Practical calculation and characteristic analysis method of short-circuit current of voltage source converter

Abstract

The application is a short-circuit current practical calculation and characteristic analysis method of a voltage source converter, which is based on the d-axis and q-axis equivalent circuit of a VSC grid-connected system, considers the converter control strategy, establishes a VSC short-circuit current calculation mathematical model according to the input and output power conservation of the converter, takes the time point when the symmetrical fault occurs as a time division point in the calculation process, calculates the oscillation frequency and attenuation coefficient of the short-circuit current, obtains the time-domain expression of the short-circuit current, and analyzes the d-axis current response law under the action of the VSC terminal voltage drop. The results of the method are compared with PSCAD simulation, which verifies the effectiveness and applicability of the method. The method has a simple calculation process, a concise time-domain expression of the short-circuit current, and a positive significance for the selection and protection setting of wind power / photovoltaic new energy related equipment.

Description

Technical Field

[0001] This invention relates to the field of voltage source converter technology, and provides a practical method for calculating and analyzing the short-circuit current of voltage source converters. Background Technology

[0002] With the rapid development of large-scale new energy power generation (wind power, photovoltaic, etc.), voltage source converters (VSCs) are increasingly being used in modern power systems, and the interaction between VSCs and the grid during grid faults is becoming increasingly significant. When the grid voltage drops, the short-circuit current and transient characteristics of the VSC become highly complex due to the regulation process of the VSC control strategy. Therefore, it is unreasonable to simply treat the VSC grid-connected power source as a load, and it is also unreasonable to ignore the short-circuit current provided by the VSC as the scale of new energy grid connection continues to increase. Studying the dynamic characteristics of grid-connected VSCs after faults is also very important for the grid connection analysis of new energy units. Relay protection mainly focuses on the short-circuit current components and their oscillation frequency, decay time constant, etc., but simulation cannot intuitively obtain these characteristics and cannot meet the relevant needs of relay protection. Therefore, it is essential to theoretically derive the components and variation laws of the short-circuit current of the VSC during grid faults. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of existing technologies and propose a scientific, reasonable, applicable, and effective practical method for calculating and analyzing the short-circuit current of voltage source converters.

[0004] The technical solution adopted to achieve the purpose of this invention is a practical calculation and characteristic analysis method for short-circuit current of a voltage source converter. This method is based on the d-axis and q-axis equivalent circuit of a VSC grid-connected system, considers the converter control strategy, and establishes a mathematical model for calculating the VSC short-circuit current based on the conservation of input and output electrical energy of the converter. The calculation process uses the occurrence of a symmetrical fault as the time boundary point to calculate the oscillation frequency and attenuation coefficient of the short-circuit current, obtains the time-domain expression of the short-circuit current, and analyzes the d-axis current response law under the action of VSC terminal voltage drop. Its features include the following specific contents:

[0005] 1) Establish VSC grid connection model

[0006] ①VSC main circuit model

[0007] The VSC converter is equivalent to a controlled voltage source. By controlling the switching state of the converter, the amplitude and phase of the output fundamental voltage are changed. In the dq coordinate system, the state equation of the converter's main circuit is:

[0008]

[0009]

[0010] In the formula, e d e q These are the d-axis and q-axis components of the VSC output voltage, respectively; u d u q For the d-axis and q-axis components of the VSC terminal voltage; i d i q The output current of VSC is represented by its d-axis and q-axis components; L f ω0 is the filter inductance; ω0 is the power frequency angular frequency.

[0011] When the grid voltage space vector orientation is adopted, that is, when the d-axis in the synchronous coordinate system is aligned with the direction of the grid voltage vector, we have: u d =u s u q =0, ignoring converter switching losses, the active power transmission and reactive power exchange between VSC and the grid are respectively:

[0012]

[0013] By controlling the d-axis and q-axis current components separately, decoupled control of active power transmission and reactive power exchange between the converter and the grid can be achieved. Therefore, i d It is called active current, i q It is called reactive current;

[0014] The main circuit of the VSC is essentially a power electronic power conversion circuit. Its function is to convert the DC power obtained from the renewable energy unit into AC power and output it to the power grid. Ignoring the switching losses of the converter, it satisfies the power balance of the converter, that is:

[0015]

[0016] In the formula, i in0 Inject current into VSC, u dc C is the DC capacitor voltage, and C is the DC capacitor.

