Virtual impedance compensation method for permanent magnet synchronous generator constant admittance modeling

Abstract

The invention discloses a virtual impedance compensation method for permanent magnet synchronous generator constant admittance modeling, and relates to the technical field of electromagnetic transient modeling of permanent magnet synchronous generators, and the method comprises the steps: firstly, carrying out the discretization of a permanent magnet synchronous generator model; secondly, decomposing the equivalent resistance matrix into a time-invariant part and a time-varying part; then, virtual impedance is added to the q axis of the generator model; thirdly, constructing a generator constant admittance model; thirdly, a converter accompanying discrete circuit model is integrated, a complete permanent magnet synchronous generator constant admittance model is formed, and a node admittance equation is established based on the Kirchhoff's current law; and finally, executing electromagnetic transient simulation. According to the method, constant admittance modeling is achieved based on virtual impedance compensation, the requirement for real-time inversion of a time-varying admittance matrix is eliminated, simulation calculation resource consumption is remarkably reduced, small errors are kept under various working conditions, and efficient simulation of a large-scale permanent magnet synchronous generator system is supported.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic transient modeling technology for permanent magnet synchronous generators, and in particular to a virtual impedance compensation method for modeling constant admittance of permanent magnet synchronous generators. Background Technology

[0002] Against the backdrop of global efforts to address climate change and promote green development, the "dual carbon" goal has spurred energy sector transformation, leading to the rapid development of new energy power generation, the expansion of the development and utilization of clean energy sources such as wind and solar power, and the gradual construction of new power systems to achieve a clean and low-carbon energy transformation and improved utilization efficiency.

[0003] Among new energy power generation equipment, permanent magnet synchronous generators (PMSGs) have significant advantages. Traditional generators rely on gearboxes to change speed, which increases equipment complexity and maintenance costs. In contrast, PMSGs eliminate the gearbox and use full-power converters, making them better adaptable to complex wind speeds and improving power generation efficiency. They are widely used in new energy power generation in new power systems.

[0004] To study wind turbine operating characteristics, optimize control strategies, and improve power generation efficiency, various wind turbine simulation models have been developed using existing technologies. The mainstream model is based on coordinate transformation. dq Both the voltage-behind-reactance (VBR) simulation model and the phase domain (PD) simulation model are derived from the phase domain simulation model. The former converts the three-phase windings into phase domain (PD) simulation models through Parker transformation. dq The winding, which simplifies the mathematical model through coordinate transformation, is convenient for analyzing dynamic characteristics and is often used in electromagnetic transient programs; the latter simplifies the calculation based on the voltage and current relationship at the motor output end and can quickly process output characteristics, but it has limitations in handling large-scale wind farm simulations.

[0005] To achieve large-scale wind energy development, real-world wind farms require the installation of numerous wind turbines, which are widely distributed and have complex electrical connections. Detailed modeling and simulation analysis are indispensable for accurately simulating wind farm operation, assessing its impact on the power grid, and developing dispatch strategies. Traditional variable admittance matrix modeling methods describe the electrical relationships of components by establishing an admittance matrix. However, when simulating large-scale wind farms, the sheer number of turbines and the large size of the admittance matrix make inversion calculations difficult, resource-intensive, and require significant storage, limiting the simulation scale and making it difficult to meet the needs of actual engineering projects. Summary of the Invention

[0006] In view of this, the present invention proposes a virtual impedance compensation method for modeling constant admittance of permanent magnet synchronous generators, in order to solve the problems of difficulty in inverting large-scale wind farm simulation and high resource consumption in the existing technology.

[0007] The specific technical solution of this invention is as follows: A virtual impedance compensation method for modeling constant admittance of a permanent magnet synchronous generator includes: First, the permanent magnet synchronous generator model is discretized to adapt to the external network interface format of the electromagnetic transient calculation program. The generator voltage equation is discretized by implicit trapezoidal method to obtain the discrete model of the generator external network interface, which includes the equivalent resistance matrix and historical voltage sources. Secondly, the equivalent resistance matrix is ​​decomposed into a time-invariant part and a time-varying part, where the time-varying part is related to the rotor position angle; Then, in the generator model q Add virtual impedance to the axis by setting parameters. q Axial equivalent impedance and d The equivalent impedances of the axes are equal, thereby eliminating the time-varying characteristics of the equivalent resistance matrix and achieving constant admittance; Next, the discrete equations are rewritten in admittance form to construct a generator constant admittance model; Subsequently, the integrated converter and discrete circuit model are used to form a complete permanent magnet synchronous generator constant admittance model, and the nodal admittance equation is established based on Kirchhoff's current law. Finally, electromagnetic transient simulations are performed, historical current sources are calculated through a prediction mechanism, and node voltages and branch currents are solved using the admittance matrix.

