A fault current analytical method for grid-connected converter based on model order reduction and time-domain convolution

Abstract

The application discloses a network converter fault current analytical method based on model order reduction and time domain convolution and belongs to the technical field of power electronic control. The method is based on the inner loop control structure of the network converter, adopts a dominant pole reservation order reduction mode to obtain a forward channel transfer function of the fault current, and combines a current coupling relationship between dq axes to establish a same-axis current response transfer function and a cross-axis current response transfer function and a dq-axis current frequency domain expression. Then, time domain unit impulse responses corresponding to the response transfer functions are obtained. Meanwhile, according to the outer loop control structure of the network converter and the depth of the power grid fault, a power angle time domain analytical expression is obtained. In combination with the dq-axis current frequency domain expression and the time domain unit impulse responses, a full-stage fault current time domain analytical expression in an abc coordinate system is obtained. The application can take into account the inner and outer loop dynamic characteristics of the network converter and improve the fault current analytical precision.

Description

Technical Field

[0001] This invention belongs to the field of power electronic control technology, specifically relating to a fault current analysis method for grid-connected converters based on model order reduction and time-domain convolution. Background Technology

[0002] Driven by new energy sources, a large number of power electronic devices are replacing synchronous machines in grid connection, leading to a continuous weakening of grid strength. Grid-connected converters, due to their strong voltage and frequency support capabilities, have become key equipment for constructing new power systems. However, during grid faults, the fault current of grid-connected converters can be much higher than the rated value due to the characteristics of their voltage sources and the coupling of control loops. Furthermore, the transient current trajectory is complex and difficult to describe accurately. The transient current response of grid-connected converters includes the short-term inrush current in the initial stage of the fault and the long-term steady-state current in the sustained stage. This current characteristic not only relates to the hardware design and control optimization of the converter but also directly affects the protection configuration of the power system. Therefore, achieving an explicit analytical characterization of the fault current of grid-connected converters throughout all stages is an important theoretical foundation for equipment optimization design and system protection configuration.

[0003] Existing analytical methods for fault current tracing heavily rely on the assumption of decoupling between inner and outer loops, typically only describing fault inrush current or fault steady-state current independently, and exhibiting significant computational errors. To address this, some studies have employed local numerical iteration methods to characterize fault currents across all stages; however, these methods are computationally burdensome, have low solution efficiency, and struggle to reveal the quantitative relationship between system parameters and fault current response, lacking clear physical meaning. Therefore, it is necessary to fully consider the coupled dynamic characteristics of the inner and outer control loops of the grid converter and adopt appropriate computational methods to achieve accurate solutions and explicit characterization of fault currents across all stages, providing effective guidance for equipment hardware design, control optimization, and system protection configuration. Summary of the Invention

[0004] To address the problems in the existing technology, this invention provides a method for analyzing fault current in grid-connected converters based on model order reduction and time-domain convolution.

[0005] The technical solution of the present invention is as follows:

[0006] This invention discloses a fault current analysis method for grid-connected converters based on model order reduction and time-domain convolution, comprising the following steps:

[0007] 1) Based on the inner loop control structure of the grid converter, the forward path transfer function of the fault current in the dq coordinate system is obtained by adopting the order reduction method of dominant pole retention. Then, combined with the current coupling relationship between the dq axes, the coaxial current response transfer function and the cross-axis current response transfer function, as well as the frequency domain expression of the dq axis current are obtained.

[0008] 2) Perform eigenvalue decomposition and inverse Laplace transform on the coaxial current response transfer function and the cross-axis current response transfer function to obtain the time-domain unit impulse response corresponding to each response transfer function;

[0009] 3) Based on the outer loop control structure of the grid converter and the grid fault depth, a nonlinear power angle differential equation is established; the power angle stable equilibrium point after the fault is obtained according to the grid fault depth, and the nonlinear power angle differential equation is analyzed at this equilibrium point to obtain the power angle time-domain analytical expression.

[0010] 4) Based on the power angle time-domain analytical expression, perform a second-order Taylor expansion on the voltage input excitation part in the dq-axis current frequency-domain expression to obtain a linearized voltage excitation time-domain expression. Then, perform time-domain convolution with the time-domain unit impulse response from step 2), and superimpose the convolution results to obtain the dq-axis current time-domain analytical expression. Combine this with the power angle time-domain analytical expression to obtain the full-stage fault current time-domain analytical expression in the abc coordinate system.

[0011] Further, in step 1), obtaining the coaxial current response transfer function and the cross-axis current response transfer function includes: obtaining the d-axis voltage input excitation and the q-axis voltage input excitation based on the phase relationship between the grid voltage and the terminal voltage in the dq coordinate system; based on the forward channel transfer function, and combined with the coupling effect of the grid converter output angular frequency and the grid equivalent inductance on the dq-axis current response, obtaining the coaxial current response transfer function characterizing the d-axis voltage input excitation to the d-axis current and the q-axis voltage input excitation to the q-axis current, and the cross-axis current response transfer function characterizing the q-axis voltage input excitation to the d-axis current and the d-axis voltage input excitation to the q-axis current.

[0012] Further, in step 1), obtaining the frequency domain expression of the dq-axis current includes: adding the product of the d-axis voltage input excitation and the coaxial current response transfer function and the product of the q-axis voltage input excitation and the cross-axis current response transfer function to obtain the frequency domain expression of the d-axis current; and subtracting the product of the d-axis voltage input excitation and the cross-axis current response transfer function from the product of the q-axis voltage input excitation and the coaxial current response transfer function to obtain the frequency domain expression of the q-axis current.

