A grid commutated converter modeling method based on sequence immittance method

Abstract

The application discloses a grid commutated converter modeling method based on a sequence admittance method, and belongs to the technical field of smart grids. The grid commutated converter is equivalent to a two-port network formed by an alternating current port and a direct current port to construct an original equivalent switch model of the grid commutated converter, trigger angles, commutation angles and direct current are taken as target variables, and the original equivalent switch model of the grid commutated converter is linearized and preliminarily simplified; the trigger angle and the commutation overlap angle are included in the model, and the description precision of commutation dynamics and impedance characteristics can be improved. The sequence admittance basic module is simplified to obtain an equivalent admittance module considering direct current closed loop coupling, the LCC body is decoupled from external alternating current networks and direct current networks, the alternating current port coupling and the frequency coupling can be uniformly represented while the commutation process is considered; finally, the controlled current source is used to represent the positive and negative sequence frequency coupling, and the LCC admittance accurately representing the multi-dimensional coupling characteristics.

Description

Technical Field

[0001] This application belongs to the field of smart grid technology, and more specifically, relates to a modeling method for grid commutator converters based on the sequential impedance method. Background Technology

[0002] High-voltage direct current (HVDC) grid-connected systems based on line commutated converters (LCCs) have become a key grid-connected technology for large-scale long-distance transmission of renewable energy and cross-regional power exchange, thanks to their core advantages of large transmission capacity, low loss, mature technology, and outstanding economic efficiency. They have been widely applied in engineering scenarios such as centralized grid connection of wind and solar power bases and asynchronous interconnection of large power grids. In recent years, with the continuous increase in the proportion of renewable energy installed capacity on the grid-connected side and the continuous decrease in the equivalent short-circuit ratio of AC systems, the dynamic interaction between LCC converter stations and sending-end renewable energy plants, receiving-end AC grids, DC networks, and multi-level control systems has significantly increased. The dynamic response of the grid-connected system in subsynchronous, near-fundamental frequency, and even supersynchronous frequency bands exhibits strong nonlinearity and multi-band coupling characteristics, placing requirements on the small-signal modeling accuracy and stability analysis reliability of the grid-connected system that are far higher than those of traditional pure AC grids.

[0003] Impedance analysis is the mainstream technical approach in the field of grid-connected system stability analysis. This method constructs port reactance models of the converter equipment and the external power grid at the grid interface. Relying on the small-signal interaction characteristics of the two, it can directly identify potential instability frequency bands, quantify the system stability margin, and clearly explain the oscillation mechanism without requiring high-order state-space modeling of the entire system. It has strong engineering adaptability in complex HVDC grid scenarios. However, under the current technical system, the reactance modeling of grid commutation converters still has a core defect of insufficient accuracy, which has become a key bottleneck restricting the reliability of grid-connected system stability analysis in weak grid scenarios. Most existing modeling methods have significant deviations in the characterization of the commutation dynamic process. They either directly ignore the physical process of commutation overlap or oversimplify the transient changes during commutation, failing to accurately reproduce the dynamic characteristics of the commutation overlap interval directly caused by the leakage inductance of the converter transformer. This results in significant deviations between the response characteristics of the established reactance model over a wide frequency range and the actual physical device. Such inaccurate impedance models cannot fully characterize the coupling effect between the AC grid-connected port and the DC grid-connected port of the LCC converter station, nor can they accurately depict the coupling propagation relationship of different frequency components in the grid-connected link. Ultimately, this will directly reduce the credibility of subsequent grid-connected system stability analysis results and cannot provide a reliable theoretical basis for broadband stability control of LCC-type high-voltage DC grid-connected systems with a high proportion of new energy access.

[0004] Therefore, developing an LCC impedance modeling and stability analysis method that can accurately account for the commutation physical process and fully characterize the multi-dimensional coupling characteristics is an important technical problem that urgently needs to be solved in this field. Summary of the Invention

[0005] In view of the above-mentioned defects or improvement needs of the existing technology, this application provides a modeling method for power grid commutated converters based on the sequential reactance method, which is used to solve the technical problem of insufficient accuracy in reactance modeling of power grid commutated converters.

[0006] To achieve the above objectives, according to one aspect of this application, a method for modeling power grid commutator converters based on the sequential reactance method is provided, comprising: S1: Equivalent the grid commutator to a two-port network consisting of AC and DC ports, and transform each variable of the AC port to the sequence domain; S2: Establish the original equivalent switching model of the two-port network corresponding to the grid commutator, including the DC voltage equivalent switching model and the converter transformer leakage inductance voltage equivalent switching model; S3: Using the firing angle, commutation angle, and DC current of the grid commutator as target variables, inject AC positive-sequence, AC negative-sequence, and DC voltage disturbances corresponding to each into the grid commutator to linearize the original equivalent switching model and obtain the target equivalent switching model; perform preliminary simplification of the target equivalent switching model to obtain the sequence admittance basic module; S4: The sequence admittance basic module is further simplified to obtain an equivalent admittance module considering DC closed-loop coupling, including: positive sequence self-admittance. Positive-to-negative-sequence coupling admittance Negative-order self-admittance Negative-sequence to positive-sequence coupling admittance ; S5: The coupling effect between the positive-sequence network and the negative-sequence network is equivalent to a controlled current source, further simplifying the equivalent admittance module to obtain the decoupled equivalent positive-sequence admittance. Y p ( s and equivalent negative order admittance Y n ( s ).

