CN112115568B - PMU measurement-based improved coupling least square transmission line parameter identification method - Google Patents

PMU measurement-based improved coupling least square transmission line parameter identification method Download PDF

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CN112115568B
CN112115568B CN202010905868.1A CN202010905868A CN112115568B CN 112115568 B CN112115568 B CN 112115568B CN 202010905868 A CN202010905868 A CN 202010905868A CN 112115568 B CN112115568 B CN 112115568B
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parameter identification
transmission line
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data
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CN112115568A (en
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王国松
唐建兴
马覃峰
刘明顺
王永刚
赵维兴
张勇
朱灵子
姚瑶
陈锐
曹杰
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Guizhou Power Grid Co Ltd
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Abstract

The invention discloses an improved coupling least square power transmission line parameter identification method based on PMU measurement, which comprises the steps of establishing a medium-short length power transmission line equivalent circuit model; establishing a time-varying scalar linear equation of the transmission line model; and carrying out transmission line parameter identification by using a modified data window coupling recursive least square method with the variable past factors. The parameter identification method provided by the invention combines the data window of the coupling recursive identification and the least square algorithm with the forgetting factor idea, does not need large-scale matrix inversion operation, can effectively take effect of the influence of abrupt change disturbance on identification, and greatly improves the quick tracking property, convergence stability and accuracy.

Description

PMU measurement-based improved coupling least square transmission line parameter identification method
Technical Field
The invention belongs to the field of power system automation, and particularly relates to an improved coupling least square power transmission line parameter identification method based on PMU measurement.
Background
Along with the development of economy and society, electric energy becomes an indispensable secondary energy source in the production and life of people, and brings endless convenience to the production and life of people. With the increasing scale of the power grid and the rapid increase of the power demand, people put higher requirements on the power supply reliability, and the online application of the power grid regulation plays a key role of more basic. As a carrier for transporting electrical energy, an electrical transmission line is an integral part of the electrical network. The electric parameters of the power transmission line are used as a model basis for online application, and the identification accuracy of the electric parameters has important significance for power system state estimation, power transmission line fault positioning, power flow analysis, protection setting and the like.
The transmission line parameters adopted by the current dispatching automation system are obtained in an off-line mode, and the obtaining mode mainly comprises theoretical calculation and off-line measurement. In the actual operation process, along with the changes of the operation environment, the operation state and the like, the parameters of the power transmission line are changed, and the changes cannot be fed back to the dispatching automation system in real time, so that the accuracy and the credibility of a dispatching strategy are seriously affected. In recent years, wide Area Measurement Systems (WAMS) based on Phasor Measurement Units (PMUs) have been popularized and applied in the field of power systems. Besides the amplitude of the voltage and the current, the PMU device can acquire the phase of the voltage and the current, and the data updating speed reaches millisecond level, so that a reliable real-time data source is provided for accurately identifying the parameters of the power transmission line. At present, in line parameter identification by using a PMU device, a least squares identification principle is largely applied. The identification of the multi-variable system by the least square algorithm generally involves matrix inversion operation, which increases the operation amount and the calculation complexity. Meanwhile, the data fluctuation at adjacent moments is too small, so that a singular matrix is formed in the identification recursion process, and the calculated numerical value is abnormal. Therefore, it is necessary to explore new and highly accurate power line parameter identification methods that effectively utilize PMU measurements.
Disclosure of Invention
It is an object of a first aspect of the present invention to provide an improved coupled least squares transmission line parameter identification method based on PMU measurements. The invention combines the coupling recursive identification with the data window and forgetting factor principle of the least square algorithm, and realizes the rapid, accurate and high-precision identification of the transmission line parameters by utilizing PMU measurement data.
