CN113419133B - Power transmission line fault positioning method and device based on dynamic equivalent model - Google Patents

Power transmission line fault positioning method and device based on dynamic equivalent model Download PDF

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CN113419133B
CN113419133B CN202110362207.3A CN202110362207A CN113419133B CN 113419133 B CN113419133 B CN 113419133B CN 202110362207 A CN202110362207 A CN 202110362207A CN 113419133 B CN113419133 B CN 113419133B
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CN113419133A (en
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潘明九
顾晨临
郑迪
余智芳
单军
刘波
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Economic and Technological Research Institute of State Grid Zhejiang Electric Power Co Ltd
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Abstract

According to the scheme, pi-type equivalent models are respectively built for the lines at the left side and the right side of a fault point, and an extended Kalman filter is adopted to simultaneously estimate parameters and electric quantity of the pi-type equivalent models of the lines at the left side and the right side of the fault point, so that the problem of complex calculation of hyperbolic function equivalent models and multi-region pi-type equivalent models is avoided, and the calculation efficiency and calculation precision of fault distance estimation are improved.

Description

Power transmission line fault positioning method and device based on dynamic equivalent model
Technical Field
The invention relates to the technical field of power systems, in particular to a power transmission line fault positioning method and device based on a dynamic equivalent model.
Background
In a power transmission system, accurate power transmission line fault location is one of effective measures for reducing fault outage loss and improving the economical efficiency of the power system. At present, the line fault positioning accumulates rich research results, and can be mainly divided into a fault positioning method based on a fault analysis method and a fault positioning method based on traveling waves. The fault positioning method based on the fault analysis method mainly utilizes the recorded electric parameters such as voltage, current and the like during faults, obtains one or more sets of equations required by positioning according to a circuit fault analysis theory, analyzes and mathematically calculates the recorded electric parameters such as fault voltage, current and the like, and finally obtains the distance of a fault point. The method has clear and easy understanding principle, is convenient to calculate, and depends on the accuracy of the model. The fault positioning method based on the traveling wave mainly solves the fault distance by extracting the arrival time of the wave head and the traveling wave transmission speed in the propagation process of the transient traveling wave, so that the fault positioning is realized, the solving is not limited by the line type and the voltage class, and therefore, the fault positioning method has good adaptability to an extra-high voltage alternating current transmission system, but the accuracy depends on the accurate detection of the traveling wave head.
The kalman filter is a minimum variance-based optimization recursive processing algorithm developed by kalman in 1960 based on wiener filters. The calculation thinking is that a state space equation, an output equation and an observation equation are established according to a mathematical model of the system, and then time data and observation data are updated, so that the optimal estimation is obtained. The existing part of documents are based on hyperbolic function models and multi-region pi-type equivalent models of the power transmission line in series to perform equivalent on the power transmission line, the electric quantity and the fault distance of the models are used as state variables, further, a Kalman filter is used for performing iterative estimation on the state variables of the models, and finally, the optimal estimation of the fault distance is obtained. However, the hyperbolic function model is relatively complex, and when the number of the multi-region pi-type equivalent models connected in series is large, the number of variables is increased, the calculation efficiency is reduced, and when the number is small, larger errors are caused.
Disclosure of Invention
In view of the above, the embodiment of the invention provides a power transmission line fault positioning method and device based on a dynamic equivalent model, so as to improve the positioning precision of a fault node.
In order to achieve the above object, the embodiment of the present invention provides the following technical solutions:
A power transmission line fault positioning method based on a dynamic equivalent model comprises the following steps:
constructing a pi-type equivalent model matched with the monitored transmission line, and estimating parameters and electric quantity of the pi-type equivalent model at the first side and the pi-type equivalent model at the second side of the fault point by adopting an extended Kalman filter to obtain a fault instant dynamic equivalent model; the dynamic equivalent model comprises a dynamic equivalent model positioned on a first side of a fault node of the monitored power transmission line and a dynamic equivalent model positioned on a second side of the fault node of the monitored power transmission line;
calculating the estimated value of the output variable of the dynamic equivalent model at the moment k
Figure SMS_1
Calculating the output variation of the dynamic equivalent model at the moment tMeasured phasor value y k Calculating the parameter variable estimated value of the dynamic equivalent model at the moment k>
Figure SMS_2
Parameter variable correction value theta of the dynamic equivalent model at t moment k The method comprises the steps of carrying out a first treatment on the surface of the Judging said->
Figure SMS_3
And y is k Whether the difference of (2) is smaller than a first preset threshold or +.>
Figure SMS_4
And the theta is equal to k Whether the difference of (2) is smaller than a second preset threshold, if said +.>
Figure SMS_5
And y is k Is smaller than a first preset threshold or +.>
Figure SMS_6
And the theta is equal to k When the difference of (2) is smaller than the second preset threshold value, extracting the formula +.>
Figure SMS_7
Is calculated according to the calculation result of (2);
Wherein the said
Figure SMS_8
And estimating a parameter variable of the dynamic equivalent model at the moment k, wherein the parameter variable comprises: unit length self-resistance R of state equivalent model of first side of fault node lsk Mutual resistance R lmk Self-inductance L lsk Mutual inductance L lmk Phase-to-phase capacitance C lpk Capacitance to ground C lgk And a unit length self-resistance R of a state-equivalent model of the second side of the fault point rsk Mutual resistance R rmk Self-inductance L rsk Mutual inductance L rmk Phase-to-phase capacitance C rpk Capacitance to ground C rgk Three-phase conductivity estimation value G of fault point fak 、G fbk 、G fck And earth conductance G gk Distance value l of fault point from left bus fk Said->
Figure SMS_9
Estimating the value of the output variable of the dynamic equivalent model at the moment K, wherein the K is the estimated value of the output variable of the dynamic equivalent model at the moment K θ Filter gain as parameter variable, y k Actually measuring a phasor value for an output variable of the dynamic equivalue model at the moment k;
correcting the parameter variable by a correction value theta k The target element in the model is taken as a fault distance correction value l at the moment k fk And outputting.
A power transmission line fault locating device based on a dynamic equivalence model, comprising:
the model acquisition unit is used for constructing a pi-type equivalent model matched with the monitored transmission line, estimating parameters and electric quantity of the pi-type equivalent model at the first side and the pi-type equivalent model at the second side of the fault point by adopting an extended Kalman filter, and obtaining a fault instant dynamic equivalent model; the dynamic equivalent model comprises a dynamic equivalent model positioned on a first side of a fault node of the monitored transmission line and a dynamic equivalent model positioned on a second side of the fault node of the monitored transmission line;
A calculation unit for calculating the estimated value of the output variable of the dynamic equivalent model at the k moment
Figure SMS_12
Calculating the actually measured output variable phasor value y of the dynamic equivalent model at the moment t k Calculating the parameter variable estimated value of the dynamic equivalent model at the moment k>
Figure SMS_13
Parameter variable correction value theta of the dynamic equivalent model at t moment k The method comprises the steps of carrying out a first treatment on the surface of the Judging said->
Figure SMS_16
And y is k Whether the difference of (2) is smaller than a first preset threshold or +.>
Figure SMS_11
And the theta is equal to k Whether the difference of (2) is smaller than the second pre-determined valueSetting a threshold value if said->
Figure SMS_14
And y is k Is smaller than a first preset threshold or +.>
Figure SMS_17
And the theta is equal to k When the difference value of (2) is smaller than the second preset threshold value, extracting the formula
Figure SMS_19
The calculation result of (2), wherein said +.>
Figure SMS_10
And estimating a parameter variable of the dynamic equivalent model at the moment k, wherein the parameter variable comprises: unit length self-resistance R of state equivalent model of first side of fault node lsk Mutual resistance R lmk Self-inductance L lsk Mutual inductance L lmk Phase-to-phase capacitance C lpk Capacitance to ground C lgk And a unit length self-resistance R of a state-equivalent model of the second side of the fault point rsk Mutual resistance R rmk Self-inductance L rsk Mutual inductance L rmk Phase-to-phase capacitance C rpk Capacitance to ground C rgk Three-phase conductivity estimation value G of fault point fak 、G fbk 、G fck And earth conductance G gk Distance value l of fault point from left bus fk Wherein, said->
Figure SMS_15
For the parameter variable estimation value of the dynamic equivalent model at the moment k, the +.>
Figure SMS_18
Estimating the value of the output variable of the dynamic equivalent model at the moment K, wherein the K is the estimated value of the output variable of the dynamic equivalent model at the moment K θ Filter gain as parameter variable, y k Actually measuring a phasor value for an output variable of the dynamic equivalent model at the moment k;
a fault distance output unit for outputting the parameter variable correction value theta k In (1) as the fault distance at time kCorrection value l fk And outputting.
Based on the technical scheme, in the scheme provided by the embodiment of the invention, pi-type equivalent models are respectively built for the circuits at the left side and the right side of the fault point, and the extended Kalman filter is adopted to simultaneously estimate the parameters and the electric quantity of the pi-type equivalent models of the circuits at the left side and the right side of the fault point, so that the problem of complex calculation of hyperbolic function equivalent models and multi-region pi-type equivalent models is avoided, and the calculation efficiency and the calculation precision of fault distance estimation are improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the description of the embodiments or the prior art will be briefly described below, it being obvious that the drawings in the description below are only embodiments of the present invention, and that other drawings can be obtained from the provided drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic flow chart of a power transmission line fault positioning method based on a dynamic equivalent model, which is disclosed in an embodiment of the present application;
FIG. 2 is a diagram of an example dynamic equivalence model of a transmission line monitored at a time of failure;
FIG. 3 is an example graph of a dynamic equivalence model of a fault point at a time of a fault;
fig. 4 is a schematic structural diagram of a power transmission line fault locating device based on a dynamic equivalent model according to an embodiment of the present application.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without creative efforts, are within the protection scope of the invention.
