CN106897942B - Distributed parallel state estimation method and device for power distribution network - Google Patents

Distributed parallel state estimation method and device for power distribution network Download PDF

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CN106897942B
CN106897942B CN201710059560.8A CN201710059560A CN106897942B CN 106897942 B CN106897942 B CN 106897942B CN 201710059560 A CN201710059560 A CN 201710059560A CN 106897942 B CN106897942 B CN 106897942B
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盛万兴
刘科研
孟晓丽
贾东梨
何开元
胡丽娟
叶学顺
刁赢龙
董伟杰
唐建岗
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State Grid Corp of China SGCC
China Electric Power Research Institute Co Ltd CEPRI
State Grid Beijing Electric Power Co Ltd
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China Electric Power Research Institute Co Ltd CEPRI
State Grid Beijing Electric Power Co Ltd
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Abstract

The invention relates to a distributed parallel state estimation method and a distributed parallel state estimation device for a power distribution network, wherein the method comprises the following steps: carrying out network partitioning on the power distribution network by utilizing a Lagrange relaxation technology; performing network decoupling on each subregion, and determining the boundary condition of each subregion; performing state estimation on each subregion in parallel, and updating the boundary condition of each subregion; according to the technical scheme provided by the invention, automatic network partitioning is realized through Lagrange relaxation technology, and partitioning parallel computation is realized through an inter-region decoupling method, so that a set of power distribution network state estimation parallel solving algorithm which is suitable for the characteristics of a power distribution network and has strong parallelism and small data correlation among tasks is developed.

Description

Distributed parallel state estimation method and device for power distribution network
Technical Field
The invention relates to the field of power distribution network state estimation, in particular to a distributed parallel state estimation method and device for a power distribution network.
Background
The power distribution network state estimation is an important component of an energy management system and a power distribution management system, and can provide a basic data source for links such as power distribution network situation perception, risk analysis and operation control. As the basis of real-time scheduling and control of the power distribution network, the power distribution network state estimation algorithm has higher requirements on the calculation speed.
On the one hand, with the increasing energy crisis and the increasing environmental problem, distributed Generation (DG) receives more and more attention due to its advantages of cleanliness, low carbon and low cost. The conventional power distribution network is gradually developed into a complex active power distribution network due to the large DG access and the continuous expansion of the scale of the power distribution network, the scale and the quantity measurement number of the state estimation network are increased, the conventional state estimation algorithm is easy to fall into the dilemma of dimensionality disaster under the existing calculation level, and the requirement on real-time performance is difficult to meet. On the other hand, as parallel machines and parallel computing technologies are continuously developed and matured, parallel computing becomes an effective way for solving the problem of state estimation of the complex active power distribution network. Parallel computing is a method of mapping multiple tasks to execute in multiple processors or mapping a real multidimensional problem to solve on multiple processors with a specific topology. The parallel algorithm can fully exert the advantages of the cluster, complete the work which needs an ultra-large computer to complete in the past at lower cost and higher speed, obviously improve the computing speed on the premise of ensuring the computing precision, and meet the real-time requirements of analysis and control. With the gradual maturity and application of the scalable clustered computer and the distributed parallel program library with high cost performance, the distributed parallel solution of the power distribution network state estimation can be realized through the computer cluster.
Disclosure of Invention
The invention provides a distributed parallel state estimation method and a distributed parallel state estimation device for a power distribution network, and aims to solve the problem of dimension disasters such as low calculation speed, insufficient computer memory, low convergence speed and the like in the problem of analyzing and calculating the state of a complex active power distribution network by adopting a centralized algorithm aiming at the continuous expansion of the scale of the power distribution network and the continuous improvement of the on-line analysis and control requirements, realize automatic network partition by adopting a Lagrangian relaxation technology, and realize partition parallel calculation by adopting an inter-region decoupling method, thereby developing a set of parallel state estimation solving algorithm for the power distribution network, which is suitable for the characteristics of the power distribution network, has strong parallelism and has small data correlation among tasks.
The purpose of the invention is realized by adopting the following technical scheme:
in a method for distributed parallel state estimation of a power distribution network, the improvement comprising:
carrying out network partitioning on the power distribution network by using a Lagrange relaxation technology;
performing network decoupling on each subregion, and determining the boundary condition of each subregion;
and carrying out state estimation on each sub-region in parallel, and updating the boundary condition of each sub-region.
Preferably, the network partitioning of the power distribution network by using the lagrangian relaxation technology includes:
a. constructing a target function and a constraint condition of a power distribution network partition;
b. converting the objective function and the constraint condition of the power distribution network partition into a Lagrange function;
c. number of initialized distribution network partitions N = N min Wherein N is min The minimum number of partitions is the distribution network;
d. solving the Lagrangian function, and acquiring and storing a partition position result and a Lagrangian function value corresponding to the current partition number N;
e. judging whether the current partition number N is equal to N or not max Wherein N is max Selecting the partition number N for the maximum partition number of the distribution network if the partition number N is equal to the maximum partition number of the distribution network min To N max And d, carrying out network partitioning on the power distribution network by using the partition position result corresponding to the partition number with the minimum corresponding Lagrangian function value, if not, enabling N = N +1 and returning to the step d.
Further, the constructing of the objective function and the constraint conditions of the power distribution network partition includes:
establishing a first objective function of the power distribution network subarea according to the following formula:
Figure BDA0001218296910000021
in the above formula, N is the number of the power distribution network partitions, N i Is the node number of the ith sub-region, i belongs to [1,n ∈ [ ]]，F 1 A first objective function value of the power distribution network partition is obtained;
establishing a second objective function of the power distribution network partition according to the following formula:
Figure BDA0001218296910000022
in the above formula, F 2 Second value of objective function, xi, for distribution network partition i Is the measurement redundancy of the ith sub-region, wherein xi i ＝m i /s i ，m i Measuring the number, s, of measurements for the ith sub-region i The number of the state quantities of the ith sub-area;
the observability constraint of the objective function of the power distribution network partition is determined according to the following formula:
Figure BDA0001218296910000023
in the above formula, eta i Is the observability of the ith sub-region, wherein,
Figure BDA0001218296910000024
when eta i =0, it means that the ith sub-region is observable when η i =1, it means that the ith sub-area is not observable;
determining the partition number constraint of the objective function of the power distribution network partition according to the following formula:
max(N min ,N F -2)≤N≤min(N max ,N F )
in the above formula, N F Is the theoretical maximum number of divisions of the distribution network, whichIn (1),
Figure BDA0001218296910000031
n all the total number of nodes of the power distribution network.
