A method for global small-signal modeling and stability analysis of power electronic-based power systems based on instantaneous complex frequency

Abstract

The application discloses a kind of global small signal modeling and stability analysis method of power electronic power system based on instantaneous complex frequency.The method first obtains system topology and equipment parameters to calculate steady-state operating point;Second, introduce the instantaneous complex frequency including amplitude-frequency strong coupling characteristics, the algebraization of main circuit differential equation is linearized and the circuit small signal model is constructed at steady-state point, and the small signal model of control link is obtained;Then, using single machine closed loop matrix and inter-node coupling matrix, the global small signal state matrix of whole system is assembled by block, seamless coupling of main circuit and control model is realized;Finally, the dominant eigenvalue is extracted to determine the global stability, and the complex frequency dynamic interaction accountability coefficient is calculated by combining the eigenvector and the benchmark normalization limit, and the system parameters are quantified and accountable.The application completely gets rid of the barrier of traditional global dq coordinate transformation, and realizes efficient modeling and accurate engineering quantification accountability of high-dimensional multi-machine system.

Description

Technical Field

[0001] This invention relates to the field of power system modeling and operation control technology, and in particular to a method for global small-signal modeling and stability analysis of power electronic power systems based on instantaneous complex frequency. Background Technology

[0002] With the large-scale grid connection of new energy sources, the power system is rapidly evolving towards a direction dominated by power electronic devices such as voltage source converters (VSCs). The low inertia and fast response characteristics of the system make the dynamic interaction and coupling mechanisms of multiple converters operating in parallel increasingly complex.

[0003] For stability analysis of multi-machine systems, existing technologies mostly rely on the traditional small-signal state-space method based on the dq coordinate system. However, when dealing with highly power electronic systems, they face the following significant limitations:

[0004] 1. Cumbersome global modeling and neglect of amplitude-frequency coupling characteristics: Traditional methods, in order to construct a complete system model, must map the "local dq coordinate system" of all parallel devices to a "global common coordinate system" through complex rotational coordinate transformations. This process introduces a large number of nonlinear trigonometric function coupling terms, leading to a sharp increase in model dimensionality and extremely cumbersome derivation. At the same time, the traditional concept of frequency is based on the "quasi-steady state" assumption, decoupling the analysis of frequency and voltage amplitude, making it difficult to fully describe the transient characteristics of "strong amplitude-frequency coupling" within a very short time scale under a unified system.

[0005] 2. Bottlenecks exist in high-precision detection of dynamic signals: Traditional detection methods often use phase-locked loops (PLLs) or frequency-locked loops (FLLs), whose closed-loop structures inevitably introduce filtering delays and phase lags; if discrete differences are used directly in digital microprocessors to approximate differential operations, it will introduce huge truncation errors and amplify high-frequency noise, making it difficult for detection accuracy to support high-dimensional fine modeling.

[0006] 3. Lack of quantitative engineering methods for attributing responsibility in instability tracing: When instability occurs in a multi-machine system, traditional methods often use "participation factors" or conventional sensitivity analysis to find the dominant state variables. However, the dimensions and orders of magnitude of physical parameters (such as extremely small line inductance) and control parameters (such as large virtual inertia) within the system differ greatly. Directly using traditional sensitivity analysis will lead to the "curse of dimensions," easily resulting in erroneous conclusions that violate common sense physics. This fails to provide power grid dispatch with accurate quantitative methods for attributing responsibility based on actual engineering boundaries.

[0007] In summary, how to break through the barriers of traditional dq coordinate system transformation and the constraints of the quasi-steady-state frequency concept, establish a unified high-precision modeling system to represent strong amplitude-frequency coupling, and provide a precise instability source tracing method with engineering physical significance is an urgent problem to be solved in the field of new power system stability. Summary of the Invention

[0008] The technical problem to be solved by this invention is to provide a precise instability tracing method with engineering and physical significance to address the shortcomings of the prior art, break through the barriers of traditional dq coordinate system transformation and the constraints of the concept of quasi-steady-state frequency, and establish a high-precision modeling system that uniformly represents strong amplitude-frequency coupling.

