CN115856601A - Method for calculating parameters under asymmetric short-circuit fault condition - Google Patents
Method for calculating parameters under asymmetric short-circuit fault condition Download PDFInfo
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Abstract
The embodiment of the application discloses a method for calculating parameters under an asymmetric short-circuit fault condition. Wherein, the method comprises the following steps: under the condition of a symmetrical short circuit fault, acquiring an oscillogram of an expected current alternating component of the symmetrical short circuit; measuring the current effective values and the phase angle differences of the current voltage at a plurality of moments through an expected current alternating component oscillogram; under the condition of asymmetric short-circuit fault, measuring to obtain voltage phase angles at multiple moments; calculating to obtain an attenuation coefficient according to the effective current value, the phase angle difference of the current and the voltage phase angle; calculating to obtain a direct current time constant according to the attenuation coefficient; the asymmetric short-circuit current expression is determined according to the current effective value, the phase angle difference of the current and the voltage, the voltage phase angle and the direct current time constant, so that the current expression under the asymmetric short-circuit fault condition can be simply and accurately obtained, and the operation amount and the error rate are reduced.
Description
Technical Field
The application relates to the technical field of short-circuit tests of high-voltage alternating-current circuit breakers, in particular to a method for calculating parameters under an asymmetric short-circuit fault condition.
Background
When the high-voltage alternating-current circuit breaker is used for breaking an asymmetric short-circuit fault in a power system, due to the fact that the time constant is large, short-circuit current cannot be attenuated to zero quickly, and therefore direct-current components exist in the short-circuit current, the current waveform is not symmetrical any more, and the phenomenon that large half waves and small half waves alternate is achieved.
At present, the current calculation method under the condition of asymmetric short-circuit fault does not consider the problem of fluctuation of effective values of alternating current components, so that a large error can be generated. Moreover, the calculation formula is complex, and more calculation data are needed, so that the calculation process is complex and the calculation time is long. Therefore, it is necessary to derive and calculate a simple and accurate current expression under asymmetric short-circuit fault conditions.
Disclosure of Invention
In view of this, the embodiment of the present application discloses a method for calculating parameters under an asymmetric short-circuit fault condition, so as to simply and accurately obtain a current expression under the asymmetric short-circuit fault condition.
The technical scheme provided by the embodiment of the application is as follows:
in a first aspect, an embodiment of the present application provides a method for calculating parameters under an asymmetric short-circuit fault condition, where the method includes:
under the condition of a symmetrical short circuit fault, acquiring an oscillogram of an expected current alternating component of the symmetrical short circuit;
measuring the phase angle difference between the current effective value and the current voltage at a plurality of moments through the expected current alternating component oscillogram;
under the condition of asymmetric short-circuit fault, measuring to obtain voltage phase angles at multiple moments;
calculating to obtain an attenuation coefficient according to the effective current value, the phase angle difference of the current and the voltage phase angle;
calculating to obtain a direct current time constant according to the attenuation coefficient;
and determining an asymmetric short-circuit current expression according to the current effective value, the phase angle difference of the current and the voltage, the voltage phase angle and the direct current time constant.
In one possible implementation, the current effective value includes an a-phase current effective value, a B-phase current effective value, and a C-phase current effective value; the phase angle difference of the current and the voltage comprises the phase angle difference of the A-phase current and the voltage, the phase angle difference of the B-phase current and the phase angle difference of the C-phase current and the voltage; the voltage phase angles comprise an A phase voltage phase angle, a B phase voltage phase angle and a C phase voltage phase angle;
calculating the attenuation coefficient of the A phase according to the following formula:
wherein, the ΔT Represents a time difference between a first time and a second time, the first time and the second time are any two times of the plurality of times, the tau represents an A-phase direct current time constant, and the I represents Aacr The effective value of the a-phase current at the first moment is shown,
represents the phase angle of the A-phase voltage at the first time instant>
Representing the phase angle of the phase voltage of phase A at a first moment in time, I Aacb Represents the effective value of the A-phase current at the second time instant, is->
The phase angle of the phase A voltage at the second instant>
A phase angle indicating a phase voltage of the a-phase current at the second timing;
and in the same way, the B-phase attenuation coefficient or the C-phase attenuation coefficient is correspondingly obtained according to the A-phase attenuation coefficient.
In one possible implementation, the expression that the a-phase current starting from the first time is changed with time is as follows:
for a small half wave:
for a large half wave:
wherein, theI above A (t) an expression representing a change in phase A current with time, p representing a percentage of a direct current component,
similarly, an expression of the phase-B current changing along with time or an expression of the phase-C current changing along with time is correspondingly obtained according to the expression of the phase-A current changing along with time;
the expression of the phase-A current changing with time, the expression of the phase-B current changing with time and the expression of the phase-C current changing with time form an asymmetric short-circuit current expression.
In a possible implementation manner, the first time is a current zero point time, the second time is a current zero point adjacent time, and the current zero point adjacent time is subjected to a time difference ΔT And then to the current zero point.
In one possible implementation, the method further includes:
determining a per unit value of the current change rate under the asymmetric short-circuit fault condition relative to the current change rate under the symmetric short-circuit fault condition according to the current effective value, the phase angle difference of the current and the voltage, the voltage phase angle and the direct current time constant;
the expression of the per unit value of the current change rate under the condition of the A-phase asymmetric short-circuit fault relative to the current change rate under the condition of the symmetric short-circuit fault is as follows:
for a small half wave:
for a large half wave:
wherein, the
Indicating that the rate of change of current under the condition of an A-phase asymmetric short circuit fault is relative to a symmetric short circuit faultPer unit value of the rate of change of the current under fault conditions, p representing the percentage of the DC component, and/or->
ω represents an angular frequency;
similarly, a per-unit value expression of the current change rate under the condition of the B-phase asymmetric short-circuit fault relative to the current change rate under the condition of the symmetric short-circuit fault or a per-unit value expression of the current change rate under the condition of the C-phase asymmetric short-circuit fault relative to the current change rate under the condition of the symmetric short-circuit fault is obtained according to the per-unit value expression of the current change rate under the condition of the A-phase asymmetric short-circuit fault relative to the current change rate under the condition of the symmetric short-circuit fault.
