CN108845176B - Calculation method for voltage distribution of resistance-type voltage transformer considering stray capacitance - Google Patents

Calculation method for voltage distribution of resistance-type voltage transformer considering stray capacitance Download PDF

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CN108845176B
CN108845176B CN201811046252.2A CN201811046252A CN108845176B CN 108845176 B CN108845176 B CN 108845176B CN 201811046252 A CN201811046252 A CN 201811046252A CN 108845176 B CN108845176 B CN 108845176B
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向川
陈新威
郭清
王仁焘
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Dalian Maritime University
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Abstract

The invention provides a method for calculating voltage distribution of a resistance-type voltage transformer considering stray capacitance. Dividing a resistance voltage divider into n tiny units, calculating the surface charge of each unit of the resistance voltage divider by a boundary element method, and further calculating a capacitance coefficient matrix of the resistance voltage divider, thereby obtaining the ground stray capacitance and the high-voltage end stray capacitance of each unit of the resistance voltage divider; according to the obtained stray capacitance to the ground and the stray capacitance to the high-voltage end of each unit, the voltage distribution of the resistance voltage divider is obtained by using a node voltage method; and according to the obtained voltage distribution, further obtaining the influence of the stray capacitance on the voltage division ratio and the phase deviation of the resistance-type voltage transformer. The method can realize rapid solution by means of computer software, and has high application value.

Description

Calculation method for voltage distribution of resistance-type voltage transformer considering stray capacitance
Technical Field
The invention relates to the technical field of power equipment running state detection, in particular to a method for calculating voltage distribution of a resistance-type voltage transformer considering stray capacitance.
Background
Electronic voltage transformers can be classified into resistive voltage transformers, resistive-capacitive voltage transformers, and capacitive voltage transformers according to the measurement principle of the transformers. Compared with other types of transformers, the resistance type voltage transformer has the following advantages:
(1) the divider resistor is reasonably selected, and the resistance type voltage transformer can obtain a size smaller than that of a capacitance type or resistance-capacitance type transformer;
(2) because of adopting a pure resistance voltage division structure, the resistance voltage transformer has no ferromagnetic resonance phenomenon and has large dynamic and linear measurement intervals;
(3) the resistance type voltage transformer can realize high-precision voltage measurement by adopting a specially designed small-size resistor.
The main body of the resistance voltage transformer is a resistance voltage divider, and the measurement precision of the resistance voltage divider directly influences the working performance of the resistance voltage transformer. For an ideal resistive divider, the division ratio k isN＝1+R1/R2Wherein R is1Is a high-voltage arm resistor, R2Is a low voltage arm resistor. The difference between the input voltage of the primary high-voltage end and the output voltage of the secondary low-voltage end is k times in amplitude, and no phase difference exists. However, in the existing resistive voltage divider, stray capacitance caused by an inherent electric field exists between the existing resistive voltage divider and the surrounding earth and high-voltage end, which not only changes the voltage dividing ratio of the voltage divider, but also causes phase deviation between the measurement output and the input.
Disclosure of Invention
According to the above proposal, for the existing resistive voltage divider, stray capacitance caused by the inherent electric field exists between the existing resistive voltage divider and the surrounding earth and high-voltage end, which not only changes the voltage dividing ratio of the voltage divider, but also causes the technical problem of phase deviation between the measurement output and the measurement input, thereby providing a method for calculating the voltage distribution of the resistive voltage transformer considering the stray capacitance.
The technical means adopted by the invention are as follows:
a method of calculating a voltage distribution of a resistive voltage transformer that accounts for stray capacitance, comprising:
s1: dividing the resistance voltage divider into n tiny units, and calculating the stray capacitance of each unit of the resistance voltage divider;
s2: according to the obtained stray capacitance of each unit, obtaining the voltage distribution of the resistance voltage divider by using a node voltage method;
s3: and further solving the voltage division ratio and the phase deviation of the stray capacitor to the resistance-type voltage transformer according to the solved voltage distribution.
Further, the step S1 is to divide the resistor voltage divider into n tiny units along the axial direction, and the calculation process of the stray capacitance of each unit of the resistor voltage divider further includes:
s101: calculating the surface charge of each unit;
s102: calculating the stray capacitance of each unit to the ground end;
s103: and calculating the stray capacitance of each unit to the high-voltage end.
Further, the process of finding the voltage distribution of the resistor voltage divider in step S2 is as follows:
s201: in step S1, the resistive divider is divided into n tiny units, and when n is large enough, each tiny unit is regarded as a node, the ground is regarded as a reference node, and the voltage of the high-voltage end node is set as
Figure BDA0001793367110000021
Calculating a node voltage equation;
s202: rewriting and sorting the node voltage equation to obtain n equation sets;
s203: and calculating the n equations to obtain the voltage distribution of the resistor divider.