[0007] Furthermore, the DC voltage equivalent switching model is expressed as: ; In the formula, This represents the DC-side voltage of a twelve-pulse LCC. They represent phases A, B, and C, respectively. This represents the three-phase voltage on the LCC valve side of the YY connection. Indicates direct current. This indicates the leakage inductance of the converter transformer. and These represent the equivalent switching functions from AC voltage to DC voltage and from DC current to DC voltage, respectively. ; ; in, m For non-zero integer harmonic orders, j The imaginary unit, The system's fundamental angular frequency. G m This indicates the setting coefficient. The equivalent switching function retains 12 pulses corresponding to the twelve-pulse commutation process. k ±1st characteristic harmonic, For trigger angle, This is the commutation overlap angle. The harmonic selectivity is formed by the superposition of two six-pulse converter bridges with a phase shift of 30°. Summation index k This represents the six commutation sections of a six-pulse converter bridge.

[0008] Furthermore, the equivalent switching model of the leakage inductance voltage of the grid commutator includes: ; In the formula, This represents the leakage inductance voltage of the A-phase converter transformer. They represent phases A, B, and C, respectively. This represents the three-phase voltage on the LCC valve side of the YY connection. Indicates direct current. This indicates the leakage inductance of the converter transformer. and These represent the equivalent switching functions from AC voltage and DC current to the leakage inductance voltage of phase A, respectively. ; In the formula, This is the commutation overlap angle. K m To account for the Fourier coefficients in the commutation overlap interval, m For non-zero integer harmonic orders, j The imaginary unit, The system's fundamental angular frequency. The trigger angle is circ(), which represents the circular matrix generation operation.

[0009] Furthermore, in step S3, the equivalent switching model is linearized to obtain the target equivalent switching model, which includes: using a small-signal linearization method for voltage and current during commutation to linearize the original equivalent switching model to obtain the target equivalent switching model; The integral relationship represents: ; The small-signal linearization method is expressed as follows: ; in, , These represent the commutation start time and commutation end time, respectively. The subscript 0 indicates the steady-state component, and the superscript " "Indicates small signal components, This indicates the leakage inductance of the converter transformer. i a,1 and v a,1 , v b,1 These represent the A-phase current and A and B-phase voltages on the valve side of the corresponding six-pulse converter bridge, respectively. i dc Indicates direct current. This represents the fundamental angular frequency; for the commutation process of other phases or another six-pulse commutator bridge, the corresponding integral relationship is obtained by phase shifting; For trigger angle and changing phase angle The equivalent switching function, For trigger angle, This is the steady-state operating point.

[0010] Furthermore, in S3, the target equivalent switching model is initially simplified to obtain the sequence admittance basic module, which includes: The target equivalent switching model is simplified using small-signal relationships to obtain the basic module of sequence admittance, which includes: self-admittance under positive-sequence perturbation at the AC port, negative-sequence perturbation at the AC port, and perturbation at the DC port. Y pp , Y nn , Y dcdc and transfer admittance Y pn , Y np , Y pdc , Y ndc , Y dcp and Y dcn ; In rectifier operation mode, the small-signal quantity of the trigger angle disturbance in the small-signal relationship is: ; In inverter operation mode, the small-signal quantity of the trigger angle disturbance in the small-signal relationship is: ; Among them, the subscript p , n and DC These represent the positive sequence AC, negative sequence AC, and DC component, respectively. To inject the frequency offset variable of the disturbance, To inject complex frequency variables that cause disturbances, f p For the perturbation frequency, The system's fundamental angular frequency. k This is the frequency offset multiple; The small signal quantity representing the phase angle of the phase-locked loop output. , For small semaphores of the firing angle, and These are small signal quantities for DC current and DC voltage, respectively. H f,idcr and H idc,r These represent the DC current measurement and filtering stage and the DC current controller in rectifier operation mode, respectively. H f,vdci and H vdc,i These represent the DC voltage measurement and filtering stage and the DC voltage controller in inverter operation mode, respectively. This refers to a phase-locked loop controller in either rectification or inverter mode. This represents the positive-sequence disturbance voltage.

[0011] Further, S4 includes: Using formula The ordered admittance basic module is further simplified to obtain the equivalent admittance module considering DC closed-loop coupling; Among them, Z dc This represents the impedance of the DC power grid.

[0012] Furthermore, in S5, the following is utilized The equivalent admittance module is further simplified.

[0013] According to another aspect of this application, a stability analysis method for a grid-connected system with a power grid commutator is provided, comprising: The equivalent positive-sequence admittance is obtained using the aforementioned grid commutator modeling method. Y p (s and equivalent negative order admittance Y n ( s ); Obtain the positive-sequence admittance of the AC network connected to the grid commutator. Y gp ( s ); Using formula L p ( s )= Y p ( s ) / Y gp ( s Construct the impedance ratio; determine the impedance ratio L. p ( s Does the Nyquist curve of ) encircle the critical point () 1, j 0); If the condition is met, the grid-connected system of the grid-commutator is determined to be in an unstable state; otherwise, it is in a stable state.

[0014] Furthermore, the stability analysis method for the grid-connected system of the power grid commutator converter also includes: The control variable method is used to change at least one of the following parameters: phase-locked loop parameters, DC current control parameters, DC voltage control parameters, AC network strength, DC network parameters, transmission power, DC voltage, or AC filter parameters, and the corresponding impedance ratio is calculated. The stability margin is calculated using the impedance ratio; if the stability margin is less than a threshold, the grid-connected system of the grid-commutated converter is determined to be in an unstable state, and then the corresponding instability frequency band is determined using the amplitude crossover frequency corresponding to the impedance ratio.

[0015] According to another aspect of this application, a control system for a grid-connected system of a grid-commutated converter is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the grid-connected system of the grid-commutated converter based on the sequential reactance method or the steps of the grid-connected system of the grid-commutated converter.

