CN110705031B - Excitation inrush current identification method based on second-order Taylor coefficient - Google Patents

Excitation inrush current identification method based on second-order Taylor coefficient Download PDF

Info

Publication number
CN110705031B
CN110705031B CN201910840972.4A CN201910840972A CN110705031B CN 110705031 B CN110705031 B CN 110705031B CN 201910840972 A CN201910840972 A CN 201910840972A CN 110705031 B CN110705031 B CN 110705031B
Authority
CN
China
Prior art keywords
taylor
matrix
inrush current
order
derivative
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201910840972.4A
Other languages
Chinese (zh)
Other versions
CN110705031A (en
Inventor
符玲
宋九渊
王俊雄
熊思宇
麦瑞坤
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Southwest Jiaotong University
Original Assignee
Southwest Jiaotong University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Southwest Jiaotong University filed Critical Southwest Jiaotong University
Priority to CN201910840972.4A priority Critical patent/CN110705031B/en
Publication of CN110705031A publication Critical patent/CN110705031A/en
Application granted granted Critical
Publication of CN110705031B publication Critical patent/CN110705031B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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
    • 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
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/12—Simultaneous equations, e.g. systems of linear equations
    • 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
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G06F17/141—Discrete Fourier transforms
    • G06F17/142—Fast Fourier transforms, e.g. using a Cooley-Tukey type algorithm
    • 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
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
    • G06Q50/06—Electricity, gas or water supply
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02H—EMERGENCY PROTECTIVE CIRCUIT ARRANGEMENTS
    • H02H7/00—Emergency protective circuit arrangements specially adapted for specific types of electric machines or apparatus or for sectionalised protection of cable or line systems, and effecting automatic switching in the event of an undesired change from normal working conditions
    • H02H7/04—Emergency protective circuit arrangements specially adapted for specific types of electric machines or apparatus or for sectionalised protection of cable or line systems, and effecting automatic switching in the event of an undesired change from normal working conditions for transformers
    • H02H7/045—Differential protection of transformers

Abstract

The invention discloses a second-order Taylor coefficient-based excitation inrush current identification method, and relates to the field of relay protection and waveform identification of a power system; which comprises the following steps of 1: judging whether a fault or an excitation inrush current occurs according to whether the differential current is larger than the brake current; step 2: carrying out short-time Fourier transform on the acquired data to acquire reference time phasor; and step 3: establishing a phasor form of an excitation inrush current simplified model; and 4, step 4: taking the set initial frequency value as a fundamental frequency, and constructing an offline matrix and an offline matrix according to the fundamental frequency; and 5: inputting the data obtained in the steps 3 and 4 into the Taylor dynamic model established in the step 2 to solve a Taylor derivative matrix, and solving according to the Taylor derivative matrix to obtain a second-order Taylor coefficient and a logarithm Q thereof; the method solves the problems that the existing magnetizing inrush current identification method causes protection delay action and weak noise resistance when in fault, and achieves the effect of accurately and quickly judging the fault of the transformer during locking.

