CN110909918A - ADAL-based transmission and distribution integrated parallel state estimation method - Google Patents

ADAL-based transmission and distribution integrated parallel state estimation method Download PDF

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CN110909918A
CN110909918A CN201911075896.9A CN201911075896A CN110909918A CN 110909918 A CN110909918 A CN 110909918A CN 201911075896 A CN201911075896 A CN 201911075896A CN 110909918 A CN110909918 A CN 110909918A
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郑骁麟
黄潇潇
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 Tianjin Electric Power Co Ltd
Electric Power Research Institute of State Grid Tianjin Electric Power Co Ltd
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Abstract

The invention relates to an ADAL (advanced data acquisition and analysis) -based integrated parallel state estimation method for transmission and distribution, which comprises the following steps of: step 1, establishing a distributed state estimation new algorithm based on an ADAL algorithm under a rectangular coordinate system; step 2, two interaction strategies are provided, and one of the two interaction strategies is selected as a constraint condition; step 3, deducing a practical algorithm based on the interactive information, and establishing a target function based on a weighted least square method; step 4, constructing a single-three phase mixed state estimation model; step 5, according to different calculation models adopted by each partition for the boundary area, 3 boundary information interaction forms are separated based on the single-three phase mixed state estimation model and the interaction strategy 2 in the step 4; and 6, adopting a double-layer structure design according to the practical parallel algorithm and the information interaction process of the parallel single-phase and three-phase mixed state estimation algorithm. The invention realizes the high-precision and quick state estimation of transmission and distribution integration.

Description

ADAL-based transmission and distribution integrated parallel state estimation method
Technical Field
The invention belongs to the technical field of electric power systems, and relates to a transmission and distribution network integrated state estimation method, in particular to an ADAL-based transmission and distribution integrated parallel state estimation method.
Background
The state estimation of each city/provincial electric power company only comprises a transmission network of 220kV or more at present, with the continuous increase of the scale of a distribution network accessed by distributed generation, the 110kV and 35kV distribution networks are gradually admitted into the city/provincial electric power company for management and regulation, the transmission and distribution integrated cooperative scheduling and management become one of key work contents of a provincial electric network and a regional electric network, the corresponding state estimation calculation range covers the transmission and distribution integrated electric network, and the calculation scale is obviously increased. Therefore, the state estimation needs to meet the speed and accuracy requirements under unified state estimation of 110kV and 35kV distribution networks and existing transmission networks. EquationSection (Next)
For the transmission and distribution integrated power grid, due to the fact that the grid-connected scale of ultra-high voltage transmission and renewable energy power generation is continuously increased, the connection between the transmission and distribution power grid is tighter and tighter, the transmission and distribution power grid is mostly operated and managed separately at present, or only the transmission power grid is analyzed and controlled, the distribution network is completely passively matched and obeyed, and the distribution network is not suitable for the current distribution network operation mode in a certain sense; accordingly, research and implementation of transmission and distribution integration are receiving more and more attention from researchers and some electric power companies. Because the network coverage range is wide under the condition of integrated analysis and control of transmission and distribution, how to realize the fast and stable operation and accurate calculation becomes one of the key problems. With the increasing urgency of deploying transmission and distribution integration advanced application software systems, high-accuracy modeling and rapid solving of transmission and distribution network integration state estimation become one of the problems to be solved urgently.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an ADAL (advanced instrumentation and instrumentation) transmission and distribution integration-based parallel state estimation method which is reasonable in design, high in accuracy and capable of being rapidly solved.
The invention solves the practical problem by adopting the following technical scheme:
an ADAL transmission and distribution integration-based parallel state estimation method comprises the following steps:
step 1, establishing a distributed state estimation new algorithm based on an ADAL algorithm under a rectangular coordinate system according to a bipartite region single-phase system;
step 2, according to the difference of the distributed state estimation new algorithm based on the ADAL algorithm and the interaction information provided in the step 1, providing two interaction strategies, and selecting one of the two interaction strategies as a constraint condition;
step 3, based on the distributed state estimation new algorithm and the constraint conditions of the ADAL algorithm, further deducing a practical algorithm based on the interactive information, and establishing a target function based on a weighted least square method;
step 4, constructing a single-three phase mixed state estimation model according to the parallel state estimation objective function established in the step 3;
step 5, according to different calculation models adopted by each partition for the boundary area, 3 boundary information interaction forms are separated based on the single-three phase mixed state estimation model and the interaction strategy 2 in the step 4;
and 6, adopting a double-layer structure design according to the practical parallel algorithm and the information interaction process of the parallel single-phase and three-phase mixed state estimation algorithm.