Further, the converting the objective function of the power distribution network partition and the constraint condition thereof into a lagrangian function includes:
standardizing the objective function of the distribution network subareas according to the following formula:
Figure BDA0001218296910000032
in the above formula, y =1,2,F y ' the y-th objective function normalized value, F, for a distribution network partition ymin Minimum value of y-th objective function normalized value for distribution network partition, F ymax Maximum value of y-th objective function normalized value of power distribution network partition, F y The y target function value is a power distribution network partition;
fusing the objective function of the power distribution network partition after the standardization treatment into a single objective function according to the following formula:
minF＝ω 1 ·F 1 '+ω 2 ·F 2 '
in the above formula, F is a single objective function value, ω 1 Weights, ω, of a first objective function normalization function for power distribution network zoning 2 Normalizing the weight of the function for a second objective function of the power distribution network partition, wherein ω is 1 And ω 2 Are all greater than 0 and omega 1 +ω 2 ＝1；
And converting the objective function of the power distribution network partition and the constraint condition thereof into a Lagrangian function F (x, y, l, u, z, w) according to the following formula:
Figure BDA0001218296910000033
in the above formula, x, l and u are original variable vectors of Lagrangian functions; y, z and w are lagrange function dual variable vectors,
Figure BDA0001218296910000034
g(x)＝N，g＝min(N min ,N F -2)，/>
Figure BDA0001218296910000035
wherein eta is i Is observability of the ith sub-region, N F The theoretical maximum number of subareas of the distribution network.
Preferably, the network decoupling is performed on each sub-region, and the determining of the boundary condition of each sub-region includes:
adding a virtual generator node a at the end partition position of the ith sub-area i,2 Wherein, node a i,2 Equivalent injection power of the head partition position of the (i + 1) th sub-area adjacent to the tail partition position of the ith sub-area;
adding a virtual generator node a at the head partition position of the (i + 1) th sub-area adjacent to the tail partition position of the ith sub-area i+1,1 Wherein, node a i+1,1 A balance node equivalent to the (i + 1) th sub-region;
at node a i+1,1 A zero-impedance virtual branch is added between the nodes connected with the partition position at the head end of the (i + 1) th sub-area in the (i + 1) th sub-area;
assigning values to the virtual generator nodes of all the subregions to enable the boundary condition Zone of the tail end partition position of the ith subregion i,2 ＝[P Gi,2 ,Q Gi,2 ,V Gi,2 ,θ Gi,2 ]Boundary condition Zone for the head partition position of the i +1 th sub-area adjacent to the tail partition position of the i-th sub-area i+1,1 ＝[P Gi+1,1 ,Q Gi+1,1 ,-V Gi+1,1 ,-θ Gi+1,1 ]；
If the measurement device is disposed at the end partition position of the ith sub-area, P Gi,2 、Q Gi,2 、V Gi,2 And theta Gi,2 Respectively injecting active power, reactive power, voltage amplitude and voltage phase angle, P, corresponding to the measuring device at the tail subarea position of the ith subarea Gi+1,1 、Q Gi+1,1 、V Gi+1,1 And theta Gi+1,1 Injecting active power, reactive power, voltage amplitude and voltage phase angle corresponding to the measuring device at the partition position at the head end of the (i + 1) th sub-area respectively; if no measuring device is configured at the end partition position of the ith sub-area, P Gi,2 ＝0，Q Gi,2 、V Gi,2 、θ Gi,2 、P Gi+1,1 And Q Gi+1,1 Respectively taking random numbers, V Gi+1,1 And theta Gi+1,1 The voltage amplitude and the voltage phase angle of the balance node of the power system are respectively.
Preferably, the state estimation is performed in parallel on each sub-area through an energy management system or a power distribution management system, and the boundary condition of each sub-area is updated.
Preferably, after performing state estimation on each sub-region in parallel and updating the boundary condition of each sub-region, the method includes:
and judging whether the boundary condition of each sub-region meets the convergence condition, if so, finishing the operation, and if not, adjusting the boundary condition of each sub-region, and then, carrying out state estimation on each sub-region in parallel again until the boundary condition of each sub-region meets the convergence condition.
Further, the boundary condition Zone of the end partition position of the ith sub-area is judged i,2 And boundary condition Zone of the head partition position of the i +1 th sub-area i+1,1 Whether or not | Zone is satisfied i,2 +Zone i+1,1 I < epsilon, where epsilon is the convergence precision;
if the boundary conditions of the first partition positions of the ith sub-area and the (i + 1) th sub-area are not satisfied, the boundary conditions of the head partition positions of the ith sub-area and the (i + 1) th sub-area are exchanged with the boundary conditions of the tail partition positions of the ith sub-area and the (i + 1) th sub-area respectively, and the state estimation is carried out on the sub-areas in parallel again until the boundary conditions of the sub-areas satisfy the convergence condition.
In a distributed parallel state estimation apparatus for a power distribution network, the improvement comprising:
the partitioning module is used for partitioning the network of the power distribution network by utilizing a Lagrange relaxation technology;
the decoupling module is used for carrying out network decoupling on each subregion and determining the boundary condition of each subregion;
and the state estimation module is used for carrying out state estimation on each sub-region in parallel and updating the boundary condition of each sub-region.
Preferably, the partition module includes:
the construction unit is used for constructing a target function of the power distribution network partition and constraint conditions thereof;
the conversion unit is used for converting the target function of the power distribution network partition and the constraint condition thereof into a Lagrange function;
an initialization unit for initializing the distribution network partition number N = N min Wherein N is min The minimum number of partitions is the distribution network;
the solving unit is used for solving the Lagrangian function, and obtaining and storing a partition position result and a Lagrangian function value corresponding to the current partition number N;
a judging unit for judging whether the current partition number N is equal to N max Wherein N is max Selecting the number of the subareas N if the maximum number of the subareas is equal to the maximum number of the subareas of the distribution network min To N max And carrying out network partitioning on the power distribution network by using the partition position result corresponding to the partition number with the minimum Lagrange function value, if not, enabling N = N +1 and returning to the solving unit.
Further, the building unit includes:
establishing a first objective function of the power distribution network subarea according to the following formula:
Figure BDA0001218296910000051
in the above formula, N is the number of power distribution network partitions, N i Is the node number of the ith sub-region, i belongs to [1,n ∈ [ ]]，F 1 A first objective function value of the power distribution network partition is obtained;
establishing a second objective function of the power distribution network partition according to the following formula:
Figure BDA0001218296910000052
in the above formula, F 2 Second value of objective function, xi, for distribution network partition i Is the measurement redundancy of the ith sub-region, wherein xi i ＝m i /s i ，m i Measuring the number, s, of measurements for the ith sub-region i The number of the state quantities of the ith sub-area;
the observability constraint of the objective function of the power distribution network partition is determined according to the following formula:
Figure BDA0001218296910000053
in the above formula, eta i Is the observability of the ith sub-region, wherein,
Figure BDA0001218296910000054
when eta i When =0, it means that the ith sub-region is observable, and when η i If =1, it means that the ith sub-area is not observable;
determining the partition number constraint of the objective function of the power distribution network partition according to the following formula:
max(N min ,N F -2)≤N≤min(N max ,N F )
in the above formula, N F The theoretical maximum number of partitions for the distribution network, wherein,
Figure BDA0001218296910000055
n all the total number of nodes of the power distribution network.
