Multi-converter system small interference stability analysis method based on discrete state space model

Abstract

The invention provides a multi-converter system small interference stability analysis method based on a discrete state space model, and the method comprises the steps: firstly building a whole multi-converter system to carry out a small interference model based on a discrete state space principle by using the advantages of discrete domain modeling, and more specifically, carrying out the small interference stability analysis of the multi-converter system; a multi-converter system is divided into two parts, namely a converter network and a connection network, so that subsequent targeted analysis on converters is facilitated; then, on the basis of the network discrete state space models on the two sides, a discrete time domain model and a discrete frequency domain model of the whole system are constructed through different matrix transformation relations; and finally, a parameter-modal sensitivity calculation method is further introduced in combination with a system discrete domain modal identification result, and the method realizes stability analysis and quantitative calculation by using a chain rule. Example analysis shows that in a multi-converter grid-connected scene, the method can realize rapid and effective evaluation and optimization of the small interference stability by the key control parameters of the system, and provides a clear parameter adjustment direction.

Description

Technical Field

[0001] The present invention relates to the field of power system stability analysis, and in particular to a small-disturbance stability analysis method for a multi-converter system based on a discrete state space model. Background Art

[0002] To address the dual challenges of the energy and climate crises, governments around the world are actively promoting the rapid development of renewable energy. With the energy transition, a large number of new energy units using power electronic converters as interface equipment have been connected to the grid, rapidly expanding the installed capacity of renewable energy, and continuously increasing its share of total capacity. Against this backdrop, the dynamic characteristics of power systems have taken on new characteristics, gradually evolving towards low inertia and weak damping. The complex interactions between weak grids and power electronic devices, and between power electronic devices themselves, have led to a certain risk of system instability in the range of a few hertz to thousands of hertz. Oscillation accidents are frequent, seriously affecting the safe and stable operation of power systems. Therefore, it is necessary to conduct small-disturbance stability assessment and optimization research on power systems with a high proportion of renewable energy connected to the grid. Depending on the model used, it can be mainly divided into two categories: time domain and frequency domain.

[0003] Time-domain analysis methods primarily rely on state-space models and utilize stability criteria to evaluate system behavior. Although time-domain analysis methods possess relatively sophisticated characteristic analysis techniques, when dealing with systems containing complex network structures, tedious topological analysis is required to select the network normal tree to determine independent variables. This preprocessing process is complex and lacks efficient, programmable implementation methods, limiting its applicability and scalability in practical engineering. Frequency-domain analysis methods, on the other hand, are based on impedance models, constructing an overall network model through step-by-step equivalent aggregation or utilizing frequency sweep techniques to perform impedance measurements and obtain port data.

[0004] In the field of system small-disturbance stability research, modal analysis methods based on frequency-domain models have gradually developed. These methods, which bear a certain equivalence to modal analysis based on time-domain models, can extract system characteristics through analytical or numerical calculations. Furthermore, key indicator analysis can identify devices that significantly influence system behavior in specific frequency bands. Compared to state-space models, impedance models offer greater modularity and flexibility. However, discrete numerical models constructed using frequency sweeps are not conducive to subsequent analysis. Quantitative studies, such as parameter sensitivity, rely heavily on explicit analytical expressions for the impedance model's transfer function matrix. When performing aggregation and equivalence based on the series and parallel connections of individual components, matrix operations involving high-order symbolic variables often occur. As the scale and complexity of the analyzed system increase, modeling, solution, and analysis efficiency decrease, further increasing the difficulty of analysis. Some researchers have proposed model-order reduction methods, sacrificing a certain degree of accuracy in exchange for modeling, computational, and analytical efficiency. However, depending on the underlying simplification and reduction criteria, each method attempts to achieve uniformity across different scenarios, which can also result in the loss of critical information.