[0009] To solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0010] First, this invention proposes a method for global small-signal modeling and stability analysis of power electronic power systems based on instantaneous complex frequencies, comprising the following steps:

[0011] S1. Obtain the topology, equipment physical parameters, and control parameters of the power electronic power system, and calculate the steady-state operating point of the system under the current operating conditions;

[0012] S2. Introducing instantaneous complex frequency, establishing the differential equation of the main circuit based on the topology, and using the properties of instantaneous complex frequency to transform the differential equation into an algebraic equation containing instantaneous complex frequency, and performing small-signal linearization at the steady-state operating point to construct a circuit small-signal model reflecting the electrical characteristics of the network; the instantaneous complex frequency is a complex physical quantity defined by the time derivative operation of any three-phase AC electrical quantity, the real part of which represents the instantaneous angular frequency, and the imaginary part of which represents the negative of the relative rate of change of the instantaneous amplitude;

[0013] S3. Based on the controller structure of the power electronic equipment, establish the time-domain differential equation of the control link, and perform linearization processing at the steady-state operating point to obtain the small-signal model of the control link.

[0014] S4. Couple the circuit small-signal model with the control loop small-signal model, eliminate intermediate variables and select system state variables, construct the global small-signal state space expression of the whole system, and extract the corresponding system feature matrix.

[0015] S5. Perform eigenvalue decomposition on the system feature matrix, extract the dominant eigenvalues ​​whose real part is closest to the right half of the complex plane, and combine the dominant eigenvalues ​​with the feature drift sensitivity of each device parameter and the reference normalization limit of the parameters to calculate the complex frequency dynamic interaction responsibility coefficient of each device parameter in the system.

[0016] S6. Based on the aforementioned complex frequency dynamic interaction responsibility coefficient, perform stability mechanism analysis and quantitative responsibility determination on the power electronic power system to accurately trace the main sources of responsibility and the supporting factors for stability that lead to system instability.

[0017] Furthermore, the power electronic power system is a VSC multi-machine system, which is a complex variable for any three-phase AC electrical quantity. Its instantaneous complex frequency The calculation formula is:

[0018] ,

[0019] Where j represents an imaginary number and t represents time.

[0020] Furthermore, the process of constructing a small-signal circuit model reflecting the electrical characteristics of the network includes:

[0021] Based on the topology of multiple VSCs connected to a common load or power grid system via transmission lines, establish the first Differential equations for the circuit topology of a virtual synchronous converter (VSC):

[0022] ,

[0023] Using the definition of instantaneous complex frequency, divide both sides of the equation by... Regarding time Differentiate and introduce the instantaneous complex frequency of voltage. The instantaneous complex frequency of the current is obtained. The dynamic evolution equation of the derivative:

[0024] ,

[0025] Linearizing the above dynamic evolution equations at the steady-state point yields the equation regarding the instantaneous complex frequency deviation of the current. The circuit-side linearized small-signal model:

[0026] ,

[0027] in, For transmission line resistance, For inductance, It is the common load impedance. It is the current frequency. Steady-state node voltage, Steady-state branch current.

[0028] Furthermore, obtaining the small-signal model of the control loop includes obtaining the small-signal model of the active power outer loop controller, the steps of which are as follows:

[0029] Calculate the first Instantaneous complex power of VSC Regarding its time By differentiating and applying the properties of complex frequencies, we obtain the expression for the power derivative:

[0030] ,

[0031] Based on the active power controller structure, establish the active power controller output variables. The time-domain differential relationship between the actual output active power and the rated output active power:

[0032]

[0033] Substituting the power derivative expression into the time-domain differential relation and performing a linear expansion, we obtain the active power outer loop small-signal state equation:

[0034]

[0035] in This represents the damping coefficient of the k-th converter. This represents the virtual rotational inertia of the k-th converter. This represents the actual instantaneous complex power output of the k-th converter. Representing the The instantaneous complex power of the reference output of the converter.

[0036] Furthermore, obtaining the small-signal model of the control loop also includes obtaining the small-signal model of the reactive power outer loop controller, the steps of which are as follows:

[0037] Establish reactive power controller output variables Time-domain differential equations:

[0038] ,

[0039] By simultaneously combining the linearized reactive power deviation and voltage amplitude deviation terms, the small-signal linearized model of the reactive power outer loop controller is obtained:

[0040] ,

[0041] in, This represents the reactive voltage control integral gain of the k-th converter. This represents the reactive voltage droop factor. This represents the rated voltage amplitude.

