CN110263500B - Modeling method for multipoint ground fault of wound core under inter-chip short circuit - Google Patents

Modeling method for multipoint ground fault of wound core under inter-chip short circuit Download PDF

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CN110263500B
CN110263500B CN201910703531.XA CN201910703531A CN110263500B CN 110263500 B CN110263500 B CN 110263500B CN 201910703531 A CN201910703531 A CN 201910703531A CN 110263500 B CN110263500 B CN 110263500B
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sheet
short circuit
core
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高仕斌
林桐
周利军
周祥宇
于兴宇
陈辰
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Tianjin Zhongtie Electrification Design Research Institute Co ltd
Southwest Jiaotong University
Zhuzhou CRRC Times Electric Co Ltd
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Tianjin Zhongtie Electrification Design Research Institute Co ltd
Southwest Jiaotong University
Zhuzhou CRRC Times Electric Co Ltd
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Abstract

The invention discloses a modeling method for multipoint ground faults of a wound iron core under an inter-sheet short circuit, which establishes a relational expression among winding path lengths, section widths and winding stages of silicon steel strips under the condition that the geometric parameters of an inner window of the wound iron core and the radius of an outer section of a core column are known. Deducing the equivalent resistance between sheets when the short circuit does not occur in the wound core; when short circuit occurs among the sheets, the short-circuit silicon steel sheets are equivalent to one sheet, and the equivalent resistance between the short-circuit silicon steel sheets and the non-short-circuit sheet is deduced; building a multi-point earth fault circuit model of the wound core according to the calculated equivalent resistance, and deducing the total equivalent resistance of the short circuit level and the non-short circuit level by using a circuit principle; the fault current of the section where the iron core grounding point is located can form a loop, the potential difference of the grounding point is obtained according to the change rate of interlinkage magnetic flux in the iron core and the Lenz law, and the calculated value of the fault grounding current is further obtained.

Description

Modeling method for multipoint ground fault of wound core under inter-chip short circuit
Technical Field
The invention belongs to the field of lumped parameter modeling and numerical calculation of equivalent circuits of transformer cores, and particularly relates to a modeling method for multipoint ground faults of a wound core under an inter-chip short circuit
Background
With the vigorous development of high-speed rails, the demand for electric energy is higher and higher, and the wound core traction transformer has smaller loss and is applied to the field of high-speed rails more and more at the present stage in order to respond to the call of national energy conservation and emission reduction. The winding core is one of main components of the traction transformer, and once the winding core breaks down, the normal operation of the transformer can be seriously influenced. The multiple-point grounding of the wound iron core is one of the most typical and most serious faults of the iron core, the cross section of the wound iron core can generate fault current, the continuous fault current can increase the loss of the wound iron core and generate a large amount of heat, the insulation between the silicon steel sheets of the iron core is damaged, even the short circuit between the sheets occurs, the eddy current loss of the wound iron core is increased, and the potential safety hazard of the wound iron core is not a little different.
At present, the current of an iron core grounding wire is generally monitored in real time, a threshold value is set by using an empirical formula to judge whether multipoint grounding faults occur, the magnitude of the grounding current of transformers with different structures is different, and the fault current is larger when short circuit occurs among the plates, so that the fault current cannot be accurately judged and analyzed. Therefore, from the fault mechanism, multipoint ground fault homogenization modeling needs to be performed on the wound core with the gradually-changed width of each stage, and a calculated value of fault current during the inter-sheet short circuit needs to be derived.