[0005] Inspired by electromagnetic transient simulation programs, discrete state space modeling was proposed and applied. Unlike the continuous time domain state space model, after the component model is discretized, the discrete state variables are independent of each other. Therefore, abnormal network parts such as pure capacitive loops and pure inductive cut sets in the system can be eliminated, solving the difficult problem of balancing modeling accuracy and efficiency. Summary of the Invention

[0006] In response to the shortcomings of the prior art, the present invention proposes a method for small-disturbance stability analysis and parameter optimization of a multi-converter system based on a discrete state space model to improve the efficiency of small-disturbance stability modeling and analysis of a multi-converter system. This method maps the system to a discrete domain for modeling and analysis, and constructs a system model that retains the topology of the converter link based on a discrete state variable model. It fully utilizes the unique advantages of discrete domain modeling, calculates system characteristics using discrete time domain state equations, and further constructs an equivalent system discrete frequency domain model. Based on the identified distribution of discrete domain characteristics of the system and the results of parameter impact analysis, targeted optimization of adjustment parameter variables is achieved, thereby effectively improving system stability. The method of the present invention not only overcomes the limitations of traditional time domain and frequency domain technical means, but also provides an efficient and reliable technical path for small-disturbance stability analysis and optimization of a high proportion of new energy access to the power network.

[0007] The purpose of the present invention can be achieved through the following technical solutions:

[0008] A method for analyzing small-disturbance stability of a multi-converter system based on a discrete state space model is characterized in that the method comprises the following steps:

[0009] 1) Based on the numerical integral substitution idea of ​​the electromagnetic transient simulation program, the system is discretized and a discrete time-domain state-space model of the multi-converter system is constructed with the grid-connected port of the converter as the dividing point:

[0010] For the differential algebraic equations reflecting the dynamic characteristics of each component in the continuous domain, a linear processing method is used to construct its small disturbance continuous state space model, which can be specifically expressed as

[0011]

[0012] Where x is the continuous domain state variable of the element; u xy and i xy are the voltage and current components in the synchronous rotating reference frame respectively; Δ is a small perturbation of the variable; A c 、B c 、C c 、D c is the coefficient matrix related to the static operating point of the component.

[0013] For non-energy storage elements, their state space model is only described by the direct mapping relationship between their input variables and output variables (output equation), without dynamic equations.

[0014] The numerical integration method (trapezoidal integration method) commonly used in electromagnetic transient simulation is used to transform the above-mentioned continuous domain small disturbance model into a discrete time domain difference equation. By performing numerical integration substitution on the differential operator, the continuous time variable is converted into a discrete time series, thereby realizing the discretization of the system. The corresponding discrete state space model is obtained as follows:

[0015]

[0016] Where h is the discrete domain state variable of the element; Δt is the step size selected in the discrete process; A d 、B d 、C d 、D d is the discrete state space coefficient matrix. The conversion formula between it and the coefficient matrix in the continuous state space model is:

[0017]

[0018] According to the output equation of the discrete state space model shown in Equation (2), the components can be represented by a Norton equivalent circuit. After discretization, the natural independence between discrete state variables allows for a fast and efficient construction of a system-level model without complex topological analysis. All components in the system are represented by the discrete domain model of Equation (2). At the same time, the entire system is divided into a converter subsystem and a network subsystem using the grid-connected ports of each converter as the dividing line. Discretized models for each subsystem are established separately, with the grid-connected port node being the common node of the subsystems on both sides.

[0019] For the converter subsystem, based on its dynamic characteristics, a discrete state space model including filters and control links is established. According to the differences in control characteristics and synchronization mechanisms, converters are divided into grid-following converters and grid-forming converters, wherein the grid-following converter detects the grid voltage phase angle through a phase-locked loop to achieve synchronous operation, and its external port characteristics are manifested as current source characteristics; the grid-forming converter adopts a power synchronization control strategy similar to that of a synchronous motor, and its external port characteristics are manifested as voltage source characteristics. Based on the above characteristics, in the modeling process of the converter subsystem, the external port characteristics of the converter are mathematically described, and its equivalent input and output variables are mixed variables, specifically including a combination of voltage and current. The overall model of the subsystem will be constructed by combining the discrete state space models of each converter element, and the coefficient matrix part is represented in block diagonal form, that is,

[0020]

[0021] For the network subsystem, which includes connecting components such as lines and transformers, the discrete state space models of each component can also be combined and constructed in sequence. The coefficient matrix is ​​represented in block diagonal form. The difference is that the input and output variables corresponding to the obtained block diagonal coefficient matrix of this subsystem are the branch voltage and current variables of each component, which can be expressed as follows:

[0022]

[0023] Where h N is a column vector containing all discrete state variables in the network subsystem; u N and i N are the branch voltage and current variables of each component; u hN is the branch voltage variable of each dynamic element.