In one possible implementation, the method further includes:
acquiring transient recovery voltage under the condition of symmetrical short-circuit fault and current under the condition of symmetrical short-circuit fault at multiple moments;
calculating to obtain a loop response parameter according to the transient recovery voltage under the symmetric short-circuit fault condition and the current under the symmetric short-circuit fault condition;
calculating to obtain currents under the asymmetric short-circuit fault condition at multiple moments by using the asymmetric short-circuit current expression;
calculating to obtain a current coefficient under the asymmetric short-circuit fault condition according to the loop response parameter and the current under the asymmetric short-circuit fault condition;
and calculating transient recovery voltages under the asymmetric short-circuit fault condition at multiple moments according to the loop response parameters and the current coefficients under the asymmetric short-circuit fault condition.
In one possible implementation, the loop response parameter is calculated according to the following formula:
Z 0 ＝loop_c(1)/T/I S0
Z 1 ＝(loop_c(2)/T-I S1 ·Z 0 )/I S0
Z 2 ＝[loop_c(3)/T-(I S1 ·Z 1 +I S2 ·Z 0 )]/I S0
……
Z i ＝[loop_c(i-1)/T-(I S1 ·Z 1 +I S2 ·Z 0 +……I Si ·Z 0 )]/I S0
wherein, I S0 、I S1 、I S2 ……I Si Representing a current coefficient under a symmetric short-circuit fault condition, wherein T represents a linear fitting step length;
loop_c(1)＝U 1
loop_c(2)＝U 2 -2U 1
loop_c(3)＝U 3 -2U 2 +U 1
……
loop_c(i)＝U i -2U i-1 +U i-2
the U is 1 Represents T 1 Transient recovery voltage under symmetrical short-circuit fault conditions of time, U 2 Represents T 2 Transient recovery voltage under symmetrical short-circuit fault conditions of time, U 3 Represents T 3 Transient recovery voltage under symmetrical short-circuit fault conditions of time, U i Represents T i Transient recovery voltage under symmetrical short-circuit fault conditions of time of day, U i-1 Represents T i-1 Transient recovery voltage under symmetrical short-circuit fault conditions of time, U i-2 Represents T i-2 The transient recovery voltage under the condition of the symmetrical short-circuit fault at the moment, wherein i is a positive integer greater than 1;
calculating the current coefficient under the condition of the symmetrical short-circuit fault according to the following formula:
I s0 ＝I 1 /T
I s1 ＝(I 2 -I s0 *T)/T
I s2 ＝[I 3 -(I s0 *2T+I s1 *T)]/T
……
I si ＝[I i+1 -(I s0 *iT+I s1 *(i-1)T+……I si-1 *T)]/T
said I 1 Represents T 1 Current under symmetrical short-circuit fault conditions of time of day, I 2 Represents T 2 Current under symmetrical short-circuit fault conditions of time of day, said I 3 Represents T 3 Current under symmetrical short-circuit fault conditions of time of day, said I i+1 Represents T i+1 Current under symmetrical short fault conditions at the moment.
In one possible implementation, the current coefficient under the asymmetric short-circuit fault condition is calculated according to the following formula:
I s0_asy ＝I 1_asy /T
I s1_asy ＝(I 2_asy -I s0_asy *T)/T
I s2_asy ＝(I 3_asy -I s0_asy *2T-I s1_asy *T)/T
……
I si-1_asy ＝(I i_asy -I s0_asy *(i-1)T-……I si-3_asy *2T-I si-2_asy *T)/T
wherein, the I 1_asy Represents T 1 Current under asymmetric short-circuit fault conditions of time of day, I 2_asy Represents T 2 Current under asymmetric short-circuit fault conditions of time of day, I i_asy Represents T i Current under asymmetric short-circuit fault conditions at a time.
In one possible implementation, the transient recovery voltage under the asymmetric short-circuit fault condition is calculated according to the following formula:
U 1_asy ＝U 1 (I s0_asy ·Z 0 ·T)
U 2_asy ＝U 1_asy +loop_t_asy(2)
……
U i_asy ＝U i-1_asy +loop_t_asy(i)
wherein the content of the first and second substances,
loop_t_asy(2)＝I s0_asy ·Z 0 ·T+(I s0_asy ·Z 1 +I s1_asy ·Z 0 )T
loop_t_asy(3)＝I s0_asy ·Z 0 ·T+(I s0_asy ·Z 1 +I s1_asy ·Z 0 )T+(I s0_asy ·Z 2 +I s1_asy ·Z 1 +I s2_asy ·Z 0 )T
……
loop_t_asy(i)＝I s0_asy ·Z 0 ·T+(I s0_asy ·Z 1 +I s1_asy ·Z 0 )T+(I s0_asy ·Z 2 +I s1_asy ·Z 1 +I s2_asy ·Z 0 )T+……(I s0_asy ·Z i-1 +I s1_asy ·Z i-2 +……I si-1_asy ·Z 0 )T
the U is 1_asy Represents T 1 Transient recovery voltage under asymmetric short-circuit fault conditions of time of day, U 1 Represents T 1 Transient recovery voltage under symmetrical short-circuit fault conditions of time, said I s0_asy Representing the current coefficient under asymmetric short-circuit fault conditions, said Z 0 Represents a loop response parameter; the U is 2_asy Represents T 2 Transient recovery voltage under asymmetric short-circuit fault condition at a moment; the U is i_asy Represents T i Transient recovery voltage under asymmetric short-circuit fault conditions of time of day, U i-1_asy Represents T i-1 Transient recovery voltage under asymmetric short-circuit fault conditions at a time.
Based on the technical scheme, the method has the following beneficial effects:
the embodiment of the application discloses a method for calculating parameters under an asymmetric short-circuit fault condition. Wherein, the method comprises the following steps: under the condition of a symmetrical short circuit fault, acquiring an oscillogram of an expected current alternating component of the symmetrical short circuit; measuring the current effective values and the phase angle differences of the current voltage at a plurality of moments through an expected current alternating component oscillogram; under the condition of asymmetric short-circuit fault, measuring to obtain voltage phase angles at multiple moments; calculating to obtain an attenuation coefficient according to the effective current value, the phase angle difference of the current and the voltage phase angle; calculating according to the attenuation coefficient to obtain a direct current time constant; and determining an asymmetric short-circuit current expression according to the current effective value, the phase angle difference of the current and the voltage, the voltage phase angle and the direct current time constant. Therefore, in the embodiment of the application, the current expression under the asymmetric short-circuit fault condition is determined by obtaining the effective value of the alternating current component under the symmetric short-circuit fault condition, so that parameter reading and calculation errors caused by fluctuation of the effective value of the alternating current component of the short-circuit current can be reduced, and the determined current expression under the asymmetric short-circuit fault condition is more accurate. Moreover, through the effective value of the current, the phase angle difference of the current and the voltage phase angle, a simple current expression under the condition of the asymmetric short-circuit fault can be conveniently and conveniently deduced, the calculation amount and the error rate are reduced, and the universality is high.