[0008] Specifically, the discretization process includes: organizing the permanent magnet synchronous generator model into a format compatible with electromagnetic transient calculation programs, clarifying the mathematical relationship between the three-phase voltage and current at the generator terminals; discretizing the generator voltage equations using the implicit trapezoidal method, eliminating flux linkage terms and simplifying them to obtain the stator outlet three-phase voltage expressions; wherein, the calculation of historical voltage sources depends on the voltage and current quantities of the previous step size and the rotor angle of the current step size, and the rotor damping winding current is represented by the historical rotor voltage quantity; finally, the discrete model of the external network interface is derived, which includes the equivalent resistance matrix and historical electromotive force.

[0009] Specifically, the equivalent resistance matrix decomposition steps include: analyzing the structure of the equivalent resistance matrix and decomposing it into constant terms of the stator impedance matrix, time-varying terms of the stator inductance matrix, and time-varying terms of the triple matrix product; wherein, the triple matrix product terms are decomposed into... d Axial components and q Axis components; applying trigonometric function formulas and sum-to-product formulas, the equivalent resistance matrix is ​​simplified to the sum of a time-invariant part and a time-varying part. The time-varying part is derived from... d Axial equivalent impedance and q It is a function of the difference in shaft equivalent impedance and the rotor position angle.

[0010] Specifically, the steps for adding virtual impedance include: for permanent magnet synchronous generators d The shaft equivalent impedance is less than q The characteristics of the shaft equivalent impedance, in q A virtual impedance is added to the axis, which includes resistance and reactance parameters; forced compensation is achieved by setting the virtual impedance parameters. q The shaft equivalent impedance is equal to d The equivalent impedance of the shaft makes the time-varying coefficients of the equivalent resistance matrix zero; after compensation, the generator model maintains the similarity of the original machine parameters, but the admittance matrix is ​​fixed and the damping characteristics are similar in the low frequency range.

[0011] Specifically, the virtual impedance parameter settings are based on the error frequency control principle: the time constant of the virtual impedance is set to be about ten times higher than the user-specified frequency.

[0012] Specifically, the steps for constructing a generator constant admittance model include: rewriting the generator discrete equations into admittance equations to obtain a constant admittance matrix and an equivalent current source; wherein, the admittance matrix is ​​a full matrix, and the off-diagonal terms represent the mutual inductance coupling relationship between the three-phase windings; the equivalent current source is calculated from the historical voltage source and the equivalent resistance matrix.

[0013] Specifically, the steps of integrating the converter-accompanying discrete circuit model include: adding a converter-accompanying discrete circuit model based on the generator constant admittance model. This model includes grid-side control and generator-side control. Grid-side control involves phase-locked loop capturing grid phase and frequency, Parker transformation converting AC quantities into DC quantities, outer loop adjusting DC bus voltage or active and reactive power, and inner loop tracking current reference values ​​and generating trigger pulses. Generator-side control performs Parker transformation and torque current control based on the rotor angle output by the generator. Finally, Kirchhoff's current law is applied to establish the overall nodal admittance equation, and the admittance matrix of this equation remains constant.

[0014] Specifically, the electromagnetic transient simulation steps include: in the simulation initialization phase, performing an inversion preprocessing on the overall admittance matrix; at each simulation step, using a prediction mechanism to calculate the historical current sources, with the prediction formula based on the voltage and current quantities of the previous step and the rotor angle of the current step; subsequently, calling the preprocessed inverse matrix to directly solve for the node voltage; next, calculating the branch current of the current step; and finally, updating the historical current sources; wherein, the generator-side control directly uses the rotor angle output by the generator module, without the need for an additional phase-locked loop.

[0015] Specifically, the method also includes a verification mechanism for virtual impedance compensation: in electromagnetic transient simulation, by comparing the baseline results of the uncompensated model, it is ensured that the error of the compensated model under steady-state, small disturbance, asymmetric fault and symmetric fault conditions does not exceed a preset threshold.