[0042] Furthermore, the coupling of the circuit small-signal model with the control loop small-signal model to construct a global small-signal state-space expression for the entire system specifically includes the following matrix cascading and block assembly steps:

[0043] S401. Constructing a single-machine locally open-loop model matrix: For the first... A converter is used to extract its state variables to form a local state vector. Extract reference input variables to construct a local input vector. Extract the complex frequency variables of the output voltage to form a local output vector. After separating the real and imaginary parts, establish the first... Local open-loop small-signal model of the converter:

[0044] ,

[0045] in, To indicate the first The self-dynamic matrix of the electromagnetic dynamics of the converter. The local input matrix characterizes the effect of the control output on the local state. For the remaining parallel nodes, pair the first The overall coupled input vector of the converter, This is the corresponding coupling matrix;

[0046] S402. Construct the droop control output mapping matrix: Based on the small-signal model of the control loop, establish the algebraic mapping relationship between instantaneous complex power and instantaneous complex frequency of output voltage, and obtain the first... The control output equation of the converter:

[0047] ,

[0048] in, The state feedback matrix describes the influence of local state variables on the output complex frequency. The feedforward transfer matrix represents the effect of the reference power input on the system output.

[0049] S403. Construct the single-machine closed-loop state matrix: Substitute the control output equation into the local open-loop small-signal model to eliminate the local output vector. , obtained the Closed-loop state equations of the converter:

[0050] ,

[0051] in, For the first The single-unit closed-loop state matrix of the converter. This is the single-machine closed-loop input matrix;

[0052] S404. Assemble the global block state space matrix: Combine the state vectors and input vectors of all converters in the system to form the global state vector. and global input vector And construct the global block state space expression for the multi-machine system:

[0053] ,

[0054] Among them, the global state matrix The matrix is ​​a block matrix, and the submatrices on its main diagonal are the single-machine closed-loop state matrices corresponding to each converter. Its off-diagonal submatrix is ​​derived from the coupling matrix. The extracted inter-node coupling submatrix; the global input matrix. The single-machine closed-loop input matrix of each converter is used. It is a block diagonal matrix of diagonal blocks.

[0055] In the single-machine local open-loop model matrix and control output mapping matrix:

[0056] The local state vector This includes the deviation between the real and imaginary parts of the instantaneous complex frequency of the current, the deviation between the real and imaginary parts of the instantaneous complex power, and the internal state variables of the controller. ;

[0057] The local input vector The deviation between the real and imaginary parts of the reference complex power, i.e. ;

[0058] The local output vector The deviation between the real and imaginary parts of the instantaneous complex frequency of the voltage, i.e. ;

[0059] The overall coupled input vector It is composed of the cascaded deviations of the real and imaginary parts of the complex frequency of the output current of the other converters.

[0060] Furthermore, the specific process for calculating the complex frequency dynamic interaction liability coefficient in S5 is as follows:

[0061] S501. Extract the system feature matrix. The largest dominant eigenvalue of the middle real part and its corresponding left eigenvector With right eigenvector ;

[0062] S502, For specific physical or control parameters to be evaluated in the system. The partial derivative of the real part of the dominant eigenvalue with respect to this parameter is calculated to obtain the feature drift sensitivity, and its calculation formula is as follows:

[0063] ,

[0064] S503, Obtain the specific parameters Benchmark normalized limits And calculate the complex frequency dynamic interaction liability coefficient of this parameter. The calculation formula is:

[0065] ,

[0066] Wherein, the benchmark normalization limit This characterizes the limit or maximum reasonable drift range that the parameter can be set under the constraints of equipment hardware or grid connection standards.

[0067] Furthermore, the specific process of stability mechanism analysis and quantitative responsibility determination in S6 is as follows:

[0068] The system stability is quantitatively determined based on the sign and magnitude of the complex frequency dynamic interaction liability coefficient: if The change in this parameter was determined to exacerbate amplitude-frequency coupled oscillations on extremely short timescales, acting as a driving factor for instability. Furthermore, the device with the highest value in this parameter across the entire system was identified as the primary source of system instability. This parameter was determined to be a stabilizing factor for the system.

[0069] Secondly, the present invention also proposes an electronic device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the method described in the present invention.