Description

Excitation inrush current identification method based on second-order Taylor coefficient
Technical Field
The invention relates to the field of relay protection and waveform identification of a power system, in particular to a second-order Taylor coefficient-based excitation inrush current identification method.
Background
With the continuous development of power grids, higher requirements are put on the reliability and the quick action performance of transformer protection on site, for example: in the Zhebei-Fuzhou-Zhefu 1000KV extra-high voltage alternating current transmission project, the transformation capacity reaches 1800WM, and any abnormal action behavior related to the protection of the transformer can cause extremely serious consequences. However, during the voltage recovery process of closing the transformer in the idle state or removing the external fault, the magnetizing inrush current may be generated, which may cause the differential protection to malfunction. At present, an engineering field mainly relies on a second harmonic braking principle and a discontinuous angle braking principle to identify magnetizing inrush current and lock differential protection. However, with the development and application of the power grid technology, the fault signal components are more complex, and the second harmonic braking principle is misjudged due to various reasons. For example, the cold rolled silicon steel sheet is commonly used as the iron core of the large transformer at present, which reduces the second harmonic content of the magnetizing inrush current. In addition, in the voltage recovery process after the external fault of the power transformer is removed, due to the combined action of the error current of the current transformer and the recovery excitation surge current, the proportion of the second harmonic can be reduced, and the differential protection misoperation is caused; the high-voltage long-distance transmission line has distributed capacitance, and the generated harmonic current can increase the content of the second harmonic of the fault current.
The development of a power grid makes the fault signal components of the transformer complex and simultaneously puts higher requirements on the protection of the transformer, and the existing magnetizing inrush current identification scheme is difficult to meet the requirement of accurately and quickly judging the fault of the transformer during the locking period. Therefore, the invention provides a magnetizing inrush current identification method with strong anti-interference performance and high discrimination speed based on the second-order Taylor coefficient. The existing method for identifying the magnetizing inrush current can be mainly divided into two categories, wherein one category is an identification method based on the waveform characteristics of the magnetizing inrush current. The method is simple and easy to implement, can quickly identify the magnetizing inrush current, and has good noise resistance. However, when an intra-area fault occurs, the method can firstly lock the protection and then open the protection after a short time, so that the delay action of the differential protection is caused. The other type is an identification method based on the electrical characteristics of the magnetizing inrush current. The method has strong identification capability, has good robustness for current transformer saturation, and has weak anti-interference performance. Therefore, it is necessary to provide a magnetizing inrush current identification method with high anti-interference performance and high determination speed.
Disclosure of Invention
The invention aims to: the invention provides a magnetizing inrush current identification method based on a second-order Taylor coefficient, which solves the problems that the existing magnetizing inrush current identification method causes protection delay action and weak noise resistance when in fault, and achieves the effect of accurately and quickly judging the fault of a transformer during locking.
The technical scheme adopted by the invention is as follows:
a magnetizing inrush current identification method based on a second-order Taylor coefficient comprises the following steps:
step 1: judging whether a fault or an excitation inrush current occurs according to whether the differential current is larger than the brake current;
step 2: carrying out short-time Fourier transform on the acquired data to acquire phasors X (-omega), X (0) and X (omega) at reference time;
and step 3: establishing a phasor form of the excitation inrush current simplified model, and obtaining a Taylor derivative matrix S and a second-order Taylor coefficient q by using Taylor expansion on the phasor model S (t)2And its logarithm Q;
the step 3 comprises the following steps:
step 3.1: establishing a simplified excitation inrush current model:
Figure GDA0003030512210000021
in the formula: t represents time; a. the1(t) represents the time-varying amplitude of the fundamental frequency component, f1Which represents the fundamental frequency of the wave,
Figure GDA0003030512210000022
representing the initial phase angle of the fundamental frequency component; a. therRepresenting the amplitude of the order r harmonic, frThe frequency of the order r of the harmonic is represented,
Figure GDA0003030512210000023
representing the initial phase angle of the R harmonic, R representing the total harmonic order in the signal(ii) a The main characteristics of the magnetizing inrush current are represented in fundamental frequency components and second harmonic components, and the power signal is subjected to simplified modeling based on the purpose of identifying the magnetizing inrush current:
Figure GDA0003030512210000024
in the formula: delta represents an error term of the simplified model, namely components except a fundamental frequency component and a second harmonic component in the signal; the phasor form of the simplified model can be expressed as:
Figure GDA0003030512210000031
step 3.2: expanding the phasor model S (t) to K order by using Taylor to obtain a power signal expression and a Taylor derivative matrix S:
taylor expansion for solving the first and second order coefficients of S (t):
Figure GDA0003030512210000032
wherein K is the maximum order of the Taylor series; s(k)Denotes the K derivative of S (t); deltaSAn error term which is a Taylor series; obtaining an expression of the power signal:
Figure GDA0003030512210000033
the sampling frequency is expressed as follows:
Figure GDA0003030512210000034
in the formula: f. ofsRepresents the sampling frequency; n-tfsRepresenting discrete sample points; s*Denotes the conjugation of s, s(k)＝S(k)(fs)-k，ω0＝2πf0/fs，f0Is the filtering frequency; obtaining Taylor derivative matrix as s [ s ](0)，…，s(K)]T