Further, the conversion unit includes:
carrying out standardization processing on the objective function of the power distribution network partition according to the following formula:
Figure BDA0001218296910000061
in the above formula, y =1,2,f y ' normalized value of y-th objective function for distribution network partition, F ymin Minimum value of y-th objective function normalized value for distribution network partition, F ymax Maximum value of y-th objective function normalized value of power distribution network partition, F y The y objective function value of the power distribution network partition is obtained;
fusing the objective function of the power distribution network partition after the standardization treatment into a single objective function according to the following formula:
minF＝ω 1 ·F 1 '+ω 2 ·F 2 '
in the above formula, F is a single objective function value, ω 1 Weights, ω, of a first objective function normalization function for power distribution network zoning 2 Normalizing the weight of the function for a second objective function of the power distribution network partition, wherein ω is 1 And ω 2 Are all greater than 0 and omega 1 +ω 2 ＝1；
Converting the objective function of the distribution network partition and the constraint condition thereof into a Lagrange function F (x, y, l, u, z, w) according to the following formula:
Figure BDA0001218296910000062
in the above formula, x, l and u are original variable vectors of Lagrangian function; y, z and w are lagrange function dual variable vectors,
Figure BDA0001218296910000063
g(x)＝N，g＝min(N min ,N F -2)，/>
Figure BDA0001218296910000064
wherein eta is i Is observability of the ith sub-region, N F The theoretical maximum number of subareas of the power distribution network.
Preferably, the decoupling module includes:
adding a virtual generator node a at the end partition position of the ith sub-area i,2 Wherein, the node a i,2 Equivalent injection power of the head partition position of the (i + 1) th sub-area adjacent to the tail partition position of the ith sub-area;
in and out ofAdding virtual generator node a to the head partition position of the (i + 1) th sub-area adjacent to the tail partition position of the i sub-areas i+1,1 Wherein, the node a i+1,1 A balance node equivalent to the (i + 1) th sub-region;
at node a i+1,1 A zero-impedance virtual branch is added between nodes connected with the partition position at the head end of the (i + 1) th sub-area in the (i + 1) th sub-area;
assigning values to the virtual generator nodes of all the subregions to enable the boundary condition Zone of the tail end subregion position of the ith subregion i,2 ＝[P Gi,2 ,Q Gi,2 ,V Gi,2 ,θ Gi,2 ]Boundary condition Zone of the head partition position of the i +1 th sub-area adjacent to the tail partition position of the i-th sub-area i+1,1 ＝[P Gi+1,1 ,Q Gi+1,1 ,-V Gi+1,1 ,-θ Gi+1,1 ]；
If the measurement device is configured at the end partition position of the ith sub-area, P Gi,2 、Q Gi,2 、V Gi,2 And theta Gi,2 Respectively injecting active power, reactive power, voltage amplitude and voltage phase angle, P, corresponding to the measuring device at the tail subarea position of the ith subarea Gi+1,1 、Q Gi+1,1 、V Gi+1,1 And theta Gi+1,1 Injecting active power, reactive power, voltage amplitude and voltage phase angle corresponding to the measuring device at the partition position at the head end of the (i + 1) th sub-area respectively; if no measuring device is configured at the end partition position of the ith sub-area, P Gi,2 ＝0，Q Gi,2 、V Gi,2 、θ Gi,2 、P Gi+1,1 And Q Gi+1,1 Respectively taking random numbers, V Gi+1,1 And theta Gi+1,1 The voltage amplitude and the voltage phase angle of the balance node of the power system are respectively.
Preferably, the state estimation is performed in parallel on each sub-area through an energy management system or a power distribution management system, and the boundary condition of each sub-area is updated.
Preferably, the apparatus further comprises:
and the judging module is used for judging whether the boundary condition of each sub-region meets the convergence condition, if so, ending the operation, and if not, adjusting the boundary condition of each sub-region and then carrying out state estimation on each sub-region in parallel again until the boundary condition of each sub-region meets the convergence condition.
Further, the boundary condition Zone of the end partition position of the ith sub-area is judged i,2 And boundary condition Zone of the head partition position of the i +1 th sub-area i+1,1 Whether or not | Zone is satisfied i,2 +Zone i+1,1 I < epsilon, where epsilon is the convergence precision;
if the boundary conditions of the first partition positions of the ith sub-area and the (i + 1) th sub-area are not satisfied, the boundary conditions of the first partition positions of the ith sub-area and the (i + 1) th sub-area are exchanged with the boundary conditions of the tail partition positions of the ith sub-area and the (i + 1) th sub-area respectively, and the state estimation is performed on the sub-areas in parallel again until the boundary conditions of the sub-areas satisfy the convergence conditions.
The invention has the beneficial effects that:
according to the technical scheme provided by the invention, the network is automatically partitioned on the basis of the Lagrange relaxation technology, a multi-target network partition model is established by taking the minimum unbalance degree of the sub-region scale and the minimum unbalance degree of the redundancy measured by the sub-region as a target function, the observability equality constraint condition and the inequality constraint condition of the total partition number of the network of the power system are considered, a model solving method based on the Lagrange relaxation technology is provided, and the inequality constraint and the equality constraint are combined into the partitioned target function, so that a non-constraint optimization solving method can be used for solving, and the solving difficulty of the optimization problem is greatly simplified; meanwhile, the technical scheme provided by the invention also provides a distributed parallel state estimation architecture, network decoupling is realized by adding the virtual generator nodes and the virtual branches, the decoupled network can carry out state estimation in a distributed and environment, and through the proposed architecture scheme, the data volume uploaded to the information coordination interaction center by each sub-region is less, the time of the information interaction process is reduced, the memory occupancy rate of a computer is further reduced, and the computing efficiency of the whole system is improved.
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FIG. 1 is a flow chart of a distributed parallel state estimation method of a power distribution network according to the present invention;
FIG. 2 is a schematic structural diagram of a 5-node system in the embodiment of the present invention;
fig. 3 is a schematic structural diagram of a distributed parallel state estimation device for a power distribution network according to the present invention.
Detailed Description
The following detailed description of the embodiments of the invention refers to the accompanying drawings.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a distributed parallel state estimation method for a power distribution network, which is characterized in that automatic network partitioning is realized by a Lagrange relaxation technology, partitioned parallel calculation is realized by an inter-region decoupling method, and global convergence is realized by an iterative convergence condition, so that a power distribution network state estimation parallel solving algorithm which is suitable for the characteristics of the power distribution network, has strong parallelism and has small data correlation among tasks is developed, and as shown in figure 1, the method comprises the following steps:
101. carrying out network partitioning on the power distribution network by using a Lagrange relaxation technology;
102. performing network decoupling on each subregion, and determining the boundary condition of each subregion;
103. and carrying out state estimation on each sub-region in parallel, and updating the boundary condition of each sub-region.