Further, the specific steps of step 1 include:
(1) for the optimization problem:
Figure BDA0002262423930000021
wherein the content of the first and second substances,
Figure BDA0002262423930000022
i is e {1,2, …, N } is NiA dimensional euclidean space non-empty closed convex set;
Figure BDA0002262423930000023
is a convex function or a second-order continuous differentiable function; a. theiIs mxniA matrix;
(2) representing the constraint in the form of Ax ═ b
Figure BDA0002262423930000024
The lagrangian function of the optimization problem (1) is then:
Figure BDA0002262423930000025
wherein β is greater than 0 and is a penalty factor;
(3) the ADAL algorithm is to convert an unconstrained optimization model shown in formula (2) into a two-layer optimization problem to be solved, wherein the iteration strategy of two adjacent partitions i and j in the k +1 step of the problem is as follows:
Figure BDA0002262423930000031
in the formula (I), the compound is shown in the specification,
Figure BDA0002262423930000032
and
Figure BDA0002262423930000033
respectively obtaining state variable estimated values of k step and k +1 step of the partition i and the partition j; tau is step size factor, tau is equal to (0,1/q), and q is [ AiAj]TMaximum number of non-zero elements in middle row.
(4) Let x be the voltage amplitude and phase angle of the partition i, and the state variables of its boundary region are respectively represented by eiAnd fiLet y be the voltage amplitude and phase angle of the partition j, and the state variables of the boundary region are respectively represented by ejAnd fjRepresents; the objective function of the system state estimation is:
o.b.minJ(x)＝Ji(x)+Jj(y) (4)
let the estimated value of the boundary region measurement of partition i be fi(x) The estimated value of the boundary area measurement of the partition j is fj(x) Then equation (4) can be equivalent to:
Figure BDA0002262423930000034
the corresponding lagrange function of equation (6) is:
Figure BDA0002262423930000035
the parallel interaction algorithm of the two partitions in the step (k + 1) can be obtained:
Figure BDA0002262423930000036
moreover, the two interaction strategies of step 2 are:
interaction strategy 1: only the node voltage and current information of the boundary area is interacted:
the boundary region interaction information only comprises the real part and the imaginary part of the node voltage, the real part and the imaginary part of the node injection and branch current, namely
Figure BDA0002262423930000041
Interaction strategy 2: the interactive information of the boundary area comprises power information:
boundary region interaction information includes node injection and branch active and reactive information, e.g.
Figure BDA0002262423930000042
P in formula (9)i(x)、Qi(x)、Pj(x)、Qj(x) And calculating information of active power and reactive power of the boundary area partition i and the boundary area partition j respectively.
Further, the specific steps of step 3 include:
(1) for partition i:
Figure BDA0002262423930000043
the last term of equation (10) is constant and the corresponding derivative is zero, and if the result of the boundary estimation for partition j is considered as a virtual measurement for partition i, the virtual measurement is made
Figure BDA0002262423930000044
And its virtual standard deviation sigmaiComprises the following steps:
Figure BDA0002262423930000045
the objective function for partition i is equivalent to:
Figure BDA0002262423930000046
the objective function form of the corresponding partition i based on the weighted least squares method is:
Figure BDA0002262423930000047
in the formula, nvirVirtual measurement number for boundary region; h isi,s(x) And
Figure BDA0002262423930000048
respectively an s-th boundary measurement calculation value and a virtual measurement value thereof; z is a radical ofi,sFor the s-th actual measurement value contained in the partition i, n, h in totali,s(x) Is calculated accordingly, σi,sThe corresponding measurement standard deviation;
(2) the method is based on a parallel state estimation objective function of an adaptive kernel density estimation model:
Figure BDA0002262423930000051
partition j is based on a weighted least squares method and an objective function based on adaptive kernel density estimation, as follows:
Figure BDA0002262423930000052
Figure BDA0002262423930000053
Figure BDA0002262423930000054
the (k + 1) th step two-partition parallel interactive algorithm (practical parallel algorithm for short) is as follows:
Figure BDA0002262423930000055
accordingly, the multi-partition practical parallel algorithm is:
Figure BDA0002262423930000056
in the formula, N is the partition number of the system; j e i represents all partitions adjacent to partition i.
