CN108173265A - A Distribution Network Reconfiguration Method Based on Linearized Power Flow - Google Patents

Abstract

The invention proposes a distribution network reconfiguration method based on linearized power flow, which belongs to the technical field of power system operation control. This method first establishes a distribution network reconstruction model composed of objective functions and constraints; transforms the objective functions and constraints respectively, and transforms the original model into a mixed integer quadratic programming model; solves the transformed model , to obtain the opening and closing state variables of each branch, and perform corresponding switching actions according to the solution results to realize network reconstruction. The invention has fast calculation speed and good convergence performance, and is suitable for being applied to scenarios such as real-time network reconstruction of distribution networks.

Description

A Distribution Network Reconfiguration Method Based on Linearized Power Flow

technical field

The invention relates to a distribution network reconfiguration method based on linearized power flow, and belongs to the technical field of power system operation control.

Background technique

The distribution network is an important part of the power system. Compared with the transmission network operating in the ring network, although the distribution network has a loop tie line, the tie line is generally disconnected during operation, and its network operation structure is radial. . Therefore, in the distribution network, the change of network structure is the basis and important means for various distribution network applications.

The network reconfiguration of the distribution network is a method to adjust the control network structure to optimize various distribution network operation indicators including the minimum network loss and load balance. It achieves specific goals through the opening and closing of branches in the network and changes in the network structure. .

The network reconfiguration model of the distribution network belongs to the nonlinear programming problem of mixed integers, and all possible network structures increase exponentially with the number of disconnectable branches in the entire network, which is an NP-hard problem. Therefore, it is necessary to realize efficient solution of distribution network reconfiguration through approximate model.

At present, the commonly used distribution network reconfiguration methods include heuristic algorithms such as genetic algorithms, and obtain feasible solutions by searching all possible reconfiguration schemes. The disadvantage is that it is difficult to obtain the optimal solution, and when the operating conditions change, it often needs Adjust the algorithm parameters to re-adapt to the new situation.

Contents of the invention

The object of the present invention is to propose a distribution network reconfiguration method based on linearized power flow in order to overcome the deficiencies of the prior art. This method takes the current power flow state as a reference point, approximates the nonlinear terms in the power flow equation, obtains a linear three-phase power flow model, and quickly obtains a network reconfiguration scheme by solving mixed integer quadratic programming problems. The invention has fast calculation speed and good convergence performance, and is suitable for being applied to scenarios such as real-time network reconstruction of distribution networks.

A distribution network reconfiguration method based on linearized power flow proposed by the present invention is characterized in that the method includes the following steps:

(1) Establish a distribution network reconfiguration model, which is composed of objective functions and constraints; the specific steps are as follows:

(1-1) Determine the objective function of the distribution network reconfiguration model;

The goal of distribution network reconfiguration is to minimize network loss, the expression is as follows:

In the above formula, I _ij is the current of branch ij, r _ij is the resistance of branch ij;

(1-2) Determine the constraints of the distribution network reconfiguration model, as follows:

(1-2-1) Radial operation constraints of the distribution network, the expression is as follows:

In the above formula, x _ij is the opening and closing state variable of any branch ij in the distribution network, 0 means open, 1 means closed; N _node is the number of all nodes in the system, and N _root is the number of root nodes in the system;

(1-2-2) Distribution network node power balance constraint, the expression is as follows:

In the above formula, the first equation represents the balance of active power of node k, and the second equation represents the balance of reactive power of node k; p _gk and p _km are the active power of branch gk and branch km respectively , q _gk , q _km are the reactive power of branch gk and branch km respectively, is the active load of node k, is the reactive load of node k; where k is a node selected arbitrarily, g is the upstream node number of node k, and m is the downstream node number of node k;

(1-2-3) Branch power constraints, the expression is as follows:

In the above formula, p _{ij, max} , q _{ij, max} are the active power upper limit and reactive power upper limit of branch ij respectively;

(1-2-4) The branch voltage equation constraint, the expression is as follows:

In the above formula, Indicates point division, v, I and s are three-dimensional column vectors, representing three-phase voltage, current and power respectively, z _gk is the three-phase impedance matrix of branch gk, which is a symmetric complex matrix of 3×3, * Represents the conjugate of a complex number, v _k and v _g represent the voltages of node k and node g respectively, i _gk represents the current of branch gk, s _gk represents the power of branch gk;

(1-2-5) Node voltage upper and lower limit constraints, the expression is as follows:

v _k,min ≤|v _k |≤v _k,max

In the above formula, v _{k, min} , v _{k, max} are the lower limit and upper limit of the voltage of node k respectively;

(2) Transform the model established in step (1); the specific steps are as follows:

(2-1) Transform the objective function of the distribution network reconfiguration model;

The square of the branch current is approximated as the sum of the squares of the active power and the reactive power of the branch, then the objective function is transformed into:

(2-2) Select the reference state and linearize the constraint of the branch voltage equation;

Conjugate both sides of the branch voltage equation and dot-multiply the original constraint expression to get:

In the above formula, |v _g | ² and |v _k | ² represent the square of the voltage amplitudes of node g and node k respectively;

The reference state is selected, and the superscript 0 is used to indicate the value of the reference state, where Represents the voltage at the reference state of node g, and respectively represent the active power of the branch gk reference state and the reactive power of the reference state;

Taylor expansion of the quadratic term gives:

Among them, R _gk and X _gk are both 3×3 matrices, It is a 3×1 vector, and its value is shown in the following formula. diag means converting the vector into a diagonal matrix:

In the above formula, and is the impedance parameter, the expression is as follows:

(2-3) Decoupling integer variables and continuous variables;

Rewrite the distribution network node power balance constraints, the expression is as follows:

Rewrite the branch power constraint, the expression is as follows:

For the linearized branch voltage equation obtained in step (2-2), use the large M method to relax, and rewrite it as:

In the above formula, M is a positive number;

(3) solving the model converted through step (2);

After the transformation in step (2), the objective function expression of the model is as follows:

The constraints are as follows:

The converted model is a mixed integer quadratic programming model. Solve the model to obtain the opening and closing state variables x _ij of each branch. 0 means that the branch ij is open, and 1 means that the branch ij is closed. According to the solution results Perform corresponding switching actions to realize network reconstruction.

Features and beneficial effects of the present invention are:

In this method, by establishing a distribution network reconfiguration model, the nonlinear branch voltage equation in the model is first-order expanded and linearized at the power of the reference point, and the integer variable and continuous variable are decoupled, and the difficult-to-solve mixed The integer nonlinear programming problem is transformed into a mixed integer quadratic programming problem for solution. Therefore, the distribution network reconfiguration method has fast calculation speed and good convergence. At the same time, it can guarantee the optimality of the results compared with the heuristic algorithm. It is suitable for real-time network reconfiguration of distribution network and other scenarios.

Description of drawings

Fig. 1 is the overall flow chart of the method of the present invention.

Detailed ways

A distribution network reconfiguration method based on linearized power flow proposed by the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

A distribution network network reconfiguration method based on linearized power flow proposed by the present invention is aimed at the radial operation of the distribution network and the network characteristics of three-phase imbalance. The overall process is shown in Figure 1, including the following steps:

(1) Establish a distribution network reconfiguration model, which is composed of objective functions and constraints; the specific steps are as follows:

(1-1) Determine the objective function of the distribution network reconfiguration model;

The goal of distribution network reconfiguration is generally chosen to minimize network loss, and the model objective function expression is as follows:

In the above formula, I _ij is the current of branch ij, r _ij is the resistance of branch ij;

(1-2) Determine the constraints of the distribution network reconfiguration model, as follows:

(1-2-1) Radial operation constraints of the distribution network, the expression is as follows:

In the above formula, x _ij is the opening and closing state variable of any branch ij in the distribution network, 0 means open, 1 means closed; N _node is the number of all nodes in the system, and N _root is the number of root nodes (feeders) in the system number.

