Fault current analysis method based on first-order Taylor expansion

Abstract

The invention relates to a fault current analysis method based on first-order Taylor expansion, and the method comprises the following steps: 1, determining a system control strategy which is a network construction type control strategy and comprises a power loop, a virtual impedance link and a voltage and current loop; the power loop comprises an active power control loop and a reactive power control loop; 2, constructing a differential algebraic equation set model capable of representing the dynamic state of the system; 3, according to the characteristic that the integral value does not suddenly change at the moment before and after the fault occurs, the steady state before the fault is utilized to solve and obtain an instant state variable value after the fault, and then an instant dq-axis current value after the fault and an instant current amplitude value after the fault are obtained; 4, performing first-order Taylor expansion on the constructed differential algebraic equation set at the solved post-fault instant state variable value and the dq-axis current value, and converting a nonlinear differential algebraic equation set model into a linear differential algebraic equation set; and 5, analyzing the fault current.

Description

Technical Field

[0001] The invention belongs to the field of fault current analysis of grid-connected converters, and in particular relates to a fault current analysis method based on a first-order Taylor expansion. Background Art

[0002] Large-scale access of wind, solar and other renewable energy sources to the grid through power electronic converters is one of the main technical features of the new generation of power systems [1]. The proportion of traditional synchronous generators is constantly decreasing, and the power system presents a "double high" characteristic [2,3]. At present, the converters widely used in practical projects adopt a grid-following control architecture, that is, vector current control is used to control the output current of the converter, thereby controlling the active / reactive power fed into the grid. At the same time, the grid connection point voltage is sampled, and the synchronization between the converter and the grid is achieved through a phase-locked loop [4]. However, large-scale renewable energy power plants are generally located in remote areas. Due to the degradation of phase-locked loop performance and the lack of inertia under weak grids, grid-following control poses a huge challenge to the stable operation of the system. Grid-building control can autonomously establish system voltage and frequency, and has higher stability and robustness in weak grids. It has gradually become a better control method for the penetration of new energy sites. Due to the control characteristics of the grid-building converter itself, the grid-building converter exhibits controlled voltage source characteristics, and its output current is closely related to the equivalent grid voltage and grid impedance [5]. Reference [6] shows that when a short circuit occurs, in order to maintain the stability of the grid-connected converter output voltage, the grid-connected converter will inject a current value of up to 6.7 pu. However, unlike a synchronous generator that can withstand a current of 5 to 8 pu, the grid-connected converter can usually only withstand a current of 1.2 to 2 pu due to the limitation of semiconductor devices. Therefore, in order to protect the grid-connected converter, it is necessary to analyze the fault current characteristics of the grid-connected converter to avoid damaging the converter.

[0003] When analyzing the fault characteristics of grid-connected converters, some documents [7-9] often directly assume that after a fault, the current reaches the current limit value, and the control strategy is switched to a current limit control strategy, ignoring the dynamic process of the current rising to the limit value after the fault. Document

[10] proposes a full-state variable succession solution method suitable for describing the time domain response of the system, but this method cannot give an approximate expression for the fault current and can only give a numerical solution. Documents [11-12] mainly use methods such as solving differential equations and Laplace transforms to model the fault current of grid-connected converters, and the calculation process is relatively complex. Document

[13] models the fault current characteristics of grid-connected converters. Its control structure is relatively simple, and the fault current expression can be solved by using the inverse Laplace transform method. However, for more complex control strategies, such as the control strategy proposed in the present invention that the active power loop considers both frequency and active power and the reactive power control loop considers both voltage and reactive power, it is difficult to use the solution proposed in document

[13] to solve the fault current.

[0004] Due to the high-order characteristics of system modeling, it is difficult to give an expression for the fault current changing with time in the above literature. Generally, the Laplace transform method is used, which involves complex complex function-related calculations, and the solution process is complicated. When the control strategy is relatively complex, it is difficult to solve it using Laplace transform and differential equations. In order to solve the above problems, the present invention proposes an approximate calculation method for fault current based on the first-order Taylor expansion, which has the advantages of simple calculation process and can solve the fault current under complex control strategies.

[0005] References

[0006] [1] Zhou Xiaoxin, Chen Shuyong, Lu Zongxiang, et al. Technical characteristics of my country's new generation power system during energy transformation[J]. Proceedings of the CSEE, 2018, 38(7): 1893-1904.

[0007] [2] Lu Zongxiang, Jiang Jiheng, Qiao Ying, et al. A review of generalized inertia analysis and optimization of new power systems [J]. Proceedings of the CSEE, 2023, 43(05): 1754-1776.

[0008] [3] Kang Chongqing, Du Ershun, Guo Hongye, et al. Analysis of six elements of new power system[J]. Power System Technology, 2023, 47(05): 1741-1750.

[0009] [4] Xu Jieyi, Liu Wei, Liu Shu, et al. Current status and development trend of power system converter control technology [J]. Power System Technology, 2022, 46(09): 3586-3595.

[0010] [5] Zhan Changjiang, Wu Heng, Wang Xiongfei, et al. A review of research on stability of grid-connected converters[J]. Proceedings of the CSEE, 2023, 43(6): 2339-2358.