Moreover, the specific method of the step 4 is as follows:
based on a single-three phase mixed state estimation model of a least square method, an expansion (13) is in a single-three phase mixed form, and a single-three phase mixed parallel state estimation target function of the ith (i is 1,2, …, N) partition in a multi-partition system can be obtained:
Figure BDA0002262423930000061
in the formula, the virtual metrology weight
Figure BDA0002262423930000062
Figure BDA0002262423930000063
And hi,s(xi) Respectively, the s-th virtual measurement of the boundary of the partition i and a calculation value thereof;
solving the equation (20) by using a Newton method, wherein the iterative equation is as follows:
Figure BDA0002262423930000064
Figure BDA0002262423930000065
Figure BDA0002262423930000066
in the formula (21), the compound represented by the formula,
Figure BDA0002262423930000067
and
Figure BDA0002262423930000068
are respectively x+And xtThe j-th iteration estimate of (1); h+tThe calculation formula is a Jacobian matrix of the single-three phase mixed model and is shown as a formula (22);
Figure BDA0002262423930000069
is an information matrix;
Figure BDA00022624239300000610
respectively correcting values of the three-phase symmetrical network state variable and the three-phase asymmetrical network state variable of the jth iteration;
in the formula (22), the reaction mixture is,
Figure BDA00022624239300000611
and
Figure BDA00022624239300000612
respectively measuring jacobian matrixes measured in relation to the boundary branch;
Figure BDA00022624239300000613
and
Figure BDA00022624239300000614
respectively measuring jacobian matrixes of a single-phase network and a three-phase network except the related measurement of the junction branch;
Figure BDA00022624239300000615
the calculation equation of the related measurement of the boundary branch is different from the measurement calculation equation of the three-phase side; h is+(x) Calculating an equation for the measurement of the three-phase symmetric network; h ist(x) Calculating an equation for the measurement of the three-phase asymmetric network;
based on the mixed state estimation model, each partition adopts a single three-phase mixed model to carry out iterative computation, and an interaction strategy 2 is adopted between every two adjacent partitions to carry out information interaction;
in the formula (23), ri NFor the regularization residual of the ith measurement,
Figure BDA0002262423930000071
is a residual covariance matrix, Δ z is a measurement vector z and its calculated value
Figure BDA0002262423930000072
The difference between them.
Further, the specific steps of step 5 include:
(1) positive sequence component of interactive boundary region information
And (3) calculating the boundary area of each partition by adopting a single-phase model, as shown in a formula (24):
Figure BDA0002262423930000073
(2) three-phase information of interactive boundary region
And (3) calculating the boundary area of each partition by adopting a three-phase model, wherein the formula (25) is as follows:
Figure BDA0002262423930000074
(3) single three-phase hybrid interaction of boundary region information
Different calculation models are adopted for the boundary regions by each partition, and the calculation formula of the positive sequence component is as follows:
Figure BDA0002262423930000075
wherein α ═ e-j120°；
For the partition j, the boundary positive sequence component of the partition i is converted into three-phase information and then transmitted to the partition j, and then the interaction is completed according to the formula (25), wherein the sequence-phase conversion formula is as follows:
Figure BDA0002262423930000076
equations (24) and (25) can be expressed in simple form as follows:
Figure BDA0002262423930000081
based on the interaction strategy 2, the lagrangian multiplier update equation of the partition i in the multi-partition system can be obtained:
Figure BDA0002262423930000082
further, the specific steps of step 6 include:
(1) reading in system network data, measurement data and a boundary area;
(2) partitioning the system according to the boundary region;
(3) creating threads, wherein the number of the threads is equal to the number of the partitions;
(4) distributing the network data and the measurement data of each partition to each thread according to the boundary area;
(5) the threads concurrently and independently execute the following (6) to (7);
(6) initializing parameters: k is 0, λ0,x0；
(7) For lagrange multiplier sequence lambdakOne thread i obtains a decision variable of the (k + 1) th step iteration of the ith partition by using a Newton solution unconstrained optimization problem formula (20)
Figure BDA0002262423930000085
The corresponding jacobian matrix and iterative equations are shown in (22) and (21), and the other threads are similar:
(8) modifying decision variables
Figure BDA0002262423930000083
(9) For thread 1, when satisfied
Figure BDA0002262423930000084
If epsilon is a convergence threshold, thread 1 stops calculating; otherwise, after all the adjacent partitions j finish one-time iterative computation, the coefficient matrix in the formula (29) is obtained through the interaction strategy 2, andupdating Lagrange multiplier according to the formula, k + +, and going to (7); the other threads work the same way.
The invention has the advantages and beneficial effects that:
1. firstly, an ADAL-based parallel state estimation algorithm and an interaction strategy between partitions are provided, and a corresponding practical parallel state estimation algorithm and an interaction strategy between the partitions are provided; then, aiming at the characteristic that three-phase asymmetry and three-phase symmetry coexist in the transmission and distribution integrated power grid, an ADAL-based parallel single-three-phase hybrid state estimation model is provided, and high-precision and rapid state estimation of the transmission and distribution integration is realized.
2. The invention provides a parallel single-phase and three-phase state estimation model based on an ADAL algorithm, and performs state estimation on a transmission and distribution integrated system based on a weighted least square method. Firstly, a parallel state estimation practical algorithm is deduced based on an ADAL algorithm, then a parallel single-phase and three-phase mixed state estimation model is deduced, different boundary interaction forms can be adopted according to different calculation models adopted by each partition for boundary areas, and state estimation is carried out on a transmission and distribution integrated system based on a weighted least square method.