Step 3.3: the phasor model S (t) is expressed by a magnitude/phase angle model, and the exponential part is expanded by Taylor to obtain a Taylor derivative matrix S and a second-order Taylor coefficient q2And the logarithm Q:
phasor s (t) can be expressed as a magnitude/phase angle model:
Figure GDA0003030512210000035
in the formula: sm(t) represents the magnitude component of s (t);
Figure GDA0003030512210000036
represents the phase angle component of S (t);
expressing the phase angle component and the amplitude component of S (t) in an exponential form of e, and performing second-order Taylor expansion on an exponential part:
Figure GDA0003030512210000041
in the formula: p is a radical of0，p1，p2Is S (t) the zeroth, first and second order Taylor coefficients of the magnitude component exponent, q0，q1，q2For S (t) the zeroth, first and second Taylor coefficients of the phase angle component index, the first and second derivatives are calculated for S (t):
Figure GDA0003030512210000042
Figure GDA0003030512210000043
by combining the above equations, solving the system of equations can yield:
Figure GDA0003030512210000044
Figure GDA0003030512210000045
to q is2Taking the logarithm can obtain Q:
Q＝log10(q2)。
and 4, step 4: taking the set initial frequency value as a fundamental frequency, and constructing an offline matrix C and an offline matrix D according to the fundamental frequency;
and 5: inputting the data obtained in the steps 2 and 4 into a Taylor dynamic model to solve a Taylor derivative matrix S, and solving according to the Taylor derivative matrix S to obtain a second-order Taylor coefficient q2And its logarithm Q;
step 6: judging whether Q is greater than a setting value, if not, identifying the Q as an internal fault, and opening protection; if yes, the circuit is identified as excitation surge current, and protection is locked.
Preferably, the step 4 comprises the steps of:
step 4.1: taking a set initial frequency value as a fundamental frequency, wherein the initial frequency value is 50 Hz;
step 4.2: and (3) constructing an offline matrix C and an offline matrix D according to the preliminary frequency values:
C(ω)=[H(0，2ω0+ω)，…，H(K，2ω0+ω)]
D(ω)＝[H(0，ω)，…，H(K，ω)]
Figure GDA0003030512210000051
in the formula: ω represents the offset frequency, h (n) represents the sampling window function, and M represents the total number of samples within a sampling window.
Preferably, the step 5 comprises the steps of:
step 5.1: substituting the reference time phasors X (-omega), X (0), X (omega), the off-line matrix C and the off-line matrix D into an equation established by using short-time Fourier transform, and solving a Taylor derivative matrix S:
Figure GDA0003030512210000052
wherein, constructing the Taylor derivative matrix S according to step 3 is: s ═ S(0)，s(1)…s(K)]T
Step 5.2: satisfy | HTUnder the condition that H | ≠ 0, solving taylor derivative values of each order of the taylor derivative matrix S after virtual-real separation by adopting a least square fitting parameter estimation method LSM:
S＝(HT·H)-1HT·X
H＝[G-u，…，Gi-1，Gi，Gi+1，…，Gu]
wherein the content of the first and second substances,
Figure GDA0003030512210000053
where Re () represents the real-valued operation, Im () represents the imaginary-valued operation, HTDenotes the transpose operation of the H matrix, (H)T·H)-1Representative pair matrix (H)TH) inversion, i represents the number of filtering frequencies, u represents the number of sampling windows, i and u are taken to be 1. .
Step 5.3: setting K to be 2, and selecting three different omega values to obtain different equations; the unknown quantity is a matrix S, and the simultaneous equations solve the matrix S through a least square method, namely, the phasor value, the first derivative value and the second derivative value of S (t) at the reference moment are solved; thus, q can be obtained by substituting the calculated S (t) and the derivatives of each order2。
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
1. the invention aims at the practical engineering problem of transformer magnetizing inrush current identification, namely the problem that the existing magnetizing inrush current identification method can lock protection in a short time when a fault occurs, so that the transformer protection delay action is caused and the anti-interference performance is insufficient. In order to improve the rapidity and the anti-interference performance of the magnetizing inrush current identification method and ensure the rapid removal of the fault by the transformer protection, the difference between the magnetizing inrush current and the fault current in the aspects of the second harmonic content, the change speed of the fundamental frequency component and the like is considered, the invention provides the magnetizing inrush current identification method based on the second-order Taylor coefficient, which can ensure the protection to have no time-delay action when the fault occurs and has strong anti-interference capability.
2. The method utilizes Taylor series to establish a dynamic excitation surge current model, represents the dynamic change characteristics of secondary harmonic waves and fundamental waves under the condition of excitation surge current, and better fits the dynamic change characteristics contained in the excitation surge current in the actual power grid. The second-order Taylor coefficient extracted from the dynamic model can reflect electrical characteristics such as second harmonic content, change speed of fundamental frequency components and the like. Therefore, the excitation inrush current identification method does not depend on a single electric quantity any more, but comprehensively considers a plurality of electric information for identification, and further improves the reliability of the identification method.
3. The invention adopts frequency domain measurement to estimate and identify the criterion, has small calculated amount, and can be suitable for online application without additional equipment such as a voltage transformer and the like.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a diagram showing the relationship between the second-order Taylor coefficient and the second harmonic and fundamental wave change rate.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
It is noted that relational terms such as "first" and "second," and the like, may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
The technical problem is as follows: the problems that the protection delay action is caused and the anti-noise capability is weak when the existing excitation inrush current identification method is in failure are solved;
the technical means is as follows: a magnetizing inrush current identification method based on a second-order Taylor coefficient comprises the following steps:
step 1: judging whether a fault or an excitation inrush current occurs according to whether the differential current is larger than the brake current;
step 2: carrying out short-time Fourier transform on the acquired data to acquire phasors X (-omega), X (0) and X (omega) at reference time;
and step 3:establishing a phasor form of the excitation inrush current simplified model, and obtaining a Taylor derivative matrix S and a second-order Taylor coefficient q by using Taylor expansion on the phasor model S (t)2And its logarithm Q;
the step 3 comprises the following steps:
step 3.1: establishing a simplified excitation inrush current model:
Figure GDA0003030512210000081
in the formula: t represents time; a. the1(t) represents the time-varying amplitude of the fundamental frequency component, f1Which represents the fundamental frequency of the wave,
Figure GDA0003030512210000082
representing the initial phase angle of the fundamental frequency component; a. therRepresenting the amplitude of the order r harmonic, frThe frequency of the order r of the harmonic is represented,
Figure GDA0003030512210000083
representing the initial phase angle of the R harmonic, wherein R represents the total harmonic number in the signal; the main characteristics of the magnetizing inrush current are represented in fundamental frequency components and second harmonic components, and the power signal is subjected to simplified modeling based on the purpose of identifying the magnetizing inrush current:
Figure GDA0003030512210000084
in the formula: delta represents an error term of the simplified model, namely components except a fundamental frequency component and a second harmonic component in the signal; the phasor form of the simplified model can be expressed as:
Figure GDA0003030512210000085
step 3.2: expanding the phasor model S (t) to K order by using Taylor to obtain a power signal expression and a Taylor derivative matrix S:
taylor expansion for solving the first and second order coefficients of S (t):
Figure GDA0003030512210000091
wherein K is the maximum order of the Taylor series; s(k)Denotes the K derivative of S (t); deltaSAn error term which is a Taylor series; obtaining an expression of the power signal:
Figure GDA0003030512210000092
the sampling frequency is expressed as follows:
Figure GDA0003030512210000093
in the formula: f. ofsRepresents the sampling frequency; n-tfsRepresenting discrete sample points; s*Denotes the conjugation of s, s(k)＝S(k)(fs)-k，ω0＝2πf0/fs，f0Is the filtering frequency; obtaining Taylor derivative matrix as s [ s ](0)，…，s(K)]T
Step 3.3: the phasor model S (t) is expressed by a magnitude/phase angle model, and the exponential part is expanded by Taylor to obtain a Taylor derivative matrix S and a second-order Taylor coefficient q2And the logarithm Q:
phasor s (t) can be expressed as a magnitude/phase angle model:
Figure GDA0003030512210000094
in the formula: sm(t) represents the magnitude component of s (t);
Figure GDA0003030512210000095
represents the phase angle component of S (t);
expressing the phase angle component and the amplitude component of S (t) in an exponential form of e, and performing second-order Taylor expansion on an exponential part:
Figure GDA0003030512210000096
in the formula: p is a radical of0，p1，p2Is S (t) the zeroth, first and second order Taylor coefficients of the magnitude component exponent, q0，q1，q2For S (t) the zeroth, first and second Taylor coefficients of the phase angle component index, the first and second derivatives are calculated for S (t):
Figure GDA0003030512210000097
Figure GDA0003030512210000101
by combining the above equations, solving the system of equations can yield:
Figure GDA0003030512210000102
Figure GDA0003030512210000103
to q is2Taking the logarithm can obtain Q:
Q＝log10(q2)。
and 4, step 4: taking the set initial frequency value as a fundamental frequency, and constructing an offline matrix C and an offline matrix D according to the fundamental frequency;
and 5: solving the Taylor derivative matrix S of the data input Taylor dynamic model obtained in the steps 2 and 4, and solving the Taylor derivative matrix S to obtain a second-order Taylor coefficient q2And its logarithm Q;
step 6: judging whether Q is greater than a setting value, if not, identifying the Q as an internal fault, and opening protection; if yes, the circuit is identified as excitation surge current, and protection is locked.
The step 4 comprises the following steps:
step 4.1: taking a set initial frequency value as a fundamental frequency, wherein the initial frequency value is 50 Hz;
step 4.2: and (3) constructing an offline matrix C and an offline matrix D according to the preliminary frequency values:
C(ω)=[H(0，2ω0+ω)，…，H(K，2ω0+ω)]
D(ω)＝[H(0，ω)，…，H(K，ω)]
Figure GDA0003030512210000104
in the formula: ω represents the offset frequency, h (n) represents the sampling window function, and M represents the total number of samples within a sampling window.
The step 5 comprises the following steps:
step 5.1: substituting the reference time phasors X (-omega), X (0), X (omega), the off-line matrix C and the off-line matrix D into an equation established by using short-time Fourier transform, and solving a Taylor derivative matrix S:
Figure GDA0003030512210000111
wherein, constructing the Taylor derivative matrix S according to step 3 is: s ═ S(0),s(1)…s(K)]T
Step 5.2: satisfy | HTUnder the condition that H | ≠ 0, solving taylor derivative values of each order of the taylor derivative matrix S after virtual-real separation by adopting a least square fitting parameter estimation method LSM:
S＝(HT.H)-1HT.X
H＝[G-u，…，Gi-1，Gi，Gi+1，…，Gu]
wherein the content of the first and second substances,
Figure GDA0003030512210000112
where Re () represents the real-valued operation, Im () represents the imaginary-valued operation, HTDenotes the transpose operation of the H matrix, (H)T·H)-1Representative pair matrix (H)TH) inversion, i represents the number of filtering frequencies, u represents the number of sampling windows, i and u are taken to be 1. .
Step 5.3: setting K to 2, and selecting different filtering frequencies and offset frequencies to obtain different equations, preferably, selecting three different ω values; the unknown quantity is a matrix S, and the simultaneous equations solve the matrix S through a least square method, namely, the phasor value, the first derivative value and the second derivative value of S (t) at the reference moment are solved; thus, q can be obtained by substituting the calculated S (t) and the derivatives of each order2。