[0016] Overall, compared with the prior art, the above-described technical solutions conceived in this application can achieve the following beneficial effects: (1) This invention provides a modeling method for grid commutator converters based on the sequential admittance method. It equates the grid commutator converter to a two-port network consisting of AC and DC ports, and then constructs an equivalent switching function model of the commutator converter. The firing angle, commutation angle, and DC current of the grid commutator converter are used as target variables. The original equivalent switching model is linearized and initially simplified to obtain the sequential admittance basic module. This design incorporates the firing angle and commutation overlap angle into the model, which can improve the accuracy of describing the commutation dynamics and impedance characteristics. The sequential admittance basic module is further simplified to obtain an equivalent admittance module that considers DC closed-loop coupling. The LCC body is decoupled from the external AC and DC networks, which can uniformly characterize AC and DC port coupling and frequency coupling while considering the commutation process. Finally, the positive and negative sequence frequency couplings are characterized by a controlled current source, and the LCC reactance that considers the commutation physical process and accurately characterizes the multi-dimensional coupling characteristics is obtained.

[0017] (2) The DC voltage equivalent switching model of this scheme is: This design takes into account that during the commutation process, the AC side voltage will form an equivalent voltage on the DC side that changes periodically with the switching state after passing through the commutation bridge, and the commutation process will change the mapping relationship between DC current and DC voltage. The advantage is that the equivalent switching function can be used to uniformly describe the conversion process of AC side voltage to DC side voltage, and the influence of the commutation process on the DC port voltage characteristics can be retained. This can provide a unified mathematical basis for the subsequent establishment of the frequency coupling relationship and sequence admittance model between AC port and DC port.

[0018] (3) The equivalent switching model of leakage inductance voltage in this scheme is: This design takes into account that the voltage drop caused by the leakage inductance of the converter transformer during commutation is directly related to the change in commutation current, which is an important factor affecting the commutation process and the characteristics of the converter port. The advantage is that the commutation voltage drop caused by the leakage inductance of the converter transformer can be explicitly introduced into the converter model in the form of an equivalent switching model without the need for additional segmented modeling of the commutation process. This can more accurately characterize the impact of commutation overlap on the small-signal characteristics of the AC and DC sides of the grid commutation converter, and improve the accuracy of the established sequence admittance model.

[0019] (4) This scheme uses the small-signal linearization method of voltage and current during commutation to linearize the original equivalent switching model to obtain the target equivalent switching model. Considering the mutual coupling relationship between the switching function, commutation angle and AC side voltage and current during commutation, it is difficult to obtain a linear relationship suitable for small-signal stability analysis by directly performing frequency domain analysis on the original nonlinear model. The advantage is that, while retaining the influence of the commutation process, the nonlinear equivalent switching relationship can be transformed into a linear disturbance relationship near the operating point, and the transmission relationship between each disturbance quantity can be clarified. This can obtain a target equivalent switching model suitable for frequency domain modeling and sequence admittance derivation, providing a foundation for the subsequent establishment of a port small-signal model that includes the influence of commutation.

[0020] (5) This scheme uses small-signal relationships to simplify the equivalent switching model of the target to obtain the sequence admittance basic module, including: self-admittance under positive-sequence disturbance at the AC port, negative-sequence disturbance at the AC port, and disturbance at the DC port. Y pp , Y nn , Y dcdc and transfer admittance Y pn , Y np , Y pdc , Y ndc , Y dcp and Y dcn This design takes into account the frequency coupling between the AC positive-sequence, AC negative-sequence, and DC ports of the grid-commutated converter. It is difficult to fully describe the disturbance propagation relationship between different ports and different sequence components using only the single AC port admittance. The advantage is that it can divide the complex small-signal relationship of the converter into the self-admittance and transferred admittance corresponding to three ports, and characterize the response of each port and the coupling response between different ports in a modular form. It can fully describe the frequency coupling characteristics between AC positive and negative sequences and between AC ports and DC ports, and improve the composability and scalability of the model.

[0021] (6) This scheme utilizes the formula The sequence admittance module is further simplified to obtain an equivalent admittance module considering DC closed-loop coupling. This design takes into account that after the grid-connected commutator is connected to the DC network, DC port disturbances will be fed back to the AC port via the DC network. This means the AC port characteristics are simultaneously affected by both the converter's own characteristics and the DC network's characteristics. The advantage is that the feedback effects of the DC port and the DC network on the AC side can be equivalently converted to the AC port. While retaining the influence of AC / DC port coupling, the number of independent port variables is reduced. This results in an equivalent admittance module that can be directly used for AC side stability analysis, and avoids ignoring impedance characteristic deviations and stability judgment errors caused by DC closed-loop coupling.

[0022] (7) In this scheme S5, the following is utilized The equivalent admittance module is further simplified. This design, considering the frequency coupling between the positive and negative sequence components, avoids the high order and complex analysis process of directly using a multivariate model containing positive and negative sequence coupling terms for stability analysis. The advantage is that it utilizes the coupling relationship between positive and negative sequence disturbances to equivalently convert the influence of the negative sequence channel on the positive sequence channel to the corresponding positive sequence admittance, thus obtaining the decoupled positive and negative sequence equivalent admittances. This reduces the model dimensionality while preserving the influence of positive and negative sequence frequency coupling, transforming the multivariate stability problem into a univariate stability problem that is easier to analyze using the Nyquist criterion.

