Method and device for improving stability of virtual synchronous generator

By performing impedance modeling and variable transient virtual impedance control on the virtual synchronous generator, the problem of insufficient stability of the virtual synchronous generator under the conditions of fluctuation of DC bus voltage and AC voltage frequency is solved, and effective suppression of power oscillation and stability improvement of system are achieved.

CN119695936AActive Publication Date: 2025-03-25XIDIAN POWER RECTIFIER XIAN +1

Patent Information

Application Number
CN202510207843.7
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-02-25
Publication Date
2025-03-25
Estimated Expiration
2045-02-25

AI Technical Summary

Technical Problem

When the DC bus voltage fluctuates or the AC voltage frequency fluctuates, the output power and output frequency are prone to oscillation, resulting in insufficient stability.

Method used

By modeling the impedance of the virtual synchronous generator, a variable transient virtual impedance control structure diagram is constructed, and the transient virtual resistor, steady-state virtual resistor and virtual inductor are calculated by using angular frequency changes, d-axis current changes, DC bus voltage fluctuations and DC bus output current changes, transient virtual resistors, steady-state virtual resistors and virtual inductors, generating and adjusting the three-phase voltage output by the virtual synchronous generator.

Benefits of technology

It effectively suppresses the power oscillation of virtual synchronous generators caused by DC bus voltage fluctuations and system frequency fluctuations, improves the stability of virtual synchronous generators under unstable operating conditions, and avoids the instability caused by traditional damping control.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention discloses a virtual synchronous generator stability improving method and device, and the method comprises the steps: carrying out the impedance modeling of a VSG, and obtaining a VSG impedance model; generating a regulation voltage based on the variable transient virtual damping control scheme; superposing the current loop output voltage and the adjusting voltage, and applying the superposed voltage to a VSG impedance model to adjust the three-phase voltage output by the VSG; in the variable transient virtual damping control scheme, a VSG impedance model is compared with a synchronous motor operation principle according to a power system similarity principle, a transient virtual resistance is calculated by using an angular frequency change output by the VSG and a d-axis current change, and a steady-state virtual resistance and a virtual inductance are calculated by using a direct-current bus voltage fluctuation and a direct-current bus output current change of the VSG; a regulated voltage is determined using the transient virtual resistance, the steady state virtual resistance, and the virtual inductance. The stability of the virtual synchronous generator can be improved.
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Description

Technical Field

[0001] The present invention relates to the technical field of power system stability analysis and control, and in particular to a method and device for improving the stability of a virtual synchronous generator. Background Art

[0002] This section is intended to provide a background or context to the embodiments of the invention recited in the claims. No admission is made that the description herein is prior art by inclusion in this section.

[0003] At present, wind power generation and photovoltaic power generation will gradually become important components of the new power system. As the energy conversion interface between renewable energy and the power grid, the stable operation of the grid-connected converter is of great significance to the new power system. Virtual Synchronous Generator (VSG), as a way of network control of grid-connected converters, can provide frequency support to weak power grids, have networking operation capabilities, and can provide effective support for the large-scale application of renewable energy. However, under the conditions of DC bus voltage fluctuations or AC voltage frequency fluctuations, the output power and output frequency of VSG will oscillate, which is a problem that needs to be solved urgently.

[0004] The existing converter control field mainly uses damping control to eliminate power oscillations. Traditional damping control is mainly based on virtual damping control or active damping control. This method can effectively suppress the output power oscillation of VSG when the DC bus voltage fluctuates or the AC voltage frequency fluctuates, but it also has corresponding disadvantages. For example, virtual damping control cannot suppress power for the specific cause of power oscillation, but suppresses power for all working conditions. Although it can effectively suppress the output power oscillation of VSG, it also reduces the output power of VSG. At the same time, since the specific oscillation cause is not analyzed, a single increase in system damping will reduce system stability. When the external conditions change greatly, it will cause system instability and have a negative impact on the power generation efficiency of the grid-connected converter. Active damping control extracts the corresponding frequency of power oscillation, generates a voltage control quantity opposite to the power oscillation frequency, and adjusts the active power reference value of VSG through feedforward compensation to achieve the purpose of power oscillation suppression. The above two mainstream control methods both suppress power oscillations by sacrificing overall power generation efficiency, and may cause VSG stability to deteriorate under large disturbance conditions such as faults. Summary of the invention

[0005] An embodiment of the present invention provides a method for improving the stability of a virtual synchronous generator, which is used to improve the stability of the virtual synchronous generator when the direct current voltage and the alternating current voltage frequency fluctuate. The method includes:

[0006] The impedance modeling of the virtual synchronous generator VSG is carried out to obtain the VSG impedance model; wherein, the VSG control includes active power loop, reactive power loop, voltage loop, current loop, speed regulator, and DC voltage loop;

[0007] Based on the variable transient virtual damping control scheme, a regulating voltage is generated; the regulating voltage is used to regulate the three-phase voltage output by the VSG; in the variable transient virtual damping control scheme: according to the principle of power system similarity, the VSG impedance model is compared with the operation principle of the synchronous motor to construct a virtual impedance control structure diagram; based on the virtual impedance control structure diagram, the transient virtual resistance is calculated using the angular frequency change and d-axis current change of the VSG output, and the steady-state virtual resistance and virtual inductance are calculated using the DC bus voltage fluctuation and DC bus output current change of the VSG; the regulating voltage is determined using the transient virtual resistance, steady-state virtual resistance and virtual inductance;

[0008] The current loop output voltage is superimposed on the adjustment voltage, and the superimposed voltage is applied to the VSG impedance model to adjust the three-phase voltage output by the VSG.