[0011] [6]TAUL GM, WANG

[0012] [7] Sun P, Tian Z, Huang M, et al. Additional Kinetic Energy Injection and Piecewise Damping Based Postfault Anti-Windup and Transient StabilityEnhanced Control for Grid-Forming Inverter[J]. IEEE Transactions on PowerElectronics, 2024.

[0013] [8] Rokrok E, Qoria T, Bruyere A, et al. Transient stability assessment and enhancement of grid-forming converters embedding current references as current limiting strategy [J]. IEEE Transactions on PowerSystems, 2021, 37(2): 1519-1531.

[0014] [9]Li Y, Lu Y, Yang J, et al. Transient stability of powersynchronization loop based grid forming converter[J]. IEEE Transactions onEnergy Conversion, 2023, 38(4): 2843-2859.

[0015]

[10] Ma Hongyue, Zheng Tao, Zhou Hao, et al. Fault calculation method for inverter grid-connected system considering control switching[J]. Power System Technology, 2024, 48(07): 2985-2994.

[0016]

[11] Jia Ke, Li Ying, Kong Jiajing, et al. Transient analysis of wind and solar power supply faults and practical calculation of short-circuit current peak value [J]. Power System Technology, 2024, 48(02): 830-840.

[0017]

[12] Jia K, Hou L, Liu Q, et al. Analytical calculation of transientcurrent from an inverter-interfaced renewable energy [J]. IEEE Transactions on Power Systems, 2021, 37(2): 1554-1563.

[0018]

[13] Zheng Tao, Wang Ziming, Zou Pengying, et al. Analytical calculation of virtual synchronous machine current and analysis of influencing factors during symmetrical short-circuit fault in power grid [J]. Power System Technology, 2023, 47(04): 1460-1475. Summary of the invention

[0019] The present invention proposes a method for fault current analysis of grid-connected converters. First, a mathematical model is established that ignores the dynamics of the current loop and the electromagnetic transients of the AC line and considers the dynamics of the power loop and the voltage loop. The mathematical model is compared with the electromagnetic transient simulation model to verify the effectiveness of the constructed mathematical model. Secondly, through this mathematical model, a method for calculating the fault instantaneous current is obtained, and the first-order Taylor expansion of the constructed mathematical model is performed using the initial value of the fault instant, and finally an analytical expression for the fault current of the grid-connected converter is obtained. The technical solution of the present invention is as follows:

[0020] A fault current analysis method based on first-order Taylor expansion includes the following steps:

[0021] Step 1: Determine the system control strategy

[0022] The control strategy adopted is a grid-forming control strategy, which mainly includes a power loop, a virtual impedance link and a voltage and current loop; the power loop includes two parts: an active power control loop and a reactive power control loop. The potential inside the converter is subtracted from the voltage drop of the virtual impedance to obtain the reference voltage of the voltage loop. The voltage loop and the current inner loop adopt vector control, wherein the input of the active power control loop is the actual value of the active power and the actual value of the angular frequency. The errors between the actual values ​​and the reference values ​​are passed through a droop link and summed to obtain the input of the PI regulator in the active power control loop. After passing through the PI regulator, the angular frequency of the grid-forming converter is obtained, and then the angular frequency of the grid-forming converter is integrated to obtain the phase angle of the synchronous rotating coordinate system corresponding to the converter; the input of the reactive power control loop is the actual value of the reactive power and the voltage at the converter end. The errors between the actual values ​​and the reference values ​​are passed through a droop link and summed to obtain the input of the PI regulator in the reactive power control loop. After passing through the PI regulator, the internal potential of the grid-forming converter is obtained;

[0023] Step 2: Construct a differential algebraic equation model that can characterize the system dynamics

[0024] Ignoring the dynamics of the inner current loop and the electromagnetic transient state of the AC line, considering the dynamics of the power loop and the voltage loop, a phase δ of the synchronous rotating coordinate system of the grid converter itself relative to the grid voltage and the integral value x of the active power loop input error are constructed. AP , the integral value of the reactive power loop input error x RP , the integral value x of the voltage loop d-axis input error ud And the integral value x of the voltage loop q-axis input error uq is the state variable, dq axis current I d and I q is an algebraic equation in algebraic variables;

[0025] Step 3: Based on the differential algebraic equation model constructed in the second step, according to the characteristic that the integral value does not change suddenly before and after the fault occurs, the differential terms of the differential algebraic equation in the second step are set to 0 by using the steady state before the fault, and the values ​​of the state variables after the fault are obtained by solving them. The values ​​of the state variables after the fault are substituted into the algebraic equations to obtain the dq axis current values ​​and the current amplitude after the fault.

[0026] Step 4: At the instantaneous state variable value and dq axis current value after the fault obtained in the third step, the differential algebraic equation system constructed in the second step is expanded by the first-order Taylor, and the nonlinear differential algebraic equation system model constructed in the second step is converted into a linear model based on δ, x AP 、x RP 、x ud and x uq is a system of linear differential algebraic equations of state variables, organized into the form of dx / dt=Ax+b;

[0027] Step 5: Based on the linear differential algebraic equations obtained in step 4, use mathematical methods to find δ and x AP 、x RP 、x ud and x uq The expressions of the five state variables changing with time are substituted into the algebraic equations of the differential algebraic equations constructed in the second step to obtain the expressions of the dq axis current and the current amplitude changing with time after the fault, thus realizing the analysis of the fault current.