[0023] (8) This scheme provides a stability analysis method for a grid-connected system with a phase-commutator converter, using formula L p ( s )= Y p ( s ) / Y gp ( s Construct the impedance ratio; determine the impedance ratio L. p ( s Does the Nyquist curve of ) encircle the critical point () 1, j 0); if it is included, the grid-connected system of the grid-commutated converter is determined to be in an unstable state; otherwise, it is in a stable state. This design, considering that after the aforementioned equivalence processing, the interaction between the positive-sequence port of the converter and the AC grid can be characterized by the equivalent admittance ratio, and the system stability depends on the closed-loop characteristics of the feedback loop at that port, has the advantage of being able to construct a single-variable open-loop transfer relationship based on the equivalent positive-sequence admittance of the converter and the positive-sequence admittance of the grid, and directly determine the stability of the closed-loop system using the Nyquist curve. This avoids directly solving for eigenvalues ​​in the high-dimensional coupling model while preserving the effects of AC / DC port coupling and positive / negative sequence frequency coupling, thus reducing the complexity of grid-connected stability analysis of the grid-commutated converter.

[0024] (9) This scheme uses the control variable method to obtain the impedance ratio corresponding to different scenarios, and uses the impedance ratio to calculate the stability margin; if the stability margin is less than the threshold, it is determined that the grid-connected system of the grid-commutated converter is in an unstable state, and then the corresponding instability frequency band is determined by the amplitude crossover frequency corresponding to the impedance ratio. In this design, considering that changes in grid strength, operating power, control parameters and AC / DC network parameters will all change the impedance matching relationship between the converter and the grid, thereby affecting the system stability margin and potential oscillation frequency, the advantage is that the influence of different operating conditions and system parameter changes on grid-connected stability can be quantified by the control variable method, and the stability margin of the impedance ratio can be used to make a unified comparison of different scenarios. It can further locate the potential instability frequency band based on the amplitude crossover frequency, identify the key factors affecting system stability, and provide a basis for parameter design and stability improvement. Attached Figure Description

[0025] Figure 1 This is a flowchart of a power grid commutator modeling method based on sequential reactance method in one embodiment of the present invention; Figure 2 This is a topology diagram of a 12-pulse LCC grid-connected system according to an embodiment of the present invention; Figure 3 This is a control structure diagram of LCC under different operating modes in one embodiment of the present invention; Figure 4 This is a schematic diagram of the frequency coupling of the injected perturbation-response in one embodiment of the present invention; Figure 5 This is a schematic diagram of a commutation process considering disturbances in one embodiment of the present invention; Figure 6 This is a block diagram considering the transmission of AC / DC port coupling sequence impedance in one embodiment of the present invention; Figure 7 This is a comparison chart of theoretical calculation values ​​and frequency sweep results in one embodiment of the present invention; Figure 8 This is a diagram illustrating the effect of different power grid intensities on stability in one embodiment of the present invention; Figure 9 This is a Nyquist curve, time-domain simulation, and FFT analysis diagram when the short-circuit ratio is 2.93 in one embodiment of the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application. Furthermore, the technical features involved in the various embodiments described below can be combined with each other as long as they do not conflict with each other.

[0027] Example 1 This embodiment provides a modeling method for power grid commutator converters based on the sequential reactance method, such as... Figure 1 As shown, it includes: S1-S5.

[0028] S1: Equivalent the grid commutator to a two-port network consisting of AC and DC ports, and transform each variable of the AC port to the sequence domain.

[0029] S2: Establish the original equivalent switching model of the two-port network corresponding to the grid commutator, including the DC voltage equivalent switching model and the converter transformer leakage inductance voltage equivalent switching model.

[0030] S3: Using the firing angle, commutation angle, and DC current of the grid commutator as target variables, inject AC positive-sequence, AC negative-sequence, and DC voltage disturbances corresponding to each into the grid commutator to linearize the original equivalent switching model and obtain the target equivalent switching model; perform preliminary simplification on the target equivalent switching model to obtain the sequence admittance basic module.

[0031] S4: The sequence admittance basic module is further simplified to obtain an equivalent admittance module considering DC closed-loop coupling, including: positive sequence self-admittance. Positive-to-negative-sequence coupling admittance Negative-order self-admittance Negative-sequence to positive-sequence coupling admittance .

[0032] S5: The coupling effect between the positive-sequence network and the negative-sequence network is equivalent to a controlled current source, further simplifying the equivalent admittance module to obtain the decoupled equivalent positive-sequence admittance. Y p ( s and equivalent negative order admittance Y n ( s ).

[0033] like Figure 2As shown, this embodiment uses a twelve-pulse LCC system as the object. The system includes an AC power grid, an AC filter, a converter transformer, a twelve-pulse LCC, a smoothing reactor, and a DC network. The twelve-pulse LCC consists of two six-pulse converter bridges with a 30° phase shift. The AC power grid can be equivalently represented as an ideal voltage source connected in series with an RL branch, and the DC network can be modeled using lumped parameter or distributed parameter models. When observing from the DC port of the LCC under analysis, the DC line, the counterpart converter station, and its AC system can all be uniformly represented as the external DC equivalent impedance. Z dc .

[0034] like Figure 3 As shown, in rectification mode, the LCC uses a phase-locked loop to track the AC grid phase and a constant DC current control to adjust the firing angle; in inverter mode, the LCC uses a phase-locked loop and a constant DC voltage control. The control structure is not limited to a single closed loop; when there is an outer loop control, additional damping control, or a limiting element, its transfer function can be incorporated into the small-signal relationship of the firing angle.

[0035] like Figure 4 As shown, the LCC is separated from the external AC and DC networks, retaining only the AC and DC ports. The AC port uses symmetrical component transformation to obtain positive and negative sequence variables. The disturbance frequency is defined as... f p The complex frequency variable and the frequency offset variable are respectively: ; in, The system's fundamental angular frequency. k This represents the frequency offset factor relative to the fundamental frequency. Positive-sequence voltage disturbances are injected into the AC ports respectively. Negative sequence voltage disturbance And inject DC voltage disturbance into the DC port. The AC positive sequence current, AC negative sequence current and DC current response were measured to obtain the nine sequence conductance basic modules shown in Table 1.