The technical effects are as follows: aiming at the practical engineering problem of transformer magnetizing inrush current identification, the invention aims at solving the problem that the existing magnetizing inrush current identification method can lock protection in a short time when a fault occurs, so that the transformer protection delay action is caused and the anti-interference performance is insufficient. In order to improve the rapidity and the anti-interference performance of the magnetizing inrush current identification method and ensure the rapid removal of the fault by the transformer protection, the difference between the magnetizing inrush current and the fault current in the aspects of the second harmonic content, the change speed of the fundamental frequency component and the like is considered, the invention provides the magnetizing inrush current identification method based on the second-order Taylor coefficient, which can ensure the protection to have no time-delay action when the fault occurs and has strong anti-interference capability.
The features and properties of the present invention are described in further detail below with reference to examples.
Example 1
As shown in fig. 1-2, a method for identifying inrush current based on second-order taylor coefficients includes the following steps:
step 1: judging whether a fault or an excitation inrush current occurs according to whether the differential current is larger than the brake current;
step 2: carrying out short-time Fourier transform on the acquired data to acquire phasors X (-omega), X (0) and X (omega) at reference time;
and step 3: establishing a phasor form of the excitation inrush current simplified model, and obtaining a Taylor derivative matrix S and a Taylor derivative matrix T by using Taylor expansion on the phasor model S (t)Second order Taylor coefficient q2And its logarithm Q;
and 4, step 4: taking the set initial frequency value as a fundamental frequency, and constructing an offline matrix C and an offline matrix D according to the fundamental frequency;
and 5: solving a Taylor derivative matrix S by the Taylor dynamic model of the data obtained in the steps 2 and 4, and solving a second-order Taylor coefficient q according to the Taylor derivative matrix S2And its logarithm Q;
step 6: judging whether Q is greater than a setting value, if not, identifying the Q as an internal fault, and opening protection; if yes, the circuit is identified as excitation surge current, and protection is locked.
Step 1, discrete sampling is carried out on voltage/current signals in a power grid by adopting an ADC (analog to digital converter), a discrete sequence x (n) of a differential current signal of a transformer is obtained, wherein n is the discrete sampling time of the ADC, and whether a fault or excitation surge current occurs is determined by judging the magnitude of the differential current and the braking current.
Step 2, performing short-time STFT with a window function h (n) on X (n) by adopting a DSP (digital signal processor) at the rated frequency of 50Hz of the power system to obtain STFT phasor values X (-omega), X (0) and X (omega) of a reference moment, wherein omega is a short-time Fourier transform time offset frequency point;
and 3, establishing a phasor form of the excitation inrush current simplified model by using Taylor series expansion, and obtaining a Taylor derivative matrix S by using the Taylor expansion of the phasor model S (t). Meanwhile, Taylor expansion is carried out on the exponential part of the phasor model S (t) by using the amplitude/phase angle model to obtain a second-order Taylor coefficient q2And its logarithm Q;
and 4, taking the 50Hz frequency as a set frequency initial value, and constructing an offline matrix C and an offline matrix D according to the set fundamental frequency.
The step 5 comprises the following steps:
step 5.1: substituting the reference time phasors X (-omega), X (0), X (omega), the off-line matrix C and the off-line matrix D into an equation established by using short-time Fourier transform, and solving a Taylor derivative matrix S:
Figure GDA0003030512210000131
wherein, constructing the Taylor derivative matrix S according to step 3 is: s ═ S(0),s(1)…s(K)]T
Step 5.2: satisfy | GTUnder the condition that G | ≠ 0, solving taylor derivative values of each order of the taylor derivative matrix S after virtual-real separation by adopting a least square fitting parameter estimation method LSM:
S＝(GT·G)-1GT·X
wherein the content of the first and second substances,
Figure GDA0003030512210000132
where Re () represents the real-valued operation, Im () represents the imaginary-valued operation, GTDenotes the transpose operation of the G matrix, (G)T·G)-1Representative pair matrix (G)TG) inversion.
Step 5.3: setting K to 2, and selecting different filtering frequencies and offset frequencies to obtain different equations; the unknown quantity is a matrix S, and the simultaneous equations solve the matrix S through a least square method, namely, the phasor value, the first derivative value and the second derivative value of S (t) at the reference moment are solved; thus, q can be obtained by substituting the calculated S (t) and the derivatives of each order2。
The invention provides a magnetizing inrush current identification method based on a second-order Taylor coefficient, aiming at the problem that the existing magnetizing inrush current identification method can be locked and protected for a short time when a fault occurs, so that the transformer protection time-delay action is caused, and the anti-interference performance is insufficient. The method can ensure the protection without time delay action when the fault occurs and has stronger anti-jamming capability.
In order to verify the recognition effect of the method under the condition of excitation inrush current, the rapidity, the anti-interference performance and the reliability of the method are verified through a PSCAD/EMTDC simulation platform; the basic parameters of the simulation model of the method are set as follows: the connection group is YNd11, the rated capacity is 50MVA, and the rated voltage is 35/10 kV. A three-phase power supply M is used to equate the left system with line voltage set at 35 kV. The simulation time length of each example is 1.5s, the sampling frequency of the difference stream and the standard sine wave sequence is 2400Hz, and 48 sampling points are arranged in each cycle. Sampling a periodic wave data window which is long, setting three frequency points by adopting a rectangular window as the data window, wherein the offset is 1rad, and taking a Taylor expansion coefficient K to be 2; and setting the action threshold value for identifying the magnetizing inrush current criterion Q to be Qset equal to 4.8.
The results of the inventive method compared to the second harmonic braking method are shown in table 1:
TABLE 1 comparison of second harmonic braking with a second order Taylor coefficient criterion