Further, the calculation process of the voltage division ratio and the phase deviation of the resistive voltage transformer in the step S3 is as follows:
obtaining the voltage division ratio deviation caused by the stray capacitance of the resistance voltage divider body:
Figure BDA0001793367110000022
k in the formulaN＝1+R1/R2The voltage division ratio of an ideal resistance voltage divider;
obtaining voltage phase deviation caused by stray capacitance of a resistor voltage divider body:
Figure BDA0001793367110000023
compared with the prior art, the method can realize quick solution by means of computer software, and has higher application value. In summary, the technical scheme of the invention is applied to divide the resistive voltage divider into a plurality of units, obtain the surface charge of each unit of the resistive voltage divider by a boundary element method, and further calculate the capacitance coefficient matrix of the resistive voltage divider, thereby obtaining the ground stray capacitance and the high-voltage end stray capacitance of each unit of the resistive voltage divider; according to the obtained stray capacitance to the ground and the stray capacitance to the high-voltage end of each unit, the voltage distribution of the resistance voltage divider is obtained by using a node voltage method; and further solving the voltage division ratio and the phase deviation of the stray capacitor to the resistance-type voltage transformer according to the solved voltage distribution.
For the reasons, the method can be widely popularized in the fields of power equipment operation state detection and the like.
Drawings
In order to more clearly illustrate the embodiments of the present invention 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, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a flowchart of the calculation process of step S1 of the method of the present invention.
FIG. 3 is a flowchart of the method of step S2 of the present invention for determining the voltage distribution of the resistor divider.
Detailed Description
In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
Examples
As shown in fig. 1,2 and 3, the present invention provides a method for calculating voltage distribution of a resistance voltage transformer with stray capacitance, including:
s1: dividing the resistance voltage divider into n tiny units, and calculating the stray capacitance of each unit of the resistance voltage divider;
the vector formed by each unit potential is expressed as U epsilon RnAnd the vector formed by the surface charges of each unit is expressed as Q epsilon RnAnd then:
CU＝Q (1)
wherein C is a capacitance coefficient matrix
S101: calculating the surface charge of each unit;
setting the potential of the ith unit as 1V and the potentials of other units as 0V, and calculating the surface total charge of each unit to obtain the ith row parameter of the C matrix; wherein the capacitance coefficient of the jth row and ith column is the charge Q on the jth unitj：
Cji＝Qj,j＝1,2,…,n (2)
Dividing all unit surfaces into m surface elements, and assuming that the charge on each surface element is uniformly distributed, then the center point x of any surface element kkThe potential of (A) is:
Figure BDA0001793367110000041
in the formula
Figure BDA0001793367110000042
For bin l at point xkThe resulting potential;
Figure BDA0001793367110000043
is bin k at xkPotential generated by a dot
Figure BDA0001793367110000044
In the formula of0Is a vacuum dielectric constant; a. thekIs the area of bin k; sigmakIs the charge density of bin k; q. q.skSurface charge of bin k
Figure BDA0001793367110000045
In the formula rklIs the distance, s, from the center of bin l to the center of any bin klIs the area of the first surface element, AlIs the l bin, σlThe charge density of the bin l, and m is the number of bins after all cells are divided;
the formula for all bins is calculated as:
Figure BDA0001793367110000051
wherein p is an m-order parameter matrix; q is an m-dimensional column vector consisting of the charge amount of each bin;
Figure BDA0001793367110000052
an m-dimensional column vector composed for each bin potential.
Similarly, setting the potentials of all surface elements on the unit i to be 1V, and the potentials of the other surface elements to be 0V, and calculating the formula (6) to obtain the surface charges of all the surface elements; calculated by substituting equation (2):
Figure BDA0001793367110000053
sequentially calculating to obtain the ith row element of the capacitance coefficient matrix C;
the whole capacitance coefficient matrix C can be obtained by a method of sequentially applying potentials to the units for solving;
s102: calculating the stray capacitance of each unit to the ground end;
the stray capacitance of the ith unit to the ground is:
Figure BDA0001793367110000054
calculating in sequence to obtain stray capacitance of all units to the ground end;
s103: and calculating the stray capacitance of each unit to the high-voltage end.
The stray capacitance of the ith unit to the high-voltage end is as follows:
Cih＝-Ci1 (9)
and calculating in sequence to obtain the stray capacitance of all the units to the high-voltage end.