[0070] The present invention adopts the above technical solution, and its technical effects compared with the prior art are as follows:

[0071] (1) By introducing instantaneous complex frequency in step S2 to algebraize the circuit differential equation, and by using the single-machine closed-loop matrix and the inter-node coupling matrix to assemble the global small-signal state matrix of the whole system in step S4, this invention completely gets rid of the dependence on global dq coordinate transformation and complex phase alignment in traditional multi-machine system modeling, and realizes efficient and modular modeling of high-dimensional multi-machine systems; (2) By combining characteristic drift sensitivity and benchmark normalization limit to calculate complex frequency dynamic interaction responsibility coefficient in step S5, this invention effectively overcomes the problem of huge differences in the dimensions of different parameters in traditional sensitivity analysis, and realizes accurate engineering quantitative responsibility and tracing of system instability responsibility source and stability support factor.

[0072] This invention completely breaks free from the barriers of traditional global dq coordinate transformation, enabling efficient modeling and accurate engineering quantitative responsibility assignment for high-dimensional multi-machine systems. Attached Figure Description

[0073] Figure 1 This is a flowchart of the small-signal modeling and stability analysis method proposed in this invention.

[0074] Figure 2 This is a schematic diagram of the physical topology of the power electronic power system to which this invention is addressed.

[0075] Figure 3 This is a typical control logic block diagram of a power electronic converter (taking virtual synchronous machine control as an example).

[0076] Figure 4 This is a diagram of the global block matrix assembly architecture of the multi-machine system of the present invention.

[0077] Figure 5 This is a bar chart of the complex frequency dynamic interaction responsibility coefficients of the system parameters of the present invention.

[0078] Figure 6 This is a comparison chart of the effects of traditional feature drift sensitivity and the complex frequency interaction determination coefficient of the present invention. Detailed Implementation

[0079] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0080] Example 1: Reference Figure 1 This invention provides a method for global small-signal modeling and stability analysis of power electronic power systems based on instantaneous complex frequency, which includes the following detailed implementation steps:

[0081] Step S1: Obtain system parameters and calculate steady-state operating point.

[0082] like Figure 2 As shown, the topology and line impedance parameters (such as transmission line resistance) of the target power electronic power system are obtained. ,inductance Common load impedance ), converter capacity and control parameters (such as virtual inertia) Damping coefficient (etc.). Steady-state electrical quantities of the system under current operating conditions are obtained through conventional power flow calculations or time-domain steady-state solutions, including steady-state node voltages. Steady-state branch current and the system steady-state synchronization angular frequency This serves as the reference operating point for subsequent small-signal linearization.

[0083] Step S2: Constructing a small-signal circuit model based on instantaneous complex frequency.

[0084] This step breaks through the traditional method. The coordinate system dependence allows for the direct establishment of the dynamic evolution equations of the main circuit in the complex domain.

[0085] For any complex variable of three-phase AC electrical quantity The formula for calculating its instantaneous complex frequency is:

[0086]

[0087] For a topology where multiple VSCs are connected to a common load via a transmission line, based on Kirchhoff's voltage / current law, the first... Differential equations for a converter:

[0088]

[0089] Using the definition of instantaneous complex frequency, divide both sides of the above equation by... Then check the time Find the derivative and introduce the instantaneous complex frequency of the voltage. It is possible to derive the complex frequency of the instantaneous current. The dynamic evolution equation of the derivative:

[0090]

[0091] The steady-state point obtained in step S1 (satisfying) Performing a small-signal perturbation linearization expansion on the above equation at point ) separates the steady-state quantity from the deviation quantity, yielding a result entirely based on the complex frequency deviation quantity. The circuit-side linearized small-signal model:

[0092]

[0093] Step S3: Construction of small signal model for control loop.

[0094] This step establishes the differential algebraic model of the converter's internal control logic. Taking VSG control as an example, the control block diagram is as follows: Figure 3 As shown, calculate the first... Instantaneous complex power of VSC Differentiating it and applying the property of complex frequency, we obtain the derivative expression of instantaneous complex power:

[0095]

[0096] The time-domain equations of the controller are linearized and expanded.

[0097] For the active outer loop: using the internal integral state quantity Taking the core as the starting point, we can expand upon it to obtain:

[0098]

[0099] For the reactive outer loop: using the internal integral state quantity Taking the core as the starting point, we can expand upon it to obtain:

[0100]

[0101] Step S4: Cascading and assembling the global small-signal state-space expressions of the entire system.