Disclosure of Invention
Aiming at the problems, the invention provides a modeling method for the multipoint ground fault of the wound core under the inter-sheet short circuit. The method considers the characteristic that the width of the cross section of the actual wound iron core is continuous and gradually changed and the influence factors of short circuit among wound iron core sheets, deduces the equivalent resistance among the sheets when the short circuit does not occur among the silicon steel sheets, and deduces the equivalent resistance among the short-circuited silicon steel sheets and the short-circuited silicon steel sheets when the short circuit occurs among the sheets; and building a multi-point grounding fault circuit model of the wound core according to the obtained resistance value to obtain the multi-point grounding fault current of the wound core. The invention is realized by the following technical means:
1) calculating the path length l of different winding levels according to the geometric parameters of the inner window of the wound iron core, including the core column length s, the iron yoke length v, the fillet radius r and the silicon steel sheet thickness di：
li＝2(s+v)+2π(r+id)-πd (1)
Wherein, i belongs to {1,2,3, …, m, m +1, m +2, …,2m }, 2m is the total layer number of winding of silicon steel sheet, and it satisfies:
Figure BDA0002151471080000028
wherein R is the radius of the outer section of the wound core,
Figure BDA0002151471080000027
is an operation of rounding up;
2) calculating parameters of various resistance units of the multipoint ground fault circuit when short circuit does not occur between the coil core sheets:
Figure BDA0002151471080000021
wherein R isxiIs the resistance, R, of a silicon steel sheet in the x direction after considering the skin effectziIs the resistance, k, of the silicon steel sheet in the z directioniFor the sectional width division coefficient of the resistance element in the z direction, it satisfies wi＝nkiN is the specific dividing number of the resistance units of the silicon steel sheet along the z direction; rsiResistance of insulating coating of silicon steel sheet along x direction, RaveIn order to consider the resistance function of the insulating varnish material, theta is a temperature coefficient;
delta is the skin depth of the silicon steel sheet material, and meets the following requirements:
Figure BDA0002151471080000022
where μ is the permeability of the wound core material and σ is the electrical conductivity of the wound core material. w is aiFor the cross-sectional widths of the different winding levels, it satisfies:
Figure BDA0002151471080000023
when short circuit does not exist between the coil core sheets, the resistor network is divided into an upper section and a lower section with the same resistance integrally: aiming at the equivalent resistance of any level, a method for simplifying the resistance network of two adjacent nodes at the starting end is considered, and the coupling relation expression of each resistance unit is written in a column mode:
Figure BDA0002151471080000024
Figure BDA0002151471080000025
as shown in FIG. 2(a), R as viewed from the ab node and the cd node in the z direction is calculated based on the principle of equivalent resistance of the infinite networkab、RcdThe value is obtained. The idea of solving the equivalent resistance by the infinite resistance network is as follows: when n is sufficiently large, ki<<wiCan be regarded as Rab＝Rcd＝RpTherefore, the formula (7) can be directly solved to obtain the intermediate parameter R of the equivalent circuit modelpExpression (c):
Figure BDA0002151471080000026
further combining the formula (6) to obtain the equivalent resistance R of any level when there is no short circuit between chipsiExpression (c):
Figure BDA0002151471080000031
3) calculating parameters of various resistance units of a multipoint ground fault circuit when short circuit occurs between the coiled iron core sheets:
Rxf＝Rxn+Rx(n+1)+Rx(n+2)+...+Rx(n+p-1) (10)
Figure BDA0002151471080000032
Rsn＝0；Rs(n-1)＝Rsi(12)
short-circuiting of core lamination from n-th sheet to n + p-th sheet, Rxf、Rzn、Rz(n+p-1)After the n-th sheet and the n + p-th sheet are short-circuited, the p-th sheet is equivalent to a sheet, the resistance along the x direction, the resistance along the z direction on the n-th sheet, the resistance along the z direction on the n + p-th sheet, and the kjFor the sectional width of the resistance element in the z-direction, the section factor ln、ln+pPath lengths of the n-th and n + p-th winding stages, RsnIs the insulation resistance between the n-th and n + p-th shorting plates, Rs(n-1)Is the insulation resistance between the (n-1) th sheet and the nth sheet;
according to the calculation method in the step 2), calculating the resistance parameter values of the sheet level of the wound core in the inter-sheet short circuit and deducing the equivalent resistance R of the lamination in the short circuitn：
Figure BDA0002151471080000033
Figure BDA0002151471080000034
Figure BDA0002151471080000035
Figure BDA0002151471080000036
Figure BDA0002151471080000037
According to R shown in FIG. 2(b)ef、RopRefers to the resistance of the resistance network between the n sheet and the n-1 sheet seen from the ef and op nodes when the p sheet is short-circuited, and the resistance R is known by the equivalent principle of infinite network resistanceefIs equal to RopCalculated to obtain RefCarrying in formula (13) to obtain the equivalent resistance R between the n-th sheet and the n-1-th sheet when the p sheets are short-circuitedn(ii) a According to FIG. 2(c), the same derivation process is performed to obtain the n + p-Equivalent resistance R between 1 piece and n + p piecen+p-1；
4) Deducing circuit parameters of a circuit model of the multipoint ground fault of the wound core under the short circuit between the sheets through the steps, and establishing the circuit model shown in the figure 2 (d); the equivalent resistance between the chips under the condition of no short circuit is RiWhen p pieces are short-circuited and equivalent to one piece, the equivalent resistance of the short-circuited piece level and the non-short-circuited piece level is RnAnd Rn+p-1Mapping the resistance parameters during the inter-chip short circuit to a circuit model; according to the circuit model, the expression of the fault current I when multipoint earthing is as follows:
Figure BDA0002151471080000041
wherein, U is the potential difference of two adjacent grounding points of the wound iron core. The fault current of the section where the iron core grounding point is located can form a loop, and the potential difference U of the grounding point is obtained according to the interlinkage magnetic flux change rate in the iron core and the Lenz law, so that the calculated value of the fault grounding current is obtained. The calculation formula for U is as follows:
Figure BDA0002151471080000042
in the formula, BavgThe average flux density in the core is determined by the voltage on the power supply side of the transformer.