The object of the first aspect of the present invention is achieved by the following technical solutions:
the PMU measurement-based improved coupling least square transmission line parameter identification method comprises the following steps:
s1, establishing an equivalent circuit model of a medium-length and short-length power transmission line;
s2, establishing a time-varying scalar linear equation of the power transmission line model according to the equivalent circuit model established in the step S1;
s3, utilizing a forgetting factor to improve a data window coupling recursion least square method to identify transmission line parameters;
and S1, establishing a medium and short-length power transmission line equivalent circuit model, namely establishing a centralized parameter pi-type equivalent circuit model applicable to the medium and short-length power transmission line, wherein the first end and the tail end of the model are respectively marked as an m end and an n end, the equivalent impedance of the line between the m end and the n end is Z, and the two ends of the model are grounded through Y/2 equivalent susceptors.
The scalar linear equation for building the transmission line model in step S2 is specifically a scalar linear equation for building the transmission line model by adopting the following steps:
A. for the equivalent circuit model established in step S1, according to kirchhoff' S current law, the relationship between the line parameters and the running state can be expressed as:
wherein the method comprises the steps ofRespectively representing voltage and current phasors at two ends of a line
B. According to the electric power definition, the relationship between the line parameters and the operating state can be expressed as:
wherein S is (m，n) 、P (m，n) 、Q (m，n) The apparent power, active power and reactive power of the line, respectively.
C. Expanding phasors on the left side and the right side of the relation equation of the step A and the step B according to a real part and an imaginary part respectively, and respectively representing the inverse of the equivalent impedance Z of the circuit by g and B, namely 1/Z=g+jb; let B denote the imaginary part of the ground susceptance Y/2, i.e. Y/2=jb. The following scalar linear equation is obtained:
wherein r and i represent the real and imaginary parts, phi, respectively, of the current phasor um 、φ un Is the phase angle of the voltage at two ends.
D. In actual operation, the current-voltage phasors all change with time t, and the line parameters are also time-varying parameters in the fluctuation process of the load, so the time-varying form of the scalar linear equation in step C can be expressed as:
in the step S3, the transmission line parameter identification is performed by using a variable forgetting factor improved data window coupling recursive least square method, specifically, the transmission line parameter identification is performed by adopting the following steps:
a. abstracting the time-varying scalar linear equation in step S2 as:
y(t)＝Φ(t)θ(t) (6)
wherein y (t) = [ I ] mr (t)，I mi (t)，I nr (t)，I ni (t)，P m (t)，Q m (t)，P n (t)，Q n (t)] T ∈R 8 Determining an output of the system for the multiple time-varying;
determining an observation matrix of a system for multi-element time variation, wherein the observation matrix corresponds to voltage and phase angle quantity measured by a PMU;
θ(t)＝[g(t)，b(t)，B(t)] T ∈R 3 and determining the phasors to be identified of the system for multiple time-varying, and corresponding to the line parameters to be identified.
b. The system is decomposed into 8 subsystems according to the number of output signals y in the step a, and each subsystem is called a multiple-input single-output system and can be expressed as:
c. taking a data segment with the PMU measurement data length d as a window, initializing identification values and information in the data window, and obtaining an identification parameter matrix with the initialized data window lengthIdentification residual matrix->The covariance matrix P is initialized as follows:
at t 0 Number =1The data points apply a single-point least square algorithm to all subsystems to obtain an identification parameter matrix and an identification residual matrix;
at t 0 The data points are=2 to d, and the subsystem coupling recursive least square algorithm is applied to each subsystem to obtain an identification parameter matrix and an identification residual matrix.
At t 0 =d data points, the covariance matrix P is initialized as follows:
d. and reasonably selecting lambda min, lambda bmark and lambda max according to the identified rapid following property and stability, and meeting the following conditions: λmin < λbmark < λmax.
e. Comparison |e i (t) | andwherein: />i=1, 2,3, …,8, identify innovation for the subsystem; t is the data point corresponding to the moment of comparison, and the t=0 data point is the t in step c 0 =d data points; n is n 1 The change degree of the state is represented in a positive slope form for the threshold coefficient, and the value is taken according to line operation experience;for the ith subsystem in step c +.>Maximum value of vector absolute value.
f. And e, judging according to the comparison result in the step e:
if |e i (t)|＜n 1 ·max{|e (i，d0) I, judging that the system is in a stable running state;
if |e i (t)|＞n 1 ·max{|e (i，d0) I, then determine systemThe state is mutated.
g. Based on the determination result of step f, assume t s Mutation of system state:
if the system is in a stable running state, and t is more than or equal to t s +d, executing parameter identification in a steady state;
if the system is mutated, and at t s ≤t＜t s And in the +d data range, executing the parameter identification leaving the original steady state.