[0024] According to Kirchhoff's voltage law and combined with the node analysis method, a subsystem discrete state space model is constructed to eliminate the voltage and current inside the network subsystem while retaining the voltage and current variables of the grid-connected port node, namely:

[0025]

[0026] Where u p,N and i p,N A is the voltage and current variables of the grid-connected port node of the converter; D,N 、B D,N 、C D,N 、D D,N is the coefficient matrix of the subsystem model, and the specific solution expression is:

[0027]

[0028] Where M nb is the node-branch association matrix; M nh is the node-dynamic branch association matrix; M np is the node-port association matrix, port is the grid-connected port of the converter, M np The unit matrix is ​​present only at the nodes corresponding to the grid-connected ports, and the rest of the values ​​are zero.

[0029] 2) Combined with Kirchhoff's law, according to the algebraic relationship of the port variables, the discrete time domain state equation of the whole system is established to obtain the corresponding discrete domain mode of the system:

[0030] Using matrix transformation, the discrete state space model of the converter subsystem is transformed into:

[0031]

[0032] Among them, the expression of the new coefficient matrix is:

[0033]

[0034] Where A D,A1 、B D,A1 、C D,A1 and D D,A1 A is the part of the coefficient matrix of the original model corresponding to the converter whose external port characteristic is a current source; D,A2 、B D,A2 、C D,A2 and D D,A2 The part of the coefficient matrix of the original model corresponding to the converter whose external port characteristic is a voltage source.

[0035] When there is no external disturbance in the system, the port voltages corresponding to the subsystems on both sides are equal, and the port currents are equal in magnitude and opposite in direction. According to this algebraic constraint relationship, the redundant variables in the entire system can be eliminated, and the discrete time domain state equation of the entire system can be obtained, namely:

[0036]

[0037] Based on the above-mentioned discrete time-domain state equation of the whole system, the state matrix is ​​decomposed into eigenvalues ​​to solve the discrete domain mode of the system.

[0038] 3) Transform the subsystem state space model to build an equivalent system discrete frequency domain model based on the closed-loop feedback relationship between the port input and output:

[0039] Using matrix transformation, the discrete state space model of the network subsystem is transformed into:

[0040]

[0041] The discrete time domain state space model of the subsystems on both sides is converted into a discrete frequency domain model. By performing Z transform on the discrete state equation, the transfer function matrix of the system is obtained as follows:

[0042]

[0043] Where z is the complex variable of Z transformation; I is the unit matrix; G A (z) and G N (z) are the equivalent discrete frequency domain models of the converter subsystem and the network subsystem, respectively, describing the relationship between the input and output variables in the frequency domain.

[0044] According to the coupling relationship between the input and output variables of the subsystems on both sides, a closed-loop feedback equivalent model is established, and its equivalent open-loop transfer function is:

[0045] L(z)=G N (z)G A(z) (13)

[0046] 4) Substitute the system modal values ​​identified in step 2) and, using the chain rule, calculate the system modal changes caused by the control parameter disturbance of the key equipment converter, i.e., the parameter-modal sensitivity:

[0047] Focus on the weakly damped / negatively damped modes in the system's discrete domain modes identified in step 2) and further perform modal analysis. Based on the chain rule, establish the sensitivity relationship between the system's modal values ​​and the key converter control parameters that affect the system's dynamic characteristics. The specific steps are as follows:

[0048] a) Calculate the sensitivity of the converter element impedance / admittance to the control parameter ρ, which can be approximately expressed as

[0049]

[0050] Where k is the kth converter; ρ+Δρ represents the result when the parameters are changed.

[0051] b) Calculate the sensitivity of the system equivalent transfer function model to the converter components. According to the block diagonal characteristics of the coefficient matrix of the discrete state space model on the converter subsystem side, G A (z) is also a block diagonal matrix, Y k Transformations only affect the elements at their corresponding positions.