[0009] The embodiment of the present invention further provides a virtual synchronous generator stability improvement device, which is used to improve the stability of the virtual synchronous generator when the DC voltage and AC voltage frequency fluctuate. The device includes:

[0010] The impedance modeling module is used to perform impedance modeling on the virtual synchronous generator VSG to obtain a VSG impedance model; wherein the VSG control includes an active power loop, a reactive power loop, a voltage loop, a current loop, a speed regulator, and a DC voltage loop;

[0011] A variable transient virtual damping control module is used to generate a regulating voltage based on a variable transient virtual damping control scheme; the regulating voltage is used to regulate the three-phase voltage output by the VSG; the current loop output voltage is superimposed with the regulating voltage, and the superimposed voltage is applied to the VSG impedance model to regulate the three-phase voltage output by the VSG; in the variable transient virtual damping control scheme: according to the power system similarity principle, the VSG impedance model is compared with the operation principle of the synchronous motor to construct a virtual impedance control structure diagram; based on the virtual impedance control structure diagram, the transient virtual resistance is calculated using the angular frequency change and d-axis current change of the VSG output, and the steady-state virtual resistance and virtual inductance are calculated using the DC bus voltage fluctuation and DC bus output current change of the VSG; the regulating voltage is determined using the transient virtual resistance, steady-state virtual resistance and virtual inductance.

[0012] An embodiment of the present invention further provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned method for improving the stability of a virtual synchronous generator when executing the computer program.

[0013] An embodiment of the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the above-mentioned method for improving the stability of a virtual synchronous generator is implemented.

[0014] An embodiment of the present invention further provides a computer program product, which includes a computer program. When the computer program is executed by a processor, the above-mentioned virtual synchronous generator stability improvement method is implemented.

[0015] The variable transient virtual impedance control scheme in the embodiment of the present invention takes into account the influence of DC voltage fluctuation and system frequency fluctuation on VSG output, calculates transient virtual resistance by using the angular frequency change and d-axis current change of VSG output, calculates steady-state virtual resistance and virtual inductance by using the DC bus voltage fluctuation and DC bus output current change of VSG; determines the adjustment voltage by using transient virtual resistance, steady-state virtual resistance and virtual inductance, superimposes the current loop output voltage and the adjustment voltage and applies them to the VSG impedance model to adjust the three-phase voltage output by VSG. Steady-state virtual resistance, virtual inductance and transient virtual resistance are used to suppress the VSG power oscillation problem caused by DC bus voltage fluctuation and system frequency fluctuation. The embodiment of the present invention effectively suppresses the cause of VSG power oscillation in a targeted manner, and can also have good effects when the power suddenly increases, avoiding the VSG instability phenomenon that may occur in traditional damping control. The embodiment of the present invention adopts the proposed scheme to effectively solve the problem of insufficient stability of virtual synchronous generators under the condition of DC voltage and AC voltage frequency fluctuations, which has a positive effect on the promotion and application of virtual synchronous generator control. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the prior art descriptions. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0017] Figure 1 It is a schematic diagram of a flow chart of a method for improving the stability of a virtual synchronous generator in an embodiment of the present invention;

[0018] Figure 2 Schematic diagram of the VSG main circuit in an embodiment of the present invention;

[0019] Figure 3 This is a VSG control block diagram in an embodiment of the present invention;

[0020] Figure 4 Schematic diagram of analogy between VSG and synchronous motor in an embodiment of the present invention;

[0021] Figure 5 A diagram showing a structure of a variable transient virtual impedance control in an embodiment of the present invention;

[0022] Figure 6 A schematic diagram of the structure of the variable transient virtual impedance control regulating voltage generation in an embodiment of the present invention;

[0023] Figure 7 It is a modulation coefficient calculation block diagram after being processed by the variable transient virtual impedance control scheme in an embodiment of the present invention;

[0024] Figure 8 It is the Bode diagram of VSG impedance without adding any suppression measures under the existing working condition -1;

[0025] Fig. 9 Bode diagram of VSG impedance with active damping control added under existing working condition -1;

[0026] Fig.10 Bode diagram of VSG impedance with active damping control added to the existing working condition-2;

[0027] Fig.11 The VSG impedance Bode diagram with variable transient virtual impedance control added under working condition-2 in the embodiment of the present invention;

[0028] Fig.12 Schematic diagram of the verification of the method for improving the stability of a virtual synchronous generator in an embodiment of the present invention Figure 1 ;

[0029] Fig.13 Schematic diagram of the verification of the method for improving the stability of a virtual synchronous generator in an embodiment of the present invention Figure 2 ;

[0030] Fig.14 Schematic diagram of the verification of the method for improving the stability of a virtual synchronous generator in an embodiment of the present invention Figure 3 ;

[0031] Fig.15 Schematic diagram of the verification of the method for improving the stability of a virtual synchronous generator in an embodiment of the present invention Figure 4 ;

[0032] Fig.16 Schematic diagram of a device for improving the stability of a virtual synchronous generator in an embodiment of the present invention. DETAILED DESCRIPTION

[0033] To make the purpose, technical solution and advantages of the embodiments of the present invention more clear, the embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings. Here, the exemplary embodiments of the present invention and their descriptions are used to explain the present invention, but are not intended to limit the present invention.

[0034] The acquisition, transmission, storage, use, and processing of data in the technical solution of this application comply with the relevant provisions of national laws and regulations.

[0035] In the prior art, the field of converter control mainly adopts damping control to eliminate power oscillation. Traditional damping control mainly adopts virtual damping control or active damping control. This method can effectively suppress the output power oscillation of VSG when the DC bus voltage fluctuates or the AC voltage frequency fluctuates, but it also has corresponding disadvantages. For example, virtual damping control cannot suppress power for the specific cause of power oscillation, but suppresses power for all operating conditions. Although it can effectively suppress the output power oscillation of VSG, it also reduces the output power of VSG. At the same time, since the specific oscillation cause is not analyzed, the single increase of system damping will reduce the stability of the system. When the external working conditions change greatly, it will cause system instability. It has a negative impact on the power generation efficiency of the grid-connected converter. Active damping control extracts the corresponding frequency of power oscillation, generates a voltage control quantity opposite to the power oscillation frequency, and suppresses the power oscillation of VSG through feedforward compensation. The above two mainstream control methods cannot suppress the specific cause of power oscillation, but suppress the power oscillation by sacrificing the overall power generation efficiency, causing negative impact.