The steady state parameter identification is executed, specifically, parameter identification of different steady state phases is executed according to the current data point t:
if t is less than or equal to d and the system is not mutated, executing a parameter identification strategy in an initial stage under a steady state;
if t > d, executing the parameter identification strategy in the running stage under the steady state.
The parameter identification strategy for executing the initial stage under the steady state is specifically implemented by adopting the following steps:
r1. comparison of |e i (t) | and |E d [e i (t)]I, determining the recognition forgetting factor:
wherein the method comprises the steps ofThe expected absolute value is new for the data window.
R2. let Δε= | (|e) i (t)|-|E d [e i (t)]I) and λ is determined according to the range of Δε i (t) linearizing the mapping to obtain reasonable forgetting factors in the range of λmin and λmax:
if delta epsilon [0, |E ] d [e i (t)]I) range, lambda is calculated i (t) mapping to (λbmark, λmax]In the interval of (2):
if delta epsilon E [ |E d [e i (t)]|，5|E d [e i (t)]I), lambda is given i (t) mapping to (λmin, λbmark)]In the interval of (2):
and R3, carrying out the following parameter identification by utilizing the genetic factors determined in the step R2:
when i=1:
when i=2, 3, …, 8:
the parameter identification strategy for executing the operation stage in the steady state is specifically implemented by adopting the following steps:
t1. comparison of |E q [e i (t)]I and I E d [e i (t)]I, determining the recognition forgetting factor:
wherein the method comprises the steps ofAbsolute value expected for local innovation; q is the local information window length, typically q < 10 or d/q > 10.
T2. let Δε= | (|e) q [e i (t)]|-|E d [e i (t)]I) and λ is determined according to the range of Δε i (t) linearizing the mapping to obtain reasonable forgetting factors within the range of lambda min and lambda max：
If delta epsilon [0, |E ] d [e i (t)]I) range, lambda is calculated i (t) mapping to (λbmark, λmax]In the interval of (2):
if delta epsilon E [ |E d [e i (t)]|，5|E d [e i (t)]I), lambda is given i (t) mapping to (λmin, λbmark)]In the interval of (2):
and T3, carrying out parameter identification by using the genetic factors determined in the step T2 and using the formulas (12) and (13).
The step of executing the parameter identification leaving the original steady state is specifically to execute the parameter identification leaving the original steady state by adopting the following steps:
I. setting the starting point of the data window to t s Data points.
Ii. at t=t s The covariance matrix P is initialized as follows:
III. comparison of |E q′ [e i (t)]I and I E d′ [e i (t)]I, determining the recognition forgetting factor:
wherein the method comprises the steps ofWindow length for local information, +.>Is the length of the identified local data window.
IV. let Δε= | (|E) q′ [e i (t)]|-|E d′ [e i (t)]I) and λ is determined according to the range of Δε i (t) linearizing the mapping to obtain reasonable forgetting factors in the range of λmin and λmax:
if delta epsilon [0, |E ] d′ [e i (t)]I) range, lambda is calculated i (t) mapping to (λbmark, λmax]In the interval of (2):
if delta epsilon E [ |E d′ [e i (t)]|，5|E d′ [e i (t)]I), lambda is given i (t) mapping to (λmin, λbmark)]In the interval of (2):
and V, carrying out the following parameter identification by utilizing the genetic factors determined in the step IV:
when i=1:
when i=2, 3, …, 8:
h.t = t+1 data points, repeating steps e-g until the manual termination algorithm saves the identification parameters.