[0016] Specifically, the complete permanent magnet synchronous generator constant admittance model is suitable for large-scale wind farm simulation. By fixing the admittance matrix, real-time inversion is avoided, and high-order matrix operations are simplified to linear multiplication. In the simulation, it supports the synchronous operation of multiple permanent magnet synchronous generator sets, and the simulation time does not increase significantly with the number of random groups, while ensuring that the accuracy is within the allowable range of engineering.

[0017] The beneficial effects of this invention are as follows: (1) By using virtual impedance compensation on the generator rotor side and discrete circuit model on the converter side, a full model of permanent magnet synchronous generator with constant admittance matrix is ​​constructed, eliminating the need for real-time inversion of time-varying admittance matrix and significantly reducing simulation computation resource consumption.

[0018] (2) By organizing the generator model into a format compatible with the electromagnetic transient calculation program, clarifying the mathematical relationship between the three-phase voltage and current at the generator terminal and discretizing it, efficient collaborative simulation with the main program of the electromagnetic transient calculation program and other network components can be achieved.

[0019] (3) Based on the external network interface model, decompose and organize the impedance matrix, clarify its relationship with the rotor position angle, implement virtual impedance compensation, eliminate the time-varying characteristics of the admittance matrix, achieve constant admittance, and limit the error of the compensated virtual impedance to a higher frequency range.

[0020] (4) Based on the constructed generator constant admittance model, the converter accompanying discrete circuit model is integrated to form a complete permanent magnet synchronous generator constant admittance model. The overall admittance matrix is ​​inverted in advance, and the inverse matrix calculation result is directly called in each subsequent simulation step to avoid real-time inversion operation and greatly reduce the amount of calculation. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a schematic diagram of the discrete circuit model of the permanent magnet direct-drive wind turbine generator set of the present invention; Figure 2 This is a schematic diagram of the electromagnetic transient algorithm logic for the permanent magnet direct-drive wind turbine generator set of the present invention; Figure 3 The following are steady-state and small-disturbance waveforms of a single generator connected to a load according to the present invention, where (a) and (c) are the generator terminal A-phase current and generator active power under steady-state operation, respectively, and (b) and (d) are the generator terminal A-phase current and generator active power under sudden load shedding, respectively. Figure 4 The diagrams show symmetrical and asymmetrical fault waveforms of a single unit connected to a load according to the present invention. (a) and (e) are the A-phase current and electromagnetic torque when the A-phase is short-circuited to ground, respectively; (c) and (g) are enlarged versions of the curves in the two diagrams, respectively; (b) and (f) are the A-phase current and electromagnetic torque when the three-phase is short-circuited to ground, respectively; (d) and (h) are enlarged versions of the curves in the two diagrams, respectively. Figure 5 The following are steady-state and small-disturbance waveforms of a single generator connected to a load according to the present invention, where (a) and (c) are the generator terminal A-phase current and generator active power under steady-state operation, respectively, and (b) and (d) are the generator terminal A-phase current and generator active power under sudden load shedding, respectively. Figure 6 The diagrams show symmetrical and asymmetrical fault waveforms of the PMSG connected load according to the present invention. (a) and (c) represent the A-phase current at the generator terminal and the active power of the generator when a single-phase short circuit to ground occurs on the A-phase side of the converter grid, respectively; (b) and (d) represent the A-phase current at the generator terminal and the active power of the generator when a three-phase short circuit to ground occurs on the converter grid side, respectively. Detailed Implementation

[0023] To make the technical problems to be solved, the technical solutions, and the beneficial effects of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.

[0024] This invention proposes a virtual impedance compensation method for constant admittance modeling of permanent magnet synchronous generators, such as... Figure 1 As shown, this method constructs a full PMSG model with a constant admittance matrix by using virtual impedance compensation on the generator rotor side and a discrete circuit model accompanying the converter side, eliminating the need to invert the time-varying admittance matrix and significantly reducing the consumption of simulation computing resources.