Aiming at the defects of the prior art, the invention discloses a power transmission line fault positioning method based on a dynamic equivalent model, which comprises the steps of firstly establishing pi-type equivalent circuits on two sides of a power transmission line fault point, and determining a state equation, a measurement equation, a state variable, a parameter variable, an output variable and an initial value thereof; then, obtaining the parameter variable initial values and covariance matrixes of pi-type equivalent circuits at two sides of a fault point of the power transmission line, and calculating the state variable initial values and covariance matrixes of the pi-type equivalent circuits at two sides of the fault point of the power transmission line by combining the voltage and current at the moment of bus faults at the first side and the second side of the line; calculating the state variable estimated value, the parameter variable estimated value and the covariance matrix estimated value of the current moment by using a state equation according to the state variable, the parameter variable and the covariance matrix of the previous moment; then, calculating an output variable estimated value at the current moment by using the measurement equation and state variables and parameter variables estimated at the current moment; then calculating a state variable correction value, a parameter variable correction value and a covariance matrix of the current moment according to the deviation between the output variable measurement value and the output variable estimation value at the current moment; and finally, outputting the correction value of the fault distance at the current moment according to the parameter variable correction value at the current moment. According to the invention, a single pi-type equivalent model is respectively built for the circuits at the left side and the right side of the fault point, the parameters and the electric quantity of the pi-type equivalent model of the circuits at the left side and the right side of the fault point are estimated simultaneously by adopting the extended Kalman filter, and the equivalent model is corrected in the iterative process, so that a dynamic equivalent model is formed, the problem of complex calculation of the hyperbolic function equivalent model and the multi-region pi-type equivalent model is avoided, and the calculation efficiency and the calculation precision of fault distance estimation are improved.
Specifically, referring to fig. 1, the power transmission line fault locating method based on the dynamic equivalent model disclosed in the embodiment of the present application may include:
step S101: constructing a pi-type equivalent model matched with the monitored transmission line, and estimating parameters and electric quantity of the pi-type equivalent model at the first side and the pi-type equivalent model at the second side of the fault point by adopting an extended Kalman filter to obtain a fault instant dynamic equivalent model; the dynamic equivalent model comprises a dynamic equivalent model positioned on a first side of a monitored power transmission line fault node and a dynamic equivalent model positioned on a second side of the monitored power transmission line fault node;
in this step, firstly, pi-type equivalent models of two measuring nodes at two sides of a fault point of a monitored power transmission line are established, an equivalent model corresponding to the pi-type equivalent model is the dynamic equivalent model, an equivalent circuit diagram of the constructed dynamic equivalent model can be shown in fig. 2, fig. 2 is an example diagram of the dynamic equivalent model when the power transmission line is faulty at k moment, when the power transmission line is faulty, an example diagram of the equivalent circuit model at the fault point is shown in fig. 3, referring to fig. 2, and the constructed equivalent model can include:
the first end of the resistor R is used as a first input end of the dynamic equivalent model;
The first end of the inductor L is connected with the second end of the resistor R, and the second end of the inductor L is used as a first output end of the dynamic equivalent model;
a first capacitor C1, where a first end of the first capacitor C1 is connected to a first end of the resistor R;
a second capacitor C2, where a first end of the second capacitor C2 is connected to the second end of the inductor L, and a second end of the second capacitor C2 is connected to a second end of the first capacitor C1:
the second end of the first capacitor C1 is used as a second input end of the dynamic equivalent model, and the second end of the second capacitor C2 is used as a second output end of the dynamic equivalent model.
Based on the dynamic equivalent model, a state equation, a measurement equation, a state variable, a parameter variable, an output variable and an initial value of the pi-type equivalent circuit can be determined; further, in the technical scheme disclosed by the application, in order to ensure the reliability of the equivalent model, an extended Kalman filter can be adopted to simultaneously estimate the parameters and the electric quantity of the pi-type equivalent model of the line at two sides of the fault point, the pi-type equivalent model is corrected in the iterative process, the corrected pi-type equivalent model is used as the dynamic equivalent model, and various parameters required by the application can be measured by adopting the dynamic equivalent model.
Step S102: calculating the estimated value of the output variable of the dynamic equivalent model at the moment k
Figure SMS_20
And calculating the actually measured output variable phase value y of the dynamic equivalent model at t time k Calculating the parameter variable estimated value of the dynamic equivalue model at the moment k>
Figure SMS_21
Parameter variable correction value theta of the dynamic equivalent model at t moment k The method comprises the steps of carrying out a first treatment on the surface of the Judging said->
Figure SMS_22
And y is k Whether the difference of (2) is smaller than a first preset threshold or +.>
Figure SMS_23
And the theta is equal to k Whether the difference of (2) is smaller than a second preset threshold, if said +.>
Figure SMS_24
And y is k Is smaller than a first preset threshold or +.>
Figure SMS_25
And the theta is equal to k When the difference value of (2) is smaller than the second preset threshold value, extracting the formula
Figure SMS_26
Is calculated according to the calculation result of (2);
wherein,,
Figure SMS_27
θ 0 the parameter variable is the parameter variable of the instantaneous dynamic equivalent model of the fault;
wherein the said
Figure SMS_28
And estimating a parameter variable of the dynamic equivalent model at the moment k, wherein the parameter variable comprises: unit length self-resistance R of state equivalent model of first side of fault node lsk Mutual resistance R lmk Self-inductance L lsk Mutual inductance L lmk Phase-to-phase capacitance C lpk Capacitance to ground C lgk And a unit length self-resistance R of a state-equivalent model of the second side of the fault point rsk Mutual resistance R rmk Self-inductance L rsk Mutual inductance L rmk Phase-to-phase capacitance C rpk Capacitance to ground C rgk Three-phase conductivity estimation value G of fault point fak 、G fbk 、G fck And earth conductance G gk Distance value l of fault point from left bus fk Said->
Figure SMS_29
Estimating the value of the output variable of the dynamic equivalent model at the moment K, wherein the K is the estimated value of the output variable of the dynamic equivalent model at the moment K θ Filter gain as parameter variable, y k Actually measuring a phasor value for an output variable of the dynamic equivalue model at the moment k;
in the technical scheme disclosed in the embodiment of the application, the
Figure SMS_30
Can be expressed by the formula
Figure SMS_31
Calculated, wherein +.>
Figure SMS_32
Unit length self-resistance R of pi-type equivalent model at k moment ls Mutual resistance R lm Self-inductance L ls Mutual inductance L lm Phase-to-phase capacitance C lp Capacitance to ground C lg And the unit length self-resistance R of pi-type equivalent model of the line at the second side of the fault point rs Mutual resistance R rm Self-inductance L rs Mutual inductance L rm Phase-to-phase capacitance C rp Capacitance to ground C rg Initial estimated value G of three-phase conductance of fault point fa 、G fb 、G fc And earth conductance G g Distance l of fault point from first side bus f Is used for the estimation of the estimated value of (a).
The said
Figure SMS_33
Can be expressed by +.>
Figure SMS_34
Calculated out->
Figure SMS_35
For the estimated phasor of the instantaneous value of the three-phase current at the moment k of the first side of the line to be tested, +.>
Figure SMS_36
Is an estimated value phasor of the instantaneous value of the three-phase current at the moment k of the second side of the line to be measured, wherein +.>
Figure SMS_37
The estimated phasors of the three-phase current instantaneous values of the buses at the two sides of the line at the moment k are respectively;
Said y k From formula y k ＝[i xk i yk ] T Calculated, i xk I is the actual measured phasor of the instantaneous value of the three-phase current at the moment k of the first side of the line to be tested yk I is the actual measured phasor of the instantaneous value of the three-phase current at time k on the second side of the line to be measured xk ＝[I xak I xbk I xck ] T 、i yk ＝[I yak I ybk I yck ] T The actual measured phasors of the instantaneous values of the three-phase currents of the first side bus and the second side bus of the line at the moment k are respectively.
The K is θ Can be represented by the formula
Figure SMS_38
Calculated, wherein->
Figure SMS_39
Estimating a value for said parameter variable +.>
Figure SMS_40
Covariance matrix of>
Figure SMS_41
Wherein E is 3×3 Single-bit matrix of 3 x 3, Z 3×3 A zero matrix of 3 x 3, said +.>
Figure SMS_42
Estimating a value for said parameter variable>
Figure SMS_43
And R is a preset measurement noise covariance matrix.
The said
Figure SMS_44
Can be expressed by the formula->
Figure SMS_45
Calculated, wherein the P θ(k-1) A covariance matrix of the parameter variable of the k-1 moment fault instant dynamic equivalent model; the Q is θ A system error covariance matrix for a preset parameter variable.
Step S103: correcting the parameter variable by a correction value theta k The target element in the model is taken as a fault distance correction value l at the moment k fk And outputting.
When the parameter variable correction value theta is calculated k Thereafter, the parameter variable correction value θ is extracted k As the target element of the k time fault distance correction value, and outputting the same.