[0036] Table 1: LCC Sequential Anti-Judge Basic Module Definition

[0037] The above subscripts p , n and DC These represent the positive-sequence AC, negative-sequence AC, and DC components, respectively. The first subscript indicates the disturbance type, and the second subscript indicates the response type. For the same device, impedance and admittance are mathematically inverses; in this paper, they are collectively referred to as reactance. Since the LCC synchronizes with the power grid through a phase-locked loop and mainly exhibits controlled current source characteristics, this embodiment preferably uses the admittance form to satisfy the self-stabilizing modeling principle.

[0038] As an optional implementation, the DC voltage equivalent switching model is expressed as: ; In the formula, This represents the DC-side voltage of a twelve-pulse LCC. They represent phases A, B, and C, respectively. This represents the three-phase voltage on the LCC valve side of the YY connection. Indicates direct current. This indicates the leakage inductance of the converter transformer. and These represent the equivalent switching functions from AC voltage to DC voltage and from DC current to DC voltage, respectively.

[0039] Furthermore, the equivalent switching model of the leakage inductance voltage of the converter transformer includes: ; In the formula, This represents the leakage inductance voltage of the A-phase converter transformer. They represent phases A, B, and C, respectively. This represents the three-phase voltage on the LCC valve side of the YY connection. Indicates direct current. This indicates the leakage inductance of the converter transformer. and These represent the equivalent switching functions from AC voltage and DC current to the leakage inductance voltage of phase A, respectively.

[0040] Specifically, for two six-pulse commutator bridges, the DC-side voltage is the sum of the DC voltages of the two bridges, and the DC current is the same. Based on the phase shift relationship, the DC voltage of the twelve-pulse LCC can be uniformly written as the following equivalent switching function form:

[0041] In the formula, This represents the DC-side voltage of a twelve-pulse LCC. This represents the three-phase voltage on the LCC valve side of the YY connection. Indicates direct current. This is the equivalent switching function of the three-phase grid voltage to DC voltage. The equivalent switching function corresponding to the rate of change of DC current This refers to the leakage inductance of the converter transformer.

[0042] The leakage inductance voltage of the converter transformer can be written as:

[0043] In the formula, and These represent the equivalent switching functions of AC voltage and DC current to the leakage inductance voltage of phase A, respectively. The twelve-pulse grid-side current is obtained through power balance and the phase shift relationship of two six-pulse bridges. The switching functions, expanded using Fourier series, can be uniformly expressed as:

[0044] In the formula, m For non-zero integer harmonic orders, j The imaginary unit; determined by the coefficient G m It can be seen that the equivalent switching function retains 12 pulses corresponding to the twelve-pulse commutation process. k ±1st characteristic harmonic, with the firing angle considered in both its amplitude and phase. Commutation overlap angle .

[0045]

[0046] In the formula, H m The harmonic selectivity coefficient is the summation subscript of the harmonic selection coefficient formed by the superposition of two six-pulse converter bridges with a phase shift of 30°. k This represents the six commutation sections of a six-pulse converter bridge.

[0047]

[0048] And satisfy:

[0049] In the formula, K m To account for the Fourier coefficients in the commutation overlap interval, circ() represents the circular matrix generation operation. D m The phase sequence rotation matrix; the leakage inductance voltage equivalent switching function contains 12 k ±2nd characteristic harmonic.

[0050] As an optional implementation, the linearization of the equivalent switching model in S3 to obtain the target equivalent switching model includes: using a small-signal linearization method for voltage and current during commutation to linearize the original equivalent switching model to obtain the target equivalent switching model; The integral relationship represents: ; The small-signal linearization method is expressed as follows: ; in, , These represent the commutation start time and commutation end time, respectively. The subscript 0 indicates the steady-state component, and the superscript " "Indicates small signal components, This indicates the leakage inductance of the converter transformer. i a,1 and v a,1 , v b,1 These represent the A-phase current and A and B-phase voltages on the valve side of the corresponding six-pulse converter bridge, respectively. i dc Indicates direct current. This represents the fundamental angular frequency; for the commutation process of other phases or another six-pulse commutator bridge, the corresponding integral relationship is obtained by phase shifting; For trigger angle and changing phase angle The equivalent switching function, For trigger angle, This is the steady-state operating point.

[0051] Furthermore, in S3, the target equivalent switching model is initially simplified to obtain the sequence admittance basic module, including: simplifying the target equivalent switching model using small-signal relationships to obtain the sequence admittance basic module, including: self-admittance under positive-sequence disturbance at the AC port, negative-sequence disturbance at the AC port, and disturbance at the DC port. Y pp , Y nn , Y dcdc and transfer admittance Y pn , Y np , Y pdc , Y ndc , Y dcp and Y dcn ; In rectifier operation mode, the small-signal quantity of the trigger angle disturbance in the small-signal relationship is: ; In inverter operation mode, the small-signal quantity of the trigger angle disturbance in the small-signal relationship is: ; Among them, the subscript p , n and DC These represent the positive sequence AC, negative sequence AC, and DC component, respectively. To inject the frequency offset variable of the disturbance, To inject complex frequency variables that cause disturbances, f pFor the perturbation frequency, The system's fundamental angular frequency. k This is the frequency offset multiple; The small signal quantity representing the phase angle of the phase-locked loop output. , For small semaphores of the firing angle, and These are small signal quantities for DC current and DC voltage, respectively. H f,idcr and H idc,r These represent the DC current measurement and filtering stage and the DC current controller in rectifier operation mode, respectively. H f,vdci and H vdc,i These represent the DC voltage measurement and filtering stage and the DC voltage controller in inverter operation mode, respectively. This refers to a phase-locked loop controller in either rectification or inverter mode. This represents the positive-sequence disturbance voltage.