[0052]

[0053] c) Calculate the eigenvalue λ z The sensitivity of the system equivalent transfer function model is:

[0054]

[0055] Where adj[·] is the adjoint matrix; det'[·] is the first-order derivative of the determinant. The specific calculation expression is:

[0056]

[0057] d) Combining the above calculation results, the parameter-modal sensitivity is obtained by using the chain rule and further normalized:

[0058]

[0059] 5) Based on the discrete modes of the original system and the parameter-modal sensitivity results, determine the adjustment direction of parameter optimization:

[0060] Analyze the sensitivity results obtained in step 4), sort them according to the absolute values ​​of the normalized parameter-modal sensitivity values, and identify the key control parameters that have the greatest impact on the system mode.

[0061] According to the vector geometry relationship, when the parameter-modal sensitivity vector is equal to the original mode λ z When the vector angle in the complex plane is acute, it means that increasing the parameter value will cause the analyzed mode to move toward a larger amplitude, which means that the stability will further deteriorate. Conversely, the stability can be optimized. Therefore, the direction of parameter adjustment can be clearly determined based on the stability requirements.

[0062] If the optimization effect does not meet expectations, repeat the above steps and further adjust the parameters until the system stability requirements are met.

[0063] The technical effects of the present invention are as follows:

[0064] The small disturbance modeling and stability analysis method of a multi-converter system based on a discrete state space model provided by the present invention can be directly applied to system modeling in new energy grid-connected scenarios. The system model matrix is ​​automatically generated by the program, which avoids the step of performing topological analysis on complex systems to select independent state variables required by traditional methods, and significantly improves the efficiency of model construction. The small disturbance stability analysis method under the discrete domain framework can quickly identify the oscillation modes affecting the system, and by constructing a system model that retains the key topological structure information of the system, the dominant parameters in the converter that affect the overall stability of the system are determined by sensitivity analysis, thereby achieving stable optimization of high-proportion new energy grid-connected systems and prevention of oscillation instability accidents. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 Schematic diagram of the multi-converter system model;

[0066] Figure 2 This is the flow chart of the modal analysis method for discrete domain systems;

[0067] Figure 3 is the converter topology diagram;

[0068] Figure 4 This is a schematic diagram of the chain rule calculation framework;

[0069] Figure 5 is the parameter-modal sensitivity analysis result diagram;

[0070] Figure 6 Optimization effect diagram for parameter adjustment. DETAILED DESCRIPTION

[0071] The present invention will be further described below with reference to the accompanying drawings, but the scope of protection of the present invention should not be limited thereto.

[0072] The present invention provides a small disturbance stability analysis method for a multi-converter system based on a discrete state space model. Figure 1 The topology diagram of a multi-converter system suitable for this method is shown in Figure 1. Without loss of generality, the diagram contains m converters, where converters 1 through k are current source converters and converters k+1 through m are voltage source converters. Some components of the network subsystem can be equivalent to RLC branches.

[0073] The present invention is based on the discrete state space model of the multi-converter system small disturbance stability analysis method, the overall solution process is shown in Figure 2 , mainly including the following steps:

[0074] 1) Based on the numerical integral substitution idea of ​​the electromagnetic transient simulation program, the system is discretized and a discrete time-domain state-space model of the multi-converter system is constructed with the grid-connected port of the converter as the dividing point:

[0075] For the differential algebraic equations reflecting the dynamic characteristics of each component in the continuous domain, a linear processing method is used to construct its small disturbance continuous state space model, which can be specifically expressed as

[0076]

[0077] Where x is the continuous domain state variable of the element; u xy and i xy are the voltage and current components in the synchronous rotating reference frame respectively; Δ is a small perturbation of the variable; A c 、B c 、C c 、D c is the coefficient matrix related to the static operating point of the component.

[0078] For non-energy storage elements, their state space model is only described by the direct mapping relationship between their input variables and output variables (output equation), without dynamic equations.