S2: according to the obtained stray capacitance of each unit, the voltage distribution of the resistance voltage divider is obtained by using a node voltage method;
s201: in step S1, the resistive divider is divided into n tiny units, and when n is large enough, each tiny unit is regarded as a node, the ground is regarded as a reference node, and the voltage of the high-voltage end node is set as
Figure BDA0001793367110000055
The node voltage equation is:
Figure BDA0001793367110000056
matrix YBIn the form of a node admittance matrix,
Figure BDA0001793367110000057
is a vector of node voltages,
Figure BDA0001793367110000059
Injecting current into the nodeQuantity, expanded in matrix form:
Figure BDA0001793367110000058
in the matrix
Figure BDA0001793367110000061
A current is injected for the node i and,
Figure BDA0001793367110000062
is the voltage to ground for node i, i ═ 1,2 … n;
Yiiis a self-admittance, whose value is equal to the current injected into the network via node i when a unit voltage is applied to node i and all other nodes are grounded;
Figure BDA0001793367110000063
Yijis a mutual admittance, whose value is equal to the current injected into the network via node j when a unit voltage is applied to node i and all other nodes are grounded;
when i is 1
Figure BDA0001793367110000064
② when i > 1 and j > i
Figure BDA0001793367110000065
Node i injects current in addition to node 1
Figure BDA0001793367110000066
By
Figure BDA0001793367110000067
And
Figure BDA0001793367110000068
two parts are formed;
Figure BDA0001793367110000069
Figure BDA00017933671100000610
the node I injection current I is obtained from the equations (15) and (16)iThe expression is as follows:
Figure BDA00017933671100000611
the node voltage equation is:
Figure BDA00017933671100000612
s202: rewriting and sorting the node voltage equation to obtain n equation sets;
rewriting the above equation (18) as:
Figure BDA0001793367110000071
the left and right sides of the equal sign of the above formula (19) are respectively rewritten as:
Figure BDA0001793367110000072
Figure BDA0001793367110000073
order to
Figure BDA0001793367110000074
Then
Figure BDA0001793367110000075
Let YB″＝P-1YB'
Then
Figure BDA0001793367110000076
The above equations (20) and (21) are rewritten as:
Figure BDA0001793367110000077
finishing to obtain:
Figure BDA0001793367110000081
the form of the expansion equation is
Figure BDA0001793367110000082
Wherein the content of the first and second substances,
Figure BDA0001793367110000083
in order to know the voltage at the high voltage terminal,
Figure BDA0001793367110000084
and
Figure BDA0001793367110000085
n quantities to be calculated;
s203: and calculating the n equations to obtain the voltage distribution of the resistor divider.
S3: and further solving the voltage division ratio and the phase deviation of the stray capacitor to the resistance-type voltage transformer according to the solved voltage distribution. The calculation process of the voltage division ratio and the phase deviation of the resistive voltage transformer in the step S3 is as follows:
calculating the voltage division ratio deviation caused by stray capacitance of the resistance voltage divider body:
Figure BDA0001793367110000086
k in the formulaN＝1+R1/R2The voltage division ratio of an ideal resistance voltage divider;
calculating voltage phase deviation caused by stray capacitance of a resistor voltage divider body:
Figure BDA0001793367110000087
in the above embodiments of the present invention, the descriptions of the respective embodiments have respective emphasis, and for parts that are not described in detail in a certain embodiment, reference may be made to related descriptions of other embodiments.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (2)

1. A method for calculating voltage distribution of a resistance-type voltage transformer considering stray capacitance is characterized by comprising the following steps:
s1: dividing the resistance voltage divider into n tiny units, and calculating the stray capacitance of each unit of the resistance voltage divider; the vector formed by each unit potential is expressed as U epsilon RnAnd the vector formed by the surface charges of each unit is expressed as Q epsilon RnAnd then:
CU＝Q (1)
wherein C is a capacitance coefficient matrix;
s101: calculating the surface charge of each unit;
let the ith unit potential be 1V and other unit potentials be 0VCalculating the surface total charge of each unit to obtain the ith row parameter of the C matrix; wherein the capacitance coefficient of the jth row and ith column is the charge Q on the jth unitj：
Cji＝Qj,j＝1,2,…,n (2)
Dividing all unit surfaces into m surface elements, and assuming that the charge on each surface element is uniformly distributed, then the center point x of any surface element kkThe potential of (A) is:
Figure FDA0002615713830000011
in the formula
Figure FDA0002615713830000012
For bin l at point xkThe resulting potential;
Figure FDA0002615713830000013
is bin k at xkPotential generated by a dot
Figure FDA0002615713830000014
In the formula of0Is a vacuum dielectric constant; a. thekIs the area of bin k; sigmakIs the charge density of bin k; q. q.skSurface charge of bin k
