Analysis Method and System for Transient Fault Current in the AC Feeding Stage after MMC Locking

Abstract

The present invention discloses an analytical method and system for transient fault current during the AC feeding stage after the MMC is blocked, which relates to the technical field of flexible DC transmission fault analysis. The key points of its technical solution are as follows: obtaining the equivalent circuit and circuit parameters of the MMC during the AC feeding stage; superimposing an attenuated DC component representing the system mutation amount on the steady-state component of the AC side current to obtain the analytical formula of the AC side current; expanding the three-phase switching function according to the Fourier series and ignoring the harmonics of the second order and above to obtain the analytical formula of the switching function; multiplying the analytical formula of the AC side current and the analytical formula of the switching function, and superimposing it with the initial value compensation current on the DC side to obtain the analytical formula of the DC side current. The present invention can obtain the analytical formulas of the transient fault currents on the AC and DC sides of the MMC during the AC feeding stage after blocking. Based on the analytical formulas, the key parameters affecting the fault current can be further analyzed, and the maximum value of the fault current can be accurately predicted, providing theoretical support for parameter design and protection setting, etc.

Description

Technical Field

[0001] The present invention relates to the technical field of flexible DC transmission fault analysis, and more specifically, to a method and system for analyzing transient fault current during the AC feeding stage after MMC blocking. Background Art

[0002] The modular multilevel converter (MMC) has many advantages such as independent active and reactive power control, no commutation failure, and high waveform quality. The flexible DC transmission and DC grid technologies based on MMC have been widely applied in fields such as large-scale new energy grid connection and transmission, asynchronous grid connection, and far-sea wind energy transmission. However, MMC is vulnerable to DC faults. After a fault, the sub-module capacitors discharge rapidly, and the fault current rises rapidly, which can easily damage the power electronic devices in the converter and threaten the safety of equipment and systems. Therefore, fault analysis and short-circuit calculation for MMC have always been a major research hotspot in the fields of flexible DC transmission and DC grids.

[0003] Existing research believes that the MMC fault process can generally be divided into three stages: ① the sub-module capacitor discharge stage; ② the stage when diodes conduct simultaneously; ③ the AC current feeding stage. Among them, the sub-module capacitor discharge stage occurs at the initial stage of the DC fault. During this stage, MMC can be equivalent to an RLC series circuit; the stage when diodes conduct simultaneously occurs at the initial stage after MMC blocking. During this stage, MMC can be equivalent to an RL series freewheeling circuit. Relatively rich research results have been obtained for the fault current calculation in the above two stages. The AC feeding stage occurs at the later stage of MMC blocking. At this time, MMC is equivalent to a diode six-pulse rectifier bridge with arm inductance, which has strong non-linear characteristics. At present, there are few reports on the calculation method of the converter fault current in this stage. In fact, since the AC current feeding mainly occurs in this stage, the AC current and the arm current will increase significantly in this stage, and the DC fault current may still continue to rise. Therefore, the calculation of the MMC fault current in this stage is of great significance for the protection design of the system and components.

[0004] However, in the AC feeding stage, both the arm current and the AC current contain large non-periodic components. The development process of the fault current is affected by multiple composite factors such as the fault moment, system parameters, and current initial value. It is extremely difficult to accurately calculate the fault current. Existing literature has proposed a calculation method using first- and second-order circuits for the evolution trajectory of the DC-side transient fault current during the AC feeding process. However, due to factors such as not considering the conduction state of the converter arm and the influence of the initial value, the existing methods have large errors in various fault scenarios and cannot know the change of the fault current on the AC side of the converter. Summary of the Invention

[0005] To address the deficiencies in the existing technology, the objective of the present invention is to provide a method and system for analyzing transient fault currents during the AC feeding stage after MMC blocking, which can obtain the analytical expressions of the transient fault currents on the AC and DC sides of the MMC during the AC feeding stage after blocking. Based on these analytical expressions, the key parameters affecting the fault current can be further analyzed, and the maximum value of the fault current can be accurately predicted, providing theoretical support for parameter design and protection setting, etc.