[0079] The numerical integration method (trapezoidal integration method) commonly used in electromagnetic transient simulation is used to transform the above-mentioned continuous domain small disturbance model into a discrete time domain difference equation. By performing numerical integration substitution on the differential operator, the continuous time variable is converted into a discrete time series, thereby realizing the discretization of the system. The corresponding discrete state space model is obtained as follows:

[0080]

[0081] Where h is the discrete domain state variable of the element; Δt is the step size selected in the discrete process; A d 、B d 、C d 、D dis the discrete state space coefficient matrix. The conversion formula between it and the coefficient matrix in the continuous state space model is:

[0082]

[0083] According to the output equation of the discrete state space model shown in formula (2), the components can be represented by a Norton equivalent circuit. After discretization, the system-level model can be constructed quickly and efficiently without complex topological analysis due to the natural independence between discrete state variables. All components in the system are represented by the discrete domain model of formula (2), and we get Figure 1 The equivalent circuit of the multi-converter discrete domain model in is constructed. At the same time, the entire system is divided into a converter subsystem and a network subsystem with the grid-connected ports of each converter as the dividing line. The discretized models of each subsystem are established separately, where the grid-connected port node is the common node of the subsystems on both sides.

[0084] For the converter subsystem, a discrete state space model including filters and control links is established based on its dynamic characteristics. The converter is divided into grid-following converter and grid-forming converter according to the difference in control characteristics and synchronization mechanism. Figure 3 There are two types of topological structures of converters. Among them, the grid-following converter detects the grid voltage phase angle through a phase-locked loop to achieve synchronous operation, and its external port characteristics are manifested as current source characteristics; the grid-building converter adopts a power synchronization control strategy similar to that of the synchronous motor, and its external port characteristics are manifested as voltage source characteristics. Based on the above characteristics, in the modeling process of the converter subsystem, the external port characteristics of the converter are mathematically described, and its equivalent input and output variables are mixed variables, specifically including a combination of voltage and current. The overall model of the subsystem will be constructed by combining the discrete state space models of each converter element, and the coefficient matrix part is represented in block diagonal form, that is,

[0085]

[0086] For the network subsystem, which includes connecting components such as lines and transformers, the discrete state space models of each component can also be combined and constructed in sequence. The coefficient matrix is ​​represented in block diagonal form. The difference is that the input and output variables corresponding to the obtained block diagonal coefficient matrix of this subsystem are the branch voltage and current variables of each component, which can be expressed as follows:

[0087]

[0088] Where h N is a column vector containing all discrete state variables in the network subsystem; u N and i N are the branch voltage and current variables of each component; u hNis the branch voltage variable of each dynamic element.

[0089] According to Kirchhoff's voltage law and combined with the node analysis method, a subsystem discrete state space model is constructed to eliminate the voltage and current inside the network subsystem while retaining the voltage and current variables of the grid-connected port node, namely:

[0090]

[0091] Where u p,N and i p,N A is the voltage and current variables of the grid-connected port node of the converter; D,N 、B D,N 、C D,N 、D D,N is the coefficient matrix of the subsystem model, and the specific solution expression is:

[0092]

[0093] Where M nb is the node-branch association matrix; M nh is the node-dynamic branch association matrix; M np is the node-port association matrix, port is the grid-connected port of the converter, M np The unit matrix is ​​present only at the nodes corresponding to the grid-connected ports, and the rest of the values ​​are zero.

[0094] 2) Combined with Kirchhoff's law, according to the algebraic relationship of the port variables, the discrete time domain state equation of the whole system is established to obtain the corresponding discrete domain mode of the system:

[0095] Using matrix transformation, the discrete state space model of the converter subsystem is transformed into:

[0096]

[0097] Among them, the expression of the new coefficient matrix is:

[0098]

[0099] Where A D,A1 、B D,A1 、C D,A1 and D D,A1 A is the part of the coefficient matrix of the original model corresponding to the converter whose external port characteristic is a current source; D,A2 、B D,A2 、C D,A2 and D D,A2 The part of the coefficient matrix of the original model corresponding to the converter whose external port characteristic is a voltage source.

[0100] When there is no external disturbance in the system, the port voltages corresponding to the subsystems on both sides are equal, and the port currents are equal in magnitude and opposite in direction. According to this algebraic constraint relationship, the redundant variables in the entire system can be eliminated, and the discrete time domain state equation of the entire system can be obtained, namely:

[0101]

[0102] Based on the above-mentioned discrete time-domain state equation of the whole system, the state matrix is ​​decomposed into eigenvalues ​​to solve the discrete domain mode of the system.