In addition to the above-mentioned k-moment fault distance correction value l fk In addition, in the technical scheme disclosed by the embodiment of the application, the state variable x of the dynamic equivalent model at the moment of the fault can be obtained through the calculation of the dynamic equivalent model 0 And parameter variable theta of instantaneous dynamic equivalent model of fault 0 State variable x 0 Covariance matrix P of (2) x0 And parameter variable theta 0 Covariance matrix P of (2) θ0 ；
Specifically, the initial parameter variable θ 0 Covariance matrix P θ0 The method comprises the following steps:
unit length self-resistance R of pi-type equivalent model of fault point first side line ls0 Mutual resistance R lm0 Self-inductance L ls0 Mutual inductance L lm0 Phase-to-phase capacitance C lp0 To ground electricCapacitor C lg0 And the unit length self-resistance R of pi-type equivalent model of the line at the second side of the fault point rs0 Mutual resistance R rm0 Self-inductance L rs0 Mutual inductance L rm0 Phase-to-phase capacitance C rp0 Capacitance to ground C rg0 Initial estimated value G of three-phase conductance of fault point fa0 、G fb0 、G fc0 And conductance to ground G g0 And an initial estimate l of the distance of the fault point from the first side busbar f0 Constitute the initial parameter variable θ 0 ＝[R ls0 R lm0 L ls0 L lm0 C lp0 C lg0 R rs0 R rm0 L rs0 L rm0 C rp0 C rg0 G fa0 G fb0 G fc0 G g0 D 0 ] T . Wherein R is ls0 ＝R rs0 ＝(2R p0 +R z0 )/3，R lm0 ＝R rm0 ＝(R z0 -R p0 )/3，L ls0 ＝L rs0 ＝(2L p0 +L z0 )/3， L lm0 ＝L rm0 ＝(L z0 -L p0 )/3，C lp0 ＝C p0 ，C lg0 ＝C rg0 ＝3C p0 C z0 /(C p0 -C z0 ). Wherein R is p0 、L p0 、 C p0 Unit length positive sequence resistor, inductor and capacitor provided by manufacturer or marked by line respectively z0 、 L z0 、C z0 The unit length zero sequence resistance, inductance and capacitance are provided or marked by manufacturers respectively; its covariance matrix P θ0 The parameter errors given by the manufacturer are obtained;
the initial state variable x 0 Covariance matrix P x0 The method comprises the following steps:
instantaneous fault point first side line pi-type equivalent model three-phase current instantaneous value phasor i l0 ＝[I la0 I lb0 I lc0 ] T Pi-type equivalent model three-phase current instantaneous value phasor i of fault point second side line r0 ＝[I ra0 I rb0 I rc0 ] T And the instantaneous value u of the three-phase voltage at the fault point f0 ＝[U fa0 U fb0 U fc0 ] T Constitute the initial state variable x 0 ＝[i l0 i r0 u f0 ] T . Wherein,,
i l0 ＝i x0 -l f0 C l0 du x0 /dt
i r0 ＝i y0 +(l t -l f0 )C r0 du y0 /dt
u f0 ＝u x0 -l f0 R l0 i l0 -l f0 L l0 di l0 /dt
in the above formula, l t For the total length of the line l f0 An initial estimated value of the distance between the fault point and the first side bus is obtained; d/dt is the differential operator; u (u) x0 ＝[U xa0 U xb0 U xc0 ] T And i x0 ＝[I xa0 I xb0 I xc0 ] T U is the instantaneous phasor of the three-phase voltage and current for the fault instant at the bus on the first side of the line y0 ＝[U ya0 U yb0 U yc0 ] T And i y0 ＝[I ya0 I yb0 I yc0 ] T The instantaneous phasors of the three-phase voltage and the current are the instantaneous value of the fault at the bus at the second side of the line; r is R l0 、L l0 、C l0 、C r0 The method comprises the steps of respectively generating a pi-type equivalent model resistance matrix, an inductance matrix and a capacitance matrix of a first side line of a fault point at the moment of fault occurrence and a pi-type equivalent model capacitance matrix of a second side line of the fault point at the moment of fault occurrence, and specifically:
Figure SMS_46
Figure SMS_47
Figure SMS_48
its initial state variable x 0 Covariance matrix P of (2) x0 Obtained from the measurement error of the synchrophasor unit.
Furthermore, the estimated value of the state variable at the moment k can be obtained through calculation of the pi-type equivalent model
Figure SMS_49
And parameter variable estimate +.>
Figure SMS_50
And covariance matrix thereof->
Figure SMS_51
And->
Figure SMS_52
Specifically, the state variable estimate at time k
Figure SMS_53
And parameter variable estimate +.>
Figure SMS_54
State variable estimate +.>
Figure SMS_55
Covariance matrix>
Figure SMS_56
And parameter variable estimate +.>
Figure SMS_57
Covariance matrix>
Figure SMS_58
The calculation formulas of (a) are respectively as follows:
Figure SMS_59
Figure SMS_60
Figure SMS_61
Figure SMS_62
in the method, in the process of the invention,
Figure SMS_63
Figure SMS_64
the k moment state variable estimated value and the parameter variable estimated value are respectively; x is x k-1 ＝[i l(k-1) i r(k-1) u f(k-1) ] T 、 θ k-1 ＝[R ls(k-1) R lm(k-1) L ls(k-1) L lm(k-1) C lp(k-1) C lg(k-1) R rs(k-1) R rm(k-1) L rs(k-1) L rm(k-1) C rp(k-1) C rg(k-1) G fa(k-1) G fb(k-1) G fc(k-1) G g(k-1) l f(k-1) ] T The state variable correction value and the parameter variable correction value at the moment k-1 are respectively; p (P) x(k-1) 、P θ(k-1) The state variable covariance matrix and the parameter variable covariance matrix at the moment k-1 are respectively obtained; w (w) x ～N(0,Q x )、w θ ～N(0,Q θ ) Systematic errors, Q, of state variables and parameter variables, respectively x 、Q θ A system error covariance matrix of the state variable and the parameter variable respectively; z k-1 ＝[u x(k-1) u y(k-1) ] T Inputting a variable for time k-1, wherein u x(k-1) ＝[U xa(k-1) U xb(k-1) U xc(k-1) ] T And u y(k-1) ＝[U ya(k-1) U yb(k-1) U yc(k-1) ] T The phase quantity is the instantaneous value phasor of the three-phase voltage at the moment k-1 at the bus of the first side and the bus of the second side of the line respectively; matrix A k-1 、B k-1 Respectively is
Figure SMS_65
Figure SMS_66
Wherein E is 3×3 、Z 3×3 A 3 x 3 identity matrix and a zero matrix, respectively; t (T) s Is the sampling period; matrix R l(k-1) 、 L l(k-1) 、R r(k-1) 、L r(k-1) 、C k-1 、G f(k-1) Respectively is
Figure SMS_67
Figure SMS_68
C k-1 ＝l f(k-1) C l(k-1) +(l t -l f(k-1) )C r(k-1)
Figure SMS_69
Wherein,,
Figure SMS_70
Figure SMS_71
G gt(k-1) ＝G fa(k-1) +G fb(k-1) +G fc(k-1) +G g(k-1)
in the technical scheme disclosed in the above embodiment of the present application, a k-moment output variable estimated value is also disclosed
Figure SMS_72
The specific calculation process of (1) is as follows: specifically, the variable estimation value +.>
Figure SMS_73
The calculation formula of (2) is
Figure SMS_74
Wherein,,
Figure SMS_75
the estimated phasors of the three-phase current instantaneous values of the first side bus and the second side bus of the line at the moment k are respectively; z k ＝[u xk u yk ] T Inputting a variable for the time k, wherein u xk ＝[U xak U xbk U xck ] T And u yk ＝[U yak U ybk U yck ] T The phase quantity is the instantaneous value phasor of the three-phase voltage at the moment k at the bus of the first side and the bus of the second side of the line respectively; v-N (0, R) is measurement noise, R is measurement noise covariance matrix; matrix C, D k Respectively is
Figure SMS_76
Wherein,,
Figure SMS_77
Figure SMS_78
furthermore, the k moment state variable correction value x can also be obtained through calculation of the pi-type equivalent model k And parameter variable correction value theta k Covariance matrix P xk And P θk Specifically, the state variable correction value x at time k k And parameter variable correction value theta k Covariance matrix P xk And P θk The calculation formulas of (a) are respectively as follows:
Figure SMS_79
Figure SMS_80
Figure SMS_81
Figure SMS_82
wherein E is 9×9 、E 17×17 Identity matrices of 9 x 9 and 17 x 17, respectively; y is k ＝[i xk i yk ] T ， i xk ＝[I xak I xbk I xck ] T 、i yk ＝[I yak I ybk I yck ] T The measured phasors are actual measured values of three-phase current instantaneous values of the first side bus and the second side bus of the line at the moment k respectively; k (K) x And K θ The filter gains of the state variable and the parameter variable are respectively calculated according to the following formulas
Figure SMS_83
Figure SMS_84
The following describes a specific embodiment of the invention by taking a 500kV power transmission line as an example, and the specific steps are as follows:
acquiring fixed parameters and initial values of time-varying parameters of a 500kV power transmission line:
fixed parameters: total length of line l t ；
Initial value of time-varying parameter: positive sequence of line unit lengthResistor R p0 Positive sequence inductance L p0 And positive sequence capacitor C p0 Zero sequence resistance R of unit length of line z0 Zero sequence inductance L z0 And zero sequence capacitance C z0 The method comprises the steps of carrying out a first treatment on the surface of the Fault point a phase conductivity initiation value G fa0 B-phase conductivity initial value G fb0 C-phase conductivity initial value G fc0 To the initial value G of the ground conductance g0 Initial value l of distance between fault point and first side bus f0 ；
After the fault occurs, three-phase voltage instantaneous value phasor u of the first side bus at k time (k=0, 1,2, …) is obtained from synchronous phasor units or protection devices installed at the first side bus and the second side bus of the circuit at 0 time instant of the fault occurrence xk ＝[U xak U xbk U xck ] T Three-phase current instantaneous value phasor i xk ＝[I xak I xbk I xck ] T And a three-phase voltage instantaneous value phasor u of the second side bus yk ＝[U yak U ybk U yck ] T Three-phase current instantaneous value phasor i yk ＝[I yak I ybk I yck ] T 。