[0025] First, the generator model is discretized to adapt to the standard external network interface format of the Electromagnetic Transient Calculation Program (EMTP). The core objective is to encapsulate the generator's internal electromagnetic characteristics into port voltage-current relationships, enabling co-simulation with the EMTP main program and other network components. The computer equipment then organizes the permanent magnet synchronous generator model into an EMTP-compatible format, specifying the three-phase terminal voltages. v abc With current i abc The mathematical relationship is determined. The generator voltage equation is discretized using the implicit trapezoidal rule, with a discretization simulation step size of Δ. t The discrete equation expression is obtained as follows: (1) In the formula Δt For discrete simulation step size, t For the current simulation moment, v abc , i abc , λ abc These are the stator three-phase voltage vector, current vector, and flux linkage vector, respectively. i DQ , λ DQ These are the rotor current vector and the flux linkage vector, respectively. r s This is the stator winding resistance vector. r r This is the rotor damping winding resistance vector.

[0026] Substituting the generator flux linkage equation into equation (1), eliminating the flux linkage term, and simplifying, we can obtain the three-phase voltage at the stator outlet: (2) Among them, the historical value of stator voltage e sh ( t )for (3) In the formula, λ abcm This represents the flux linkage component of the permanent magnet on the stator side.

[0027] Rotor damping winding current i DQ It can be represented as (4) Among them, the historical electromotive force of the rotor e rh ( t )for: (5) Substituting the rotor current formula (4) into equation (2), we can obtain the three-phase port voltage of the permanent magnet synchronous generator stator: (6) In the formula r eq ( t The equivalent impedance matrix can be expressed as: (7) Historical electromotive force e h ( t ) can be represented as (8) In summary, the discrete model derivation of the external network interface of the permanent magnet synchronous generator is complete, and the stator three-phase port voltage is expressed as... L s For stator equivalent inductance, L r The equivalent inductance of the rotor damping winding is... L ss The stator self-inductance matrix is ​​the current step size. L sr , L rs The current step size is the mutual inductance matrix between the stator and rotor. L rr Rotor damping winding self-inductance matrix e h The total historical electromotive force is related to the circuit parameters of the previous step and also to the value of this step.

[0028] Next, based on the above external network interface model and its equivalent impedance matrix... r eq ( t Impedance matrix decomposition and rearrangement are performed to clarify... r eq ( t ) and rotor position angle θ The functional relationship. Analysis. r eq ( t As can be seen from the structure, this matrix consists of three parts: the stator impedance matrix. r s (Constant), Stator inductance matrix term 2 / Δ t × L ss ( t (Time-varying), and the triple matrix product term -4 / Δ t 2 × L sr ( t ) ( r r +2 / Δ t × L rr ) -1 L rs ( t (Time-varying). For permanent magnet synchronous generators, the impedance matrix... r eq ( t The second and third terms are both related to the rotor position angle. θ Related. To achieve constant admittance, time-varying components need to be separated, specifically by decomposing the triple matrix product terms into... d shaft and qAxis components: (9) In the formula, L srd , L srq They represent the mutual inductance between the stator and rotor, respectively. d shaft and q Axial components, r rd , r rd These represent the rotor damping windings respectively. d shaft and q Axial components, L rrd , L rrq These represent the self-inductance of the rotor windings, respectively. d shaft and q Axial components.

[0029] In equation (9) d The inverse matrix of the axis can be rewritten as: (10) In the formula, L lD express d Shaft damping winding inductance, L md express d Shaft magnetized inductor, Z lD express d Shaft damping winding impedance, Z md express d Axial magnetization impedance.

[0030] Similarly, rewrite q The inverse matrix of the axis is the product of the triple matrix in the equivalent resistance matrix (7). d axis q The sum of the two matrices along the axis. Substituting the simplified triple matrix product terms into the impedance matrix (7), and applying the trigonometric function formulas and the sum-to-product formulas, we can... r eq ( t Simplify to the time-invariant part r eq0 ( t Add the time-varying part r eqt ( t In the form of ), it can be represented as: (11) (12) In the formula: θ The rotor position angle; Z ls Stator leakage magnetic impedance; Z d , Z q for dq Axial equivalent impedance, Z a This is the armature reaction impedance.