[0103] 3) Transform the subsystem state space model to build an equivalent system discrete frequency domain model based on the closed-loop feedback relationship between the port input and output:

[0104] Using matrix transformation, the discrete state space model of the network subsystem is transformed into:

[0105]

[0106] The discrete time domain state space model of the subsystems on both sides is converted into a discrete frequency domain model. By performing Z transform on the discrete state equation, the transfer function matrix of the system is obtained as follows:

[0107]

[0108] Where z is the complex variable of Z transformation; I is the unit matrix; G A (z) and G N (z) are the equivalent discrete frequency domain models of the converter subsystem and the network subsystem, respectively, describing the relationship between the input and output variables in the frequency domain.

[0109] According to the coupling relationship between the input and output variables of the subsystems on both sides, a closed-loop feedback equivalent model is established to obtain Figure 1 The multi-converter system in the figure has an equivalent multi-input and multi-output relationship, and its equivalent open-loop transfer function is:

[0110] L(z)=G N (z)G A (z) (13)

[0111] 4) Substitute the previously identified system modal values ​​and, using the chain rule, calculate the system modal changes caused by the control parameter disturbance of the key equipment converter, i.e., the parameter-modal sensitivity:

[0112] Focus on identifying the weakly damped / negatively damped modes in the discrete domain mode of the system and further conduct modal analysis. Parameter disturbances will eventually affect the system modal characteristics through step-by-step transmission. Figure 4The chain rule shown can establish the sensitivity relationship between the system modal values ​​and the key converter control parameters that affect the system dynamic characteristics. The specific steps are as follows:

[0113] a) Calculate the sensitivity of the converter element impedance / admittance to the control parameter ρ, which can be approximately expressed as

[0114]

[0115] Where k is the kth converter; ρ+Δρ represents the result when the parameters are changed.

[0116] b) Calculate the sensitivity of the system equivalent transfer function model to the converter components. According to the block diagonal characteristics of the coefficient matrix of the discrete state space model on the converter subsystem side, G A (z) is also a block diagonal matrix, Y k Transformations only affect the elements at their corresponding positions.

[0117]

[0118] c) Calculate the eigenvalue λ z The sensitivity of the system equivalent transfer function model is:

[0119]

[0120] Where adj[·] is the adjoint matrix; det'[·] is the first-order derivative of the determinant. The specific calculation expression is:

[0121]

[0122] d) Combining the above calculation results, the parameter-modal sensitivity is obtained by using the chain rule and further normalized:

[0123]

[0124] 5) Based on the discrete modes of the original system and the parameter-modal sensitivity results, determine the adjustment direction of parameter optimization:

[0125] Analyze the sensitivity results obtained in the previous step, sort them according to the absolute values ​​of the normalized parameter-modal sensitivity values, and identify the key control parameters that have the greatest impact on the system mode.

[0126] According to the vector geometry relationship, when the parameter-modal sensitivity vector is equal to the original mode λ z When the vector angle in the complex plane is acute, it means that increasing the parameter value will cause the analyzed mode to move toward a larger amplitude, which means that the stability will further deteriorate. Conversely, the stability can be optimized. Therefore, the direction of parameter adjustment can be clearly determined based on the stability requirements.

[0127] The following simulation examples are used to further illustrate the effect of the method proposed in the present invention. The topology of the multi-converter grid-connected system is as follows: Figure 1 As mentioned above, it includes 3 current source converters and 1 voltage source converter, and the network subsystem adopts the classic four-machine and two-area connection network topology, including transformers, traditional loads and transmission lines.

[0128] By calculating the sensitivity of each converter's control parameters to the system's dominant discrete mode, the key control parameters of the dominant device are analyzed. The parameter-modal sensitivity results are as follows: Figure 5 As shown, according to the amplitude of the sensitivity vector, it can be judged that by changing the parameter size to the same extent, the damping coefficient D of the grid-type converter p , reactive power loop integral coefficient k iQ , voltage loop proportional integral coefficient k pV and k iV , current loop proportional coefficient k pI The influence on the mode is greater than that of other control parameters, while reducing the virtual inertia coefficient J p , current loop integral coefficient k iI And the voltage loop integral coefficient k iV Or increase and increase other controls are conducive to the optimization of the stability performance of the dominant mode. Taking the voltage loop proportional coefficient as an example, increase its parameter value and decrease its parameter value respectively, inject a small disturbance into the system at 2s, and observe the time domain waveform of the three-phase current at the port as shown in the figure below: Figure 6 As shown, increasing the voltage loop proportional coefficient is beneficial to stability optimization. After the same disturbance, the time it takes to recover to the pre-disturbance state is shorter than before the modification. However, decreasing the voltage loop proportional coefficient degrades stability. After the disturbance, the system cannot recover to its pre-disturbance state and loses its stable operation state. This proves the reliability of the previous sensitivity analysis results. Experimental simulations demonstrate the effectiveness and feasibility of this method in small-disturbance stability analysis and optimization research of multi-converter systems.