[0006] The above technical objective of the present invention is achieved through the following technical solutions:

[0007] In the first aspect, a method for analyzing transient fault currents during the AC feeding stage after MMC blocking is provided, including the following steps:

[0008] Obtain the equivalent circuit and circuit parameters of the MMC during the AC feeding stage;

[0009] Superimpose a decaying DC component representing the system mutation amount on the steady-state component of the AC side current to obtain the analytical expression of the AC side current;

[0010] Expand the three-phase switching function in Fourier series and ignore the harmonics of the second order and above to obtain the analytical expression of the switching function;

[0011] Multiply the analytical expression of the AC side current and the analytical expression of the switching function, and superimpose the initial value compensation current on the DC side to obtain the analytical expression of the DC side current.

[0012] Furthermore, the specific expression of the analytical expression of the AC side current is:

[0013]

[0014]

[0015]

[0016] Among them, i sa represents the current of phase a on the AC side; i sb represents the current of phase b on the AC side; i sc represents the current of phase c on the AC side; I sm represents the amplitude of the steady-state current on the AC side; ω represents the system angular frequency; t represents time; represents the phase angle of the steady-state current on the AC side; τ ac represents the decay time constant on the AC side; A represents the amplitude of the decaying DC component of phase a; B represents the amplitude of the decaying DC component of phase b; C represents the amplitude of the decaying DC component of phase c.

[0017] Furthermore, the specific calculation formula for the amplitude of the steady-state current on the AC side is:

[0018]

[0019] Among them, U s represents the amplitude of the AC equivalent power supply phase voltage; L ac represents the equivalent inductance on the AC side; R dc represents the equivalent resistance on the DC side; L a represents the arm inductance.

[0020] Furthermore, the specific calculation formula for the phase angle of the steady-state current on the AC side is:

[0021]

[0022] Among them, U s represents the amplitude of the AC equivalent power supply phase voltage; R dc represents the equivalent resistance on the DC side; I dc_ave represents the average value of the steady-state fault current on the DC side;

[0023] And / or, the specific calculation formula for the decay time constant on the AC side is:

[0024]

[0025] Furthermore, the specific calculation formula for the average value of the steady-state fault current on the DC side is:

[0026]

[0027] Furthermore, the specific calculation formula for the initial value compensation current on the DC side is:

[0028]

[0029]

[0030]

[0031] Among them, Δi dc represents the initial value compensation current on the DC side; I dc0 represents the initial value of the DC current at the start of the AC feeding stage; I sm represents the amplitude of the steady-state current on the AC side; A represents the amplitude of the decaying DC component in phase a; B represents the amplitude of the decaying DC component in phase b; C represents the amplitude of the decaying DC component in phase c; represents the phase angle of the steady-state current on the AC side; τ dc represents the decay time constant on the DC side; t represents time; L a represents the arm inductance; R dc represents the equivalent resistance on the DC side; L dc represents the equivalent inductance on the DC side.

[0032] Further, the specific calculation formula for the amplitude of the decaying DC component is as follows:

[0033]

[0034]

[0035]

[0036] Among them, I a0 represents the initial value of the current in phase a on the valve side of the converter at the initial moment of the AC feeding stage; I b0 represents the initial value of the current in phase b on the valve side of the converter at the initial moment of the AC feeding stage; I c0 represents the initial value of the current in phase c on the valve side of the converter at the initial moment of the AC feeding stage.

[0037] Further, the specific expression of the switching function analytical formula is as follows:

[0038]

[0039]

[0040]

[0041] Among them, S a represents the switching function of diode D1; S b represents the switching function of diode D3; S c represents the switching function of diode D5; ω represents the system angular frequency; t represents time; represents the phase angle of the steady-state current on the AC side.

