Network construction converter fault current analysis method based on fast and slow scale dynamic separation

Abstract

The invention relates to a fast and slow scale dynamic separation-based fault current analysis method for a network construction converter, which comprises the following steps of: 1, constructing a network construction converter grid-connected system with a control strategy comprising an active power control link, a reactive power control link, a virtual impedance link and a classic voltage and current vector control loop; 2, based on the fact that the dynamic state of a voltage and current inner ring is far faster than the dynamic state of a power ring, constructing a network construction converter equivalent circuit model; 3, based on the difference between the power loop of the network construction converter and the current dynamic time scale, separating the power loop dynamic state of the synchronous time scale from the current dynamic state of the electromagnetic transient time scale; 4, simplifying the power ring to obtain an analytical expression of the internal potential of the network construction converter; and a fifth step of combining the current dynamic and internal potential analytic expressions, and solving to obtain a fault current analytic expression of the network construction converter.

Description

Technical Field

[0001] The present invention belongs to the field of fault current analysis of a grid-connected converter, and in particular relates to a fault current analysis method of a grid-connected converter based on dynamic separation of fast and slow scales. Background Art

[0002] The high proportion of renewable energy access to the power grid leads to the weakening of grid inertia and damping, and the decline of system strength and stability. The grid-connected converter, with its ability to provide virtual inertia and damping, provides a new technical solution to solve the above problems. [1-4] Unlike the grid-following converter, the grid-building converter presents a controlled voltage source characteristic under normal working conditions, and the output current is closely related to the grid voltage and line impedance. [5] When a grid fault occurs, in order to maintain voltage stability, the grid converter may inject a fault current far exceeding the rated current into the grid. [6] Considering the current carrying capacity of semiconductor devices [7] Under the premise of ensuring the safety and stability of the system, the grid converter will usually enter the current limiting mode during the fault period. [8-9] At this time, the grid-connected converter loses its voltage source characteristics and presents the characteristics of a controlled current source to the outside world, and the fault current is completely determined by the pre-set current limiting strategy. It is worth noting that when the grid-connected converter is connected to a weak grid with a relatively low short circuit, the grid-connected converter's overload capacity is improved, or a virtual impedance current limiting control strategy is adopted. [10-11] In such cases, the grid converter often operates in non-current limiting mode during the fault period and still presents voltage source characteristics to the outside. Unlike the grid converter in current limiting mode, the fault current of the grid converter is affected by many factors such as grid voltage, line impedance ratio and control strategy. The fault current presents significant nonlinear dynamic characteristics. This characteristic brings new theoretical challenges to power system design. Specifically, the capacity optimization configuration of the grid converter

[12] , Setting of relay protection values for power systems containing high-proportion grid-type equipment

[13] Key links such as fault current analysis and fault current analysis need to be scientifically planned and implemented based on the premise of clarifying the fault current characteristics. Therefore, establishing a mathematical model of the fault current of the grid-connected converter and clarifying the characteristics of the fault current have important theoretical value and engineering practical significance. It can provide an accurate theoretical basis for the design of system reliability and stability.

[0003] References

[0004] [1] Zhao Dongmei, Pei Jiannan, Bai Junhui, et al. Research on frequency regulation capability improvement technology of grid-connected converter in weak and extremely weak power grid scenarios [J]. Proceedings of the CSEE, 2024, 44(S1): 215-226.

[0005] [2] Wang Wei, Zhou Shaoze, Huang Meng, et al. Network-building technology: evolution, functional positioning and application prospects [J]. Automation of Electric Power Systems, 2025, 49(01): 1-13.

[0006] [3] M.Tozak, S.Taskin, I.Sengor and BPHayes, "Modeling and ControlofGrid Forming Converters: A Systematic Review," in IEEE Access, vol.12, pp.107818-107843, 2024, doi:10.1109 / ACCESS.2024.3437236.

[0007] [4]H.Zhang, W.Xiang, W.Lin and J.Wen, "Grid Forming Converters in Renewable Energy Sources Dominated Power Grid: Control Strategy, Stability, Application, and Challenges," in Journal of Modern Power Systems and CleanEnergy, vol.9, no.6, pp.1239-1256, November2021, doi:10.35833 / MPCE.2021.000257.

[0008] [5] N.Baeckeland, D.Chatterjee, M.Lu, B.Johnson and G.-S.Seo, "OvercurrentLimiting in Grid-Forming Inverters: A Comprehensive Review and Discussion," inIEEE Transactions on Power Electronics, vol.39, no.11, pp.14493-14517, Nov.2024, doi:10.1109 / TPEL.2024.3430316.

[0009] [6]TAUL G M,WANG X,DAVAR P,et al.Current Limiting Control WithEnhanced Dynamics ofGrid-Forming Converters During Fault Conditions[J].IEEEJournal ofEmerging and Selected Topics in Power Electronics,2020,8(2):1062-1073.

[0010] [7]Denis,G.,Prevost,T.,Debry,M.-S.,et al.The Migrate project:thechallenges of operating a transmission grid with only inverter-basedgeneration.A grids-forming control improvement with transient current-limiting control[[J].IET Renewable Power Generation,2018,12(5):523-529.