[0036] Therefore, in view of the shortcomings of traditional damping control in the prior art, the embodiments of the present invention can take targeted measures against the VSG power oscillation caused by the DC bus fluctuations and AC voltage frequency fluctuations of the grid-connected converter, and this design concept can be extended to be used in various abnormal working conditions to improve the stability of the grid-connected converter.

[0037] Figure 1 FIG. 1 is a flow chart of a method for improving the stability of a virtual synchronous generator according to an embodiment of the present invention. Figure 1 As shown, the method includes:

[0038] Step 101, impedance modeling of the virtual synchronous generator VSG is performed to obtain a VSG impedance model; wherein the VSG control includes an active power loop, a reactive power loop, a voltage loop, a current loop, a speed regulator, and a DC voltage loop;

[0039] Step 102, based on the variable transient virtual damping control scheme, generate a regulating voltage; the regulating voltage is used to regulate the three-phase voltage output by the VSG; in the variable transient virtual damping control scheme: according to the principle of power system similarity, the VSG impedance model is compared with the operation principle of the synchronous motor to construct a virtual impedance control structure diagram; based on the virtual impedance control structure diagram, the transient virtual resistance is calculated using the angular frequency change and d-axis current change of the VSG output, and the steady-state virtual resistance and virtual inductance are calculated using the DC bus voltage fluctuation and DC bus output current change of the VSG; the regulating voltage is determined using the transient virtual resistance, steady-state virtual resistance and virtual inductance;

[0040] Step 103: superimpose the current loop output voltage and the adjustment voltage, and apply the superimposed voltage to the VSG impedance model to adjust the three-phase voltage output by the VSG.

[0041] The following is a detailed explanation of the method for improving control stability of a virtual synchronous generator in an embodiment of the present invention.

[0042] The scheme adopted in the embodiment of the present invention is based on a variable transient virtual impedance control method with angular frequency, DC bus voltage and output current as input quantities. First, the VSG impedance model is obtained by impedance modeling of the VSG. Secondly, the specific implementation method and theoretical derivation of the variable transient virtual impedance control are explained, and the impedance model Bode diagram is used to analyze the influence of active damping control and variable transient virtual control on stability when the external working conditions change. Finally, the effectiveness of the proposed method is verified under two working conditions: DC bus voltage fluctuation and output voltage frequency fluctuation through an experimental platform, and compared with the existing active damping control.

[0043] Figure 2 Schematic diagram of the main circuit of VSG in an embodiment of the present invention. Figure 2 As shown, Figure 2 in, u dc is the DC bus voltage, i dc is the DC bus current, C dc is the DC bus capacitance, u cabc is the three-phase voltage output by VSG, L c and R c is the inductance and resistance of the VSG output filter, u 0 is the grid voltage, i Labc is the grid-connected current, i.e., VSG output current, L g and R g is the grid line inductance and line resistance, u g is the grid voltage, and the dashed box indicates the PWM modulation of VSG after the transient virtual damping control scheme is applied. S abc Is a switching signal, PWM means pulse width modulation, , are the modulation coefficient to be applied to VSG, d abc is the duty cycle, dq and abc represent the two-phase rotating coordinate system and the three-phase stationary coordinate system, and θ is the coordinate transformation angle.

[0044] Figure 3 FIG. 1 is a VSG control block diagram in an embodiment of the present invention, as shown in FIG. Figure 3 As shown in Figure 1, VSG control mainly includes: active power loop, reactive power loop, voltage and current loop, and sampling circuit. In the active power loop, ω g is the grid angular frequency, ω 0 is the VSG angular frequency, k pv is the primary frequency modulation coefficient, ΔP is the primary frequency modulation power change, P e is the VSG electromagnetic power, P ref is the VSG active power reference value, J is the virtual inertia coefficient, D p is the virtual damping coefficient, ω is the transient value of the VSG angular frequency, s is the differential operator, θ is the VSG power angle, and it also serves as the coordinate transformation angle for coordinate change, Δω 1 is the DC voltage control output, G dc is the DC voltage control transfer function, u dc is the DC voltage sampling value, u dc.ref is the DC voltage reference value. In the reactive power loop, Q e is the reactive power sampling value, Q ref is the reactive power reference value, k q is the reactive droop coefficient, s is the differential operator, is the d-axis component of the VSG output voltage reference value, is the q-axis component of the VSG output voltage reference value. In the voltage loop and current loop, , They are the d-axis component and q-axis component of the VSG output voltage sampling value, G vc is the voltage control transfer function, , , , They are the d-axis component of the VSG output current sampling value, the q-axis component of the sampling value, the d-axis component of the reference value, and the q-axis component of the reference value, respectively. cc is the current control transfer function, G f is the feedforward link transfer function, L c is the output filter inductor. In the sampling circuit, u ca 、u cb 、u cc VSG outputs a, b, c phase voltages respectively, i La 、i Lb 、i LcThe VSG outputs a, b, and c phase currents respectively.

[0045] In one embodiment, the active power loop is used to control the active power of the VSG by simulating the swing equation of the synchronous generator. The active power loop has the frequency regulation capability of the synchronous generator speed regulator, and introduces the DC bus voltage change into the active power loop to perform active power control, thereby enhancing the dynamic response capability of the VSG to the DC voltage change. Figure 3 The active power loop in simulates the swing equation of the synchronous generator, so that the grid-connected converter has the external characteristics of the synchronous generator. The active power loop also has the frequency regulation capability of the synchronous generator speed regulator, while taking into account the response capability of the DC bus voltage change. The output of the reactive power loop is used as the d-axis reference value of the voltage loop , the embodiment of the present invention adopts unity power factor control, so The voltage loop and current loop adjust the VSG output voltage and output current. The sampling circuit completes the signal sampling and coordinate transformation functions.