Figure GDA0003030512210000141
Figure GDA0003030512210000151
As can be seen from Table 1, the discrimination time required by the method of the invention is shorter than that of the second harmonic braking method under various working conditions, and the accurate identification of the magnetizing inrush current can be ensured under extreme conditions, thereby reflecting the great advantages of the method in the aspects of reliability and quick-acting property.
Example 2
As shown in fig. 1-2, based on example 1, step 3: a dynamic excitation inrush current model is established by using Taylor series, the dynamic change characteristics of second harmonic waves and fundamental waves under the condition of excitation inrush current are represented, and the dynamic change characteristics included in the excitation inrush current in an actual power grid are better fitted. And (3) obtaining a Taylor derivative matrix S by using a Taylor expansion part of the phasor model S (t). Meanwhile, Taylor expansion is carried out on the exponential part of the phasor model S (t) by using the amplitude/phase angle model to obtain a second-order Taylor coefficient q2And its logarithm Q. The second-order Taylor coefficient extracted from the dynamic model can reflect electrical characteristics such as second harmonic content, change speed of fundamental frequency components and the like. Therefore, the excitation inrush current identification method does not depend on a single electric quantity any more, but comprehensively considers a plurality of electric information for identification, and further improves the reliability of the identification method.
The step 3 comprises the following steps:
step 3.1: establishing a simplified excitation inrush current model:
Figure GDA0003030512210000161
in the formula: t represents time; a. the1(t) represents the time-varying amplitude of the fundamental frequency component, f1Which represents the fundamental frequency of the wave,
Figure GDA0003030512210000162
representing the initial phase angle of the fundamental frequency component; a. therRepresenting the amplitude of the order r harmonic, frThe frequency of the order r of the harmonic is represented,
Figure GDA0003030512210000163
representing the initial phase angle of the R harmonic, wherein R represents the total harmonic number in the signal; the main characteristics of the magnetizing inrush current are represented in fundamental frequency components and second harmonic components, and the power signal is subjected to simplified modeling based on the purpose of identifying the magnetizing inrush current:
Figure GDA0003030512210000164
in the formula: delta represents an error term of the simplified model, namely components except a fundamental frequency component and a second harmonic component in the signal; the phasor form of the simplified model can be expressed as:
Figure GDA0003030512210000165
step 3.2: expanding the phasor model S (t) to K order by using Taylor to obtain a power signal expression and a Taylor derivative matrix S:
taylor expansion for solving the first and second order coefficients of S (t):
Figure GDA0003030512210000166
wherein K is the maximum order of the Taylor series; s(k)Denotes the K derivative of S (t); deltaSIs a Taylor seriesThe error term of (2); due to load fluctuation factors, the signals of the power system present dynamic characteristics, and the second-order Taylor expansion obtains an accurate fitting result, so that an error term delta of a Taylor series is ignoredS(ii) a Obtaining an expression of the power signal:
Figure GDA0003030512210000167
the sampling frequency is expressed as follows:
Figure GDA0003030512210000168
in the formula: f. ofsRepresents the sampling frequency; n-tfsRepresenting discrete sample points; s*Denotes the conjugation of s, s(k)＝S(k)(fs)-k，ω0＝2πf0/fs，f0Is the filtering frequency; obtaining Taylor derivative matrix as S [ S ](0)，…，s(K)]T
Step 3.3: expressing the phasor model S (t) by using a magnitude/phase angle model, and obtaining a Taylor derivative matrix S and a second-order Taylor coefficient q by using Taylor expansion on an exponential part2And the logarithm Q:
phasor s (t) can be expressed as a magnitude/phase angle model:
Figure GDA0003030512210000171
in the formula: sm(t) represents the magnitude component of s (t);
Figure GDA0003030512210000172
represents the phase angle component of S (t);
expressing the phase angle component and the amplitude component of S (t) in an exponential form of e, and performing second-order Taylor expansion on an exponential part:
Figure GDA0003030512210000173
in the formula: p is a radical of0，p1，p2Is S (t) the zeroth, first and second order Taylor coefficients of the magnitude component exponent, q0，q1，q2For S (t) the zeroth, first and second Taylor coefficients of the phase angle component index, the first and second derivatives are calculated for S (t):
Figure GDA0003030512210000174
Figure GDA0003030512210000175
by combining the above equations, solving the system of equations can yield:
Figure GDA0003030512210000176
Figure GDA0003030512210000177
to q is2Taking the logarithm can obtain Q:
Q＝log10(q2)。
in order to better fit the dynamic change characteristics contained in the magnetizing inrush current in the actual power grid by considering the dynamic change characteristics of the second harmonic and the fundamental wave under the condition of the magnetizing inrush current, the invention establishes a signal dynamic model by using Taylor series and deduces a second-order Taylor coefficient from the dynamic model. The second-order Taylor coefficient is influenced by a plurality of electrical quantities such as second harmonic content, fundamental frequency component change rate, initial phase angle and the like, and can reflect multidimensional electrical characteristics such as second harmonic content, fundamental frequency component change speed and the like. The traditional magnetizing inrush current identification method usually depends on single electrical information for judgment, so that the condition of wrong judgment can occur under extreme working conditions. The excitation inrush current identification method based on the second-order Taylor coefficient is used for judging based on a plurality of pieces of electrical information, and has better adaptability and higher reliability under the condition of coping with the complexity and the changeability of a power network.
While there have been shown and described what are at present considered the fundamental principles and essential features of the invention and its advantages, it will be apparent to those skilled in the art that the invention is not limited to the details of the foregoing exemplary embodiments, but is capable of other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.