The method has the advantages that the multipoint ground fault current of the wound core is obtained through the modeling method, and the wound core is judged whether to generate the inter-lamination short circuit and the multipoint ground fault or not by taking the multipoint ground fault current as the standard and combining with the ground current data actually measured on site.
Drawings
Fig. 1 is a schematic diagram of a multi-point earth fault current flowing in different directions of a cross section of a wound core according to the present invention.
FIG. 2 is a schematic diagram of a circuit model and a derivation of equivalent resistance of a multi-point ground fault in consideration of an inter-sheet short circuit in a wound core according to the present invention.
Detailed Description
The following describes the process of the present invention in detail with reference to the accompanying drawings.
Fig. 1 is a schematic diagram of a multi-point earth fault current flowing in different directions of a cross section of a wound core according to the present invention. When a multipoint short-circuit fault of the iron core occurs, the iron core forms a loop through the ground, and current is generated in the alternating electromagnetic field on the loop, wherein the flowing direction of the current is mainly along the directions of x and z as shown in fig. 1. Because of the influence of skin effect, current only flows at two sides of the silicon steel sheet, equivalent resistance parameters between each level of silicon steel sheet are deduced, the current flowing area is obtained from the skin depth delta, and the winding length l of each level of silicon steel sheet must be considered in a resistance calculation formulai。
1) Calculating the path length l of different winding levels according to the geometric parameters of the inner window of the wound iron core, including the core column length s, the iron yoke length v, the fillet radius r and the silicon steel sheet thickness di：
li＝2(s+v)+2π(r+id)-πd (1)
Wherein, i belongs to {1,2,3,., m, m +1, m +2,. and 2m }, 2m is the total layer level of silicon steel sheet winding, and satisfies the following conditions:
Figure BDA0002151471080000056
wherein R is the radius of the outer section of the wound core,
Figure BDA0002151471080000057
is an operation of rounding up;
2) calculating parameters of various resistance units of the multipoint ground fault circuit when short circuit does not occur between the coil core sheets:
Figure BDA0002151471080000051
wherein R isxiIs the resistance, R, of a silicon steel sheet in the x direction after considering the skin effectziIs the resistance, k, of the silicon steel sheet in the z directioniFor the sectional width division coefficient of the resistance element in the z direction, it satisfies wi＝nkiN is the specific dividing number of the resistance units of the silicon steel sheet along the z direction; rsiResistance of insulating coating of silicon steel sheet along x direction, RaveIn order to consider the resistance function of the insulating varnish material, theta is a temperature coefficient; δ is the skin depth of the silicon steel sheet material, which satisfies:
Figure BDA0002151471080000052
where μ is the permeability of the wound core material and σ is the electrical conductivity of the wound core material. w is aiFor the cross-sectional widths of the different winding levels, it satisfies:
Figure BDA0002151471080000053
calculating the equivalent resistance between chips when no short circuit occurs according to the graph (a) in FIG. 2; the resistor network shown in fig. 1 is divided into an upper section and a lower section with the same resistance value, a resistor network of two adjacent nodes at the starting end is considered for any level of equivalent resistance to carry out a simplification method, and the coupling relation expression of each resistor unit is written in a column:
Figure BDA0002151471080000054
Figure BDA0002151471080000055
as shown in FIG. 2(a), R as viewed from the ab node and the cd node in the z direction is calculated based on the principle of equivalent resistance of the infinite networkab、RcdThe value is obtained. The idea of solving the equivalent resistance by the infinite resistance network is as follows: when n is sufficiently large, ki<<wiCan be regarded as Rab＝Rcd＝RpTherefore, the formula (7) can be directly solved to obtain the intermediate parameter R of the equivalent circuit modelpExpression (c):
Figure BDA0002151471080000061
further combining the formula (6) to obtain the equivalent resistance R of any level when there is no short circuit between chipsiExpression (c):
Figure BDA0002151471080000062
3) when the silicon steel sheet generating sheets are short-circuited, the short-circuited silicon steel sheets can be equivalent to one silicon steel sheet, so that the insulation resistance between the short-circuited sheets is 0, and the equivalent x-direction resistance value of the silicon steel sheets is the x-direction resistance value of the p short-circuited silicon steel sheets which are connected in series to obtain a formula (10); the z-direction resistance value of the equivalent silicon steel sheet is obtained by the formula (11). Equivalent resistance values of the short-circuited silicon steel sheet on both sides and the short-circuited silicon steel sheet not occurring are calculated according to (b) and (c) of fig. 2, and obtained by equations (15) and (16).