[0046] In one embodiment, impedance modeling of a virtual synchronous generator (VSG) is performed to obtain a VSG impedance model, which may include: determining an output voltage expression and a DC current expression of the VSG according to a power balance principle; establishing an angular frequency expression of the VSG output; introducing DC bus voltage disturbance and AC voltage frequency disturbance into the angular frequency expression, and deriving an active power expression and a reactive power expression considering DC voltage disturbance and AC voltage frequency disturbance; converting the voltage expression, DC current expression, angular frequency expression, active power expression and reactive power expression from a VSG system coordinate system to a VSG control coordinate system, and obtaining a VSG impedance model considering DC voltage disturbance and AC voltage frequency disturbance; wherein the VSG system coordinate system is established based on a VSG main circuit, and the VSG control coordinate system is based on a VSG control block diagram; and the VSG control block diagram is used to control the VSG main circuit.

[0047] When implementing, you can Figure 2 The VSG output voltage expression is:

[0048] (1)

[0049] The character Δ in the formula indicates that the variable involved changes very little, that is, it changes within a small range near the working point. Ld 、i Lq are the dq axis components of the VSG output current sampling value, u od 、u oq 、u cd 、u cq They are the dq axis components of the VSG output voltage, the dq axis components of the VSG output voltage in the control coordinate system, and Z fis the VSG output filter impedance. According to the power balance principle, the VSG output voltage and DC current can be deduced as:

[0050] (2)

[0051] (3)

[0052] In formula (2), Δm d , Δm q are the dq small signal changes of the modulation coefficient, m d0 、m q0 They are the steady-state dq small signal variation of the modulation coefficient, i.e. the fixed modulation coefficient, u dc0 is the steady-state value of DC voltage, Δu dc is the small signal change of DC voltage.

[0053] In formula (3), i dc0 , Δi dc are the DC current steady-state value and the DC current small signal variation, u cd0 、u cq0 are the steady-state voltage dq axis components of the VSG output, i Ld0 、i Lq0 They are respectively the dq components of the steady-state value of the VSG output current, that is, the dq components of the steady-state value of the grid-connected current.

[0054] make , , The current loop can be expressed as:

[0055] (4)

[0056] in, , , , , .

[0057] in, , are the modulation coefficient dq components in the control coordinate system, T s is the switching cycle.

[0058] Similarly, the voltage loop can be expressed as:

[0059] (5)

[0060] The VSG output angular frequency can be expressed as:

[0061] (6)

[0062] By adding the DC bus voltage disturbance and AC voltage frequency disturbance to formula (6) and performing small signal linearization, the small signal model of the VSG active power loop output can be obtained as follows:

[0063] (7)

[0064] Where J is the virtual inertia coefficient. Similarly, the reactive power loop can also be expressed as:

[0065] (8)

[0066] Add disturbance to equation (8) and perform small signal linearization processing to obtain the small signal model of VSG reactive power loop output:

[0067] (9)

[0068] The VSG main circuit model and control model can be expressed by equations (1)-(9), and equation (10) is used to express the transformation relationship between the VSG control coordinate system and the VSG system coordinate system, namely:

[0069] (10)

[0070] In formula (10), , , Δf d , Δf q 、f d0 、f q0 , They are respectively the dq-axis components of different variables in the VSG control coordinate system, the dq-axis components of different components, the dq-axis components of different component steady-state values, and the d-axis components of the VSG output voltage reference value in the VSG control coordinate system.

[0071] f is the different variables in the VSG system, T 1 , T 2 is the transformation matrix, which can be expressed as:

[0072] (11)

[0073] (12)

[0074] Among them, θ 0 is the deviation of different coordinate systems in steady state. At the same time, from equations (7) and (9), we can get:

[0075] (13)

[0076] in, , They are the proportional coefficient and integral coefficient of DC voltage control respectively.

[0077] In addition, the small signal expression of DC bus voltage and angular frequency is:

[0078] (14)

[0079] (15)

[0080] Among them, C dc is the DC bus capacitor.

[0081] In steady state, let , , .

[0082] According to the above analysis, the conversion relationship between the system dq coordinate system and the control dq coordinate system can be obtained as follows:

[0083] (16)

[0084] (17)

[0085] (18)

[0086] Among them, G m1 , G i1 , G v1 It can be expressed by the following formula:

[0087] (19)

[0088] (20)

[0089] (twenty one)

[0090] Therefore, the VSG output active power and reactive power can be expressed as:

[0091] (twenty two)

[0092] After adding disturbance to equation (22) and linearizing it, we can obtain:

[0093] (twenty three)

[0094] in, , , we can further get:

[0095] (twenty four)

[0096] The VSG system coordinate system can be obtained The expression is:

[0097] (25)

[0098] The matrix EH can be expressed as:

[0099] (26)

[0100] The modulation coefficient can be obtained The small signal model is:

[0101] (27)

[0102] Among them, it can be expressed as:

[0103] (28)

[0104] (29)

[0105] Therefore, the small signal model of the modulation coefficient in the VSG system coordinate system is obtained as follows:

[0106] (30)

[0107] Among them, L, P, Q can be expressed as:

[0108] (31)

[0109] (32)

[0110] (33)

[0111] Therefore, we can get:

[0112] (34)

[0113] Combining the above analysis, the VSG impedance model can be obtained as follows:

[0114] (35)

[0115] Next, the specific implementation method and theoretical derivation of variable transient virtual impedance control are explained.

[0116] The rotor motion equation of VSG can be compared to the dynamic equation of DC voltage change. The DC side voltage equation of VSG can be expressed as:

[0117] (36)

[0118] Among them, Hc is the DC capacitor inertia time constant, P m is the active power on the DC side. And it satisfies: H c =(C dc ×u dc.ref ) / (2×S n ), S n is the capacity of VSG. At the same time, the rotor motion equation of VSG is:

[0119] (37)

[0120] H J is the inertia time constant of the VSG rotor. Comparing equation (36) and equation (37), we can obtain:

[0121] (38)

[0122] According to formula (38), the DC voltage u dc Dynamic characteristics and angular frequency ω 0 Similarly, and by the principle of similarity, it can be deduced that the inertia time constant H of the DC capacitor is c Similar to the rotor time constant H J , so the active power of VSG is expressed in another form:

[0123] (39)

[0124] in, , X 1 is the impedance between VSG and the grid, is the phase angle error between VSG output voltage and grid voltage, is the VSG rotor flux, X 2 is the equivalent reactance of VSG, is the angle of attack of VSG.