Specifically, the step 101 includes:
a. constructing a target function and constraint conditions of the power distribution network partition;
b. converting the target function of the distribution network partition and the constraint condition thereof into a Lagrange function;
c. initializationThe number of the power distribution network partitions is N = N min Wherein N is min The minimum number of partitions is the distribution network;
d. solving the Lagrangian function, and acquiring and storing a partition position result and a Lagrangian function value corresponding to the current partition number N;
e. judging whether the current partition number N is equal to N or not max Wherein N is max Selecting the number of the subareas N if the maximum number of the subareas is equal to the maximum number of the subareas of the distribution network min To N max And d, carrying out network partitioning on the distribution network according to the partition position result corresponding to the partition number with the minimum Lagrange function value, if not, enabling N = N +1, and returning to the step d.
Further, the constructing of the objective function and the constraint conditions of the power distribution network partition includes:
in the distributed parallel state estimation algorithm, the calculation time of each subregion depends on the size of the subregion scale, the overall calculation time is the calculation time of the maximum-scale subregion, and the closer the sizes of the subregions are, the higher the overall calculation efficiency is, so that a first objective function of the power distribution network partition, namely a subregion scale unbalance degree index, is established according to the following formula:
Figure BDA0001218296910000091
in the above formula, N is the number of the power distribution network partitions, N i Is the node number of the ith sub-region, i belongs to [1,n ∈ [ ]]，F 1 A first objective function value of the power distribution network partition is obtained;
smaller objective function values indicate lower imbalance of the scale of each sub-region, and the overall calculation efficiency after partitioning is higher.
The existence of redundant measurements is the basis on which state estimation can improve data accuracy. In an active power distribution network, part of DGs are provided with real-time measuring equipment at a grid-connected point, so that the system redundancy is improved, and the improvement of the precision of a state estimation result is obviously influenced. In order to enable the sub-regions after the sub-regions have the substantially same data estimation accuracy, the measurement redundancies of the sub-regions are substantially the same, and therefore a second objective function of the power distribution network sub-regions, namely an imbalance degree index of the measurement redundancies of the sub-regions, is established according to the following formula:
Figure BDA0001218296910000092
in the above formula, F 2 Second value of objective function xi for distribution network partition i Measurement redundancy for ith sub-region, wherein ξ i ＝m i /s i ，m i Measuring the number, s, of measurements for the ith sub-region i The number of the state quantities of the ith sub-area;
the smaller the objective function value is, the lower the redundancy unbalance degree of the sub-region measurement is, and the closer the estimation precision of each sub-region is.
The observability of the power system is a precondition for performing state estimation calculation, so that the observability constraint of the objective function of the power distribution network partition needs to be satisfied while the objective function is optimal:
Figure BDA0001218296910000093
in the above formula, eta i Is the observability of the ith sub-region, wherein,
Figure BDA0001218296910000094
when eta i When =0, it means that the ith sub-region is observable, and when η i =1, it means that the ith sub-area is not observable;
while the observable equality constraint of each sub-area is satisfied, the inequality constraint of the total number of partitions of the network is also satisfied. If the number of the subareas is too small, the calculation amount of each subarea is too large, and the advantages of the subareas are difficult to embody. Too many partitions affect the observability of each sub-area and the convergence of the system. And comprehensively considering the two factors, determining the partition number constraint of the objective function of the power distribution network partition according to the following formula:
max(N min ,N F -2)≤N≤min(N max ,N F )
in the above formula，N F The theoretical maximum number of partitions for the distribution network, wherein,
Figure BDA0001218296910000095
n all the total number of nodes of the power distribution network.
Because the power distribution network is a radial network, when the network only has one partition point, the total partition number of the network obtains a minimum value of 2.
Converting the objective function of the power distribution network partition and the constraint condition thereof into a Lagrange function, wherein the method comprises the following steps:
in order to make the magnitude of each objective function value identical, the objective functions of the power distribution network partitions are standardized according to the following formula:
Figure BDA0001218296910000101
in the above formula, y =1,2,F y ' normalized value of y-th objective function for distribution network partition, F ymin Minimum value of y-th objective function normalized value for distribution network partition, F ymax Maximum value of y-th objective function normalized value of power distribution network partition, F y The y target function value is a power distribution network partition;
fusing the objective function of the power distribution network partition after the standardization treatment into a single objective function according to the following formula:
minF＝ω 1 ·F 1 '+ω 2 ·F 2 '
in the above formula, F is a single objective function value, ω 1 Weights, ω, of a first objective function normalization function for power distribution network zoning 2 Normalizing the weight of the function for a second objective function of the power distribution network partition, wherein ω is 1 And ω 2 Are all greater than 0 and omega 1 +ω 2 =1, in this example, ω 1 ＝0.6,ω 2 ＝0.4；
The process of converting the objective function of the power distribution network partition and the constraint condition thereof into the Lagrange function comprises the following steps:
the above network partition optimization problem can be abbreviated as the following constrained optimization problem model:
min f(x)
s.t.h(x)＝0
Figure BDA0001218296910000102
in the formula: f (x) is an objective function; x is an n-dimensional optimization variable; h (x) =0 is observability equality constraint, and m equality constraints are assumed in the model; g (x) is inequality constraint of total network partition number, and it is assumed that r inequality constraints exist in the model.
Firstly, non-negative relaxation variables l and u are introduced to convert inequality constraints in a mathematical model into equality constraints and variable inequality constraints, and the result is as follows:
Figure BDA0001218296910000103
then, a barrier constant mu > 0 is introduced to change the original objective function into a barrier function, and the result is as follows:
Figure BDA0001218296910000104
in the formula: when l is i Or u i When (i = 1.. Multidot.r) is close to the boundary (close to 0), the barrier objective function tends to be infinite, so that a minimal solution cannot be found on the boundary, as is known from the nature of the logarithmic function.
Finally, lagrangian multiplier vectors y, z and w are introduced (y is equal to R) m ,z∈R r ,w∈R r ) Introducing the equality constraint into the objective function, one can derive the lagrangian function defined by the above equation as follows:
Figure BDA0001218296910000111
through Lagrange relaxation technology processing, inequality constraint and equality constraint are combined into a partitioned objective function, so that a non-constraint optimization solving method can be used for solving, the solving difficulty of the optimization problem is greatly simplified, the Lagrange function is further optimized, and the final function is obtained in the following form:
Figure BDA0001218296910000112
in the above formula, x, l and u are original variable vectors of Lagrangian functions; y, z and w are lagrange function dual variable vectors,
Figure BDA0001218296910000113
g(x)＝N，g＝min(N min ,N F -2)，/>
Figure BDA0001218296910000114
wherein eta i Is observability of the ith sub-region, N F The theoretical maximum number of subareas of the power distribution network.