3. The invention can realize the high-precision and quick state estimation of transmission and distribution integration, and has wide application prospect and great engineering value in the practical engineering application because the algorithm is visual and simple and the proposed practical parallel state estimation model is very close to the existing state estimation model.
Drawings
FIG. 1 is a diagram of a two-tier information interaction algorithm of the present invention;
FIG. 2 is a diagram of a synchronized parallel computing strategy for adjacent partitions under a thread in accordance with the present invention;
FIG. 3 is a schematic diagram of a two-zone interconnect system according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a single-phase calculation model of a boundary region of a two-partition interconnect system according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of a three-phase calculation model of a boundary region of a two-partition interconnect system according to an embodiment of the present invention;
fig. 6 is a schematic diagram of a hybrid calculation model of a boundary region of a two-partition interconnection system according to an embodiment of the present invention.
Detailed Description
The embodiments of the invention will be described in further detail below with reference to the accompanying drawings:
an ADAL-based integrated parallel state estimation method for transmission and distribution, as shown in fig. 1, includes the following steps:
step 1, establishing a distributed state estimation new algorithm based on an ADAL algorithm under a rectangular coordinate system according to a bipartite region single-phase system;
the specific steps of the step 1 comprise:
(1) first for the optimization problem:
Figure BDA0002262423930000101
wherein the content of the first and second substances,
Figure BDA0002262423930000102
i is e {1,2, …, N } is NiA dimensional euclidean space non-empty closed convex set;
Figure BDA0002262423930000103
is a convex function or a second-order continuous differentiable function; a. theiIs mxniAnd (4) matrix.
(2) For convenience, the constraint is expressed in the form Ax ═ b
Figure BDA0002262423930000104
The lagrangian function of the optimization problem (1) is then:
Figure BDA0002262423930000105
wherein β is greater than 0 and is a penalty factor;
(3) the ADAL algorithm is to convert an unconstrained optimization model shown in formula (2) into a two-layer optimization problem to be solved, and an iterative strategy of k +1 steps of the problem in two adjacent partitions i and j is (referred to as a parallel algorithm 1 for short):
Figure BDA0002262423930000106
in the formula (I), the compound is shown in the specification,
Figure BDA0002262423930000107
and
Figure BDA0002262423930000108
respectively obtaining state variable estimated values of k step and k +1 step of the partition i and the partition j; tau is step size factor, tau is equal to (0,1/q), and q is [ AiAj]TMaximum number of non-zero elements in middle row.
(4) Taking the two-partition single-phase system shown in fig. 3 as an example, the invention provides a new distributed state estimation algorithm based on the ADAL algorithm in a rectangular coordinate system. Let x be the voltage amplitude and phase angle of the partition i, and the state variables of its boundary region are respectively represented by eiAnd fiLet y be the voltage amplitude and phase angle of the partition j, and the state variables of the boundary region are respectively represented by ejAnd fjAnd (4) showing. The objective function of the system state estimation is:
o.b.minJ(x)＝Ji(x)+Jj(y) (4)
let the estimated value of the boundary region measurement of partition i be fi(x) The estimated value of the boundary area measurement of the partition j is fj(x) Then equation (4) can be equivalent to:
Figure BDA0002262423930000111
the corresponding lagrange function of equation (6) is:
Figure BDA0002262423930000112
the parallel interaction algorithm of the two partitions in the step (k + 1) can be obtained:
Figure BDA0002262423930000113
step 2, according to the difference of the distributed state estimation new algorithm based on the ADAL algorithm and the interaction information provided in the step 1, providing two interaction strategies, and selecting one of the two interaction strategies as a constraint condition;
the two interaction strategies in the step 2 are as follows:
as can be seen from the equation (7), when the state quantity of the k +1 th step of the partition i is solved, only the state quantity of the k-th iteration of the adjacent partition j is needed, and the partition j is also needed, so that the decoupling iterative computation of different partitions is realized. There are two interaction strategies according to the difference of the interaction information.
Interaction strategy 1: interacting only boundary region node voltage and current information
The boundary region interaction information only comprises the real part and the imaginary part of the node voltage, the real part and the imaginary part of the node injection and branch current, namely
Figure BDA0002262423930000114
Interaction strategy 2: the interactive information of the boundary area includes power information.
Boundary region interaction information includes node injection and branch active and reactive information, e.g.
Figure BDA0002262423930000115
P in formula (9)i(x)、Qi(x)、Pj(x)、Qj(x) And calculating information of active power and reactive power of the boundary area partition i and the boundary area partition j respectively.