The object of the second aspect of the present invention is achieved by the following technical solutions:
a computer apparatus comprising a memory, a processor and a computer program stored on the memory and capable of running on the processor, the processor implementing a method as hereinbefore described when executing the computer program.
The object of the third aspect of the present invention is achieved by the following technical solutions:
a computer readable storage medium having stored thereon a computer program which when executed by a processor implements a method as described above.
The beneficial effects of the invention are as follows:
(1) According to the power transmission line parameter identification method, coupling recursion identification is combined with the data window and forgetting factor ideas of a least square algorithm, so that recursion is prevented from falling into data saturation, the advantages of coupling recursion and the limited data window ideas are reserved in the whole design, and the parameter identification performance is improved.
(2) Compared with other multivariable system identification methods, the parameter identification method does not need to perform large-scale matrix inversion operation, and shows the superiority in calculation speed and precision in simulation;
(3) According to the parameter identification method, the algorithm is optimized by combining with the dynamic adjustment of the forgetting factor, the running state of the system is judged by comparing the information of the subsystem, and the forgetting factor is dynamically adjusted, so that the rapid tracking performance of the algorithm on time-varying parameters and the convergence stability performance of the time-invariant parameters are further enhanced;
(4) The method of the invention adopts a mode of redefining the combination of the covariance matrix and the variable forgetting factor variable data window for the system mutation situation, thereby effectively reducing the influence of mutation disturbance on identification
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof.
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For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings, in which:
FIG. 1 is a schematic flow chart of the method of the present invention.
Detailed Description
Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. It should be understood that the preferred embodiments are presented by way of illustration only and not by way of limitation.
The invention provides an improved coupling least square power transmission line parameter identification method for PMU measurement, which comprises the following specific steps of:
s1, establishing an equivalent circuit model of a medium-length and short-length power transmission line, wherein the equivalent circuit model comprises the following steps of:
and establishing a centralized parameter pi-type equivalent circuit model suitable for the medium and short-length power transmission lines, wherein the first end and the tail end of the model are respectively marked as an m end and an n end, the equivalent impedance of the line between the m end and the n end is Z, and the two ends of the model are grounded through Y/2 equivalent susceptors.
S2, according to the equivalent circuit model established in the step S1, establishing a time-varying scalar linear equation of the power transmission line model, wherein the steps are as follows:
A. for the equivalent circuit model established in step S1, according to kirchhoff' S current law, the relationship between the line parameters and the running state can be expressed as:
wherein the method comprises the steps ofRespectively representing voltage and current phasors at two ends of a line
B. According to the electric power definition, the relationship between the line parameters and the operating state can be expressed as:
wherein S is (m，n) 、P (m，n) 、Q (m，n) The apparent power, active power and reactive power of the line, respectively.
C. Expanding phasors on the left side and the right side of the relation equation of the step A and the step B according to a real part and an imaginary part respectively, and respectively representing the inverse of the equivalent impedance Z of the circuit by g and B, namely 1/Z=g+jb; let B denote the imaginary part of the ground susceptance Y/2, i.e. Y/2=jb. The following scalar linear equation is obtained:
wherein r and i represent the real and imaginary parts, phi, respectively, of the current phasor um 、φ un Is the phase angle of the voltage at two ends.
D. In actual operation, the current-voltage phasors all change with time t, and the line parameters are also time-varying parameters in the fluctuation process of the load, so the time-varying form of the scalar linear equation in step C can be expressed as:
s3, carrying out transmission line parameter identification by using a forgetting factor improved data window coupling recursion least square method, and referring to FIG. 1, specifically comprising the following steps:
a. PMU measurement data is obtained.
b. Abstracting the time-varying scalar linear equation in step S2 as:
y(t)＝Φ(t)θ(t) (6)
wherein y (t) = [ I ] mr (t)，I mi (t)，I nr (t)，I ni (t)，P m (t)，Q m (t)，P n (t)，Q n (t)] T ∈R 8 Determining an output of the system for the multiple time-varying;
determining an observation matrix of a system for multi-element time variation, wherein the observation matrix corresponds to voltage and phase angle quantity measured by a PMU;
θ(t)＝[g(t)，b(t)，B(t)] T ∈R 3 and determining the phasors to be identified of the system for multiple time-varying, and corresponding to the line parameters to be identified.
c. The system is decomposed into 8 subsystems according to the number of output signals y in the step a, and each subsystem is called a multiple-input single-output system and can be expressed as:
d. and (3) performing initialization setting: taking a data segment with the PMU measurement data length d as a window, initializing identification values and information in the data window, and obtaining an identification parameter matrix with the initialized data window lengthIdentification residual matrix->And reasonably selecting lambda min, lambda bmark and lambda max according to the identified rapid following property and stability, and meeting the following conditions: λmin < λbmark < λmax; the covariance matrix P is initialized as follows:
at t 0 The data point=1 applies a single-point least square algorithm to all subsystems to obtain an identification parameter matrix and an identification residual matrix;
at t 0 The data points are=2 to d, and the subsystem coupling recursive least square algorithm is applied to each subsystem to obtain an identification parameter matrix and an identification residual matrix.
At t 0 =d data points, the covariance matrix P is initialized as follows:
e. executing a parameter identification strategy of an initial stage under a steady state, wherein the method comprises the following specific steps:
r1. comparison of |e i (t) | and |E d [e i (t)]I, determining the recognition forgetting factor:
wherein:i=1, 2,3, …,8, identify innovation for the subsystem; t is the data point corresponding to the moment of comparison, and the t=0 data point is the t in the step d 0 =d data points; />The expected absolute value is new for the data window.
R2. let Δs= | (|e) i (t)|-|E d [e i (t)]I) and λ is determined according to the range of Δε i (t) linearizing the mapping to obtain reasonable forgetting factors in the range of λmin and λmax:
if delta epsilon [0, |E ] d [e i (t)]I), lambda is given i (t) mapping to (λbmark, λmax]In the interval of (2):
if delta epsilon E [ |E d [e i (t)]|，5|E d [e i (t)]I), lambda is given i (t) mapping to (λmin, λbmark)]In the interval of (2):
and R3, carrying out the following parameter identification by utilizing the genetic factors determined in the step R2:
when i=1:
when i=2, 3, …, 8:
f. as shown in fig. 1, the time is increased by 1 and the time is shifted backward.
g. Comparison |e i (t) | andwherein n is 1 The change degree of the state is represented in a positive slope form for the threshold coefficient, and the value is taken according to line operation experience; />For the ith subsystem in step d +.>Maximum value of vector absolute value.
If |e i (t)|＜n 1 ·max{|e (i，d0) I, judging that the system is in a stable running state;
if |e i (t)|＞n 1 ·max{|e (i，d0) And (3) judging that the system state is suddenly changed.
h. Based on the determination result of step f, assume t s Mutation of system state:
1) If the system is mutated, and at t s ≤t＜t s In the +d data range, the parameter identification leaving the original steady state is executed, and the specific steps are as follows:
I. setting the starting point of the data window to t s Data points.
Ii. at t=t s The covariance matrix P is initialized as follows:
III. comparison of |E q′ [e i (t)]I and E d′ [e i (t)]I, determining the recognition forgetting factor:
wherein the method comprises the steps ofWindow length for local information, +.>Is the length of the identified local data window.