[0031] Subsequently, based on the time-varying and time-invariant decomposition results of the impedance matrix obtained in step 2, virtual impedance compensation is implemented to eliminate the time-varying characteristics of the admittance matrix and achieve constant admittance. For conventional permanent magnet synchronous generators, Z d and Z q Not equal (usually) Z d < Z q ),make r eqt (t) coefficient Z q - Z d ≠ 0. To compensate for this dynamic change, in q Add virtual impedance to axis Z lQ2 Parameters include resistance r Q2 and reactance L lQ2 By setting Z lQ2 Parameters, forced q Axial equivalent impedance Z q *and Z d Equal, thus making r eq ( t The coefficient is zero. Compared to the original generator model, the compensated generator model has similar machine parameters, a fixed admittance matrix, and slightly different damping characteristics. The impedance relationship after compensation is: (13) use Z q* To represent the generator model after compensation q The equivalent discrete subtransient impedance of the axis, then Z q* satisfy: (14) In the model, the discrete subtransient impedance depends only on the generator's machine parameters and the discrete time step. After compensation...d axis q Same shaft impedance Z q* =Z d .

[0032] The added virtual impedance Q2 is altered by adding poles to the corresponding transfer function. q Shaft impedance affects the damping characteristics of the generator, and the error caused by this method is concentrated at higher frequencies, while the damping characteristics of the two are similar at lower frequencies.

[0033] To limit the error to a higher frequency, the added pole time constant should be placed at a frequency higher than the user-specified frequency. f r At a position approximately ten times higher, that is: (15) In the formula, τ Q2 This represents the time constant of the virtual impedance Q2.

[0034] Furthermore, the corresponding time constant can also be calculated as follows: (16) Analysis of equations (16) and (17) shows that by changing the reactance of the compensation impedance... L lQ2 This can change the frequency range of the error, limiting the error of compensating for virtual impedance to a higher frequency.

[0035] By rewriting the generator equation (6) in the form of the admittance equation, we can obtain the constant admittance model of the synchronous generator, which can be expressed as: (17) (18) Admittance matrix of generator components Y eq It is a full matrix. The off-diagonal terms in the matrix represent the coupling relationship between the three phases, which in terms of physical relationship represents the mutual inductance between the stator and rotor windings.

[0036] Furthermore, based on the generator constant admittance model constructed above, an integrated converter-associated discrete circuit model (ADC) is used to construct a complete PMSG constant admittance model. The directions of voltage and current in the generator branches are specifically defined, while the directions of discrete power supplies in the other branches are opposite to the given directions of the circuit. Applying Kirchhoff's Current Law (KCL) to each node, the PMSG node admittance equations are obtained: (19) (20) In the formula,v n This is the column vector of node voltages.

[0037] Since the admittance matrix is ​​fixed, the overall admittance matrix is ​​preprocessed by inverting it before calculation. Subsequent simulation steps directly call the inverse matrix calculation result, avoiding real-time inversion. High-order matrix operations are simplified to linear multiplication, significantly reducing the computational load.

[0038] Based on the complete PMSG constant admittance model constructed above, the algorithm logic of the PMSG constant admittance model is clarified and electromagnetic transient simulation is performed. The computer equipment operates according to the following procedure: In the primary circuit section, the historical current source... i h The calculation of (t) depends on the voltage and current of the previous step size and the rotor angle of the current step size. θ Given that the speed change during motor transients is minimal, a prediction mechanism is employed, and the prediction formula is as follows: (twenty one) In the formula, ω The rotor angular velocity, P This represents the number of pole pairs of the generator. J For rotational inertia, T m For mechanical torque, T e It is electromagnetic torque.

[0039] Calculate the historical current source i h (t) Then, the admittance matrix is ​​used to calculate the node voltage at the current step size, followed by the branch current at the current step size, and finally the historical current source is updated.

[0040] In the secondary control section of the program, the grid-side control requires a phase-locked loop (PLL), Parker transform, and inner / outer loop control to finally obtain the trigger pulse: the PLL captures the grid phase and frequency in real time, providing a synchronization reference; the Parker transform converts the three-phase AC quantities into... dq The shaft current is simplified for direct current flow; the outer loop adjusts the DC bus voltage or active / reactive power as needed, outputting a current reference value. The inner loop tracks this reference value to suppress disturbances, and finally generates a converter trigger pulse via pulse width modulation to achieve stable grid connection. On the generator side, a phase-locked loop is not required; the generator module can output the rotor angle. θ The permanent magnet synchronous generator rotor contains permanent magnets. Its module can directly output the rotor angle by estimating the rotor angle through position sensors or electromagnetic equations, without the need for additional synchronization via a phase-locked loop. Based on this rotor angle, Parker transformation and inner / outer loop torque / current control are performed, and the output trigger pulse drives the generator-side converter to achieve speed regulation and maximum wind energy capture. The electromagnetic transient algorithm logic is as follows: Figure 2 As shown.

