Method for Generating Short-Circuit Breaking Voltage and Current Waveforms of Circuit Breaker and Obtaining Parameters

Abstract

The present invention discloses a method for generating the short - circuit breaking voltage and current waveforms of a circuit breaker and obtaining parameters, which is characterized in that by obtaining the positive - sequence reactance X1, positive - sequence resistance R1, and zero - sequence reactance X0 of the node where the circuit breaker is located, the total current, alternating - current component current, direct - current component current, and power - frequency recovery voltage during the short - circuit breaking process of the circuit breaker are calculated by applying a three - phase equivalent circuit model. Further, the parameters of the last half - wave of the short - circuit breaking current are obtained: the duration ΔT, the peak value I peak , the direct - current component p at the current zero - crossing point, and from p, the di / dt at the current zero - crossing point and the TRV parameters under the condition of modified asymmetrical short - circuit breaking can be calculated. The short - circuit breaking voltage and current parameters of the high - voltage alternating - current circuit breaker obtained by the method of the present invention can provide reference and basis for the evaluation of the breaking capacity of the circuit breaker and phase - selective breaking.

Description

Technical Field:

[0001] The present invention belongs to the technical field of phase - selective opening of high - voltage AC circuit breakers, and particularly relates to a calculation method for generating the short - circuit opening voltage and current waveforms of a high - voltage AC circuit breaker and obtaining parameters. Background Art:

[0002] High - voltage AC circuit breakers play an important role in the power grid. They are the executive elements for relay protection actions in the power system and also the executive elements for line switching. In particular, when a short - circuit fault occurs near the corresponding moment of the zero value of the power supply voltage, or when the circuit breaker closes short - circuit near the corresponding moment of the zero value of the power supply voltage during reclosing, due to the fact that the current in the inductive loop cannot change suddenly, a DC component current approximately equal to the peak value of the short - circuit current will be generated in the system and then decay according to the inherent time constant. Therefore, the short - circuit current consists of an AC component part and a DC current component part, and the assessment of the short - circuit opening ability of high - voltage AC circuit breakers is relatively strict, which is called asymmetrical short - circuit fault opening.

[0003] In recent years, with the increase of short - circuit current in the power grid, components such as high - impedance transformers and series reactors have caused the DC time constant of the power system to exceed the rated time constant. Although some current - limiting measures are taken, the increase of the DC time constant makes the high - voltage AC circuit breaker open the asymmetrical short - circuit fault current may exceed its rated opening ability range, posing a certain threat to the safe and stable operation of the power grid.

[0004] Phase - selective opening is a feasible solution. By using a phase - selective tripping controller, the circuit breaker can perform short - circuit opening within a suitable time window, thereby reducing the DC component at the moment of contact separation of the circuit breaker, avoiding the occurrence of the first - opening large half - wave and extended large half - wave situations, and ensuring the opening ability of the circuit breaker. Currently, electromagnetic transient simulation calculation software can only calculate the full - current waveform and parameters of the short - circuit opening current, and cannot obtain the DC component current and AC component current at any moment during the opening process, resulting in the inability to accurately calculate the phase - selective opening control algorithm. Therefore, it is necessary to develop a calculation method for generating the short - circuit opening voltage and current waveforms of the circuit breaker and obtaining parameters, to obtain the DC component, AC component and electrical parameters at any moment, providing reference and basis for the assessment of the circuit breaker's opening ability and phase - selective opening. Summary of the Invention:

[0005] The object of the present invention is to provide a calculation method for generating the short - circuit opening voltage and current waveforms of a high - voltage AC circuit breaker, which solves the technical problems of waveform generation and parameter calculation of the contact - opening voltage, AC component of the current and DC component of the current during the short - circuit opening of the circuit breaker.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A calculation method for generating short - circuit breaking voltage and current waveforms and obtaining parameters of a high - voltage AC circuit breaker, characterized by the following steps:

[0008] 1) Based on the actual operation of the power network, the power grid is dynamically divided into an internal area and an external area, and the positive - sequence reactance X1, positive - sequence resistance R1, and zero - sequence reactance X0 of the node where the circuit breaker is located in the internal area are calculated. Take the power supply voltage U of the node S =1.05U N , U N is the nominal voltage, and the power supply voltages of phases A, B, and C are set as:

[0009]

[0010] where ω = 2πf, f is the frequency, and a is the starting phase angle of the voltage of phase A. The three - phase of the circuit is balanced, and the voltage of the neutral point is u e (t)=u A (t)+u B (t)+u C (t)=0. Assume that a three - phase short - circuit fault occurs at t = 0. According to Equation (1), the short - circuit currents of phases A, B, and C can be obtained as:

[0011]

[0012] where I S =U S / (R1 + jX1), is the loop power - factor angle, and τ is the DC time constant. The expected breaking time t open of the circuit breaker can be obtained, and the zero - crossing time t R of the first breaking pole R phase and the second breaking pole S phase and the third breaking pole T phase can be obtained.