[0011] [8]L.Huang,H.Xin,Z.Wang,L.Zhang,K.Wu and J.Hu,"Transient StabilityAnalysis and Control Design ofDroop-Controlled Voltage Source ConvertersConsidering Current Limitation,"in IEEE Transactions on Smart Grid,vol.10,no.1,pp.578-591,Jan.2019,doi:10.1109 / TSG.2017.2749259.

[0012] [9]K.Zhuang, H.Xin, P.Hu and Z.Wang, "Current Saturation Analysis and Anti-Windup Control Design of Grid-Forming Voltage Source Converter," in IEEETransactions on Energy Conversion, vol.37, no.4, pp.2790-2802, Dec.2022, doi:10.1109 / TEC.2022.3208060.

[0013]

[10]

[0014]

[11] C.Luo et al., "Two-Stage Transient Control for VSG consideringFault Current Limitation and Transient Angle Stability," in IEEE Transactionson Industrial Electronics, vol.71, no.7, pp.7169-7179, July 2024, doi:10.1109 / TIE.2023.3292877.

[0015]

[12] Leng Ruohan, Zhuang Kehao, Hou Zhixian, et al. Functional positioning and capacity optimization configuration of grid-connected converter considering low voltage ride-through characteristics of grid-connected renewable energy [J / OL]. Proceedings of the CSEE, 1-11 [2025-03-21]. https: / / doi.org / 10.13334 / j.0258-8013.pcsee.241257.

[0016]

[13] Li Yan, Zhou Bohao, He Jiawei, et al. Challenges and countermeasures faced by AC relay protection in the flexible direct current transmission system of Shagohuang large-scale renewable energy base[J]. High Voltage Technology, 2025, 51(02): 489-506. Summary of the Invention

[0017] The present invention proposes a fault current analysis method for a grid-connected converter based on dynamic separation of fast and slow scales. The implementation steps and specific technical solutions are as follows:

[0018] The present invention proposes a method for analyzing fault current of a grid-connected converter based on dynamic separation of fast and slow scales, comprising the following steps:

[0019] Step 1: Build a grid-connected converter system

[0020] The control strategy for the grid-connected converter system includes an active power control loop, a reactive power control loop, a virtual impedance link, and a voltage and current vector control loop. In the active power control loop, the grid converter's own angular frequency and phase angle are generated through a virtual synchronization link. In the reactive power control loop, its control objective is to maintain the voltage stability of the grid converter's connection point and generate an internal potential. In the virtual impedance loop, the voltage reference value of the voltage loop is generated by subtracting the voltage drop across the virtual impedance from the internal potential amplitude. The voltage and current loops use a vector control strategy.

[0021] Step 2: Constructing the equivalent circuit model of the grid-connected converter

[0022] Combined with the grid-connected system control strategy of the grid-connected converter, an equivalent circuit model is constructed. The equivalent circuit model consists of two voltage sources, a resistor, and an inductor. The amplitude, frequency, and phase angle of one voltage source are the amplitude, frequency, and phase angle of the infinite bus, and the amplitude, frequency, and phase angle of the other voltage source are the amplitude, frequency, and phase angle of the potential within the grid-connected converter. The resistor is composed of the line resistance of the grid-connected system of the grid-connected converter and the virtual resistance of the grid-connected converter. The inductor is composed of the line inductance of the grid-connected system of the grid-connected converter and the virtual inductance of the grid-connected converter.

[0023] Step 3: Solve the potential inside the grid converter based on the power loop dynamics of the synchronous time scale

[0024] The dynamics of the active power control loop and the reactive power control loop belong to the synchronous transient time scale, while the dynamics of the fault current belong to the electromagnetic transient time scale. By separating the dynamics of the power loop from the dynamics of the fault current, and simplifying the power loop, an analytical expression for the potential inside the grid converter is obtained.

[0025] Step 4: Dynamic solution of fault current based on electromagnetic transient time scale

[0026] Substitute the analytical expression of the internal potential obtained in the third step into the equivalent circuit model obtained in the second step, solve the fault current differential equation, and obtain the analytical expression of the fault current.

[0027] Furthermore, according to the control strategy described in the first step, the expression of the active power control loop is shown in formula (1);

[0028]

[0029] Where δ represents the phase angle difference between the grid converter and the infinite bus, Δω represents the difference between the angular frequency of the grid converter and the rated angular frequency, H and D represent the inertia coefficient and damping coefficient respectively, and P ref and P represent the reference value and actual value of the active power output by the grid converter, respectively. The ‘.’ above δ and Δω represent the first-order derivatives of δ and Δω with respect to time t, respectively. The symbol ‘.’ above the variables in the following text has the same meaning.

[0030] The expression of the reactive power control loop is shown in formula (2);

[0031]

[0032] Where, E, Q ref ,Q,U ref ,U,K v and K q They are the internal potential amplitude of the grid converter, reactive power reference value, reactive power actual value, grid connection point voltage reference value, grid connection point voltage, VQ droop coefficient and integral gain.