[0041] To verify the effectiveness of the method, this invention performs simulation experiments based on the MATLAB platform, covering two configurations: single generator load and complete PMSG unit load, comparing the VBR model, dq Precise benchmarks such as models are used. The simulation step size is uniformly set to 10μs, and the simulation system parameters are shown in Table 1. Table 1 Parameters of Permanent Magnet Synchronous Generator

[0042] Scenario 1: The load shedding disturbance in the simulation experiment is a sudden reduction of the generator load parameters to half. The disturbance occurs at a time of 0.02s and lasts for 0.1s. The steady-state normal operation waveforms and the waveforms of the sudden single-unit load shedding are shown below. Figure 3 As shown, due to the lack of converter-side control, the generator output power is affected by the load and cannot be maintained at rated operation. The output power changes during load shedding, eventually stabilizing at the next equilibrium point. The curves show that the generator model using virtual impedance compensation has higher simulation accuracy in steady state and under small disturbances, and its fit with the simulation results of the unapproximated, accurate model is relatively high.

[0043] Scenario 2: The symmetrical fault in the simulation experiment is set as a three-phase short-circuit to ground fault at the generator terminal and a single-phase short-circuit to ground fault in phase A. The fault occurrence time is 0.01s, and the fault duration is 0.1s. The waveforms of the symmetrical and asymmetrical short-circuit faults are as follows: Figure 4 As shown. By Figure 4 It can be seen that in single-phase short-circuit grounding and three-phase short-circuit grounding faults, the generator model using virtual impedance compensation still has high simulation accuracy. Compared with the VBR model and... dq Compared to accurate simulation models that have not undergone calculation approximation, the error is no more than the order of 1%.

[0044] Scenario 3: Waveforms of a complete PMSG unit with generator connected to the grid via converter under steady-state operation and load shedding conditions at the generator terminals. The load shedding disturbance in the simulation experiment is a sudden shedding of half the load at the generator terminals, with a disturbance occurrence time of 0.01s and a duration of 0.1s. The waveforms of steady-state normal operation and sudden single-unit load shedding are as follows: Figure 5 As shown, the complete PMSG unit experiences minimal grid-side influence on the generator side due to converter control, and its generator operation is largely unaffected by load fluctuations. Output power remains essentially unchanged during load shedding. The curves demonstrate that the generator model employing virtual impedance compensation exhibits high simulation accuracy under steady-state and small-disturbance conditions, showing a high degree of fit with the simulation results of the unapproximated, precise model.

[0045] Scenario 4: The fault is located at the grid-side outlet of the converter, resulting in a single-phase short-circuit to ground fault and a three-phase short-circuit to ground fault in phase A. The fault occurrence time is 0.02s, and the fault duration is 0.1s. The waveforms of the symmetrical and asymmetrical short-circuit faults are as follows: Figure 6 As shown. By Figure 6 It can be seen that when a grid-side fault occurs in the PMSG converter, due to the presence of rectification and inversion stages in the converter, the impact of the grid-side fault on the generator side is relatively small, and the generator curve fluctuation and distortion are minimal. Furthermore, under these circumstances, the generator model using virtual impedance compensation still maintains high simulation accuracy, comparable to the VBR model. dq The model simulation results show a high degree of fit.

[0046] The verification results are summarized in Table 3: Table 3 Model Results Analysis

[0047] In terms of accuracy, the error for all operating conditions (terminal current, active power, and electromagnetic torque) is 0.0015%–2.3461%, which meets engineering standards. Regarding efficiency, the PMSG steady-state simulation time is only 47.536% of the VBR model, and the peak time for fault conditions is 60.317%, significantly reducing resource consumption. In terms of scale, it supports simultaneous simulation of 100+ PMSG units without a significant increase in time, breaking through traditional limitations. In summary, this method optimizes computational efficiency, expands simulation scale, and adapts to multi-platform applications while ensuring accuracy.