Drawings
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, it is obvious that the drawings in the following description are only embodiments of the present application, and for those skilled in the art, other drawings can be obtained according to the disclosed drawings without creative efforts.
Fig. 1 is a flowchart of a method for calculating parameters under an asymmetric short-circuit fault condition according to an embodiment of the present application;
FIG. 2 is a schematic diagram of an asymmetric short circuit current and an expected AC component according to an embodiment of the present disclosure;
fig. 3 is a schematic diagram of loop response parameter calculation according to an embodiment of the disclosure.
Detailed Description
The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments in the present application without making any creative effort belong to the protection scope of the present application.
The terms "comprising," "including," "having," and variations thereof in this specification mean "including, but not limited to," unless expressly specified otherwise. It should be noted that, in the description of the embodiments of the present application, the terms "first", "second", and the like are used for distinguishing the description, and are not to be construed as indicating or implying relative importance or order.
When the high-voltage alternating-current circuit breaker is used for breaking an asymmetric short-circuit fault in a power system, due to the fact that the time constant is large, short-circuit current cannot be attenuated to zero quickly, and therefore direct-current components exist in the short-circuit current, the current waveform is not symmetrical any more, and the phenomenon that large half waves and small half waves alternate is achieved. In the actual asymmetric short-circuit fault test process, a closing phase angle and different closing phases have certain randomness, so that the problems of complex formula, poor flexibility and the like exist by using the current calculation method under the existing asymmetric short-circuit fault condition. The current calculation method under the condition of the asymmetric short-circuit fault comprises the following steps: when the A phase and the B phase are switched on in advance and the C phase is switched on after a delta T time interval, the expressions of the A phase, the B phase and the C phase short-circuit current in the switching-on period are as follows:
when in use
When in use
In this way, when calculating the three-phase current after the Δ T time, it is necessary to calculate the following equation:
From the expressions (1), (2) and (3), it can be found that the alternating current components of the current are set to be unchanged, and more data need to be calculated, and when the generator is used as a power supply in a large-capacity short-circuit test, the effective value of the alternating current components of the short-circuit current fluctuates due to limited energy stored in a unit and the influence of a forced excitation system, so that a larger error is generated by the conventional calculation method. Moreover, the formula and calculation process are more complicated when calculating the late open-phase current parameter.
Therefore, the embodiment of the application discloses a method for calculating parameters under the condition of asymmetric short-circuit fault. Wherein, the method comprises the following steps: under the condition of a symmetrical short circuit fault, acquiring an oscillogram of an expected current alternating component of the symmetrical short circuit; measuring the current effective values and the phase angle differences of the current voltage at a plurality of moments through an expected current alternating component oscillogram; under the condition of asymmetric short-circuit fault, measuring to obtain voltage phase angles at multiple moments; calculating to obtain an attenuation coefficient according to the effective current value, the phase angle difference of the current and the voltage phase angle; calculating to obtain a direct current time constant according to the attenuation coefficient; and determining an asymmetric short-circuit current expression according to the current effective value, the phase angle difference of the current and the voltage, the voltage phase angle and the direct current time constant. Therefore, in the embodiment of the application, the current expression under the asymmetric short-circuit fault condition is determined by obtaining the effective value of the alternating current component under the symmetric short-circuit fault condition, so that parameter reading and calculation errors caused by fluctuation of the effective value of the alternating current component of the short-circuit current can be reduced, and the determined current expression under the asymmetric short-circuit fault condition is more accurate. Moreover, through the effective value of the current, the phase angle difference of the current and the voltage and the phase angle of the voltage, a simple current expression under the condition of asymmetric short-circuit fault can be conveniently and conveniently deduced, the calculation amount and the error rate are reduced, and the universality is high.
Some of the terms are explained below:
large half wave/small half wave: the duration of the current is greater than/less than half a half cycle of the power frequency.
Asymmetric short circuit break test (T100 a)/symmetric short circuit break test (T100 s): when a high-voltage large-capacity short circuit occurs, if the effective value of the alternating current component of the short-circuit current is the rated short-circuit current value of the circuit breaker, the current cannot change suddenly due to the inductive loop, so that the current comprises the alternating current component and the direct current component at the initial moment, the alternating current component and the direct current component have the same magnitude and the opposite directions. In the short-circuit process, the short-circuit current simultaneously comprises an alternating current component and a direct current component, the alternating current component is changed in a sine wave mode, the direct current component is exponentially attenuated according to a time constant (generally more than 45 ms), when the direct current component is greater than 20% of the alternating current component, the current is not symmetrical any more, the current is generally represented as a waveform with large half waves and small half waves alternating, the waveform tends to be symmetrical step by step, and the breaker on-off test performed at the moment is a T100a test mode. When the direct current component is attenuated to be less than 20% of the alternating current component, the current is in a symmetrical state, and the breaker opening test performed at this time is a T100s test mode.
Closing phase angle: the phase of the voltage (relative to ground) at which the current starts.
Percent of direct current component: a percentage of the ratio of the short circuit current dc component to the peak value of the short circuit current ac component.
Expected alternating current component: by adjusting the closing phase angle, three-phase fully-symmetrical short-circuit current (the direct current component is less than 20%) can be obtained, and therefore the effective values of the alternating current components of the three-phase current corresponding to different moments are measured.
Current zero point: the instant the current value is zero.
First-opening phase/late-opening phase: when a three-phase short-circuit current is switched off by a three-pole circuit breaker, the current stops flowing in one phase, namely a first-open phase, and the currents of the other two phases stop flowing in succession, namely a later-open phase.
Referring to fig. 1, a flowchart of a method for calculating parameters under an asymmetric short-circuit fault condition disclosed in an embodiment of the present application includes:
s101, acquiring an oscillogram of an expected current alternating component of a symmetrical short circuit under the condition of a symmetrical short circuit fault;
in a possible implementation manner, in the embodiment of the present application, a three-phase short-circuit current without a direct-current component can be obtained by switching on a phase-selecting switch at a specific phase of a power supply voltage, and an oscillogram of an expected alternating-current component of a symmetrical short-circuit current is obtained. The specific method can be as follows: two phases are firstly combined, wherein the two phases can be an A phase and a B phase, and the two phases are firstly combined when the phase angle of the A phase voltage is a-pi/6, wherein the currents of the first two phases are symmetrical before the short circuit of the third phase, and the third phase is switched on after a quarter of cycle, so that the three-phase currents are symmetrical and have no direct current component. It should be noted that historical data such as the single-component current data or debug data of the symmetric breaking test T100s at the same test voltage and current may also be referred to. The method is not particularly limited and can be selected according to actual conditions.