[0033] In the virtual impedance link, the voltage loop dq axis reference voltage u is obtained by subtracting the voltage drop on the virtual impedance from the potential amplitude E in the converter. dref and u qref , its expression is shown in formula (3);

[0034]

[0035] Where i gd and i gq Represent the dq axis current, R v and L v Denote virtual resistance and virtual inductance respectively, and ω0 denotes the rated angular frequency. The voltage and current loops adopt vector control.

[0036] Furthermore, considering that the grid converter has a certain virtual inertia, it is believed that during the fault period, the grid converter angular frequency ω≈ω g =ω0,ω g and ω0 represent the grid angular frequency and rated angular frequency respectively, and the grid angular frequency is consistent with the rated angular frequency. The phase angle difference between the grid converter and the infinite bus is δ≈δ0, where δ0 represents the phase angle difference between the grid converter and the infinite bus under normal working conditions. The frequency and phase angle of the internal potential of the grid converter are obtained, as well as the simplified mathematical model of the internal potential amplitude as shown in formula (4):

[0037]

[0038] Among them, the expressions of Q and U are shown in formula (5), where X g represents the line reactance between the grid converter and the infinite bus, X g =ω0L g , X v Indicates the virtual inductance L v The corresponding virtual reactance, X v =ω0L v , R Σ Indicates the line resistance R g and virtual resistor R v The sum, R Σ =R g +R v , X Σ Indicates line reactance X g and virtual reactance X v The sum, X Σ =X g +X v ;

[0039]

[0040] The grid-connected point voltage U of the grid-connected converter is regarded as a function of the internal potential amplitude E and is linearly expanded at E=E0. E0 represents the initial value of the internal potential during the fault. The expression of U after linear expansion is substituted into Equation (4), and the solved internal potential amplitude is expanded in a power series to obtain the approximate expression of the internal potential amplitude E as shown in Equation (6):

[0041]

[0042] Wherein, the expressions of E1, E2 and b are shown in formula (7).

[0043]

[0044] Where U g1 Indicates infinite bus fault voltage.

[0045] Furthermore, the analytical expression of the internal potential amplitude obtained in the third step is introduced into the equivalent circuit model obtained in the second step to obtain the fault current i a The differential equation is shown in formula (8):

[0046]

[0047] Among them, L Σ Indicates the virtual inductance L v and line inductance L g The sum, L Σ =L v +Lg , α represents the phase of the infinite bus voltage. Solving equation (8), we get the analytical expression of the fault current as shown in equation (9):

[0048]

[0049] Among them, C1, C2, C3, C4, The expression of U is shown in formula (10), g0 and U g1 They represent the normal working voltage and fault voltage of the infinite busbar respectively;

[0050]

[0051] The present invention proposes a method for analyzing fault current of a grid-connected converter: 1) a high-order, strongly nonlinear, multi-time-scale coupled mathematical model of the fault current of the grid-connected converter is simplified into a second-order mathematical model suitable for analyzing the fault current of the grid-connected converter, which is composed of the fast and slow time scales separated by the dynamics of the reactive power control link and the current dynamics, through a series of rational assumptions; 2) based on the mathematical model constructed in 1), an analytical expression for the amplitude of the potential in the grid-connected converter is first obtained by analytical analysis; 3) based on the calculation result of 2), the analytical expression for the potential in the grid-connected converter is substituted into a first-order differential equation representing the dynamics of the fault current to obtain an analytical expression for the fault current of the grid-connected converter. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 Grid-connected converter system topology and control strategy

[0053] Figure 2 Grid Converter Equivalent Circuit

[0054] Figure 3 Phase diagram when the infinite bus voltage has a phase angle jump

[0055] Figure 4 Simulation results of mathematical model and electromagnetic transient model DETAILED DESCRIPTION

[0056] The present invention will be described below with reference to the accompanying drawings and embodiments.

[0057] (1) System control strategy

[0058] The topology of the grid-connected converter system considered in the present invention is as follows: Figure 1 As shown, where L f and R f They represent the filter inductor and the resistance of the filter inductor on the converter side, C f Indicates the filter capacitor, L g and Rg Represents line inductance and line resistance respectively, U g Indicates infinite bus voltage, flowing through the converter side filter inductor L f The current is i abc , the grid connection point of the converter AC side (voltage is u abc , the current flowing through the line is i gabc The measured i abc 、u abc and i gabc The components in the synchronous rotating coordinate system are obtained by Park transformation and are denoted as i d 、i q 、u d 、u q 、i gd and i gq .

[0059] The control strategy of the grid converter is as follows: Figure 1 As shown in the control strategy block diagram, it mainly includes active power control, reactive power control, virtual impedance control loop and inner loop voltage and current control.

[0060] In the active power control loop, the grid converter’s own angular frequency ω and phase angle θ are generated through the virtual synchronization link. Here, the phase angle difference between the grid converter and the infinite bus is defined as δ. At the same time, the rated angular frequency ω0 of the grid converter and the angular frequency ω of the infinite bus voltage are considered. g Equal, that is, ω0=ω g , so the expression of δ can be obtained as shown in the following formula (1).

[0061] δ=θ-θ g =∫(ω-ω g )dt=∫Δωdt (1)

[0062] Among them, θ g Indicates the infinite bus voltage phase. Combined with the virtual synchronization link, the active power control dynamics of the grid-connected converter can be obtained as shown in the following formula (2).