Wherein, the objective function processed by Lagrange relaxation technology is solved by adopting a Genetic Algorithm (GA).
After the step 101, a multi-criteria network partition optimization model can be solved by a GA to realize network decomposition, each sub-region is relatively independent by using a network decoupling technology, each sub-region only needs to exchange a small amount of boundary information, and a network can be subjected to state estimation in a distributed parallel environment, so the step 102 includes:
adding a virtual generator node a at the end partition position of the ith sub-area i,2 Wherein, node a i,2 Equivalent injection power of the head partition position of the (i + 1) th sub-area adjacent to the tail partition position of the ith sub-area;
adding a virtual generator node a at the head partition position of the (i + 1) th sub-area adjacent to the tail partition position of the ith sub-area i+1,1 Wherein, the node a i+1,1 A balance node equivalent to the (i + 1) th sub-region;
at node a i+1,1 And the head of the (i + 1) th sub-region and the (i + 1) th sub-regionAdding a zero-impedance virtual branch between nodes connected with end partition positions;
assigning values to the virtual generator nodes of all the subregions to enable the boundary condition Zone of the tail end subregion position of the ith subregion i,2 ＝[P Gi,2 ,Q Gi,2 ,V Gi,2 ,θ Gi,2 ]Boundary condition Zone for the head partition position of the i +1 th sub-area adjacent to the tail partition position of the i-th sub-area i+1,1 ＝[P Gi+1,1 ,Q Gi+1,1 ,-V Gi+1,1 ,-θ Gi+1,1 ]；
If the measurement device is configured at the end partition position of the ith sub-area, P Gi,2 、Q Gi,2 、V Gi,2 And theta Gi,2 Respectively injecting active power, reactive power, voltage amplitude and voltage phase angle, P, corresponding to the measuring device at the tail subarea position of the ith subarea Gi+1,1 、Q Gi+1,1 、V Gi+1,1 And theta Gi+1,1 Injecting active power, reactive power, voltage amplitude and voltage phase angle corresponding to the measuring device at the partition position at the head end of the (i + 1) th sub-area respectively; if no measuring device is configured at the end partition position of the ith sub-area, P Gi,2 ＝0，Q Gi,2 、V Gi,2 、θ Gi,2 、P Gi+1,1 And Q Gi+1,1 Respectively taking random numbers, V Gi+1,1 And theta Gi+1,1 The voltage amplitude and the voltage phase angle of the balance node of the power system are respectively.
For example, in the 5-node system shown in fig. 2, assuming that the node 3 is a selected partition point, the branch is divided into the sub-area 1 at the partition point after the network is divided, and the virtual generator node 3 (a) is added to equalize the injected power of the sub-area 2 at the virtual node, and the voltage of the virtual generator G1 is the node voltage at the node 3 (a). In the sub-area 2, a virtual generator node 3 (b) is added to be equivalent to a balance node of the sub-area 2, a zero-impedance virtual branch 3 (b) -3 is added at the same time, the node degree at the balance node is 1, the optional position of a partition point is increased, and the injected power of the virtual generator G2 is the power of the head end of the branch 3 (b) -3. And selecting the injection power and the voltage of the two virtual generators as boundary conditions, and uploading information to coordinate the interaction center for processing.
In step 103, the State estimation may be performed in parallel on each sub-area through the energy management System or the power distribution management System, and the boundary condition of each sub-area is updated, where in the prior art, the State estimation (State Estimator) of the power System in the energy management System may be used to perform the State estimation on each sub-area in parallel, and the DAS (Deep Analysis System) of the power distribution management System may be used to perform the State estimation on each sub-area in parallel.
After obtaining the state variable estimation values in each sub-region, in the information coordination interaction center, performing boundary condition coordination interaction on the sub-regions that do not satisfy the boundary convergence condition, where step 103 includes:
and judging whether the boundary condition of each sub-region meets the convergence condition, if so, finishing the operation, and if not, adjusting the boundary condition of each sub-region, and then, carrying out state estimation on each sub-region in parallel again until the boundary condition of each sub-region meets the convergence condition.
Specifically, the boundary condition Zone for determining the end partition position of the ith sub-area i,2 And boundary condition Zone of the head partition position of the i +1 th sub-area i+1,1 Whether or not | Zone is satisfied i,2 +Zone i+1,1 I is less than epsilon, wherein epsilon is convergence precision;
if the boundary conditions of the first partition positions of the ith sub-area and the (i + 1) th sub-area are not satisfied, the boundary conditions of the head partition positions of the ith sub-area and the (i + 1) th sub-area are exchanged with the boundary conditions of the tail partition positions of the ith sub-area and the (i + 1) th sub-area respectively, and the state estimation is carried out on the sub-areas in parallel again until the boundary conditions of the sub-areas satisfy the convergence condition.
The invention also provides a distributed parallel state estimation device for a power distribution network, as shown in fig. 3, the device comprises:
the partitioning module is used for partitioning the network of the power distribution network by utilizing a Lagrange relaxation technology;
the decoupling module is used for carrying out network decoupling on each subregion and determining the boundary condition of each subregion;
and the state estimation module is used for carrying out state estimation on each sub-region in parallel and updating the boundary condition of each sub-region.
The partitioning module includes:
the construction unit is used for constructing a target function of the power distribution network partition and constraint conditions thereof;
the conversion unit is used for converting the target function of the power distribution network partition and the constraint condition thereof into a Lagrange function;
an initialization unit for initializing the number of the power distribution network partitions N = N min Wherein N is min The minimum number of partitions is the distribution network;
the solving unit is used for solving the Lagrangian function, and obtaining and storing a partition position result and a Lagrangian function value corresponding to the current partition number N;
a judging unit for judging whether the current partition number N is equal to N max Wherein N is max Selecting the number of the subareas N if the maximum number of the subareas is equal to the maximum number of the subareas of the distribution network min To N max And carrying out network partitioning on the power distribution network by using the partition position result corresponding to the partition number with the minimum corresponding Lagrangian function value, if not, enabling N = N +1 and returning to the solving unit.