[0028] Further, according to the control strategy described in the first step, the expression of the active power loop is shown in formula (1);

[0029]

[0030] In the formula, ω and P represent the actual value of the converter angular frequency and the actual value of the output active power, respectively. set , P setThey represent the converter angular frequency reference value and output active power reference value respectively, K p , K f They represent the active power droop coefficient and frequency droop coefficient respectively, K pAPC and K iAPC Respectively represent the proportional coefficient and integral coefficient of the active power control loop PI regulator, ω B represents the angular frequency reference value, θ represents the phase angle of the synchronous rotating coordinate system corresponding to the converter, and s is the Laplace transform operator;

[0031] The expression of reactive power loop is shown in equation (2);

[0032]

[0033] In the formula, U and Q represent the actual value of the converter terminal voltage and the actual value of the output reactive power, respectively. set , Q set They represent the converter terminal voltage reference value and output reactive power reference value respectively, K q , K v Respectively represent reactive power droop coefficient and voltage droop coefficient, K pRPC and K iRPC They represent the proportional coefficient and integral coefficient of the reactive power control loop PI regulator, U ref represents the potential inside the converter, s is the Laplace transform operator;

[0034] In the virtual impedance link, the potential U in the converter is ref Subtract the voltage drop on the virtual impedance to get the voltage loop dq axis reference voltage U dref and U qref , its expression is shown in formula (3);

[0035]

[0036] In the formula, I d and I q Respectively represent the dq axis current, R v and X v denote virtual resistance and virtual reactance respectively;

[0037] In the voltage loop, the voltage loop input is the error between the voltage reference and the actual voltage value. This error is summed with the current feedforward term through the PI link to obtain the current reference value of the current inner loop. Its expression is shown in formula (4);

[0038]

[0039] Where U dref and U qref Respectively represent the dq axis reference voltage, Ud and U q Respectively represent the actual voltage of dq axis, I gd and I gq They represent the dq axis current on the grid side of the filter circuit, K pu and K iu Respectively represent the proportional coefficient and integral coefficient of the voltage loop, K if Represents the current feed-forward coefficient, I dref and I qref They represent the reference values ​​of the voltage loop dq axis current respectively.

[0040] Furthermore, the differential algebraic equation model constructed in the second step that can characterize the system dynamics ignores the dynamics of the inner current loop and the electromagnetic transient state of the AC line, assumes that the actual current value of the current loop can track the current reference value in real time, ignores the filter capacitor current, and assumes that I td =I gd =I tdref , I tq =I gq =I tqref , considering the dynamics of the power loop and the voltage loop, the differential algebraic equations that can characterize the system dynamics are shown in equation (5).

[0041]

[0042] Among them, δ represents the phase of the synchronous rotating coordinate system of the grid-connected converter itself relative to the grid voltage, ω B Indicates the reference value of angular frequency, K p , K f They are active power, angular frequency droop coefficient, K pAPC and K iAPC They are the proportional coefficient and integral coefficient of the PI link of the active power loop, P set ,ω set They represent the reference value of the converter output active power and the reference value of the angular frequency, respectively. AP Represents the integral value of the active power loop input error, which is x AP =∫[K f (ω set -ω)+K p (P set -P)]dt. K q and K v are reactive power and voltage droop coefficient, K pRPC and K iRPC are the proportional coefficient and integral coefficient of the reactive power loop PI link, Q set and U setThey represent the reference value of the reactive power output of the converter and the reference value of the terminal voltage, respectively. Q and U represent the actual value of the reactive power output of the converter and the actual value of the terminal voltage, respectively. RP Represents the integral value of the reactive power loop input error, which is x RP =∫[K v (U set -U)+K p (Q set -Q)]dt. U ref Indicates the potential inside the converter, U s Indicates the grid voltage, I d ,I q Respectively represent the dq axis current, R v and X v Represent virtual resistance and virtual reactance respectively, R g and X g Respectively represent the filter resistance and filter reactance between the converter and the grid, R s and X s Respectively represent the line resistance and line reactance between the converter and the grid, x ud and x uq Respectively represent the integral value of the voltage loop dq axis input error. pu Indicates the proportional coefficient of the voltage loop PI link, K iu Indicates the integral coefficient, K if Represents the feedforward coefficient of the grid-side current.

[0043] Furthermore, in the calculation of the instantaneous current after the fault in the third step, the state variables δ, x AP 、x RP 、x ud and x uq It is obtained through the integration process. At the moment before and after the fault occurs, the values ​​of these state variables remain unchanged. The values ​​of the above state variables are calculated through the steady state before the fault. In the steady state before the fault, the above five state variables do not change, and their first-order derivatives are 0, that is, all the differential terms in formula (5) are 0. The solution expression is shown in formula (6):

[0044]

[0045] By solving equation (6), we can get the values ​​of the five state variables immediately after the fault. s The sudden decrease causes the reactive power Q output by the converter and the voltage U at the converter terminal to change. Due to the effect of the droop coefficient and the proportional coefficient in the reactive power loop, the potential U inside the converter is ref changes, resulting in changes in the output current, but these changes must satisfy the equality constraints shown in formula (7). Through the equation group shown in formula (7), the instantaneous dq axis current I after the fault is obtainedd and I q And the current amplitude I mag ;

[0046]

[0047] Formula (6) is used to calculate the instantaneous state variable value after the fault. Formula (7) uses the result of formula (6) to calculate the current value after the fault. Substitute the grid voltage U into formula (6): s It should be the grid voltage value before the fault. Substitute the grid voltage U into formula (7): s It should be the grid voltage value after the fault.

[0048] Furthermore, in the fourth step, at the instantaneous state variable value and the instantaneous current value after the fault obtained in the third step, the differential algebraic equation model constructed in the second step is subjected to a first-order Taylor expansion, and the expression after the first-order Taylor expansion is shown in formula (8):

[0049]

[0050] In formula (8), I d and I q Eliminate and rearrange to get the equation (9).

[0051]

[0052] in,

[0053]

[0054] Furthermore, in the fifth step, the mathematical model for the first-order Taylor expansion in the fourth step is organized into the form shown in formula (11):

[0055]

[0056] In the formula, A is the coefficient matrix and b is the bias vector. By solving the linear differential equations, the state variables δ and x are obtained. AP 、x RP 、x ud 、x uq The analytical expression of is shown in formula (11):

[0057]

[0058] In the formula, the eigenvalues ​​and eigenvectors of the coefficient matrix A are denoted as v i and λ i (i=1,2,3,4,5),δ p 、x APp 、x RPp、x udp 、x uqp For equation A[δ p ,x APp ,x RPp ,x udp ,x uqp ] T +b=0; then using equation (8), we can get the current amplitude I mag An expression that changes over time.

[0059] The present invention proposes a fault current analysis method for grid-connected converters: 1) constructing a mathematical model that ignores the current loop dynamics and the electromagnetic transients of the AC line and considers the power loop dynamics and the voltage loop dynamics, so as to directly analyze the system fault current from a mathematical perspective; 2) solving the current at the moment of the fault based on the mathematical model constructed in 1); 3) using the calculation result of 2), using the first-order Taylor expansion, an analytical expression for the fault current can be obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 Grid-connected converter control strategy block diagram

[0061] Figure 2 Schematic diagram of the relationship between DQ coordinate system and dq coordinate system

[0062] Figure 3 Comparison between the mathematical model of the whole process of power grid voltage drop fault shown in equation (8) and the electromagnetic transient simulation model

[0063] Figure 4 Instantaneous current after fault after grid voltage drops

[0064] Figure 5 Comparison of the fifth-order mathematical model, the first-order Taylor expansion model and the electromagnetic transient simulation model when the grid voltage drops to 0.4pu DETAILED DESCRIPTION

[0065] The present invention is described below in conjunction with the accompanying drawings and embodiments.

[0066] (1) System control strategy

[0067] The grid-connected control strategy of the grid-connected converter considered in the present invention is as follows: Figure 1 As shown. In the power electronic converter grid-connected circuit, L f and L g Respectively represent the filter inductance of the converter side and the grid side, C f is the filter capacitor, U s and L s are the inductance and voltage of the equivalent Thevenin circuit of the power grid, I tabc and I gabcare the currents on the converter side and the grid side, U tabc is the voltage of the converter filter capacitor. After Park transformation, the corresponding dq axis voltage component U dq And the current component I tdq and I gdq .P set ,ω set , Q set and U set K represents the reference value of the converter output active power, angular frequency, reactive power and terminal voltage respectively, and P, ω, Q and U represent the actual value of the converter output active power, angular frequency, reactive power and terminal voltage respectively. p , K f , K q and K v They are active power, angular frequency, reactive power and voltage droop coefficient, K pAPC and K iAPC They are the proportional coefficient and integral coefficient of the active power loop PI link, K pRPC and K iRPC are the proportional coefficient and integral coefficient of the reactive power loop PI link respectively. p times and angular frequency error K f The converter angular frequency ω is obtained through the active power loop PI link, and the converter phase θ is obtained through the integral link, where ω B Represents the angular frequency reference value, which is 314.15926rad / s here. K of reactive power error q times and voltage error K v times through the reactive power loop PI link, and then with U set The voltage reference U ref In order to suppress the impact current and avoid excessive current during fault, a virtual impedance Z is introduced. v =R v +jω B L v , R v The resistance representing the virtual impedance, L v Inductance representing virtual impedance. U ref Subtract the voltage drop on the virtual impedance to obtain the dq axis voltage reference value U of the converter grid connection point. dref and U qref dq axis voltage reference value U dref and U qref The actual value of dq axis voltage U d , U q The error is then converted into the grid-side dq axis current I through the PI link. gd ,I gq With Kif The sum of the products is the dq axis current reference value I dref and I qref , where the proportional coefficient of the voltage loop PI link is K pu , the integral coefficient is K iu , K if Indicates the feedforward coefficient of the grid-side current. dq axis current reference value I tdref and I tqref The actual value of dq axis current I td ,I tq The error is connected through the PI link and is respectively tq ω B L f , -I td ω B L f And the dq axis voltage U d , U q The dq axis modulation voltage U is obtained by summing dpwm with U qpwm dq axis modulation voltage U dpwm , U qpwm and the converter phase θ are input to the PWM generator to generate modulation signals for each switch tube.