[0063]

[0064] Where Δω represents the difference between the angular frequency of the grid converter and the rated angular frequency, H and D represent the inertia coefficient and damping coefficient respectively, and P ref and P represent the reference value and actual value of the active power output by the grid converter, respectively. The ‘.’ above δ and Δω represent the first-order derivatives of δ and Δω with respect to time t, respectively. The symbol ‘.’ above the variables in the following text has the same meaning.

[0065] In the reactive power control loop, the control objective is to maintain the voltage U at the grid connection point of the grid converter stable and generate internal potential.

[0066] according to Figure 1 The control strategy of the grid-connected converter is shown in the following equation (3).

[0067]

[0068] Among them, E, Q ref ,Q,U ref , K v and K q They are the internal potential amplitude of the grid converter, reactive power reference value, reactive power actual value, grid connection point voltage reference value, VQ droop coefficient and integral gain.

[0069] Virtual impedance has significant advantages in suppressing fault currents in grid-connected converters and achieving power decoupling control. This paper studies fault currents in grid-connected converters, focusing on the role of virtual impedance in fault current suppression. In the virtual impedance loop, the voltage drop across the virtual impedance is subtracted from the internal potential amplitude E to generate the voltage reference value of the voltage loop. The dynamics of the virtual impedance link are shown in Equation (4).

[0070]

[0071] Among them, u dref and u qref Respectively represent the reference values of the dq axis components in the voltage loop, L v and R v Represent virtual inductance and virtual resistance respectively, i gd and i gq where d and q represent the grid-connected current components of the grid-connected converter, respectively. The voltage and current loops use classic vector control, which will not be described here.

[0072] against Figure 1 In the grid-connected system of the grid-connected converter shown in FIG, considering that the dynamics of the voltage and current inner loop are much faster than the dynamics of the power loop, it can be considered that the current i injected by the grid-connected converter into the infinite bus dq Can track the current reference value i in real time dqref , grid voltage u dq It can also track the voltage reference value u in real time dqref ,therefore, Figure 1 The grid-connected system of the grid-connected converter shown in the figure can be equivalent to Figure 2 The circuit shown, Figure 2 The fault current of the system shown can be considered to be Figure 1 The fault current of the grid-connected system of the grid-connected converter is shown.

[0073] based on Figure 2 The equivalent circuit of the grid-connected converter is shown in Equation (2) and Equation (3), and the dynamics of the grid-connected converter is shown in Equation (5).

[0074]

[0075] According to the network quasi-steady-state model, the d-axis and q-axis components of the grid-connected side current of the grid-connected converter can be obtained: gd and i gq Satisfies the following equation:

[0076]

[0077] Among them, U g Indicates infinite bus voltage, X g represents the line reactance between the grid converter and the infinite bus, X g =ω0L g , X v Indicates the virtual reactance corresponding to the virtual inductance, X v =ω0L v .

[0078] Solving equation (6), we can get the d-axis and q-axis components i of the grid-connected side current of the grid-connected converter: gd and i gq As shown in formula (7):

[0079]

[0080] Among them, R Σ Indicates the line resistance R g and virtual resistor R v The sum, R Σ =R g +R v , X Σ Indicates line reactance X g and virtual reactance X v The sum, X Σ =X g +X v .

[0081] According to formula (7) and the circuit equation, the d-axis and q-axis components u of the grid-connected point voltage of the grid-connected converter can be calculated: d 、u q The expression of is shown in formula (8):

[0082]

[0083] Substituting equation (7) into equation (8), the grid-connected point voltage U of the grid-connected converter can be calculated as shown in equation (9).

[0084]

[0085] According to the power calculation formula, the expressions of the active power P and reactive power Q output by the grid converter can be obtained as shown in formula (10).

[0086]

[0087] (2) Overall solution ideas

[0088] When the grid-connected converter enters the current limiting mode, its fault current is determined by the preset current limit value. When the grid-connected converter does not enter the current limiting mode during a fault and maintains the voltage source characteristics, its fault current is affected by multiple parameters such as its own control parameters and the physical parameters of the external circuit. The grid-connected converter fault current that the present invention focuses on is the fault current when the grid-connected converter does not enter the current limiting mode.

[0089] When the grid converter does not enter the current limiting mode and maintains the voltage source characteristics, it can be used Figure 2 The equivalent circuit shown in the figure describes the virtual resistor R v and virtual inductance L v It can be regarded as the internal impedance of the voltage source E, Figure 2 The short-circuit current of the grid-connected converter equivalent circuit shown in the figure can be considered as the short-circuit current of the grid-connected converter system. Referring to the three-phase short-circuit current calculation process of the constant voltage source circuit, the voltage source amplitude, frequency and phase are known, and the short-circuit current of the system under fault conditions can be solved by the current differential equation. Similarly, for Figure 2 The equivalent circuit of the grid converter shown in FIG. 1 can also be used to solve the fault current of the grid converter by using the differential equation of current when the amplitude, frequency and phase of the potential E in the grid converter are known.