[0102] This step is the core and key aspect of this invention. In traditional methods, constructing the global matrix requires introducing a phase angle deviation matrix. and extremely complex global coordinate transformation matrices This is to forcibly align the parallel converters. However, under the "instantaneous complex frequency" framework proposed in this invention, since the complex frequency itself already contains unified dynamic information, no common coordinate system mapping is required. Figure 4 As shown, this invention employs a standardized "partial open loop" approach. Control closed loop The "global assembly" matrix cascading technology significantly improves model building efficiency. The specific implementation process is detailed below:

[0103] S401. Constructing a single-machine local open-loop model matrix

[0104] Extract the first For all independent microvariables in the operation of the converter, the standardized interface vector must first be defined:

[0105] Local state vector : Including the inherent states of the main circuit and controller, i.e. ;

[0106] Local input vector This refers to the deviation of the external reference control command. ;

[0107] Local output vector Since the converter behaves as a controlled voltage source, its final output physical quantity is reflected in the change of complex voltage frequency. Therefore, an output vector is defined. ;

[0108] Globally coupled input vector : Consisting of all other related nodes ( The complex frequency of the output current is formed by cascading the real and imaginary parts.

[0109] Based on the above interface, the real and imaginary parts of the circuit model in S2 and the control model in S3 are separated to construct a unified local open-loop small-signal model:

[0110]

[0111] Among them, the self-dynamic matrix Characterizing the local eigenvalue evolution of the converter in the absence of output voltage feedback closed loop; local input matrix Characterizing the physical driving effect of instantaneous complex frequency fluctuations in output voltage on the internal current and power state of the converter; coupling matrix. This represents the network admittance matrix in the complex frequency domain, characterizing the physical intrusion effect of transient currents from other nodes crossing the common impedance on this node.

[0112] S402. Construct the droop control output mapping matrix.

[0113] The droop control small-signal model is rearranged into algebraic equations:

[0114] ,

[0115] Among them, the state feedback matrix A control gain network characterizing the mapping of state variables (such as instantaneous power deviation and PI integral state) to the complex frequency of the output voltage; feedforward transfer matrix Characterizes the direct transfer mapping from external reference commands to output physical quantities.

[0116] S403, Construct the single-machine closed-loop state matrix

[0117] A physical converter is a self-contained closed-loop system whose controller directly drives the main circuit. The control mapping equation (i.e., vector...) is... Substituting the expression into the open-loop model, local output vectors are hidden using algebraic elimination. , obtained the Closed-loop state equations of the converter:

[0118]

[0119] definition This is the closed-loop state matrix for a single machine. This is the single-machine closed-loop input matrix. The matrix fully encompasses the self-feedback closed-loop characteristics of the single device, which consists of the control parameters and internal physical parameters. Its eigenvalues ​​determine the single-machine stability domain of the device during grid-connected operation.

[0120] S404, Assemble the global block state space matrix

[0121] Concatenate the local states of all parallel devices in the system into a unified dimension: Define a global state vector. Global input vector Then, the global state-space expression of the multi-machine system is assembled according to the block-based principle:

[0122]

[0123] Global state matrix The structure clearly reflects the physical topology of the system: its main diagonal... Each sub-matrix perfectly corresponds to the single-machine closed-loop state matrix of each converter. And its off-diagonal submatrices Then, by directly matching the source node and target node numbers, the coupling matrix mentioned above can be used to determine the coupling effect. Extract and fill in the columns.

[0124] Global input matrix This is based on the closed-loop input matrices of each individual machine. It is a block diagonal matrix of diagonal blocks.

[0125] Through the above matrix operations, this invention successfully avoids the forced global solution based on the system of calculus equations, transforming complex multi-machine modeling into a low-level standard matrix. The linear algebraic splicing of ) makes the system expansion extremely flexible and greatly reduces the dimensionality and memory overhead when solving the problem by computer.

[0126] Step S5: Feature root extraction and calculation of complex frequency dynamic interaction liability coefficient.

[0127] This step, based on the completed global state-space expression, uses eigenvalue analysis and creatively integrates equipment physical tolerances and control constraints to calculate the interactive liability coefficient that eliminates dimensional differences. The specific implementation process is as follows:

[0128] S501. Extract dominant feature roots and feature vectors.