IV. let Δε= | (|E) q′ [e i (t)]|-|E d′ [e i (t)]I) and λ is determined according to the range of Δε i (t) linearizing the mapping to obtain reasonable forgetting factors in the range of λmin and λmax:
if delta epsilon [0, |E ] d′ [e i (t)]I), lambda is given i (t) mapping to (λbmark, λmax]In the interval of (2):
if delta epsilon E [ |E d′ [e i (t)]|，5|E d′ [e i (t)]I), lambda is given i (t) mapping to (λmin, λbmark)]In the interval of (2):
and V, carrying out the following parameter identification by utilizing the genetic factors determined in the step IV:
when i=1:
when i=2, 3, …, 8:
2) If the system is in a stable running state, and t is more than or equal to t s +d, determining to execute parameter identification of different steady-state phases according to the current data point t:
w1, if t is more than d, that is, if the current data point is greater than the window length from the initial data point, executing a parameter identification strategy of an operation stage in a steady state, wherein the specific steps are as follows:
t1. comparison of |E q [e i (t)]I and I E d [e i (t)]I, determining the recognition forgetting factor:
wherein the method comprises the steps ofAbsolute value expected for local innovation; q is the local information window length, typically q < 10 or d/q > 10.
T2. let Δε= | (|e) q [e i (t)]|-|E d [e i (t)]I) and λ is determined according to the range of Δε i (t) linearizing the mapping to obtain reasonable forgetting factors in the range of λmin and λmax:
if delta epsilon [0, |E ] d [e i (t)]I), lambda is given i (t) mapping to (λbmark, λmax]In the interval of (2):
if delta epsilon [ |E d [e i (t)]|，5|E d [e i (t)]I), lambda is given i (t) mapping to (λmin, λbmark)]In the interval of (2):
and T3, carrying out parameter identification by using the genetic factors determined in the step T2 and using the formulas (12) and (13).
And W2, repeating the steps e to h if t is less than or equal to d, namely, if the distance between the current data point and the initial data point is greater than the window length.
i. Judging whether the algorithm exit condition is received or not:
if accepted, the algorithm terminates the saving of the identification data
If not, repeating the steps f to i.
It should be noted that any process or method descriptions in flow charts of the present invention or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and that preferred embodiments of the present invention include additional implementations in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the embodiments of the present invention.
Logic and/or steps represented in the flowcharts or otherwise described herein, e.g., a ordered listing of executable instructions for implementing logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic device) having one or more wires, a portable computer diskette (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). In addition, the computer readable medium may even be paper or other suitable medium on which the program is printed, as the program may be electronically captured, via, for instance, optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner, if necessary, and then stored in a computer memory.
It is to be understood that portions of the present invention may be implemented in hardware, software, firmware, or a combination thereof. In the above-described embodiments, the various steps or methods may be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, may be implemented using any one or combination of the following techniques, as is well known in the art: discrete logic circuits having logic gates for implementing logic functions on data signals, application specific integrated circuits having suitable combinational logic gates, programmable Gate Arrays (PGAs), field Programmable Gate Arrays (FPGAs), and the like.
Those of ordinary skill in the art will appreciate that all or a portion of the steps carried out in the method of the above-described embodiments may be implemented by a program to instruct related hardware, where the program may be stored in a computer readable storage medium, and where the program, when executed, includes one or a combination of the steps of the method embodiments.
In addition, each functional unit in the embodiments of the present invention may be integrated in one processing module, or each unit may exist alone physically, or two or more units may be integrated in one module. The integrated modules may be implemented in hardware or in software functional modules. The integrated modules may also be stored in a computer readable storage medium if implemented in the form of software functional modules and sold or used as a stand-alone product.
The above-mentioned storage medium may be a read-only memory, a magnetic disk or an optical disk, or the like. The computer program can be applied to the input data to perform the functions described herein, thereby converting the input data to generate output data that is stored to the non-volatile memory. The output information may also be applied to one or more output devices such as a display. In a preferred embodiment of the invention, the transformed data represents physical and tangible objects, including specific visual depictions of physical and tangible objects produced on a display.
Finally, it is noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to be covered by the claims of the present invention.

