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CN113985210A - Voltage sag domain calculation method considering voltage sag amplitude and duration - Google Patents

Voltage sag domain calculation method considering voltage sag amplitude and duration Download PDF

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Publication number
CN113985210A
CN113985210A CN202111282851.6A CN202111282851A CN113985210A CN 113985210 A CN113985210 A CN 113985210A CN 202111282851 A CN202111282851 A CN 202111282851A CN 113985210 A CN113985210 A CN 113985210A
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sag
voltage
line
bus
fault
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CN113985210B (en
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刘海涛
张匡翼
马丙泰
张埕瑜
黄铖
陆恒
耿宗璞
袁华骏
王宇昊
张效诚
仲聪
朱康凯
马佳伊
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Nanjing Institute of Technology
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    • G01—MEASURING; TESTING
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Abstract

The invention relates to a voltage sag domain calculation method considering voltage sag amplitude and duration, which comprises the following steps: determining a sensitive load voltage sag threshold and a duration threshold according to a sensitive load voltage tolerance curve; calculating the residual voltage amplitude of a bus connected to a sensitive load when the head end and the tail end of a certain line in the system have faults, and comparing the residual voltage amplitude with a voltage sag threshold value to obtain a voltage judgment quantity; acquiring line fault clearing time according to the system protection information, and comparing the line fault clearing time with a duration threshold value to obtain duration judgment quantity; and preliminarily judging whether the line is positioned in a sag domain according to the voltage judgment quantity and the duration judgment quantity: solving the critical point by adopting a quadratic interpolation method and a secant iteration method; and traversing all lines in the system to obtain a final sag domain of the sensitive load. Compared with the prior art, the voltage sag amplitude and the duration are considered at the same time, so that the voltage sag domain range of the sensitive load can be determined more accurately.

Description

Voltage sag domain calculation method considering voltage sag amplitude and duration
Technical Field
The invention belongs to the field of power distribution network voltage sag domain evaluation, and particularly relates to a voltage sag domain calculation method considering voltage sag amplitude and duration.
Background
With the development of modern industry, the sensitive load connected into the power system is more and more, and the economic loss brought to users by the voltage sag as a main power quality problem is more and more. In the system, short-circuit faults, large-scale motor starting, lightning stroke and the like all cause bus voltage sag, wherein the short-circuit faults are main reasons for causing the voltage sag. Therefore, the method has very important significance for accurately evaluating the voltage sag problem of the sensitive load access point during the power grid fault.
The voltage sag domain refers to the fact that faults in the region can cause the concerned sensitive load points to be incapable of working normally, and voltage sag domain analysis is the premise and the basis for comprehensively evaluating the voltage sag. At present, the conventional sag domain identification method mainly comprises a fault point method, a critical distance method, an analysis method and the like. The existing methods all have certain defects, for example, the critical distance method is simple and applicable to a radiation type network, but is not applicable to a looped network; the fault point method has the disadvantages that more fault points must be set if the accuracy is higher, the calculation amount is large, and the method is low in efficiency in a large-scale power system. In addition, the current sag domain analysis method only considers the influence of the voltage sag amplitude value and does not combine with an actual sensitive load voltage tolerance curve.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a voltage sag domain calculation method considering the amplitude and the duration of voltage sag, which adopts the following technical scheme:
a voltage sag domain calculation method considering the amplitude and duration of a voltage sag comprises the following steps:
step 1: determining a sensitive load voltage sag threshold U according to a sensitive load voltage tolerance curvethAnd a duration threshold Tth；
Step 2: when the head end and the tail end of a certain line in the computing system have faults, the residual voltage amplitude of a bus S connected into a sensitive load
Figure BDA0003331770980000011
And
Figure BDA0003331770980000012
and then the voltage is compared with a voltage sag threshold UthComparing to obtain the voltage determination amount sagU，
Figure BDA0003331770980000013
And step 3: obtaining line fault clearing time T according to system protection information, and comparing the line fault clearing time T with a duration time threshold TthComparing to obtain the duration determination amount sagT，
Figure BDA0003331770980000021
And 4, step 4: determination of amount of sag from voltageUSum duration determination amount sagTPreliminarily judging whether the line is positioned in a sag domain:
if sagU0 or sagTIf the line is 0, the line is completely positioned outside the sag domain;
if sag U1 and sag T1, the line part is located in the sag domain and only one critical point exists;
if sag U2 and sagTCalculating the maximum value of the residual voltage of the bus S by golden section searching method when the value is 1
Figure BDA0003331770980000022
If it is
Figure BDA0003331770980000023
The line is partially located in the sag domain and two critical points exist, otherwise the line is completely located in the sag domain;
and 5: solving the critical point by adopting a quadratic interpolation method and a secant iteration method;
step 6: and traversing all lines in the system, and obtaining a final sag domain of the sensitive load according to the steps.