[0129] For the characteristic matrix of the whole system Perform eigenvalue decomposition. If there exists an eigenvalue with a real part greater than or equal to zero, it is determined that the current system cannot resolve itself after a small disturbance and is at risk of instability. Extract the eigenvalue with the largest real part (i.e., closest to the right half of the complex plane, dominating the divergence or oscillation trend of the system) from all eigenvalues ​​as the "dominant eigenvalue". "and simultaneously extract its corresponding left feature vector With right eigenvector .

[0130] S502, Calculate the characteristic drift sensitivity

[0131] For specific physical or control parameters to be evaluated in a multi-machine system (e.g., line inductance) Sag coefficient Virtual inertia (etc.), calculate the partial derivative of the real part of the dominant eigenvalue with respect to this parameter, and obtain the "feature drift sensitivity". Its mathematical formula is:

[0132]

[0133] In the practical engineering implementation of computer programs, to avoid the extremely complex global matrix notation differentiation, the partial derivative can be obtained with respect to specific parameters. A high-precision approximate solution is obtained by applying a central difference method with a small numerical perturbation.

[0134] S503, Introduce a benchmark normalization limit and calculate the complex frequency dynamic interaction liability coefficient.

[0135] Traditional sensitivity analysis directly compares different parameters Because physical parameters such as inductance differ greatly in dimensions and orders of magnitude from control parameters such as inertia, severe "curse of dimensions" and misjudgments can easily occur. Therefore, this embodiment configures a "benchmark normalization limit" for each parameter being evaluated. "" represents the maximum allowable span or maximum reasonable drift range of this parameter under the conditions of meeting the equipment hardware withstand voltage and overcurrent constraints and grid connection standards and specifications.

[0136] Combining the aforementioned characteristic drift sensitivity and benchmark normalization limit, the "complex frequency dynamic interaction liability coefficient" of this parameter is calculated. ":

[0137]

[0138] The physical meaning of this formula lies in: utilizing The sensitivity of pure mathematics is transformed into physical destructive force that conforms to actual engineering constraints, and percentage normalization is performed by summing the absolute values ​​of the entire system. The calculated... It intuitively and quantitatively reflects the absolute contribution of specific parameters to the shift of the dominant eigenvalue to the right half-plane.

[0139] Step S6: Stability mechanism analysis and system quantitative responsibility determination.

[0140] This step is based on the complex frequency dynamic interaction liability coefficient calculated in step S5. This involves in-depth stability mechanism analysis and instability source attribution for power electronic power systems. The specific analysis and application logic is as follows:

[0141] When the liability coefficient of a specific parameter The value of this parameter indicates that an increase in its value will drive the dominant characteristic root of the system to move to the right half-plane. From the perspective of instantaneous complex frequency mechanism, this shows that the change in this parameter exacerbates the "strong amplitude-frequency coupled oscillation" on an extremely short time scale, weakens the damping level of the system, and is identified as an "instability driving factor".

[0142] When the liability coefficient of a specific parameter When the value is positive, it indicates that the parameter has a pulling effect on the movement of the characteristic root to the left half-plane, and it is determined to be a "system stability support factor". The more negative the value, the stronger the positive damping effect of the parameter on smoothing the complex frequency (i.e., smoothing the synchronous and violent fluctuations of the frequency and voltage amplitude) under the current operating conditions.

[0143] like Figure 6 As shown, when tracing the source of an unstable system, if traditional pure mathematical partial derivatives are used, the sensitivity values ​​will be extremely distorted (resulting in a 'dimensional catastrophe') due to the different physical meanings of the system parameters, thus erroneously masking the true cause of instability. However, by using the complex frequency dynamic interactive liability determination coefficient proposed in this invention, and by introducing a benchmark normalization limit for correction of engineering physical scale, the true destructive force / support force weights of each system parameter are successfully restored, and the actual control equipment and its parameters that caused the instability are accurately identified. This demonstrates the outstanding engineering value of this invention in determining liability for on-site accidents.

[0144] In summary, this embodiment fully leverages the inherent advantage of instantaneous complex frequency in avoiding global coordinate rotation, utilizes an efficient matrix assembly architecture to achieve dimensionality reduction and decoupling of small-signal models in multi-machine high-dimensional systems, and provides engineering quantitative responsibility indicators that directly guide on-site dispatching based on this, thus providing a complete theoretical system and implementation path for ensuring the stability of power electronic power systems.