Obtaining initial state variables and parameter variables and covariance matrixes thereof:
initial parameter variable θ 0 Covariance matrix P θ0 The method comprises the following steps:
θ 0 ＝[R ls0 R lm0 L ls0 L lm0 C lp0 C lg0 R rs0 R rm0 L rs0 L rm0 C rp0 C rg0 G fa0 G fb0 G fc0 G g0 D 0 ] T
wherein,,
R ls0 ＝R rs0 ＝(2R p0 +R z0 )/3，R lm0 ＝R rm0 ＝(R z0 -R p0 )/3
L ls0 ＝L rs0 ＝(2L p0 +L z0 )/3，L lm0 ＝L rm0 ＝(L z0 -L p0 )/3
C lp0 ＝C p0 ，C lg0 ＝C rg0 ＝3C p0 C z0 /(C p0 -C z0 )
covariance matrix P of initial parameter variables θ0 The parameter errors given by the manufacturer are obtained;
initial state variable x 0 Covariance matrix P x0 The method comprises the following steps:
instantaneous fault point first side line pi-type equivalent model three-phase current instantaneous value phasor i l0 ＝[I la0 I lb0 I lc0 ] T Pi-type equivalent model three-phase current instantaneous value phasor i of fault point second side line r0 ＝[I ra0 I rb0 I rc0 ] T And the instantaneous value u of the three-phase voltage at the fault point f0 ＝[U fa0 U fb0 U fc0 ] T Constitute the initial state variable x 0 ＝[i l0 i r0 u f0 ] T . Wherein,,
i l0 ＝i x0 -l f0 C l0 du x0 /dt
i r0 ＝i y0 +(l t -l f0 )C r0 du y0 /dt
u f0 ＝u x0 -l f0 R l0 i l0 -l f0 L l0 di l0 /dt
wherein, I t For the total length of the line l f0 An initial estimated value of the distance between the fault point and the first side bus is obtained; d/dt is the differential operator; u (u) x0 ＝[U xa0 U xb0 U xc0 ] T And i x0 ＝[I xa0 I xb0 I xc0 ] T U is the instantaneous phasor of the three-phase voltage and current for the fault instant at the bus of the first side of the line y0 ＝[U ya0 U yb0 U yc0 ] T And i y0 ＝[I ya0 I yb0 I yc0 ] T The instantaneous phasors of the three-phase voltage and the current are the instantaneous value of the fault at the bus at the second side of the line; r is R l0 、L l0 、C l0 、C r0 The matrix is a pi-type equivalent model resistance matrix, an inductance matrix and a capacitance matrix of a first side line of a moment fault point of a fault, and a pi-type equivalent model capacitance matrix of a second side line of the moment fault point of the fault, specifically
Figure SMS_85
Figure SMS_86
Figure SMS_87
Its covariance matrix P x0 Obtained from the measurement errors of the synchrophasor units or the protection devices.
Calculating a state variable estimated value and a parameter variable estimated value at the moment k and a covariance matrix thereof:
the calculation formula of the state variable estimated value at the moment k and the covariance matrix thereof is as follows
Figure SMS_88
Figure SMS_89
In the method, in the process of the invention,
Figure SMS_90
the state variable estimated value at the moment k; x is x k-1 ＝[i l(k-1) i r(k-1) u f(k-1) ] T A state variable correction value at the moment k-1; p (P) x(k-1) A covariance matrix of the state variable at the moment k-1; w (w) x ～N(0,Q x ) Systematic error as state variable, Q x A system error covariance matrix which is a state variable; z k-1 ＝[u x(k-1) u y(k-1) ] T Inputting a variable for time k-1, wherein u x(k-1) ＝[U xa(k-1) U xb(k-1) U xc(k-1) ] T And u y(k-1) ＝[U ya(k-1) U yb(k-1) U yc(k-1) ] T The phase quantity is the instantaneous value phasor of the three-phase voltage at the moment k-1 at the bus of the first side and the bus of the second side of the line respectively; matrix A k-1 、B k-1 Respectively is
Figure SMS_91
/>
Figure SMS_92
Wherein E is 3×3 、Z 3×3 A 3 x 3 identity matrix and a zero matrix, respectively; t (T) s Is the sampling period; matrix R l(k-1) 、L l(k-1) 、R r(k-1) 、L r(k-1) 、C k-1 、G f(k-1) Respectively is
Figure SMS_93
Figure SMS_94
C k-1 ＝l f(k-1) C l(k-1) +(l t -l f(k-1) )C r(k-1)
Figure SMS_95
Wherein,,
Figure SMS_96
Figure SMS_97
G gt(k-1) ＝G fa(k-1) +G fb(k-1) +G fc(k-1) +G g(k-1)
the calculation formula of the k-moment parameter variable estimated value and the covariance matrix thereof is as follows
Figure SMS_98
Figure SMS_99
In the method, in the process of the invention,
Figure SMS_100
the estimated value of the parameter variable at the moment k; p (P) θ(k-1) A covariance matrix of the parameter variable at the moment k-1; w (w) θ ～N(0,Q θ ) Systematic error as parameter variable, Q θ A systematic error covariance matrix for the parameter variables.
Calculating an estimated value of an output variable at the moment k:
output variable estimated value at k time
Figure SMS_101
The calculation formula of (2) is
Figure SMS_102
Wherein,,
Figure SMS_103
the estimated phasors of the three-phase current instantaneous values of the first side bus and the second side bus of the line at the moment k are respectively; z k ＝[u xk u yk ] T Input variable for k time, where u xk ＝[U xak U xbk U xck ] T And u yk ＝[U yak U ybk U yck ] T The phase quantity is the instantaneous value phasor of the three-phase voltage at the moment k at the bus of the first side and the bus of the second side of the line respectively; v-N (0, R) is the measurement noise,r is a measurement noise covariance matrix; matrix C, D k Respectively is
Figure SMS_104
Wherein,,
Figure SMS_105
Figure SMS_106
calculating a state variable correction value and a parameter variable correction value at the moment k and a covariance matrix of the state variable correction value and the parameter variable correction value at the moment k:
k moment state variable correction value x k Covariance matrix P xk The calculation formula of (2) is
Figure SMS_107
Figure SMS_108
Wherein E is 9×9 A 9×9 identity matrix; y is k ＝[i xk i yk ] T ，i xk ＝[I xak I xbk I xck ] T 、 i yk ＝[I yak I ybk I yck ] T Real measured phasors of three-phase current instantaneous values of the first side bus and the second side bus of the line at the moment k respectively; k (K) x The filter gain is a state variable and the calculation formula is
Figure SMS_109
k moment parameter variable correction value theta k Covariance matrix P θk The calculation formula of (2) is
Figure SMS_110
Figure SMS_111
Wherein E is 17×17 A unit matrix of 17×17; k (K) θ The filter gain as parameter variable is calculated by the following formula
Figure SMS_112
/>
Outputting a fault distance correction value at the moment k:
at this time, the k-time fault distance correction value is the k-time parameter variable correction value θ k Is the 17 th element of (c).
Corresponding to the method, the application also discloses a power transmission line fault locating device based on the dynamic equivalent model, and specific working contents of each unit in the device are referred to in the embodiment of the method, and the power transmission line fault locating device based on the dynamic equivalent model provided by the embodiment of the invention is described below, and the power transmission line fault locating device based on the dynamic equivalent model and the power transmission line fault locating method based on the dynamic equivalent model described below can be referred to correspondingly.
Referring to fig. 4, the power transmission line fault locating device based on the dynamic equivalence model may include:
the model acquisition unit 100 is used for constructing a pi-type equivalent model matched with the monitored transmission line, estimating parameters and electric quantity of the pi-type equivalent model at the first side and the pi-type equivalent model at the second side of the fault point by adopting an extended Kalman filter, and obtaining a fault instant dynamic equivalent model; the dynamic equivalent model comprises a dynamic equivalent model positioned on a first side of a monitored power transmission line fault node and a dynamic equivalent model positioned on a second side of the monitored power transmission line fault node;
a calculation unit 200 forCalculating the estimated value of the output variable of the dynamic equivalent model at the moment k
Figure SMS_115
Calculating the actually measured output variable phasor value y of the dynamic equivalent model at the moment t k Calculating the parameter variable estimated value of the dynamic equivalent model at the moment k>
Figure SMS_118
Parameter variable correction value theta of the dynamic equivalent model at t moment k The method comprises the steps of carrying out a first treatment on the surface of the Judging said->
Figure SMS_120
And y is k Whether the difference of (2) is smaller than a first preset threshold or +.>
Figure SMS_114
And the theta is equal to k Whether the difference of (2) is smaller than a second preset threshold, if said +.>
Figure SMS_116
And y is k Is smaller than a first preset threshold or +. >
Figure SMS_119
And the theta is equal to k When the difference value of (2) is smaller than the second preset threshold value, extracting the formula
Figure SMS_121
Is calculated according to the calculation result of (2); wherein said->
Figure SMS_113
For the parameter variable estimation value of the dynamic equivalent model at the moment k, the +.>
Figure SMS_117
Estimating the value of the output variable of the dynamic equivalent model at the moment K, wherein the K is the estimated value of the output variable of the dynamic equivalent model at the moment K θ Filter gain for parameter variables, y k Actually measuring a phasor value for an output variable of the dynamic equivalent model at the moment k;
a fault distance output unit 300 for outputting the fault distanceParameter variable correction value theta k The target element in the model is taken as a fault distance correction value l at the moment k fk And outputting.