[0048] The beneficial effects of this invention are as follows: (1) Significantly reduced computational complexity and improved simulation efficiency: This invention successfully fixes the time-varying admittance matrix of the generator model as a constant matrix through virtual impedance compensation. Combined with the constant admittance ADC model of the converter, the admittance matrix of the entire PMSG system remains constant during the simulation process, eliminating the need to repeatedly calculate and invert the time-varying matrix at each step. The simulation calculation is simplified from nonlinear, time-varying iterative solution to linear algebraic operations, significantly reducing computational resource consumption and greatly improving simulation speed (experiments show that simulation time can be reduced by about 40%-50%), which is particularly beneficial for the rapid electromagnetic transient simulation of large-scale wind farm groups.

[0049] (2) High simulation accuracy is guaranteed: By optimizing the design of virtual impedance parameters, the model error is mainly limited to the high-frequency range. In the power frequency and the low-frequency range of the main transient processes, the constant admittance model established by this invention, compared with the accurate VBR model and dq model, shows a highly consistent dynamic response under various operating conditions such as steady state, small disturbance, symmetrical and asymmetrical faults, with extremely small simulation error (usually below 1%, and less than 0.1% in most scenarios), which fully meets the engineering accuracy requirements.

[0050] (3) Enhanced model versatility and applicability: The constant admittance model has a simple form and a unified interface, making it easy to integrate into various electromagnetic transient simulation programs. More importantly, since its calculation process is mainly linear, it is very suitable for implementation on discrete hardware simulation platforms based on parallel processing, such as FPGA, providing an efficient and accurate model foundation for real-time simulation of power systems and hardware-in-the-loop testing, thus expanding the application scope of the model.

[0051] (4) It provides an effective tool for the simulation analysis of large-scale new energy access systems: This method effectively solves the "computational bottleneck" problem faced by traditional models in the simulation of large-scale wind farms, making it possible to conduct detailed electromagnetic transient analysis of complex power systems with a large number of new energy units under limited computing resources. It has important practical value for the planning, operation and safety and stability analysis of new power systems.

[0052] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A virtual impedance compensation method for permanent magnet synchronous generator constant admittance modeling, characterized in that, The application relates to a method for building a permanent magnet synchronous generator (PMSG) constant admittance model for electromagnetic transient simulation. Firstly, a PMSG model is discretized to adapt to an external network interface format of an electromagnetic transient calculation program, a generator voltage equation is discretized through an implicit trapezoidal method, and a discrete model of the external network interface of the generator is obtained, the model comprising an equivalent resistance matrix and a historical voltage source; Secondly, the equivalent resistance matrix is decomposed into a time-invariant part and a time-varying part, wherein the time-varying part is related to a rotor position angle; Then, the virtual impedance is added to the generator model q axis, and the time-varying characteristics of the equivalent resistance matrix are eliminated by setting the parameters of the virtual impedance q axis equivalent impedance and d axis equivalent impedance, so as to realize constant admittance. Then, the discrete equation is rewritten into an admittance form to construct the generator constant admittance model; Subsequently, a converter companion discrete circuit model is integrated to form a complete PMSG constant admittance model, and a node admittance equation is established based on Kirchhoff's current law; Finally, electromagnetic transient simulation is performed, a historical current source is calculated through a prediction mechanism, and node voltages and branch currents are solved by using an admittance matrix.

2. The virtual impedance compensation method of permanent magnet synchronous generator constant-nu modeling according to claim 1, characterized in that, The discretization processing step comprises the following steps: arranging a PMSG model into a format compatible with an electromagnetic transient calculation program, and clearly defining the mathematical relationship between three-phase voltages and currents at the motor end; applying an implicit trapezoidal method to discretize a generator voltage equation, eliminating a flux linkage term and simplifying, and obtaining a three-phase voltage expression at the stator outlet end; wherein the calculation of a historical voltage source depends on the voltage and current of the previous step length and the current step length rotor angle, and the rotor damping winding current is represented by a rotor voltage historical quantity; finally, a discrete model of the external network interface is derived, and the model comprises an equivalent resistance matrix and a historical electromotive force.

3. The virtual impedance compensation method of permanent magnet synchronous generator constant-nu modeling according to claim 1, characterized in that, The equivalent resistance matrix decomposition step comprises: analyzing the equivalent resistance matrix structure, splitting it into a constant term of the stator impedance matrix, a time-varying term of the stator inductance matrix, and a time-varying term of a triple matrix product; wherein the triple matrix product term is decomposed into d the axis component and q the axis component; applying a trigonometric function formula and a sum-difference product formula, the equivalent resistance matrix is simplified into a sum of a time-invariant part and a time-varying part, the time-varying part is composed of d the difference between the axis equivalent impedances and q the difference between the axis equivalent impedances and the rotor position angle.

4. The virtual impedance compensation method of permanent magnet synchronous generator constant-nu modeling as claimed in claim 1, wherein, The adding virtual impedance step comprises: for the permanent magnet synchronous generator d The shaft equivalent impedance is less than q The characteristic of the shaft equivalent impedance, in q The shaft adds a virtual impedance, which comprises resistance and reactance parameters; by setting the virtual impedance parameters, the compensated generator model keeps the original machine parameter similarity, but the admittance matrix is fixed and the damping characteristic is similar in the low frequency band. q The shaft equivalent impedance is equal to d The shaft equivalent impedance makes the time-varying part coefficient of the equivalent resistance matrix zero; the compensated generator model keeps the original machine parameter similarity, but the admittance matrix is fixed and the damping characteristic is similar in the low frequency band.

5. The virtual impedance compensation method of permanent magnet synchronous generator constant-nu modeling according to claim 4, characterized in that, The parameter setting of the virtual impedance is based on the error frequency control principle: the time constant of the virtual impedance is set to be about ten times higher than the user-specified frequency.

6. The virtual impedance compensation method of permanent magnet synchronous generator constant-nu modeling as claimed in claim 1, wherein, The step of constructing the generator constant admittance model comprises the following steps: rewriting the generator discrete equation into an admittance equation form to obtain a constant admittance matrix and an equivalent current source; wherein the admittance matrix is a full matrix, and the non-diagonal terms represent the mutual inductive coupling relationship among the three-phase windings; and the equivalent current source is calculated from the historical voltage source and the equivalent resistance matrix.

7. The virtual impedance compensation method of permanent magnet synchronous generator constant-nu modeling as claimed in claim 1, wherein, The step of integrating the converter companion discrete circuit model comprises the following steps: adding a converter companion discrete circuit model to the generator constant admittance model, and the model comprises a grid-side control part and a machine-side control part; the grid-side control involves phase-locked loop capture of the grid phase and frequency, park transformation conversion of alternating current into direct current, outer loop regulation of the direct current bus voltage or active and reactive power, and inner loop tracking of the current reference value and generation of a trigger pulse; the machine-side control is based on the rotor angle output by the generator to perform park transformation and torque current control; finally, the overall node admittance equation is established by applying Kirchhoff's current law, and the admittance matrix of the equation is fixed and unchanged.

8. The virtual impedance compensation method of permanent magnet synchronous generator constant-nu modeling as claimed in claim 1, wherein, The step of performing electromagnetic transient simulation comprises the following steps: in the simulation initialization stage, the overall admittance matrix is once inversely preprocessed; in each simulation step, a prediction mechanism is used to calculate a historical current source, and a prediction formula is based on the voltage and current of the previous step length and the current step length rotor angle; subsequently, a preprocessed inverse matrix is called to directly solve the node voltage; then, the current step length branch current is calculated; finally, the historical current source is updated; wherein the machine-side control directly uses the rotor angle output by the generator module, and an additional phase-locked loop is not needed.

9. The virtual impedance compensation method of permanent magnet synchronous generator constant-nu modeling as claimed in claim 1, wherein, The method also comprises a verification mechanism of virtual impedance compensation: in the electromagnetic transient simulation, by comparing the reference results of the uncompensated model, it is ensured that the error of the compensated model under steady state, small disturbance, asymmetric fault and symmetric fault conditions does not exceed a preset threshold.

10. The virtual impedance compensation method of permanent magnet synchronous generator constant-nab modeling of claim 1, wherein, The complete permanent magnet synchronous generator constant admittance model is applicable to large-scale wind farm simulation, avoids real-time inversion by fixing the admittance matrix, and simplifies high-order matrix operation into linear multiplication; in the simulation, synchronous operation of multiple permanent magnet synchronous generator sets is supported, the simulation time does not increase significantly with the number of generator sets, while the precision is ensured within the engineering allowable range.

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