[0013] Further, step 2) includes: solving for the eigenvalues ​​of the coaxial current response transfer function and the cross-axis current response transfer function to obtain two pairs of eigenvalues; decomposing the coaxial current response transfer function and the cross-axis current response transfer function based on the two pairs of eigenvalues, and performing inverse Laplace transform on the decomposition results to obtain the time-domain unit impulse response corresponding to each response transfer function.

[0014] Further, in step 4), obtaining the linearized voltage excitation time-domain expression includes: substituting the power angle time-domain analytical expression into the voltage excitation expression in the dq coordinate system composed of the d-axis voltage input excitation and the q-axis voltage input excitation, and then performing a second-order Taylor expansion on the obtained expression at the power angle stable equilibrium point after the fault to obtain the linearized voltage excitation time-domain expression.

[0015] Compared with the prior art, the present invention has the following beneficial technical effects:

[0016] (1) This invention obtains the forward path transfer function of the fault current in the dq coordinate system by using the inner loop control structure of the grid converter and the order reduction method of retaining the dominant poles to preserve the main dynamic characteristics of the inner loop control structure that affect the dynamic response of the fault current. At the same time, it obtains the coaxial current response transfer function and the cross-axis current response transfer function, as well as the frequency domain expression of the dq axis current by combining the dq axis current coupling relationship. This overcomes the problem that the existing methods rely on the assumption of decoupling between the inner and outer loops and are difficult to describe the coupling dynamic characteristics of the inner and outer control loops. Thus, it can uniformly analyze and characterize the impact current in the initial stage of the fault occurrence and the steady-state current in the fault duration stage, and realize the accurate description of the fault current in the grid converter in all stages.

[0017] (2) This invention obtains the time-domain unit impulse response by performing eigenvalue decomposition and inverse Laplace transform on the response transfer function, and performs time-domain convolution in combination with the voltage excitation time-domain expression. This avoids the problems of heavy computational burden and low solution efficiency of existing numerical iterative methods when solving the fault current of the whole process, thereby obtaining the time-domain analytical expression of the fault current with explicit analytical form and improving the analytical calculation efficiency of fault current.

[0018] (3) This invention establishes a fault current analysis logic that includes inner loop control dynamics, outer loop power angle dynamics, and the influence of grid fault depth. This enables the fault current response to establish a correspondence with grid converter control parameters, grid parameters, and operating status parameters in an analytical expression form. This overcomes the problem that existing methods cannot reveal the quantitative relationship between system parameters and fault current response, thereby improving the physical interpretability of fault current analysis results and providing a theoretical basis for grid converter hardware parameter design, control parameter optimization, and power system protection configuration.

[0019] (4) By constructing a fault current analysis method based on model order reduction and time-domain convolution, the present invention enables the analysis model to be adjusted according to different grid fault depths, line parameters and control parameters, and is applicable to the analysis of fault current characteristics of grid converters under different operating conditions, thereby improving the applicability and expansion capability of the fault current analysis method. Attached Figure Description

[0020] Figure 1A schematic diagram of the equivalent circuit and control structure of a traditional grid-connected converter;

[0021] Figure 2 The flowchart shows the analytical method for fault current of a grid converter based on model order reduction and time-domain convolution.

[0022] Figure 3 This is a structural diagram of the frequency domain reduced-order model of fault current proposed in this invention;

[0023] Figure 4 Comparison of simulation and theoretical results of grid converter fault current in dq and abc coordinate systems after symmetrical voltage drop in the traditional method;

[0024] Figure 5 The figure shows a comparison between the simulation and theoretical results of the fault current of the grid converter in the dq and abc coordinate systems after the grid voltage symmetrical drop under the method proposed in this invention. Detailed Implementation

[0025] The present invention will be further described and illustrated below with reference to specific embodiments. The embodiments described are merely examples of the content of this disclosure and do not limit the scope of the invention. The technical features of each embodiment in the present invention can be combined accordingly, provided that there is no mutual conflict.

[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the following describes the invention in further detail, taking a grid converter controlled by a virtual synchronous machine under a symmetrical voltage dip fault in the power grid as an example, in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0027] Figure 1 This is a schematic diagram of the equivalent circuit and control structure of a traditional grid-connected converter. The traditional grid-connected converter acquires data from the filter inductor L. f Current I L and filter capacitor C f voltage U f And by transforming it to the dq synchronous rotating coordinate system, it can be achieved. Figure 1 The grid converter control shown is illustrated. PCC is the point of common coupling, and V... dc X is the input voltage of the grid-connected converter, I is the fault output current of the grid-connected converter, which is also the current solved analytically in this invention. g Let E be the equivalent impedance of the power grid, and E be the power grid voltage.