[0090] The dynamics of the power loop fall within the synchronous transient timescale, while the dynamics of the fault current fall within the electromagnetic transient timescale. Due to the significant timescale differences between these two dynamic processes, this paper proposes a method based on the separation of fast and slow dynamic scales to hierarchically model and solve the dynamic characteristics at these two timescales. First, the dynamics of the power loop at the synchronous timescale are considered. Combined with the circuit equation, the amplitude, frequency, and phase of the potential within the grid-connected converter are obtained by simplifying the power loop dynamics and the grid-connected point voltage U. Then, the dynamics of the current at the electromagnetic transient timescale are considered, and an expression for the fault current is obtained by establishing a differential equation for the fault current.

[0091] (3) Solution of the potential inside the grid-connected converter based on the power loop dynamics of the synchronous time scale

[0092] Considering that the grid converter has a certain virtual inertia, it can be considered that during the fault period, the grid converter angular frequency ω≈ω g=ω0, the phase angle difference between the grid converter and the infinite bus is δ≈δ0, where δ0 represents the phase angle difference between the grid converter and the infinite bus under normal working conditions, ignoring the dynamics of the active loop. Therefore, the following conclusions can be drawn:

[0093] 1) During the fault period, the mathematical model (5) can be simplified to the mathematical model (11). Different from equations (9) and (10), in equation (11), the expressions of reactive power Q and terminal voltage U are δ=δ0, U g =U g1 , U g1 Indicates infinite bus voltage during fault period.

[0094]

[0095] 2) The frequency and phase characteristics of the voltage at the grid converter terminal during the fault period are clear: the frequency of the voltage at the grid converter terminal is the infinite bus frequency ω0, and the phase angle is δ0+α, where α represents the phase angle of the infinite bus.

[0096] 3) The potential amplitude E in the grid converter satisfies equation (11). Solving equation (11) can obtain the potential amplitude E in the grid converter.

[0097] By observing formula (11), it can be found that the grid-connected point voltage U of the grid-connected converter has strong nonlinearity, making it difficult to solve the differential equation for the internal potential E shown in formula (11). Therefore, it is necessary to simplify the grid-connected point voltage U. The present invention adopts a linearization method to simplify the grid-connected point voltage U of the grid-connected converter: the grid-connected point voltage U of the grid-connected converter can be regarded as a function of E, U = f(E), and is linearly expanded at E = E0. E0 represents the initial value of the internal potential during the fault period. According to formula (11), the internal potential E cannot change suddenly before and after the fault, so E0 is the steady-state value of the internal potential when the grid-connected converter is operating normally.

[0098] First, solve the first-order derivative of the grid connection point voltage U with respect to E at E=E0:

[0099]

[0100] When E=E0, the grid connection point voltage U is expressed as follows:

[0101]

[0102] According to equations (12) and (13), the voltage at the grid-connected point of the grid-connected converter can be obtained as follows after linearization:

[0103]

[0104] make

[0105]

[0106] Then the grid-connected point voltage U of the grid-connected converter after linearization can be simplified as formula (8).

[0107] U=U1E+U0 (16)

[0108] Substitute the expression of reactive power Q into the equation (11) and K q [(Q ref -Q)+K v (U ref -U)] part can be obtained:

[0109]

[0110] make

[0111]

[0112] The differential equation for the internal potential E is shown in Equation (19), and it is obvious that b<0.

[0113]

[0114] Given the mathematical form of the differential equation (19), the separation of variables method is usually used to solve it, and the equation E needs to be 2 +a1E+a0=0 root. g < <X g , R v < <X v Therefore, the expressions of a1 and a0 can be simplified to formula (20). The line short circuit ratio is usually between 1 and 10, so 0.1≤X g ≤1.0, according to the grid-connected standard of the grid-connected converter, VQ droop coefficient K v It should be within the range of 12.5 to 33.3, so K v X g ≥1.25, and U g1 ≤1.0, so a1>0. Usually the grid converter terminal voltage reference value U ref =1.0, reactive power reference value Q ref =0, so in a0, K v U g1 -2(Q ref +K v U ref )<0,K v U g1 -(Q ref +K v U ref )≤0, thus a0<0.

[0115]

[0116] Therefore, for the differential equation (19), a0 < 0, b < 0, and a1 2 -4a0 > 0. Therefore, the right side of the equation can be factorized as follows, where E2 < 0 < E1, and both are the solutions when the differential terms in equation (19) are zero. Therefore, the physical meaning of E1 is the value of the internal electromotive force at steady state during the fault:

[0117]

[0118] Therefore, separating variables for equation (19) gives equation (22).

[0119]

[0120] Integrating both sides of equation (22) gives the expression of E as shown in equation (23), where c is the integration constant.

[0121]

[0122] Substituting the initial value E0 at t = 0 into equation (23), the integration constant c is solved as shown in equation (24).

[0123]

[0124] Therefore, solving the differential equation (19) gives the expression of the amplitude E of the internal electromotive force of the network-forming converter as shown in equation (25).

[0125]

[0126] Different from the constant amplitude of the ideal power supply, the amplitude E of the internal electromotive force of the network-forming converter changes with the reactive power Q output by the network-forming converter and the terminal voltage U. Note that the exponential term in the expression (25) of the internal electromotive force amplitude is in the denominator, which is difficult to calculate. To solve this problem, the present invention uses the form of a power series to simplify equation (25).