[0013] 2) After phase R is broken, the state equations of the voltages and currents of phases S and T are:

[0014]

[0015] where R = R1. Solving Equation (3) can obtain the currents i S (t), i T (t) of phases S and T. The voltage of the neutral point is

[0016] 3) From the i S (t), i T (t) obtained by solving in step 2, the zero - crossing time of the second breaking pole S can be obtained as t S . After phase S is broken, the circuit equations of the voltage and current of phase T are:

[0017]

[0018] Solving Equation (4), the current \(i\) of phase T can be obtained T (t). The voltage of the neutral point is

[0019] 4) From the \(i\) obtained by solving in step 3 T (t), the zero-crossing time \(t\) of the third breaking pole T can be obtained T . After phase T is broken, the currents of phases R, S, and T are zero. The voltage of the neutral point is \(u\) e (t) = 0.

[0020] 5) During the breaking process, the power frequency voltages \(U\) between the breaker contacts of phases A, B, and C _prA 、\(U\) _prB 、\(U\) _prC are obtained by subtracting the voltage of the neutral point from the power supply voltage, that is:

[0021]

[0022] A further improvement of the present invention is that in steps 1) to 5), a three-phase equivalent circuit is applied for calculating electrical parameters and waveforms, and a neutral point grounding reactance \(X\) e is introduced between the neutral point of the equivalent circuit and the ground, that is:

[0023]

[0024] where \(k\) pp is the first-breaking pole coefficient. The first-breaking pole coefficient

[0025] A further improvement of the present invention is that in step 1), the opening time \(t\) o and the shortest arcing time \(t\) arcmin of the breaker where the node is located are obtained from the database, and the relay protection operation time is \(t\) b , then the minimum breaking time of the breaker is:

[0026] \(t\) openmin = \(t\) o +\(t\) arcmin +\(t\) b (7)

[0027] The currents of phases A, B, and C are as shown in Equation (2). When \(t\geq t\) openmin , the phase where the first current zero-crossing point is located is defined as phase R, and the corresponding breaking time is \(t\) R. The second and third interrupted phases are defined as phases S and T. The mapping vectors of phases R, S, T and phases A, B, C are n = [n1 n2 n3]. When n1 = 1, n2 = 3, n3 = 2; when n1 = 2, n2 = 1, n3 = 3; when n1 = 3, n2 = 2, n3 = 1. Among them, 1 maps to phase A, 2 maps to phase B, and 3 maps to phase C.

[0028] A further improvement of the present invention lies in: in step 2), after phase R is interrupted, the AC and DC components of the currents of phases S and T are:

[0029]

[0030] In the formula, z1 = R + jω(L + L e ), z2 = jωL e , i S_ac (t), i S_dc (t) are respectively the AC component and the DC component of the current of phase S, and i T_ac (t), i T_dc (t) are respectively the AC component and the DC component of the current of phase T.

[0031] A further improvement of the present invention lies in: in step 3), after phase S is interrupted, the AC and DC components of the current of phase T are:

[0032]

[0033] In the formula, i T_ac (t), i T_dc (t) are respectively the AC component and the DC component of the current of phase T.

[0034] A further improvement of the present invention lies in: the short-circuit current waveform produced can be directly read or the last half-wave parameters of the short-circuit breaking current can be automatically obtained: the duration ΔT, the peak value I peak , and the DC component p at the current zero crossing. Further, the di / dt at the current zero crossing can be calculated from p, and the TRV parameters under the condition of corrected asymmetrical short-circuit breaking can be obtained.

[0035] A further improvement of the present invention lies in: the short-circuit breaking calculation process and the parameter acquisition method are applicable to both the case of generating short-circuit current by phase-selection closing with a three-phase independent operating mechanism for a high-voltage AC circuit breaker and the case of phase-selection opening with a three-phase independent operating mechanism.