[0052] Specifically, during steady-state operation, the trigger angle Commutation overlap angle and DC current I dc0 These are constant values; under small-signal perturbations, each of the three generates a perturbation amount. and .like Figure 5 As shown, the trigger time and commutation end time vary with the disturbance, therefore it is necessary to linearize both the integrand and the upper and lower limits of the commutation integral. Taking phase A commutation as an example, the following can be established:

[0053] The relationship between the commutation start time, commutation end time, and arc extinction angle is as follows:

[0054] In the formula, the subscript 0 represents the steady-state component, and the symbol " "Indicates small signal components, i a,1 and v a,1 , v b,1 These represent the A-phase current and A and B-phase voltages on the valve side of the corresponding six-pulse converter bridge, respectively. The fundamental angular frequency is represented by . For the commutation process of other phases or another six-pulse commutator bridge, the corresponding integral relationship is obtained by phase shifting. Subsequently, the formula in Example 1 is linearized to obtain the DC voltage disturbance, leakage inductance voltage disturbance, and AC positive and negative sequence current responses.

[0055] The phase angle disturbance of the control coordinate system caused by the phase-locked loop can be expressed as:

[0056] In rectifier operation mode, the firing angle disturbance is determined by both the DC current closed-loop output and the phase angle disturbance of the phase-locked loop:

[0057] In inverter operation mode, the DC current closed loop is replaced with a DC voltage closed loop:

[0058] In the formula, H f,idcr and H idc,r These represent the DC current measurement and filtering stage and the DC current controller in rectifier operation mode, respectively. H f,vdci and H vdc,i These represent the DC voltage measurement and filtering stage and the DC voltage controller in inverter operation mode, respectively. This represents a small signal quantity indicating the phase angle of the phase-locked loop output.

[0059] This allows for the extraction of... Y pp , Y pn and Y pdc The remaining modules are obtained in a similar manner. Using the conjugate relation of real signal phasors, the nine modules can be reduced to five independent modules:

[0060] In the formula, This represents complex conjugate. When the final model is applied to the converter transformer grid side, it still needs to be calculated based on the turns ratio. k T Voltage and current are converted into a unified value.

[0061] As an optional implementation, S4 includes: Using formula The ordered admittance basic module is further simplified to obtain the equivalent admittance module considering DC closed-loop coupling; Among them, Z dc This represents the impedance of the DC power grid.

[0062] As an optional implementation, S5 utilizes The equivalent admittance module is further simplified.

[0063] Specifically, such as Figure 5 and Figure 6 As shown, when a positive-sequence perturbation of frequency fp is injected into the AC port, the AC port generates a frequency f p positive sequence response and frequency f p 2 f The negative sequence response of 0 generates a frequency at the DC port. f p f The response to 0; negative order perturbations are mapped to respectively. f p , f p +2 f 0 and f p + f 0; DC disturbances are mapped to the AC side respectively. f p ± f 0 and DC side f p Positive-sequence voltage disturbances generate positive-sequence current both directly through the AC port and through... Y pdc DC network Z dc and Y dcp The feedback loop returns to the AC port, thus forming a closed-loop feedback. Considering this feedback, the positive-sequence direct module and the positive-sequence to negative-sequence coupled module are as follows:

[0064] Under negative order perturbation, the corresponding module is:

[0065] In the positive-sequence equivalent loop, the coupling effect of the negative-sequence network on the positive-sequence network is equivalent to a controlled current source; in the negative-sequence equivalent loop, the coupling effect of the positive-sequence network on the negative-sequence network is represented in the same way. Therefore:

[0066] in, Y gp and Y gn These are the positive-order admittance and negative-order admittance of the communication network, respectively.

[0067] The above steps first simplify the AC / DC coupled network, which contains nine basic modules, into four port coupled modules, and then obtain two decoupled models: positive-sequence and negative-sequence. In actual stability analysis, if the negative-sequence open-loop circuit is stable within the engineering operating range, stability determination can be completed using only the positive-sequence equivalent model.

[0068] Example 2 This embodiment provides a stability analysis method for a grid-connected system with a commutator, including the following steps: obtaining the equivalent positive-sequence admittance using the aforementioned grid commutator modeling method. Y p ( s and equivalent negative order admittance Y n ( s ); Obtain the positive-sequence admittance of the AC network connected to the grid commutator. Y gp ( s Using formula L p ( s )= Y p ( s ) / Y gp ( s Construct the impedance ratio; determine the impedance ratio L. p ( s Does the Nyquist curve of ) encircle the critical point () 1, j 0); if it is included, the grid-connected system of the grid-commutator is determined to be in an unstable state; otherwise, it is in a stable state.

[0069] As an optional implementation, the stability analysis method for the grid-connected system of the grid-commutated converter further includes: changing at least one of the phase-locked loop parameters, DC current control parameters, DC voltage control parameters, AC network strength, DC network parameters, transmission power, DC voltage, or AC filter parameters using the control variable method, and calculating the corresponding impedance ratio; calculating the stability margin using the impedance ratio; if the stability margin is less than a threshold, determining that the grid-connected system of the grid-commutated converter is in an unstable state, and then determining the corresponding instability frequency band using the amplitude crossover frequency corresponding to the impedance ratio.

