CN111162533B - Smart power grid hidden topology structure identification method based on convex optimization - Google Patents
Smart power grid hidden topology structure identification method based on convex optimization Download PDFInfo
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Abstract
A smart grid hidden topology structure identification method based on convex optimization comprises the following steps: according to the topological structure of the low-voltage distribution network, a mathematical model of multiple linear regression is established based on real-time user data of the intelligent electric meter and the electric energy conservation principle; constructing a target function by using all terminal user electric quantity data matrixes X, all distribution transformer electric quantity data matrixes Y and a linear regression matrix B of a topological structure, and converting a low-voltage distribution network topology identification problem into a solvable convex optimization problem by using a norm approximation principle; and solving the convex optimization problem through a CVX tool box, and calculating a linear regression matrix B of the topological structure. According to the intelligent power grid hidden topology structure identification method based on convex optimization, the accuracy of low-voltage distribution network topology identification can be improved.
Description
Technical Field
The invention relates to a power grid hidden topology structure identification method. In particular to a smart grid hidden topology structure identification method based on convex optimization.
Background
With the progress of science and technology, the construction of the smart grid is rapidly developed, and the scale and complexity of the smart grid are increased day by day. The low-voltage distribution network is used as an important component of the intelligent power grid, is directly connected with a large number of transformer substations and users, and has the most direct influence on social life. The topological information of the low-voltage distribution network is the basis of data system calculation, power failure range control and load transfer analysis, and accurate state monitoring data and intelligent instrument data can be generated based on an accurate topological structure of the low-voltage distribution network. Because the topological structure of the low-voltage distribution network can be changed due to equipment updating, repairing and maintaining, a power grid operator can not obtain the change information of the topological structure in time, and the trouble is brought to the operation of a power grid company, so that the quick acquisition of the accurate topological information of the low-voltage distribution network has important practical significance.
The method for identifying the topological structure and the topological change of the power distribution network by using the voltage phase measuring device increases the equipment cost, and is inconvenient for operating the low-voltage power distribution network with a large number of nodes; the method for verifying the topological structure of the low-voltage distribution network based on the Pearson correlation coefficient can not realize accurate identification due to the influence of the geographical position of a user; the bionic algorithm such as particle swarm and the like for solving the optimization model has the advantages of conveniently solving a multi-objective problem, and has the defects of easy trapping in local optimization and lower searching speed. With the popularization of the intelligent electric meters, a topology identification method based on measurement data of the intelligent electric meters is generated, the intelligent electric meters can collect massive real-time electricity utilization information of users, and potential electricity stealing behaviors can be found in time by comparing total electric meter data with all electric meter data below the total electric meter data. Because the intelligent electric meter has strong data information interaction capacity, the problem of identifying the topological structure of the low-voltage distribution network based on the measurement data of the intelligent electric meter is an important research topic. Therefore, the invention provides a convex optimization-based low-voltage distribution network topological structure identification algorithm, which utilizes electric quantity measurement data of an intelligent ammeter to carry out topological identification.
Disclosure of Invention
The invention aims to solve the technical problem of providing a smart power grid hidden topology structure identification method based on convex optimization, which can improve the accuracy of low-voltage distribution network topology identification.
The technical scheme adopted by the invention is as follows: a smart grid hidden topology structure identification method based on convex optimization comprises the following steps:
1) according to the topological structure of the low-voltage distribution network, a mathematical model of multiple linear regression is established based on real-time user data of the intelligent electric meter and the electric energy conservation principle;
2) constructing a target function by using all terminal user electric quantity data matrixes X, all distribution transformer electric quantity data matrixes Y and a linear regression matrix B of a topological structure, and converting a low-voltage distribution network topology identification problem into a solvable convex optimization problem by using a norm approximation principle;
3) and solving the convex optimization problem through a CVX tool box, and calculating a linear regression matrix B of the topological structure.