Fig. 2 is a schematic diagram of an asymmetric short-circuit current and an expected ac component according to an embodiment of the present application. Wherein, the abscissa is time, the ordinate is the per unit value of the instantaneous value of the current relative to the effective value of the current, and the horizontal line is a curve of the effective value of the current changing with time. A-phase current ac component i Aac Namely, the waveform of the A-phase short-circuit current obtained under the condition of the symmetric short-circuit fault. It will be appreciated that the current waveforms for the B, C two-phase symmetric short circuit fault condition are not shown in fig. 2 for simplicity.
S102, measuring to obtain phase angle differences of current effective values and current voltages at multiple moments through the expected current alternating component oscillogram;
the current effective value comprises an A-phase current effective value, a B-phase current effective value and a C-phase current effective value; the phase angle difference of the current voltages includes the phase angle difference of the a-phase current voltage, the phase angle difference of the B-phase current voltage, and the phase angle difference of the C-phase current voltage.
In the embodiment of the application, the effective value I (t) of the current at the moment t of each phase and the phase angle difference of the current voltage at the moment are measured and read through an oscillogram of an expected current alternating component
Wherein, for convenient reading, the time difference of the same phase current and voltage peak near can be approximately selected, as shown in fig. 2, the electric angle converted to the corresponding power frequency is 2 pi ft, the reading precision can be usually as accurate as 5ms according to the actual requirement, namely, the three-phase current effective value is measured and read once every 5ms from the short circuit, such as the starting time of the short circuit10ms, 15ms, 20ms, 25ms, 30ms, 35ms, 40ms, 45ms, 50ms, and the like, which are not particularly limited and can be set according to actual requirements.
S103, measuring to obtain voltage phase angles at multiple moments under the condition of asymmetric short-circuit fault;
the voltage phase angle comprises an A phase voltage phase angle, a B phase voltage phase angle and a C phase voltage phase angle.
In the embodiment of the application, the voltage phases of the three phases of the generator relative to the ground can be measured through a voltage transformer or a voltage divider, the voltage phase of one-phase voltage or the voltage phase between two phases can also be measured, and the voltage phases of other phases can be deduced through the phase sequence. If the phase angle of the voltage of phase A at the time of the next vertical line in FIG. 2 is a, the phase B is
The C phase is->
It is understood that the specific measurement method is not limited, and may be selected according to actual requirements.
S104, calculating to obtain an attenuation coefficient according to the effective current value, the phase angle difference of the current and the voltage and the phase angle of the voltage;
note that, the current zero point time i A (t) =0, so that the dc component of the current at the first time can be found to be:
wherein i rdc Represents the DC component of the A-phase current at the first moment, I Aacr The effective value of the a-phase current at the first moment is shown,
represents the phase angle of the A-phase voltage at the first time instant>
Represents the first timePhase angle of the phase voltage of phase a current at the moment.
Similarly, the dc component of the current at the second time may be calculated as:
wherein i bdc Represents the DC component of the A-phase current at the second moment, I Aacb Representing the effective value of the a-phase current at the second moment,
the phase angle of the phase A voltage at the second instant>
The phase angle of the a-phase current voltage at the second timing is shown.
Therefore, in the embodiment of the application, the a-phase attenuation coefficient can be calculated according to the following formula:
where Δ T represents a time difference between a first time and a second time, the first time and the second time are any two times among the plurality of times, and τ represents an a-phase dc time constant.
And in the same way, the B-phase attenuation coefficient or the C-phase attenuation coefficient is correspondingly obtained according to the A-phase attenuation coefficient.
In a possible implementation manner, the first time in the embodiment of the present application may be a current zero time, which corresponds to a time of a following vertical line in fig. 2; the second time may be a time when the current zero point is adjacent, which corresponds to a time of a previous vertical line in fig. 2; and after the time difference delta T between the adjacent moments of the current zero point reaches the moment of the current zero point.
For convenience of calculation, the current at the current zero point may be used to calculate the current analytic expression in the embodiment of the present application, but the present application is not limited thereto. Can be communicated in factThe difference between the expected current value and the actual current value i at any time dc ＝i-i ac To calculate the DC component of the current and randomly select two moments i dc And obtaining the percentage of the direct current component, and further deducing an analytic expression of the current.
S105, calculating to obtain a direct current time constant according to the attenuation coefficient;
it should be noted that, since the half-wave duration is usually not more than 15ms and the short-circuit time is usually longer than 30ms, the visible time constant is not changed during this time interval.
And S106, determining an asymmetric short-circuit current expression according to the current effective value, the phase angle difference of the current and the voltage, the voltage phase angle and the direct current time constant.
In this embodiment of the application, the expression of the time-varying a-phase current starting with the first time as a time may be:
for a small half wave:
for a large half wave:
wherein, the i A (t) an expression representing a change in phase A current with time, p representing a percentage of a direct current component,
similarly, an expression of the phase-B current changing along with time or an expression of the phase-C current changing along with time is correspondingly obtained according to the expression of the phase-A current changing along with time;
the expression of the time-varying expression of the A-phase current, the time-varying expression of the B-phase current and the time-varying expression of the C-phase current form an asymmetric short-circuit current expression.
In the same manner, the current expression for extending the large half wave can be obtained in the same manner.
It can be seen that in the present embodiment, the current i = i ac +i dc (wherein i ac Is an alternating current component of current i dc Is the direct current component of the current) is taken as a theoretical basis, an asymmetric short-circuit current expression is deduced and calculated by determining the alternating current component of the current under the condition of a symmetric short-circuit fault, synchronous closing, asynchronous closing, first opening and late opening are all applicable, the expected symmetric short-circuit current can be measured by debugging, the calculation error caused by the fluctuation of the alternating current component of the short-circuit current and the change of a direct-current attenuation time constant is reduced, and the requirements of engineering application are better met.
In the embodiment of the application, the expression of the current is determined by determining the alternating current component of the short-circuit current zero point. The alternating current component of the current is irrelevant to the closing phase angle and closing synchronism, is not influenced by the direct current component, and can be conveniently obtained through the voltage phase, so that the details of whether three-phase closing is synchronous or not, the three-phase closing phase angle and the like do not need to be considered, and the method has the advantages of simple expression, strong universality and simplicity in calculation.