Claims (3)

1. An improved coupling least square power transmission line parameter identification method based on PMU measurement comprises the following steps:
s1, establishing an equivalent circuit model of a medium-length and short-length power transmission line; the step S1 of establishing the equivalent circuit model of the medium-length and short-length transmission line specifically comprises the following steps: establishing a centralized parameter pi-type equivalent circuit model applicable to medium and short-length power transmission lines, wherein the first end and the tail end of the model are respectively marked as an m end and an n end, the equivalent impedance of the line between the m end and the n end is Z, and the two ends of the model are grounded through Y/2 equivalent susceptors;
s2, establishing a time-varying scalar linear equation of the power transmission line model according to the equivalent circuit model established in the step S1; in step S2, the time-varying scalar linear equation of the transmission line model includes the following steps:
A. for the equivalent circuit model established in step S1, according to kirchhoff' S current law, the relationship between the line parameters and the running state can be expressed as:
wherein the method comprises the steps ofRespectively representing voltage phasors and current phasors at two ends of a line;
B. according to the electric power definition, the relationship between the line parameters and the operating state can be expressed as:
wherein S is (m,n) 、P (m,n) 、Q (m,n) Apparent power, active power and reactive power of the line respectively;
C. expanding phasors on the left side and the right side of the relation equation of the step A and the step B according to a real part and an imaginary part respectively, and respectively representing the inverse of the equivalent impedance Z of the circuit by g and B, namely 1/Z=g+jb; let B denote the imaginary part of the ground susceptance Y/2, i.e. Y/2=jb; the following scalar linear equation is obtained:
wherein r and i represent the real and imaginary parts, phi, respectively, of the current phasor um 、φ un Is the phase angle of the voltage at two ends;
D. in actual operation, the current-voltage phasors all change with time t, and the line parameters are also time-varying parameters in the fluctuation process of the load, so the time-varying form of the scalar linear equation in step C can be expressed as:
s3, utilizing a forgetting factor to improve a data window coupling recursive least square method to identify transmission line parameters; in step S3, the method for identifying the transmission line parameters by using the variable forgetting factor improved data window coupling recursive least square method includes the following steps:
a. abstracting the time-varying scalar linear equation in step S2 as:
y(t)＝Φ(t)θ(t) (6)
wherein y (t) = [ I ] mr (t)，I mi (t)，I nr (t)，I ni (t)，P m (t)，Q m (t)，P n (t)，Q n (t)] T ∈R 8 Determining an output of the system for the multiple time-varying;
determining an observation matrix of a system for multi-element time variation, wherein the observation matrix corresponds to voltage and phase angle quantity measured by a PMU;
θ(t)＝[g(t),b(t),B(t)] T ∈R 3 determining the phasors to be identified of the system for multiple time-varying, and corresponding to the line parameters to be identified;
b. the system is decomposed into 8 subsystems according to the number of output signals y in the step a, and each subsystem is called a multiple-input single-output system and can be expressed as:
c. taking a data segment with the PMU measurement data length d as a window, initializing identification values and information in the data window, and obtaining an identification parameter matrix with the initialized data window lengthIdentification residual matrix->The covariance matrix P is initialized as follows:
at t 0 The data point=1 applies a single-point least square algorithm to all subsystems to obtain an identification parameter matrix and an identification residual matrix;
at t 0 2-d data points, and using a subsystem coupling recursive least square algorithm to obtain an identification parameter matrix and an identification residual matrix for each subsystem;
at t 0 =d data points, the covariance matrix P is initialized as follows:
d. and reasonably selecting lambda min, lambda bmark and lambda max according to the identified rapid following property and stability, and meeting the following conditions: λmin < λbmark < λmax;
e. comparison |e i (t) | andwherein: />Identifying information for the subsystem; t is the data point corresponding to the moment of comparison, and the t=0 data point is the t in step c 0 =d data points; n is n 1 The change degree of the state is represented in a positive slope form for the threshold coefficient, and the value is taken according to line operation experience; />For the ith subsystem in step c +.>Vector absolute valueIs the maximum value of (2);