[0068] (2) Establishment of system mathematical model

[0069] In the process of establishing the mathematical model, the following assumptions are considered to be valid:

[0070] (a) Ignore the electromagnetic transient process of the AC line;

[0071] (b) Ignoring the inner loop dynamics of the current, it is assumed that the current can track the reference value in real time, that is, it is assumed that I td =I tdref , I tq =I tqref ;

[0072] (c) Since the filter capacitor has a small capacitance, the current of the filter capacitor in the filter is ignored, that is, I td =I gd , I tq =I gq .

[0073] To simplify the expression, I td , I tdref , I gd Written as I d , will I tq , I tqref , I gq Written as I q .

[0074] In the modeling process of the present invention, the following Figure 2 The q-axis shown lags behind the d-axis synchronous rotating coordinate system, the synchronous rotating coordinate system oriented with the grid voltage d-axis voltage is defined as the DQ axis, the synchronous rotating coordinate system oriented with the converter terminal voltage d-axis voltage is defined as the dq axis, and δ represents the phase difference between the d-axis and the D-axis, that is.

[0075] Ignoring the electromagnetic transient process of the AC line and the converter filter capacitor current, according to Kirchhoff's voltage law, the dq-axis component of the converter terminal voltage U d and U q With grid voltage U s The relationship is expressed as shown in formula (1).

[0076]

[0077] In the formula, R g and X g Respectively represent the filter resistance and filter inductance L between the converter and the grid g The corresponding reactance, R s and X s They represent the line resistance and line reactance between the converter and the grid respectively.

[0078] The expressions of active power and reactive power output by the converter are shown in equation (2).

[0079]

[0080] Substituting equation (1) into equation (2), we can get the expressions of the converter output active power and reactive power as shown in equation (3).

[0081]

[0082] according to Figure 1 The grid-connected converter control strategy shown in the figure can be used to write the expression of the power control loop as shown in equation (4).

[0083]

[0084] Where δ represents the phase of the synchronous rotating coordinate system of the grid-connected converter itself relative to the grid voltage. AP and x RP They represent the integral values ​​of the input errors of the active power loop and the reactive power loop, which is x AP =∫[K f (ω set -ω)+K p (P set -P)]dt,x RP =∫[K v (U set-U)+K p (Q set -Q)]dt, U represents the voltage at the converter terminal, U=(U d 2 +U q 2 ) 1 / 2 .

[0085] Rearranging equation (4), the dynamics of the power loop can be expressed as shown in equation (5).

[0086]

[0087] according to Figure 1 For the grid-connected converter control strategy shown in FIG, the dynamics of the virtual impedance link and the voltage loop can be expressed as shown in Equation (6) and Equation (7), respectively.

[0088]

[0089]

[0090] In formula (6), X v Indicates the virtual inductance L v The corresponding reactance. In formula (7), x ud and x uq They represent the integral values ​​of the voltage loop dq axis input errors, that is, x ud =∫(U dref -U d )dt,x uq =∫(U qref -U q )dt.

[0091] By reorganizing the above equations (1)-(7), we can obtain a set of differential algebraic equations describing the system dynamics, as shown in equation (8).

[0092]

[0093] (3) Mathematical model verification

[0094] Here, by setting the grid voltage drop condition, the mathematical model corresponding to equation (8) is compared with the output results of the electromagnetic transient simulation model to verify the effectiveness of the mathematical model shown in equation (8).

[0095] by Figure 1 The grid-connected converter shown in the figure is taken as an example for analysis and simulation verification. The parameters of the electromagnetic transient simulation model of the grid-connected converter built in the electromagnetic transient simulation software PSCAD / EMTDC are shown in Table 1.

[0096] When a symmetrical three-phase short circuit occurs in the power grid at 3.5s, the voltage Us The voltage of the power grid drops to 0.4 pu, and the fault is cleared at 3.6 s, and the power grid voltage recovers to 1.0 pu. From the occurrence of the power grid fault to the clearing of the power grid fault, and then to the recovery of the converter to normal working state, in this process, the mathematical model shown in formula (8) is consistent with the Figure 1 The simulation results of the electromagnetic transient simulation model built with the structure and parameters in Table 1 are as follows Figure 3 As shown, in Figure 3 In the figure, the red solid line represents the calculation result of the mathematical model shown in equation (8), and the blue dotted line represents the simulation result of the electromagnetic transient model.

[0097] according to Figure 3 δ, x shown in AP 、x RP 、x ud 、x uq And the dq axis current I d ,I q With the current amplitude I mag The results show that the mathematical model shown in formula (8) can effectively describe Figure 1 The dynamics of the system in which the grid-connected converter is connected to the grid are shown.