Corresponding to the above method, the calculation unit is further configured to base on a formula
Figure SMS_122
Calculating to obtain the estimated value of the parameter variable +.>
Figure SMS_123
Wherein->
Figure SMS_124
Respectively the self-resistance R of unit length lsk Mutual resistance R lmk Self-inductance L lsk Mutual inductance L lmk Phase-to-phase capacitance C lpk Capacitance to ground C lgk And the unit length self-resistance R of the state equivalent model of the second side of the fault point rsk Mutual resistance R rmk Self-inductance L rsk Mutual inductance L rmk Phase-to-phase capacitance C rpk Capacitance to ground C rgk Three-phase conductivity estimation value G of fault point fak 、G fbk 、 G fck And earth conductance G gk Distance l of fault point from left bus fk Is used for the estimation of the estimated value of (a).
Corresponding to the above method, the calculation unit is further configured to base on a formula
Figure SMS_125
Calculating to obtain the estimated value of the output variable +.>
Figure SMS_126
Based on formula y k ＝[i xk i yk ] T Calculating to obtain the measured phasor value y of the output variable k 。
In the scheme, pi-type equivalent circuits on two sides of a power transmission line fault point are firstly established, and a state equation, a measurement equation, a state variable, a parameter variable, an output variable and initial values thereof are determined;
corresponding to the above method, the computing unit may also be adapted to:
calculating to obtain state variable x of fault instant dynamic equivalent model 0 And parameter variable theta of instantaneous dynamic equivalent model of fault 0 State variable x 0 Covariance matrix P of (2) x0 And parameter variable theta 0 Covariance matrix P of (2) θ0 ；
Specifically, the initial parameter variable θ 0 Covariance matrix P θ0 The method comprises the following steps:
unit length self-resistance R of pi-type equivalent model of fault point first side line ls0 Mutual resistance R lm0 Self-inductance L ls0 Mutual inductance L lm0 Phase-to-phase capacitance C lp0 Capacitance to ground C lg0 And the unit length self-resistance R of pi-type equivalent model of the line at the second side of the fault point rs0 Mutual resistance R rm0 Self-inductance L rs0 Mutual inductance L rm0 Phase-to-phase capacitance C rp0 Capacitance to ground C rg0 Initial estimated value G of three-phase conductance of fault point fa0 、G fb0 、G fc0 And conductance to ground G g0 And an initial estimate l of the distance of the fault point from the first side busbar f0 Constitute the initial parameter variable θ 0 ＝[R ls0 R lm0 L ls0 L lm0 C lp0 C lg0 R rs0 R rm0 L rs0 L rm0 C rp0 C rg0 G fa0 G fb0 G fc0 G g0 D 0 ] T . Wherein R is ls0 ＝R rs0 ＝(2R p0 +R z0 )/3，R lm0 ＝R rm0 ＝(R z0 -R p0 )/3，L ls0 ＝L rs0 ＝(2L p0 +L z0 )/3， L lm0 ＝L rm0 ＝(L z0 -L p0 )/3，C lp0 ＝C p0 ，C lg0 ＝C rg0 ＝3C p0 C z0 /(C p0 -C z0 ). Wherein R is p0 、L p0 、 C p0 Unit length positive sequence resistor, inductor and capacitor provided by manufacturer or marked by line respectively z0 、L z0 、C z0 The unit length zero sequence resistance, inductance and capacitance are provided or marked by manufacturers respectively; its covariance matrix P θ0 The parameter errors given by the manufacturer are obtained;
the initial state variable x 0 Covariance matrix P x0 The method comprises the following steps:
instantaneous fault point first side line pi-type equivalent model three-phase current instantaneous value phasor i l0 ＝[I la0 I lb0 I lc0 ] T Pi-type equivalent model three-phase current instantaneous value phasor i of fault point second side line r0 ＝[I ra0 I rb0 I rc0 ] T And the instantaneous value u of the three-phase voltage at the fault point f0 ＝[U fa0 U fb0 U fc0 ] T Constitute the initial state variable x 0 ＝[i l0 i r0 u f0 ] T . Wherein,,
i l0 ＝i x0 -l f0 C l0 du x0 /dt
i r0 ＝i y0 +(l t -l f0 )C r0 du y0 /dt
u f0 ＝u x0 -l f0 R l0 i l0 -l f0 L l0 di l0 /dt
in the above formula, l t For the total length of the line l f0 An initial estimated value of the distance between the fault point and the first side bus is obtained; d/dt is the differential operator; u (u) x0 ＝[U xa0 U xb0 U xc0 ] T And i x0 ＝[I xa0 I xb0 I xc0 ] T U is the instantaneous phasor of the three-phase voltage and current for the fault instant at the bus on the first side of the line y0 ＝[U ya0 U yb0 U yc0 ] T And i y0 ＝[I ya0 I yb0 I yc0 ] T The instantaneous phasors of the three-phase voltage and the current are the instantaneous value of the fault at the bus at the second side of the line; r is R l0 、L l0 、C l0 、C r0 Respectively the instant fault points of the faultsPi-type equivalent model resistance, inductance and capacitance matrix of first side line and pi-type equivalent model capacitance matrix of second side line at moment of fault occurrence, specifically:
Figure SMS_127
Figure SMS_128
Figure SMS_129
Its initial state variable x 0 Covariance matrix P of (2) x0 Obtained from the measurement error of the synchrophasor unit.
Further, corresponding to the above method, the calculating unit may further calculate a state variable estimated value at time k through the pi-type equivalent model
Figure SMS_130
And parameter variable estimate +.>
Figure SMS_131
And covariance matrix thereof->
Figure SMS_132
And->
Figure SMS_133
/>
Specifically, the state variable estimate at time k
Figure SMS_134
And parameter variable estimate +.>
Figure SMS_135
State variable estimate +.>
Figure SMS_136
Covariance matrix>
Figure SMS_137
Digital variable estimate +.>
Figure SMS_138
Covariance matrix>
Figure SMS_139
The calculation formulas of (a) are respectively as follows:
Figure SMS_140
Figure SMS_141
Figure SMS_142
Figure SMS_143
in the method, in the process of the invention,
Figure SMS_144
Figure SMS_145
the k moment state variable estimated value and the parameter variable estimated value are respectively; x is x k-1 ＝[i l(k-1) i r(k-1) u f(k-1) ] T 、 θ k-1 ＝[R ls(k-1) R lm(k-1) L ls(k-1) L lm(k-1) C lp(k-1) C lg(k-1) R rs(k-1) R rm(k-1) L rs(k-1) L rm(k-1) C rp(k-1) C rg(k-1) G fa(k-1) G fb(k-1) G fc(k-1) G g(k-1) l f(k-1) ] T The state variable correction value and the parameter variable correction value at the moment k-1 are respectively; p (P) x(k-1) 、P θ(k-1) The state variable covariance matrix and the parameter variable covariance matrix at the moment k-1 are respectively obtained; w (w) x ～N(0,Q x )、w θ ～N(0,Q θ ) Systematic errors, Q, of state variables and parameter variables, respectively x 、Q θ A system error covariance matrix of the state variable and the parameter variable respectively; z k-1 ＝[u x(k-1) u y(k-1) ] T Inputting a variable for time k-1, wherein u x(k-1) ＝[U xa(k-1) U xb(k-1) U xc(k-1) ] T And u y(k-1) ＝[U ya(k-1) U yb(k-1) U yc(k-1) ] T The phase quantity is the instantaneous value phasor of the three-phase voltage at the moment k-1 at the bus of the first side and the bus of the second side of the line respectively; matrix A k-1 、B k-1 Respectively is
Figure SMS_146
Figure SMS_147
Wherein E is 3×3 、Z 3×3 A 3 x 3 identity matrix and a zero matrix, respectively; t (T) s Is the sampling period; matrix R l(k-1) 、 L l(k-1) 、R r(k-1) 、L r(k-1) 、C k-1 、G f(k-1) Respectively is
Figure SMS_148
Figure SMS_149
C k-1 ＝l f(k-1) C l(k-1) +(l t -l f(k-1) )C r(k-1)
Figure SMS_150
Wherein,,
Figure SMS_151
Figure SMS_152
G gt(k-1) ＝G fa(k-1) +G fb(k-1) +G fc(k-1) +G g(k-1)
in the technical scheme disclosed in the above embodiment of the present application, a k-moment output variable estimated value is also disclosed
Figure SMS_153
The specific calculation process of (1) is as follows: specifically, the variable estimation value +.>
Figure SMS_154
The calculation formula of (2) is
Figure SMS_155
Wherein,,
Figure SMS_156
the estimated phasors of the three-phase current instantaneous values of the first side bus and the second side bus of the line at the moment k are respectively; z k ＝[u xk u yk ] T Inputting a variable for the time k, wherein u xk ＝[U xak U xbk U xck ] T And u yk ＝[U yak U ybk U yck ] T The phase quantity is the instantaneous value phasor of the three-phase voltage at the moment k at the bus of the first side and the bus of the second side of the line respectively; v-N (0, R) is measurement noise, R is measurement noise covariance matrix; matrix C, D k Respectively is
Figure SMS_157
Wherein,,
Figure SMS_158
Figure SMS_159
further, corresponding to the above method, the calculating unit may further calculate a k moment state variable correction value x through the pi-type equivalent model k And parameter variable correction value theta k Covariance matrix P xk And P θk Specifically, the state variable correction value x at time k k And parameter variable correction value theta k Covariance matrix P xk And P θk The calculation formulas of (a) are respectively as follows:
Figure SMS_160
Figure SMS_161
Figure SMS_162
Figure SMS_163
wherein E is 9×9 、E 17×17 Identity matrices of 9 x 9 and 17 x 17, respectively; y is k ＝[i xk i yk ] T ， i xk ＝[I xak I xbk I xck ] T 、i yk ＝[I yak I ybk I yck ] T The measured phasors are actual measured values of three-phase current instantaneous values of the first side bus and the second side bus of the line at the moment k respectively; k (K) x And K θ Filtering of state variables and parameter variables, respectively The gain of the device is calculated according to the following formulas
Figure SMS_164
Figure SMS_165
In summary, the invention discloses a power transmission line fault positioning scheme based on a dynamic equivalent model, which comprises the steps of firstly establishing pi-type equivalent models on two sides of a monitored power transmission line fault point, and determining a state equation, a measurement equation, a state variable, a parameter variable, an output variable and an initial value of the pi-type equivalent model; then, obtaining parameter variable initial values and covariance matrixes in pi-type equivalent circuits at two sides of a power transmission line fault point, and calculating state variable initial values and covariance matrixes of the pi-type equivalent circuits at two sides of the power transmission line fault point by combining voltage and current at the moment of fault of a first side line and a second side line of the fault node; calculating a state variable estimated value, a parameter variable estimated value and a covariance matrix estimated value thereof at the current moment by using a state equation according to the state variable, the parameter variable and the covariance matrix of the previous moment; then, calculating an output variable estimated value at the current moment by using the measurement equation and the state variable and the parameter variable estimated at the current moment; then calculating a state variable correction value, a parameter variable correction value and a covariance matrix of the current moment according to the deviation between the measured value of the current moment output variable and the estimated value of the output variable; and finally, outputting the correction value of the fault distance at the current moment according to the parameter variable correction value at the current moment. According to the invention, a single pi-type equivalent model is respectively built for the circuits at the left side and the right side of the fault point, the parameters and the electric quantity of the pi-type equivalent model of the circuits at the left side and the right side of the fault point are estimated simultaneously by adopting the extended Kalman filter, and the equivalent model is corrected in the iterative process, so that a dynamic equivalent model is formed, the problem of complex calculation of the hyperbolic function equivalent model and the multi-region pi-type equivalent model is avoided, and the calculation efficiency and the calculation precision of fault distance estimation are improved.