[0070] LCC equivalent positive-sequence admittance Y p With AC network positive sequence impedance Z gp This forms a closed loop. The LCC uses grid-following control, and its normal design requires it to operate stably when connected to an ideal voltage source. Y p It contains no right-half-plane poles; the impedance or admittance of a passive AC network also contains no right-half-plane poles. If the open-loop negative-sequence circuit is stable, then it can be constructed as follows:

[0071] For L p ( sPlot the Nyquist curve. If the curve does not encircle the critical point ( 1, j 0), the system is considered stable; if the curve encircles the critical point ( 1, j 0) indicates system instability. Further, the stability margin can be calculated based on the impedance amplitude crossing position, phase difference, and the distance between the Nyquist curve and the critical point, with the critical frequency used as the potential oscillation frequency. Compared to the generalized Nyquist criterion, this method does not require calculating the right-half-plane poles of the open-loop lag ratio matrix.

[0072] In parameter sensitivity analysis, the AC grid strength, AC filter parameters, smoothing reactor, DC line parameters, PLL bandwidth, DC current loop or DC voltage loop PI parameters, transmission power and DC voltage can be changed sequentially, and the model calculation and stability judgment can be repeated to obtain the stability boundary and the main affected frequency band.

[0073] like Figures 7-9 As shown, the established model can be verified through frequency sweep simulation. Specifically, a positive-sequence or negative-sequence voltage disturbance with a sufficiently small amplitude is injected into the AC port, and a DC voltage disturbance is injected into the DC port. The corresponding current response is recorded and the basic module is calculated. The amplitude and phase of the theoretical model are compared with the frequency sweep results. Subsequently, by changing the grid strength or control parameters, the system is made to cross the stability boundary, and the predicted oscillation frequency is verified by time-domain simulation or field monitoring.

[0074] An example system parameter is shown in Table 2. These parameters are only used to illustrate the implementation process of this invention and do not constitute a limitation on the scope of protection.

[0075] Table 2 Example parameters of LCC system

[0076] In a set of verification conditions, as the AC grid strength decreases, the AC network impedance and the LCC equivalent positive sequence impedance are more prone to amplitude crossover. When the operating short-circuit ratio decreases to approximately 2.93, the model predicts a phase difference exceeding 180° at approximately 87.8 Hz, with the corresponding Nyquist curve encircling the critical point, indicating system instability; symmetrical oscillatory components at approximately 12.5 Hz and 87.5 Hz can be observed in the time-domain signal. This result demonstrates that the frequency-coupled model can simultaneously explain the oscillatory components symmetrical about the fundamental frequency.

[0077] Comparing models that do not consider coupling, only consider AC / DC port coupling, and consider both AC / DC port coupling and frequency coupling, it can be found that ignoring coupling will cause significant deviations in the amplitude and phase characteristics in the low-frequency band and near the fundamental frequency, and may lead to misjudgments of stability margin or oscillation frequency. The theoretical results of the complete model are more consistent with the frequency sweep and time-domain results, and the given stability boundaries are more conservative, which is beneficial for engineering safety design.

[0078] Example 3 This embodiment provides a control system for a grid-connected system of a grid-commutated converter, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements the steps of the grid-connected system modeling method based on the sequential reactance method or the steps of the grid-connected system stability analysis method.

[0079] This system can be a computing device such as a desktop computer, laptop, handheld computer, or cloud server. The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The memory can be used to store computer programs and / or modules. The processor implements various system functions by running or executing the computer programs and / or modules stored in the memory, and by accessing data stored in the memory.

[0080] Example 4 This application also relates to a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described above.

[0081] Specifically, the memory may include high-speed random access memory, as well as non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart media cards (SMC), secure digital (SD) cards, flash cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0082] Example 5 This application provides a computer program product or computer program that includes computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the steps of the method described in the above embodiments of this application.

[0083] The technical features of the embodiments described above can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification. It should be noted that the terms "in one embodiment," "for example," and "as in another example" in this application are intended to illustrate the application and are not intended to limit the application.

[0084] The embodiments described above are merely examples of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application.

Claims

1. A method for modeling power grid commutator converters based on sequential reactance method, characterized in that, include: S1: Equivalent the grid commutator to a two-port network consisting of AC and DC ports, and transform each variable of the AC port to the sequence domain; S2: Establish the original equivalent switching model of the two-port network corresponding to the grid commutator, including the DC voltage equivalent switching model and the converter transformer leakage inductance voltage equivalent switching model; S3: Using the firing angle, commutation angle, and DC current of the grid commutator as target variables, inject AC positive-sequence, AC negative-sequence, and DC voltage disturbances corresponding to each into the grid commutator to linearize the original equivalent switching model and obtain the target equivalent switching model; perform preliminary simplification of the target equivalent switching model to obtain the sequence admittance basic module; S4: The sequence admittance basic module is further simplified to obtain an equivalent admittance module considering DC closed-loop coupling, including: positive sequence self-admittance. Positive-to-negative-sequence coupling admittance Negative-order self-admittance Negative-sequence to positive-sequence coupling admittance ; S5: The coupling effect between the positive-sequence network and the negative-sequence network is equivalent to a controlled current source, further simplifying the equivalent admittance module to obtain the decoupled equivalent positive-sequence admittance. Y p ( s and equivalent negative order admittance Y n ( s ).

2. The grid commutator modeling method based on sequential reactance method as described in claim 1, characterized in that, The DC voltage equivalent switching model is expressed as follows: ； In the formula, This represents the DC-side voltage of a twelve-pulse LCC. They represent phases A, B, and C, respectively. This represents the three-phase voltage on the LCC valve side of the YY connection. Indicates direct current. This indicates the leakage inductance of the converter transformer. and These represent the equivalent switching functions from AC voltage to DC voltage and from DC current to DC voltage, respectively. ； ； in, m For non-zero integer harmonic orders, j The imaginary unit, The system's fundamental angular frequency. G m This indicates the setting coefficient. The equivalent switching function retains 12 pulses corresponding to the twelve-pulse commutation process. k ±1st characteristic harmonic, For trigger angle, This is the commutation overlap angle. The harmonic selectivity is formed by the superposition of two six-pulse converter bridges with a phase shift of 30°. Summation index k This represents the six commutation sections of a six-pulse converter bridge.