[0098] Table 1 Parameters of grid-connected converter

[0099]

[0100] (4) Method for calculating instantaneous current after a fault

[0101] Due to the limitation of the current carrying capacity of the switch tube in the grid-connected converter, a limiting link is usually added to the current inner loop control strategy to limit the current during the fault. When the instantaneous current after the fault exceeds the limit value, the converter will enter the current limiting mode, and the current output by the converter will follow the current limit value. At this time, the voltage outer loop and other functions will all fail; when the instantaneous current after the fault is within the limit value, the converter current inner loop will not enter the current limiting model, and the effects of the voltage loop and the power loop will still affect the current dynamics. Therefore, it is necessary to analyze whether the current of the converter is overcurrent at the moment after the fault. The following mainly introduces the solution method for solving the instantaneous current of the converter after the fault.

[0102] Immediately after the fault occurs, due to δ, x AP 、x RP 、x ud 、x uq These five variables are obtained through integration, and changes require a certain amount of time to accumulate. Therefore, immediately after the fault, δ, x AP 、x RP 、x ud 、x uqThese five variables will not change, and their values ​​are consistent with the steady state before the fault. Before the fault, when the system reaches a steady state, the corresponding δ, x in equation (8) AP 、x RP 、x ud 、x uq The differential terms of are all zero, that is, equation (9) is established. Using equation (9), we can obtain δ and x at the moment of fault. AP 、x RP 、x ud 、x uq The numerical value of .

[0103]

[0104] When a grid voltage drop fault occurs on the grid side, the grid voltage amplitude U s changes, noting that the reactive power loop generates U ref There is a proportional link in the process (the proportional coefficient is K pRPC ), which will cause the fault instant U ref changes, resulting in U dref and U qref changes, and at the same time, the proportional link in the voltage loop (the proportional coefficient is K pu ) will also cause the dq axis current I d and I q changes, which in turn leads to U d , U q and Q change, and so on and so forth, the converter output current is constantly adjusted immediately after the fault, so as to achieve a balance, that is, the instantaneous current after the fault. ref , dq axis voltage reference value U dref and U qref , dq axis current I d and I q The process of finally reaching a steady state can be expressed by a set of nonlinear equations as shown in equation (10).

[0105]

[0106] Solving equation (9) yields δ, x RP 、x ud 、x uq Substituting into equation (10), we can get the instantaneous dq axis current I after the fault: d and I q And the current amplitude I mag .

[0107] Using the above method, the grid voltage dropped to 0.4pu at 3.5s for verification. The results of mathematical model calculation and electromagnetic transient simulation results are as follows: Figure 4 As shown, in Figure 4 The red dots represent the instantaneous dq axis current I after the fault calculated by the mathematical model shown in equation (10). d and I q And the current amplitude I mag , the blue dotted line represents the electromagnetic transient simulation result, and the error between the mathematical model and the electromagnetic transient simulation model is shown in Table 2. Figure 4 Compared with the results in Table 2, the proposed calculation method can effectively calculate the initial value of the post-fault current within a certain error range.

[0108] Table 2 Error table of the calculation results of the mathematical model of instantaneous current after fault and the electromagnetic transient simulation results

[0109]

[0110] (5) Fault current solution method

[0111] from Figure 3 Comparing the results of the mathematical model shown in formula (8) with the electromagnetic transient model, it can be seen that the mathematical model shown in formula (8) can be used to describe Figure 1 The system shown in the figure shows the dynamics of the fault current after the grid voltage drops. However, for judging whether the fault current reaches the current limit value after a period of time after the fault, or judging whether the fault current reaches the current limit value during the entire fault process under a certain set of control parameters, the mathematical model shown in formula (8) can only be solved step by step from the moment of the fault start by the differential equation numerical solution method according to the time sequence, and the current value at a certain moment cannot be quickly obtained. To solve this problem, the present invention proposes a fault current solution method based on the first-order Taylor expansion.

[0112] In δ, x AP 、x RP 、x ud 、x uq And the dq axis current I d ,I q The values ​​immediately after the fault are δ0, x AP0 , x RP0 , x ud0 、x uq0 , I d0 ,I q0 For the mathematical model shown in formula (8), at δ0, x AP0 , x RP0 , x ud0 、x uq0 , I d0 ,I q0By performing a first-order Taylor expansion at , equation (8) can be transformed into the form shown in equation (11).

[0113]

[0114] For equation (11), we can use the voltage loop equation to eliminate I d and I q , which can be converted into AP 、x RP 、x ud 、x uq The differential equations for the state variables can be organized as shown in equation (12).

[0115]

[0116] In formula (12),

[0117]

[0118] Formula (12) can be expressed as shown in formula (13).

[0119]

[0120] Where A is the coefficient matrix and b is the bias vector. According to formula (13), we can get the state variables δ, x AP 、x RP 、x ud 、x uq The analytical expression of is shown in formula (14).

[0121]

[0122] Among them, the eigenvalues ​​and eigenvectors of the coefficient matrix A are denoted as v i and λ i (i=1,2,3,4,5),δ p 、x APp 、x RPp 、x udp 、x uqp For equation A[δ p ,x APp ,x RPp ,x udp ,x uqp ] T +b=0. Then, using the equation in (12), we can find the current amplitude I mag An expression that changes over time.