For convenience of description, the above system is described as being functionally divided into various modules, respectively. Of course, the functions of each module may be implemented in the same piece or pieces of software and/or hardware when implementing the present invention.
In this specification, each embodiment is described in a progressive manner, and identical and similar parts of each embodiment are all referred to each other, and each embodiment mainly describes differences from other embodiments. In particular, for a system or system embodiment, since it is substantially similar to a method embodiment, the description is relatively simple, with reference to the description of the method embodiment being made in part. The system and system embodiments described above are merely illustrative, wherein the elements described as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
Those of skill would further appreciate that the elements and algorithm steps of the embodiments described in connection with the embodiments disclosed herein may be embodied in electronic hardware, in computer software, or in a combination of the two, and that the various illustrative components and steps have been described above generally in terms of function in order to clearly illustrate the interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. The software modules may be disposed in Random Access Memory (RAM), memory, read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.
It should also be noted that in this document, relational terms such as first and second, and the like are 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. Moreover, 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 one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (10)

1. A power transmission line fault positioning method based on a dynamic equivalent model is characterized by comprising the following steps:
constructing a pi-type equivalent model matched with the monitored transmission line, and estimating parameters and electric quantity of the pi-type equivalent model at the first side and the pi-type equivalent model at the second side of the fault point by adopting an extended Kalman filter to obtain a fault instant dynamic equivalent model; the dynamic equivalent model comprises a dynamic equivalent model positioned on a first side of a monitored power transmission line fault node and a dynamic equivalent model positioned on a second side of the monitored power transmission line fault node;
calculating the estimated value of the output variable of the dynamic equivalent model at the moment k
Figure FDA0004171691820000011
Calculating the actually measured output variable phasor value y of the dynamic equivalent model at the moment k k Calculating the parameter variable estimated value of the dynamic equivalent model at the moment k>
Figure FDA0004171691820000012
Parameter variable correction value theta of dynamic equivalent model at k moment k The method comprises the steps of carrying out a first treatment on the surface of the Judging said->
Figure FDA0004171691820000013
And y is k Whether the difference of (2) is smaller than a first preset threshold or +.>
Figure FDA0004171691820000014
And the theta is equal to k Whether the difference of (2) is smaller than a second preset threshold, if said +.>
Figure FDA0004171691820000015
And y is k Is smaller than a first preset threshold or +.>
Figure FDA0004171691820000016
And the theta is equal to k When the difference of (2) is smaller than the second preset threshold value, extracting the formula +.>
Figure FDA0004171691820000017
Is calculated according to the calculation result of (2);
wherein the said
Figure FDA0004171691820000018
And estimating a parameter variable of the dynamic equivalent model at the moment k, wherein the parameter variable comprises:unit length self-resistance R of dynamic equivalent model of first side of fault node lsk Mutual resistance R lmk Self-inductance L lsk Mutual inductance L lmk Phase-to-phase capacitance C lpk Capacitance to ground C lgk And the unit length self-resistance R of the dynamic equivalent model of the second side of the fault point rsk Mutual resistance R rmk Self-inductance L rsk Mutual inductance L rmk Phase-to-phase capacitance C rpk Capacitance to ground C rgk Three-phase conductivity estimation value G of fault point fak 、G fbk 、G fck And earth conductance G gk Distance value l of fault point from left bus fk Said->
Figure FDA0004171691820000019
Estimating the value of the output variable of the dynamic equivalent model at the moment K, wherein the K is the estimated value of the output variable of the dynamic equivalent model at the moment K θ Filter gain as parameter variable, y k Actually measuring a phasor value for an output variable of the dynamic equivalent model at the moment k;
correcting the parameter variable by a correction value theta k The target element in the model is taken as a fault distance correction value l at the moment k fk And outputting.
2. The power transmission line fault locating method based on the dynamic equivalence model as claimed in claim 1, wherein,
the said
Figure FDA0004171691820000021
Wherein (1)>
Figure FDA0004171691820000022
Unit length self-resistance R of dynamic equivalent model of first side of fault point lsk Mutual resistance R lmk Self-inductance L lsk Mutual inductance L lmk Phase-to-phase capacitance C lpk Capacitance to ground C lgk And the unit length self-resistance R of the dynamic equivalent model of the second side of the fault point rsk Mutual resistance R rmk Self-inductance L rsk Mutual electricitySense of L rmk Phase-to-phase capacitance C rpk Capacitance to ground C rgk Three-phase conductivity estimation value G of fault point fak 、G fbk 、G fck And earth conductance G gk Distance l of fault point from first side bus fk Is used for the estimation of the estimated value of (a).
3. The power transmission line fault locating method based on the dynamic equivalence model as claimed in claim 2, wherein,
Figure FDA0004171691820000023
wherein (1)>
Figure FDA0004171691820000024
z k ＝[u xk u yk ] T ，/>
Figure FDA0004171691820000025
The estimated value of the state variable at the moment k, and v is measurement noise;
the E is 3×3 A unit matrix of 3*3, said Z 3×3 A zero matrix of 3*3, said u xk ＝[U xak U xbk U xck ] T For the instantaneous value phasor of the three-phase voltage at the moment K at the bus of the first side of the line, the u yk ＝[U yak U ybk U yck ] T The phase quantity is the instantaneous value phasor of the three-phase voltage at the moment k at the bus of the second side of the line;
the l is t Is the total length of the line;
Figure FDA0004171691820000026
Figure FDA0004171691820000027
y k ＝[i xk i yk ] T ，i xk i is the actual measured phasor of the instantaneous value of the three-phase current at the moment k of the first side of the line to be tested yk Is the actual measured phasor of the instantaneous value of the three-phase current at the moment k of the second side of the line to be measured.
4. The power transmission line fault locating method based on the dynamic equivalence model as claimed in claim 2, wherein,
the said
Figure FDA0004171691820000031
Wherein,,
Figure FDA0004171691820000032
estimating a value for said parameter variable>
Figure FDA0004171691820000033
Covariance matrix of>
Figure FDA0004171691820000034
Wherein E is 3×3 Identity matrix of 3 x 3, Z 3×3 A zero matrix of 3 x 3, said +.>
Figure FDA0004171691820000035
Estimating a value for said parameter variable>
Figure FDA0004171691820000036
And R is a preset measurement noise covariance matrix.