[0127] Since E0 represents the internal electromotive force when the network-forming converter is operating normally before the fault, E0 > 0. Considering E2 < 0 < E1 and E1 + E2 = -a1 < 0 in equation (25), the inequality (26) always holds.

[0128]

[0129] (E1 - E2)b < 0

[0130]

[0131] Thus, the power series expansion of equation (25) can be performed to obtain the expression of the amplitude E of the internal electromotive force of the network-forming converter as shown in equation (27).

[0132]

[0133] From the fault current simulation comparison and verification results, it can be seen that when n = 1, it is sufficient to describe the dynamics of the fault current of the grid converter during the fault. Therefore, n = 1, that is, the expression of the potential E in the grid converter is shown in Equation (28).

[0134]

[0135] At this point, the amplitude of the potential inside the grid converter is obtained as shown in Equation (28), with a frequency of ω0 and a phase angle of δ0+α.

[0136] (4) Dynamic solution of fault current based on electromagnetic transient time scale

[0137] The following uses phase A as an example to illustrate the method for calculating the fault current. Figure 2 The equivalent circuit of the grid converter shown in the figure shows the instantaneous current i during the entire dynamic process from the occurrence of the infinite bus fault to the stable output of the grid converter. a Satisfies formula (29).

[0138]

[0139] Among them, L Σ Indicates the virtual inductance L v and line inductance L g The sum, L Σ =L v +L g .

[0140] Due to the line inductance L g With virtual inductance L v The current in the differential equation cannot change suddenly, so Equation (29) is an ordinary differential equation with boundary conditions. The solution of this differential equation consists of two parts: one is the forced component, which is determined by the excitation term on the right side of the differential equation and has the same change law as the excitation term; the other is the free component, which is independent of the excitation term on the right side of the differential equation and decays according to the exponential law. The decay time constant of the free component is T = L Σ / R Σ , the expression is shown in formula (30), where C1 is the integration constant determined by the initial conditions.

[0141] i a1 =C1 exp(-t / T)=C1 exp(-tR Σ / L Σ ) (30)

[0142] Considering that the expression of the potential amplitude E in the grid converter contains a constant term and an exponential decay term, the forced component of equation (29) consists of two parts. One part is a stable periodic component that changes according to the sinusoidal law, denoted as i a2 , the other part is the attenuation period component whose amplitude decays according to the exponential law and changes according to the sine law, denoted as i a3 The following uses the method of undetermined coefficients to solve these two forced components.

[0143] First, I introduce a2 The solution method. Since i a2 It is a stable periodic component that changes according to the sinusoidal law. We can set i a2 The expression of is shown in formula (31), where A1, A2, A3, and A4 are unknown coefficients.

[0144] i a2 =A1 sin(ω0t+α+δ0)+A2 cos(ω0t+α+δ0)+A3 sin(ω0t+α)+A4cos(ω0t+α)(31)

[0145] Substitute equation (31) into equation (32)

[0146]

[0147] After sorting, we can get the equation group about A1, A2, A3, and A4 as shown in equation (33).

[0148]

[0149] Substituting the solution of equation (33) into equation (31), we get i a2 The expression of is shown in formula (34).

[0150]

[0151] in, represents the impedance angle, and its expression is shown in formula (35).

[0152]

[0153] The following is an introduction to a3 The solution method. Since i a3 It is the decay period component whose amplitude decays according to the exponential law and changes according to the sine law, and its decay time constant is -1 / ((E1-E2)b), so we can set i a3 The expression of is shown in formula (36), where B1 and B2 are unknown coefficients.

[0154] i a3=B1 exp((E1-E2)bt)sin(ω0t+α+δ0)+B2 exp((E1-E2)bt)cos(ω0t+α+δ0) (36)

[0155] Substitute equation (36) into equation (37)

[0156]

[0157] After sorting, we can get the equation group for the unknown coefficients B1 and B2 as shown in equation (38).

[0158]

[0159] Substituting the solution of equation (38) into equation (36), we get i a3 The expression of is shown in formula (39).

[0160]

[0161] in, The expression is shown in formula (40).

[0162]

[0163] Combining equations (30), (34) and (39), the instantaneous current expression of phase A can be obtained as shown in equation (41).

[0164]

[0165] Before the fault occurs, the instantaneous current expression of phase A is:

[0166]

[0167] Assume that the fault occurs at time t=0. Since the current in the line cannot change suddenly, equation (43) holds.

[0168] i a0 (t=0 - )=i a (t=0 + ) (43)

[0169] In formula (43), 0 - and 0 + Representing the instant before t=0 and the instant after t=0, solving equation (43), we can get the expression of the integral constant C1 as shown in equation (44).

[0170]

[0171] Therefore, the instantaneous current of phase A i aThe expression is abbreviated as formula (45).

[0172]

[0173] Among them, C1, C2, C3, C4, The expression of U is shown in formula (46), g0 and U g1 They represent the voltage of the infinite busbar during normal operation and the fault voltage respectively.