Further, in step 2, the residual voltage amplitude
Figure BDA0003331770980000024
And
Figure BDA0003331770980000025
the residual voltage of the A phase of the bus S when the head end and the tail end of a certain line have faults,
Figure BDA0003331770980000026
wherein,
Figure BDA0003331770980000027
and
Figure BDA0003331770980000028
respectively occurring at the head end and the tail end of the linePhase a voltage, Δ U, of the pre-barrier bus SATo be a variation value of the a-phase voltage at the time of the malfunction,
if the fault is a single-phase ground short circuit fault,
Figure BDA0003331770980000029
if the fault is a two-phase short-circuit fault,
Figure BDA00033317709800000210
if the fault is a two-phase short-circuit fault,
Figure BDA00033317709800000211
if the fault is a three-phase short-circuit fault,
Figure BDA00033317709800000212
wherein,
Figure BDA00033317709800000213
the voltage amplitude before the failure occurs for the failure point F, and
Figure BDA00033317709800000214
the voltage amplitudes of the head bus m and the tail bus n of the line before the fault occurs respectively, wherein lambda is the fault position information quantity of the line and lambda is equal to lmF/lmn，lmFIs the distance of the fault point F from the head end of the line, lmnIs the line length;
Figure BDA0003331770980000031
is the impedance of each sequence between the fault point F and the bus S, and
Figure BDA0003331770980000032
Figure BDA0003331770980000033
for each bus m and S at the head end of the lineThe impedance of the two phases is in turn,
Figure BDA0003331770980000034
the mutual impedance of each sequence between the bus n and the bus S at the tail end of the line;
Figure BDA0003331770980000035
is the respective impedance of the fault point F, and
Figure BDA0003331770980000036
Figure BDA0003331770980000037
for each sequence impedance of the line head bus m,
Figure BDA0003331770980000038
for each respective impedance of the line end busbar n,
Figure BDA0003331770980000039
for each sequence of mutual impedance between the head bus m and the tail bus n of the circuit,
Figure BDA00033317709800000310
the respective impedances of the line.
Further, in step 4, the maximum value of the residual voltage of the bus S is calculated by adopting a golden section searching method
Figure BDA00033317709800000311
The method comprises the following specific steps:
s4.1, defining two initial value points lambda1And λ2Let us order
Figure BDA00033317709800000312
λa＝0，λb＝1；
S4.2, calculating | f (lambda)1) I and f (lambda)2)|，
If | f (λ)1)|≥|f(λ2) I, make lambdab＝λ2，λ2＝λ1，
Figure BDA00033317709800000313
If | f (λ)1)|＜|f(λ2) I, make lambdaa＝λ1，λ1＝λ2，
Figure BDA00033317709800000314
S4.3, if lambdab-λaIf | < ε then λmax＝(λb+λa) /2, otherwise return to S4.2 until lambdab-λaIf | < epsilon, epsilon is iteration precision;
s4.4, setting the maximum value of the residual voltage of the bus S
Figure BDA00033317709800000315
Expressed as:
Figure BDA00033317709800000316
wherein,
Figure BDA00033317709800000317
the a-phase voltage of the bus S before the fault,
Figure BDA00033317709800000318
Figure BDA00033317709800000319
further, the step 5 comprises the following steps:
s5.1, selecting lambda1＝0、λ2＝0.5、λ2Taking 1 three points as interpolation points to carry out secondary interpolation to obtain an interpolation equation
Uth＝a0+a1λ+a2λ2，
Wherein, a0＝|f(0)|，a1＝-3|f(0)|+4|f(0.5)|-|f(1)|，a2＝2|f(0)|-4|f(0.5)|+2|f(1)|；
S5.2, solving the roots of the interpolation equation on [0,1], wherein the number of the roots is the number of critical points;
s5.3 for root λrootTaking the obtained value as an approximate value of the critical point and obtaining an accurate value of the critical point by a secant iteration method:
determining the iteration interval of the secant method as [ lambda ]root,λroot+0.01]And [ lambda ]root-0.01,λroot]And sequentially performing the following iterations in an iteration interval respectively:
Figure BDA0003331770980000041
λfrom＝λend，λend＝λnew，
until the iteration end condition is satisfied | | | f (lambda)new)|-UthIf | < ε, then λ isnewIs root of λrootPrecise value of the corresponding critical point, λfromAnd λendThe left end point value and the right end point value of the iteration interval are respectively, and if the iteration condition cannot be met in a certain iteration interval, the other iteration interval is converted.
Further, the iteration precision ∈ is 0.001.
Compared with the prior art, the voltage sag amplitude and the duration are considered at the same time, so that the voltage sag domain range of the sensitive load can be determined more accurately.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of a line fault in the present invention;
FIG. 3 is a flow chart of the golden section method of the present invention.
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings.
As shown in fig. 1, the present invention mainly comprises the following steps:
step 1: determining a sensitive load voltage sag threshold U according to a sensitive load voltage tolerance curvethAnd a duration threshold Tth。
Step 2: when the head end and the tail end of a certain line in the computing system have faults, the residual voltage amplitude of a bus S connected into a sensitive load
Figure BDA0003331770980000042
And
Figure BDA0003331770980000043
and then the voltage is compared with a voltage sag threshold UthComparing to obtain the voltage determination amount sagU，
Figure BDA0003331770980000044
Amplitude of residual voltage
Figure BDA0003331770980000045
And
Figure BDA0003331770980000046
for the A-phase residual voltage of the bus S when the head end and the tail end of a certain line fail, an
Figure BDA0003331770980000051
Wherein,
Figure BDA0003331770980000052
and
Figure BDA0003331770980000053
the A-phase voltage, Delta U, of the bus S before the fault occurs at the head end and the tail end of the lineATo be a variation value of the a-phase voltage at the time of the malfunction,
if the fault is a single-phase ground short circuit fault,
Figure BDA0003331770980000054
if the fault is a two-phase short-circuit fault,
Figure BDA0003331770980000055
if the fault is a two-phase short-circuit fault,
Figure BDA0003331770980000056
if the fault is a three-phase short-circuit fault,
Figure BDA0003331770980000057
wherein,
Figure BDA0003331770980000058
the voltage amplitude before the failure occurs for the failure point F, and
Figure BDA0003331770980000059
the voltage amplitudes of the head bus m and the tail bus n of the line before the fault occurs respectively, wherein lambda is the fault position information quantity of the line and lambda is equal to lmF/lmn，lmFIs the distance of the fault point F from the head end of the line, lmnFor this line length, the fault line is schematically shown in fig. 2;
Figure BDA00033317709800000510
is the impedance of each sequence between the fault point F and the bus S, and
Figure BDA00033317709800000511
Figure BDA00033317709800000512
for each sequence of mutual impedance between the bus m and the bus S at the head end of the line,
Figure BDA00033317709800000513
between the end bus n and the bus S of the lineMutual impedance of each sequence;
Figure BDA00033317709800000514
is the respective impedance of the fault point F, and
Figure BDA00033317709800000515
Figure BDA00033317709800000516
for each sequence impedance of the line head bus m,
Figure BDA00033317709800000517
for each respective impedance of the line end busbar n,
Figure BDA00033317709800000518
for each sequence of mutual impedance between the head bus m and the tail bus n of the circuit,
Figure BDA00033317709800000519
the respective impedances of the line.
And step 3: obtaining line fault clearing time T according to system protection information, and comparing the line fault clearing time T with a duration time threshold TthComparing to obtain the duration determination amount sagT，
Figure BDA00033317709800000520
And 4, step 4: determination of amount of sag from voltageUSum duration determination amount sagTPreliminarily judging whether the line is positioned in a sag domain:
if sag U0 or sagTIf the line is 0, the line is completely positioned outside the sag domain;
if sag U1 and sag T1, the line part is located in the sag domain and only one critical point exists;
if sag U2 and sagTWhen 1, adoptCalculating the maximum value of the residual voltage of the bus S by golden section search method
Figure BDA0003331770980000061
If it is
Figure BDA0003331770980000062
Then the line is partially within the sag domain and there are two critical points, otherwise the line is fully within the sag domain.
As shown in FIG. 3, the maximum value of the residual voltage of the bus S is calculated by the golden section search method
Figure BDA0003331770980000063
The method comprises the following specific steps:
s4.1, defining two initial value points lambda1And λ2Let us order
Figure BDA0003331770980000064
λa＝0，λb＝1；
S4.2, calculating | f (lambda)1) I and I f (lambda)2)|，
If | f (λ)1)|≥|f(λ2) I, make lambdab＝λ2，λ2＝λ1，
Figure BDA0003331770980000065
If | f (λ)1)|＜|f(λ2) I, make lambdaa＝λ1，λ1＝λ2，
Figure BDA0003331770980000066
S4.3, if lambdab-λaIf | < ε then λmax＝(λb+λa) /2, otherwise return to S4.2 until lambdab-λaIf | < epsilon, epsilon is iteration precision;
s4.4, setting the maximum value of the residual voltage of the bus S
Figure BDA00033317709800000611
Expressed as:
Figure BDA0003331770980000067
wherein,
Figure BDA0003331770980000068
the a-phase voltage of the bus S before the fault,
Figure BDA0003331770980000069
Figure BDA00033317709800000610
and 5: solving the critical point by adopting a quadratic interpolation method and a secant iteration method, which specifically comprises the following steps:
s5.1, selecting lambda1＝0、λ2＝0.5、λ2Taking 1 three points as interpolation points to carry out secondary interpolation to obtain an interpolation equation
Uth＝a0+a1λ+a2λ2，
Wherein, a0＝|f(0)|，a1＝-3|f(0)|+4|f(0.5)|-|f(1)|，a2＝2|f(0)|-4|f(0.5)|+2|f(1)|；
S5.2, solving the roots of the interpolation equation on [0,1], wherein the number of the roots is the number of critical points;
s5.3 for root λrootTaking the obtained value as an approximate value of the critical point and obtaining an accurate value of the critical point by a secant iteration method:
determining the iteration interval of the secant method as [ lambda ]root,λroot+0.01]And [ lambda ]root-0.01,λroot]And sequentially performing the following iterations in an iteration interval respectively:
Figure BDA0003331770980000071
until the stack is satisfiedGeneration end condition | | f (λ)new)|-UthIf | < epsilon, epsilon is generally 0.001, then λ is obtainednewIs root of λrootPrecise value of the corresponding critical point, λfromAnd λendThe left end point value and the right end point value of the iteration interval are respectively, and if the iteration condition cannot be met in a certain iteration interval, the other iteration interval is converted.
Step 6: and traversing all lines in the system, and obtaining a final sag domain of the sensitive load according to the steps.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.

Claims (5)

1. A voltage sag domain calculation method considering the amplitude and duration of a voltage sag, characterized by comprising the following steps:
step 1: determining a sensitive load voltage sag threshold U according to a sensitive load voltage tolerance curvethAnd a duration threshold Tth；
Step 2: when the head end and the tail end of a certain line in the computing system have faults, the residual voltage amplitude of a bus S connected into a sensitive load
Figure FDA0003331770970000011
And
Figure FDA0003331770970000012
and then the voltage is compared with a voltage sag threshold UthComparing to obtain the voltage determination amount sagU，
Figure FDA0003331770970000013
And step 3: according to the system protection letterAcquiring the line fault clearing time T and comparing the time T with the duration threshold TthComparing to obtain the duration determination amount sagT，
Figure FDA0003331770970000014
And 4, step 4: determination of amount of sag from voltageUSum duration determination amount sagTPreliminarily judging whether the line is positioned in a sag domain:
if sagU0 or sagTIf the line is 0, the line is completely positioned outside the sag domain;
if sagU1 and sagT1, the line part is located in the sag domain and only one critical point exists;
if sagU2 and sagTCalculating the maximum value of the residual voltage of the bus S by golden section searching method when the value is 1
Figure FDA0003331770970000015
If it is
Figure FDA0003331770970000016
The line is partially located in the sag domain and two critical points exist, otherwise the line is completely located in the sag domain;
and 5: solving the critical point by adopting a quadratic interpolation method and a secant iteration method;
step 6: and traversing all lines in the system, and obtaining a final sag domain of the sensitive load according to the steps.
2. The method as claimed in claim 1, wherein the residual voltage amplitude is calculated in step 2 by considering the voltage sag amplitude and the duration
Figure FDA0003331770970000017
And
Figure FDA0003331770970000018
the residual voltage of the A phase of the bus S when the head end and the tail end of a certain line have faults,
Figure FDA0003331770970000019
wherein,
Figure FDA00033317709700000110
and
Figure FDA00033317709700000111
the A-phase voltage, Delta U, of the bus S before the fault occurs at the head end and the tail end of the lineATo be a variation value of the a-phase voltage at the time of the malfunction,
if the fault is a single-phase ground short circuit fault,
Figure FDA0003331770970000021
if the fault is a two-phase short-circuit fault,
Figure FDA0003331770970000022
if the fault is a two-phase short-circuit fault,
Figure FDA0003331770970000023
if the fault is a three-phase short-circuit fault,
Figure FDA0003331770970000024
wherein,
Figure FDA0003331770970000025
the voltage amplitude before the failure occurs for the failure point F, and
Figure FDA0003331770970000026
Figure FDA0003331770970000027
the voltage amplitudes of the head bus m and the tail bus n of the line before the fault occurs respectively, wherein lambda is the fault position information quantity of the line and lambda is equal to lmF/lmn，lmFIs the distance of the fault point F from the head end of the line, lmnIs the line length;
Figure FDA0003331770970000028
is the impedance of each sequence between the fault point F and the bus S, and
Figure FDA0003331770970000029
Figure FDA00033317709700000210
for each sequence of mutual impedance between the bus m and the bus S at the head end of the line,
Figure FDA00033317709700000211
the mutual impedance of each sequence between the bus n and the bus S at the tail end of the line;
Figure FDA00033317709700000212
is the respective impedance of the fault point F, and
Figure FDA00033317709700000213
Figure FDA00033317709700000214
for each sequence impedance of the line head bus m,
Figure FDA00033317709700000215
for each respective impedance of the line end busbar n,
Figure FDA00033317709700000216
for each sequence of mutual impedance between the head bus m and the tail bus n of the circuit,
Figure FDA00033317709700000217
the respective impedances of the line.
3. The method of claim 2, wherein in step 4, the maximum value of the residual voltage of the bus S is calculated by a golden section search method
Figure FDA00033317709700000218
The method comprises the following specific steps:
s4.1, defining two initial value points lambda1And λ2Let us order
Figure FDA00033317709700000219
S4.2, calculating | f (lambda)1) I and I f (lambda)2)|，
If | f (λ)1)|≥|f(λ2) I, make lambdab＝λ2，λ2＝λ1，
Figure FDA00033317709700000220
If | f (λ)1)|＜|f(λ2) I, make lambdaa＝λ1，λ1＝λ2，
Figure FDA0003331770970000031
S4.3, if lambdab-λaIf | < ε then λmax＝(λb+λa) /2, otherwise return to S4.2 until lambdab-λaIf | < epsilon, epsilon is iteration precision;
s4.4, setting the maximum value of the residual voltage of the bus S
Figure FDA0003331770970000032
Expressed as:
Figure FDA0003331770970000033
wherein,
Figure FDA0003331770970000034
the a-phase voltage of the bus S before the fault,
Figure FDA0003331770970000035
Figure FDA0003331770970000036
4. the voltage sag domain calculation method considering voltage sag amplitude and duration as claimed in claim 3, wherein the step 5 comprises the steps of:
s5.1, selecting lambda1＝0、λ2＝0.5、λ2Taking 1 three points as interpolation points to carry out secondary interpolation to obtain an interpolation equation
Uth＝a0+a1λ+a2λ2，
Wherein, a0＝|f(0)|，a1＝-3|f(0)|+4|f(0.5)|-|f(1)|，a2＝2|f(0)|-4|f(0.5)|+2|f(1)|；
S5.2, solving the roots of the interpolation equation on [0,1], wherein the number of the roots is the number of critical points;
s5.3 for root λrootTaking the obtained value as an approximate value of the critical point and obtaining an accurate value of the critical point by a secant iteration method:
determining the iteration interval of the secant method as [ lambda ]root,λroot+0.01]And [ lambda ]root-0.01,λroot]And sequentially performing the following iterations in an iteration interval respectively:
Figure FDA0003331770970000037
λfrom＝λend，λend＝λnew，
until the iteration end condition is satisfied | | | f (lambda)new)|-UthIf | < ε, then λ isnewIs root of λrootPrecise value of the corresponding critical point, λfromAnd λendThe left end point value and the right end point value of the iteration interval are respectively, and if the iteration condition cannot be met in a certain iteration interval, the other iteration interval is converted.
5. The voltage sag domain calculation method considering the magnitude and duration of a voltage sag, as set forth in claim 3, wherein the iteration precision ε is 0.001.
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