[0042] Further, the specific expression of the DC-side current analytical formula is as follows:

[0043]

[0044] Among them, i dc represents the DC-side current; I sm represents the amplitude of the steady-state current on the AC side; τ ac represents the decay time constant on the AC side; ω represents the system angular frequency; t represents time; represents the phase angle of the steady-state current on the AC side; A represents the amplitude of the decaying DC component in phase a; B represents the amplitude of the decaying DC component in phase b; C represents the amplitude of the decaying DC component in phase c; Δi dc represents the initial value compensation current of the DC side introduced with first-order decay.

[0045] In the second aspect, a transient fault current analysis system during the AC feeding stage after MMC locking is provided, including:

[0046] The equivalent circuit module is used to obtain the equivalent circuit and circuit parameters of the MMC during the AC feeding stage;

[0047] The AC analysis module is used to superimpose an exponentially decaying DC component representing the system mutation on the steady-state component of the AC-side current to obtain the analytical formula of the AC-side current;

[0048] The switch analysis module is used to expand the three-phase switch function in Fourier series and ignore the harmonics of the second order and above to obtain the analytical formula of the switch function;

[0049] The DC analysis module is used to multiply the analytical formula of the AC-side current and the analytical formula of the switch function, and superimpose it with the initial DC-side compensation current to obtain the analytical formula of the DC-side current.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] 1. The transient fault current analysis method for the AC feeding stage after the MMC is blocked provided by the present invention can obtain the analytical formulas of the transient fault currents on the AC and DC sides of the MMC during the AC feeding stage after blocking. Based on the analytical formulas, the key parameters affecting the fault current can be further analyzed, and the maximum value of the fault current can be accurately predicted, providing theoretical support for parameter design and protection setting, etc.;

[0052] 2. The present invention can better restore the development trends of the AC and DC side currents during the AC feeding stage. When calculating the switch function, the high-order harmonics are ignored. Therefore, the change trend of the DC current ripple is ignored in the obtained DC current analytical formula. The error of the maximum DC current in the embodiments of the present invention is less than 1%, verifying the effectiveness of the proposed analytical formula. Description of the Drawings

[0053] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, form a part of this application, and do not limit the embodiments of the present invention. In the drawings:

[0054] Figure 1 is a schematic diagram of the equivalent circuit of the MMC during the AC feeding stage in the embodiment of the present invention;

[0055] Figure 2 is a schematic diagram of the DC current and AC current waveforms during the entire fault process in the embodiment of the present invention;

[0056] Figure 3 is a comparison diagram of the fault current analytical value obtained by the present invention and the simulation value during the AC feeding stage in the embodiment of the present invention;

[0057] Figure 4 is a system block diagram in the embodiment of the present invention. Detailed Embodiments

[0058] To make the objectives, technical solutions, and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with embodiments and the accompanying drawings. The illustrative embodiments of the present invention and their descriptions are only used to explain the present invention and are not intended to limit the present invention.

[0059] Embodiment 1: Analytical method for transient fault current during the AC feeding stage after MMC blocking.

[0060] Taking the half-bridge MMC converter as an example for illustration, its equivalent circuit after blocking is as Figure 1 shown.

[0061] Step 1: Obtain the equivalent circuit and parameters of the MMC during the AC feeding stage.

[0062] Figure 1 In, e a , e b , e c are the three-phase equivalent power supplies of the AC power grid respectively. Assuming the initial phase angle of the a-phase power supply voltage is zero, then:

[0063] e a =U s sin(ωt)

[0064] e b =U s sin(ωt - 2π / 3)

[0065] e c =U s sin(ωt + 2π / 3) (1)

[0066] In the formula, U s is the amplitude of the phase voltage of the AC equivalent power supply, and ω is the system angular frequency.

[0067] R ac , L ac represent the equivalent resistance and inductance on the AC side. The value of R ac is taken as the equivalent resistance R g of the AC power grid. L ac is the sum of the equivalent inductance L g of the AC power grid and the equivalent inductance L t of the transformer.