In the embodiment of the application, the effective value of the alternating current component can be obtained through the expected current, the direct current component percentage can be obtained through the current zero phase, the direct current component percentage can still be obtained through calculation on the asymmetric current which only flows through 1 half-wave, and the problem that the direct current component percentage cannot be calculated under the conditions that the current zero is too few (such as less than 4) and the envelope distortion is caused by the fluctuation of the alternating current component in the three-peak method is solved.
The embodiment of the application discloses a method for calculating parameters under an asymmetric short-circuit fault condition, wherein an oscillogram of an expected current alternating-current component of a symmetric short circuit is obtained under the symmetric short-circuit fault condition; measuring the current effective values and the phase angle differences of the current voltage at a plurality of moments through an expected current alternating component oscillogram; under the condition of asymmetric short-circuit fault, measuring to obtain voltage phase angles at multiple moments; calculating to obtain an attenuation coefficient according to the effective current value, the phase angle difference of the current and the voltage phase angle; calculating to obtain a direct current time constant according to the attenuation coefficient; and determining an asymmetric short-circuit current expression according to the current effective value, the phase angle difference of the current and the voltage, the voltage phase angle and the direct current time constant. Therefore, in the embodiment of the application, the current expression under the asymmetric short-circuit fault condition is determined by obtaining the effective value of the alternating current component under the symmetric short-circuit fault condition, so that parameter reading and calculation errors caused by fluctuation of the effective value of the alternating current component of the short-circuit current can be reduced, and the determined current expression under the asymmetric short-circuit fault condition is more accurate. Moreover, through the effective value of the current, the phase angle difference of the current and the voltage phase angle, a simple current expression under the condition of the asymmetric short-circuit fault can be conveniently and conveniently deduced, the calculation amount and the error rate are reduced, and the universality is high.
At present, the percentage of the direct current component of the current in the short circuit test process is generally read by adopting a three-peak method, namely GB/T1984-2014 figure 8, namely the effective value of the alternating current component of the current is obtained by drawing an upper envelope and a lower envelope at the peak value of the current. The percentage of the direct current component is calculated by the following formula:
based on the theoretical condition that the effective value of the alternating current component of the current is basically kept unchanged, when the alternating current component of the current fluctuates greatly, particularly within 0-20ms, the attenuation of the effective value of the current is fast, the situation that the envelope lines of the upper limit intersect occurs, and the reading error of the method is large. When the current half wave number is less than 4, the situation that the envelope curve of the upper end or the lower end cannot be drawn occurs, so that the method cannot be used.
In a possible implementation manner, the parameter calculation method under the asymmetric short-circuit fault condition provided in the embodiment of the present application further includes:
determining a per unit value of the current change rate under the asymmetric short-circuit fault condition relative to the current change rate under the symmetric short-circuit fault condition according to the current effective value, the phase angle difference of the current and the voltage, the voltage phase angle and the direct current time constant;
the per unit value expression of the current change rate under the condition of the A-phase asymmetric short-circuit fault relative to the current change rate under the condition of the symmetric short-circuit fault is as follows:
for a small half wave:
for a large half wave:
wherein, the
A unit value representing the current change rate under the A-phase asymmetric short-circuit fault condition relative to the current change rate under the symmetric short-circuit fault condition, wherein p represents the percentage of the DC component, and/or>
ω represents an angular frequency;
similarly, a per-unit value expression of the current change rate under the condition of the B-phase asymmetric short-circuit fault relative to the current change rate under the condition of the symmetric short-circuit fault or a per-unit value expression of the current change rate under the condition of the C-phase asymmetric short-circuit fault relative to the current change rate under the condition of the symmetric short-circuit fault is obtained according to the per-unit value expression of the current change rate under the condition of the A-phase asymmetric short-circuit fault relative to the current change rate under the condition of the symmetric short-circuit fault.
Therefore, in the embodiment of the application, the percentage of the direct current component can be quickly and accurately determined according to the phase angle difference and the voltage phase angle of the current and the voltage, and the expression of the current change rate under the asymmetric short-circuit fault condition relative to the per unit value of the current change rate under the symmetric short-circuit fault condition can be quickly and accurately determined according to the effective value of the current, the phase angle difference of the current and the voltage, the voltage phase angle and the direct current time constant, so that the operation amount and the error rate are reduced, and the universality is high.
At present, a two-stage fitting mode is adopted to obtain Transient Recovery Voltage (TRV) under an asymmetric short-circuit fault condition, so that the calculation precision is not high, and the calculated transient Recovery Voltage is not accurate. To this end, the following method for calculating the transient recovery voltage under the asymmetric short-circuit fault condition is proposed in the embodiment of the present application.
In a possible implementation manner, the parameter calculation method under the asymmetric short-circuit fault condition provided in the embodiment of the present application further includes:
s201, acquiring transient recovery voltages under a symmetrical short-circuit fault condition and currents under the symmetrical short-circuit fault condition at multiple moments;
it should be noted that, referring to fig. 3, the current under the symmetric short-circuit fault condition can be directly calculated according to the following formula:
I 1 ＝sin(ω·T 1 )
I 2 ＝sin(ω·T 2 )
……
I i ＝sin(ω·T i )
wherein, I i For voltage recovery T i Symmetrical current injected at a time, i.e. T i The fault at a time is symmetrical to the current under a short-circuit fault condition. If equal step length is adopted and the step length is set to be T, then T 1 ＝T，T 2 ＝2T……T i And = i × T. It should be noted that the subsequent formulas are derived by calculating with equal step length T.
Voltage recovery T i Expected TRV of time, i.e. T i The transient recovery voltage under symmetric short-circuit fault conditions at the moment can be measured from the expected TRV envelope, with specific parameters referring to fig. 3.
S202, calculating to obtain a loop response parameter according to the transient recovery voltage under the symmetric short-circuit fault condition and the current under the symmetric short-circuit fault condition;
it should be noted that the transient recovery voltage after the breaker opens the current can be regarded as a voltage response of a current with the same magnitude and the opposite direction as the short-circuit current injected into the outlet terminal of the breaker. But any type of waveformSeen at each time step, approximately as a superimposed ramp component. Fig. 3 is a schematic diagram of loop response parameter calculation disclosed in the embodiment of the present application. T in FIG. 3 1 The time of day is the time, T, to reach the first reference voltage u1 of the four-parameter TRV as specified in GB1984-2014 2 The time instant is to reach the second reference voltage uc of the four-parameter TRV as specified in GB 1984-2014.