[0036] Compared with the prior art, the present invention has at least the following technical effects:

[0037] The present invention discloses a calculation method for generating short-circuit breaking voltage and current waveforms and obtaining parameters of a high-voltage AC circuit breaker. It is characterized in that by obtaining the positive-sequence reactance X1, positive-sequence resistance R1, and zero-sequence reactance X0 of the node where the circuit breaker is located, the total current, AC component current, DC component current, and power-frequency recovery voltage during the short-circuit breaking process of the circuit breaker are calculated using a three-phase equivalent circuit model. Further, the parameters of the last half-wave of the short-circuit breaking current are obtained: the duration ΔT, the peak value I peak , the DC component p at the current zero-crossing point, and from p, the di / dt at the current zero-crossing point and the TRV parameters under the corrected asymmetrical short-circuit breaking conditions can be calculated. The short-circuit breaking voltage and current parameters of the high-voltage AC circuit breaker obtained by the method of the present invention can provide reference and basis for the evaluation of the breaking capacity of the circuit breaker and phase-selection breaking. Brief Description of the Drawings:

[0038] Figure 1 is the calculation waveform diagram of the short-circuit breaking voltage and current of the circuit breaker in a neutral-point effectively grounded system - the first-opening pole factor is 1.3.

[0039] Figure 2 is the calculation waveform diagram of the short-circuit breaking voltage and current of the circuit breaker in a neutral-point non-effectively grounded system - the first-opening pole factor is 1.5. Detailed Embodiments:

[0040] The present invention will be described in detail below with reference to the drawings and specific embodiments.

[0041] Embodiment 1

[0042] As Figure 1 , a calculation method for generating short-circuit breaking voltage and current waveforms and obtaining parameters of a high-voltage AC circuit breaker, applied to a neutral-point effectively grounded system, includes the following steps:

[0043] 1) By equivalent calculation of the electrical network, the positive-sequence reactance X1 = 3.3151 Ω, positive-sequence resistance R1 = 0.1759 Ω, and zero-sequence reactance X0 = 9.9453 Ω of the node where the circuit breaker is located are obtained, and the equivalent voltage source U S = 230 kV, the first-opening pole factor k pp = 1.3 is calculated, and a neutral-point grounding reactance X e = 2.4863 Ω is introduced between the neutral point and the ground. Assuming the starting phase angle of the phase A voltage is 0 and the frequency f is 50 Hz, the power supply voltages of phases A, B, and C are:

[0044]

[0045] A three-phase short-circuit fault occurs at t = 0. According to Equation (1), the short-circuit currents of phases A, B, and C can be obtained as:

[0046]

[0047] 2) The opening time t of the circuit breaker o = 0.026 s and the shortest arcing time t arcmin = 0.008 s. The operation time of the relay protection is t b = 0.010 s. Then the minimum opening time t of the circuit breaker openmin = 0.044 s. When t ≥ 0.044 s, from Equation (2), it can be obtained that the phase where the first current zero-crossing point is located is Phase C, and the corresponding opening moment is t R = 0.0474 s. The mapping vectors of phases R, S, T and phases A, B, C are n = [3 2 1].

[0048] 3) After Phase R is opened, the state equations of the voltages and currents of phases S and T are:

[0049]

[0050] Solving Equation (3), the currents i S (t), i T (t) of phases S and T can be obtained. The voltage of the neutral point is u e (t) = 0.3(u S (t) + u T (t)). After Phase R is opened, the AC and DC components of the currents of phases S and T are:

[0051]

[0052] In the formula, i S_ac (t), i S_dc (t) are respectively the AC component and the DC component of the current of Phase S, and i T_ac (t), i T_dc (t) are respectively the AC component and the DC component of the current of Phase T.

[0053] 4) From the i S (t), i T (t) obtained by solving in Step 3, the zero-crossing moment of the second breaking pole S can be obtained as t S = 0.0533 s. After Phase S is opened, the circuit equations of the voltage and current of Phase T are:

[0054]

[0055] Solving Equation (5), the current i T (t) of Phase T can be obtained. The voltage of the neutral point is u e (t) = 0.4286u T (t). After Phase S is opened, the AC and DC components of the current of Phase T are:

[0056]

[0057] Wherein, i T_ac (t) and i T_dc (t) are respectively the AC component and DC component of the phase T current.

[0058] 5) During the opening process, the power frequency voltages U _prA , U _prB , U _prC between the breaker contacts of phases A, B, and C are obtained by the difference between the supply voltage and the neutral point voltage, i.e.:

[0059]

[0060] 6) Select the reference value of voltage as and the reference value of current as Perform per-unit conversion on the calculation results to obtain Figure 1 the results.