[0174]

[0175] In addition to voltage drop, infinite bus phase angle jump is also a common fault type. Figure 3 As shown, assuming that at t = 0, the infinite bus voltage drops to U g1 At the same time, the phase angle jumps forward by β, and the phase angle of the infinite bus changes from α before the phase angle jump to α+β, while the phase angle of the grid converter terminal voltage remains unchanged at δ0+α. Therefore, after the infinite bus phase angle jump occurs, the mathematical model (45) is rewritten as formula (47).

[0176]

[0177] Among them, the expression of C1 is shown in formula (48), C2, C3, C4, The expression of is consistent with that of formula (46).

[0178]

[0179] Similarly, by replacing α in Equation (47) with α-2π / 3 and α+2π / 3, we can obtain the instantaneous current expressions i after the fault of phase B and phase C: b and i c .

[0180] According to the mathematical model (47), the fault current of the grid-connected converter is mainly composed of a DC component, a periodic component, and a periodic component with amplitude decay. The DC component decays exponentially, and its initial value is mainly affected by the infinite bus voltage before and after the fault and the steady-state internal potential of the converter. Due to the different instantaneous currents at the time of the three-phase fault, the DC component shows three-phase asymmetry. For a certain phase, the size of its DC component will also vary depending on the fault time. The DC component decay time constant is determined by the line impedance and virtual impedance. When the line reactance or virtual reactance increases, the decay time constant decreases and the DC component decay speed slows down. The periodic component depends on the control parameters of the grid-connected converter, the infinite bus voltage, and the line impedance, and its amplitude is a constant value. The amplitude of the amplitude decay periodic component decays exponentially. In addition to being affected by the line impedance and virtual impedance, the decay time constant is also affected by other control parameters of the grid-connected converter.

[0181] (5) Mathematical model verification

[0182] To verify the effectiveness of the grid-connected converter fault current analytical mathematical model constructed in this paper, a simulation example of the grid-connected converter system is built in the electromagnetic transient simulation software PSCAD / EMTDC. The detailed parameters are shown in Table 1.

[0183] Table 1 System parameters

[0184]

[0185] This embodiment sets the following 6 simulation conditions: Assume that at time t = 0, a three-phase symmetrical fault occurs at the infinite bus, the fault lasts for 100ms, and at time t = 0.1s, the three-phase voltage at the infinite bus returns to normal. The active power reference value P of each condition is ref , infinite bus voltage amplitude during fault period U g1 , line inductance L g , virtual inductance L v The forward jump angle β of the infinite bus voltage is shown in Table 2. The other parameters are consistent with Table E1 in Appendix E. The simulation results of the potential and fault current in each working condition are shown in Table 2. Figure 4 As shown in the figure, the solid line represents the electromagnetic transient simulation results, and the dotted line represents the mathematical model calculation results. The maximum errors between the internal potential and fault current mathematical model calculation results and the electromagnetic transient simulation results in each working condition are shown in Table 2. Emax and Δ Imax shown.

[0186] Table 2 Working condition settings

[0187]

[0188] from Figure 4 The following conclusions can be drawn:

[0189] 1) The mathematical model (47) constructed by the present invention is suitable for analyzing the fault current of the grid-connected converter. Figure 4 The maximum error data of the simulation results and the internal potential, fault current calculation results and electromagnetic transient simulation results in Table 1 show that the calculation results of mathematical model (28) and mathematical model (47) are highly consistent with the simulation results based on the detailed model, verifying the effectiveness of mathematical model (28) and mathematical model (47). Therefore, mathematical model (47) can be used to calculate the fault current of the grid-connected converter. At the same time, it proves the rationality of various simplified calculations in the process of analyzing the internal potential of the grid-connected converter.

[0190] 2) According to the simulation results of working condition 1 and working condition 2, when the active power reference value P refWhen the fault current is different, there is basically no difference. This also illustrates again that the present invention considers that the grid converter has a certain virtual inertia when solving the fault current of the grid converter. The angular frequency of the grid converter during the fault period is ω≈ω g =ω0, the assumption that the phase angle difference between the grid converter and the infinite bus δ≈δ0 is feasible.

[0191] 3) According to the simulation results of working conditions 1, 3, 4 and 5, the higher the infinite bus voltage, the larger the line inductance and the larger the virtual inductance during the fault period, the smaller the fault current.

[0192] 4) According to all simulation results, the impact of the fault current occurs within about one cycle after the fault, which is similar to the fault current of the synchronous machine.

[0193] 5) In the comprehensive modeling process, the reason for the errors between the calculation results of mathematical model (28) and mathematical model (47) and the electromagnetic transient simulation results is mainly due to a series of assumptions and simplifications in the modeling process of the present invention. Although the calculation accuracy is sacrificed, the present invention provides an approximate analytical expression for the fault current of the grid-connected system of the grid-connected converter, which is a major contribution of the present invention.