The construction unit comprises:
establishing a first objective function of the power distribution network partition according to the following formula:
Figure BDA0001218296910000131
in the above formula, N is the number of the power distribution network partitions, N i Is the node number of the ith sub-region, i is E [1,n]，F 1 A first objective function value of the power distribution network partition;
establishing a second objective function of the power distribution network partition according to the following formula:
Figure BDA0001218296910000132
in the above formula, F 2 For distributing powerSecond value of objective function, xi, of network partition i Measurement redundancy for ith sub-region, wherein ξ i ＝m i /s i ，m i Measuring the number, s, of measurements for the ith sub-region i The number of the state quantities of the ith sub-area;
the observability constraint of the objective function of the power distribution network partition is determined according to the following formula:
Figure BDA0001218296910000133
in the above formula, eta i Is the observability of the ith sub-region, wherein,
Figure BDA0001218296910000134
when eta i When =0, it means that the ith sub-region is observable, and when η i =1, it means that the ith sub-area is not observable;
determining the partition number constraint of the objective function of the power distribution network partition according to the following formula:
max(N min ,N F -2)≤N≤min(N max ,N F )
in the above formula, N F The theoretical maximum number of partitions for the distribution network, wherein,
Figure BDA0001218296910000135
n all the total number of nodes of the power distribution network.
The conversion unit includes:
carrying out standardization processing on the objective function of the power distribution network partition according to the following formula:
Figure BDA0001218296910000141
in the above formula, y =1,2,F y ' normalized value of y-th objective function for distribution network partition, F ymin Minimum value of y-th objective function normalized value for distribution network partition, F ymax Maximum value of y-th objective function normalized value of power distribution network partition, F y The y objective function value of the power distribution network partition is obtained;
fusing the objective function of the power distribution network partition after the standardization treatment into a single objective function according to the following formula:
minF＝ω 1 ·F 1 '+ω 2 ·F 2 '
in the above formula, F is a single objective function value, ω 1 Weight, ω, of a first objective function normalization function for power distribution network zoning 2 Normalizing the weight of the function for a second objective function of the power distribution network partition, wherein ω is 1 And ω 2 Are all greater than 0 and omega 1 +ω 2 ＝1；
Converting the objective function of the distribution network partition and the constraint condition thereof into a Lagrange function F (x, y, l, u, z, w) according to the following formula:
Figure BDA0001218296910000142
in the above formula, x, l and u are original variable vectors of Lagrangian functions; y, z and w are dual variable vectors of a Lagrangian function,
Figure BDA0001218296910000143
g(x)＝N，g＝min(N min ,N F -2)，/>
Figure BDA0001218296910000144
wherein eta is i Observability of the ith sub-region, N F The theoretical maximum number of subareas of the power distribution network.
The decoupling module comprises:
adding a virtual generator node a at the end partition position of the ith sub-area i,2 Wherein, node a i,2 Equivalent injection power of the head partition position of the (i + 1) th sub-area adjacent to the tail partition position of the ith sub-area;
adding a virtual generator node a at the head partition position of the (i + 1) th sub-area adjacent to the tail partition position of the ith sub-area i+1,1 Wherein, node a i+1,1 A balance node equivalent to the (i + 1) th sub-region;
at node a i+1,1 A zero-impedance virtual branch is added between nodes connected with the partition position at the head end of the (i + 1) th sub-area in the (i + 1) th sub-area;
assigning values to the virtual generator nodes of all the subregions to enable the boundary condition Zone of the tail end partition position of the ith subregion i,2 ＝[P Gi,2 ,Q Gi,2 ,V Gi,2 ,θ Gi,2 ]Boundary condition Zone of the head partition position of the i +1 th sub-area adjacent to the tail partition position of the i-th sub-area i+1,1 ＝[P Gi+1,1 ,Q Gi+1,1 ,-V Gi+1,1 ,-θ Gi+1,1 ]；
If the measurement device is disposed at the end partition position of the ith sub-area, P Gi,2 、Q Gi,2 、V Gi,2 And theta Gi,2 Respectively injecting active power, reactive power, voltage amplitude and voltage phase angle, P, corresponding to the measuring device at the tail subarea position of the ith subarea Gi+1,1 、Q Gi+1,1 、V Gi+1,1 And theta Gi+1,1 Injecting active power, reactive power, voltage amplitude and voltage phase angle corresponding to the measuring device at the partition position at the head end of the (i + 1) th sub-area respectively; if no measuring device is configured at the end partition position of the ith sub-area, P Gi,2 ＝0，Q Gi,2 、V Gi,2 、θ Gi,2 、P Gi+1,1 And Q Gi+1,1 Respectively taking random numbers, V Gi+1,1 And theta Gi+1,1 The voltage amplitude and the voltage phase angle of the balance node of the power system are respectively.
And performing state estimation on each sub-area in parallel through an energy management system or a power distribution management system, and updating the boundary condition of each sub-area.
The device further comprises:
and the judging module is used for judging whether the boundary condition of each subregion meets the convergence condition or not, if so, finishing the operation, and if not, adjusting the boundary condition of each subregion and then carrying out state estimation on each subregion in parallel again until the boundary condition of each subregion meets the convergence condition.
Boundary condition Zone for judging tail partition position of ith sub-area i,2 And boundary condition Zone of the head partition position of the i +1 th sub-area i+1,1 Whether or not | Zone is satisfied i,2 +Zone i+1,1 I < epsilon, where epsilon is the convergence precision;
if the boundary conditions of the first partition positions of the ith sub-area and the (i + 1) th sub-area are not satisfied, the boundary conditions of the head partition positions of the ith sub-area and the (i + 1) th sub-area are exchanged with the boundary conditions of the tail partition positions of the ith sub-area and the (i + 1) th sub-area respectively, and the state estimation is carried out on the sub-areas in parallel again until the boundary conditions of the sub-areas satisfy the convergence condition.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.

Claims (14)

1. A power distribution network distributed parallel state estimation method is characterized by comprising the following steps:
carrying out network partitioning on the power distribution network by using a Lagrange relaxation technology;
performing network decoupling on each subregion, and determining the boundary condition of each subregion;
performing state estimation on each subregion in parallel, and updating the boundary condition of each subregion;
the network decoupling is performed on each sub-region, and the boundary condition of each sub-region is determined, including:
adding a virtual generator node a at the end partition position of the ith sub-area i,2 Wherein, node a i,2 Equivalent injection power of the head partition position of the (i + 1) th sub-area adjacent to the tail partition position of the ith sub-area;
in the ith sub-areaThe virtual generator node a is added at the head partition position of the (i + 1) th sub-area adjacent to the tail partition position i+1,1 Wherein, node a i+1,1 The balance node of the (i + 1) th equivalent sub-region;
at node a i+1,1 A zero-impedance virtual branch is added between the nodes connected with the partition position at the head end of the (i + 1) th sub-area in the (i + 1) th sub-area;
assigning values to the virtual generator nodes of all the subregions to enable the boundary condition Zone of the tail end partition position of the ith subregion i,2 ＝[P Gi,2 ,Q Gi,2 ,V Gi,2 ,θ Gi,2 ]Boundary condition Zone for the head partition position of the i +1 th sub-area adjacent to the tail partition position of the i-th sub-area i+1,1 ＝[P Gi+1,1 ,Q Gi+1,1 ,-V Gi+1,1 ,-θ Gi+1,1 ]；
If the measurement device is configured at the end partition position of the ith sub-area, P Gi,2 、Q Gi,2 、V Gi,2 And theta Gi,2 Respectively injecting active power, reactive power, voltage amplitude and voltage phase angle, P, corresponding to the measuring device at the tail partition position of the ith sub-area Gi+1,1 、Q Gi+1,1 、V Gi+1,1 And theta Gi+1,1 Injecting active power, reactive power, voltage amplitude and voltage phase angle corresponding to the measuring device at the partition position at the head end of the (i + 1) th sub-area respectively; if no measuring device is configured at the end partition position of the ith sub-area, P Gi,2 ＝0，Q Gi,2 、V Gi,2 、θ Gi,2 、P Gi+1,1 And Q Gi+1,1 Respectively taking random numbers, V Gi+1,1 And theta Gi+1,1 The voltage amplitude and the voltage phase angle of the balance node of the power system are respectively.