[0061] 7) Applying the short-circuit current waveforms produced, the last half-wave durations of the short-circuit breaking currents of phases A, B, and C are respectively 13.00 ms, 12.57 ms, and 8.28 ms, the last half-wave peaks are respectively 71.24 kA, 68.38 kA, and 41.54 kA, and the DC component percentages at the current zero-crossings are respectively 23.0%, 24.5%, and 24.8%. Further, the di / dt at the current zero-crossings of phases A, B, and C are calculated from p to be 0.59 pu, 0.88 pu, and 0.96 pu respectively.

[0062] Embodiment 2

[0063] As Figure 2 , a calculation method for generating short-circuit breaking voltage and current waveforms and obtaining parameters of a high-voltage AC circuit breaker, which is applied to an uneffectively grounded neutral system, includes the following steps:

[0064] 1) By equivalent calculation of the electrical network, the positive-sequence reactance X1 = 2.2101 Ω, positive-sequence resistance R1 = 0.1172 Ω, zero-sequence reactance X0 = 9999 Ω (tending to infinity), and equivalent voltage source U S = 115 kV of the node where the circuit breaker is located are obtained. The first-opening pole coefficient k pp = 1.5 is calculated, and a neutral grounding reactance X e = 9999 Ω (tending to infinity) is introduced between the neutral point and the ground. Assuming the starting phase angle of the phase A voltage is 0 and the frequency f is 50 Hz, the supply voltages of phases A, B, and C are:

[0065]

[0066] A three-phase short-circuit fault occurs at t = 0. According to Equation (1), the short-circuit currents of Phase A, Phase B, and Phase C can be obtained as follows:

[0067]

[0068] 2) The opening time t o of the circuit breaker is 0.028 s, and the shortest arcing time t arcmin is 0.01 s. The operating time of the relay protection is t b = 0.010 s. Then the minimum opening time t openmin of the circuit breaker is 0.048 s. When t ≥ 0.048 s, from Equation (2), it can be obtained that the phase where the first current zero-crossing occurs is Phase B, and the corresponding opening time is t R = 0.0521 s. The mapping vectors of Phase R, Phase S, Phase T and Phase A, Phase B, Phase C are n = [2 1 3].

[0069] 3) After Phase R is opened, the state equations of the voltages and currents of Phase S and Phase T are as follows:

[0070]

[0071] By solving Equation (3), the currents i S (t) and i T (t) of Phase S and Phase T can be obtained. The voltage of the neutral point is u e (t) = 0.5(u S (t) + u T (t)). After Phase R is opened, the AC and DC components of the currents of Phase S and Phase T are:

[0072]

[0073] In the formula, i S_ac (t) and i S_dc (t) are the AC component and DC component of the current of Phase S respectively, and i T_ac (t) and i T_dc (t) are the AC component and DC component of the current of Phase T respectively.

[0074] 4) Since it is a non-effectively grounded neutral system, the second breaking pole S and the third breaking pole T are simultaneously zero-crossing opened. From the i S (t) and i T (t) obtained by solving in Step 3, the zero-crossing time of the two later-breaking poles is t S = 0.0576 s.

[0075] 5) During the opening process, the power frequency voltages U _prA , U _prB , U _prCObtained by differentiating the power supply voltage and the neutral point voltage, i.e.:

[0076]

[0077] 6) Select the reference value of voltage as The reference value of current is Perform per-unit conversion on the calculation results to obtain Figure 2 The result of

[0078] 7) Apply the short-circuit current waveform produced to obtain that the last half-wave durations of the short-circuit breaking currents of phases A, B, and C are 14.39 ms, 11.35 ms, and 10.24 ms respectively, the last half-wave peaks are 60.90 kA, 51.28 kA, and 49.82 kA respectively, and the percentages of the DC component at the current zero-crossing are 29.5%, 19.0%, and 29.5% respectively. Further, the di / dt values at the current zero-crossings of phases A, B, and C are calculated from p to be 0.84 pu, 0.99 pu, and 0.84 pu respectively.