The function of the transient recovery voltage over time under the symmetric short-circuit fault condition may be as follows:
U(t)＝U s0 +U s1 *ε(t-T)+U s2 *ε(t-2T)+U s3 *ε(t-3T)+......
U s0 、U s1 、U s2 、U s3 the like represents the voltage coefficient under symmetric short-circuit fault conditions, i.e., the coefficient of the unit ramp function; ε represents the unit ramp function, T represents time, and T represents the step size of the linear fit.
U s0 ＝U 1 /T
U s1 ＝(U 2 -U s01 *T)/T
U s2 ＝[U 3 -(U s0 *2T+U s1 *T)]/T
……
U 1 Represents T 1 Transient recovery voltage, U, under symmetrical short-circuit fault conditions at a time 2 Represents T 2 Transient recovery voltage, U, under symmetrical short-circuit fault conditions at a time 3 Represents T 3 Transient recovery voltage under symmetrical short fault conditions at the moment.
The function of the current over time under a symmetric short-circuit fault condition may be as follows:
I(t)＝I s0 +U s1 *ε(t-T)+I s2 *ε(t-2T)+I s3 *ε(t-3T)+......
I s0 、I s1 、I s2 、I s3 etc. represent the current coefficient under symmetric short-circuit fault conditions, i.e. the coefficient of the unit ramp function; ε represents the unit ramp function, T represents time, and T represents the step size of the linear fit.
I s0 ＝I 1 /T
I s1 ＝(I 2 -I s0 *T)/T
I s2 ＝[I 3 -(I s0 *2T+I s1 *T)]/T
I s3 ＝[I 4 -(I s0 *3T+I s1 *2T+I s2 *T)]/T
……
I 1 Represents T 1 Current under symmetrical short-circuit fault conditions of time of day, I 2 Represents T 2 Current under symmetrical short-circuit fault conditions of time, I 3 Represents T 3 Current under symmetrical short-circuit fault conditions of time, I 4 Represents T 4 Current under symmetrical short fault conditions at the moment.
By pulling changes, i.e.
TRV sym (s) represents an expression of the transient recovery voltage after linear fitting after pull-type transformation, and s represents a Laplace operator.
By pulling changes, i.e.
I sym (s) represents an expression of the current after the linear fitting after the pull-type transformation, and s represents a Laplace operator.
Wherein Z(s) represents the response function of a pull-type domain loop, Z 0 And the like represent loop response parameters, i.e., coefficients of a pull-type expression.
The TRV can be obtained by respectively carrying out Laplace conversion on the TRV reference voltage and the short-circuit current which are symmetrically cut off sym (s)、I sym (s) obtaining a response function Z(s).
However in accordance with
After the calculation, the analytic expression in the Z(s) time domain cannot be obtained directly through the pull-type inverse transformation, so that the subsequent calculation cannot be performed. Therefore, the embodiment of the present application provides a time domain-based calculation method, which can obtain the following formula:
U 1 ＝I S0 ·Z 0 ·T
U 2 ＝I S0 ·Z 0 ·2T+(I S0 ·Z 1 +I S1 ·Z 0 )T
U 3 ＝I S0 ·Z 0 ·3T+(I S0 ·Z 1 +I S1 ·Z 0 )2T+(I S0 ·Z 2 +I S1 ·Z 1 +I S2 ·Z 0 )T
……
further variations are possible, resulting in functions loop _ t (i) and loop _ c (i).
loop_t(2)＝U 2 -U 1 ＝I S0 ·Z 0 ·T+(I S0 ·Z 1 +I S1 ·Z 0 )T
loop_t(3)＝U 3 -U 2 ＝I S0 ·Z 0 ·T+(I S0 ·Z 1 +I S1 ·Z 0 )T+(I S0 ·Z 2 +I S1 ·Z 1 +I S2 ·Z 0 )T
loop_c(1)＝U 1 ＝I S0 ·Z 0 ·T
loop_c(2)＝loop_t(2)-loop_t(1)＝(I S0 ·Z 1 +I S1 ·Z 0 )T
loop_c(3)＝loop_t(3)-loop_t(2)＝(I S0 ·Z 2 +I S1 ·Z 1 +I S2 ·Z 0 )T
Thus, the loop response parameter is calculated according to the following formula:
Z 0 ＝loop_c(1)/T/I S0
Z 1 ＝(loop_c(2)/T-I S1 ·Z 0 )/I S0
Z 2 ＝[loop_c(3)/T-(I S1 ·Z 1 +I S2 ·Z 0 )]/I S0
……
Z i ＝[loop_c(i-1)/T-(I S1 ·Z 1 +I S2 ·Z 0 +……I Si ·Z 0 )]/I S0
wherein, I S0 、I S1 、I S2 ……I Si Representing a current coefficient under a symmetric short-circuit fault condition, wherein T represents a linear fitting step length;
loop_c(1)＝U 1
loop_c(2)＝U 2 -2U 1
loop_c(3)＝U 3 -2U 2 +U 1
……
loop_c(i)＝U i -2U i-1 +U i-2
the U is 1 Represents T 1 Transient recovery voltage under symmetrical short-circuit fault conditions of time, U 2 Represents T 2 Transient recovery voltage under symmetrical short-circuit fault conditions of time, U 3 Represents T 3 Transient recovery voltage under symmetrical short-circuit fault conditions of time, U i Represents T i Transient recovery voltage under symmetrical short-circuit fault conditions of time of day, U i-1 Represents T i-1 Transient recovery voltage under symmetrical short-circuit fault conditions of time, U i-2 Represents T i-2 The transient recovery voltage under the condition of the symmetrical short-circuit fault at the moment, wherein i is a positive integer greater than 1;
calculating the current coefficient under the condition of the symmetrical short-circuit fault according to the following formula:
I s0 ＝I 1 /T
I s1 ＝(I 2 -I s0 *T)/T
I s2 ＝[I 3 -(I s0 *2T+I s1 *T)]/T
……
I si ＝[I i+1 -(I s0 *iT+I s1 *(i-1)T+……I si-1 *T)]/T
said I 1 Represents T 1 Effective value of current at time I 2 Represents T 2 Effective value of current at time, said I 3 Represents T 3 Effective value of current at time, said I i+1 Represents T i+1 The effective value of the current at the moment.