Calculating parameters of various resistance units of the multipoint ground fault circuit when short circuit occurs between the coil core sheets:
Rxf＝Rxn+Rx(n+1)+Rx(n+2)+...+Rx(n+p-1) (10)
Figure BDA0002151471080000063
Rsn＝0；Rs(n-1)＝Rsi (12)
short-circuiting of core lamination from n-th sheet to n + p-th sheet, Rxf、Rzn、Rz(n+p-1)After the n-th sheet and the n + p-th sheet are short-circuited, the p-th sheet is equivalent to a sheet, the resistance along the x direction, the resistance along the z direction on the n-th sheet, the resistance along the z direction on the n + p-th sheet, and the kjFor the sectional width of the resistance element in the z-direction, the section factor ln、ln+pPath lengths of the n-th and n + p-th winding stages, RsnIs the insulation resistance between the n-th and n + p-th shorting plates, Rs(n-1)Is the insulation resistance between the (n-1) th sheet and the nth sheet;
according to the calculation method in the step 2), calculating the resistance parameter values of the sheet level of the coil iron chip during short circuit and deducing the equivalent resistance of the lamination during short circuit:
Figure BDA0002151471080000064
Figure BDA0002151471080000065
Figure BDA0002151471080000066
Figure BDA0002151471080000071
Figure BDA0002151471080000072
according to FIG. 2(b), Ref、RopRefers to the resistance of the resistance network between the n sheet and the n-1 sheet seen from the ef and op nodes when the p sheet is short-circuited, and the resistance R is known by the equivalent principle of infinite network resistanceefIs equal to RopCalculated to obtain RefCarrying in formula (13) to obtain the equivalent resistance R between the n-th sheet and the n-1-th sheet when the p sheets are short-circuitedn(ii) a According to the method shown in FIG. 2(c), the equivalent resistance R between the n + p-1 th sheet and the n + p th sheet in the case of p-sheet short circuit is obtained through the same derivation processn+p-1；
4) Establishing a multipoint grounding circuit model under the short-circuit fault as shown in fig. 2(d) according to the calculated circuit parameters; the equivalent resistance between the chips is R when no short circuit occursiWhen p pieces are short-circuited and equivalent to one piece, the equivalent resistance of the short-circuited piece level and the non-short-circuited piece level is RnAnd Rn+p-1Therefore, the resistance parameter during the inter-chip short circuit is mapped to a circuit model, and the expression of the fault current I during the multipoint grounding is as follows: :
Figure BDA0002151471080000073
wherein, U is the potential difference of two adjacent grounding points of the wound iron core. The fault current of the section where the iron core grounding point is located can form a loop, and the potential difference U of the grounding point is obtained according to the interlinkage magnetic flux change rate in the iron core and the Lenz law, so that the fault grounding current value is calculated. The calculation formula for U is as follows:
Figure BDA0002151471080000074
in the formula, BavgThe average flux density in the core is determined by the voltage on the power supply side of the transformer.