[0028] This grid control structure employs cascaded voltage and current control as the inner loop control scheme in the dq synchronous rotating coordinate system to achieve closed-loop regulation and active support of the grid connection point voltage. Both voltage and current control are based on proportional-integral (PI) controllers to achieve closed-loop zero steady-state error control. The proportional coefficient and integral coefficient of the voltage control are k and k, respectively. up and k ui The proportional coefficient and integral coefficient of the current control are k and k, respectively. ip and k ii ; through a gain coefficient of ωC f The cross-decoupling control term avoids the voltage control coupling effect between the d-axis and q-axis in the dq rotating coordinate system, through a gain coefficient of ωL. f The cross-decoupling control term avoids the current control coupling effect between the d-axis and q-axis in the dq rotating coordinate system. Specifically, the current-controlled d-axis control command value i... Ldref and q-axis control command value i Lqref These are generated by voltage-controlled d-axis and q-axis PI controllers, respectively. The voltage-controlled d-axis control command value u... dref Set the voltage reference value U0 and the q-axis control command value u. qref Set to 0 to enable active support and control of the terminal voltage coordinate system orientation. Figure 1 The middle i Ld For filter inductor L f Current I L d-axis current after dq transformation; i Lq The q-axis current is the generator-side current of the grid converter after dq transformation.

[0029] In the grid control structure, voltage U f The amplitude is controlled by constant terminal voltage control, that is, the reference values ​​for the dq axis voltages are u and u, respectively. dref = U0 and u qref = 0, where U0 is the output voltage reference value of the grid converter. Simultaneously, the voltage U f The phase angle value θ is determined by the network control method.

[0030] like Figure 1 As shown, P0 is the control command value for the active power of the grid-connected converter, i.e., the reference value for the active power of the grid-connected converter; P e The actual measured value of the active power of the grid-connected converter, i.e., the actual power value of the grid-connected converter, can be expressed by equation P based on instantaneous power theory. e = u d i d + u q i q It is obtained through real-time calculation of voltage and current sampling values, where u dThe output voltage of the grid converter is the d-axis voltage after dq transformation; i d The d-axis current is the output current of the grid converter after dq transformation; u q The output voltage of the grid converter is the q-axis voltage after dq transformation; i q The output current of the grid converter is the q-axis current after dq transformation.

[0031] Figure 1 In the virtual synchronous machine control algorithm shown, ω0 is the grid angular frequency base value, which is set to 2π×50rad. ω is the first output angular frequency value of the grid converter at the current moment. Subtracting the grid angular frequency base value ω0 from ω0 yields the angular frequency deviation value Δω, calculated as Δω = ω – ω0. Multiplying the angular frequency deviation value Δω by the damping coefficient D of the grid converter yields the damping power, calculated as D×Δω. The deviation between the active power control command value (i.e., the power reference value) and the actual measured value is P0 – P. e After further subtracting the damping power, the result is fed into the inertial simulation loop 1 / Hs to calculate the second output angular frequency value of the grid-connected converter. This achieves synchronization between the grid-connected converter and the power grid. The second output angular frequency value of the grid-connected converter obtained at this time serves as the first output angular frequency value for the next acquisition of the actual phase angle value. The phase angle value θ is obtained by integrating the second output angular frequency value. The phase angle value θ is used in coordinate transformation and other processes. Therefore, the formula for calculating the phase angle value is: , where s is the Laplace operator and H is the inertial time constant of the grid converter.

[0032] In conclusion, Figure 1 The invention details the typical inner and outer loop control structures of grid-connected converters, clarifying the dynamic relationships between electrical quantities such as terminal voltage, current, active power, output angular frequency, and phase angle, and control quantities. This provides a foundation for the subsequent establishment of a fault current model and simplification of the control structure for grid-connected converters. Building upon this foundation, the invention further addresses the different time-scale characteristics of the fast dynamics of the inner loop and the slow power angle dynamics of the outer loop in grid-connected converters. While retaining the dominant dynamics affecting the fault current response and the coupling relationship between the inner and outer loops, the original control model is reduced in order, and an analytical model of the fault current of the grid-connected converter at all stages is established by combining the power angle dynamics of the outer loop.

[0033] To address the problem that traditional fault current description methods heavily rely on the assumption of decoupling between inner and outer loops and local numerical iterations, leading to excessive current analysis errors and unclear physical meanings of system parameters, this invention establishes a reduced-order fault current model while fully preserving the dominant dynamics and coupling characteristics of the inner and outer loops. Simultaneously, by utilizing a hierarchical time-domain convolution method of the outer loop fault voltage excitation and the inner loop unit impulse response, a time-domain analytical function for fault current with concise expression, clear physical relationships, and excellent computational accuracy is established, enabling a clear and analytical characterization of fault currents throughout all stages of the grid-connected converter.

[0034] like Figure 2 The fault current analysis method for grid converters based on model order reduction and time-domain convolution proposed in this invention includes the following steps:

[0035] S1: Obtain the inner loop control structure of the grid converter to be analyzed for fault current. Ignore the fast dynamics of the inner loop current and use the order reduction method of retaining the dominant poles to simplify the inner loop dynamics. That is, for poles far from the imaginary axis, with small corresponding time constants and fast decay rates, their dynamics are approximately ignored; for poles close to the imaginary axis that determine the main transient response of the system, they are retained, thus obtaining the forward path transfer function of the fault current in the dq coordinate system.

[0036] The original inner-loop control structure of the grid converter contains multiple dynamic paths, corresponding to multiple dynamic processes with different rates of change. The purpose of the aforementioned order reduction process is to retain the dynamic characteristics that play a major role in the transient changes of fault current while omitting dynamic processes that terminate in duration or weaken rapidly, thereby simplifying the previous inner-loop model into an analytical low-order model.