[0068] Among them, L g , R g can be obtained through the short-circuit ratio SCR (Short Circuit Ratio) of the AC system and the short-circuit resistance-reactance ratio R / X (Network Short-Circuit Resistance to Reactance ratio):

[0069]

[0070] In the formula, P is the rated active power of the converter.

[0071] The equivalent inductance L of the transformer t can be expressed as:

[0072]

[0073] In the formula, X t_pu is the per-unit value of the positive-sequence leakage reactance of the transformer, U 1N is the rated voltage of the primary side, and S is the capacity of the transformer. During calculation, the above AC-side electrical quantities are all converted to the secondary side.

[0074] L a represents the arm inductance, R dc and L dc respectively represent the equivalent resistance and inductance values on the DC side, u dc and i dc respectively represent the DC-side voltage and current, i1 to i6 respectively represent the currents flowing through diodes D1 to D6, i sa , i sb and i sc respectively represent the AC-side abc-phase currents.

[0075] For Figure 1 the circuit in, according to the KCL theorem, at any moment, the DC-side current can be expressed as the sum of the upper-arm currents or the sum of the lower-arm currents. Let the switching functions of diodes D1, D3, and D5 be S a , S b , S c , then the DC-side current can be expressed as:

[0076] i dc = i sa S a + i sb S b + i sc S c (4)

[0077] According to Equation (4), if the analytical formulas of the three-phase currents on the AC side and the switching function analytical formula are obtained respectively, the DC current analytical formula can be obtained through the sum of the products of the two.

[0078] Step 2: Analyze the analytical formula of the AC-side current

[0079] The blocked converter is a system containing multiple inductive elements and switching elements. When viewed from the AC side, the converter is equivalent to an integral unit. When the converter is blocked, it can be regarded as a sudden change in the state of the AC system. To prevent sudden changes in the magnetic flux and current in the inductive circuit, a decaying DC component representing the sudden change in the system will be superimposed on the steady-state component of the AC-side current. Therefore, during the transient process, the AC-side current can be expressed as:

[0080]

[0081]

[0082]

[0083] where, I sm is the amplitude of the steady-state AC-side current, and its calculation method is as follows:

[0084]

[0085] I dc_ave represents the average value of the steady-state DC-side fault current, and its calculation formula is as follows:

[0086]

[0087] is the phase angle of the steady-state AC-side current, which can be obtained from the conservation of steady-state power on the AC and DC sides:

[0088]

[0089] τ ac represents the decaying time constant on the AC side:

[0090]

[0091] A, B, and C are the amplitudes of the decaying DC component. Assume that the initial values of the three-phase currents on the valve side of the converter at the initial moment of the AC feeding stage are I a0 , I b0 and I c0 , then A, B, and C can be expressed as:

[0092]

[0093]

[0094]

[0095] Step 3: Determine the analytical formula of the switching function

[0096] For the blocked MMC converter, when the DC-side resistance satisfies Equation (11), whether in the transient stage or the steady state stage after blocking, there are exactly 3 bridge arms conducting at any moment in the converter. The upper and lower bridge arms of any phase will conduct alternately for 180° within an AC cycle. The three-phase switching function is a square wave with the same phase as the AC-side current of the converter, as shown in Equation (12), specifically as follows:

[0097]

[0098]

[0099]

[0100]

[0101] Since the exact switching function is a discontinuous function, it is not convenient for product calculation. Therefore, here the switching function is expanded in Fourier series and the harmonics of the second order and above are ignored. Then the analytical formula of the switching function can be expressed as:

[0102]

[0103]

[0104]

[0105] Step 4: Solve the analytical formula of the DC-side transient current.