f. and e, judging according to the comparison result in the step e:
if |e i (t)|＜n 1 ·max{|e (i,t0) I, judging that the system is in a stable running state;
if |e i (t)|＞n 1 ·max{|e (i,t0) I, judging that the system state is suddenly changed;
g. based on the determination result of step f, assume t s Mutation of system state:
if the system is in a stable running state, and t is more than or equal to t s +d, executing parameter identification in a steady state;
if the system is mutated, and at t s ≤t＜t s In the +d data range, executing the parameter identification leaving the original steady state; in step g, the executing steady-state parameter identification is to determine to execute parameter identification of different steady-state phases according to the current data point t:
if t is less than or equal to d and the system is not mutated, executing a parameter identification strategy in an initial stage under a steady state;
if t is more than d, executing a parameter identification strategy in the running stage under the steady state;
the executing the parameter identification strategy in the initial stage under the steady state comprises the following steps:
r1. comparison of |e i (t) | and |E d [e i (t)]I, determining the recognition forgetting factor:
wherein the method comprises the steps ofExpected absolute values for data window innovation;
r2. let Δε= | (|e) i (t)|-|E d [e i (t)]I) and λ is determined according to the range of Δε i (t) linearizing the mapping to obtain reasonable forgetting factors in the range of λmin and λmax:
if delta epsilon [0, |E ] d [e i (t)]I), lambda is given i (t) mapping to (λbmark, λmax]In the interval of (2):
if delta epsilon E [ |E d [e i (t)]|,5|E d [e i (t)]I), lambda is given i (t) mapping to (λmin, λbmark)]In the interval of (2):
and R3, carrying out the following parameter identification by utilizing the forgetting factor determined in the step R2:
when i=1:
when i=2, 3, …, 8:
the parameter identification strategy for executing the operation stage in the steady state comprises the following steps:
t1. comparison of |E q [e i (t)]I and I E d [e i (t)]I, determining the recognition forgetting factor:
wherein the method comprises the steps ofAbsolute value expected for local innovation; q is the local information window length, q< 10 or d/q > 10;
t2. let Δε= | (|e) q [e i (t)]|-|E d [e i (t)]I) and λ is determined according to the range of Δε i (t) linearizing the mapping to obtain reasonable forgetting factors in the range of λmin and λmax:
if delta epsilon [0, |E ] d [e i (t)]I), lambda is given i (t) mapping to (λbmark, λmax]In the interval of (2):
if delta epsilon E [ |E d [e i (t)]|,5|E d [e i (t)]I), lambda is given i (t) mapping to (λmin, λbmark)]In the interval of (2):
t3, utilizing the forgetting factor determined in the step T2, and utilizing the formulas (12) and (13) to perform parameter identification;
the step g of performing parameter identification leaving the original steady state includes the following steps:
i, setting the starting point of the data window as t s Data points;
II. at t=t s The covariance matrix P is initialized as follows:
III. Comparison of |E q′ [e i (t)]I and I E d′ [e i (t)]I, determining the recognition forgetting factor:
wherein the method comprises the steps ofWindow length for local information, +.>The length of the local data window is identified;
IV. Let Δε= | (|E) q′ [e i (t)]|-|E d′ [e i (t)]I) and λ is determined according to the range of Δε i (t) linearizing the mapping to obtain reasonable forgetting factors in the range of λmin and λmax:
if delta epsilon [0, |E ] d′ [e i (t)]I), lambda is given i (t) mapping to (λbmark, λmax]In the interval of (2):
if delta epsilon E [ |E d′ [e i (t)]|,5|E d′ [e i (t)]I), lambda is given i (t) mapping to (λmin, λbmark)]In the interval of (2):
and V, carrying out the following parameter identification by utilizing the forgetting factor determined in the step IV:
when i=1:
when i=2, 3, …, 8:
h.t = t+1 data points, repeating steps e-g until the manual termination algorithm saves the identification parameters.
2. A computer apparatus comprising a memory, a processor, and a computer program stored on the memory and capable of running on the processor, characterized by: the processor, when executing the computer program, implements the method of claim 1.
3. A computer-readable storage medium having stored thereon a computer program, characterized by: which computer program, when being executed by a processor, implements the method as claimed in claim 1.
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