[0145] Example 2: This example proposes an electronic device, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the method described in this invention.

[0146] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention can be implemented using various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0147] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0148] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0149] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0150] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

Claims

1. A method for global small-signal modeling and stability analysis of power electronic power systems based on instantaneous complex frequency, characterized in that, Includes the following steps: S1. Obtain the topology, equipment physical parameters, and control parameters of the power electronic power system, and calculate the steady-state operating point of the system under the current operating conditions; S2. Introducing instantaneous complex frequency, establishing the differential equation of the main circuit based on the topology, and using the properties of instantaneous complex frequency to transform the differential equation into an algebraic equation containing instantaneous complex frequency, and performing small-signal linearization at the steady-state operating point to construct a circuit small-signal model reflecting the electrical characteristics of the network; the instantaneous complex frequency is a complex physical quantity defined by the time derivative operation of any three-phase AC electrical quantity, the real part of which represents the instantaneous angular frequency, and the imaginary part of which represents the negative of the relative rate of change of the instantaneous amplitude; S3. Based on the controller structure of the power electronic equipment, establish the time-domain differential equation of the control link, and perform linearization processing at the steady-state operating point to obtain the small-signal model of the control link. S4. Couple the circuit small-signal model with the control loop small-signal model, eliminate intermediate variables and select system state variables, construct the global small-signal state space expression of the whole system, and extract the corresponding system feature matrix. S5. Perform eigenvalue decomposition on the system feature matrix, extract the dominant eigenvalues ​​whose real part is closest to the right half of the complex plane, and combine the dominant eigenvalues ​​with the feature drift sensitivity of each device parameter and the reference normalization limit of the parameters to calculate the complex frequency dynamic interaction responsibility coefficient of each device parameter in the system. S6. Based on the aforementioned complex frequency dynamic interaction responsibility coefficient, perform stability mechanism analysis and quantitative responsibility determination on the power electronic power system to achieve accurate tracing of the main responsibility sources and stabilizing support factors that lead to system instability.

2. The method according to claim 1, characterized in that, The power electronic power system is a VSC multi-machine system, which is a complex variable for any three-phase AC electrical quantity. Its instantaneous complex frequency The calculation formula is: ， Where j represents an imaginary number and t represents time.

3. The method according to claim 1, characterized in that, The process of constructing a small-signal circuit model that reflects the electrical characteristics of the network includes: Based on the topology of multiple VSCs connected to a common load or power grid system via transmission lines, establish the first Differential equations for the circuit topology of a virtual synchronous converter (VSC): ， Using the definition of instantaneous complex frequency, divide both sides of the equation by... Regarding time Differentiate and introduce the instantaneous complex frequency of voltage. The instantaneous complex frequency of the current is obtained. The dynamic evolution equation of the derivative: ， Linearizing the above dynamic evolution equations at the steady-state point yields the equation regarding the instantaneous complex frequency deviation of the current. The circuit-side linearized small-signal model: ， in, For transmission line resistance, For inductance, It is the common load impedance. It is the current frequency. Steady-state node voltage, Steady-state branch current.

4. The method according to claim 3, characterized in that, The process of obtaining the small-signal model of the control loop includes obtaining the small-signal model of the active power outer loop controller, and the steps are as follows: Calculate the first Instantaneous complex power of VSC Regarding its time By differentiating and applying the properties of complex frequencies, we obtain the expression for the power derivative: ， Based on the active power controller structure, establish the active power controller output variables. The time-domain differential relationship between the actual output active power and the rated output active power: ， Substituting the power derivative expression into the time-domain differential relation and performing a linear expansion, we obtain the active power outer loop small-signal state equation: ， in This represents the damping coefficient of the k-th converter. This represents the virtual rotational inertia of the k-th converter. This represents the actual instantaneous complex power output of the k-th converter. Representing the The instantaneous complex power of the reference output of the converter.

5. The method according to claim 3, characterized in that, The process of obtaining the small-signal model of the control loop also includes obtaining the small-signal model of the reactive power outer loop controller, and the steps are as follows: Establish reactive power controller output variables Time-domain differential equations: ， By simultaneously combining the linearized reactive power deviation and voltage amplitude deviation terms, the small-signal linearized model of the reactive power outer loop controller is obtained: ， in, This represents the reactive voltage control integral gain of the k-th converter. This represents the reactive voltage droop factor. This represents the rated voltage amplitude.