(1-2-2) Distribution network node power balance constraint, the expression is as follows:

In the above formula, the first equation represents the balance of active power of node k, and the second equation represents the balance of reactive power of node k; p _gk and p _km are the active power of branch gk and branch km respectively , q _gk and q _km are the reactive power of branch gk and branch km respectively, is the active load of node k, is the reactive load of node k; where k is a node randomly selected in the distribution network, g is the upstream node number of node k, and m is the downstream node number of node k

(1-2-3) Branch power constraints, the expression is as follows:

In the above formula, p _{ij, max} , q _{ij, max} are the active power upper limit and reactive power upper limit of branch node k respectively;

(1-2-4) The branch voltage equation constraint, the expression is as follows:

In the above formula, Represents point division, v, I and s are three-dimensional column vectors, representing three-phase voltage, current and power respectively, z _gk is the three-phase impedance matrix of branch gk, which is a symmetric complex matrix of 3×3, the following The subscript g represents the number of the first node of the branch, the subscript k represents the number of the end node of the branch, * represents the conjugate of the complex number, v _k and v _g represent the voltages of node k and node g respectively, and i _gk represents the branch gk current, s _gk represents the power of branch gk.

(1-2-5) Node voltage upper and lower limit constraints, the expression is as follows:

v _k,min ≤|v _k |≤v _k,max

In the above formula, v _{k, min} , v _{k, max} are the lower limit and upper limit of the voltage of node k respectively.

(2) Transform the model established in step (1); the specific steps are as follows:

(2-1) Transform the objective function of the distribution network reconfiguration model;

Since the per-unit voltage of each node in the distribution network is approximately 1, the square of the branch current is approximated as the sum of the squares of the active power and reactive power of the branch, that is, the objective function is transformed into:

(2-2) Select the reference state and linearize the constraint of the branch voltage equation;

Conjugate both sides of the branch voltage equation and dot-multiply the original constraint expression to get:

In the above formula, |v _g | ² and |v _k | ² represent the squares of the voltage amplitudes of node g and node k respectively.

In order to linearize the branch voltage equation, it is necessary to select a reference state. In actual operation, the current state of the power system can be used as the reference state, and the superscript 0 is used to indicate the value of the reference state, including: Represents the voltage value of the reference state of node g, Respectively represent the active power of the branch gk reference state and the reactive power of the reference state

Taylor expansion of the quadratic term gives:

Among them, R _gk and X _gk are both 3×3 matrices, It is a 3×1 vector, and its value is shown in the following formula. diag means converting the vector into a diagonal matrix:

In the above formula, and is the impedance parameter, the expression is as follows:

(2-3) Decoupling integer variables and continuous variables;

In the distribution network node power balance constraint, the form of multiplying the integer variable x _gk , x _km and the continuous variable of power p _gk , p _km , q _gk , q _km appears. This nonlinear form of the product of different variables increases the optimization The difficulty of solving the model. Therefore, the node power balance constraint is rewritten, and the expression is as follows:

Rewrite the branch power constraint, the expression is as follows:

For the linearized branch voltage equation in (2-2), when the line i-j is disconnected, the voltage at both ends of the disconnected branch should not have a direct relationship, so the large M method is used for relaxation, and it is rewritten as:

M represents a large enough positive number, and its size should be more than one hundred times the normal voltage amplitude, so if the branch gk is disconnected (x _ij is 0), M _ij is more than one hundred times the normal voltage amplitude, so that | v _g | ² - |v _k | ² is limited between one hundred times the normal voltage amplitude and one hundred times the normal voltage amplitude, this constraint can always be satisfied, which is equivalent to the node voltage at both ends of the disconnected branch There are no direct restrictions in between. If the branch gk is closed (x _gk is 1) then the above constraint is equivalent to the linearized branch voltage equation.