The step 1) comprises the following steps:
n end users are connected to m distribution transformers, data sampling is carried out on the intelligent electric meter at set time intervals by taking watt per hour as a unit, U is set to be {1, …, n } as an index set of end user nodes, T is set to be {1, …, m } as an index set of distribution transformer nodes, and K is set to be {1, …, K } as an electric quantity measurement index set based on a time sequence; bijRepresenting the connection relationship between the ith terminal user and the jth distribution transformer, and obtaining:
wherein i belongs to U, and j belongs to T; let xi＝[xi,1,…,xi,k]TDefined as the electricity measurement data sequence of the ith end user, define yi＝[yj,1,…,yj,k]TMeasuring a data sequence for the electric quantity of the jth distribution transformer;
the electric quantity measurement value is interfered by random noise, and an error exists:
xi＝si+vi (2)
wherein s isiIs the actual sequence of measured values, viIs a noise-induced error sequence; errors are independent and identically distributed:
vi～N(0,σ2) (3)
wherein, N represents that errors obey Gaussian distribution, and the mean value is 0; sigma2Represents the variance of the error;
the linear relationship between the measured values of all end users and the measured values of the electric quantity of all distribution transformers in the upper layer, i.e. the mathematical model of multiple linear regression, is expressed in a simplified form by matrix multiplication as:
Y＝BX (4)
wherein X ═ X1,x2,…,xn]The electric quantity data matrix is used for all terminal users; y ═ Y1,y2,…,yn]The method comprises the following steps of (1) obtaining an electric quantity data matrix of all distribution transformers; and B is a linear regression matrix of the topological structure.
The step 2) comprises the following steps:
considering that each end user can only be connected to a certain distribution transformer, i.e. the connection relationship is unique, it is determined that only one element of the row vector of the linear regression matrix beta of the topology is 1, and the other elements are 0, the relationship is expressed as:
wherein: a is a row vector with elements of all 1 and the length of n; t ═ {1, …, m } is an index set of distribution transformer nodes; bijRepresenting the connection relationship between the ith end user and the jth distribution transformer;
the topology identification problem is represented as an optimization problem under multiple constraints:
wherein: | | Y-BX | non-conducting phosphorL0Representing the number of non-zero elements in the objective function, L0 representing the zero norm of the matrix, a first constraint
Corresponding to the requirement of the row vector of the linear regression matrix B of the topological structure in the formula (5); second constraint s.t.bijThe e {0,1} corresponds to a domain of definition of an element in a linear regression matrix B of the topological structure in the formula (1), and is a 0-1 planning problem;
the objective function in the optimization problem formulation under multiple constraints is non-convex, with the L0 norm being replaced by its convex approximation to avoid the non-convex problem; the feasible domains of the 0-1 planning problem are not continuous and do not conform to the definition of a convex set; the model in the optimization problem formula under multiple constraints needs to be converted into a convex optimization model, and the specific operations are as follows:
1) replacing the non-convex L0 norm with the L1 norm of the objective function, wherein the L1 norm is the optimal convex approximation of the L0 norm;
2) the 0-1 planning problem needs to be relaxed to an inequality constraint problem, so the topology solving problem is relaxed to a convex problem:
the problem described by equation (7) is a typical convex optimization problem.
The step 3) comprises the following steps:
(1) sampling electric quantity of each electric meter at intervals of 30min, and setting data of k time intervals to obtain electric quantity data matrixes X of all terminal users and electric quantity data matrixes Y of all distribution transformers;
(2) setting a linear regression matrix B for solving the topological structure, wherein the number of rows is n, and the number of columns is m;
(3) setting the target function as Y-BXL1；
(4) Setting a constraint condition:
(5) the optimization problem comprises n multiplied by m variables to be optimized, n equality limits and n multiplied by m inequality limits, an SDPT3 solver is selected for solving, and a linear regression matrix B of the topological structure is calculated;
(6) and (4) repeating the (1) th to (5) th iteration by taking different amounts of sampling data, and drawing a relation graph between the accuracy rate and the number k of the time intervals.