S203, calculating to obtain currents under the asymmetric short-circuit fault condition at multiple moments by using the asymmetric short-circuit current expression;
s204, calculating a current coefficient under the asymmetric short-circuit fault condition according to the loop response parameters and the current under the asymmetric short-circuit fault condition;
calculating the current coefficient under the asymmetric short-circuit fault condition according to the following formula:
I s0_asy ＝I 1_asy /T
I s1_asy ＝(I 2_asy -I s0_asy *T)/T
I s2_asy ＝(I 3_asy -I s0_asy *2T-I s1_asy *T)/T
……
I si-1_asy ＝(I i_asy -I s0_asy *(i-1)T-……I si-3_asy *2T-I si-2_asy *T)/T
wherein, the I 1_asy Represents T 1 Current under asymmetric short-circuit fault conditions of time of day, I 2_asy Represents T 2 Current under asymmetric short-circuit fault conditions of time of day, I i_asy Represents T i Current under asymmetric short-circuit fault conditions at a time.
And S205, calculating to obtain transient recovery voltages under the asymmetric short-circuit fault condition at multiple moments according to the loop response parameters and the current coefficients under the asymmetric short-circuit fault condition.
Calculating the transient recovery voltage under the asymmetric short-circuit fault condition according to the following formula:
U 1_asy ＝U 1 (I s0_asy ·Z 0 ·T)
U 2_asy ＝U 1_asy +loop_t_asy(2)
……
U i_asy ＝U i-1_asy +loop_t_asy(i)
wherein the content of the first and second substances,
loop_t_asy(2)＝I s0_asy ·Z 0 ·T+(I s0_asy ·Z 1 +I s1_asy ·Z 0 )T
loop_t_asy(3)＝I s0_asy ·Z 0 ·T+(I s0_asy ·Z 1 +I s1_asy ·Z 0 )T+(I s0_asy ·Z 2 +I s1_asy ·Z 1 +I s2_asy ·Z 0 )T
……
loop_t_asy(i)＝I s0_asy ·Z 0 ·T+(I s0_asy ·Z 1 +I s1_asy ·Z 0 )T+(I s0_asy ·Z 2 +I s1_asy ·Z 1 +I s2_asy ·Z 0 )T+……(I s0_asy ·Z i-1 +I s1_asy ·Z i-2 +……I si-1_asy ·Z 0 )T
the U is 1 asy Represents T 1 Transient recovery voltage under asymmetric short-circuit fault conditions of time, U 1 Represents T 1 Transient recovery voltage under symmetrical short-circuit fault conditions of time of day, I s0 asy Representing the current coefficient under asymmetric short-circuit fault conditions, said Z 0 Represents a loop response parameter; the U is 2 asy Represents T 2 Transient recovery voltage under asymmetric short-circuit fault condition at a moment; the U is i asy Represents T i Transient recovery voltage under asymmetric short-circuit fault conditions of time, U i-1 asy Represents T i-1 Transient recovery voltage under asymmetric short-circuit fault conditions at a time.
Therefore, the transient recovery voltage under the asymmetric short-circuit fault condition is calculated by adopting a time domain analysis method in the embodiment of the application, so that the current is fitted through a plurality of gradient functions, and the calculation efficiency and accuracy are improved.
As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that all or part of the steps in the above embodiment methods can be implemented by software plus a necessary general hardware platform. Based on such understanding, the technical solution of the present application may be essentially or partially implemented in the form of a software product, which may be stored in a storage medium, such as a ROM/RAM, a magnetic disk, an optical disk, etc., and includes several instructions for enabling a computer device (which may be a personal computer, a server, or a network communication device such as a media gateway, etc.) to execute the method according to the embodiments or some parts of the embodiments of the present application.
It should be noted that, in the present specification, the embodiments are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments may be referred to each other.
Finally, it should also be noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrases "comprising a," "8230," "8230," or "comprising" does not exclude the presence of additional like elements in a process, method, article, or apparatus that comprises the element.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (9)
1. A method for calculating parameters under asymmetric short circuit fault conditions, the method comprising:
under the condition of a symmetrical short circuit fault, acquiring an oscillogram of an expected current alternating component of the symmetrical short circuit;
measuring the phase angle difference between the current effective value and the current voltage at a plurality of moments through the expected current alternating component oscillogram;
under the condition of asymmetric short-circuit fault, measuring to obtain voltage phase angles at multiple moments;
calculating to obtain an attenuation coefficient according to the effective current value, the phase angle difference of the current and the voltage phase angle;
calculating to obtain a direct current time constant according to the attenuation coefficient;
and determining an asymmetric short-circuit current expression according to the current effective value, the phase angle difference of the current and the voltage, the voltage phase angle and the direct current time constant.
2. The method of claim 1, wherein the current effective values comprise an A-phase current effective value, a B-phase current effective value, and a C-phase current effective value; the phase angle difference of the current and the voltage comprises the phase angle difference of the A-phase current and the voltage, the phase angle difference of the B-phase current and the phase angle difference of the C-phase current and the voltage; the voltage phase angles comprise an A phase voltage phase angle, a B phase voltage phase angle and a C phase voltage phase angle;
calculating the attenuation coefficient of the A phase according to the following formula:
wherein Δ T represents a time difference between a first time and a second time, the first time and the second time are any two times of the plurality of times, τ represents an a-phase direct current time constant, and I represents Aacr Representing the effective value of the A-phase current at a first moment in time, said
Represents the phase angle of the A-phase voltage at a first point in time, the ^ er>
Representing the phase angle of the phase voltage of phase A at a first instant, I Aacb Represents the effective value of the A-phase current at the second point in time, the->
Phase angle of A-phase voltage at second time, said
A phase angle indicating a phase voltage of the a-phase current at the second timing;
and in the same way, the B-phase attenuation coefficient or the C-phase attenuation coefficient is correspondingly obtained according to the A-phase attenuation coefficient.
3. The method of claim 2, wherein the phase a current over time starting at the first time instant is represented by:
for a small half wave:
for a large half wave:
wherein, the i A (t) an expression representing a change in phase A current with time, p representing a percentage of a direct current component,
similarly, an expression of the phase-B current changing along with time or an expression of the phase-C current changing along with time is correspondingly obtained according to the expression of the phase-A current changing along with time;
the expression of the phase-A current changing with time, the expression of the phase-B current changing with time and the expression of the phase-C current changing with time form an asymmetric short-circuit current expression.
4. The method of claim 2, wherein the first time is a current zero time and the second time is a current zero adjacent time, and wherein the current zero adjacent times are subject to a time difference ΔT And then to the current zero point.