[0106] Substitute Equation (5) and Equation (13) into Equation (4) to obtain:

[0107]

[0108] Since the high-order harmonics are ignored in the Fourier decomposition process of the switching function, there will be an error between the analytical value of the fault current obtained from Equation (14) and the initial value of the true fault current in Equation (4). To solve this problem, a first-order decaying DC-side initial value compensation current is introduced into the analytical formula of the DC-side transient current, as shown in Equation (15):

[0109]

[0110] In the formula, Δi dc | t＝0 is the difference between the initial value of the DC current (I dc0 ) at the starting moment of the AC feeding stage and the DC current obtained from Equation (14) at t = 0, and can be expressed as:

[0111]

[0112] In the formula, τ dcis the DC-side decay time constant, and its value is:

[0113]

[0114] Therefore, the analytical formula of the DC-side transient fault current after blocking can be finally expressed as:

[0115]

[0116] Step Five: Validity Verification

[0117] To verify the effectiveness of the method proposed in the present invention, a half-bridge MMC converter was built in PSCAD, using a detailed sub-module model (Full Detailed Model). Each arm is composed of 4 series-connected half-bridge sub-modules. The simulation model parameters are shown in Table 1.

[0118] Table 1 Simulation Test Model Parameters

[0119]

[0120] To verify the effectiveness of the proposed analytical formula, a bipolar short-circuit fault was set at the outlet of the current-limiting reactor, with a fault resistance of 30 ohms. The arm current blocking threshold was set at 4 kA. The DC-side and AC-side fault current curves obtained from the simulation are as Figure 2 shown. As can be seen from Figure 2 it, the fault development has gone through three stages. Before the converter is blocked, it is the capacitor discharge stage. After blocking, it is the stage where diodes conduct simultaneously and the AC feeding stage. Among them, the comparison between the transient fault current curve of the AC feeding stage obtained from the analytical formula proposed in the present invention and the simulation curve is as Figure 3 shown, where the solid line is the simulation value and the dashed line is the analytical value. As can be seen from Figure 3 it, the analytical formula proposed in the present invention can better restore the development trend of the AC and DC side currents in the AC feeding stage. When calculating the switching function, high-order harmonics are ignored. Therefore, the DC current analytical formula obtained ignores the change trend of the DC current ripple. In the embodiment, the maximum error of the DC current is less than 1%, verifying the effectiveness of the proposed analytical formula.

[0121] Embodiment 2: An analytical system for the transient fault current in the AC feeding stage after MMC blocking. This system is used to implement the method for analyzing the transient fault current in the AC feeding stage after MMC blocking described in Embodiment 1, as Figure 4 shown, including an equivalent circuit module, an AC analysis module, a switching analysis module, and a DC analysis module.

[0122] Among them, the equivalent circuit module is used to obtain the equivalent circuit and circuit parameters of the MMC during the AC feeding stage; the AC analysis module is used to superimpose an attenuated DC component representing the system mutation amount on the steady-state component of the AC-side current to obtain the AC-side current analytical formula; the switching analysis module is used to expand the three-phase switching function in Fourier series and ignore the harmonics of the second order and above to obtain the switching function analytical formula; the DC analysis module is used to multiply the AC-side current analytical formula and the switching function analytical formula, and superimpose the DC-side initial value compensation current to obtain the DC-side current analytical formula.

[0123] Working principle: The transient fault current analysis method for the AC feeding stage after the MMC is blocked provided by the present invention can obtain the transient fault current analytical formulas of the AC and DC sides of the MMC during the AC feeding stage after the block. Based on the analytical formulas, the key parameters affecting the fault current can be further analyzed, and the maximum value of the fault current can be accurately predicted, providing theoretical support for parameter design and protection setting, etc.