[0017] ② Simplification of VSC control strategy

[0018] The transient characteristics of VSC depend on the converter's control strategy, and its control circuit determines the converter's output characteristics. The VSC control system adopts dual-loop control, with an outer loop being a DC voltage control loop and an inner loop being a current control loop. The outer loop controller generates reference values ​​for active and reactive current components, and the deviation from the actual values ​​is used by the inner loop PI controller to obtain the converter reference voltage.

[0019] Based on the outer loop of DC voltage

[0020]

[0021] In the formula: k is the active current reference value. up k ui For the voltage outer loop proportional and integral coefficients, This is the reference value for the DC bus voltage;

[0022] Based on the inner current loop

[0023]

[0024] In the formula, k ip k ii These are the proportional and integral coefficients of the inner current loop, respectively; This is a reference value for reactive current.

[0025] Because the inner current loop responds quickly, the active current rapidly tracks its reference value, i.e. Therefore, the analysis of active current i d The influence of the inner current loop is ignored during transient processes;

[0026] When the power grid is operating normally, the VSC operates at unity power factor and does not send reactive power to the grid, i.e., i q =0, active power does not affect the dynamic characteristics of reactive power; therefore, reactive current i is not considered. q Transient process;

[0027] 2) Derivation of short-circuit current

[0028] When the grid voltage drops symmetrically due to a three-phase short circuit, the VSC terminal voltage changes from u d0 Change to u d Then, equation (3) has:

[0029]

[0030] Define unbalanced power ΔP = i dc0 u dc0 -u d i d0 =u d0 i d0 -u d i d0 =Δu d i d0 Ignoring higher-order terms, we get:

[0031]

[0032] Performing Laplace transform on both sides of equation (6) simultaneously, we get:

[0033] (i dc0 -Cu dc0 s)Δudc (s)=u d Δi d (s)-ΔP(s) (7)

[0034] According to equation (3), we get:

[0035] Δi d =k up Δu dc +k ui ∫Δu dc dt (8)

[0036] Performing Laplace transform on both sides of equation (8) simultaneously, we get:

[0037]

[0038] Substituting equation (6) into equation (9), we get:

[0039]

[0040] We can obtain Δi d The time-domain response of (s):

[0041]

[0042] Where: Damping ratio Natural oscillating angular frequency Oscillation angular frequency ω d =ω n (1-ξ 2 ) 1 / 2 Damping angle α = arctan((1-ξ) 2 ) 1 / 2 / ξ); where the oscillation frequency

[0043] From the derivation of short-circuit current equations (5)-(11), it can be known that the steady-state value of the short-circuit current is related to the unbalanced power and the degree of voltage drop, and the oscillation frequency and decay time constant of the transient component are related to the grid-side converter control parameters.

[0044] This invention provides a practical method for calculating and analyzing the short-circuit current of a voltage source converter. Based on the equivalent circuit of the d-axis and q-axis of a VSC grid-connected system, and considering the converter control strategy, this method establishes a mathematical model for calculating the VSC short-circuit current according to the conservation of input and output electrical energy. The calculation process uses the occurrence of a symmetrical fault as the time boundary point to calculate the oscillation frequency and attenuation coefficient of the short-circuit current, obtaining the time-domain expression of the short-circuit current. This technical solution analyzes the d-axis current response law under the influence of VSC voltage dips. It has advantages such as simple calculation process, concise time-domain expression of short-circuit current, strong applicability, and good results, and is of positive significance for the selection and protection setting of wind power / photovoltaic new energy related equipment. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the VSC system structure involved in the present invention;

[0046] Figure 2 This is a schematic diagram of the equivalent circuit of the d-axis and q-axis of a VSC grid-connected system.