[0125] Figure 4 FIG. 1 is a schematic diagram of analogy between a VSG and a synchronous motor in an embodiment of the present invention. Figure 4 As shown in the figure, in the transient virtual damping control scheme: according to the power system similarity principle, the modulation coefficient of the VSG impedance model is analogous to the rotor flux of the synchronous motor, and the DC capacitor inertia time constant of the VSG impedance model is analogous to the rotor time constant H of the synchronous motor. J , the DC voltage of the VSG impedance model is analogous to the angular frequency ω of the synchronous motor 0 .

[0126] VSG power angle It can be expressed as:

[0127] (40)

[0128] ω Bg is the grid angular frequency base value, and the output voltage power angle of VSG and DC voltage have the following relationship:

[0129] (41)

[0130] Through the above analysis, the transient virtual impedance control structure diagram is constructed. Figure 5 This is a diagram of a variable transient virtual impedance control structure in an embodiment of the present invention. Figure 5 In, k 1 is the active coefficient of the transient virtual damping control and satisfies k 1 =1 / (u 0 -u g ). 2 is the damping coefficient of transient virtual damping control, k 3 is the virtual inertia coefficient of transient virtual damping control, and k is taken 3 =0.5. is the output voltage phase angle of VSG in steady state. VTVR , R VI , L VI are transient virtual resistance, steady-state virtual resistance and virtual inductance respectively, Z VI is the virtual impedance. 1 ,ω 2 Represents the cutoff frequency of the filter. The two cutoff frequencies can determine the effective working range of the filter. Take ω 1 =ω 2 =1e 3 rad / s.

[0131] The transient virtual impedance control scheme in the embodiment of the present invention takes into account the influence of DC voltage fluctuation and system frequency fluctuation on VSG output. According to the angular frequency change and the d-axis output current change, the transient virtual resistance R can be calculated. VTVR Take the value and pass k 2 , k 3 Adjust the size. At the same time, by adjusting ω 1 ,ω 2 The size can control the effective frequency range of the transient virtual resistance. The steady-state virtual resistance R is calculated by the DC bus voltage fluctuation and output current change. VI and virtual inductance L VI , using steady-state virtual resistance, virtual inductance, and transient virtual resistance to suppress VSG power oscillation problems caused by DC bus voltage fluctuations and system frequency fluctuations. The embodiments of the present invention effectively suppress the causes of VSG power oscillations in a targeted manner, and can also have good effects when power suddenly increases, avoiding VSG instability that may occur in traditional damping control.

[0132] according to Figure 5 The steady-state damping ratio σ can be obtained ss and transient damping ratio σ tr It is expressed as:

[0133] (42)

[0134] At the same time, the damping coefficient k 2 , through the limit get:

[0135] (43)

[0136] The parameters used for transient virtual impedance control can be obtained through equations (36) to (43). After all parameters are obtained, the corresponding adjustment voltage needs to be generated.

[0137] Figure 6 The schematic diagram of the structure of the voltage generation by the variable transient virtual impedance control in the embodiment of the present invention is combined with Figure 6 , the transient virtual resistance, steady-state virtual resistance and virtual inductance are calculated according to the following formula:

[0138] (44)

[0139] In the formula, R VTVR , R VI , L VI They are transient virtual resistance, steady-state virtual resistance and virtual inductance, is the d-axis component of the VSG output current reference value, is the d-axis component of the VSG output current sampling value, ω 0 is the VSG angular frequency, ω 1 ,ω 2 are the cutoff frequencies of the filters, ω g is the grid angular frequency, k 1 , k 2 , k 3 are respectively the active coefficient of variable transient virtual damping control, the damping coefficient of variable transient virtual damping control, and the virtual inertia coefficient of variable transient virtual damping control, u dc_pu is the DC voltage per unit value, ω g_pu is the per unit value of the grid angular frequency, ω Bg is the grid angular frequency base value, s is the differential operator, is the output voltage phase angle of VSG in steady state;

[0140] Combination Figure 6 , the regulation voltage is determined using the transient virtual resistance, steady-state virtual resistance and virtual inductance according to the following formula:

[0141] (45)

[0142] In the formula, , are the output voltage dq components of transient virtual damping control, T 1 is the time constant of transient virtual damping control.

[0143] Finally, the current loop output voltage is superimposed on the adjustment voltage, and the superimposed voltage is applied to the VSG impedance model to adjust the three-phase voltage output by the VSG.

[0144] Figure 7 : is a block diagram of the modulation coefficient calculation after being processed by the variable transient virtual impedance control scheme in the embodiment of the present invention, such as Figure 7 As shown, the regulated voltage is superimposed on the current loop output voltage as a new control quantity in the VSG control structure to control the converter and achieve the control goal, that is, to eliminate the influence of DC voltage and AC frequency fluctuations on VSG stability.

[0145] Figure 8 The Bode diagram of the VSG impedance without any suppression measures under the existing working condition -1, Δu dc = ±10V, Δω g =0.628rad / s,P out =25kW, by Figure 8 It can be seen that the Bode diagram of the impedance model corresponds to At f=50.8Hz, the phase angle is 0185.95°, indicating Negative resistance behavior will occur, which will affect the stable operation of the VSG. Similarly, insufficient phase margin will occur when f<10 Hz. In short, if no additional power oscillation suppression measures are taken, the VSG will be unstable.