Claims

1. A small disturbance stability analysis method for a multi-converter system based on a discrete state space model, characterized in that: The following steps are involved: 1) Based on the numerical integral substitution method of the electromagnetic transient simulation program, the continuous domain system model is discretized, and a discrete time-domain state-space model including the converter subsystem and the network subsystem is constructed with the converter grid-connected port as the dividing point; 2) Combining Kirchhoff's law and the algebraic relationship of the port variables, the discrete time domain state equation of the entire system is established, and the corresponding discrete domain mode of the system is obtained through eigenvalue decomposition; 3) Convert the discrete state space models of the converter subsystem and network subsystem into discrete frequency domain models, and build an equivalent discrete frequency domain model of the system based on the closed-loop feedback relationship between the port input and output; 4) Based on the system modal values ​​identified in step 2), combined with the chain rule, calculate the system modal changes caused by the control parameter disturbance of the key equipment converter, that is, the parameter-modal sensitivity; 5) Based on the discrete modes of the original system and the parameter-modal sensitivity results, determine the parameter adjustment direction to optimize the system stability.

2. The method for small-disturbance stability analysis of a multi-converter system based on a discrete state space model according to claim 1, characterized in that: The discretization process in step 1) includes: According to the dynamic characteristics of power system components in the continuous domain, a set of differential algebraic equations reflecting the dynamic behavior of the components is constructed, and a small-disturbance continuous state space model is obtained through linearization, which is expressed as: Where x is the continuous domain state variable of the element; u xy and i xy are the voltage and current components in the synchronous rotating reference frame respectively; Δ is a small perturbation of the variable; A c 、B c 、C c 、D c is the coefficient matrix related to the static operating point of the component; The trapezoidal integration method is used to transform the continuous domain small disturbance model into a difference equation in the discrete time domain. By performing numerical integration substitution on the differential operator, the continuous time variable is converted into a discrete time series, thereby realizing the discretization of the system and obtaining the corresponding discrete state space model, which is expressed as: Where h is the discrete domain state variable of the element; Δt is the step size selected in the discrete process; A d 、B d 、C d 、D d is the discrete state space coefficient matrix; the conversion formula between it and the coefficient matrix in the continuous state space model is: All components in the system are expressed using the discrete domain model of formula (2). At the same time, the entire system is divided into the converter subsystem and the network subsystem with the grid-connected ports of each converter as the dividing line. The discretized models of each subsystem are established separately, where the grid-connected port node is the common node of the subsystems on both sides. For the converter subsystem, a discrete state-space model including filters and control links is established based on its dynamic characteristics. Converters are divided into grid-following converters and grid-forming converters based on the differences in control characteristics and synchronization mechanisms. The grid-following converter detects the grid voltage phase angle through a phase-locked loop to achieve synchronous operation, and its external port characteristics are current source characteristics. The grid-forming converter adopts a power synchronization control strategy similar to that of a synchronous motor, and its external port characteristics are voltage source characteristics. The overall model of the subsystem is constructed by combining the discrete state space models of each converter component, and the coefficient matrix is ​​represented by a block diagonal form, that is, For the network subsystem, which includes connecting components such as lines and transformers, the discrete state space models of each component can also be combined and constructed in sequence. The coefficient matrix is ​​represented in block diagonal form. The difference is that the input and output variables corresponding to the obtained block diagonal coefficient matrix of this subsystem are the branch voltage and current variables of each component, which can be expressed as follows: Where h N is a column vector containing all discrete state variables in the network subsystem; u N and i N are the branch voltage and current variables of each component; u hN is the branch voltage variable of each dynamic element; According to Kirchhoff's voltage law and combined with the node analysis method, a subsystem discrete state space model is constructed to eliminate the voltage and current inside the network subsystem while retaining the voltage and current variables of the grid-connected port node, namely: Where u p,N and i p,N A is the voltage and current variables of the grid-connected port node of the converter; D,N 、B D,N 、C D,N 、D D,N is the coefficient matrix of the subsystem model, and the specific solution expression is: Where M nb is the node-branch association matrix; M nh is the node-dynamic branch association matrix; M np is the node-port association matrix, port is the grid-connected port of the converter, M np The unit matrix is ​​present only at the nodes corresponding to the grid-connected ports, and the rest of the values ​​are zero.