(3) solving the model converted through step (2);

After the transformation in step (2), the objective function expression of the model is as follows:

The constraints are as follows:

The transformed model is a mixed integer quadratic programming model, which can be efficiently solved by various commercial solvers such as Gurobi and Cplex using the branch and bound method _. Represents that the branch ij is open, 1 represents that the branch ij is closed, and corresponding switching actions can be performed according to the solution results to realize network reconstruction.

Claims (1)

1. A distribution network reconfiguration method based on linearized power flow, characterized in that the method may further comprise the steps: (1) Establish a distribution network reconfiguration model, which is composed of objective functions and constraints; the specific steps are as follows: (1-1) Determine the objective function of the distribution network reconfiguration model; The goal of distribution network reconfiguration is to minimize network loss, the expression is as follows: In the above formula, I _ij is the current of branch ij, r _ij is the resistance of branch ij; (1-2) Determine the constraints of the distribution network reconfiguration model, as follows: (1-2-1) Radial operation constraints of the distribution network, the expression is as follows: In the above formula, x _ij is the opening and closing state variable of any branch ij in the distribution network, 0 means open, 1 means closed; N _node is the number of all nodes in the system, and N _root is the number of root nodes in the system; (1-2-2) Distribution network node power balance constraint, the expression is as follows: In the above formula, the first equation represents the balance of active power of node k, and the second equation represents the balance of reactive power of node k; p _gk and p _km are the active power of branch gk and branch km respectively , q _gk , q _km are the reactive power of branch gk and branch km respectively, is the active load of node k, is the reactive load of node k; where k is a node selected arbitrarily, g is the upstream node number of node k, and m is the downstream node number of node k; (1-2-3) Branch power constraints, the expression is as follows: In the above formula, _pij,max ,q _ij,max are respectively the upper limit of active power and upper limit of reactive power of branch ij; (1-2-4) The branch voltage equation constraint, the expression is as follows: In the above formula, Indicates point division, v, I and s are all in the form of three-dimensional column vectors, representing the voltage, current and power of the three phases respectively, z _gk is the three-phase impedance matrix of the branch gk, which is a symmetric complex matrix of 3×3, * Represents the conjugate of a complex number, v _k and v _g represent the voltages of node k and node g respectively, i _gk represents the current of branch gk, s _gk represents the power of branch gk; (1-2-5) Node voltage upper and lower limit constraints, the expression is as follows: v _k,min ≤|v _k |≤v _k,max In the above formula, v _{k, min} , v _{k, max} are the lower limit and upper limit of the voltage of node k respectively; (2) Transform the model established in step (1); the specific steps are as follows: (2-1) Transform the objective function of the distribution network reconfiguration model; The square of the branch current is approximated as the sum of the squares of the active power and the reactive power of the branch, then the objective function is transformed into: (2-2) Select the reference state and linearize the constraint of the branch voltage equation; Conjugate both sides of the branch voltage equation and dot-multiply the original constraint expression to get: In the above formula, |v _g | ² and |v _k | ² represent the square of the voltage amplitudes of node g and node k respectively; The reference state is selected, and the superscript 0 is used to indicate the value of the reference state, where Represents the voltage at the reference state of node g, and respectively represent the active power of the branch gk reference state and the reactive power of the reference state; Taylor expansion of the quadratic term gives: Among them, R _gk and X _gk are both 3×3 matrices, It is a 3×1 vector, and its value is shown in the following formula. diag means converting the vector into a diagonal matrix: In the above formula, and is the impedance parameter, the expression is as follows: (2-3) Decoupling integer variables and continuous variables; Rewrite the distribution network node power balance constraints, the expression is as follows: Rewrite the branch power constraint, the expression is as follows: For the linearized branch voltage equation obtained in step (2-2), use the large M method to relax, and rewrite it as: In the above formula, M is a positive number; (3) solving the model converted through step (2); After the transformation in step (2), the objective function expression of the model is as follows: The constraints are as follows: The converted model is a mixed integer quadratic programming model. Solve the model to obtain the opening and closing state variables x _ij of each branch. 0 means that the branch ij is open, and 1 means that the branch ij is closed. According to the solution results Perform corresponding switching actions to realize network reconstruction.