6. The method according to any one of claims 4 or 5, characterized in that, The coupling of the circuit small-signal model with the control loop small-signal model to construct a global small-signal state-space expression for the entire system specifically includes the following matrix cascading and block assembly steps: S401. Constructing a single-machine locally open-loop model matrix: For the first... A converter is used to extract its state variables to form a local state vector. Extract reference input variables to construct a local reference input vector. Extract the complex frequency variables of the output voltage to form a local output vector. After separating the real and imaginary parts, establish the first... Local open-loop small-signal model of the converter: ， in, To indicate the first The self-dynamic matrix of the electromagnetic dynamics of the converter. The local input matrix characterizes the effect of the control output on the local state. For the remaining parallel nodes, pair the first The overall coupled input vector of the converter, This is the corresponding coupling matrix; S402. Construct the droop control output mapping matrix: Based on the small-signal model of the control loop, establish the algebraic mapping relationship between instantaneous complex power and instantaneous complex frequency of output voltage, and obtain the first... Control output equations of the converter: ， in, The state feedback matrix describes the influence of local state variables on the output complex frequency. The feedforward transfer matrix represents the effect of the reference power input on the system output. S403. Construct the single-machine closed-loop state matrix: Substitute the control output equation into the local open-loop small-signal model to eliminate the local output vector. , obtained the Closed-loop state equations of the converter: ， in, For the first The single-unit closed-loop state matrix of the converter. This is the single-machine closed-loop input matrix; S404. Assemble the global block state space matrix: Combine the state vectors and input vectors of all converters in the system to form the global state vector. and global input vector And construct the global block state space expression for the multi-machine system: ， Among them, the global state matrix The matrix is ​​a block matrix, and the submatrices on its main diagonal are the single-machine closed-loop state matrices corresponding to each converter. Its off-diagonal submatrix is ​​derived from the coupling matrix. The extracted inter-node coupling submatrix; the global input matrix. The single-machine closed-loop input matrix of each converter is used. It is a block diagonal matrix of diagonal blocks.

7. The method according to claim 6, characterized in that, In the single-machine local open-loop model matrix and control output mapping matrix: The local state vector This includes the deviation between the real and imaginary parts of the instantaneous complex frequency of the current, the deviation between the real and imaginary parts of the instantaneous complex power, and the internal state variables of the controller. ; The local input vector The deviation between the real and imaginary parts of the reference complex power, i.e. ; The local output vector The deviation between the real and imaginary parts of the instantaneous complex frequency of the voltage, i.e. ; The overall coupled input vector It is composed of the cascaded deviations of the real and imaginary parts of the complex frequency of the output current of the other converters.

8. The method according to claim 1, characterized in that, The specific process for calculating the complex frequency dynamic interaction liability coefficient in S5 is as follows: S501. Extract the system feature matrix. The largest dominant eigenvalue of the middle real part and its corresponding left eigenvector With right eigenvector ; S502, For specific physical or control parameters to be evaluated in the system. The partial derivative of the real part of the dominant eigenvalue with respect to this parameter is calculated to obtain the feature drift sensitivity, and its calculation formula is as follows: ， S503, Obtain the specific parameters Benchmark normalized limits And calculate the complex frequency dynamic interaction liability coefficient of this parameter. The calculation formula is: ， Wherein, the benchmark normalization limit This characterizes the limit or maximum reasonable drift range that the parameter can be set under the constraints of equipment hardware or grid connection standards.

9. The method according to claim 1, characterized in that, The specific process of stability mechanism analysis and quantitative responsibility determination in S6 is as follows: The system stability is quantitatively determined based on the sign and magnitude of the complex frequency dynamic interaction liability coefficient: if The change in this parameter was determined to exacerbate amplitude-frequency coupled oscillations on extremely short timescales, acting as a driving factor for instability. Furthermore, the device with the highest value in this parameter across the entire system was identified as the primary source of system instability. This parameter was determined to be a stabilizing factor for the system.

10. An electronic device, comprising: At least one processor; And a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, characterized in that the instructions are executed by the at least one processor to enable the at least one processor to perform the method according to any one of claims 1-9.

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