[0146] Fig. 9 The impedance Bode diagram of VSG with active damping control added under the existing working condition -1, Δu dc = ±10V, Δω g =0.628rad / s,P out =25kW, by Fig. 9 It can be seen that after adding active damping control, At f=50.8Hz, the phase is range, indicating that there is no negative resistance behavior at this time, and There is also sufficient phase margin in the low frequency band. Therefore, adding active damping control can ensure the stable operation of VSG when the DC bus voltage fluctuates or the system frequency fluctuates. However, due to the phase lag caused by active damping control, if the power surge effect is taken into account, the VSG will become unstable.

[0147] Fig.10 Another VSG impedance Bode diagram with active damping control added under the existing working condition-2, Δu dc = ±10V, Δω g =1.884rad / s,P out =40kW, by Fig.10 It can be seen that when the system frequency fluctuation increases from 0.628rad / s to 1.884rad / s, Negative resistance behavior occurs in the frequency band f<100Hz, and the phase margin is insufficient. , , Obvious phase lag also appears in the mid-frequency band, which fully demonstrates that the phase lag effect of active damping control will cause the VSG to become unstable when the external disturbance is large.

[0148] Fig.11 The impedance Bode diagram of the VSG with transient virtual impedance control added under working condition 2 in the embodiment of the present invention, Δu dc = ±10V, Δω g =1.884rad / s,P out =40kW, by Fig.11 It can be seen that in Fig.10 Under the same working conditions, the transient virtual impedance control There is no negative resistance behavior and the phase margin is sufficient. , , The phase lag in the mid-frequency band is also significantly reduced. Therefore, it can be seen that when the external conditions change greatly, the transient virtual impedance control can improve the stability of the VSG.

[0149] The following describes the verification process of the method for improving the stability of a virtual synchronous generator in an embodiment of the present invention.

[0150] Working condition 1:

[0151] DC bus voltage fluctuation: Δu dc =±10V, system angular frequency fluctuation: Δω g =0.628rad / s, test duration: 6 s, load (15 kW) is applied at 3 s.

[0152] Working condition-2:

[0153] DC bus voltage fluctuation: Δu dc =±10V, system angular frequency fluctuation: Δω g =1.884rad / s, test duration: 6 s, load (30 kW) is applied at 3 s.

[0154] Fig.12 Schematic diagram of the verification of the method for improving the control stability of a virtual synchronous generator in an embodiment of the present invention Figure 1 ,like Fig.12 As shown in Figure 1, the VSG output waveform without additional control in working condition 1 is shown, including (a) output current, (b) output frequency, (c) active power, and (d) reactive power.

[0155] Fig.13 Schematic diagram of the verification of the method for improving the stability of a virtual synchronous generator in an embodiment of the present invention Figure 2 , Fig.13 The output waveform of the VSG with active damping control in working condition 1 is shown, (a) output current, (b) output frequency, (c) active power, and (d) reactive power. Fig.13 It can be seen that after the load is applied at 3 s, the VSG can operate stably under the active damping control, but the frequency also fluctuates greatly.

[0156] Fig.14 Schematic diagram of the verification of the method for improving the control stability of a virtual synchronous generator in an embodiment of the present invention Figure 3 , Fig.14 The output waveform of the VSG with active damping control in working condition 2 is shown, (a) output current, (b) output frequency, (c) active power, and (d) reactive power. Fig.14 It can be seen that after the load is applied at 3s, although active damping control is added, the VSG still experiences power oscillation and the frequency also fluctuates greatly.

[0157] Fig.15 Schematic diagram of the verification of the method for improving the control stability of a virtual synchronous generator in an embodiment of the present invention Figure 4 , Fig.15 The output waveforms of the VSG under time-varying transient virtual impedance control in working condition 2 are shown: (a) output current, (b) output frequency, (c) active power, and (d) reactive power. Fig.15 It can be seen that after the load is applied at 3s, the VSG can operate stably and the frequency does not fluctuate after adding the variable transient virtual impedance control.

[0158] In summary, the active damping control in the prior art can improve the stability of the VSG under working condition -1, but working condition -2 will cause VSG oscillation. The variable transient virtual impedance control scheme proposed in the embodiment of the present invention can ensure the stable operation of the VSG even in working condition -2 with large external changes, highlighting the effectiveness and advancement of the embodiment of the present invention. Therefore, the scheme proposed in the embodiment of the present invention can effectively solve the problem of insufficient stability of the virtual synchronous generator under the condition of DC voltage and AC voltage frequency fluctuations, and has a positive effect on the promotion and application of virtual synchronous generators.

[0159] The present invention also provides a virtual synchronous generator stability improvement device, as described in the following embodiments. Since the principle of the device to solve the problem is similar to the virtual synchronous generator stability improvement method, the implementation of the device can refer to the implementation of the virtual synchronous generator stability improvement method, and the repeated parts will not be repeated.

[0160] Fig.16 Schematic diagram of a device for improving the stability of a virtual synchronous generator according to an embodiment of the present invention. Fig.16 , the device 1600 comprises:

[0161] The impedance modeling module 1601 is used to perform impedance modeling on the virtual synchronous generator VSG to obtain a VSG impedance model; wherein the VSG control includes an active power loop, a reactive power loop, a voltage loop, a current loop, a speed regulator, and a DC voltage loop;

[0162] The variable transient virtual damping control module 1602 is used to generate a regulating voltage based on the variable transient virtual damping control scheme; the regulating voltage is used to regulate the three-phase voltage output by the VSG; the current loop output voltage is superimposed with the regulating voltage, and the superimposed voltage is applied to the VSG impedance model to regulate the three-phase voltage output by the VSG; in the variable transient virtual damping control scheme: according to the principle of power system similarity, the VSG impedance model is compared with the operation principle of the synchronous motor to construct a variable transient virtual impedance control structure diagram; based on the variable transient virtual impedance control structure diagram, the transient virtual resistance is calculated using the angular frequency change and d-axis current change of the VSG output, and the steady-state virtual resistance and virtual inductance are calculated using the DC bus voltage fluctuation and DC bus output current change of the VSG; the regulating voltage is determined using the transient virtual resistance, steady-state virtual resistance and virtual inductance.