[0124] The specific embodiments described above further elaborate on the purpose, technical solutions, and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. Analytical method for transient fault current in the AC feeding stage after MMC locking, characterized in that It includes the following steps: Obtain the equivalent circuit and circuit parameters of the MMC during the AC feeding stage; Superimpose an exponentially decaying DC component representing the system mutation on the steady-state component of the AC side current to obtain the analytical formula of the AC side current; Expand the three-phase switching function in Fourier series and neglect the harmonics of the second order and above to obtain the analytical formula of the switching function; Multiply the analytical formula of the AC side current and the analytical formula of the switching function, and superimpose it with the initial value compensation current on the DC side to obtain the analytical formula of the DC side current; The specific expression of the analytical formula of the AC side current is: where, i sa represents the current of phase a on the AC side; i sb represents the current of phase b on the AC side; i sc represents the current of phase c on the AC side; I sm represents the amplitude of the steady-state current on the AC side; ω represents the system angular frequency; t represents time; represents the phase angle of the steady-state current on the AC side; τ ac represents the decay time constant on the AC side; A represents the amplitude of the decaying DC component of phase a; B represents the amplitude of the decaying DC component of phase b; C represents the amplitude of the decaying DC component of phase c; The specific calculation formula of the amplitude of the AC side steady-state current is: Among them, U s represents the amplitude of the AC equivalent power supply phase voltage; L ac represents the equivalent inductance on the AC side; R dc represents the equivalent resistance on the DC side; L a represents the arm inductance; The specific calculation formula of the phase angle of the AC side steady-state current is: Among them, U s represents the amplitude of the AC equivalent power supply phase voltage; R dc represents the DC side equivalent resistance; I dc_ave represents the average value of the DC side steady-state fault current; The specific calculation formula of the exponentially decaying time constant on the AC side is: The specific calculation formula of the average value of the DC side steady-state fault current is: The specific calculation formula of the initial value compensation current on the DC side is: Among them, Δi dc represents the initial value compensation current on the DC side; I dc0 represents the initial value of the DC current at the starting moment of the AC feeding stage; I sm represents the amplitude of the steady-state current on the AC side; A represents the amplitude of the decaying DC component in phase a; B represents the amplitude of the decaying DC component in phase b; C represents the amplitude of the decaying DC component in phase c; represents the phase angle of the steady-state current on the AC side; τ dc represents the decaying time constant on the DC side; t represents time; L a represents the arm inductor; R dc represents the equivalent resistance on the DC side; L dc represents the equivalent inductance on the DC side; The specific calculation formula of the amplitude of the exponentially decaying DC component is: Among them, I a0 represents the initial value of the a-phase current on the valve side of the converter at the initial moment of the AC feeding stage; I b0 represents the initial value of the b-phase current on the valve side of the converter at the initial moment of the AC feeding stage; I c0 represents the initial value of the c-phase current on the valve side of the converter at the initial moment of the AC feeding stage; The specific expression of the analytical formula of the switching function is: Among them, S a represents the switching function of diode D1; S b represents the switching function of diode D3; S c represents the switching function of diode D5; ω represents the system angular frequency; t represents time; represents the phase angle of the steady-state current on the AC side; The specific expression of the analytical formula of the DC side current is: Among them, i dc represents the DC side current; I sm represents the amplitude of the AC side steady-state current; τ ac represents the AC side decay time constant; ω represents the system angular frequency; t represents time; represents the phase angle of the AC side steady-state current; A represents the amplitude of the decaying DC component of phase a; B represents the amplitude of the decaying DC component of phase b; C represents the amplitude of the decaying DC component of phase c; Δi dc represents the initial value compensation current of the DC side introducing first-order decay.

2. Transient fault current analysis system during AC feeding stage after MMC locking, applied to the transient fault current analysis method during AC feeding stage after MMC locking according to claim 1, characterized in that, It includes: An equivalent circuit module for obtaining the equivalent circuit and circuit parameters of the MMC during the AC feeding stage; An AC analysis module for superimposing an exponentially decaying DC component representing the system mutation on the steady-state component of the AC side current to obtain the analytical formula of the AC side current; A switching analysis module for expanding the three-phase switching function in Fourier series and neglecting the harmonics of the second order and above to obtain the analytical formula of the switching function; A DC analysis module for multiplying the analytical formula of the AC side current and the analytical formula of the switching function, and superimposing it with the initial value compensation current on the DC side to obtain the analytical formula of the DC side current.

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