Claims (1)

1. A modeling method for multipoint ground faults of a wound core under an inter-chip short circuit is characterized in that the multipoint ground faults of the wound core are modeled when different stages of lamination sheets are in short circuit, and the modeling method comprises the following steps:
1) calculating the path length l of different winding levels according to the geometric parameters of the inner window of the wound iron core, including the core column length s, the iron yoke length v, the fillet radius r and the silicon steel sheet thickness di：
li＝2(s+v)+2π(r+id)-πd (1)
Wherein, i belongs to {1,2,3, …, m, m +1, m +2, …,2m }, 2m is the total layer number of winding of silicon steel sheet, and it satisfies:
Figure FDA0003562766060000011
wherein R is the radius of the outer section of the wound core,
Figure FDA0003562766060000012
is an operation of rounding up;
2) calculating parameters of various resistance units of the non-short circuit multipoint ground fault circuit between the coil core sheets:
Figure FDA0003562766060000013
wherein R isxiIs the resistance, R, of a silicon steel sheet in the x direction after considering the skin effectziIs the resistance of the silicon steel sheet in the z direction, RsiResistance, k, of insulating coating for silicon steel sheet in x directioniFor the sectional width division coefficient of the resistance element in the z direction, it satisfies wi＝nkiN is the specific dividing number of the resistance units of the silicon steel sheet along the z direction; raveIn order to consider the resistance function of the insulating varnish material, theta is a temperature coefficient; δ is the skin depth of the silicon steel sheet material, which satisfies:
Figure FDA0003562766060000014
where μ is the permeability of the wound core material and σ is the conductivity of the wound core material; w is aiFor the cross-sectional widths of the different winding levels, it satisfies:
Figure FDA0003562766060000015
when short circuit does not exist between the coil core sheets, the resistor network is divided into an upper section and a lower section with the same resistance integrally: aiming at the equivalent resistance of any level, a method for simplifying the resistance network of two adjacent nodes at the starting end is considered, and the coupling relation expression of each resistance unit is written in a column mode:
Figure FDA0003562766060000016
Figure FDA0003562766060000021
in the formula, RabIs seen from the ab node in the z-directionPast equivalent resistance, RcdIs the equivalent resistance as seen from the cd node in the z direction; solving the equivalent resistance according to the modeling thought of the infinite resistance network: let n>50, then there is ki<<wiAnd further to obtain Rab＝Rcd＝RpTherefore, the formula (7) is directly solved to obtain the intermediate parameter R of the equivalent circuit modelpExpression (c):
Figure FDA0003562766060000022
further combining the formula (7), the equivalent resistance R of any level when there is no short circuit between chips is obtainediExpression (c):
Figure FDA0003562766060000023
(3) calculating parameters of various resistance units of the multipoint ground fault circuit when short circuit occurs between the coil core sheets:
Rxf＝Rxn+Rx(n+1)+Rx(n+2)+...+Rx(n+p-1) (10)
Figure FDA0003562766060000024
Rsn＝0；Rs(n-1)＝Rsi (12)
short-circuiting of core lamination from n-th sheet to n + p-th sheet, Rxn、Rx(n+1)、…、Rx(n+p-1)Respectively, the resistances of the n-th to n + p-1-th sheets in the x-direction, Rxf、Rzn、Rz(n+p-1)When p silicon steel sheets are equivalent to one sheet, the resistance along the x direction, the resistance along the z direction on the nth sheet, the resistance along the z direction on the n + p sheet, and kjFor the sectional width of the resistance element in the z-direction, the section factor ln、ln+pPath lengths of the n-th and n + p-th winding stages, RsnInsulation resistance between the n-th and n + p-th shorting plates，Rs(n-1)Is the insulation resistance between the (n-1) th sheet and the nth sheet;
according to the calculation method in the step 2), calculating the resistance parameter values of the sheet level of the roll iron core in the inter-sheet short circuit and deducing the equivalent resistance R of the lamination in the short circuitn：
Figure FDA0003562766060000025
Figure FDA0003562766060000026
Figure FDA0003562766060000027
Figure FDA0003562766060000031
Figure FDA0003562766060000032
Ref、RopThe resistance of the resistance network between the nth sheet and the (n-1) th sheet looking into the nodes of ef and op when the p sheets are in short circuit is referred to; rnP-sheet short circuit is equivalent to an equivalent resistance between an n-th sheet and an n-1 th sheet, Rn+p-1The p-piece short circuit is equivalent to equivalent resistance between an n + p-1 piece and an n + p piece;
4) establishing a multipoint grounding fault circuit model of the wound core under the short circuit between the sheets, and obtaining an expression of fault current I when multipoint grounding:
Figure FDA0003562766060000033
wherein, U is the potential difference of the cross-section internal window and the outside at the coiled core grounding point, and it satisfies:
Figure FDA0003562766060000034
in the formula, BavgThe average flux density in the core is determined by the voltage on the power supply side of the transformer.
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