5. The power transmission line fault locating method based on the dynamic equivalence model as claimed in claim 4, wherein,
further comprises: calculating state variable x of the dynamic equivalent model at the moment of failure 0 And parameter variable theta 0 State variable x 0 Covariance matrix P of (2) x0 And parameter variablesθ 0 Covariance matrix P of (2) θ0 ；
Calculating state variable estimated value of the dynamic equivalent model at k moment
Figure FDA0004171691820000037
And parameter variable estimation value of the dynamic equivalent model +.>
Figure FDA0004171691820000038
State variable estimate +. >
Figure FDA0004171691820000039
Covariance matrix>
Figure FDA00041716918200000310
And parameter variable estimate +.>
Figure FDA00041716918200000311
Covariance matrix>
Figure FDA00041716918200000312
Calculating a state variable correction value x of the dynamic equivalent model at the moment k k And the parameter variable correction value theta of the dynamic equivalent model k Correction value x of state variable k Covariance matrix P of (2) xk And parameter variable correction value theta k Covariance matrix P of (2) θk ；
Specific:
the theta is as follows 0 ＝[R ls0 R lm0 L ls0 L lm0 C lp0 C lg0 R rs0 R rm0 L rs0 L rm0 C rp0 C rg0 G fa0 G fb0 G fc0 G g0 l f0 ] T In the scheme, the subscript 0 indicates the initial time, the subscript k indicates the k time, and R ls0 ＝R rs0 ＝(2R p0 +R z0 )/3，R lm0 ＝R rm0 ＝(R z0 -R p0 )/3,R lm0 ＝R rm0 ＝(R z0 -R p0 )/3，L ls0 ＝L rs0 ＝(2L p0 +L z0 )/3，L lm0 ＝L rm0 ＝(L z0 -L p0 )/3，C lp0 ＝C p0 ，C lg0 ＝C rg0 ＝3C p0 C z0 /(C p0 -C z0 ) Wherein R is p0 、L p0 、C p0 Respectively a positive sequence resistance, an inductance and a capacitance of a unit length of the monitored line, R z0 、L z0 、C z0 The zero sequence resistance, inductance and capacitance of the unit length of the tested line are respectively;
P θ0 is a preset value;
x 0 ＝[i l0 i r0 u f0 ] T wherein, the instantaneous value vector i of three-phase current of the first side dynamic equivalent model at the moment of the fault l0 ＝[I la0 I lb0 I lc0 ] T The I is la0 、I lb0 And I lc0 The current instantaneous values of a phase, b phase and c phase of the three-phase current of the dynamic equivalent model at the first side at the moment of the fault are respectively the current instantaneous value vector i of the three-phase current of the dynamic equivalent model at the second side at the moment of the fault r0 ＝[I ra0 I rb0 I rc0 ] T The I is ra0 、I rb0 And I rc0 The current instantaneous values of a phase, b phase and c phase of the three-phase current of the first side dynamic equivalent model at the moment of failure are respectively the three-phase voltage instantaneous value u at the point of failure f0 ＝[U fa0 U fb0 U fc0 ] T The U is fa0 、U fb0 And U fc0 The voltage instantaneous values of a phase, b phase and c phase of the three-phase voltage at the moment of failure respectively,
i l0 ＝i x0 -l f0 C l0 du x0 /dt
i r0 ＝i y0 +(l t -l f0 )C r0 du y0 /dt
u f0 ＝u x0 -l f0 R l0 i l0 -l f0 L l0 di l0 /dt
Wherein, I t For the total length of the tested line, l f0 An initial estimated value of the distance between the fault point and the first side bus is obtained; d/dt is the differential operator; u (u) x0 ＝[U xa0 U xb0 U xc0 ] T And i x0 ＝[I xa0 I xb0 I xc0 ] T U is the instantaneous value vector of three-phase voltage and current at the moment of fault at the bus of the first side of the line y0 ＝[U ya0 U yb0 U yc0 ] T And i y0 ＝[I ya0 I yb0 I yc0 ] T The instantaneous value vector of the three-phase voltage and the current is the instantaneous value vector of the fault at the bus on the second side of the line; r is R l0 、L l0 、C l0 、C r0 The dynamic equivalent model resistance matrix, the inductance matrix and the capacitance matrix of the first side of the moment fault point of the fault and the dynamic equivalent model capacitance matrix of the second side of the moment fault point of the fault are respectively, specifically
Figure FDA0004171691820000041
Figure FDA0004171691820000042
Figure FDA0004171691820000043
Covariance matrix P x0 The measurement error of the synchronous phasor unit;
Figure FDA0004171691820000051
Figure FDA0004171691820000052
Figure FDA0004171691820000053
Figure FDA0004171691820000054
in the method, in the process of the invention,
Figure FDA0004171691820000055
Figure FDA0004171691820000056
the k moment state variable estimated value and the parameter variable estimated value are respectively;
x k-1 ＝[i l(k-1) i r(k-1) u f(k-1) ] T 、
θ k-1 ＝[R ls(k-1) R lm(k-1) L ls(k-1) L lm(k-1) C lp(k-1) C lg(k-1) R rs(k-1) R rm(k-1) L rs(k-1) L rm(k-1) C rp(k-1) C rg(k-1) G fa(k-1) G fb(k-1) G fc(k-1) G g(k-1) l f(k-1) ] T the state variable correction value and the parameter variable correction value at the moment k-1 are respectively; p (P) x(k-1) 、P θ(k-1) The state variable covariance matrix and the parameter variable covariance matrix at the moment k-1 are respectively obtained; w (w) x ～N(0,Q x )、w θ ～N(0,Q θ ) Systematic errors, Q, of state variables and parameter variables, respectively x 、Q θ A system error covariance matrix of the state variable and the parameter variable respectively; z k-1 ＝[u x(k-1) u y(k-1) ] T Inputting a variable for time k-1, wherein u x(k-1) ＝[U xa(k-1) U xb(k-1) U xc(k-1) ] T And u y(k-1) ＝[U ya(k-1) U yb(k-1) U yc(k-1) ] T The instantaneous value vectors of the three-phase voltage at the moment k-1 at the left bus and the right bus of the line are respectively; matrix A k-1 、B k-1 Respectively is
Figure FDA0004171691820000057
Figure FDA0004171691820000061
Wherein E is 3×3 、Z 3×3 A 3 x 3 identity matrix and a zero matrix, respectively; t (T) s Is the sampling period; matrix R l(k-1) 、L l(k-1) 、R r(k-1) 、L r(k-1) 、C k-1 、G f(k-1) Respectively is
Figure FDA0004171691820000062
Figure FDA0004171691820000063
C k-1 ＝l f(k-1) C l(k-1) +(l t -l f(k-1) )C r(k-1)
Figure FDA0004171691820000064
Wherein,,
Figure FDA0004171691820000065
Figure FDA0004171691820000066
G gt(k-1) ＝G fa(k-1) +G fb(k-1) +G fc(k-1) +G g(k-1)
the subscript k-1 in the formula represents the moment;
Figure FDA0004171691820000071
Figure FDA0004171691820000072
Figure FDA0004171691820000073
Figure FDA0004171691820000074
wherein E is 9×9 、E 17×17 Identity matrices of 9 x 9 and 17 x 17, respectively; y is k ＝[i xk i yk ] T ，i xk ＝[I xak I xbk I xck ] T 、i yk ＝[I yak I ybk I yck ] T The actual measured value vectors of three-phase current instantaneous values of the left bus and the right bus of the line at the moment k are respectively; k (K) x And K θ The filter gains of the state variable and the parameter variable are respectively calculated according to the following formulas
Figure FDA0004171691820000075
Figure FDA0004171691820000076
6. The utility model provides a transmission line fault locating device based on dynamic equivalence model which characterized in that includes:
the model acquisition unit is used for constructing a pi-type equivalent model matched with the monitored transmission line, estimating parameters and electric quantity of the pi-type equivalent model at the first side and the pi-type equivalent model at the second side of the fault point by adopting an extended Kalman filter, and obtaining a fault instant dynamic equivalent model; the dynamic equivalent model comprises a dynamic equivalent model positioned on a first side of a monitored power transmission line fault node and a dynamic equivalent model positioned on a second side of the monitored power transmission line fault node;
a calculation unit for calculating the estimated value of the output variable of the dynamic equivalent model at the k moment
Figure FDA0004171691820000077
Calculating the actually measured output variable phasor value y of the dynamic equivalent model at the moment k k Calculating the parameter variable estimated value of the dynamic equivalent model at the moment k
Figure FDA0004171691820000078
Parameter variable correction value theta of dynamic equivalent model at k moment k The method comprises the steps of carrying out a first treatment on the surface of the Judging said->
Figure FDA0004171691820000079
And y is k Whether the difference of (2) is smaller than a first preset threshold or +.>
Figure FDA00041716918200000710
And the theta is equal to k Whether the difference of (2) is smaller than a second preset threshold, if said +.>
Figure FDA00041716918200000711
And y is k Is smaller than a first preset threshold or +.>
Figure FDA00041716918200000712
And the theta is equal to k When the difference value of (2) is smaller than the second preset threshold value, extracting the formula
Figure FDA00041716918200000713
Wherein, the +.>
Figure FDA00041716918200000714
And estimating a parameter variable of the dynamic equivalent model at the moment k, wherein the parameter variable comprises: unit length self-resistance R of dynamic equivalent model of first side of fault node lsk Mutual resistance R lmk Self-inductance L lsk Mutual inductance L lmk Phase-to-phase capacitance C lpk Capacitance to ground C lgk And the unit length self-resistance R of the dynamic equivalent model of the second side of the fault point rsk Mutual resistance R rmk Self-inductance L rsk Mutual inductance L rmk Phase-to-phase capacitance C rpk Capacitance to ground C rgk Three-phase conductivity estimation value G of fault point fak 、G fbk 、G fck And earth conductance G gk Distance value l of fault point from left bus fk Wherein, said->
Figure FDA0004171691820000081
For the parameter variable estimation value of the dynamic equivalent model at the moment k, the +.>
Figure FDA0004171691820000082
Estimating the value of the output variable of the dynamic equivalent model at the moment K, wherein the K is the estimated value of the output variable of the dynamic equivalent model at the moment K θ Filter gain as parameter variable, y k Actually measuring a phasor value for an output variable of the dynamic equivalent model at the moment k;
a fault distance output unit for outputting the parameter variable correction value theta k The target element in the model is taken as a fault distance correction value l at the moment k fk And outputting.
7. According to claim 6The power transmission line fault positioning device based on the dynamic equivalent model is characterized in that the computing unit is also used for being based on a formula
Figure FDA0004171691820000083
Calculating to obtain the estimated value of the parameter variable +.>
Figure FDA0004171691820000084
Wherein->
Figure FDA0004171691820000085
Unit length self-resistance R of dynamic equivalent model of first side of fault point lsk Mutual resistance R lmk Self-inductance L lsk Mutual inductance L lmk Phase-to-phase capacitance C lpk Capacitance to ground C lgk And the unit length self-resistance R of the dynamic equivalent model of the second side of the fault point rsk Mutual resistance R rmk Self-inductance L rsk Mutual inductance L rmk Phase-to-phase capacitance C rpk Capacitance to ground C rgk Three-phase conductivity estimation value G of fault point fak 、G fbk 、G fck And earth conductance G gk Distance l of fault point from left bus fk Is used for the estimation of the estimated value of (a).
8. The power transmission line fault locating device based on the dynamic equivalence model as claimed in claim 6, wherein,
Figure FDA0004171691820000086
wherein (1)>
Figure FDA0004171691820000087
z k ＝[u xk u yk ] T ，/>
Figure FDA0004171691820000088
The estimated value of the state variable at the moment k, v is the measurement noiseSound;
The E is 3×3 A unit matrix of 3*3, said Z 3×3 A zero matrix of 3*3, said u xk ＝[U xak U xbk U xck ] T For the instantaneous value phasor of the three-phase voltage at the moment K at the bus of the first side of the line, the u yk ＝[U yak U ybk U yck ] T The phase quantity is the instantaneous value phasor of the three-phase voltage at the moment k at the bus of the second side of the line;
the l is t Is the total length of the line;
Figure FDA0004171691820000091
Figure FDA0004171691820000092
y k ＝[i xk i yk ] T ，i xk i is the actual measured phasor of the instantaneous value of the three-phase current at the moment k of the first side of the line to be tested yk Is the actual measured phasor of the instantaneous value of the three-phase current at the moment k of the second side of the line to be measured.
9. The power transmission line fault locating device based on the dynamic equivalence model as claimed in claim 6, wherein,
the said
Figure FDA0004171691820000093
Wherein,,
Figure FDA0004171691820000094
estimating a value for said parameter variable>
Figure FDA0004171691820000095
Covariance matrix of>
Figure FDA0004171691820000096
Wherein E is 3×3 Identity matrix of 3 x 3, Z 3×3 A zero matrix of 3 x 3, said +.>
Figure FDA0004171691820000097
Estimating a value for said parameter variable>
Figure FDA0004171691820000098
And R is a preset measurement noise covariance matrix.
10. The power transmission line fault locating device based on a dynamic equivalence model according to claim 9, wherein the computing unit is further configured to:
calculating state variable x of the dynamic equivalent model at the moment of failure 0 And parameter variable theta 0 State variable x 0 Covariance matrix P of (2) x0 And parameter variable theta 0 Covariance matrix P of (2) θ0 ；
Calculating state variable estimated value of the dynamic equivalent model at k moment
Figure FDA0004171691820000101
And parameter variable estimation value of the dynamic equivalent model +.>
Figure FDA0004171691820000102
State variable estimate +.>
Figure FDA0004171691820000103
Covariance matrix>
Figure FDA0004171691820000104
And parameter variable estimate +.>
Figure FDA0004171691820000105
Covariance matrix>
Figure FDA0004171691820000106
Calculating a state variable correction value x of the dynamic equivalent model at the moment k k And the parameter variable correction value theta of the dynamic equivalent model k Correction value x of state variable k Covariance matrix P of (2) xk And parameter variable correction value theta k Covariance matrix P of (2) θk ；
Specific:
the theta is as follows 0 ＝[R ls0 R lm0 L ls0 L lm0 C lp0 C lg0 R rs0 R rm0 L rs0 L rm0 C rp0 C rg0 G fa0 G fb0 G fc0 G g0 l f0 ] T In the scheme, the subscript 0 indicates the initial time, the subscript k indicates the k time, and R ls0 ＝R rs0 ＝(2R p0 +R z0 )/3，R lm0 ＝R rm0 ＝(R z0 -R p0 )/3，L ls0 ＝L rs0 ＝(2L p0 +L z0 )/3，L lm0 ＝L rm0 ＝(L z0 -L p0 )/3，C lp0 ＝C p0 ，C lg0 ＝C rg0 ＝3C p0 C z0 /(C p0 -C z0 ) Wherein R is p0 、L p0 、C p0 Respectively a positive sequence resistance, an inductance and a capacitance of a unit length of the monitored line, R z0 、L z0 、C z0 The zero sequence resistance, inductance and capacitance of the unit length of the tested line are respectively;
P θ0 is a preset value;
x 0 ＝[i l0 i r0 u f0 ] T wherein, the instantaneous value vector i of three-phase current of the first side dynamic equivalent model at the moment of the fault l0 ＝[I la0 I lb0 I lc0 ] T The I is la0 、I lb0 And I lc0 A phase, b phase and c phase of three-phase current of a first side dynamic equivalent model at the moment of failureInstantaneous value of phase current, instantaneous value vector i of instantaneous value of phase current of second side dynamic equivalent model of fault r0 ＝[I ra0 I rb0 I rc0 ] T The I is ra0 、I rb0 And I rc0 The current instantaneous values of a phase, b phase and c phase of the three-phase current of the first side dynamic equivalent model at the moment of failure are respectively the three-phase voltage instantaneous value u at the point of failure f0 ＝[U fa0 U fb0 U fc0 ] T The U is fa0 、U fb0 And U fc0 The voltage instantaneous values of a phase, b phase and c phase of the three-phase voltage at the moment of failure respectively,
i l0 ＝i x0 -l f0 C l0 du x0 /dt
i r0 ＝i y0 +(l t -l f0 )C r0 du y0 /dt
u f0 ＝u x0 -l f0 R l0 i l0 -l f0 L l0 di l0 /dt
wherein, I t For the total length of the tested line, l f0 An initial estimated value of the distance between the fault point and the first side bus is obtained; d/dt is the differential operator; u (u) x0 ＝[U xa0 U xb0 U xc0 ] T And i x0 ＝[I xa0 I xb0 I xc0 ] T U is the instantaneous value vector of three-phase voltage and current at the moment of fault at the bus of the first side of the line y0 ＝[U ya0 U yb0 U yc0 ] T And i y0 ＝[I ya0 I yb0 I yc0 ] T The instantaneous value vector of the three-phase voltage and the current is the instantaneous value vector of the fault at the bus on the second side of the line; r is R l0 、L l0 、C l0 、C r0 The dynamic equivalent model resistance matrix, the inductance matrix and the capacitance matrix of the first side of the moment fault point of the fault and the dynamic equivalent model capacitance matrix of the second side of the moment fault point of the fault are respectively, specifically
Figure FDA0004171691820000111
Figure FDA0004171691820000112
Figure FDA0004171691820000113
Covariance matrix P x0 The measurement error of the synchronous phasor unit;
Figure FDA0004171691820000114
Figure FDA0004171691820000115
Figure FDA0004171691820000116
Figure FDA0004171691820000117
in the method, in the process of the invention,
Figure FDA0004171691820000118
Figure FDA0004171691820000119
the k moment state variable estimated value and the parameter variable estimated value are respectively;
x k-1 ＝[i l(k-1) i r(k-1) u f(k-1) ] T 、
θ k-1 ＝[R ls(k-1) R lm(k-1) L ls(k-1) L lm(k-1) C lp(k-1) C lg(k-1) R rs(k-1) R rm(k-1) L rs(k-1) L rm(k-1) C rp(k-1) C rg(k-1) G fa(k-1) G fb(k-1) G fc(k-1) G g(k-1) l f(k-1) ] T the state variable correction value and the parameter variable correction value at the moment k-1 are respectively; p (P) x(k-1) 、P θ(k-1) The state variable covariance matrix and the parameter variable covariance matrix at the moment k-1 are respectively obtained; w (w) x ～N(0,Q x )、w θ ～N(0,Q θ ) Systematic errors, Q, of state variables and parameter variables, respectively x 、Q θ A system error covariance matrix of the state variable and the parameter variable respectively; z k-1 ＝[u x(k-1) u y(k-1) ] T Inputting a variable for time k-1, wherein u x(k-1) ＝[U xa(k-1) U xb(k-1) U xc(k-1) ] T And u y(k-1) ＝[U ya(k-1) U yb(k-1) U yc(k-1) ] T The instantaneous value vectors of the three-phase voltage at the moment k-1 at the left bus and the right bus of the line are respectively; matrix A k-1 、B k-1 Respectively is
Figure FDA0004171691820000121
Figure FDA0004171691820000122
Wherein E is 3×3 、Z 3×3 A 3 x 3 identity matrix and a zero matrix, respectively; t (T) s Is the sampling period; matrix R l(k-1) 、L l(k-1) 、R r(k-1) 、L r(k-1) 、C k-1 、G f(k-1) Respectively is
Figure FDA0004171691820000123
Figure FDA0004171691820000124
C k-1 ＝l f(k-1) C l(k-1) +(l t -l f(k-1) )C r(k-1)
Figure FDA0004171691820000131
Wherein,,
Figure FDA0004171691820000132
Figure FDA0004171691820000133
G gt(k-1) ＝G fa(k-1) +G fb(k-1) +G fc(k-1) +G g(k-1)
the subscript k-1 in the formula represents the moment;
Figure FDA0004171691820000134
Figure FDA0004171691820000135
Figure FDA0004171691820000136
Figure FDA0004171691820000137
wherein E is 9×9 、E 17×17 Identity matrices of 9 x 9 and 17 x 17, respectively; y is k ＝[i xk i yk ] T ，i xk ＝[I xak I xbk I xck ] T 、i yk ＝[I yak I ybk I yck ] T The actual measured value vectors of three-phase current instantaneous values of the left bus and the right bus of the line at the moment k are respectively; k (K) x And K θ The filter gains of the state variable and the parameter variable are respectively calculated according to the following formulas
Figure FDA0004171691820000138
Figure FDA0004171691820000139
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