[0037] In step 1), the frequency domain reduced-order model of the fault current obtained by dominant pole preservation is as follows: Figure 2 As shown, its forward channel transfer function for:

[0038]

[0039] in, For the Laplace operator; This is the equivalent inductance of the power grid; , These are all intermediate variables, without any actual physical meaning, and , , For filtering capacitors; and These are all intermediate variables and have no actual physical meaning; and The definition of is:

[0040]

[0041] in, and These are all intermediate variables and have no actual physical meaning; For filtering inductors; The integral coefficient for voltage control; This is the proportional coefficient for current control; This is the voltage control proportional coefficient.

[0042] From the above relationship, it can be seen that, , , , , and This is only used to simplify the expression of the forward channel transfer function; its value is ultimately determined by the filter inductor. Equivalent inductance of the power grid Filter capacitor Voltage control proportional coefficient Voltage control integral coefficient and current control proportional coefficient The parameters were jointly determined. Therefore, the obtained forward transfer function still retains the influence of the main electrical parameters and inner loop control parameters of the grid converter on the dynamic response to fault current.

[0043] Based on the phase relationship between grid voltage and terminal voltage in the dq coordinate system, the reference value of the grid-connected converter terminal voltage is located in the d-axis direction. After a grid fault, the grid voltage changes with the power angle between the grid-connected converter and the grid. Corresponding voltage components are formed in the d-axis and q-axis directions. Therefore, Figure 2 In the frequency domain reduced-order model of the fault current shown, the difference between the grid converter terminal voltage and the grid voltage in the dq-axis direction is used as the voltage input excitation of the fault current. The voltage input excitation is defined as:

[0044]

[0045] in, The excitation is the d-axis voltage input. This is the reference value for the output voltage of the grid converter; The depth of the power grid fault after a power grid fault; The power angle between the grid converter and the power grid; The excitation is the q-axis voltage input.

[0046] The d-axis voltage input excitation and q-axis voltage input excitation are used to determine the frequency domain expression of the dq-axis current in conjunction with the fault current frequency domain order reduction model.

[0047] S2: According to Figure 2The frequency domain reduced-order model of fault current in the model is first based on the forward path transfer function. The current coupling relationship between the d and q axes is used to obtain the coaxial current response transfer function and the cross-axis current response transfer function. Then, the frequency domain expression of the d and q axis current is obtained according to the superposition theorem.

[0048] Specifically, in the dq-axis coordinate system, the d-axis voltage input excitation not only acts on the d-axis current, and the q-axis voltage input excitation not only acts on the q-axis current, but also, due to the current coupling relationship between the d and q axes, the q-axis voltage input excitation also acts on the d-axis current, and vice versa. Therefore, the input-output relationship between the d-axis voltage input excitation and the q-axis voltage input excitation is defined as the coaxial current response, and the input-output relationship between the q-axis voltage input excitation and the d-axis voltage input excitation is defined as the cross-axis current response.

[0049] Based on the forward channel transfer function And combined with the output angular frequency of the grid converter Equivalent inductance of the power grid The coupling effect on the dq-axis current response, the transfer functions of the coaxial current response and the cross-axis current response are as follows:

[0050]

[0051] in, This is the coaxial current response transfer function, used to characterize the transfer relationship between d-axis voltage input excitation and d-axis current, and between q-axis voltage input excitation and q-axis current. This is the cross-axis current response transfer function, used to characterize the transfer relationship between q-axis voltage input excitation and d-axis current, and between d-axis voltage input excitation and q-axis current.

[0052] Excitation based on d-axis voltage input and q-axis voltage input excitation For the d-axis current, the current component formed by the d-axis voltage input excitation through the coaxial current response transfer function is superimposed with the current component formed by the q-axis voltage input excitation through the cross-axis current response transfer function; for the q-axis current, the current component formed by the q-axis voltage input excitation through the coaxial current response transfer function is superimposed with the current component formed by the d-axis voltage input excitation through the cross-axis current response transfer function in opposite coupling directions. Therefore, according to the superposition theorem, the frequency domain expression for the dq-axis current is obtained:

[0053]

[0054]

[0055] in, This is the d-axis frequency domain output current; This is the q-axis frequency domain output current; This represents the d-axis current response component generated after the d-axis voltage input excitation is applied by the coaxial current response transfer function. This represents the d-axis current response component generated after the q-axis voltage input excitation is processed by the cross-axis current response transfer function; This represents the q-axis current response component generated after the q-axis voltage input excitation is applied by the coaxial current response transfer function. This represents the q-axis current response component generated after the d-axis voltage input excitation is applied by the cross-axis current response transfer function.

[0056] As can be seen from the above expressions, the d-axis frequency domain output current is composed of the coaxial current response generated by the d-axis voltage input excitation and the cross-axis current response generated by the q-axis voltage input excitation; the q-axis frequency domain output current is composed of the coaxial current response generated by the q-axis voltage input excitation and the cross-axis current response generated by the d-axis voltage input excitation.

[0057] S3: Solve for the eigenvalues ​​of the coaxial current response transfer function and the cross-axis current response transfer function. That is, set the denominator of the coaxial current response transfer function and the cross-axis current response transfer function to 0, solve for two pairs of eigenvalues, and based on the two pairs of eigenvalues, decompose the coaxial current response transfer function and the cross-axis current response transfer function into the sum of two second-order frequency domain responses, and then perform an inverse Laplace transform on each second-order frequency domain response to obtain the time-domain unit impulse response corresponding to the coaxial current response transfer function and the time-domain unit impulse response corresponding to the cross-axis current response transfer function.

[0058] In step 3), as can be seen from step 2), the coaxial current response transfer function... and cross-axis current response transfer function Since they have the same denominator, they share the same characteristic roots. Setting their common denominator to 0 yields the characteristic roots. , and characteristic roots , They are:

[0059]

[0060] in, and These are the first pair of characteristic roots. , The real and imaginary parts; The imaginary unit; and These are the second pair of characteristic roots. , The real and imaginary parts.

[0061] The calculations for the real and imaginary parts are as follows:

[0062]

[0063] in, The output angular frequency of the grid converter; , These are all intermediate variables and have no practical significance. , The calculation formula is:

[0064]

[0065] in, , , These are all intermediate variables and have no practical significance. Represents a symbolic function.

[0066] Based on the two pairs of eigenvalues ​​obtained, eigenvalue decomposition is performed on the coaxial current response transfer function and the cross-axis current response transfer function, respectively, so that each response transfer function can be expressed as the sum of two second-order frequency domain responses. Specifically:

[0067]

[0068] in, , , , , , , , , and These are all intermediate variables and have no practical significance; the formula for calculating intermediate variables is:

[0069]

[0070] in, , and This is an intermediate variable with no practical significance; the formula for calculating the intermediate variable is: Therefore, both the coaxial current response transfer function and the cross-axis current response transfer function are transformed into a superposition of two second-order frequency domain responses. By performing an inverse Laplace transform on each second-order frequency domain response and adding the two time-domain responses belonging to the same response transfer function, the time-domain unit impulse response corresponding to the coaxial current response transfer function is obtained. The time-domain unit impulse response corresponding to the cross-axis current response transfer function :

[0071]

[0072] in, , , , , , , and These are all intermediate variables and have no practical significance; the formula for calculating intermediate variables is:

[0073]

[0074] Through the above processing, the coaxial current response transfer function and the cross-axis current response transfer function are converted from frequency domain form into the corresponding time domain unit impulse response, which provides a basis for subsequent time-domain convolution of the voltage excitation time-domain expression with the time-domain unit impulse response.

[0075] 4) Obtain the outer loop control structure of the grid converter and the grid fault depth. Based on the outer loop control structure, obtain the complete nonlinear power angle differential equation. Then, combine the grid fault depth to calculate the power angle stable equilibrium point after the fault. At the power angle stable equilibrium point after the fault, use a first-order Taylor expansion to obtain the linearized power angle differential equation. Then, obtain the power angle time-domain analytical expression according to the standard differential equation solution formula.

[0076] In step 4), the outer loop control structure adopts a virtual synchronous machine control structure. The control command value for the active power of the grid converter is... Actual measured value of active power of grid converter After subtracting the damping power from the deviation, the output angular frequency of the grid converter is obtained through inertial simulation. The damping power is determined by the damping coefficient of the grid converter. The output angular frequency of the grid converter relative to the grid angular frequency base value The power angle of the grid converter is obtained by multiplying the deviations. The time integral of the difference between the output angular frequency and the base value of the grid angular frequency is:

[0077]

[0078] Therefore, the first derivative of the power angle corresponds to the deviation between the output angular frequency of the grid converter and the baseline angular frequency of the grid, and the second derivative of the power angle... The rate of change of the corresponding angular frequency deviation. Substituting the above power angle relationship into the outer loop control relationship of the virtual synchronizer, we obtain:

[0079]

[0080] in, This is the inertial time constant of the grid converter.

[0081] Furthermore, the voltage amplitude during the fault is determined by the fault depth. Characterization, equivalent impedance of the power grid for Ignoring the rapid voltage inner-loop dynamic process, based on the power transmission characteristics of transmission lines, the real-time power of the grid converter is...

[0082]

[0083] in, This is the reference value for the output voltage of the grid converter.

[0084] Substituting the real-time power into the aforementioned outer-loop control relationship, the power angle differential equation contains... Therefore, we obtain information about the work angle. The nonlinear power angle differential equation characterizes the dynamic process of the power angle under the combined effects of active power variation, damping, and inertia during a power grid fault.

[0085] According to the aforementioned nonlinear power angle differential equation, when the power angle remains stable, i.e., both the first and second derivatives of the power angle are zero, the stable equilibrium point of the power angle before the fault can be calculated based on the fault depth of the power grid before and after the fault. and the stable equilibrium point of the power angle after the fault The expressions for the two are as follows:

[0086]

[0087] in, Indicates the depth of the power grid fault before the fault occurs, i.e. .

[0088] The stable equilibrium point of the power angle before the fault This represents the power angle at which the active power of the grid converter reached equilibrium before the fault occurred, and the stable equilibrium point of the power angle after the fault. Indicates the depth of the power grid fault after a power grid failure. The power angle corresponding to when the grid converter regains power balance.

[0089] Because the real-time power in the nonlinear power angle differential equation includes To obtain a directly solvable time-domain analytical expression for the power angle, the power angle stabilizes at the equilibrium point after the fault. to Performing a first-order Taylor expansion, the nonlinear work angle differential equation is linearized to obtain the linearized work angle differential equation:

[0090]

[0091] The linearization process will reduce the power angle. Represented as the stable equilibrium point of the power angle after the fault. The relationship between the power angle offset and the power angle offset is used to transform the original nonlinear power angle differential equation into a second-order linear differential equation with respect to the power angle offset.

[0092] Before the fault occurred, the grid converter was in a stable operating state, and no frequency change occurred at the moment of the fault. Therefore, the initial conditions for the first and second derivatives of the power angle are:

[0093]

[0094] Based on the linearized power angle differential equation and the initial conditions described above, and according to the solution formula for the second-order standard differential equation, the time-domain analytical expression of the power angle is obtained:

[0095]

[0096] in, This is the dynamic offset of the power angle relative to the stable equilibrium point of the power angle after the fault. Characterizes the magnitude of the dynamic offset of the power angle; Characterizes the degree of attenuation of dynamic offset of power angle; Characterizing the oscillation characteristics of dynamic offset of power angle; The initial phase characterizing the dynamic offset of the power angle.

[0097] Therefore, the time-domain analytical expression for the power angle can describe how the power angle of the grid converter changes from the stable equilibrium point of the power angle before the fault after a grid fault occurs. Towards the stable equilibrium point of the power angle after the fault The dynamic process of the transition serves as the basis for subsequent calculations of the linearized voltage excitation expression.

[0098] S5: Substitute the power angle analytical expression in S4 into the voltage input excitation expression in S1 to obtain the complete voltage excitation time-domain expression. At the power angle stable equilibrium point after the fault, perform a second-order Taylor expansion on the complete voltage excitation time-domain expression to obtain the linearized voltage excitation time-domain expression.

[0099] In S5, substituting the power angle analytical expression from S4 into the voltage input excitation expression from S1 yields the complete voltage excitation time-domain expression:

[0100]

[0101] Stable equilibrium point of power angle after fault Near the vicinity, the change in the power angle is relatively small, therefore, the voltage excitation time-domain expression is respectively... and Performing a second-order Taylor expansion on the term yields the linearized voltage excitation expression:

[0102]

[0103] in, Let the Taylor expansion order be given.

[0104] S6: Based on the frequency domain expression of the dq-axis current in S2, the linearized voltage excitation time domain expression in S5 is convolved with the time domain unit impulse response corresponding to the coaxial current response transfer function and the time domain unit impulse response corresponding to the cross-axis current response transfer function in S3 by the convolution theorem. The corresponding convolution results are then added to obtain the time domain analytical expression of the dq-axis current.

[0105] Specifically, based on the frequency domain expression of the dq-axis current obtained in S2, and according to the convolution theorem, the product of the transfer function and the input excitation in the frequency domain corresponds to the convolution of the unit impulse response and the input excitation in the time domain. Therefore, the linearized voltage excitation time domain expression obtained in S5 is convolved with the time domain unit impulse responses corresponding to the coaxial current response transfer function and the cross-axis current response transfer function, respectively, to obtain the current response components under different voltage excitations.

[0106] Among them, the coaxial current response transfer function corresponds to the voltage excitation and current response relationship in the same coordinate axis direction, and its time-domain unit impulse response characterizes the dynamic process of d-axis voltage excitation generating d-axis current response and q-axis voltage excitation generating q-axis current response, respectively; the cross-axis current response transfer function corresponds to the voltage coupling response relationship between different coordinate axes, and its time-domain unit impulse response characterizes the dynamic process of q-axis voltage excitation generating d-axis current response and d-axis voltage excitation generating q-axis current response, respectively.

[0107] Based on the superposition relationship in the frequency domain expression of the dq-axis current in S2, the convolution results of the coaxial response and the cross-axis response are superimposed to obtain the time domain analytical expression of the dq-axis current, that is, the time domain analytical expression of the d-axis current and the time domain analytical expression of the q-axis current:

[0108]

[0109] S7: Use the inverse Park transformation to transform the current in S6 from the dq coordinate system to the abc coordinate system, and then substitute the power angle time-domain analytical expression in S4 to obtain the full-stage fault current time-domain analytical expression in the abc coordinate system.

[0110] Since the current time-domain analytical expression obtained by S6 is the fault current expression in the dq-axis coordinate system, in order to obtain the fault current in the three-phase stationary coordinate system in the actual power grid, it is necessary to use the inverse Park transformation to convert the current in the dq-axis coordinate system to the abc coordinate system.

[0111] The rotation angle in the inverse Park transformation is determined by the power angle of the grid converter. Therefore, the power angle time-domain analytical expression obtained in S4 is used as the angle input for the inverse Park transformation so that the transformed three-phase current contains the dynamic change information of the power angle during the fault process.

[0112] Based on the inverse Park transformation relation, we obtain:

[0113]

[0114] Substituting the power angle time-domain analytical expression in S4 into the above equation, we obtain the full-stage fault current time-domain analytical expression in the abc coordinate system:

[0115]

[0116] To verify the accuracy of the analytical expression for fault current, simulations were performed on the Matlab / Simulink platform using the following parameter settings: the input voltage V of the grid converter. dc The voltage is 800V, the base AC voltage is 380V, the fundamental frequency of the AC grid is 50Hz, the rated capacity of the grid converter is 10kVA, the switching frequency is 10kHz, and the sampling frequency is 10kHz. The rated grid voltage E is 1.0pu, and the equivalent inductance X of the grid is... g The filter inductance of the grid converter is 0.22 pu, and the filter inductance is L. f The value is 0.02 pu, and the filter capacitor C is... f The voltage control proportional coefficient k is 0.36 pu. up The integral coefficient k of the voltage control is 0.2. ui The current control proportional coefficient k is 400. ip The integral coefficient k of the current control is 5. ii The damping coefficient D of the grid converter is 100, the inertial time constant H of the grid converter is 5s, the reference value of the output voltage U0 of the grid converter is 1.0pu, and the reference value of the active power P0 of the grid converter is 1.0pu.

[0117] Figure 4This figure compares the simulated fault current results of the grid converter in the dq and abc coordinate systems after a symmetrical voltage drop, obtained using the traditional method, with the theoretical calculation results. At t = 0.04s, the grid voltage symmetrically drops to 0.5 pu. The solid line represents the fault current result obtained from the Matlab / Simulink simulation, i.e., the simulation result, while the dashed line represents the fault current result calculated using the traditional method, i.e., the traditional calculation result. It can be seen that in the initial stage of the fault, because the traditional method ignores the inner-loop dynamics, the theoretical calculation results cannot accurately represent the fault impact current, and its current amplitude deviates significantly from the simulation results. As the fault process continues, due to the influence of numerical iteration calculation errors, there is still a significant deviation between the theoretical calculation results and the simulation results in the steady-state stage of the fault.

[0118] Figure 5 The diagram shows a comparison between analytical and simulation results of the grid converter fault current in the dq and abc coordinate systems after a symmetrical voltage drop under the method proposed in this invention. Similarly, at t=0.04s, the grid voltage symmetrically drops to 0.5pu, which is the grid fault depth in the analytical expression. When the value is 0.5 pu, the solid line represents the simulation result and the dashed line represents the analytical calculation result of the present invention. It can be seen that the analytical result of the fault current obtained by the present invention is in high agreement with the simulation result in both the initial stage and the continuous stage of the fault. It can accurately characterize the fault impact current and the fault steady-state current, and verify the correctness of the analytical expression of the fault current.

[0119] contrast Figure 4 and Figure 5 It is known that traditional methods suffer from significant errors in calculating the inrush current during the initial stage of a fault due to neglecting the dynamics of the inner loop of the grid-connected converter. Furthermore, the accuracy of calculating the current during the fault's duration is limited by numerical iteration errors. In contrast, this invention establishes a reduced-order fault current model while preserving the dominant dynamics and coupling characteristics of the inner and outer loops of the grid-connected converter. It then employs time-domain convolution to obtain an analytical expression for the fault current, enabling accurate characterization of both the inrush current during the initial stage and the steady-state current during the fault's duration. Therefore, this invention significantly improves the analytical accuracy of the fault current throughout all stages of the grid-connected converter, achieving a unified analytical description of the entire fault current process.

[0120] To further verify the analytical accuracy of the proposed method under different operating parameters and fault conditions, this embodiment introduces the Normalized Root Mean Square Error (NRMSE) to perform error analysis on the proposed method. The calculation method is as follows: it can be seen that the smaller the NRMSE, the smaller the calculation error.

[0121]

[0122] in, , Representing the first Simulated and analytically calculated values ​​of fault current at each sampling time; The total number of fault current sampling points involved in error calculation; The normalized root mean square error is used to characterize the degree of deviation between the analytical calculation results and the simulation results of the fault current.

[0123] Table 1 presents the normalized root mean square error (NRMSE) values ​​between the analytical and simulation results of the fault current under eight different operating conditions. The NRMSE values ​​vary depending on the grid fault depth. Equivalent inductance of power grid Damping coefficient Inertial time constant Voltage control proportional coefficient and voltage control integral coefficient We constructed verification conditions under different operating conditions.

[0124] As shown in Table 1, under different grid fault depths, line parameters, and control parameters, the NRMSE is less than 0.1%, indicating that the fault current analysis results of this invention have a high degree of consistency with the Matlab / Simulink simulation results, proving the correctness of the fault current analysis method.

[0125] Table 1 Error analysis of the proposed analytical method under different working conditions

[0126]

[0127] As shown in Table 1, even with changes in grid fault depth, equivalent grid inductance, damping coefficient, inertia time constant, and voltage control parameters, the normalized root mean square error between the fault current analysis results and simulation results of this invention remains at a low level. This indicates that the fault current analysis method of this invention has good adaptability to different fault conditions, line parameters, and control parameters. Combined with... Figure 4 and Figure 5 The comparison results further illustrate that the present invention can maintain high analytical accuracy while taking into account both the transient impact current in the initial stage of the fault and the steady-state current in the continuous stage of the fault, thereby achieving a unified analytical characterization of the fault current in the grid converter throughout all stages.

[0128] The above-described embodiments are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. Those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A method for analyzing fault current in a grid-connected converter based on model order reduction and time-domain convolution, characterized in that, Includes the following steps: 1) Based on the inner loop control structure of the grid converter, the forward path transfer function of the fault current in the dq coordinate system is obtained by adopting the order reduction method of dominant pole retention. Then, combined with the current coupling relationship between the dq axes, the coaxial current response transfer function and the cross-axis current response transfer function, as well as the frequency domain expression of the dq axis current are obtained. 2) Perform eigenvalue decomposition and inverse Laplace transform on the coaxial current response transfer function and the cross-axis current response transfer function to obtain the time-domain unit impulse response corresponding to each response transfer function; 3) Based on the outer loop control structure of the grid converter and the grid fault depth, a nonlinear power angle differential equation is established; the power angle stable equilibrium point after the fault is obtained according to the grid fault depth, and the nonlinear power angle differential equation is analyzed at this equilibrium point to obtain the power angle time-domain analytical expression. 4) Based on the power angle time-domain analytical expression, perform a second-order Taylor expansion on the voltage input excitation part in the dq-axis current frequency-domain expression to obtain a linearized voltage excitation time-domain expression. Then, perform time-domain convolution with the time-domain unit impulse response from step 2), and superimpose the convolution results to obtain the dq-axis current time-domain analytical expression. Combine this with the power angle time-domain analytical expression to obtain the full-stage fault current time-domain analytical expression in the abc coordinate system.

2. The method for analyzing fault current in a grid-connected converter based on model order reduction and time-domain convolution as described in claim 1, characterized in that, In step 1), obtaining the forward path transfer function of the fault current in the dq coordinate system includes: obtaining the poles corresponding to the inner loop control structure, retaining the dominant poles corresponding to the transient response of the fault current of the grid converter, and reducing the order of the inner loop control structure based on the retained dominant poles to obtain the forward path transfer function.

3. The method for analyzing fault current in a grid-connected converter based on model order reduction and time-domain convolution as described in claim 1, characterized in that, In step 1), obtaining the coaxial current response transfer function and the cross-axis current response transfer function includes: obtaining the d-axis voltage input excitation and the q-axis voltage input excitation based on the phase relationship between the grid voltage and the terminal voltage in the dq coordinate system; based on the forward channel transfer function, and combined with the coupling effect of the grid converter output angular frequency and the grid equivalent inductance on the dq-axis current response, obtaining the coaxial current response transfer function characterizing the d-axis voltage input excitation to the d-axis current and the q-axis voltage input excitation to the q-axis current, and the cross-axis current response transfer function characterizing the q-axis voltage input excitation to the d-axis current and the d-axis voltage input excitation to the q-axis current.

4. The method for analyzing fault current in a grid-connected converter based on model order reduction and time-domain convolution as described in claim 3, characterized in that, In step 1), obtaining the frequency domain expression of the dq-axis current includes: adding the product of the d-axis voltage input excitation and the coaxial current response transfer function and the product of the q-axis voltage input excitation and the cross-axis current response transfer function to obtain the frequency domain expression of the d-axis current; and subtracting the product of the d-axis voltage input excitation and the cross-axis current response transfer function from the product of the q-axis voltage input excitation and the coaxial current response transfer function to obtain the frequency domain expression of the q-axis current.

5. The method for analyzing fault current in a grid-connected converter based on model order reduction and time-domain convolution as described in claim 1, characterized in that, Step 2) includes: solving for the eigenvalues ​​of the coaxial current response transfer function and the cross-axis current response transfer function to obtain two pairs of eigenvalues; decomposing the coaxial current response transfer function and the cross-axis current response transfer function based on the two pairs of eigenvalues, and performing inverse Laplace transform on the decomposition results to obtain the time-domain unit impulse response corresponding to each response transfer function.

6. The method for analyzing fault current in a grid-connected converter based on model order reduction and time-domain convolution as described in claim 1, characterized in that, In step 3), establishing the nonlinear power angle differential equation includes: obtaining the output angular frequency of the grid converter based on the outer loop control structure, and obtaining the power angle based on the output angular frequency of the grid converter; obtaining the real-time power of the grid converter based on the grid fault depth, power angle and grid equivalent inductance, and establishing the nonlinear power angle differential equation based on the outer loop control structure and real-time power.

7. The method for analyzing fault current in a grid-connected converter based on model order reduction and time-domain convolution as described in claim 1, characterized in that, In step 3), obtaining the stable equilibrium point of the power angle after the fault includes: obtaining the stable equilibrium point of the power angle after the fault based on the fault depth of the power grid, combined with the reference value of the output voltage of the grid converter, the equivalent impedance of the power grid and the power transmission characteristics of the transmission line. The process of obtaining the time-domain analytical expression for the power angle includes: performing a first-order Taylor expansion on the power angle term in the nonlinear power angle differential equation at the power angle stable equilibrium point after the fault to obtain a linearized power angle differential equation; and solving the linearized power angle differential equation using the power angle stable equilibrium point before the fault as the initial power angle condition when the fault occurs to obtain the time-domain analytical expression for the power angle.

8. The method for analyzing fault current in a grid-connected converter based on model order reduction and time-domain convolution as described in claim 4, characterized in that, In step 4), obtaining the linearized voltage excitation time-domain expression includes: substituting the power angle time-domain analytical expression into the voltage excitation expression in the dq coordinate system composed of the d-axis voltage input excitation and the q-axis voltage input excitation, and then performing a second-order Taylor expansion on the obtained expression at the power angle stable equilibrium point after the fault to obtain the linearized voltage excitation time-domain expression.

9. The method for analyzing fault current in a grid-connected converter based on model order reduction and time-domain convolution as described in claim 1, characterized in that, In step 4), obtaining the time-domain analytical expression of the dq-axis current includes: performing time-domain convolution of the voltage excitation time-domain expression with the time-domain unit impulse responses corresponding to the coaxial current response transfer function and the cross-axis current response transfer function, respectively, and superimposing the convolution results according to the superposition relationship in the frequency-domain expression of the dq-axis current to obtain the time-domain analytical expression of the dq-axis current.

10. The method for analyzing fault current in a grid-connected converter based on model order reduction and time-domain convolution as described in claim 1, characterized in that, In step 4), the time-domain analytical expression of the dq-axis current is subjected to inverse Park transformation, and then substituted into the time-domain analytical expression of the power angle to obtain the time-domain analytical expression of the full-stage fault current in the abc coordinate system.

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