CN110907720B - Complete parameter identification method for short-circuit same-tower double-circuit line based on PMU measurement - Google Patents

Complete parameter identification method for short-circuit same-tower double-circuit line based on PMU measurement Download PDF

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CN110907720B
CN110907720B CN201911075892.0A CN201911075892A CN110907720B CN 110907720 B CN110907720 B CN 110907720B CN 201911075892 A CN201911075892 A CN 201911075892A CN 110907720 B CN110907720 B CN 110907720B
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CN110907720A (en
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黄潇潇
郑骁麟
郭凌旭
陈建
张�杰
康宁
张志君
袁中琛
杜明
韩磊
赵玉新
丁一
宋红宇
梁海深
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State Grid Corp of China SGCC
State Grid Tianjin Electric Power Co Ltd
Electric Power Research Institute of State Grid Tianjin Electric Power Co Ltd
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State Grid Corp of China SGCC
State Grid Tianjin Electric Power Co Ltd
Electric Power Research Institute of State Grid Tianjin Electric Power Co Ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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    • G—PHYSICS
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Abstract

The invention relates to a complete parameter identification method for short circuit on the same tower double circuit based on PMU measurement, which comprises the following steps: step 1, respectively establishing impedance models of short-circuit same-pole double-circuit lines with the same phase sequence and the non-same phase sequence according to whether the short-circuit same-pole double-circuit lines are symmetrical or not; step 2, establishing a parameter identification target function of multi-time PMU measurement based on a least square method; step 3, selecting PMU measurement at N moments and N +1 moments respectively, substituting the PMU measurement into the parameter identification objective function established in the step 2, and obtaining corresponding parameter identification results alphaN、αN+1(ii) a Setting an initial value N to be 2 for the same-phase sequence line; setting an initial value N to be 4 for the non-same phase sequence line; step 4, judging alpha in step 3N、αN+1Whether or not | α is satisfiedN‑αN+1If the | is less than or equal to lambda, exiting the loop to complete parameter identification; if not, making N equal to N +1, returning to step 2 for recalculation until parameter identification is completed. The method can accurately and quickly obtain the impedance parameters of the short-circuit double-circuit lines on the same tower.

Description

Complete parameter identification method for short-circuit same-tower double-circuit line based on PMU measurement
Technical Field
The invention belongs to the technical field of power system parameter identification, and relates to a complete parameter identification method for a short circuit on the same tower double circuit, in particular to a complete parameter identification method for a short circuit on the same tower double circuit based on PMU measurement.
Background
With the development of economy, the demand on the power system is higher and higher, and the power grid is more and more complex. As a carrier for transporting electrical energy, transmission lines are an indispensable part of the power grid. The research on the related problems of the transmission line has important significance on the analysis and calculation of the power system. The transmission line parameters are basic data of a power system for short-circuit current calculation, relay protection setting, transient stability calculation, load flow calculation, fault distance measurement and the like. If the transmission line parameter error for analysis and calculation is large, many problems are caused. With the development of power grid construction, higher requirements are provided for the accuracy of the parameters of the power transmission line, and the timely and accurate acquisition of the parameters of the power transmission line is of great importance.
Due to the reasons of environment, power transmission corridor, construction cost limitation and the like, the construction quantity of double circuit lines (less than 100km) on the same pole without transposition in the urban power grid is more and more. Due to the mutual impedance asymmetry of the double-circuit lines on the same pole without transposition, when the state estimation is carried out on the double-circuit lines, the estimation error of the reactive power of the double-circuit lines can greatly exceed the allowed range. However, no relevant research is directed at analyzing impedance parameters of the short circuit non-transposition double-circuit line on the same tower, so that the invention researches the impedance parameters of the short circuit non-transposition double-circuit line on the same tower, and lays a foundation for realizing state estimation and accurate load flow calculation of the short circuit double-circuit line on the same tower.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a complete parameter identification method for a short circuit on the same tower double-circuit line based on PMU measurement, which is reasonable in design, visual, simple, and capable of accurately and quickly obtaining impedance parameters of the short circuit on the same tower double-circuit line.
The invention solves the practical problem by adopting the following technical scheme:
1. a complete parameter identification method for short circuit on the same tower double circuit based on PMU measurement comprises the following steps:
step 1, respectively establishing impedance models of short-circuit same-pole double-circuit lines with the same phase sequence and the non-same phase sequence according to whether the short-circuit same-pole double-circuit lines are symmetrical or not;
step 2, establishing a parameter identification target function of multi-time PMU measurement based on a least square method according to the impedance model established in the step 1;
step 3, selecting PMU measurement at N moments and N +1 moments respectively, substituting the PMU measurement into the parameter identification objective function established in the step 2, and obtaining corresponding parameter identification results alphaN、αN+1(ii) a Setting an initial value N to be 2 for the same-phase sequence line; setting an initial value N to be 4 for the non-same phase sequence line;
step 4, judging alpha in step 3N、αN+1Whether or not | α is satisfiedN-αN+1If the | is less than or equal to lambda, exiting the loop to complete parameter identification; if not, making N equal to N +1, returning to step 2 for recalculation until parameter identification is completed.
Further, the specific steps of step 1 include:
(1) for the same-tower double-circuit line of the vertical type same-phase sequence arrangement abc-a 'b' c 'and the vertical type different-phase sequence arrangement abc-a' b 'c', the line impedance Z can be expressed as the same-phase sequence 1.1 and the non-same-phase sequence 1.2 without counting the line susceptance to the ground:
Figure BDA0002262424540000021
Figure BDA0002262424540000022
in the formula, Z1The self-impedance matrix of the I line in the double-circuit line is obtained; z2A self-impedance matrix of a line II in the double-circuit line; z12A mutual inductance matrix of the I wire pair II wire; z21A mutual inductance impedance matrix of the II line pair I line;
(2) when Z is1,Z12,Z21,Z2If the inverses of Z are all present, then the inverse Y of Z is obtained by the block matrix inversion method:
Figure BDA0002262424540000031
wherein the content of the first and second substances,
Figure BDA0002262424540000032
the node voltage is regarded as approximate three-phase symmetry, and a line current calculation formula is used for:
Figure BDA0002262424540000033
the conjugate of current phasor of each line can be obtained
Figure BDA0002262424540000034
The real part and the imaginary part of (c) are respectively:
Figure BDA0002262424540000035
Figure BDA0002262424540000036
in the formula (I), the compound is shown in the specification,
Figure BDA0002262424540000037
respectively a real part and an imaginary part of the conjugate of the current phasor at the head end of the wire s;
Figure BDA0002262424540000038
respectively a real part and an imaginary part of the voltage of a head end node of a wire s;
Figure BDA0002262424540000039
respectively a real part and an imaginary part of the voltage of a node at the tail end of the wire s;
the equation 5 includes 12 equations, in which there are 36 line admittance parameters, and the admittance parameters are:
yij,(i＝1,2,3,4,5,6；j＝1,2,3,4,5,6) (6)
still further according to equation 7
Figure BDA00022624245400000310
Figure BDA00022624245400000311
The i-side active and reactive calculation formula 8 of the line can be obtained:
Figure BDA0002262424540000041
the admittance parameters of the circuit are 36 and are the same as the formula 5;
(3) for the same-phase sequence short line and same-pole double loop, in the formula (1.1), due to the symmetry characteristic of Z: z1＝Z2In the form of a symmetrical matrix, the matrix is,
Figure BDA0002262424540000042
is a symmetric matrix; such that: y isΙ＝YΙΙ，YΙ-ΙΙ＝YΙΙ-Ι,
Figure BDA0002262424540000043
Namely, it is
y22＝y55
y11＝y44
y33＝y66
y12＝y21＝y45＝y54
y13＝y31＝y46＝y64
y23＝y32＝y65＝y56
y15＝y51＝y24＝y42
y41＝y14,y25＝y52,y36＝y63
y61＝y16＝y43＝y34
y62＝y26＝y53＝y35
Subscripts 1,2 and 3 correspond to phases a, b and c of the line I respectively, and subscripts 4,5 and 6 correspond to phases a, b and c of the line II respectively, so that the lines have 12 admittance parameters which are different from each other;
for the non-same-phase sequence short circuit same-pole parallel double circuit line as formula 1.2, the admittance matrix will not satisfy the above symmetrical relation any more, so the circuits have 36 admittance parameters different from each other;
equation 4 the current calculation equation can be converted to matrix expression 9 according to equation 5, as follows:
Figure BDA0002262424540000051
I＝XY (10)
in the formula 9, Ii(i-1, 2,3,4,5,6) is [2 × 1%]The block matrix comprises a first row of elements, a second row of elements and a third row of elements, wherein the first row of elements is a real current part of the ith line, and the first row of elements is an imaginary current part of the ith line; u is [ 2X 6]]The blocking matrix, as shown in equation 11,
Figure BDA0002262424540000052
respectively an imaginary part and a real part of the voltage difference at two ends of the i lines; i isiIs [ 6X 1]]The block matrix is as shown in equation 12, yis(s ═ 1,2,3,4,5,6, i ═ 1,2,3,4,5,6) are admittance parameters;
Figure BDA0002262424540000053
Yi＝[yi1 yi2 yi3 yi4 yi5 yi6]T (12)
the power calculation formula can be converted into a matrix expression 13 according to equations 6 and 7 as follows:
Figure BDA0002262424540000054
S＝VI＝VXY (14)
in formula 13, Sij(═ 1,2,3,4,5,6) is [2 × 1%]A block matrix which is respectively the active power and the reactive power at the j end of the ith line, Vij(i-1, 2,3,4,5,6) is [2 × 2]]The blocking matrix, as shown in equation 15,
Figure BDA0002262424540000055
the real part and the imaginary part of the voltage at the j end of the ith line are shown;
Figure BDA0002262424540000061
from equations 9 through 15, a matrix-form measurement calculation equation 16 is obtained as follows:
Figure BDA0002262424540000062
wherein, Z is a matrix of [24 × 1] and comprises real part and imaginary part of each line current and active power reactive power, E is a unit matrix of [12 × 12], A is a coefficient matrix of [24 × 36], and Y is an admittance matrix of [36 × 1 ];
(5) considering the influence of PMU measurement error, the combination of equation 5 and equation 7 is written in matrix form, and then:
β＝Aα+v (17)
in the formula, β is a one-dimensional column phasor composed of 12 transmission current quantities and 12 active and passive quantity measurements, a is a matrix represented by voltage values at two ends of a line, α represents a parameter column phasor estimated by a line band, and v is a measurement residual phasor.
Moreover, the specific method of the step 2 is as follows:
consider an overdetermined system of equations:
Figure BDA0002262424540000063
wherein m represents m equations, n represents n unknowns x, m > n; vectorizing the vector as follows:
Ax＝y (19)
Figure BDA0002262424540000064
introducing a residual sum of squares function S:
S(x)＝||Ax-y||2 (20)
when in use
Figure BDA0002262424540000071
Then, S (x) takes the minimum value and is recorded as:
Figure BDA0002262424540000072
by differentiating and solving the most value of s (x), it is possible to obtain:
Figure BDA0002262424540000073
if the matrix A isTA is nonsingular then x has a unique solution:
Figure BDA0002262424540000074
in identifying system parameters, when the controlled object is a controlled autoregressive model, the difference equation can be expressed as:
A(z-1)Z(k)＝B(z-1)u(k)+e(k) (24)
in the formula, A (z)-1)＝1+a1z-1+…+anaz-na；
Figure BDA0002262424540000075
u (k) is the input and output quantities of the system; e (k) is interference noise of the system; assuming a system model order naAnd nbHas been determined, and na>nbThen equation 24 is rewritten as a least squares format:
z(k)＝hT(k)θ+e(k) (25)
wherein the parameter phasor θ is defined as:
θ＝[a1 a2 … an b1 b2 … bn]T (26)
the information vector h (k) is defined as:
h(k)＝[-z(k-1) -z(k-na) -u(k-1) -u(k-nb)]T (27)
wherein h (k) is composed of observed data, and θ is a parameter to be estimated; estimation criterion function fetch
Figure BDA0002262424540000076
The least squares method of parameter estimation can then be derived for the parameters to be identified:
θ＝[hT(k)h(k)]-1h(k)z(k) (29)
from equation 17 and PMU multiple time measurements, the objective function of the least squares method for traditional line parameter identification is obtained as:
Figure BDA0002262424540000081
where N is the number of sampling instants, PiAnd ViThe ith observation value and the residual are respectively, and the parameter identification result is as follows:
α＝(ATPA)-1ATPβ (31)
wherein P is a diagonal element of PiThe diagonal elements of the weight matrix of (1) are the inverse of the measurement variance;
from the formulae (16) and (31)
(ATPA)Y＝AT Pβ (32)
The admittance parameter of the short circuit on the same tower and double circuit lines can be obtained by solving the linear equation set 32, beta is a measured value, and Y corresponds to alpha in the formula (31).
The invention has the advantages and beneficial effects that:
1. according to the method, the impedance model of the short circuit on-tower double-circuit line is established, and the line parameters are accurately identified on line based on the PMU, so that the accurate line parameters of the short circuit on-tower double-circuit line are obtained, and a solid foundation is laid for load flow calculation, state estimation and the like of the power system.
2. The invention provides an impedance model of a short-circuit same-tower double-circuit line, and realizes accurate line parameter identification of the short-circuit same-tower double-circuit line based on PMU (phasor measurement Unit) online measurement and a least square method. Firstly, deducing an impedance model of a short-circuit same-tower double-circuit line, and comprehensively considering the influence of asymmetry on the impedance of the line; based on a least square method, parameter identification of the short circuit on-line double circuit lines on the same tower is achieved by utilizing PMU on-line actual measurement data. The method and the device can realize the online identification of the parameters of the short circuit on the same tower and double circuit lines based on the PMU, and lay a foundation for the load flow calculation, the state estimation and the like of the power system. The algorithm is visual and simple, and can accurately and quickly obtain the impedance parameters of the short-circuit double-circuit lines on the same tower, so that the method has wide application prospect and great engineering value in practical engineering application.
Drawings
FIG. 1 is a flow chart of the present invention for identifying parameters of a short circuit on the same tower;
fig. 2 is a schematic diagram of a double-circuit line on the same tower in a vertical arrangement according to the present invention.
Detailed Description
The embodiments of the invention will be described in further detail below with reference to the accompanying drawings:
a complete parameter identification method for short circuit on the same tower and double circuit based on PMU measurement, as shown in fig. 1, includes the following steps:
step 1, respectively establishing impedance models of short-circuit same-pole double-circuit lines with the same phase sequence and the non-same phase sequence according to whether the short-circuit same-pole double-circuit lines are symmetrical or not;
the specific steps of the step 1 comprise:
(1) for the same-tower double-circuit line of the vertical type same-phase sequence arrangement abc-a 'b' c 'and the vertical type different-phase sequence arrangement abc-a' b 'c', the line impedance Z can be expressed as the same-phase sequence (1.1) and the non-same-phase sequence (1.2) without counting the line susceptance to the ground:
Figure BDA0002262424540000091
Figure BDA0002262424540000092
in the formula, Z1The self-impedance matrix of the I line in the double-circuit line is obtained; z2A self-impedance matrix of a line II in the double-circuit line; z12A mutual inductance matrix of the I wire pair II wire; z21Is a mutual inductance impedance matrix of the II line pair I line. z is a radical ofiIs line self-inductance (i ═ a, b, c, a ', b ', c '), zijLine mutual inductance (j ≠ i, i ═ a, b, c, a ', b ', c ');
(2) when Z is1,Z2,Z12,Z21When the inverses of Z are all present, the inverse Y of Z can be obtained by a block matrix inversion method:
Figure BDA0002262424540000101
wherein the content of the first and second substances,
Figure BDA0002262424540000102
the node voltage is regarded as approximate three-phase symmetry, and a formula is calculated by the line current
Figure BDA0002262424540000103
The conjugate of current phasor of each line can be obtained
Figure BDA0002262424540000104
The real part and the imaginary part of (c) are respectively:
Figure BDA0002262424540000105
Figure BDA0002262424540000106
in the formula (I), the compound is shown in the specification,
Figure BDA0002262424540000107
respectively a real part and an imaginary part of the conjugate of the current phasor at the head end of the wire s;
Figure BDA0002262424540000108
respectively a real part and an imaginary part of the voltage of a head end node of a wire s;
Figure BDA0002262424540000109
respectively the real part and the imaginary part of the voltage of the node at the end of the wire s.
The equation (5) includes 12 equations, in which there are 36 line admittance parameters, and the admittance parameters are:
yst,(s＝1,2,3,4,5,6；t＝1,2,3,4,5,6) (6)
further according to formula (7)
Figure BDA0002262424540000111
The active and reactive calculation formulas of the i side of the line can be obtained:
Figure BDA0002262424540000112
and the admittance parameters of the line are 36 and are the same as the formula (5).
Wherein, PI,i，QI,iIs the active power and reactive power, P, of line IΠ,i，QΠ,iThe active power and the reactive power of the circuit pi.
(3) For the same-phase sequence short circuit on the same tower double-circuit line, on-lineIn (1.1), due to the symmetry of Z: z1＝Z2In the form of a symmetrical matrix, the matrix is,
Figure BDA0002262424540000113
is a symmetric matrix; such that: y isΙ＝YΙΙ，YΙ-ΙΙ＝YΙΙ-Ι,
Figure BDA0002262424540000114
Namely, it is
y22＝y55
y11＝y44
y33＝y66
y12＝y21＝y45＝y54
y13＝y31＝y46＝y64
y23＝y32＝y65＝y56
y15＝y51＝y24＝y42
y41＝y14,y25＝y52,y36＝y63
y61＝y16＝y43＝y34
y62＝y26＝y53＝y35
Subscripts 1,2 and 3 correspond to phases a, b and c of the line I respectively, and subscripts 4,5 and 6 correspond to phases a, b and c of the line II respectively, so that the lines have 18 admittance parameters which are different from each other;
for the non-same-phase sequence short circuit same-pole parallel double circuit lines, the admittance matrix does not satisfy the symmetry relation any more, so the lines have 36 admittance parameters which are different from each other;
equation (4) the current calculation equation can be converted into a matrix expression according to equation (5), as follows:
Figure BDA0002262424540000121
I＝XY (10)
in the formula (9), Ii(i-1, 2,3,4,5,6) is [2 × 1%]The block matrix comprises a first row of elements, a second row of elements and a third row of elements, wherein the first row of elements is a real current part of the ith line, and the first row of elements is an imaginary current part of the ith line; u is [ 2X 6]]The blocking matrix, as shown in equation 11,
Figure BDA0002262424540000122
respectively the imaginary part and the real part of the voltage difference at the two ends of the i lines. I isiIs [ 6X 1]]The block matrix is as shown in equation (12) yis(s ═ 1,2,3,4,5,6, i ═ 1,2,3,4,5,6) are admittance parameters;
Figure BDA0002262424540000123
Yi＝[yi1 yi2 yi3 yi4 yi5 yi6]T (12)
the power calculation formula may be converted into a matrix expression (13) according to equations (6) and (7), as follows:
Figure BDA0002262424540000124
S＝VI＝VXY (14)
in formula (13), Sij(═ 1,2,3,4,5,6) is [2 × 1%]A block matrix which is respectively the active power and the reactive power at the j end of the ith line, Vij(i-1, 2,3,4,5,6) is [2 × 2]]The block matrix is represented by equation (15),
Figure BDA0002262424540000131
the real part and the imaginary part of the voltage at the j end of the ith line are shown;
Figure BDA0002262424540000132
from equation (9) -equation (15), a matrix-form metrology calculation equation is obtained as follows:
Figure BDA0002262424540000133
wherein Z is a matrix of [24 × 1] and comprises real parts and imaginary parts of current of each line and active power reactive power, E is a unit matrix of [12 × 12], A is a coefficient matrix of [24 × 36], and Y is an admittance matrix of [36 × 1 ];
(5) considering the influence of PMU measurement error, the combination of equation (5) and equation (7) is written in matrix form, and then:
β＝Aα+v (17)
in the formula, β is a one-dimensional column phasor composed of 12 transmission current quantities and 12 active and passive quantity measurements, a is a matrix represented by voltage values at two ends of a line, α represents a parameter column phasor estimated by a line band, and v is a measurement residual phasor.
Step 2, establishing a parameter identification target function of multi-time PMU measurement based on a least square method according to the impedance model established in the step 1;
the specific method of the step 2 comprises the following steps:
consider an overdetermined system of equations (the overdetermined unknowns are less than the number of equations):
Figure BDA0002262424540000134
wherein m represents m equations, n represents n unknowns x, m > n; vectorizing the vector as follows:
Ax＝y (19)
Figure BDA0002262424540000141
it is clear that the system of equations is generally unsolved, so in order to choose the most suitable x to make the equation "true" as much as possible, the residual sum of squares function S is introduced
S(x)＝||Ax-y||2 (20)
When in use
Figure BDA0002262424540000142
Then, S (x) takes the minimum value and is recorded as:
Figure BDA0002262424540000143
by differentiating and solving the most value of s (x), it is possible to obtain:
Figure BDA0002262424540000144
if the matrix A isTA is nonsingular then x has a unique solution:
Figure BDA0002262424540000145
in the field of system identification, the least square method is a classic data processing method. In identifying system parameters, when the controlled object is a controlled autoregressive model, it can be expressed as a difference equation
A(z-1)Z(k)＝B(z-1)u(k)+e(k) (24)
In the formula, A (z)-1)＝1+a1z-1+…+anaz-na；
Figure BDA0002262424540000146
u (k) and z (k) are inputs and outputs of the system; e (k) is the interference noise of the system. Assuming a system model order naAnd nbHas been determined, and na>nbThen equation (24) is rewritten to the least squares format as:
z(k)＝hT(k)θ+e(k) (25)
wherein the parameter phasor theta is defined as
θ＝[a1 a2 … an b1 b2 … bn]T (26)
The information vector h (k) is defined as:
h(k)＝[-z(k-1) -z(k-na) -u(k-1) -u(k-nb)]T (27)
where h (k) is composed of observed data, and θ is a parameter to be estimated. Estimation criterion function fetch
Figure BDA0002262424540000151
It can then be concluded that the least squares method of parameter estimation is used to identify the parameters:
θ＝[hT(k)h(k)]-1h(k)z(k) (29)
from equation (17) and PMU multi-time measurements, the objective function of the least square method for traditional line parameter identification is obtained as:
Figure BDA0002262424540000152
where N is the number of sampling instants, PiAnd ViThe ith observation value and the residual are respectively, and the parameter identification result is as follows:
α＝(ATPA)-1ATPβ (31)
wherein P is a diagonal element of PiThe diagonal elements of the weight matrix of (1) are the inverse of the variance of the quantity measurement.
From the formulae (16) and (31)
(ATPA)Y＝AT Pβ (32)
And solving a linear equation set (32) to obtain admittance parameters of the short circuit double-circuit lines on the same tower of the short circuit, wherein beta is a measured value, and Y corresponds to alpha in the formula (31).
Step 3, selecting PMU measurement at N moments and N +1 moments respectively, substituting the PMU measurement into the parameter identification objective function established in the step 2, and obtaining corresponding parameter identification results alphaN、αN+1(ii) a Setting an initial value N to be 2 for the same-phase sequence line; setting an initial value N to be 4 for the non-same phase sequence line;
in this embodiment, for the same-phase sequence short line and the same-tower double-circuit line, the line impedance model includes 24 equations and 18 admittance parameters to be identified are different from each other. Therefore, at least N is more than or equal to 1, namely, the parameters can be identified only by measuring the quantity of at least 1 time of PMU. In order to realize accurate identification of the parameters by adopting a least square method, an initial value N is not less than 2, namely, the parameters can be identified only by measuring the quantity of at least 2 moments of obtaining PMU.
For the non-same-phase sequence short line same-tower double-circuit line, the line impedance model comprises 24 equations and 36 admittance parameters to be identified which are different from each other. Therefore, in this case, at least N ≧ 2 is taken, i.e., at least 2 time-point measurements of PMUs are obtained. In order to realize accurate identification of the parameters by adopting a least square method, an initial value N is not less than 3, namely, the parameters can be identified only by measuring at least 4 moments of PMU.
Step 4, judging alpha in step 3N、αN+1Whether or not | α is satisfiedN-αN+1If the lambda is smaller positive number, quitting circulation and finishing parameter identification; if not, making N equal to N +1, returning to step 2 for recalculation until parameter identification is completed.
In this embodiment, the short-line parameter identification process on the same tower as shown in fig. 2 is as follows:
(1) and reading system network data and M different time measurement data.
(2) And S01, judging whether the short circuit on the same tower double-circuit line is symmetrical, and selecting the parameter identification scheme of the short circuit on the same tower double-circuit line with the same phase sequence and the non-same phase sequence according to the symmetry. Since the same phase sequence needs to identify 18 parameters, the different phase sequence needs to identify 36 parameters, and the two require different measurement quantities, the former enters stage S02, and the latter enters stage S06.
(3) The PMU measurements at N and N +1 different times are selected as described above to obtain the objective function (22), and the process proceeds to stage S03 or S07.
(4) The initial value of N is 2 for stage S03 and 3 for stage S07. Establishing a vertical (32) medium coefficient matrix A based on voltage measurements in PMU measurements at N and N +1 different timesNAnd AN+1Thereby obtaining a letterInformation matrix
Figure BDA0002262424540000161
And
Figure BDA0002262424540000162
by LU decomposition
Figure BDA0002262424540000163
And
Figure BDA0002262424540000164
respectively obtain YNAnd YN+1。
(5) Judging whether the two groups of results meet the absolute value of YN-YN+1If | < lambda, quitting circulation if satisfied, completing parameter identification, selecting YN+1Is the final result; if not, the loop is executed in stage S05 or S09, and returns to stage S02 or S06 until the recognition is successful or N-M exits the loop.
It should be emphasized that the examples described herein are illustrative and not restrictive, and thus the present invention includes, but is not limited to, those examples described in this detailed description, as well as other embodiments that can be derived from the teachings of the present invention by those skilled in the art and that are within the scope of the present invention.