[0163] In one embodiment, the active power loop is used to control the active power of the VSG by simulating the swing equation of the synchronous generator. The active power loop has the frequency regulation capability of the synchronous generator speed regulator and introduces the DC bus voltage changes into the active power loop to improve the VSG's response capability to DC voltage changes.

[0164] In one embodiment, the impedance modeling module 1601 is specifically used to: determine the output voltage expression and DC current expression of the VSG according to the power balance principle; establish the angular frequency expression of the VSG output; introduce DC bus voltage disturbance and AC voltage frequency disturbance into the angular frequency expression, and derive the active power expression and reactive power expression considering the two disturbances; convert the voltage expression, DC current expression, angular frequency expression, active power expression and reactive power expression from the VSG system coordinate system to the VSG control coordinate system, and obtain the VSG impedance model considering the DC voltage disturbance and AC voltage frequency disturbance; wherein, the VSG system coordinate system is established based on the VSG main circuit, and the VSG control coordinate system is based on the VSG control block diagram; the VSG control block diagram is used to control the VSG main circuit.

[0165] In one embodiment, in the transient virtual damping control scheme: according to the power system similarity principle, the modulation coefficient of the VSG impedance model is analogous to the rotor flux of the synchronous motor, the DC capacitor inertia time constant of the VSG impedance model is analogous to the rotor time constant of the synchronous motor, and the DC voltage of the VSG impedance model is analogous to the synchronous motor. .

[0166] In one embodiment, the variable transient virtual damping control module is specifically used for:

[0167] The transient virtual resistance, steady-state virtual resistance and virtual inductance are calculated according to the following formula:

[0168] ;

[0169] In the formula, R VTVR , R VI , L VI They are transient virtual resistance, steady-state virtual resistance and virtual inductance, , They are the d-axis component of the output current reference value and the d-axis component of the output current sampling value, ω 0 is the VSG angular frequency, ω 1 ,ω 2 is the cutoff frequency of the filter, ω g is the grid angular frequency, k 1 is the active coefficient of the transient virtual damping control, k 2 is the damping coefficient of transient virtual damping control, k 3 is the virtual inertia coefficient of transient virtual damping control, u dc_pu is the DC voltage per unit value, ω g_pu is the per unit value of the grid angular frequency, ω Bg is the grid angular frequency base value, s is the differential operator, is the output voltage phase angle of VSG in steady state;

[0170] The regulation voltage is determined using the transient virtual resistance, steady-state virtual resistance, and virtual inductance as follows:

[0171] ;

[0172] In the formula, , are the dq components of the output voltage of the transient virtual damping control, T 0 is the time constant of transient virtual damping control.

[0173] An embodiment of the present invention further provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned method for improving the stability of a virtual synchronous generator when executing the computer program.

[0174] An embodiment of the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the above-mentioned method for improving the stability of a virtual synchronous generator is implemented.

[0175] An embodiment of the present invention further provides a computer program product, which includes a computer program. When the computer program is executed by a processor, the above-mentioned virtual synchronous generator stability improvement method is implemented.

[0176] The variable transient virtual impedance control scheme in the embodiment of the present invention takes into account the influence of DC voltage fluctuation and system frequency fluctuation on VSG output, calculates transient virtual resistance by using the angular frequency change and d-axis current change of VSG output, calculates steady-state virtual resistance and virtual inductance by using the DC bus voltage fluctuation and DC bus output current change of VSG; determines the adjustment voltage by using transient virtual resistance, steady-state virtual resistance and virtual inductance, superimposes the current loop output voltage and the adjustment voltage and applies them to the VSG impedance model to adjust the three-phase voltage output by VSG. Steady-state virtual resistance, virtual inductance and transient virtual resistance are used to suppress the VSG power oscillation problem caused by DC bus voltage fluctuation and system frequency fluctuation. The embodiment of the present invention effectively suppresses the cause of VSG power oscillation in a targeted manner, and can also have good effects when the power suddenly increases, avoiding the VSG instability phenomenon that may occur in traditional damping control. The embodiment of the present invention adopts the proposed scheme to effectively solve the problem of insufficient stability of virtual synchronous generators under the condition of DC voltage and AC voltage frequency fluctuations, which has a positive effect on the promotion and application of virtual synchronous generators.

[0177] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0178] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0179] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0180] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0181] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for improving the stability of a virtual synchronous generator, characterized in that: include: The impedance modeling of the virtual synchronous generator VSG is carried out to obtain the VSG impedance model; wherein, the VSG control includes active power loop, reactive power loop, voltage loop, current loop, speed regulator, and DC voltage loop; Based on the variable transient virtual damping control scheme, a regulating voltage is generated; the regulating voltage is used to regulate the three-phase voltage output by the VSG; in the variable transient virtual damping control scheme: according to the principle of power system similarity, the VSG impedance model is compared with the operation principle of the synchronous motor to construct a virtual impedance control structure diagram; based on the virtual impedance control structure diagram, the transient virtual resistance is calculated using the angular frequency change and d-axis current change of the VSG output, and the steady-state virtual resistance and virtual inductance are calculated using the DC bus voltage fluctuation and DC bus output current change of the VSG; the regulating voltage is determined using the transient virtual resistance, steady-state virtual resistance and virtual inductance; The current loop output voltage is superimposed on the adjustment voltage, and the superimposed voltage is applied to the VSG impedance model to adjust the three-phase voltage output by the VSG.

2. The method according to claim 1, characterized in that The active power loop is used to control the VSG by simulating the swing equation of the synchronous generator. The active power loop has the frequency regulation capability of the synchronous generator speed regulator to perform active power control.