[0047] Figure 3 This is a schematic diagram of the outer loop control of the VSC DC voltage.

[0048] Figure 4 This is a schematic diagram of the VSC current inner loop decoupling control.

[0049] Figure 5 A schematic diagram comparing the active current output by the grid-connected VSC and its reference value;

[0050] Figure 6 This diagram illustrates the comparison between the calculated and simulated active current results of the grid-connected VSC. Detailed Implementation

[0051] The following will describe in further detail, with reference to the accompanying drawings, a practical method for calculating and analyzing the short-circuit current of a voltage source converter according to the present invention.

[0052] Reference Figures 1-4 This invention provides a practical method for calculating and analyzing the short-circuit current of a voltage source converter. The method is based on the d-axis and q-axis equivalent circuit of a VSC grid-connected system, considers the converter control strategy, and establishes a mathematical model for calculating the VSC short-circuit current based on the conservation of input and output electrical energy. The calculation process uses the occurrence of a symmetrical fault as the time boundary point to calculate the oscillation frequency and attenuation coefficient of the short-circuit current, obtaining the time-domain expression of the short-circuit current. The method also analyzes the d-axis current response under the influence of VSC voltage dips. Specifically, the method includes the following:

[0053] 1) Establish VSC grid connection model

[0054] ①VSC main circuit model

[0055] The VSC converter is equivalent to a controlled voltage source. By controlling the switching state of the converter, the amplitude and phase of the output fundamental voltage are changed. In the dq coordinate system, the state equation of the converter's main circuit is:

[0056]

[0057]

[0058] In the formula, e d e q These are the d-axis and q-axis components of the VSC output voltage, respectively; u d u q For the d-axis and q-axis components of the VSC terminal voltage; i d i q The output current of VSC is represented by its d-axis and q-axis components; L f ω0 is the filter inductance; ω0 is the power frequency angular frequency.

[0059] When the grid voltage space vector orientation is adopted, that is, when the d-axis in the synchronous coordinate system is aligned with the direction of the grid voltage vector, we have: u d =u s u q =0, ignoring converter switching losses, the active power transmission and reactive power exchange between VSC and the grid are respectively:

[0060]

[0061] By controlling the d-axis and q-axis current components separately, decoupled control of active power transmission and reactive power exchange between the converter and the grid can be achieved. Therefore, i d It is called active current, i q It is called reactive current;

[0062] The main circuit of the VSC is essentially a power electronic power conversion circuit. Its function is to convert the DC power obtained from the renewable energy unit into AC power and output it to the power grid. Ignoring the switching losses of the converter, it satisfies the power balance of the converter, that is:

[0063]

[0064] In the formula, i in0 Inject current into VSC, u dc C is the DC capacitor voltage, and C is the DC capacitor.

[0065] ② Simplification of VSC control strategy

[0066] The transient characteristics of VSC depend on the converter's control strategy, and its control circuit determines the converter's output characteristics. The VSC control system adopts dual-loop control, with an outer loop being a DC voltage control loop and an inner loop being a current control loop. The outer loop controller generates reference values ​​for active and reactive current components, and the deviation from the actual values ​​is used by the inner loop PI controller to obtain the converter reference voltage.

[0067] Based on the outer loop of DC voltage

[0068]

[0069] In the formula: k is the active current reference value. up k ui For the voltage outer loop proportional and integral coefficients, This is the reference value for the DC bus voltage;

[0070] Based on the inner current loop

[0071]

[0072] In the formula, k ip k ii These are the proportional and integral coefficients of the inner current loop, respectively; This is a reference value for reactive current.

[0073] Because the inner current loop responds quickly, the active current rapidly tracks its reference value, i.e. Therefore, the analysis of active current i d The influence of the inner current loop is ignored during transient processes;

[0074] When the power grid is operating normally, the VSC operates at unity power factor and does not send reactive power to the grid, i.e., i q =0, active power does not affect the dynamic characteristics of reactive power; therefore, reactive current i is not considered. q Transient process;

[0075] 2) Derivation of short-circuit current

[0076] When the grid voltage drops symmetrically due to a three-phase short circuit, the VSC terminal voltage changes from u d0 Change to u d Then, equation (3) has:

[0077]

[0078] Define unbalanced power ΔP = i dc0 u dc0 -u d i d0 =u d0 i d0 -ud i d0 =Δu d i d0 Ignoring higher-order terms, we get:

[0079]

[0080] Performing Laplace transform on both sides of equation (6) simultaneously, we get:

[0081] (i dc0 -Cu dc0 s)Δu dc (s)=u d Δi d (s)-ΔP(s) (7)

[0082] According to equation (3), we get:

[0083] Δi d =k up Δu dc +k ui ∫Δu dc dt (8)

[0084] Performing Laplace transform on both sides of equation (8) simultaneously, we get:

[0085]

[0086] Substituting equation (6) into equation (9), we get:

[0087]

[0088] We can obtain Δi d The time-domain response of (s):

[0089]

[0090] Where: Damping ratio Natural oscillating angular frequency Oscillation angular frequency ω d =ω n (1-ξ 2 ) 1 / 2 Damping angle α = arctan((1-ξ) 2 ) 1 / 2 / ξ); where the oscillation frequency

[0091] From the derivation of short-circuit current equations (5)-(11), it can be known that the steady-state value of the short-circuit current is related to the unbalanced power and the degree of voltage drop, and the oscillation frequency and decay time constant of the transient component are related to the grid-side converter control parameters.

[0092] A specific example: The feasibility of the practical calculation and characteristic analysis method for short-circuit current of a voltage source converter of the present invention is verified by taking a case study of the grid connection of a photovoltaic power plant's VSC system. The VSC system parameters are shown in Table 1.

[0093] Table 1 VSC System Parameters

[0094]

[0095]

[0096] By simulating a three-phase symmetrical fault in the power grid by changing the VSC grid-connected voltage, the voltage at the grid-connected VSC terminal drops by 10% at t=5s, thus verifying the feasibility of the invented method.

[0097] Because the inner current loop responds very quickly, the active current strictly tracks its reference value. The grid-connected VSC output active current and its reference value are as follows: Figure 5 As shown. The active current calculation result expression obtained by this invention has higher accuracy compared with the simulation result. The active current calculation result and the simulation result are compared as follows: Figure 6 As shown in Table 2, the characteristic parameters of the short-circuit current calculated using this invention are shown in Table 2.

[0098] Table 2 Short-circuit current characteristic parameters

[0099]

[0100] The above examples also illustrate the feasibility and effectiveness of the practical calculation and characteristic analysis method for short-circuit current of a voltage source converter described in this invention.

[0101] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications, equivalent changes, or alterations made by those skilled in the art using the disclosed technical content shall fall within the protection scope of the present invention.