3. The grid commutator modeling method based on sequential reactance method as described in claim 1 or 2, characterized in that, The equivalent switching model of the leakage inductance voltage of the grid commutator includes: ； In the formula, This represents the leakage inductance voltage of the A-phase converter transformer. They represent phases A, B, and C, respectively. This represents the three-phase voltage on the LCC valve side of the YY connection. Indicates direct current. This indicates the leakage inductance of the converter transformer. and These represent the equivalent switching functions from AC voltage and DC current to the leakage inductance voltage of phase A, respectively. ； In the formula, This is the commutation overlap angle. K m To account for the Fourier coefficients in the commutation overlap region, m For non-zero integer harmonic orders, j The imaginary unit, The system's fundamental angular frequency. The trigger angle is circ(), which represents the circular matrix generation operation.

4. The grid commutator modeling method based on sequential reactance method as described in claim 1, characterized in that, The process of linearizing the equivalent switching model in step S3 to obtain the target equivalent switching model includes: using a small-signal linearization method for voltage and current during commutation to linearize the original equivalent switching model to obtain the target equivalent switching model; The integral relationship represents: ； The small-signal linearization method is expressed as follows: ; in, , These represent the commutation start time and commutation end time, respectively. The subscript 0 indicates the steady-state component, and the superscript " "Indicates small signal components, This indicates the leakage inductance of the converter transformer. i a,1 and v a,1 , v b,1 These represent the A-phase current and A and B-phase voltages on the valve side of the corresponding six-pulse converter bridge, respectively. i dc Indicates direct current. This represents the fundamental angular frequency; for the commutation process of other phases or another six-pulse commutator bridge, the corresponding integral relationship is obtained by phase shifting; For trigger angle and changing phase angle The equivalent switching function, For trigger angle, This is the steady-state operating point.

5. The grid commutator modeling method based on sequential reactance method as described in claim 4, characterized in that, The S3 step involves a preliminary simplification of the target equivalent switching model to obtain the sequence admittance basic module, which includes: The target equivalent switching model is simplified using small-signal relationships to obtain the basic module of sequence admittance, which includes: self-admittance under positive-sequence perturbation at the AC port, negative-sequence perturbation at the AC port, and perturbation at the DC port. Y pp , Y nn , Y dcdc and transfer admittance Y pn , Y np , Y pdc , Y ndc , Y dcp and Y dcn ; In rectifier operation mode, the small-signal quantity of the trigger angle disturbance in the small-signal relationship is: ； In inverter operation mode, the small-signal quantity of the trigger angle disturbance in the small-signal relationship is: ； Among them, the subscript p , n and DC These represent the positive sequence AC, negative sequence AC, and DC component, respectively. To inject the frequency offset variable of the disturbance, To inject complex frequency variables that cause disturbances, f p For the perturbation frequency, The system's fundamental angular frequency. k This is the frequency offset multiple; The small signal quantity representing the phase angle of the phase-locked loop output. , For small semaphores of the firing angle, and These are small signal quantities for DC current and DC voltage, respectively. H f,idcr and H idc,r These represent the DC current measurement and filtering stage and the DC current controller in rectifier operation mode, respectively. H f,vdci and H vdc,i These represent the DC voltage measurement and filtering stage and the DC voltage controller in inverter operation mode, respectively. This refers to a phase-locked loop controller in either rectification or inverter mode. This represents the positive-sequence disturbance voltage.

6. The grid commutator modeling method based on sequential reactance method as described in claim 5, characterized in that, S4 includes: Using formula The ordered admittance basic module is further simplified to obtain the equivalent admittance module considering DC closed-loop coupling; Among them, Z dc This represents the impedance of the DC power grid.

7. The grid commutator modeling method based on sequential reactance method as described in claim 6, characterized in that, S5 utilizes The equivalent admittance module is further simplified.

8. A stability analysis method for a grid-connected system with a phase-commutated converter, characterized in that, include: The equivalent positive-sequence admittance is obtained using the power grid commutator modeling method according to any one of claims 1-7. Y p ( s and equivalent negative order admittance Y n ( s ); Obtain the positive-sequence admittance of the AC network connected to the grid commutator. Y gp ( s ); Using formula L p ( s )= Y p ( s ) / Y gp ( s Construct the impedance ratio; determine the impedance ratio L. p ( s Does the Nyquist curve of ) encircle the critical point () 1, j 0); If the condition is met, the grid-connected system of the power grid phase-commutator is determined to be in an unstable state; otherwise, it is in a stable state.

9. The stability analysis method for a grid-connected system with a phase-commutated converter as described in claim 8, characterized in that, Also includes: The control variable method is used to change at least one of the following parameters: phase-locked loop parameters, DC current control parameters, DC voltage control parameters, AC network strength, DC network parameters, transmission power, DC voltage, or AC filter parameters, and the corresponding impedance ratio is calculated. The stability margin is calculated using the impedance ratio; if the stability margin is less than a threshold, the grid-connected system of the grid-commutated converter is determined to be in an unstable state, and then the corresponding instability frequency band is determined using the amplitude crossover frequency corresponding to the impedance ratio.

10. A control system for a grid-connected phase-commutator converter system, comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the grid commutator modeling method based on the sequential reactance method as described in any one of claims 1 to 7, or the steps of the grid-connected system stability analysis method of the grid commutator as described in claim 8 or 9.

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