Claims (1)

1. A complete parameter identification method for short circuit on the same tower double circuit based on PMU measurement is characterized in that: the method comprises the following steps:
step 1, respectively establishing impedance models of short-circuit same-pole double-circuit lines with the same phase sequence and the non-same phase sequence according to whether the short-circuit same-pole double-circuit lines are symmetrical or not;
step 2, establishing a parameter identification target function of multi-time PMU measurement based on a least square method according to the impedance model established in the step 1;
step 3, selecting PMU measurement at N moments and N +1 moments respectively, substituting the PMU measurement into the parameter identification objective function established in the step 2, and obtaining corresponding parameter identification results alphaN、αN+1(ii) a For the same phase sequence line, letSetting an initial value N to be 2; setting an initial value N to be 4 for the non-same phase sequence line;
step 4, judging alpha in step 3N、αN+1Whether or not | α is satisfiedN-αN+1If the | is less than or equal to lambda, exiting the loop to complete parameter identification; if not, making N equal to N +1, returning to the step 2 for recalculation until parameter identification is completed;
the specific steps of the step 1 comprise:
(1) for the same-tower double-circuit line of the vertical type same-phase sequence arrangement abc-a 'b' c 'and the vertical type different-phase sequence arrangement abc-a' b 'c', the line impedance Z can be expressed as the same-phase sequence 1.1 and the non-same-phase sequence 1.2 without counting the line susceptance to the ground:
Figure FDA0003342413430000011
Figure FDA0003342413430000021
in the formula, Z1The self-impedance matrix of the I line in the double-circuit line is obtained; z2A self-impedance matrix of a line II in the double-circuit line; z12A mutual inductance matrix of the I wire pair II wire; z21A mutual inductance impedance matrix of the II line pair I line;
(2) when Z is1,Z12,Z21,Z2If the inverses of Z are all present, then the inverse Y of Z is obtained by the block matrix inversion method:
Figure FDA0003342413430000022
Figure FDA0003342413430000023
Y2＝(Z2-Z21Z1 -1Z12)-1
Figure FDA0003342413430000024
wherein the content of the first and second substances,
Figure FDA0003342413430000025
the node voltage is regarded as approximate three-phase symmetry, and a line current calculation formula is used for:
Figure FDA0003342413430000026
the conjugate of current phasor of each line can be obtained
Figure FDA0003342413430000027
The real part and the imaginary part of (c) are respectively:
Figure FDA0003342413430000028
Figure FDA0003342413430000029
in the formula (I), the compound is shown in the specification,
Figure FDA00033424134300000210
respectively a real part and an imaginary part of the conjugate of the current phasor at the head end of the wire s;
Figure FDA00033424134300000211
respectively a real part and an imaginary part of the voltage of a head end node of a wire s;
Figure FDA00033424134300000212
respectively a real part and an imaginary part of the voltage of a node at the tail end of the wire s;
the equation 5 includes 12 equations, in which there are 36 line admittance parameters, and the admittance parameters are:
yij,(i＝1,2,3,4,5,6；j＝1,2,3,4,5,6) (6)
still further according to equation 7
Figure FDA0003342413430000031
Figure FDA0003342413430000032
The i-side active and reactive calculation formula 8 of the line can be obtained:
Figure FDA0003342413430000033
the admittance parameters of the circuit are 36 and are the same as the formula 5;
(3) for the same-phase sequence short line and same-pole double loop, in the formula (1.1), due to the symmetry characteristic of Z: z1＝Z2In the form of a symmetrical matrix, the matrix is,
Figure FDA0003342413430000034
is a symmetric matrix; such that: y isΙ＝YΙΙ，YΙ-ΙΙ＝YΙΙ-Ι,
Figure FDA0003342413430000035
Namely, it is
y22＝y55
y11＝y44
y33＝y66
y12＝y21＝y45＝y54
y13＝y31＝y46＝y64
y23＝y32＝y65＝y56
y15＝y51＝y24＝y42
y41＝y14,y25＝y52,y36＝y63
y61＝y16＝y43＝y34
y62＝y26＝y53＝y35
Subscripts 1,2 and 3 correspond to phases a, b and c of the line I respectively, and subscripts 4,5 and 6 correspond to phases a, b and c of the line II respectively, so that the lines have 12 admittance parameters which are different from each other;
for the non-same-phase sequence short circuit same-pole parallel double circuit line as formula 1.2, the admittance matrix will not satisfy the above symmetrical relation any more, so the circuits have 36 admittance parameters different from each other;