5. The method of claim 2, further comprising:
determining a per unit value of the current change rate under the asymmetric short-circuit fault condition relative to the current change rate under the symmetric short-circuit fault condition according to the current effective value, the phase angle difference of the current and the voltage, the voltage phase angle and the direct current time constant;
the per unit value expression of the current change rate under the condition of the A-phase asymmetric short-circuit fault relative to the current change rate under the condition of the symmetric short-circuit fault is as follows:
for a small half wave:
for a large half wave:
wherein, the
A unit value representing the current change rate under the A-phase asymmetric short-circuit fault condition relative to the current change rate under the symmetric short-circuit fault condition, wherein p represents the percentage of the DC component, and/or>
ω represents an angular frequency;
similarly, a per-unit value expression of the current change rate under the condition of the B-phase asymmetric short-circuit fault relative to the current change rate under the condition of the symmetric short-circuit fault or a per-unit value expression of the current change rate under the condition of the C-phase asymmetric short-circuit fault relative to the current change rate under the condition of the symmetric short-circuit fault is obtained according to the per-unit value expression of the current change rate under the condition of the A-phase asymmetric short-circuit fault relative to the current change rate under the condition of the symmetric short-circuit fault.
6. The method of claim 1, further comprising:
acquiring transient recovery voltage under the condition of symmetrical short-circuit fault and current under the condition of symmetrical short-circuit fault at multiple moments;
calculating to obtain a loop response parameter according to the transient recovery voltage under the symmetric short-circuit fault condition and the current under the symmetric short-circuit fault condition;
calculating to obtain currents under the asymmetric short-circuit fault condition at multiple moments by using the asymmetric short-circuit current expression;
calculating to obtain a current coefficient under the asymmetric short-circuit fault condition according to the loop response parameter and the current under the asymmetric short-circuit fault condition;
and calculating transient recovery voltages under the asymmetric short-circuit fault condition at multiple moments according to the loop response parameters and the current coefficients under the asymmetric short-circuit fault condition.
7. The method of claim 1, wherein the loop response parameter is calculated according to the formula:
Z 0 ＝loop_c(1)/T/I S0
Z 1 ＝(loop_c(2)/T-I S1 ·Z 0 )/I S0
Z 2 ＝[loop_c(3)/T-(I S1 ·Z 1 +I S2 ·Z 0 )]/I S0
……
Z i ＝[loop_c(i-1)/T-(I S1 ·Z 1 +I S2 ·Z 0 +……I Si ·Z 0 )]/I S0
wherein, I S0 、I S1 、I S2 ……I Si Representing a current coefficient under a symmetric short-circuit fault condition, wherein T represents a linear fitting step length;
loop_c(1)＝U 1
loop_c(2)＝U 2 -2U 1
loop_c(3)＝U 3 -2U 2 +U 1
……
loop_c(i)＝U i -2U i-1 +U i-2
the U is 1 Represents T 1 Transient recovery voltage under symmetrical short-circuit fault conditions of time, U 2 Represents T 2 Transient recovery voltage under symmetrical short-circuit fault conditions of time, U 3 Represents T 3 Transient recovery voltage under symmetrical short-circuit fault conditions of time, U i Represents T i Transient recovery voltage under symmetrical short-circuit fault conditions of time, U i-1 Represents T i-1 Transient recovery voltage under symmetrical short-circuit fault conditions of time, U i-2 Represents T i-2 The transient recovery voltage under the condition of the symmetrical short-circuit fault at the moment, wherein i is a positive integer greater than 1;
calculating the current coefficient under the condition of the symmetrical short-circuit fault according to the following formula:
I s0 ＝I 1 /T
I s1 ＝(I 2 -I s0 *T)/T
I s2 ＝[I 3 -(I s0 *2T+I s1 *T)]/T
……
I si ＝[I i+1 -(I s0 *iT+I s1 *(i-1)T+……I si-1 *T)]/T
said I 1 Represents T 1 Current under symmetrical short-circuit fault conditions of time, I 2 Represents T 2 Current under symmetrical short-circuit fault conditions of time of day, said I 3 Represents T 3 Current under symmetrical short-circuit fault conditions of time of day, said I i+1 Represents T i+1 Current under symmetrical short fault conditions of time.
8. The method of claim 7, wherein the current coefficient under the asymmetric short-circuit fault condition is calculated according to the following equation:
I s0_asy ＝I 1_asy /T
I s1_asy ＝(I 2_asy -I s0_asy *T)/T
I s2_asy ＝(I 3_asy -I s0_asy *2T-I s1_asy *T)/T
……
I si-1_asy ＝(I i_asy -I s0_asy *(i-1)T-……I si-3_asy *2T-I si-2_asy *T)/T
wherein, the I 1_asy Represents T 1 Current under asymmetric short-circuit fault conditions of time of day, I 2_asy Represents T 2 Current under asymmetric short-circuit fault conditions of time of day, I i_asy Represents T i Current under asymmetric short-circuit fault conditions at a time.
9. The method of claim 8, wherein the transient recovery voltage under the asymmetric short-circuit fault condition is calculated according to the following equation:
U 1_asy ＝U 1 (I s0_asy ·Z 0 ·T)
U 2_asy ＝U 1_asy +loop_t_asy(2)
……
U i_asy ＝U i-1_asy +loop_t_asy(i)
wherein the content of the first and second substances,
loop_t_asy(2)＝I s0_asy ·Z 0 ·T+(I s0_asy ·Z 1 +I s1_asy ·Z 0 )T
loop_t_asy(3)＝I s0_asy ·Z 0 ·T+(I s0_asy ·Z 1 +I s1_asy ·Z 0 )T+(I s0_asy ·Z 2 +I s1_asy ·Z 1 +I s2_asy ·Z 0 )T
……
loop_t_asy(i)＝I s0_asy ·Z 0 ·T+(I s0_asy ·Z 1 +I s1_asy ·Z 0 )T+(I s0_asy ·Z 2 +I s1_asy ·Z 1 +I s2_asy ·Z 0 )T+……(I s0_asy ·Z i-1 +I s1_asy ·Z i-2 +……I si-1_asy ·Z 0 )T
the U is 1_asy Represents T 1 Transient recovery voltage under asymmetric short-circuit fault conditions of time, U 1 Represents T 1 Transient recovery voltage under symmetrical short-circuit fault conditions of time, said I s0_asy Representing the current coefficient under asymmetric short-circuit fault conditions, said Z 0 Represents a loop response parameter; the U is 2_asy Represents T 2 Transient recovery voltage under asymmetric short-circuit fault condition at a moment; the U is i_asy Represents T i Transient recovery voltage under asymmetric short-circuit fault conditions of time, U i-1_asy Represents T i-1 Transient recovery voltage under asymmetric short-circuit fault conditions at a time.
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