According to the intelligent power grid hidden topology structure identification method based on convex optimization, the accuracy of low-voltage power distribution network topology identification can be improved. Has the following advantages:
1. the algorithm avoids the problem that other algorithms are easy to fall into the local optimal solution, and the obtained solution is the global optimal solution. And a new topological matrix constraint function is added, so that the accuracy of topology identification is improved.
2. The measurement data of the intelligent electric meter is used for calculation, equipment of a low-voltage distribution network does not need to be added, and the cost of topology identification is saved.
3. The algorithm can be accessed to online data to be updated in real time, change information of a network topology structure is detected, and the algorithm has higher stability due to an optimization scheme based on global information.
Drawings
FIG. 1 is a flow chart of a smart grid hidden topology identification method based on convex optimization according to the invention;
FIG. 2 is a tree structure diagram of the low voltage distribution network of the present invention;
FIG. 3 is a graph of the results of the iterative optimization of the present invention.
Detailed Description
The method for identifying the hidden topological structure of the smart grid based on convex optimization is described in detail below with reference to embodiments and drawings.
As shown in fig. 1, the method for identifying the hidden topology structure of the smart grid based on convex optimization includes the following steps:
1) according to the topological structure of the low-voltage distribution network, a mathematical model of multiple linear regression is established based on real-time user data of the intelligent electric meter and the electric energy conservation principle;
nodes of a low voltage distribution network may be divided into different layers according to voltage levels, with nodes of the same layer having the same voltage level. The connection relationship between adjacent layers is determined. The simplified tree structure diagram of the low-voltage distribution network is shown in fig. 2, wherein the nodes of the solid lines are end users of the distribution network, and the nodes of the dotted lines are mother nodes and are connected with the child nodes downwards. The method comprises the following steps:
the method is characterized in that n end users are connected to m distribution transformers, and data sampling is carried out on the intelligent electric meter at set time intervals in units of watt per hour (Wh), wherein the intervals are 30 min. Setting U as {1, …, n } as an index set of end user nodes, T as {1, …, m } as an index set of distribution transformer nodes, and K as {1, …, K } as an index set of electric quantity measurement based on time series; bijRepresenting the connection relationship between the ith terminal user and the jth distribution transformer, and obtaining:
wherein i belongs to U, and j belongs to T; let xi＝[xi,1,…,xi,k]TDefined as the electricity measurement data sequence of the ith end user, define yi＝[yj,1,…,yj,k]TMeasuring a data sequence for the electric quantity of the jth distribution transformer;
the electric quantity measurement value is interfered by random noise, and an error exists:
xi＝si+vi (2)
wherein s isiIs the actual sequence of measured values, viIs a noise-induced error sequence; errors are independent and identically distributed:
vi～N(0,σ2) (3)
wherein N represents that the error obeys Gaussian distribution, and the mean value is 0; sigma2Represents the variance of the error;
the principle of conservation of power shows that, at any time interval, the power consumption of a distribution transformer is equal to the sum of the power consumptions of all the users connected to the transformer. According to this principle, the linear relationship between the measured values of all end users and the measured values of the electrical quantities of all distribution transformers of the upper layers, i.e. the mathematical model of the multiple linear regression, is represented in simplified form by a matrix multiplication:
Y＝BX (4)
wherein X ═ X1,x2,…,xn]The electric quantity data matrix is used for all terminal users; y ═ Y1,y2,…,yn]The method comprises the following steps of (1) obtaining an electric quantity data matrix of all distribution transformers; and B is a linear regression matrix of the topological structure.
2) Constructing a target function by using all terminal user electric quantity data matrixes X, all distribution transformer electric quantity data matrixes Y and a linear regression matrix B of a topological structure, and converting a low-voltage distribution network topology identification problem into a solvable convex optimization problem by using a norm approximation principle; the method comprises the following steps:
considering that each end user can only be connected to a certain distribution transformer, that is, the connection relationship is unique, which determines that only one element of the row vector of the linear regression matrix beta of the topology is 1, and the other elements are 0, the relationship is expressed as:
wherein: a is a row vector with elements of all 1 and the length of n; t ═ {1, …, m } is an index set of distribution transformer nodes; bijRepresenting the connection relationship between the ith end user and the jth distribution transformer;
the topology identification problem of the invention is to solve a linear regression matrix B of a topological structure between nodes with different voltage levels under a plurality of constraint conditions. The topology identification problem is represented as an optimization problem under multiple constraints:
wherein: | | Y-BX | non-conducting phosphorL0Representing the number of non-zero elements in the objective function, L0 representing the zero norm of the matrix, a first constraint
Corresponding to the requirement of the row vector of the linear regression matrix B of the topological structure in the formula (5); second constraint s.t.bijThe e {0,1} corresponds to a domain of definition of an element in a linear regression matrix B of the topological structure in the formula (1), and is a 0-1 planning problem;
the objective function in the optimization problem formulation under multiple constraints is non-convex, with the L0 norm being replaced by its convex approximation to avoid the non-convex problem; the feasible domains of the 0-1 planning problem are not continuous and do not conform to the definition of a convex set; the model in the optimization problem formula under multiple constraints needs to be converted into a convex optimization model, and the specific operations are as follows:
1) the non-convex L0 norm is replaced by the L1 norm of the objective function, wherein the L1 norm is the optimal convex approximation of the L0 norm, and the solution and the optimization are easier;
2) the 0-1 planning problem needs to be relaxed to an inequality constraint problem, so the topology solving problem is relaxed to a convex problem:
the problem described by equation (7) is a typical convex optimization problem. The tool box is simple in solving form, and both the objective function and the constraint condition can be kept in the expression form in the formula (7).
3) The convex optimization problem is solved through the CVX tool box, a linear regression matrix B of the topological structure is calculated, a more accurate topological structure matrix is obtained under the condition of using less data, and the efficiency and the accuracy of the identification work of the topological structure are improved. The method comprises the following steps:
(1) sampling electric quantity of each electric meter at intervals of 30min, and setting data of k time intervals to obtain electric quantity data matrixes X of all terminal users and electric quantity data matrixes Y of all distribution transformers;
(2) setting a linear regression matrix B for solving the topological structure, wherein the number of rows is n, and the number of columns is m;
(3) setting the target function as Y-BXL1；
(4) Setting a constraint condition:
bij∈[0,1]；
(5) the optimization problem comprises n multiplied by m variables to be optimized, n equality limits and n multiplied by m inequality limits, an SDPT3 solver is selected for solving, and a linear regression matrix B of the topological structure is calculated;
(6) iteration is carried out by repeating the steps (1) to (5) by taking different amounts of sampling data, namely, the number k of different time intervals is taken for solving for multiple times, a relation graph between the accuracy and the number k of the time intervals is drawn, and the result is shown in fig. 3.
In summary, according to the intelligent power grid hidden topology structure identification method based on convex optimization, the accuracy can reach 100% under the condition that the sampling data are enough, and compared with a traditional optimization algorithm, the accuracy of topology structure identification is obviously improved.
