1, 2, ..., N, and there are N converters in total; θ plli and ω plli are the phase-locked loop output phase angle and angular frequency, respectively, plli is the output of the phase-locked loop integral controller, K ii and K pi are the proportional and integral coefficients of the phase-locked loop respectively; U gqi is the q-axis component of the converter terminal voltage; Convert the current and voltage in the public coordinate system of the AC power grid to the local coordinate system of the converter; The state space form of the converter transient model is specifically expressed as: Where, Xi=[θp11i xp11i]T, Indicates the rated angular frequency of the power grid, U gdqi =[U gdi U gqi ] T , U gdi +jU gqi is the terminal voltage of the i-th converter in the dq coordinate system.

3. The method for determining transient synchronous stability of a multi-converter series system according to claim 2, wherein: The converter local coordinate system dq determined by the phase-locked loop and the AC grid public coordinate system xy have the following relationship: Among them, I gxi +jI gyi and I gdi +jI gqi are the output current of converter i in xy and dq coordinate systems respectively; U gxi +jU gyi is the voltage at terminal i of the converter in the xy coordinate system; The converter output current in the converter local coordinate system dq is the same as the reference value, which can be expressed as: Among them, I gdi ref and I gqi ref are the d-axis and q-axis current inner loop control reference values ​​of the i-th converter respectively.

4. The method for determining transient synchronous stability of a multi-converter series system according to claim 2, wherein: Construct a transient model of a series system consisting of N converters, which can be expressed as follows: I g =diag[T xyi ]I gdq ; U gdq =diag[T dqi ]U g ; Among them, diag[M i ] indicates that the diagonal elements are M i The block diagonal matrix of ; U g1 represents the terminal voltage of converter 1, ..., U gN represents the terminal voltage of the converter N, I gi =[I gxi I gyi ] T , I gxi 、jI gyi is the output current of converter i in the xy coordinate system, I gdqi =[I gdi I gqi ] T , I gdi 、jI gqi is the output current of converter i in the dq coordinate system, The power grid network equation is described by the node impedance matrix, which is specifically expressed as: U g =Z g I g +U CM ; Among them, Z g is the system node impedance matrix; U c =[U cx U cy ] T , U cx +jU cy is the voltage of bus C in the xy coordinate system, where C is the node identifier; The series system transient model and the power grid network equation are combined and specifically expressed as follows: Where A=diag[A i ],b1=[B1T dq1 T B2T dq2 T … B N T dqN T ] T ,b2=diag[B i T dqi ]Z g diag[T xyi ].

5. The method for determining transient synchronous stability of a multi-converter series system according to claim 4, characterized in that: When the line resistance is ignored, the system node impedance matrix Z g Specifically expressed as: in, When i≤j, i,j=1,2,…,N;x ij =x ji ;x k is the line reactance connecting the kth converter and the (k-1)th converter, x L is the reactance of the transmission line; k=1,2,…,N.

6. The method for determining transient synchronous stability of a multi-converter series system according to claim 5, characterized in that: For matrix X g Perform eigendecomposition on the eigenvalue λ i And the orthogonal eigenvector matrix U, satisfying: U T X g U=diag[λ i ]; Define the coordinate transformation, specifically expressed as: IN g =U2U y ,AND g =U2I y ; in, E2 is a 2nd order unit matrix, U yi and I yi are 2-dimensional column vectors, i=1,2,…,N.

7. The method for determining transient synchronous stability of a multi-converter series system according to claim 6, characterized in that: The block diagonal matrix is ​​converted into a unified form by Kronecker product, and the transient model of the series system is simplified as follows: I yN =T xy I ydqN ; U ydqN =T dq U yN ; U yN =λ N NO yN +u sN U C ; AND c =in sN IN C AND yN ; Among them, for the matrix X g Eigenvalues ​​and eigenvectors of: λ i ≈λ Li ,u i ≈u Li ,λ i is the matrix X g The eigenvalue of Li is the approximate eigenvalue of the simplified model, u i is the matrix X g The corresponding eigenvector, u Li is the approximate eigenvector of the simplified model, Y N is the state variable set of the aggregation model, A and B are the coefficient matrices of the system state space model, and U ydqN is the input voltage vector after dq coordinate transformation, I yN is the aggregate output current vector, T xy is the coordinate transformation matrix, I ydqN is the current component in the dq coordinate system, T dq is the dq coordinate transformation matrix, U yN is the output voltage vector, λ N is the equivalent polymerization impedance parameter, E is the equivalent potential source amplitude, u sN is the modulation signal amplitude, U C is the voltage amplitude at the grid connection point, I c is the equivalent output current amplitude.

8. The method for determining transient synchronous stability of a multi-converter series system according to claim 7, characterized in that: The single-machine aggregation model of the multi-converter series system is specifically expressed as follows: oh' pll =ω′0+(x′ pll +K p U yNq ); Among them, U cq =-U c sinθ′ pll ,and θ′ pll is the equivalent phase angle of the phase-locked loop output, x′ pll is the state variable of the phase-locked loop integral link, K p , K i is the proportional and integral control coefficient of the phase-locked loop, U yNq is the q-axis output voltage component, ω0′ is the reference angular frequency of the phase-locked loop, ω pll ′ is the angular frequency estimated by the phase-locked loop, I yNd ,I yNq : d-axis and q-axis current components, U yNd ,U yNq : d-axis and q-axis voltage components, U cx ,U cy : The rectangular coordinate component of the grid connection point voltage.

9. The method for determining transient synchronous stability of a multi-converter series system according to claim 8, characterized in that: The equivalent rotor motion equation is constructed based on the single-machine aggregation model, which is specifically expressed as: in, Indicates mechanical power, u sN K i U c sinθ′ pll +ω′ pll u sN K p U c cosθ′ pll It indicates that electromagnetic power can be used to analyze the transient synchronous stability of the system based on the equal area rule.

10. The method for determining transient synchronous stability of a multi-converter series system according to claim 1, wherein: The equal-area rule is applied to analyze the acceleration area and deceleration area to determine the transient synchronous stability of the multi-converter series system. If the acceleration area is greater than the deceleration area, the system is considered unstable.

11. A system for determining transient synchronous stability of a multi-converter series system, characterized in that: Includes the following modules: A converter transient modeling module is used to establish a converter transient model including phase-locked loop dynamics. The model is based on the phase-locked loop proportional-integral control parameters, the terminal voltage q-axis component and the grid rated angular frequency and is represented by a state-space equation; A series system modeling module is used to construct a series system transient model based on the transient models of N converters. The model integrates the states of each converter through a block diagonal matrix and combines it with the grid node impedance matrix to describe the electrical connection relationship between converters. An equivalent decoupling module is used to perform eigenvalue decomposition and coordinate transformation on the transient model of the series system, and to decouple the high-dimensional system into a single-machine aggregate model through Kronecker product. The state variables and matrices of the aggregate model are derived from the eigenvalues ​​and eigenvectors of the original system. A stability determination module, based on the single-machine aggregation model, uses the equal area rule to calculate the acceleration area and the deceleration area, and determines the transient synchronization stability of the system by comparing the area sizes; The data interaction module is used to obtain the grid fault type, grid connection point voltage amplitude and converter output current reference value in real time, and output the stability judgment result.

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