Step 3, based on the distributed state estimation new algorithm and the constraint conditions of the ADAL algorithm, further deducing a practical algorithm based on the interactive information, and establishing a target function based on a weighted least square method;
(1) for partition i:
Figure BDA0002262423930000121
of formula (10)The last term is a constant and the corresponding derivative is zero. If the estimation result of the boundary of the partition j is regarded as the virtual measurement of the partition i, the virtual measurement is made
Figure BDA0002262423930000122
And its virtual standard deviation sigmaiComprises the following steps:
Figure BDA0002262423930000123
the objective function for partition i is equivalent to:
Figure BDA0002262423930000124
the objective function form of the corresponding partition i based on the weighted least squares method is:
Figure BDA0002262423930000125
in the formula, nvirVirtual measurement number for boundary region; h isi,s(x) And
Figure BDA0002262423930000126
respectively an s-th boundary measurement calculation value and a virtual measurement value thereof; z is a radical ofi,sFor the s-th actual measurement value contained in the partition i, n, h in totali,s(x) Is calculated accordingly, σi,sCorresponding standard deviation of measurement.
As can be seen from the comparison of the equations (7) and (13), if the target function of the partition i in the equation (7) is solved by directly adopting the lagrangian multiplier method, the first derivative of the corresponding target function to the lagrangian multiplier is inevitably calculated, and unnecessary programming quantity is increased; if the estimation of the boundary region by the adjacent region is regarded as pseudo measurement, the objective function of the partition i shown in the formula (13) is obtained, and the form of the objective function is completely the same as that of the objective function in the case of non-parallel calculation, and at this time, the virtual measurement can be added to the objective function only by modifying the upper boundary of the summation cycle on the state program of serial calculation and by a small modification amount, which is very convenient.
(2) The method is based on a parallel state estimation objective function of an adaptive kernel density estimation model:
Figure BDA0002262423930000127
partition j is based on a weighted least squares method and an objective function based on adaptive kernel density estimation, as follows:
Figure BDA0002262423930000131
Figure BDA0002262423930000132
Figure BDA0002262423930000133
the (k + 1) th step two-partition parallel interactive algorithm (practical parallel algorithm for short) is as follows:
Figure BDA0002262423930000134
accordingly, the multi-partition practical parallel algorithm is:
Figure BDA0002262423930000135
in the formula, N is the partition number of the system; j e i represents all partitions adjacent to partition i.
Step 4, constructing a single-three phase mixed state estimation model according to the parallel state estimation objective function established in the step 3;
the specific method of the step 4 comprises the following steps:
based on a single-three phase mixed state estimation model of a least square method, an expansion (13) is in a single-three phase mixed form, and a single-three phase mixed parallel state estimation target function of the ith (i is 1,2, …, N) partition in a multi-partition system can be obtained:
Figure BDA0002262423930000141
in the formula, the virtual metrology weight
Figure BDA0002262423930000142
Figure BDA0002262423930000143
And hi,s(xi) Respectively, the s-th virtual measurement of the boundary of the partition i and a calculation value thereof;
solving the equation (20) by using a Newton method, wherein the iterative equation is as follows:
Figure BDA0002262423930000144
Figure BDA0002262423930000145
Figure BDA0002262423930000146
in the formula (21), the compound represented by the formula,
Figure BDA0002262423930000147
and
Figure BDA0002262423930000148
are respectively x+And xtThe j-th iteration estimate of (1); h+tThe calculation formula is a Jacobian matrix of the single-three phase mixed model and is shown as a formula (22);
Figure BDA0002262423930000149
is an information matrix;
Figure BDA00022624239300001410
and respectively correcting values of the three-phase symmetrical network state variable and the three-phase asymmetrical network state variable of the jth iteration.
In the formula (22)，
Figure BDA00022624239300001411
And
Figure BDA00022624239300001412
respectively measuring jacobian matrixes measured in relation to the boundary branch;
Figure BDA00022624239300001413
and
Figure BDA00022624239300001414
respectively measuring jacobian matrixes of a single-phase network and a three-phase network except the related measurement of the junction branch;
Figure BDA00022624239300001415
the calculation equation of the related measurement of the boundary branch is different from the measurement calculation equation of the three-phase side; h is+(x) Calculating an equation for the measurement of the three-phase symmetric network; h ist(x) An equation is calculated for the measurement of the three-phase asymmetric network.
Based on the mixed state estimation model, each partition adopts a single three-phase mixed model to carry out iterative computation, and an interaction strategy 2 is adopted between every two adjacent partitions to carry out information interaction.
In the formula (23), ri NFor the regularization residual of the ith measurement,
Figure BDA0002262423930000151
is a residual covariance matrix, Δ z is a measurement vector z and its calculated value
Figure BDA0002262423930000152
The difference between them.
Step 5, according to different calculation models adopted by each partition for the boundary area, 3 boundary information interaction forms are separated based on the single-three phase mixed state estimation model and the interaction strategy 2 in the step 4;
(1) positive sequence component of interactive boundary region information
Each partition adopts single-phase model calculation for the boundary region, taking two partitions i and j as an example, as shown in fig. 4, since the three-phase symmetry of the boundary region is good, the partition i and the partition j adopt single-phase models for the boundary region to perform state estimation, and the interaction information at this time is the positive sequence component of the boundary region, as shown in formula (24).
Figure BDA0002262423930000153
(2) Three-phase information of interactive boundary region
Each partition adopts three-phase model calculation for the boundary area, taking two partitions i and j as an example, as shown in fig. 5, because three symmetries of the boundary area are poor, the partition i and the partition j adopt three-phase models for state estimation for the boundary area, and the interactive information at this time is three-phase information of the boundary area, as shown in formula (25).
Figure BDA0002262423930000154
(3) Single three-phase hybrid interaction of boundary region information
Each partition adopts different calculation models for the boundary area, and taking two partitions i and j as an example, as shown in fig. 6, since the three-phase symmetry of the boundary area relative to the partition i is good, the partition i adopts a single-phase model for the boundary area to perform state estimation, and the three-phase symmetry of the boundary area relative to the partition j is poor, so that the partition j adopts a three-phase model for the boundary area to perform state estimation;
at this time, for the partition i, a positive sequence component obtained by phase sequence conversion of the boundary abc three-phase state variable of the partition j is transmitted to the partition i as interaction information, and then the interaction is completed according to a formula (24), wherein the calculation formula of the positive sequence component is as follows:
Figure BDA0002262423930000155
wherein α ═ e-j120°。
For the partition j, the boundary positive sequence component of the partition i is converted into three-phase information and then transmitted to the partition j, and then the interaction is completed according to the formula (25), wherein the sequence-phase conversion formula is as follows:
Figure BDA0002262423930000161
equations (24) and (25) can be expressed in simple form as follows:
Figure BDA0002262423930000162
based on the interaction strategy 2, the lagrangian multiplier update equation of the partition i in the multi-partition system can be obtained:
Figure BDA0002262423930000163
and 6, adopting a double-layer structure design according to the practical parallel algorithm and the information interaction process of the parallel single-phase and three-phase mixed state estimation algorithm.
The information interaction process of the practical parallel algorithm and the parallel single-phase and three-phase mixed state estimation algorithm adopts a double-layer structure design, as shown in fig. 1. Each sub-partition calculates the (k + 1) th iteration result of each sub-partition by utilizing the (k) th Lagrange multiplier transmitted by the coordination layer and the k-th iteration result transmitted by the adjacent sub-partition and combining the k-th iteration result of the sub-partition per se, and transmits the k + 1-th iteration result to the coordination layer; and the coordination layer obtains a k +1 step updating value by utilizing the k +1 step iteration result transmitted by each sub-partition and combining the k step Lagrange multiplier calculation, and transmits the k +1 step updating value to the partition layer, and the steps are repeatedly interacted until the algorithm converges.
As shown in fig. 2, the step 6 includes the following specific steps:
(1) reading in system network data, measurement data and a boundary area;
(2) partitioning the system according to the boundary region;
(3) creating threads, wherein the number of the threads is equal to the number of the partitions;
(4) distributing the network data and the measurement data of each partition to each thread according to the boundary area;
(5) the threads concurrently and independently execute the following (6) to (7);
(6) initializing parameters: k is 0, λ0,x0；
(7) For lagrange multiplier sequence lambdakOne thread i obtains a decision variable of the (k + 1) th step iteration of the ith partition by using a Newton solution unconstrained optimization problem formula (20)
Figure BDA0002262423930000164
The corresponding jacobian matrix and iterative equations are shown in (22) and (21), and the other threads are similar:
(8) modifying decision variables
Figure BDA0002262423930000171
(9) For thread 1, when satisfied
Figure BDA0002262423930000172
(ε is the convergence threshold), thread 1 stops computing; otherwise, after all the adjacent partitions j are subjected to one-time iterative computation, the coefficient matrix in the formula (29) is obtained through the interactive strategy 2, and the Lagrange multiplier, k + +, is updated according to the formula, and then the operation goes to the step (7); the other threads work the same way.
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 (7)

1. An ADAL-based transmission and distribution integrated parallel state estimation method is characterized by comprising the following steps: the method comprises the following steps:
step 1, establishing a distributed state estimation new algorithm based on an ADAL algorithm under a rectangular coordinate system according to a bipartite region single-phase system;
step 2, according to the difference of the distributed state estimation new algorithm based on the ADAL algorithm and the interaction information provided in the step 1, providing two interaction strategies, and selecting one of the two interaction strategies as a constraint condition;
step 3, based on the distributed state estimation new algorithm and the constraint conditions of the ADAL algorithm, further deducing a practical algorithm based on the interactive information, and establishing a target function based on a weighted least square method;
step 4, constructing a single-three phase mixed state estimation model according to the parallel state estimation objective function established in the step 3;
step 5, according to different calculation models adopted by each partition for the boundary area, 3 boundary information interaction forms are separated based on the single-three phase mixed state estimation model and the interaction strategy 2 in the step 4;
and 6, adopting a double-layer structure design according to the practical parallel algorithm and the information interaction process of the parallel single-phase and three-phase mixed state estimation algorithm.