equation 4 the current calculation equation can be converted to matrix expression 9 according to equation 5, as follows:
Figure FDA0003342413430000041
I＝XY (10)
in the formula 9, Ii(i-1, 2,3,4,5,6) is [2 × 1%]The block matrix comprises a first row of elements, a second row of elements and a third row of elements, wherein the first row of elements is a real current part of the ith line, and the first row of elements is an imaginary current part of the ith line; u is [ 2X 6]]The blocking matrix, as shown in equation 11,
Figure FDA0003342413430000042
respectively an imaginary part and a real part of the voltage difference at two ends of the i lines; i isiIs [ 6X 1]]The block matrix is as shown in equation 12, yis(s ═ 1,2,3,4,5,6, i ═ 1,2,3,4,5,6) are admittance parameters;
Figure FDA0003342413430000043
Yi＝[yi1 yi2 yi3 yi4 yi5 yi6]T (12)
the power calculation formula can be converted into a matrix expression 13 according to equations 6 and 7 as follows:
Figure FDA0003342413430000044
S＝VI＝VXY (14)
in formula 13, Sij(═ 1,2,3,4,5,6) is [2 × 1%]A block matrix which is respectively the active power and the reactive power at the j end of the ith line, Vij(i-1, 2,3,4,5,6) is [2 × 2]]The blocking matrix, as shown in equation 15,
Figure FDA0003342413430000045
the real part and the imaginary part of the voltage at the j end of the ith line are shown;
Figure FDA0003342413430000051
from equations 9 through 15, a matrix-form measurement calculation equation 16 is obtained as follows:
Figure FDA0003342413430000052
wherein, Z is a matrix of [24 × 1] and comprises real part and imaginary part of each line current and active power reactive power, E is a unit matrix of [12 × 12], A is a coefficient matrix of [24 × 36], and Y is an admittance matrix of [36 × 1 ];
(5) considering the influence of PMU measurement error, the combination of equation 5 and equation 7 is written in matrix form, and then:
β＝Aα+v (17)
in the formula, beta is a one-dimensional column phasor formed by 12 transmission current quantities and 12 active and passive quantity measurements, A is a matrix represented by voltage values at two ends of a line, alpha is a parameter column phasor estimated by a line band, and v is a measurement residual phasor;
the specific method of the step 2 comprises the following steps:
consider an overdetermined system of equations:
Figure FDA0003342413430000053
wherein m represents m equations, n represents n unknowns x, m > n; vectorizing the vector as follows:
Ax＝y (19)
Figure FDA0003342413430000054
introducing a residual sum of squares function S:
S(x)＝||Ax-y||2 (20)
when in use
Figure FDA0003342413430000061
Then, S (x) takes the minimum value and is recorded as:
Figure FDA0003342413430000062
by differentiating and solving the most value of s (x), it is possible to obtain:
Figure FDA0003342413430000063
if the matrix A isTA is nonsingular then x has a unique solution:
Figure FDA0003342413430000064
in identifying system parameters, when the controlled object is a controlled autoregressive model, the difference equation can be expressed as:
A(z-1)Z(k)＝B(z-1)u(k)+e(k) (24)
in the formula, A (z)-1)＝1+a1z-1+…+anaz-na；
Figure FDA0003342413430000065
u (k) is the input and output quantities of the system; e (k) is interference noise of the system; assuming a system model order naAnd nbHas been determined, and na>nbThen equation 24 is rewritten as a least squares format:
z(k)＝hT(k)θ+e(k) (25)
wherein the parameter phasor θ is defined as:
θ＝[a1 a2…an b1 b2…bn]T (26)
the information vector h (k) is defined as:
h(k)＝[-z(k-1) -z(k-na) -u(k-1) -u(k-nb)]T (27)
wherein h (k) is composed of observed data, and θ is a parameter to be estimated; estimation criterion function fetch
Figure FDA0003342413430000066
The least squares method of parameter estimation can then be derived for the parameters to be identified:
θ＝[hT(k)h(k)]-1h(k)z(k) (29)
from equation 17 and PMU multiple time measurements, the objective function of the least squares method for traditional line parameter identification is obtained as:
Figure FDA0003342413430000071
wherein N is the sampling timeNumber, PiAnd ViThe ith observation value and the residual are respectively, and the parameter identification result is as follows:
α＝(ATPA)-1ATPβ (31)
wherein P is a diagonal element of PiThe diagonal elements of the weight matrix of (1) are the inverse of the measurement variance;
from the formulae (16) and (31)
(ATPA)Y＝ATPβ (32)
The admittance parameter of the short circuit on the same tower and double circuit lines can be obtained by solving the linear equation set 32, beta is a measured value, and Y corresponds to alpha in the formula (31).
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