3. The method for small-disturbance stability analysis of a multi-converter system based on a discrete state space model according to claim 1, characterized in that: The establishment of the discrete time-domain state equation of the entire system in step 2) includes: Through matrix transformation, the discrete state space model of the converter subsystem is transformed into: Among them, the expression of the new coefficient matrix is: Where A D,A1 、B D,A1 、C D,A1 and D D,A1 A is the part of the coefficient matrix of the original model corresponding to the converter whose external port characteristic is a current source; D,A2 、B D,A2 、C D,A2 and D D,A2 The part of the coefficient matrix of the original model corresponding to the converter whose external port characteristic is a voltage source; When there is no external disturbance in the system, the port voltages corresponding to the subsystems on both sides are equal, and the port currents are equal in magnitude and opposite in direction. Based on this algebraic constraint relationship, the redundant variables within the entire system are eliminated, and the discrete time domain state equation of the entire system is obtained, namely: Based on the above-mentioned discrete time-domain state equation of the whole system, the state matrix is ​​decomposed into eigenvalues ​​to solve the discrete domain mode of the system.

4. The method for small-disturbance stability analysis of a multi-converter system based on a discrete state space model according to claim 1, characterized in that: The specific content of the step 3) is: Using matrix transformation, the discrete state space model of the network subsystem is transformed into: The discrete time domain state space model of the subsystems on both sides is converted into a discrete frequency domain model. By performing Z transform on the discrete state equation, the transfer function matrix of the system is obtained as follows: Where z is the complex variable of Z transformation; I is the unit matrix; G A (z) and G N (z) are equivalent discrete frequency domain models representing the converter subsystem and the network subsystem, describing the relationship between input and output variables in the frequency domain; According to the coupling relationship between the input and output variables of the subsystems on both sides, a closed-loop feedback equivalent model is established, and its equivalent open-loop transfer function is: L(z)=G N (z)G A (z) (13)。 5. The method for small-disturbance stability analysis of a multi-converter system based on a discrete state space model according to claim 1, characterized in that: The calculation of the parameter-modal sensitivity in step 4) includes: S4.1 Calculate the sensitivity of the converter element impedance / admittance to the control parameter ρ, which can be approximately expressed as: Where k is the kth converter; ρ+Δρ represents the result when the parameters are changed; S4.2 Calculate the sensitivity of the system equivalent transfer function model to the converter components using the following formula: Where G A (z) is a block diagonal matrix; G A,ij (z) represents G A The element in row i and column j of (z); It means partial differential. S4.3 Calculate the eigenvalue λ z The sensitivity of the system equivalent transfer function model is as follows: Where adj[·] is the adjoint matrix; det'[·] is the first-order derivative of the determinant. The specific calculation expression is: S4.4 uses the chain rule to obtain the parameter-modal sensitivity and perform normalization: .

6. The method for small-disturbance stability analysis of a multi-converter system based on a discrete state space model according to claim 1, characterized in that: The parameter optimization direction determination in step 5) includes: Analyze the sensitivity results obtained in step 4), sort them according to the absolute values ​​of the normalized parameter-modal sensitivity values, and identify the key control parameters that have the greatest impact on the system mode; According to the vector geometry relationship, when the parameter-modal sensitivity vector is equal to the original mode λ z When the vector angle in the complex plane is acute, it means that increasing the parameter value will move the analyzed mode toward a larger amplitude, which means that the stability will be further deteriorated. Conversely, the stability can be improved. Therefore, the direction of parameter adjustment can be clearly determined based on the stability requirements. If the optimization effect does not meet your expectations, repeat the above steps and adjust the parameters until the system stability requirements are met.

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