Claims (3)

1. A magnetizing inrush current identification method based on a second-order Taylor coefficient is characterized in that: the method comprises the following steps:
step 1: judging whether the power signal is abnormal according to whether the differential current is larger than the brake current or not, and starting an excitation inrush current identification criterion according to the judgment;
step 2: carrying out short-time Fourier transform on the acquired data to acquire phasors X (-omega), X (0) and X (omega) at reference time;
and step 3: establishing a phasor form of the excitation inrush current simplified model, and obtaining a Taylor derivative matrix S and a second-order Taylor coefficient q by using Taylor expansion on the phasor model S (t)2And its logarithm Q;
the step 3 comprises the following steps:
step 3.1: establishing a simplified excitation inrush current model:
Figure FDA0003030512200000011
in the formula: t represents time; a. the1(t) represents the time-varying amplitude of the fundamental frequency component, f1Which represents the fundamental frequency of the wave,
Figure FDA0003030512200000012
representing the initial phase angle of the fundamental frequency component; a. therRepresenting the amplitude of the order r harmonic, frThe frequency of the order r of the harmonic is represented,
Figure FDA0003030512200000013
representing the initial phase angle of the R harmonic, wherein R represents the total harmonic number in the signal; the main characteristics of the magnetizing inrush current are represented in fundamental frequency components and second harmonic components, and the power signal is subjected to simplified modeling based on the purpose of identifying the magnetizing inrush current:
Figure FDA0003030512200000014
in the formula: delta represents an error term of the simplified model, namely components except a fundamental frequency component and a second harmonic component in the signal; the phasor form of the simplified model can be expressed as:
Figure FDA0003030512200000015
step 3.2: expanding the phasor model S (t) to K order by using Taylor to obtain a power signal expression and a Taylor derivative matrix S:
taylor expansion for solving the first and second order coefficients of S (t):
Figure FDA0003030512200000021
wherein K is the maximum order of the Taylor series; s(k)Denotes the K derivative of S (t); deltaSAn error term which is a Taylor series; obtaining an expression of the power signal:
Figure FDA0003030512200000022
the sampling frequency is expressed as follows:
Figure FDA0003030512200000023
in the formula: f. ofsRepresents the sampling frequency; n-tfsRepresenting discrete sample points; s*Denotes the conjugation of s, s(k)＝S(k)(fs)-k，ω0＝2πf0/fs，f0Is the filtering frequency; obtaining Taylor derivative matrix as s ═ s(0)，…，s(K)]T
Step 3.3: the phasor model S (t) is expressed by a magnitude/phase angle model, and the exponential part is expanded by Taylor to obtain a Taylor derivative matrix S and a second-order Taylor coefficient q2And the logarithm Q:
phasor s (t) can be expressed as a magnitude/phase angle model:
Figure FDA0003030512200000024
in the formula: sm(t) represents the magnitude component of s (t);
Figure FDA0003030512200000025
represents the phase angle component of S (t);
expressing the phase angle component and the amplitude component of S (t) in an exponential form of e, and performing second-order Taylor expansion on an exponential part:
Figure FDA0003030512200000026
in the formula: p is a radical of0，p1，p2Is S (t) the zeroth, first and second order Taylor coefficients of the magnitude component exponent, q0，q1，q2For S (t) the zeroth, first and second Taylor coefficients of the phase angle component index, the first and second derivatives are calculated for S (t):
Figure FDA0003030512200000027
Figure FDA0003030512200000031
by combining the above equations, solving the system of equations can yield:
Figure FDA0003030512200000032
Figure FDA0003030512200000033
to q is2Taking the logarithm can obtain Q:
Q＝log10(q2)；
and 4, step 4: taking the set initial frequency value as a fundamental frequency, and constructing an offline matrix C and an offline matrix D according to the fundamental frequency;
and 5: inputting the data obtained in the steps 2 and 4 into a Taylor dynamic model to solve a Taylor derivative matrix S, and solving according to the Taylor derivative matrix S to obtain a second-order Taylor coefficient q2And its logarithm Q;
step 6: judging whether Q is greater than a setting value, if not, identifying the Q as an internal fault, and opening protection; if yes, the circuit is identified as excitation surge current, and protection is locked.
2. The method for identifying the magnetizing inrush current based on the second-order Taylor coefficient as claimed in claim 1, wherein: the step 4 comprises the following steps:
step 4.1: taking a set initial frequency value as a fundamental frequency, wherein the initial frequency value is 50 Hz;
step 4.2: and (3) constructing an offline matrix C and an offline matrix D according to the preliminary frequency values:
C(ω)＝[H(0，2ω0+ω)，…，H(K，2ω0+ω)]
D(ω)＝[H(0，ω)，…，H(K，ω)]
Figure FDA0003030512200000034
in the formula: ω represents the offset frequency, h (n) represents the sampling window function, and M represents the total number of samples within a sampling window.
3. The method for identifying the magnetizing inrush current based on the second-order Taylor coefficient as claimed in claim 1, wherein: the step 5 comprises the following steps:
step 5.1: substituting the reference time phasors X (-omega), X (0), X (omega), the off-line matrix C and the off-line matrix D into an equation established by using short-time Fourier transform, and solving a Taylor derivative matrix S:
Figure FDA0003030512200000041
wherein, constructing the Taylor derivative matrix S according to step 3 is: s ═ S(0)，s(1)…s(K)]T
Step 5.2: satisfy | HTUnder the condition that H | ≠ 0, solving taylor derivative values of each order of the taylor derivative matrix S after virtual-real separation by adopting a least square fitting parameter estimation method LSM:
S＝(HT·H)-1HT·X
wherein，
Figure FDA0003030512200000042
Wherein, S ═ Re (S)-u T)，Im(S-u T)，…，Re(Si T)，Im(Si T)，…，Re(Su T)，Im(Su T)]T
Where Re () represents the real-valued operation, Im () represents the imaginary-valued operation, HTDenotes the transpose operation of the H matrix, (H)T·H)-1Representative pair matrix (H)TH) inversion, i represents the number of filtering frequencies, u represents the number of sampling windows, i and u are taken to be 1;
step 5.3: setting K to be 2, and selecting three different omega values to obtain different equations; the unknown quantity is a matrix S, and the simultaneous equations solve the matrix S through a least square method, namely, the phasor value, the first derivative value and the second derivative value of S (t) at the reference moment are solved; thus, q can be obtained by substituting the calculated S (t) and the derivatives of each order2。
CN201910840972.4A 2019-09-06 2019-09-06 Excitation inrush current identification method based on second-order Taylor coefficient Active CN110705031B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910840972.4A CN110705031B (en) 2019-09-06 2019-09-06 Excitation inrush current identification method based on second-order Taylor coefficient