[0123] The following is a verification of the fault current solution method based on the first-order Taylor expansion proposed in the present invention by setting the grid voltage drop condition. The condition is set as follows: when a symmetrical three-phase short circuit fault occurs in the grid at 3.5s, the voltage U s The fault drops to 0.4 pu, and the fault is cleared at 3.6 s, and the grid voltage recovers to 1.0 pu. In the first 3.5 s to 3.6 s, the fault current curves obtained by the electromagnetic transient simulation model, the mathematical model corresponding to equation (8), and the proposed method based on the first-order Taylor expansion are as follows: Figure 5 The dotted line, solid line and dashed line are shown. Figure 5 It can be seen from the comparison results that the fault current solution method based on the first-order Taylor expansion proposed in the present invention can effectively reflect the dynamics of the fault current.

Claims

1. A fault current analysis method based on first-order Taylor expansion, comprising the following steps: Step 1: Determine the system control strategy The control strategy adopted is a network control strategy, which mainly includes a power loop, a virtual impedance link and a voltage and current loop; the power loop includes two parts: an active power control loop and a reactive power control loop. The voltage potential in the converter is subtracted from the voltage drop of the virtual impedance to obtain the reference voltage of the voltage loop. The voltage loop and the current inner loop adopt vector control, where: The input of the active power control loop is the actual value of active power and the actual value of angular frequency. The errors of the actual values ​​and the reference values ​​are summed through the droop link to obtain the input of the PI regulator in the active power control loop. After passing through the PI regulator, the angular frequency of the grid-forming converter is obtained, and then the angular frequency of the grid-forming converter is integrated to obtain the phase angle of the synchronous rotating coordinate system corresponding to the converter; the input of the reactive power control loop is the actual value of reactive power and the voltage at the converter end. The errors of the actual values ​​and the reference values ​​are summed through the droop link to obtain the input of the PI regulator in the reactive power control loop. After passing through the PI regulator, the internal potential of the grid-forming converter is obtained; Step 2: Construct a differential algebraic equation model that can characterize the system dynamics Ignoring the dynamics of the inner current loop and the electromagnetic transient state of the AC line, considering the dynamics of the power loop and the voltage loop, a phase δ of the synchronous rotating coordinate system of the grid converter itself relative to the grid voltage and the integral value x of the active power loop input error are constructed. AP , the integral value of the reactive power loop input error x RP , the integral value of the voltage loop d-axis input error x ud And the integral value x of the voltage loop q-axis input error uq is the state variable, dq axis current I d and I q is an algebraic equation in algebraic variables; Step 3: Based on the differential algebraic equation model constructed in the second step, according to the characteristic that the integral value does not change suddenly before and after the fault occurs, the differential terms of the differential algebraic equation in the second step are set to 0 by using the steady state before the fault, and the values ​​of the state variables after the fault are obtained by solving them. The values ​​of the state variables after the fault are substituted into the algebraic equations to obtain the dq axis current values ​​and the current amplitude after the fault. Step 4: At the instantaneous state variable value and dq axis current value after the fault obtained in the third step, the differential algebraic equation system constructed in the second step is expanded by the first-order Taylor, and the nonlinear differential algebraic equation system model constructed in the second step is converted into a linear model based on δ, x AP 、x RP 、x ud and x uq is a system of linear differential algebraic equations of state variables, organized into the form of dx / dt=Ax+b; Step 5: Based on the linear differential algebraic equations obtained in step 4, use mathematical methods to find δ and x AP 、x RP 、x ud and x uq The expressions of the five state variables changing with time are substituted into the algebraic equations of the differential algebraic equations constructed in the second step to obtain the expressions of the dq axis current and the current amplitude changing with time after the fault, thus realizing the analysis of the fault current.

2. The grid-connected converter control method according to claim 1, characterized in that: According to the control strategy described in the first step, the expression of the active power loop is shown in formula (1); In the formula, ω and P represent the actual value of the converter angular frequency and the actual value of the output active power, respectively. set , P set They represent the converter angular frequency reference value and output active power reference value respectively, K p , K f They represent the active power droop coefficient and frequency droop coefficient respectively, K pAPC and K iAPC Respectively represent the proportional coefficient and integral coefficient of the active power control loop PI regulator, ω B represents the angular frequency reference value, θ represents the phase angle of the synchronous rotating coordinate system corresponding to the converter, and s is the Laplace transform operator; The expression of the reactive power loop is shown in equation (2); In the formula, U and Q represent the actual value of the converter terminal voltage and the actual value of the output reactive power, respectively. set , Q set They represent the converter terminal voltage reference value and output reactive power reference value respectively, K q , K v Respectively represent reactive power droop coefficient and voltage droop coefficient, K pRPC and K iRPC They represent the proportional coefficient and integral coefficient of the reactive power control loop PI regulator, U ref represents the potential inside the converter, s is the Laplace transform operator; In the virtual impedance link, the potential U in the converter is ref Subtract the voltage drop on the virtual impedance to get the voltage loop dq axis reference voltage U dref and U qref , its expression is shown in formula (3); In the formula, I d and I q Respectively represent the dq axis current, R v and X v denote virtual resistance and virtual reactance respectively; In the voltage loop, the voltage loop input is the error between the voltage reference and the actual voltage value. This error is summed with the current feedforward term through the PI link to obtain the current reference value of the current inner loop. Its expression is shown in formula (4); Where U dref and U qref Respectively represent the dq axis reference voltage, U d and U q Respectively represent the actual voltage of dq axis, I gd and I gq They represent the dq axis current on the grid side of the filter circuit, K pu and K iu Respectively represent the proportional coefficient and integral coefficient of the voltage loop, K if Represents the current feed-forward coefficient, I dref and I qref They represent the reference values ​​of the voltage loop dq axis current respectively.