2. The method of claim 1, wherein the network partitioning of the power distribution network using lagrangian relaxation techniques comprises:
a. constructing a target function and constraint conditions of the power distribution network partition;
b. converting the target function of the distribution network partition and the constraint condition thereof into a Lagrange function;
c. number of initialized distribution network partitions N = N min Wherein N is min The minimum number of partitions of the power distribution network is set;
d. solving the Lagrangian function, and acquiring and storing a partition position result and a Lagrangian function value corresponding to the current partition number N;
e. judging whether the current partition number N is equal to N or not max Wherein, N is max Selecting the number of the subareas N if the maximum number of the subareas is equal to the maximum number of the subareas of the distribution network min To N max And d, carrying out network partitioning on the power distribution network by using the partition position result corresponding to the partition number with the minimum corresponding Lagrangian function value, if not, enabling N = N +1 and returning to the step d.
3. The method of claim 2, wherein the constructing the objective function and the constraint condition of the power distribution network partition comprises:
establishing a first objective function of the power distribution network subarea according to the following formula:
Figure FDA0004020416410000021
in the above formula, N is the number of the power distribution network partitions, N i Is the node number of the ith sub-region, i belongs to [1,N ∈ [ ]]，F 1 A first objective function value of the power distribution network partition is obtained;
establishing a second objective function of the power distribution network subarea according to the following formula:
Figure FDA0004020416410000022
in the above formula, F 2 Second value of objective function, xi, for distribution network partition i Is the measurement redundancy of the ith sub-region, wherein xi i ＝m i /s i ，m i Measuring the number, s, of measurements for the ith sub-region i The number of the state quantities of the ith sub-area;
the observability constraint of the objective function of the power distribution network partition is determined according to the following formula:
Figure FDA0004020416410000023
in the above formula, eta i Is the observability of the ith sub-region, wherein,
Figure FDA0004020416410000024
when eta i =0, it means that the ith sub-region is observable when η i If =1, it means that the ith sub-area is not observable;
determining the partition number constraint of the objective function of the power distribution network partition according to the following formula:
max(N min ,N F -2)≤N≤min(N max ,N F )
in the above formula, N F The theoretical maximum number of partitions for the distribution network, wherein,
Figure FDA0004020416410000025
n all the total number of nodes of the power distribution network.
4. The method of claim 2, wherein converting the objective function of the distribution grid partition and its constraints into a lagrangian function comprises:
standardizing the objective function of the distribution network subareas according to the following formula:
Figure FDA0004020416410000026
in the above formula, y =1,2,F y ' normalized value of y-th objective function for distribution network partition, F ymin Minimum value of y-th objective function normalized value for distribution network partition, F ymax Maximum value of y-th objective function normalized value of power distribution network partition, F y Y for partitioning of the distribution networkA target function value;
fusing the objective function of the power distribution network partition after the standardization treatment into a single objective function according to the following formula:
min F＝ω 1 ·F 1 '+ω 2 ·F 2 '
in the above formula, F is a single objective function value, ω 1 Weights, ω, of a first objective function normalization function for power distribution network zoning 2 Normalizing the weight of the function for a second objective function of the power distribution network partition, wherein ω is 1 And ω 2 Are all greater than 0 and omega 1 +ω 2 ＝1；
Converting the objective function of the distribution network partition and the constraint condition thereof into a Lagrange function F (x, y, l, u, z, w) according to the following formula:
Figure FDA0004020416410000031
in the above formula, x, l and u are original variable vectors of Lagrangian functions; y, z and w are lagrange function dual variable vectors,
Figure FDA0004020416410000032
g(x)＝N，g＝min(N min ,N F -2)，/>
Figure FDA0004020416410000033
wherein eta is i Is observability of the ith sub-region, N F F (x) is an objective function and mu is a barrier constant, wherein f is the theoretical maximum partition number of the distribution network.
5. The method of claim 1, wherein the state estimation is performed in parallel for each sub-region by an energy management system or a power distribution management system, and the boundary conditions for each sub-region are updated.
6. The method of claim 1, wherein after the performing state estimation for each sub-region in parallel and updating the boundary conditions of each sub-region, the method comprises:
and judging whether the boundary condition of each subregion meets a convergence condition, if so, finishing the operation, and if not, adjusting the boundary condition of each subregion, and then carrying out state estimation on each subregion in parallel until the boundary condition of each subregion meets the convergence condition.
7. The method of claim 6, wherein the boundary condition Zone for determining the location of the end partition of the ith sub-area i,2 And boundary condition Zone of the head partition position of the i +1 th sub-area i+1,1 Whether or not | Zone is satisfied i,2 +Zone i+1,1 |<Epsilon, wherein epsilon is the convergence precision;
if the boundary conditions of the first partition positions of the ith sub-area and the (i + 1) th sub-area are not satisfied, the boundary conditions of the head partition positions of the ith sub-area and the (i + 1) th sub-area are exchanged with the boundary conditions of the tail partition positions of the ith sub-area and the (i + 1) th sub-area respectively, and the state estimation is carried out on the sub-areas in parallel again until the boundary conditions of the sub-areas satisfy the convergence condition.