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910840972.4A CN110705031B (en) 2019-09-06 2019-09-06 Excitation inrush current identification method based on second-order Taylor coefficient

Publications (2)

Publication Number Publication Date
CN110705031A CN110705031A (en) 2020-01-17
CN110705031B true CN110705031B (en) 2021-07-06

Family

ID=69194591

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910840972.4A Active CN110705031B (en) 2019-09-06 2019-09-06 Excitation inrush current identification method based on second-order Taylor coefficient

Country Status (1)

Country Link
CN (1) CN110705031B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116187064B (en) * 2023-02-14 2024-03-12 中国科学院国家空间科学中心 Numerical simulation method for second derivative of continuous signal time sequence

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105140893A (en) * 2015-07-27 2015-12-09 许继集团有限公司 Differential protection current transformer (CT) saturation recognition method
CN107765076A (en) * 2016-08-19 2018-03-06 中国电力科学研究院 A kind of excitation flow recognition method and identification device
CN109324228A (en) * 2018-11-21 2019-02-12 西南交通大学 It is a kind of based on multi-frequency-Taylor's dynamic model synchronous phasor measuring method

Family Cites Families (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3832600A (en) * 1973-05-17 1974-08-27 Westinghouse Electric Corp Transformer internal fault detector
CN101764391B (en) * 2009-08-20 2012-10-03 北京四方继保自动化股份有限公司 Method and system for braking magnetizing inrush current in differential protection of ultra-high voltage transformer
CN102570392A (en) * 2012-01-17 2012-07-11 上海电力学院 Method for identifying exciting inrush current of transformer based on improved probability neural network
CN103675415B (en) * 2012-08-31 2017-03-01 西门子公司 Excitation surge current detection method, braking magnetizing inrush current method and its device
CN103545789B (en) * 2013-08-26 2016-12-28 江苏科技大学 The excitation surge current fuzzy recognition method of transformer differential protection
CN103683198B (en) * 2013-12-03 2017-01-04 昆明理工大学 The excitation surge current method for quickly identifying of consecutive points distance in a kind of plane based on difference current adjacent order difference composition
US9891289B2 (en) * 2014-06-03 2018-02-13 Cooper Technologies Company Power transformer inrush current detector
CN104200055B (en) * 2014-09-26 2017-06-20 国家电网公司 Inrush Simulation method and device in the case of extra-high voltage transformer idle-loaded switching-on
CN108399147B (en) * 2018-01-25 2021-07-13 山东科技大学 Transformer excitation inrush current identification method based on MEEMD algorithm
CN109103847B (en) * 2018-08-01 2019-12-20 西南交通大学 Converter transformer saturation protection method based on direct current component estimation

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105140893A (en) * 2015-07-27 2015-12-09 许继集团有限公司 Differential protection current transformer (CT) saturation recognition method
CN107765076A (en) * 2016-08-19 2018-03-06 中国电力科学研究院 A kind of excitation flow recognition method and identification device
CN109324228A (en) * 2018-11-21 2019-02-12 西南交通大学 It is a kind of based on multi-frequency-Taylor's dynamic model synchronous phasor measuring method

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
An empirical Fourier transform-based power transfomer differential protection;Senthil Kumar Murugan, Sishaj P Simon, Kinattingal Sundareswaran;《IEEE TRANSACTIONS ON POWER DELIVERY》;20170228;全文 *
利用半波傅里叶算法的两面积法识别励磁涌流;张冬林等;《电力系统及其自动化学报》;20160229;第69-72页 *

Also Published As

Publication number Publication date
CN110705031A (en) 2020-01-17

Similar Documents

Publication Publication Date Title
CN108107321B (en) Fault waveform comparison method for power system
US8680873B2 (en) Method and apparatus for fault identification in a power tansmission line
EP0846271A1 (en) Method of locating a single-phase ground fault in a power distribution network
CN110068759A (en) A kind of fault type preparation method and device
CN112564157B (en) Fixed arc extinguishing angle control improvement method for inhibiting continuous commutation failure
CN106501602A (en) One kind is based on the detached fundamental wave measurement method of parameters of sliding window frequency spectrum
CN105606955B (en) A kind of faulty line method of discrimination based on numerical differentiation and empirical mode decomposition
CN110705031B (en) Excitation inrush current identification method based on second-order Taylor coefficient
CN110718932B (en) Commutation failure prediction method considering waveform distortion and direct current change
CN109375037B (en) Design method of single-phase earth fault alarm of medium-voltage ship power system
CN102435896A (en) Intermittent grounding fault rapid identification method of ship medium-voltage power system
CN112557948A (en) Power distribution network single-phase earth fault identification method based on fault multi-feature extraction
Hasan et al. Application of the automatic segmented Hilbert Huang transform method for the evaluation of the single-event characteristics of voltage sags in power systems
CN110531195B (en) Method for identifying magnetizing inrush current and internal fault of transformer
CN112255495A (en) Micro-grid high-resistance fault detection method
Patel et al. Auto‐reclosing scheme with adaptive dead time control for extra‐high‐voltage transmission line
CN115219787A (en) Power grid phasor movement measurement method, system and medium based on improved matrix bundle
CN112345826B (en) Frequency and transient harmonic measurement method under isolated network instability state
CN109103847B (en) Converter transformer saturation protection method based on direct current component estimation
Abdolkhalig et al. Evaluation of IEC 61850-9-2 samples loss on total vector error of an estimated phasor
CN112649694A (en) Method for judging single-phase earth fault of small-current grounding system
Xiong et al. A Multiple-Frequency-Taylor-Model based estimator for dynamic synchrophasor considering decaying DC component
Moreto et al. Using disturbance records to automate the diagnosis of faults and operational procedures in power generators
CN111597688B (en) Method and system for extracting time-varying power frequency and subsynchronous frequency components
Zhang et al. A method of grounding fault location in power system based on adaptive filtering

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant