CN107153146A - Reactor inductance computational methods under a kind of shorted-turn fault state - Google Patents

Reactor inductance computational methods under a kind of shorted-turn fault state Download PDF

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CN107153146A
CN107153146A CN201710327537.2A CN201710327537A CN107153146A CN 107153146 A CN107153146 A CN 107153146A CN 201710327537 A CN201710327537 A CN 201710327537A CN 107153146 A CN107153146 A CN 107153146A
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short
circle
circuit
reactor
inductance
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陈炯
高源�
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Shanghai University of Electric Power
University of Shanghai for Science and Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/50—Testing of electric apparatus, lines, cables or components for short-circuits, continuity, leakage current or incorrect line connections
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R27/00—Arrangements for measuring resistance, reactance, impedance, or electric characteristics derived therefrom
    • G01R27/02—Measuring real or complex resistance, reactance, impedance, or other two-pole characteristics derived therefrom, e.g. time constant
    • G01R27/26—Measuring inductance or capacitance; Measuring quality factor, e.g. by using the resonance method; Measuring loss factor; Measuring dielectric constants ; Measuring impedance or related variables
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations

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Abstract

Include the invention discloses reactor inductance computational methods under a kind of shorted-turn fault state：Step 1, set up dry-type air-core reactor multilayer multiturn coil model；Step 2, the computational methods for setting up air reactor total magnetic vector potential during without short-circuit circle；Step 3, calculate in the model set up total magnetic vector potential and coupling inductance at short-circuit circle；Step 4, based on Kirchoff s voltage equilibrium equation, utilize short-circuit circle AC resistance, short-circuit circle coupling inductance, short-circuit circle inductance to calculate the short circuit current flow of short-circuit circle；Reverse magnetic linkage caused by the short-circuit circle of step 5, the calculation of short-circuit current based on short-circuit circle, calculated using the method in step 2 and the magnetic linkage for obtaining non-shorting circle is calculated based on total magnetic arrow at non-shorting circle, according to the flux linkage calculation reactor total inductance of the reverse magnetic linkage of short-circuit circle and non-shorting circle, the weakening effect that take into account circulation in short-circuit circle to reactor inductance is realized, the technique effect of total inductance value computational accuracy under dry-type air-core reactor malfunction is improved.

Description

Reactor inductance computational methods under a kind of shorted-turn fault state
Technical field
It is analysis field the present invention relates to power equipment numerical computations, in particular it relates to a kind of dry-type air-core reactor circle Between under short-circuit condition reactor inductance computational methods.
Background technology
In recent years, dry-type air-core reactor is often faulty in operation occurs, from the reality of domestic and international dry-type air-core reactor From the point of view of border operation conditions and a large amount of statistics, the reason for dry-type air-core reactor burns mainly shorted-turn fault is caused. Therefore diagnosis to dry type hollow reactor interturn short circuit fault and on-line monitoring important in inhibiting.In research turn-to-turn short circuit Reactor parameter calculates particularly significant during the diagnosis of failure and on-line monitoring, due to the special electrical structure of reactor, Parameters variation caused by its turn-to-turn short circuit is mainly reflected on inductance.Current pair with the calculating method of inductance of dry-type air-core reactor Mainly there are sensing Y-factor method Y, BARTKY converter techniques, energy conversion method etc., but the application above method is to turn-to-turn fault state at present The influence of circulation in short-circuit circle is not considered in lower dry-type air-core reactor inductance value analysis, therefore can not accurately calculate turn-to-turn Inductance value under malfunction.
In summary, present inventor has found above-mentioned technology extremely during the present application technical scheme is realized There is following technical problem less：In the prior art, reactor inductance under existing dry type hollow reactor interturn short circuit state Computational methods are measured, exists and ignores in short-circuit circle circulation to the weakening effect of reactor inductance, causes to calculate inaccurate technology and asks Topic.
The content of the invention
The invention provides reactor inductance computational methods under a kind of shorted-turn fault state, existing dry type is solved Reactor inductance amount computational methods under hollow reactor interturn short circuit state, exist and ignore in short-circuit circle circulation to reactor inductance Weakening effect, cause to calculate inaccurate technical problem, realize and take into account in short-circuit circle circulation to reactor inductance Weakening effect, improves the technique effect of total inductance value computational accuracy under dry-type air-core reactor malfunction.
In order to solve the above technical problems, this application provides a kind of emulated computation method of power system arrester, it is described Method includes：
Step 1, set up dry-type air-core reactor multilayer multiturn coil model；
Step 2, the computational methods for setting up air reactor total magnetic vector potential during without short-circuit circle；
Step 3, calculate in the model set up total magnetic vector potential and coupling inductance at short-circuit circle；
Step 4, based on Kirchoff s voltage equilibrium equation, utilize short-circuit circle AC resistance, short-circuit circle coupling inductance, short circuit Circle inductance calculates the short circuit current flow of short-circuit circle；
Reverse magnetic linkage caused by the short-circuit circle of step 5, the calculation of short-circuit current based on short-circuit circle, utilizes the method in step 2 The magnetic linkage for being calculated based on total magnetic arrow at non-shorting circle and obtaining non-shorting circle is calculated, according to the reverse magnetic linkage and non-shorting circle of short-circuit circle Flux linkage calculation reactor total inductance.
Reactor analysis method based on magnetic vector potential method is specially：
It is as shown in Figure 1 a wire annulus, the radius of ring is a, is loaded with electric current I.In Fig. 1, because electric current only has tangentially Component, magnetic vector potential also only has tangential component Aθ, and AθIt is unrelated with θ, then for space any point P (r, z), have：
OrderThenThen formula (1) can be rewritten as：
Parameter k, complete elliptic integral of the first kind K, complete elliptic integral of the second kind E are re-introduced into,
Then formula (2) can be further rewritten as：
Such as Fig. 2, according to above-mentioned single wire annulus in the calculating of space any point magnetic vector potential, hollow electricity can be extrapolated The calculation formula of sensor self-induction：Assuming that an air reactor laterally there are m layers, per interlamellar spacing Δ b, longitudinally there is n-layer, per interlamellar spacing Δ H, then it is I to have electric current in (m+1) (n+1) individual electric current annulus, each electric current annulus, and annulus P (i', j') represents it in horizontal position In the i-th ' layer, longitudinal direction be located at jth ' layer, then P (i', j') be represented by the magnetic vector potential that annulus Q (i, j) place is produced：
In formula, R is hollow radius in air reactor, and Henry is H, and parasang is m.
In formula, ai'=R+ (i'-1) Δs b；ri=R+ (i-1) Δs b；zjj'=(j-j') Δh。
The magnetic vector potential that whole coil is produced at Q (i, j) place is folded equal to the magnetic vector potential that each ring-shaped current is produced at Q (i, j) place Plus：
Because magnetic vector potential only has tangential component A at thisθ, then the magnetic flux Φ (i, j) through annulus Q (i, j) be
Φ (i, j)=Aθ(i,j)·2πri (7)
Magnetic flux Φ (i, j) interlinkage coil produce magnetic linkage ψ (i, j) be
ψ (i, j)=Φ (i, j) (8)
Then the magnetic linkage ψ that whole coil is interlinked is：
Reactor inductance L can then be obtained1Calculation expression be：
Inductance value is calculated under turn-to-turn fault state：
Using the side for ignoring failure coil during dry-type air-core reactor inductance value is calculated under traditional turn-to-turn fault state Method is calculated inductance value.But in practice, when shorted-turn fault occurs for dry reactor, normal coil passes through electromagnetism It is coupling in failure coil and forms circulation, the magnetic field that the circulation is formed is opposite with the magnetic field that normal current is formed.Thus may be used See to realize the accurate calculating to inductance value under dry-type air-core reactor turn-to-turn fault state, it is impossible to ignore circulation and cause it Influence.
Such as Fig. 2, it is assumed that point Q (in1,jn1) represent to be located at i-thn1OK, jthn1The short-circuited conducting sleeve of row, now total magnetic vector potential A at Qθ (in1,jn1) be：
Short-circuit circle is now disregarded during magnetic vector potential accumulation calculating.Coupling inductance M is on short-circuit circle：
Wherein, ai’For the radius of electric current loop, k2=4ar/ [(a+r)2+z2], K and E are respectively that the first kind and Equations of The Second Kind are complete Ellptic integral, rn1For the radius of short-circuited coil, μ0For the magnetic conductivity under vacuum state, I is the electric current on electric current loop, AθTo be a certain The magnetic vector potential that non-shorting coil is formed on failure coil under coil short failure, M is non-shorting under a certain coil short failure The mutual inductance that coil is formed on failure coil.For existing during multiple short-circuit circles, because the quantity of short trouble coil is seldom, therefore Ignore the mutual inductance between failure coil, non-shorting coil shape on failure coil in the case where carrying out above-mentioned a certain short-circuited coil failure Into mutual inductance calculating process in, eliminate all short trouble circles.
Assuming that the AC resistance of short-circuited conducting sleeve is R with inductanceIt is shortAnd LIt is short, resistance RIt is shortActual measurement can be carried out to reactor to obtain, Inductance LIt is shortIt can be calculated according to reactor size, then the voltage on short-circuited conducting sleeve can be obtained by Kirchhoff's second law Equilibrium equation is：
(RIt is short+jωLIt is short)IIt is short+ j ω MI=0 (13)
Wherein, RIt is shortFor the AC resistance of short-circuited coil, LIt is shortFor the self-induction of short-circuited coil, IIt is shortFor the electric current of short-circuited coil still, ω is the angular frequency of power supply.
Then short circuit current flow I on short-circuit circleIt is shortIt is represented by：
IIt is short=-j ω MI/ (RIt is short+jωLIt is short) (14)
The magnetic linkage ψ produced using magnetic vector potential method to above-mentioned short circuit current flowInsteadCalculated：
Wherein, ψInsteadThe magnetic linkage formed for failure coil on non-faulting coil, ψ is total magnetic linkage of non-faulting coil formation, ψAlwaysFor total magnetic linkage of the failure dry-type air-core reactor containing short-circuit circle, L is the failure dry-type air-core reactor containing short-circuit circle Inductance.For existing during multiple short-circuit circles, ψInstead=ψAnti- 1+ψAnti- 2+…+ψAnti- n, as each short trouble coil is in non-faulting line The magnetic linkage summation formed on circle.
After short trouble, short-circuit circle magnetic linkage is disregarded, the magnetic linkage ψ that remaining coil is produced is：
Phase after being superimposed in the opposite direction due to the magnetic linkage that the magnetic linkage and normal coil of circulation formation are formed under normal current Mutually offset, therefore dry-type air-core reactor is in the total magnetic linkage ψ for occurring to be formed when single turn is short-circuitAlwaysFor：
ψAlways=ψ-ψInstead (17)
Then it can thus be concluded that the accurate expression that the inductance L after shorted-turn fault occurs for dry-type air-core reactor is
One or more technical schemes that the application is provided, have at least the following technical effects or advantages：
Due in the inductance value calculation under dry type hollow reactor interturn short circuit fault state, it is contemplated that short-circuit circle circulation shape Into influence of the reverse magnetic linkage to the total magnetic linkage of reactor, so, efficiently solve existing dry type hollow reactor interturn short circuit Reactor inductance amount computational methods under state, exist and ignore circulation in short-circuit circle the technology of the weakening effect of reactor inductance is asked Topic, and then realize the technology effect for improving the technique effect of total inductance value computational accuracy under dry-type air-core reactor malfunction Really.Meanwhile, it can be seen that from analysis above, with the raising of supply frequency, calculating of the failure circulation on inductance value influences It is bigger.
Brief description of the drawings
Accompanying drawing described herein is used for providing further understanding the embodiment of the present invention, constitutes one of the application Point, do not constitute the restriction to the embodiment of the present invention；
Fig. 1 is single turn reactor ring-shaped current magnetic vector potential schematic diagram in the application；
Fig. 2 is dry-type air-core reactor lattice coil model schematic in the application；
Fig. 3 is the schematic flow sheet of the computational methods of reactor inductance in the application；
Fig. 4 a are reactor non-shorting circle current curve schematic diagrames under a circle short-circuit condition in the application；
Fig. 4 b are the short-circuit circle current curve schematic diagrames of reactor in the application；
Fig. 5 is inductance value comparing result schematic diagram before and after the turn-to-turn short circuit of reactor one under different frequency in the application.
Embodiment
The invention provides reactor inductance computational methods under a kind of shorted-turn fault state, existing dry type is solved Reactor inductance amount computational methods under hollow reactor interturn short circuit state, exist and ignore in short-circuit circle circulation to reactor inductance Weakening effect, cause to calculate inaccurate technical problem, realize and take into account in short-circuit circle circulation to reactor inductance Weakening effect, improves the technique effect of total inductance value computational accuracy under dry-type air-core reactor malfunction.
It is below in conjunction with the accompanying drawings and specific real in order to be more clearly understood that the above objects, features and advantages of the present invention Mode is applied the present invention is further described in detail.It should be noted that in the case where not conflicting mutually, the application's Feature in embodiment and embodiment can be mutually combined.
Many details are elaborated in the following description to facilitate a thorough understanding of the present invention, still, the present invention may be used also Implemented with the other modes in the range of being different from being described herein using other, therefore, protection scope of the present invention is not by under The limitation of specific embodiment disclosed in face.
This application provides a kind of computational methods of reactor inductance, Fig. 3 is refer to, methods described includes：
Step 1, set up dry-type air-core reactor multilayer multiturn coil model；
Step 2, the computational methods for setting up air reactor total magnetic vector potential during without short-circuit circle；
Step 3, calculate in the model set up total magnetic vector potential and coupling inductance at short-circuit circle；
Step 4, based on Kirchoff s voltage equilibrium equation, utilize short-circuit circle AC resistance, short-circuit circle coupling inductance, short circuit Circle inductance calculates the short circuit current flow of short-circuit circle；
Reverse magnetic linkage caused by the short-circuit circle of step 5, the calculation of short-circuit current based on short-circuit circle, utilizes the method in step 2 The magnetic linkage for being calculated based on total magnetic arrow at non-shorting circle and obtaining non-shorting circle is calculated, according to the reverse magnetic linkage and non-shorting circle of short-circuit circle Flux linkage calculation reactor total inductance.
Illustrate below and the present processes are introduced, such as in kind using individual layer dry-type air-core reactor, above-mentioned reactance Device relevant parameter in kind is as shown in the table：
Table 3-1 reactor relevant parameters
Apply amplitude to above-mentioned reactor and shake voltage for 5774V power frequency, calculating obtains the non-shorting circle of reactor and short Electric current in the circle of road is simultaneously depicted as curve, as shown in Figure 4.
The inductance value of reactor is calculated before and after short trouble according to formula (9) and formula (11) and curve is drawn, as shown in figure 5, By comparing it can be seen that the curve that method inductance value is drawn in the application is more accurate.
Technical scheme in above-mentioned the embodiment of the present application, at least has the following technical effect that or advantage：
Due in the inductance value calculation under dry type hollow reactor interturn short circuit fault state, it is contemplated that short-circuit circle circulation shape Into influence of the reverse magnetic linkage to the total magnetic linkage of reactor, so, efficiently solve existing dry type hollow reactor interturn short circuit Reactor inductance amount computational methods under state, exist and ignore circulation in short-circuit circle the technology of the weakening effect of reactor inductance is asked Topic, and then realize the technology effect for improving the technique effect of total inductance value computational accuracy under dry-type air-core reactor malfunction Really.Meanwhile, it can be seen that from analysis above, with the raising of supply frequency, calculating of the failure circulation on inductance value influences It is bigger.
, but those skilled in the art once know basic creation although preferred embodiments of the present invention have been described Property concept, then can make other change and modification to these embodiments.So, appended claims are intended to be construed to include excellent Select embodiment and fall into having altered and changing for the scope of the invention.
Obviously, those skilled in the art can carry out the essence of various changes and modification without departing from the present invention to the present invention God and scope.So, if these modifications and variations of the present invention belong to the scope of the claims in the present invention and its equivalent technologies Within, then the present invention is also intended to comprising including these changes and modification.

Claims (6)

1. reactor inductance computational methods under a kind of shorted-turn fault state, it is characterised in that methods described includes：
Step 1, set up dry-type air-core reactor multilayer multiturn coil model；
Step 2, the computational methods for setting up air reactor total magnetic vector potential during without short-circuit circle；
Step 3, calculate in the model set up total magnetic vector potential and coupling inductance at short-circuit circle；
Step 4, based on Kirchoff s voltage equilibrium equation, utilize short-circuit circle AC resistance, short-circuit circle coupling inductance, short-circuit circle electricity Sense calculates the short circuit current flow of short-circuit circle；
Reverse magnetic linkage caused by the short-circuit circle of step 5, the calculation of short-circuit current based on short-circuit circle, utilizes the method in step 2 to calculate The magnetic linkage for obtaining non-shorting circle is calculated based on total magnetic arrow at non-shorting circle, according to the reverse magnetic linkage of short-circuit circle and the magnetic of non-shorting circle Chain calculating reactance device total inductance.
2. reactor inductance computational methods under shorted-turn fault state according to claim 1, it is characterised in that described Reactor multilayer multiturn coil model is specially：Air reactor laterally has m layer line circles, per interlamellar spacing Δ b；There is n-layer line longitudinal direction Circle, per interlamellar spacing Δ h.
3. the computational methods of reactor inductance according to claim 1, it is characterised in that for a circle failure coil, if Point Q (in1,jn1) represent to be located at i-thn1OK, jthn1The short-circuited conducting sleeve of row, now non-shorting circle total magnetic vector potential A at Qθ(in1,jn1) For：
Coupling inductance M is on short-circuit circle：
Wherein, ai’For the radius of electric current loop, k2=4ar/ [(a+r)2+z2], K and E are respectively that the first kind and Equations of The Second Kind are completely oval Integration, rn1For the radius of short-circuited coil, μ0For the magnetic conductivity under vacuum state, I is the electric current on electric current loop, AθFor a certain coil The magnetic vector potential that non-shorting coil is formed on failure coil under short trouble, M is non-shorting coil under a certain coil short failure The mutual inductance formed on failure coil.
4. reactor inductance computational methods under shorted-turn fault state according to claim 1, it is characterised in that short circuit Voltage equation is on ring：
(RIt is short+jωLIt is short)IIt is short+ j ω MI=0
Wherein, RIt is shortFor the AC resistance of short-circuited coil, LIt is shortFor the self-induction of short-circuited coil, IIt is shortFor the electric current of short-circuited coil still, ω is The angular frequency of power supply.
5. reactor inductance computational methods under shorted-turn fault state according to claim 1, it is characterised in that short circuit Short circuit current flow I on circleIt is shortIt is represented by
IIt is short=-j ω MI/ (RIt is short+jωLIt is short) 。
6. reactor inductance computational methods under shorted-turn fault state according to claim 1, it is characterised in that utilize The magnetic linkage ψ that magnetic vector potential method is produced to short circuit current flowInsteadCalculated：
Remaining coil produce magnetic linkage ψ be：
Dry-type air-core reactor is in the total magnetic linkage ψ for occurring to be formed when single turn is short-circuitAlwaysFor：
ψAlways=ψ-ψInstead
Dry-type air-core reactor occur shorted-turn fault after inductance L be：
Wherein, ψInsteadThe magnetic linkage formed for failure coil on non-faulting coil, ψ is total magnetic linkage of non-faulting coil formation, ψAlwaysFor Total magnetic linkage of failure dry-type air-core reactor containing short-circuit circle, L is the electricity of the failure dry-type air-core reactor containing short-circuit circle Sense.
CN201710327537.2A 2017-05-09 2017-05-09 Reactor inductance computational methods under a kind of shorted-turn fault state Pending CN107153146A (en)

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CN108387769A (en) * 2018-02-26 2018-08-10 河海大学 A kind of computational methods of reactor interturn short circuit electric current
CN109239544A (en) * 2018-08-22 2019-01-18 珠海华网科技有限责任公司 A kind of oscillatory wave system air reactor design method
CN109444581A (en) * 2018-11-06 2019-03-08 华北电力大学 A kind of test method and test device of dry-type air-core reactor

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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108387769A (en) * 2018-02-26 2018-08-10 河海大学 A kind of computational methods of reactor interturn short circuit electric current
CN109239544A (en) * 2018-08-22 2019-01-18 珠海华网科技有限责任公司 A kind of oscillatory wave system air reactor design method
CN109239544B (en) * 2018-08-22 2020-10-20 珠海华网科技有限责任公司 Design method of air reactor for oscillatory wave system
CN109444581A (en) * 2018-11-06 2019-03-08 华北电力大学 A kind of test method and test device of dry-type air-core reactor

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