Claims

1. A method for analyzing fault current in a grid-connected converter based on dynamic separation of fast and slow scales, comprising the following steps: Step 1: Build a grid-connected converter system The control strategy for the grid-connected converter system includes an active power control loop, a reactive power control loop, a virtual impedance link, and a voltage and current vector control loop. In the active power control loop, the grid converter's own angular frequency and phase angle are generated through a virtual synchronization link. In the reactive power control loop, its control objective is to maintain the voltage stability of the grid converter's connection point and generate an internal potential. In the virtual impedance loop, the voltage reference value of the voltage loop is generated by subtracting the voltage drop across the virtual impedance from the internal potential amplitude. The voltage and current loops use a vector control strategy. Step 2: Constructing the equivalent circuit model of the grid-connected converter Combined with the grid-connected system control strategy of the grid-connected converter, an equivalent circuit model is constructed. The equivalent circuit model consists of two voltage sources, a resistor, and an inductor. The amplitude, frequency, and phase angle of one voltage source are the amplitude, frequency, and phase angle of the infinite bus, and the amplitude, frequency, and phase angle of the other voltage source are the amplitude, frequency, and phase angle of the potential within the grid-connected converter. The resistor is composed of the line resistance of the grid-connected system of the grid-connected converter and the virtual resistance of the grid-connected converter. The inductor is composed of the line inductance of the grid-connected system of the grid-connected converter and the virtual inductance of the grid-connected converter. Step 3: Solve the potential inside the grid converter based on the power loop dynamics of the synchronous time scale The dynamics of the active power control loop and the reactive power control loop belong to the synchronous transient time scale, while the dynamics of the fault current belong to the electromagnetic transient time scale. By separating the dynamics of the power loop from the dynamics of the fault current, and simplifying the power loop, an analytical expression for the potential inside the grid converter is obtained. Step 4: Dynamic solution of fault current based on electromagnetic transient time scale Substitute the analytical expression of the internal potential obtained in the third step into the equivalent circuit model obtained in the second step, solve the fault current differential equation, and obtain the analytical expression 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 control loop is shown in formula (1); Where δ represents the phase angle difference between the grid converter and the infinite bus, Δω represents the difference between the angular frequency of the grid converter and the rated angular frequency, H and D represent the inertia coefficient and damping coefficient respectively, and P ref and P represent the reference value and actual value of the active power output by the grid converter, respectively. The '.' above δ and Δω represent the first-order derivatives of δ and Δω with respect to time t, respectively. The symbol '.' above the variables in the following text has the same meaning. The expression of the reactive power control loop is shown in formula (2); Where, E, Q ref ,Q,U ref ,U,K v and K q They are the internal potential amplitude of the grid converter, reactive power reference value, reactive power actual value, grid connection point voltage reference value, grid connection point voltage, VQ droop coefficient and integral gain; In the virtual impedance link, the voltage loop dq axis reference voltage u is obtained by subtracting the voltage drop on the virtual impedance from the potential amplitude E in the converter. dref and u qref , its expression is shown in formula (3); Where i gd and i gq Represent the dq axis current, R v and L v Represent virtual resistance and virtual inductance respectively, ω0 represents rated angular frequency; the voltage and current loops adopt vector control.

3. The method for solving the internal potential of a grid-connected converter based on the power loop dynamics of the synchronous time scale according to claim 1 is characterized in that: In the third step, considering that the grid converter has a certain virtual inertia, it is assumed that during the fault period, the grid converter angular frequency ω≈ω g =ω0,ω g and ω0 represent the grid angular frequency and rated angular frequency respectively, and the grid angular frequency is consistent with the rated angular frequency. The phase angle difference between the grid converter and the infinite bus is δ≈δ0, where δ0 represents the phase angle difference between the grid converter and the infinite bus under normal working conditions. The frequency and phase angle of the internal potential of the grid converter are obtained, as well as the simplified mathematical model of the internal potential amplitude as shown in formula (4): Among them, the expressions of Q and U are shown in formula (5), where X g represents the line reactance between the grid converter and the infinite bus, X g =ω0L g , X v Indicates the virtual inductance L v The corresponding virtual reactance, X v =ω0L v , R Σ Indicates the line resistance R g and virtual resistor R v The sum, R Σ =R g +R v , X Σ Indicates line reactance X g and virtual reactance X v The sum, X Σ =X g +X v ; The grid-connected point voltage U of the grid-connected converter is regarded as a function of the internal potential amplitude E and is linearly expanded at E=E0. E0 represents the initial value of the internal potential during the fault. The expression of U after linear expansion is substituted into Equation (4), and the solved internal potential amplitude is expanded in a power series to obtain the approximate expression of the internal potential amplitude E as shown in Equation (6): Where, the expressions of E1, E2 and b are shown in formula (7); Where U g1 Indicates infinite bus fault voltage.

4. The method for dynamically solving fault current based on electromagnetic transient time scale according to claim 3, characterized in that: In the fourth step, the analytical expression of the internal potential amplitude obtained in the third step is substituted into the equivalent circuit model obtained in the second step to obtain the fault current i a The differential equation is shown in formula (8): Among them, L Σ Indicates the virtual inductance L v and line inductance L g The sum, L Σ =L v +L g , α represents the phase of the infinite bus voltage. Solving equation (8), we get the analytical expression of the fault current as shown in equation (9): Among them, C1, C2, C3, C4, The expression of U is shown in formula (10), g0 and U g1 They represent the normal working voltage and fault voltage of the infinite busbar respectively:

Images