Claims (2)
1. A smart grid hidden topology structure identification method based on convex optimization is characterized by comprising the following steps:
1) according to the topological structure of the low-voltage distribution network, a mathematical model of multiple linear regression is established based on real-time user data of the intelligent electric meter and the electric energy conservation principle; the method comprises the following steps:
n end users are connected to m distribution transformers, data sampling is carried out on the intelligent electric meter at set time intervals by taking watt per hour as a unit, U is set to be {1, …, n } as an index set of end user nodes, T is set to be {1, …, m } as an index set of distribution transformer nodes, and K is set to be {1, …, K } as an electric quantity measurement index set based on a time sequence; bijRepresenting the connection relationship between the ith terminal user and the jth distribution transformer, and obtaining:
wherein i belongs to U, and j belongs to T; let xi＝[xi,1,…,xi,k]TDefined as the electricity measurement data sequence of the ith end user, define yi＝[yj,1,…,yj,k]TMeasuring a data sequence for the electric quantity of the jth distribution transformer;
the electric quantity measurement value is interfered by random noise, and an error exists:
xi＝si+vi (2)
wherein s isiIs the actual sequence of measured values, viIs a noise-induced error sequence; errors are independent and identically distributed:
vi～N(0,σ2) (3)
wherein N represents that the error obeys Gaussian distribution, and the mean value is 0; sigma2Represents the variance of the error;
the linear relationship between the measured values of all end users and the measured values of the electric quantity of all distribution transformers in the upper layer, i.e. the mathematical model of multiple linear regression, is expressed in a simplified form by matrix multiplication as:
Y＝BX (4)
wherein X ═ X1,x2,…,xn]The electric quantity data matrix is used for all terminal users; y ═ Y1,y2,…,yn]The method comprises the following steps of (1) obtaining an electric quantity data matrix of all distribution transformers; b is a linear regression matrix of the topological structure;
2) constructing a target function by using all terminal user electric quantity data matrixes X, all distribution transformer electric quantity data matrixes Y and a linear regression matrix B of a topological structure, and converting a low-voltage distribution network topology identification problem into a solvable convex optimization problem by using a norm approximation principle; the method comprises the following steps:
considering that each end user can only be connected to a certain distribution transformer, i.e. the connection relationship is unique, it is determined that only one element of the row vector of the linear regression matrix beta of the topology is 1, and the other elements are 0, the relationship is expressed as:
wherein: a is a row vector with elements of all 1 and the length of n; t {1, …, m } is an index set of distribution transformer nodes; bijRepresenting the connection relationship between the ith end user and the jth distribution transformer;
the topology identification problem is represented as an optimization problem under multiple constraints:
wherein: | | Y-BX | non-conducting phosphorL0Representing the number of non-zero elements in the objective function, L0 representing the zero norm of the matrix, a first constraint
Corresponding to the requirement of the row vector of the linear regression matrix B of the topological structure in the formula (5); second constraint s.t.bijThe e {0,1} corresponds to a domain of definition of an element in a linear regression matrix B of the topological structure in the formula (1), and is a 0-1 planning problem;
the objective function in the optimization problem formulation under multiple constraints is non-convex, with the L0 norm being replaced by its convex approximation to avoid the non-convex problem; the feasible domains of the 0-1 planning problem are not continuous and do not conform to the definition of a convex set; the model in the optimization problem formula under multiple constraints needs to be converted into a convex optimization model, and the specific operations are as follows:
1) replacing the non-convex L0 norm with the L1 norm of the objective function, wherein the L1 norm is the optimal convex approximation of the L0 norm;
2) the 0-1 planning problem needs to be relaxed to an inequality constraint problem, so the topology solving problem is relaxed to a convex problem:
the problem described by equation (7) is a typical convex optimization problem;
3) and solving the convex optimization problem through a CVX tool box, and calculating a linear regression matrix B of the topological structure.
2. The convex optimization-based smart grid hidden topology identification method according to claim 1, wherein the step 3) comprises:
(1) sampling electric quantity of each electric meter at intervals of 30min, and setting data of k time intervals to obtain electric quantity data matrixes X of all terminal users and electric quantity data matrixes Y of all distribution transformers;
(2) setting a linear regression matrix B for solving the topological structure, wherein the number of rows is n, and the number of columns is m;
(3) setting the target function as Y-BXL1；
(4) Setting a constraint condition:
(5) the optimization problem comprises n multiplied by m variables to be optimized, n equality limits and n multiplied by m inequality limits, an SDPT3 solver is selected for solving, and a linear regression matrix B of the topological structure is calculated;
(6) and (4) repeating the (1) th to (5) th iteration by taking different amounts of sampling data, and drawing a relation graph between the accuracy rate and the number k of the time intervals.
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