8. A distributed parallel state estimation apparatus for a power distribution network, the apparatus comprising:
the partitioning module is used for partitioning the network of the power distribution network by utilizing a Lagrange relaxation technology;
the decoupling module is used for carrying out network decoupling on each subregion and determining the boundary condition of each subregion;
the state estimation module is used for carrying out state estimation on all the sub-regions in parallel and updating the boundary conditions of all the sub-regions;
the decoupling module comprises:
adding a virtual generator node a at the end partition position of the ith sub-area i,2 Wherein, node a i,2 The injection power of the head partition position of the (i + 1) th sub-area adjacent to the tail partition position of the ith sub-area is equivalent;
at the i +1 th sub-region adjacent to the end partition position of the i-th sub-regionVirtual generator node a is added to the head-end partition position of the subarea i+1,1 Wherein, node a i+1,1 A balance node equivalent to the (i + 1) th sub-region;
at node a i+1,1 A zero-impedance virtual branch is added between nodes connected with the partition position at the head end of the (i + 1) th sub-area in the (i + 1) th sub-area;
assigning values to the virtual generator nodes of all the subregions to enable the boundary condition Zone of the tail end partition position of the ith subregion i,2 ＝[P Gi,2 ,Q Gi,2 ,V Gi,2 ,θ Gi,2 ]Boundary condition Zone for the head partition position of the i +1 th sub-area adjacent to the tail partition position of the i-th sub-area i+1,1 ＝[P Gi+1,1 ,Q Gi+1,1 ,-V Gi+1,1 ,-θ Gi+1,1 ]；
If the measurement device is configured at the end partition position of the ith sub-area, P Gi,2 、Q Gi,2 、V Gi,2 And theta Gi,2 Respectively injecting active power, reactive power, voltage amplitude and voltage phase angle, P, corresponding to the measuring device at the tail partition position of the ith sub-area Gi+1,1 、Q Gi+1,1 、V Gi+1,1 And theta Gi+1,1 Injecting active power, reactive power, voltage amplitude and voltage phase angle corresponding to the measuring device at the partition position at the head end of the (i + 1) th sub-area respectively; if no measuring device is configured at the end partition position of the ith sub-area, P Gi,2 ＝0，Q Gi,2 、V Gi,2 、θ Gi,2 、P Gi+1,1 And Q Gi+1,1 Respectively taking random numbers, V Gi+1,1 And theta Gi+1,1 The voltage amplitude and the voltage phase angle of the balance node of the power system are respectively.
9. The apparatus of claim 8, wherein the partition module comprises:
the construction unit is used for constructing a target function of the power distribution network partition and constraint conditions thereof;
the conversion unit is used for converting the target function of the power distribution network partition and the constraint condition thereof into a Lagrange function;
an initialization unit for initializing the distribution network partition number N = N min Wherein N is min The minimum number of partitions is the distribution network;
the solving unit is used for solving the Lagrangian function, and obtaining and storing a partition position result and a Lagrangian function value corresponding to the current partition number N;
a judging unit for judging whether the current partition number N is equal to N max Wherein, N is max Selecting the number of the subareas N if the maximum number of the subareas is equal to the maximum number of the subareas of the distribution network min To N max And carrying out network partitioning on the power distribution network by using the partition position result corresponding to the partition number with the minimum corresponding Lagrangian function value, if not, enabling N = N +1 and returning to the solving unit.
10. The apparatus of claim 9, wherein the building unit comprises:
establishing a first objective function of the power distribution network partition according to the following formula:
Figure FDA0004020416410000051
in the above formula, N is the number of the power distribution network partitions, N i Is the node number of the ith sub-region, i belongs to [1,N ∈ [ ]]，F 1 A first objective function value of the power distribution network partition is obtained;
establishing a second objective function of the power distribution network partition according to the following formula:
Figure FDA0004020416410000052
in the above formula, F 2 Second value of objective function xi for distribution network partition i Is the measurement redundancy of the ith sub-region, wherein xi i ＝m i /s i ，m i Measuring the number, s, of measurements for the ith sub-region i The number of the state quantities of the ith sub-area;
the observability constraint of the objective function of the power distribution network partition is determined according to the following formula:
Figure FDA0004020416410000053
in the above formula, eta i Is the observability of the ith sub-region, wherein,
Figure FDA0004020416410000054
when eta i =0, it means that the ith sub-region is observable when η i If =1, it means that the ith sub-area is not observable;
determining the partition number constraint of the objective function of the power distribution network partition according to the following formula:
max(N min ,N F -2)≤N≤min(N max ,N F )
in the above formula, N F The theoretical maximum number of partitions for the distribution network, wherein,
Figure FDA0004020416410000055
n all the total number of nodes of the power distribution network.
11. The apparatus of claim 9, wherein the conversion unit comprises:
standardizing the objective function of the distribution network subareas according to the following formula:
Figure FDA0004020416410000056
in the above formula, y =1,2,f y ' normalized value of y-th objective function for distribution network partition, F ymin Minimum value of y-th objective function normalized value for distribution network partition, F ymax Maximum value of y-th objective function normalized value of power distribution network partition, F y The y objective function value of the power distribution network partition is obtained;
fusing the objective function of the power distribution network partition after the standardization treatment into a single objective function according to the following formula:
min F＝ω 1 ·F 1 '+ω 2 ·F 2 '
in the above formula, F is the value of a single objective function, omega 1 Weights, ω, of a first objective function normalization function for power distribution network zoning 2 Normalizing the weight of the function for a second objective function of the power distribution network partition, where ω is 1 And omega 2 Are all greater than 0 and omega 1 +ω 2 ＝1；
Converting the objective function of the distribution network partition and the constraint condition thereof into a Lagrange function F (x, y, l, u, z, w) according to the following formula:
Figure FDA0004020416410000061
in the above formula, x, l and u are original variable vectors of Lagrangian functions; y, z and w are lagrange function dual variable vectors,
Figure FDA0004020416410000062
g(x)＝N，g＝min(N min ,N F -2)，/>
Figure FDA0004020416410000063
wherein eta i Observability of the ith sub-region, N F F (x) is an objective function and mu is a barrier constant, wherein f is the theoretical maximum partition number of the distribution network.
12. The apparatus of claim 8, wherein the boundary conditions for each sub-region are updated by performing state estimation for each sub-region in parallel by an energy management system or a power distribution management system.
13. The apparatus of claim 8, wherein the apparatus further comprises:
and the judging module is used for judging whether the boundary condition of each subregion meets the convergence condition or not, if so, finishing the operation, and if not, adjusting the boundary condition of each subregion and then carrying out state estimation on each subregion in parallel again until the boundary condition of each subregion meets the convergence condition.
14. The apparatus of claim 13, wherein the boundary condition Zone for determining the location of the end partition of the ith sub-area i,2 And boundary condition Zone of the head partition position of the i +1 th sub-area i+1,1 Whether or not | Zone is satisfied i,2 +Zone i+1,1 |<Epsilon, wherein epsilon is the convergence precision;
if the boundary conditions of the first partition positions of the ith sub-area and the (i + 1) th sub-area are not satisfied, the boundary conditions of the first partition positions of the ith sub-area and the (i + 1) th sub-area are exchanged with the boundary conditions of the tail partition positions of the ith sub-area and the (i + 1) th sub-area respectively, and the state estimation is performed on the sub-areas in parallel again until the boundary conditions of the sub-areas satisfy the convergence conditions.
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