Figure FDA0002615713830000015
In the formula rklIs the distance, s, from the center of bin l to the center of any bin klIs the area of the first surface element, AlIs the l bin, σlThe charge density of the bin l, and m is the number of bins after all cells are divided;
the formula for all bins is calculated as:
Figure FDA0002615713830000016
wherein p is an m-order parameter matrix; q is an m-dimensional column vector consisting of the charge amount of each bin;
Figure FDA0002615713830000017
an m-dimensional column vector composed of the potentials of each bin;
similarly, setting the potentials of all surface elements on the unit i to be 1V, and the potentials of the other surface elements to be 0V, and calculating the formula (6) to obtain the surface charges of all the surface elements; calculated by substituting equation (2):
Figure FDA0002615713830000021
sequentially calculating to obtain the ith row element of the capacitance coefficient matrix C;
the whole capacitance coefficient matrix C can be obtained by a method of sequentially applying potentials to the units for solving;
s102: calculating the stray capacitance of each unit to the ground end;
the stray capacitance of the ith unit to the ground is:
Figure FDA0002615713830000022
calculating in sequence to obtain stray capacitance of all units to the ground end;
s103: calculating the stray capacitance of each unit to the high-voltage end;
the stray capacitance of the ith unit to the high-voltage end is as follows:
Cih＝-Ci1 (9)
calculating in sequence to obtain stray capacitance of all units to the high-voltage end;
s2: according to the obtained stray capacitance of each unit, obtaining the voltage distribution of the resistance voltage divider by using a node voltage method;
s201: in step S1, the resistive divider is divided into n tiny units, and when n is large enough, each tiny unit is regarded as a node, the ground is regarded as a reference node, and the voltage of the high-voltage end node is set as
Figure FDA0002615713830000023
The node voltage equation is:
Figure FDA0002615713830000024
matrix YBIn the form of a node admittance matrix,
Figure FDA0002615713830000025
is a vector of node voltages,
Figure FDA0002615713830000026
Injecting current vectors for nodes, and expanding the current vectors into a matrix form:
Figure FDA0002615713830000027
in the matrix
Figure FDA0002615713830000028
A current is injected for the node i and,
Figure FDA0002615713830000029
is the voltage to ground for node i, i ═ 1,2 … n;
Yiiis a self-admittance, whose value is equal to the current injected into the network via node i when a unit voltage is applied to node i and all other nodes are grounded;
Figure FDA0002615713830000031
Yijis a mutual admittance of a value equal to the unit voltage applied at node i, otherwiseWhen all the nodes are grounded, current is injected into the network through the node j;
when i is 1
Figure FDA0002615713830000032
② when i > 1 and j > i
Figure FDA0002615713830000033
Node i injects current in addition to node 1
Figure FDA0002615713830000034
By
Figure FDA0002615713830000035
And
Figure FDA0002615713830000036
two parts are formed;
Figure FDA0002615713830000037
Figure FDA0002615713830000038
the node I injection current I is obtained from the equations (15) and (16)iThe expression is as follows:
Figure FDA0002615713830000039
the node voltage equation is:
Figure FDA00026157138300000310
s202: rewriting and sorting the node voltage equation to obtain n equation sets;
rewriting the above equation (18) as:
Figure FDA0002615713830000041
the left and right sides of the equal sign of the above formula (19) are respectively rewritten as:
Figure FDA0002615713830000042
Figure FDA0002615713830000043
order to
Figure FDA0002615713830000044
Then
Figure FDA0002615713830000045
Let YB″＝P-1YB'
Then
Figure FDA0002615713830000046
The above equations (20) and (21) are rewritten as:
Figure FDA0002615713830000047
finishing to obtain:
Figure FDA0002615713830000051
the form of the expansion equation is
Figure FDA0002615713830000052
Wherein the content of the first and second substances,
Figure FDA0002615713830000053
in order to know the voltage at the high voltage terminal,
Figure FDA0002615713830000054
and
Figure FDA0002615713830000055
n quantities to be calculated;
s203: obtaining voltage distribution of the resistor divider by operating the n equations;
s3: and further solving the voltage division ratio and the phase deviation of the stray capacitor to the resistance-type voltage transformer according to the solved voltage distribution.
2. The method of claim 1, wherein the resistive voltage transformer voltage division ratio and the phase deviation in step S3 are calculated as follows:
calculating the voltage division ratio deviation caused by stray capacitance of the resistance voltage divider body:
Figure FDA0002615713830000056
k in the formulaN＝1+R1/R2The voltage division ratio of an ideal resistance voltage divider;
calculating voltage phase deviation caused by stray capacitance of a resistor voltage divider body:
Figure FDA0002615713830000057
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