2. An ADAL-based transport and distribution integration parallel state estimation method according to claim 1, wherein: the specific steps of the step 1 comprise:
(1) for the optimization problem:
Figure FDA0002262423920000011
wherein the content of the first and second substances,
Figure FDA0002262423920000012
i is e {1,2, …, N } is NiA dimensional euclidean space non-empty closed convex set;
Figure FDA0002262423920000013
is a convex function or a second-order continuous differentiable function; a. theiIs mxniA matrix;
(2) representing the constraint in the form of Ax ═ b
Figure FDA0002262423920000014
Then optimize problem (1)) The lagrange function of (a) is:
Figure FDA0002262423920000015
wherein β is greater than 0 and is a penalty factor;
(3) the ADAL algorithm is to convert an unconstrained optimization model shown in formula (2) into a two-layer optimization problem to be solved, wherein the iteration strategy of two adjacent partitions i and j in the k +1 step of the problem is as follows:
Figure FDA0002262423920000021
in the formula (I), the compound is shown in the specification,
Figure FDA0002262423920000022
and
Figure FDA0002262423920000023
respectively obtaining state variable estimated values of k step and k +1 step of the partition i and the partition j; tau is step size factor, tau is equal to (0,1/q), and q is [ AiAj]TMaximum number of non-zero elements in the middle row;
(4) let x be the voltage amplitude and phase angle of the partition i, and the state variables of its boundary region are respectively represented by eiAnd fiLet y be the voltage amplitude and phase angle of the partition j, and the state variables of the boundary region are respectively represented by ejAnd fjRepresents; the objective function of the system state estimation is:
o.b.minJ(x)＝Ji(x)+Jj(y)(4)
let the estimated value of the boundary region measurement of partition i be fi(x) The estimated value of the boundary area measurement of the partition j is fj(x) Then equation (4) can be equivalent to:
Figure FDA0002262423920000024
the corresponding lagrange function of equation (6) is:
Figure FDA0002262423920000025
the parallel interaction algorithm of the two partitions in the step (k + 1) can be obtained:
Figure FDA0002262423920000026
3. an ADAL-based transport and distribution integration parallel state estimation method according to claim 1, wherein: the two interaction strategies in the step 2 are as follows:
interaction strategy 1: only the node voltage and current information of the boundary area is interacted:
the boundary region interaction information only comprises the real part and the imaginary part of the node voltage, the real part and the imaginary part of the node injection and branch current, namely
Figure FDA0002262423920000031
Interaction strategy 2: the interactive information of the boundary area comprises power information:
boundary region interaction information includes node injection and branch active and reactive information, e.g.
Figure FDA0002262423920000032
P in formula (9)i(x)、Qi(x)、Pj(x)、Qj(x) And calculating information of active power and reactive power of the boundary area partition i and the boundary area partition j respectively.
4. An ADAL-based transport and distribution integration parallel state estimation method according to claim 1, wherein: the specific steps of the step 3 comprise:
(1) for partition i:
Figure FDA0002262423920000033
the last term of equation (10) is constant and the corresponding derivative is zero, and if the result of the boundary estimation for partition j is considered as a virtual measurement for partition i, the virtual measurement is made
Figure FDA0002262423920000034
And its virtual standard deviation sigmaiComprises the following steps:
Figure FDA0002262423920000035
the objective function for partition i is equivalent to:
Figure FDA0002262423920000036
the objective function form of the corresponding partition i based on the weighted least squares method is:
Figure FDA0002262423920000037
in the formula, nvirVirtual measurement number for boundary region; h isi,s(x) And
Figure FDA0002262423920000038
respectively an s-th boundary measurement calculation value and a virtual measurement value thereof; z is a radical ofi,sFor the s-th actual measurement value contained in the partition i, n, h in totali,s(x) Is calculated accordingly, σi,sThe corresponding measurement standard deviation;
(2) the method is based on a parallel state estimation objective function of an adaptive kernel density estimation model:
Figure FDA0002262423920000041
partition j is based on a weighted least squares method and an objective function based on adaptive kernel density estimation, as follows:
Figure FDA0002262423920000042
Figure FDA0002262423920000043
Figure FDA0002262423920000044
the (k + 1) th step two-partition parallel interactive algorithm (practical parallel algorithm for short) is as follows:
Figure FDA0002262423920000045
accordingly, the multi-partition practical parallel algorithm is:
Figure FDA0002262423920000051
in the formula, N is the partition number of the system; j e i represents all partitions adjacent to partition i.