Claims

1. A method for generating short-circuit breaking voltage and current waveforms and obtaining parameters of a circuit breaker, characterized in that, It includes the following steps: 1) Based on the actual operation of the power grid, the power grid is dynamically divided into an internal area and an external area, and the positive-sequence reactance X1, positive-sequence resistance R1, and zero-sequence reactance X0 of the nodes where the circuit breakers in the internal area are located are calculated, and the power supply voltage U of the nodes is taken S = 1.05U N , U N is the nominal voltage, and the power supply voltages of phases A, B, and C are set as: where ω = 2πf, f is the frequency, a is the starting phase angle of the phase A voltage, the three phases of the circuit are balanced, and the voltage of the neutral point is u e (t) = u A (t) + u B (t) + u C (t) = 0. Assuming that a three-phase short-circuit fault occurs at t = 0, according to Equation (1), the short-circuit currents of phases A, B, and C can be obtained as follows: Wherein, I S = U S / (R1 + jX1), is the circuit power factor angle, τ is the DC time constant, and the expected opening time t open of the circuit breaker. The zero-crossing times t R of the first breaking pole phase R, the second breaking pole phase S, and the third breaking pole phase T can be obtained; After phase R is opened, the state equations of the voltages and currents of phases S and T are as follows: In the formula, When R = R1 and solving Equation (3), the currents i S (t) and i T (t) of phases S and T can be obtained. The voltage of the neutral point is X e is the neutral grounding reactance; After phase R is opened, the AC and DC components of the currents of phases S and T are: where z1 = R + jω(L + L e ), z2 = jωL e , i S_ac (t) and i S_dc (t) are the AC component and DC component of the S-phase current respectively, and i T_ac (t) and i T_dc (t) are the AC component and DC component of the T-phase current respectively; 3) The i obtained by solving in step 2 S (t), i T (t), it can be obtained that the zero-crossing time of the second breaking pole phase S is t S . After phase S is broken, the circuit equations of the voltage and current of phase T are as follows: Solving Equation (4), the current \(i\) of phase T can be obtained T (t), and the voltage of the neutral point is 4) The i T (t) obtained by solving in step 3) can be used to obtain the zero-crossing time t T of the third breaking pole T; after the T-phase is broken, the currents of the R, S, and T phases are zero, and the voltage of the neutral point is u e (t) = 0; 5) During the opening process, the power frequency voltages u _prA , u _prB , u _prC between the breaker contacts of phases A, B, and C are obtained by differentiating the supply voltage and the neutral point voltage, i.e.:

2. The method for generating the short-circuit breaking voltage and current waveforms of a circuit breaker and obtaining parameters according to claim 1, wherein: In Steps 1) to 5), a three-phase equivalent circuit is applied to calculate electrical parameters and waveforms, and a neutral grounding reactance X is introduced between the neutral point of the equivalent circuit and the ground, i.e.: e , namely: where k pp is the initial pole coefficient, and the initial pole coefficient 3. The method for generating the short-circuit breaking voltage and current waveforms and obtaining parameters of the circuit breaker according to claim 1, characterized in that: In step 1), obtain the opening time t of the circuit breaker where the node is located in the database o and the shortest arcing time t arcmin , the relay protection operation time is t b , then the minimum breaking time of the circuit breaker is: t openmin = t o + t arcmin + t b (7) The three-phase currents of A, B, and C are shown in Equation (2). When t ≥ t openmin , the phase where the first current zero-crossing occurs is defined as the R phase, and the corresponding breaking time is t R . The second and third breaking phases are defined as the S and T phases. The mapping vectors of the R, S, T phases and the A, B, C phases are n = [n1 n2 n3]. When n1 = 1, n2 = 3, n3 = 2; when n1 = 2, n2 = 1, n3 = 3; when n1 = 3, n2 = 2, n3 = 1. Among them, 1 maps to the A phase, 2 maps to the B phase, and 3 maps to the C phase.

4. The method for generating the short-circuit breaking voltage and current waveforms and obtaining parameters of the circuit breaker according to claim 1, characterized in that: In step 3), after phase S is opened, the AC and DC components of the current of phase T are: where \(i\) T_ac (t) and \(i\) T_dc (t) are the AC component and the DC component of the current in phase T, respectively.

5. The method for generating the short-circuit breaking voltage and current waveform and obtaining parameters of the circuit breaker according to any one of claims 1 to 4, characterized in that: The short-circuit current waveform produced by the application can directly read or automatically obtain the last half-wave parameters of the short-circuit breaking current: duration ΔT, peak value I peak , DC component p at the current zero-crossing. Further, from p, the di / dt at the current zero-crossing and the TRV parameters under the condition of modified asymmetrical short-circuit breaking can be calculated.

6. The method for generating the short-circuit breaking voltage and current waveforms and obtaining parameters of the circuit breaker according to claim 5, characterized in that: The short-circuit breaking calculation process and parameter acquisition method are applicable to both the case of generating short-circuit current by phase selection closing of a high-voltage AC circuit breaker with a three-phase independent operating mechanism and the case of phase selection opening of a three-phase independent operating mechanism.

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