3. The fault current analysis method according to claim 2, characterized in that: The differential algebraic equation model constructed in the second step that can characterize the system dynamics ignores the dynamics of the inner current loop and the electromagnetic transient state of the AC line. It is assumed that the actual current value of the current loop can track the current reference value in real time, and the filter capacitor current is ignored. It is assumed that I td =I gd =I tdref , I tq =I gq =I tqref , considering the dynamics of the power loop and the voltage loop, the differential algebraic equations that can characterize the system dynamics are shown in equation (5): Among them, δ represents the phase of the synchronous rotating coordinate system of the grid-connected converter itself relative to the grid voltage, ω B Indicates the reference value of angular frequency, K p , K f They are active power, angular frequency droop coefficient, K pAPC and K iAPC They are the proportional coefficient and integral coefficient of the PI link of the active power loop, P set ,ω set They represent the reference value of the converter output active power and the reference value of the angular frequency, respectively. AP Represents the integral value of the active power loop input error, which is x AP =∫[K f (ω set -ω)+K p (P set -P)]dt;K q and K v are reactive power and voltage droop coefficient, K pRPC and K iRPC are the proportional coefficient and integral coefficient of the reactive power loop PI link, Q set and U set They represent the reference value of the reactive power output of the converter and the reference value of the terminal voltage, respectively. Q and U represent the actual value of the reactive power output of the converter and the actual value of the terminal voltage, respectively. RP Represents the integral value of the reactive power loop input error, which is x RP =∫[K v (U set -U)+K p (Q set -Q)]dt;U ref represents the potential inside the converter, U s Indicates the grid voltage, I d ,I q Respectively represent the dq axis current, R v and X v Represent virtual resistance and virtual reactance respectively, R g and X g Respectively represent the filter resistance and filter reactance between the converter and the grid, R s and X s Respectively represent the line resistance and line reactance between the converter and the grid, x ud and x uq Respectively represent the integral value of the voltage loop dq axis input error; K pu Represents the proportional coefficient of the voltage loop PI link, K iu Indicates the integral coefficient, K if Represents the feedforward coefficient of the grid-side current.

4. The fault current analysis method according to claim 3, characterized in that: In the third step, in the calculation of the instantaneous current after the fault, the state variables δ, x AP 、x RP 、x ud and x uq It is obtained through the integration process. At the moment before and after the fault occurs, the values ​​of these state variables remain unchanged. The values ​​of the above state variables are calculated through the steady state before the fault. In the steady state before the fault, the above five state variables do not change, and their first-order derivatives are 0, that is, all the differential terms in formula (5) are 0. The solution expression is shown in formula (6): By solving equation (6), we can get the values ​​of the five state variables immediately after the fault. s The sudden decrease causes the reactive power Q output by the converter and the voltage U at the converter terminal to change. Due to the effect of the droop coefficient and the proportional coefficient in the reactive power loop, the potential U inside the converter is ref changes, resulting in changes in the output current, but these changes must satisfy the equality constraints shown in formula (7). Through the equation group shown in formula (7), the instantaneous dq axis current I after the fault is obtained d and I q And the current amplitude I mag ; Formula (6) is used to calculate the instantaneous state variable value after the fault. Formula (7) uses the result of formula (6) to calculate the current value after the fault. Substitute the grid voltage U into formula (6): s It should be the grid voltage value before the fault. Substitute the grid voltage U into formula (7) s It should be the grid voltage value after the fault.

5. The fault current analysis method according to claim 1, characterized in that: In the fourth step, at the instantaneous state variable value and instantaneous current value after the fault obtained in the third step, the differential algebraic equation model constructed in the second step is subjected to a first-order Taylor expansion, and the expression after the first-order Taylor expansion is shown in formula (8); In formula (8), I d and I q Eliminate and arrange to get the formula (9); in, 6. The fault current analysis method according to claim 5, characterized in that: In the fifth step, the mathematical model for the first-order Taylor expansion in the fourth step is organized into the form shown in formula (11): In the formula, A is the coefficient matrix and b is the bias vector. By solving the linear differential equations, the state variables δ and x are obtained. AP 、x RP 、x ud 、x uq The analytical expression of is shown in formula (12); In the formula, the eigenvalues ​​and eigenvectors of the coefficient matrix A are denoted as v i and λ i (i=1,2,3,4,5),δ p 、x APp 、x RPp 、x udp 、x uqp For equation A[δ p ,x APp ,x RPp ,x udp ,x uqp ] T +b=0; then using equation (8), we can get the current amplitude I mag An expression that changes over time.

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