5. An ADAL-based transport and distribution integration parallel state estimation method according to claim 1, wherein: the specific method of the step 4 comprises the following steps:
based on a single-three phase mixed state estimation model of a least square method, an expansion (13) is in a single-three phase mixed form, and a single-three phase mixed parallel state estimation target function of the ith (i is 1,2, …, N) partition in a multi-partition system can be obtained:
Figure FDA0002262423920000052
in the formula, the virtual metrology weight
Figure FDA0002262423920000053
Figure FDA0002262423920000054
And hi,s(xi) Respectively, the s-th virtual measurement of the boundary of the partition i and a calculation value thereof;
solving the equation (20) by using a Newton method, wherein the iterative equation is as follows:
Figure FDA0002262423920000055
Figure FDA0002262423920000056
Figure FDA0002262423920000061
in the formula (21), the compound represented by the formula,
Figure FDA0002262423920000062
and
Figure FDA0002262423920000063
are respectively x+And xtThe j-th iteration estimate of (1); h+tThe calculation formula is a Jacobian matrix of the single-three phase mixed model and is shown as a formula (22);
Figure FDA0002262423920000064
is an information matrix;
Figure FDA0002262423920000065
respectively correcting values of the three-phase symmetrical network state variable and the three-phase asymmetrical network state variable of the jth iteration;
in the formula (22), the reaction mixture is,
Figure FDA0002262423920000066
and
Figure FDA0002262423920000067
respectively measuring jacobian matrixes measured in relation to the boundary branch;
Figure FDA0002262423920000068
and
Figure FDA0002262423920000069
respectively measuring jacobian matrixes of a single-phase network and a three-phase network except the related measurement of the junction branch;
Figure FDA00022624239200000610
the calculation equation of the related measurement of the boundary branch is different from the measurement calculation equation of the three-phase side; h is+(x) Calculating an equation for the measurement of the three-phase symmetric network; h ist(x) Calculating an equation for the measurement of the three-phase asymmetric network;
based on the mixed state estimation model, each partition adopts a single three-phase mixed model to carry out iterative computation, and an interaction strategy 2 is adopted between every two adjacent partitions to carry out information interaction;
in the formula (23), ri NFor the regularization residual of the ith measurement,
Figure FDA00022624239200000611
is a residual covariance matrix, Δ z is a measurement vector z and its calculated value
Figure FDA00022624239200000612
The difference between them.
6. An ADAL-based transport and distribution integration parallel state estimation method according to claim 1, wherein: the specific steps of the step 5 comprise:
(1) positive sequence component of interactive boundary region information
And (3) calculating the boundary area of each partition by adopting a single-phase model, as shown in a formula (24):
Figure FDA00022624239200000613
(2) three-phase information of interactive boundary region
And (3) calculating the boundary area of each partition by adopting a three-phase model, wherein the formula (25) is as follows:
Figure FDA00022624239200000614
(3) single three-phase hybrid interaction of boundary region information
Different calculation models are adopted for the boundary regions by each partition, and the calculation formula of the positive sequence component is as follows:
Figure FDA0002262423920000071
wherein α ═ e-j120°；
For the partition j, the boundary positive sequence component of the partition i is converted into three-phase information and then transmitted to the partition j, and then the interaction is completed according to the formula (25), wherein the sequence-phase conversion formula is as follows:
Figure FDA0002262423920000072
equations (24) and (25) can be expressed in simple form as follows:
Figure FDA0002262423920000073
based on the interaction strategy 2, the lagrangian multiplier update equation of the partition i in the multi-partition system can be obtained:
Figure FDA0002262423920000074
7. an ADAL-based transport and distribution integration parallel state estimation method according to claim 1, wherein: the specific steps of the step 6 comprise:
(1) reading in system network data, measurement data and a boundary area;
(2) partitioning the system according to the boundary region;
(3) creating threads, wherein the number of the threads is equal to the number of the partitions;
(4) distributing the network data and the measurement data of each partition to each thread according to the boundary area;
(5) the threads concurrently and independently execute the following (6) to (7);
(6) initializing parameters: k is 0, λ0,x0；
(7) For lagrange multiplier sequence lambdakOne thread i obtains a decision variable of the (k + 1) th step iteration of the ith partition by using a Newton solution unconstrained optimization problem formula (20)
Figure FDA0002262423920000075
The corresponding jacobian matrix and iterative equations are shown in (22) and (21), and the other threads are similar:
(8) modifying decision variables
Figure FDA0002262423920000081
(9) For thread 1, when satisfied
Figure FDA0002262423920000082
If epsilon is a convergence threshold, thread 1 stops calculating; otherwise, after all the adjacent partitions j are subjected to one-time iterative computation, the coefficient matrix in the formula (29) is obtained through the interactive strategy 2, and the Lagrange multiplier, k + +, is updated according to the formula, and then the operation goes to the step (7); the other threads work the same way.
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