3. The method according to claim 1, characterized in that The impedance modeling of the virtual synchronous generator VSG is carried out to obtain the VSG impedance model, including: According to the power balance principle, determine the output voltage expression and DC current expression of VSG; Establish the angular frequency expression of VSG output; Introduce DC bus voltage disturbance and AC voltage frequency disturbance into the angular frequency expression, and derive the active power expression and reactive power expression considering the two disturbances; The voltage expression, DC current expression, angular frequency expression, active power expression and reactive power expression are transformed from the VSG system coordinate system to the VSG control coordinate system to obtain the VSG impedance model considering the DC voltage disturbance and the AC voltage frequency disturbance; wherein, the VSG system coordinate system is established based on the VSG main circuit, and the VSG control coordinate system is based on the VSG control block diagram; the VSG control block diagram is used to control the VSG main circuit.

4. The method according to claim 1, characterized in that In the variable transient virtual damping control scheme: according to the power system similarity principle, the modulation coefficient of the VSG impedance model is analogized to the rotor flux of the synchronous motor, the DC capacitor inertia time constant of the VSG impedance model is analogized to the rotor time constant of the synchronous motor, and the DC voltage of the VSG impedance model is analogized to the angular frequency of the synchronous motor.

5. The method according to claim 1, characterized in that Generate regulated voltage based on variable transient virtual damping control scheme, including: The transient virtual resistance, steady-state virtual resistance and virtual inductance are calculated according to the following formula: ; In the formula, R VTVR , R VI , L VI They are transient virtual resistance, steady-state virtual resistance and virtual inductance, , are the d-axis component of the output current reference value and the d-axis component of the output current sampling value, ω0 is the VSG angular frequency, ω1 and ω2 are the cutoff frequencies of the filter, ω g is the grid angular frequency, k1 is the active coefficient of the variable transient virtual damping control, k2 is the damping coefficient of the variable transient virtual damping control, k3 is the virtual inertia coefficient of the variable transient virtual damping control, u dc_pu is the DC voltage per unit value, ω g_pu is the per unit value of the grid angular frequency, ω Bg is the grid angular frequency base value, s is the differential operator, is the output voltage phase angle of VSG in steady state; The regulation voltage is determined using the transient virtual resistance, steady-state virtual resistance, and virtual inductance as follows: ; In the formula, , are the dq components of the output voltage of the variable transient virtual damping control, and T0 is the time constant of the variable transient virtual damping control.

6. A virtual synchronous generator stability improvement device, characterized in that: include: The impedance modeling module is used to perform impedance modeling on the virtual synchronous generator VSG to obtain a VSG impedance model; wherein the VSG control includes an active power loop, a reactive power loop, a voltage loop, a current loop, a speed regulator, and a DC voltage loop; A variable transient virtual damping control module is used to generate a regulating voltage based on a variable transient virtual damping control scheme; the regulating voltage is used to regulate the three-phase voltage output by the VSG; the current loop output voltage is superimposed with the regulating voltage, and the superimposed voltage is applied to the VSG impedance model to regulate the three-phase voltage output by the VSG; in the variable transient virtual damping control scheme: according to the power system similarity principle, the VSG impedance model is compared with the operation principle of the synchronous motor to construct a virtual impedance control structure diagram; based on the virtual impedance control structure diagram, the transient virtual resistance is calculated using the angular frequency change and d-axis current change of the VSG output, and the steady-state virtual resistance and virtual inductance are calculated using the DC bus voltage fluctuation and DC bus output current change of the VSG; the regulating voltage is determined using the transient virtual resistance, steady-state virtual resistance and virtual inductance.

7. The device according to claim 6, characterized in that The active power loop is used to control the VSG by simulating the swing equation of the synchronous generator. The active power loop has the frequency regulation capability of the synchronous generator speed regulator to perform active power control.

8. The device according to claim 6, characterized in that The Impedance Modeling module is specifically used for: According to the power balance principle, determine the output voltage expression and DC current expression of VSG; Establish the angular frequency expression of VSG output; The DC bus voltage disturbance and AC voltage frequency disturbance are introduced into the angular frequency expression, and the active power expression and reactive power expression under the two disturbances are derived; The voltage expression, DC current expression, angular frequency expression, active power expression and reactive power expression are transformed from the VSG system coordinate system to the VSG control coordinate system to obtain the VSG impedance model considering the DC voltage disturbance and the AC voltage frequency disturbance; wherein, the VSG system coordinate system is established based on the VSG main circuit, and the VSG control coordinate system is based on the VSG control block diagram; the VSG control block diagram is used to control the VSG main circuit.

9. The device according to claim 6, characterized in that In the variable transient virtual damping control scheme: according to the power system similarity principle, the modulation coefficient of the VSG impedance model is analogized to the rotor flux of the synchronous motor, the DC capacitor inertia time constant of the VSG impedance model is analogized to the rotor time constant of the synchronous motor, and the DC voltage of the VSG impedance model is analogized to the angular frequency of the synchronous motor.

10. The device according to claim 6, characterized in that The transient virtual damping control module is specifically used for: The transient virtual resistance, steady-state virtual resistance and virtual inductance are calculated according to the following formula: ; In the formula, R VTVR , R VI , L VI They are transient virtual resistance, steady-state virtual resistance and virtual inductance, , are the d-axis component of the output current reference value and the d-axis component of the output current sampling value, ω0 is the VSG angular frequency, ω1 and ω2 are the cutoff frequencies of the filter, ω g is the grid angular frequency, k1 is the active coefficient of the variable transient virtual damping control, k2 is the damping coefficient of the variable transient virtual damping control, k3 is the virtual inertia coefficient of the variable transient virtual damping control, u dc_pu is the DC voltage per unit value, ω g_pu is the per unit value of the grid angular frequency, ω Bg is the grid angular frequency base value, s is the differential operator, is the output voltage phase angle of VSG in steady state; The regulation voltage is determined using the transient virtual resistance, steady-state virtual resistance, and virtual inductance as follows: ; In the formula, , are the dq components of the output voltage of the variable transient virtual damping control, and T0 is the time constant of the variable transient virtual damping control.

11. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the method according to any one of claims 1 to 5 is implemented.

12. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 5 is implemented.

13. A computer program product, characterized in that The computer program product comprises a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 5 is implemented.

Citation Information

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