Claims

1. A practical method for calculating and analyzing the short-circuit current of a voltage source converter (VSC), the method being based on the d-axis and q-axis equivalent circuit of a VSC grid-connected system, considering the converter control strategy, and establishing a mathematical model for calculating the VSC short-circuit current based on the conservation of input and output electrical energy of the converter. The calculation process uses the occurrence of a symmetrical fault as the time boundary point, calculates the oscillation frequency and attenuation coefficient of the short-circuit current, obtains the time-domain expression of the short-circuit current, and analyzes the d-axis current response law under the action of VSC terminal voltage drop. Its characteristic is that… Specifically, the content includes: 1) Establish VSC grid connection model ①VSC main circuit model The VSC converter is equivalent to a controlled voltage source. By controlling the switching state of the converter, the amplitude and phase of the output fundamental voltage are changed. In the dq coordinate system, the state equation of the converter's main circuit is: In the formula, e d e q These are the d-axis and q-axis components of the VSC output voltage, respectively; u d u q For the d-axis and q-axis components of the VSC terminal voltage; i d i q The output current of VSC is represented by its d-axis and q-axis components; L f ω0 is the filter inductance; ω0 is the power frequency angular frequency. When the grid voltage space vector orientation is adopted, that is, when the d-axis in the synchronous coordinate system is aligned with the direction of the grid voltage vector, we have: u d =u s u q =0, ignoring converter switching losses, the active power transmission and reactive power exchange between VSC and the grid are respectively: By controlling the d, q-axis current components respectively, the decoupled control of active power transmission and reactive power exchange between the converter and the grid can be achieved, so usually i d is called active current, i q is called reactive current; The main circuit of the VSC is essentially a power electronic power conversion circuit. Its function is to convert DC power obtained from renewable energy units into AC power for output to the power grid. Ignoring the switching losses of the converter, it satisfies the power balance of the converter, that is: wherein i dc0 is the VSC injected current, u dc is the DC capacitor voltage, C is the DC capacitor; ② Simplification of VSC control strategy The transient characteristics of VSC depend on the control strategy of the converter, and its control circuit determines the output characteristics of the converter. The VSC control system adopts dual-loop control, with the outer loop being a DC voltage control loop and the inner loop being a current control loop. The active and reactive current reference values ​​are generated through the outer loop controller, and the deviation from the actual values ​​is used to obtain the converter reference voltage through the inner loop PI controller. Based on the outer loop of DC voltage In the formula: is the active current reference value, k up , k ui is the voltage outer loop proportional and integral coefficient, is the DC bus voltage reference value; Based on the inner current loop In the formula, k ip , k ii are current inner loop proportional and integral coefficients, respectively; is the reactive current reference value; Since the response speed of the current inner loop is fast, the active current quickly tracks the reference value, i.e. Therefore, the active current i d The influence of the current inner loop is ignored during the transient process. When the power grid is in normal operation, the VSC operates at unity power factor, i.e. i q = 0, the active power does not affect the dynamic characteristics of the reactive power, therefore, the transient process of the reactive current i q is not considered. 2) Derivation of short-circuit current When the grid voltage drops symmetrically due to a three-phase short circuit, the VSC terminal voltage changes from its initial value u. d0 Change to u d Then, equation (3) has: In the formula, u dc0 , Δu dc These represent the initial value and the change in the DC capacitor voltage, respectively. i d0 is the initial value of the active current; Define unbalanced power ΔP = i dc0 u dc0 -u d i d0 =u d0 i d0 -u d i d0 =Δu d i d0 ,Δu d Let VSC be the d-axis component change of the terminal voltage, and neglecting higher-order terms, we get: Performing Laplace transform on both sides of equation (6) simultaneously, we get: (i dc0 -Cu dc0 s)Δu dc (s)=u d Δi d (s)-ΔP(s) (7) According to equation (3), we get: Δi d = k up Δu dc + k ui ∫Δu dc dt (8) Performing Laplace transform on both sides of equation (8) simultaneously, we get: Substituting equation (6) into equation (9), we get: Available Δi d Time domain response of (s): In the formula: Damping ratio ξ=(k up u d -i dc0 ) / 2(Cu dc0 k ui u d ) 1 / 2 Natural oscillating angular frequency ω n =(k ui u d / Cu dc0 ) 1 / 2 ; Oscillation angular frequency ω d =ω n (1-ξ 2 ) 1 / 2 Damping angle α = arctan((1-ξ) 2 ) 1 / 2 / ξ); where the oscillation frequency From the derivation of short-circuit current equations (5)-(11), it can be known that the steady-state value of the short-circuit current is related to the unbalanced power and the degree of voltage drop, and the oscillation frequency and decay time constant of the transient component are related to the grid-side converter control parameters.

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