CN108173265B - Power distribution network reconstruction method based on linearized power flow - Google Patents

Abstract

The invention proposes a distribution network network reconstruction method based on linearized power flow, which belongs to the technical field of power system operation control. The method firstly establishes a distribution network reconstruction model composed of objective function and constraints; transforms the objective function and constraints respectively, and transforms the original model into a mixed integer quadratic programming model; solves the transformed model , get each branch's open and close state variables, and perform corresponding switching actions according to the solution results to realize network reconstruction. The invention has fast calculation speed and good convergence, and is suitable for use in scenarios such as real-time network reconstruction of the distribution network.

Description

A Reconfiguration Method of Distribution Network 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 operated by the ring network, although the distribution network has loop tie lines, the tie lines are generally disconnected during operation, and the network operation structure is radial. . Therefore, in the distribution network, the change of the 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 minimum network loss, load balancing, etc. It achieves specific purposes through the opening and closing of branches in the network and changes in network structure. .

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

At present, the commonly used distribution network reconfiguration methods include heuristic algorithms such as genetic algorithm, which can obtain feasible solutions by searching all possible reconfiguration schemes. Adjust the algorithm parameters to re-adapt to the new situation.

SUMMARY OF THE INVENTION

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

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

(1) Establish a distribution network network reconstruction model, which consists 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 reconstruction is to minimize network losses, which can be expressed as follows:

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

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

(1-2-1) The radial operation constraint of the distribution network, the expression is as follows:

In the above formula, x _ij is the open and closed 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) Power balance constraints of distribution network nodes, the expression is as follows:

是节点k的有功负荷，

是节点k的无功负荷；其中k是任意选取的一个节点，g是节点k上游节点编号，m是节点k下游节点编号；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 , p _km are the active power of branch gk and branch km, respectively , q _gk and q _km are the reactive powers of branch gk and branch km, respectively,

is the active load of node k,

is the reactive load of node k; where k is an arbitrarily selected node, g is the node number upstream of node k, and m is the node number downstream of node k;

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

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

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

表示点除，v，I和s都是三维的列向量形式，分别代表三相的电压、电流和功率，z_gk是支路gk的三相阻抗矩阵，为3×3的对称复矩阵，*代表复数的共轭，v_k和v_g分别表示节点k和节点g的电压，i_gk表示支路gk的电流，s_gk表示支路gk的功率；In the above formula,

Represents point division, v, I and s are all three-dimensional column vector forms, representing three-phase voltage, current and power respectively, z _gk is the three-phase impedance matrix of branch gk, which is a 3×3 symmetric complex matrix, * Represents the conjugate of complex numbers, v _k and v _g represent the voltage 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) The upper and lower limit constraints of the node voltage are expressed as follows:

v _k,min ≤|v _k |≤v _k,max

In the above formula, v _k,min , v _k,max are the lower and upper voltage limits of node k, respectively;

(2) transform the model established in step (1); the concrete steps are as follows:

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

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

(2-2) Select a reference state, and linearize the branch voltage equation constraints;

Taking the conjugate of both sides of the branch voltage equation and multiplying it with the original constraint expression, we 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;

代表节点g参考状态的电压，

和

分别代表支路gk参考状态的有功功率和参考状态的无功功率；Select the reference state, use the superscript 0 to indicate the value of the reference state, where

voltage representing 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;

The Taylor expansion of the quadratic term can be obtained:

是3×1的向量，取值如下式所示，diag表示将向量转化为对角矩阵：Among them, R _gk and X _gk are both 3 × 3 matrices,

is a 3 × 1 vector, the value is shown in the following formula, diag means to convert the vector into a diagonal matrix:

和

是阻抗参数，表达式如下：In the above formula,

and

is the impedance parameter, the expression is as follows:

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

The distribution network node power balance constraint constraint is rewritten, and the expression is as follows:

Rewriting 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 transformed by 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, and the model is solved to obtain the open and closed state variables x _ij of each branch, 0 means the branch ij is open, 1 means the branch ij is closed, and according to the solution result Perform corresponding switching actions to realize network reconfiguration.

The characteristics and beneficial effects of the present invention are:

By establishing a distribution network reconfiguration model, this method linearizes the nonlinear branch voltage equations in the model at the reference point power, and decouples the integer variables and continuous variables. The integer nonlinear programming problem is transformed into a mixed integer quadratic programming problem to solve. Therefore, the distribution network reconstruction method has fast calculation speed and good convergence, and at the same time, compared with the heuristic algorithm, it can ensure the optimality of the results, and is suitable for real-time network reconstruction of the distribution network and other scenarios.

Description of drawings

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

Detailed ways

A method for reconfiguring a distribution network network based on linearized power flow proposed by the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

A distribution network network reconstruction method based on linearized power flow proposed by the present invention, aiming 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 network reconstruction model, which consists 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 reconstruction is generally chosen to minimize network losses, and the model objective function is expressed as follows:

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

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

(1-2-1) The radial operation constraint of the distribution network, the expression is as follows:

In the above formula, x _ij is the open and closed 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 root node (feeder) in the system. number.

(1-2-2) Power balance constraints of distribution network nodes, the expression is as follows:

是节点k的有功负荷，

是节点k的无功负荷；其中k是配电网中任意选取的一个节点，g是节点k上游节点编号，m是节点k下游节点编号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 powers of branch gk and branch km, respectively,

is the active load of node k,

is the reactive load of node k; where k is an arbitrarily selected node in the distribution network, g is the node number upstream of node k, and m is the node number downstream of node k

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

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

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

表示点除，v，I和s都是三维的列向量形式，分别代表三相的电压，电流和功率，z_gk是支路gk的三相阻抗矩阵，为3×3的对称复矩阵，下标g代表支路的首端节点编号，下标k代表支路的末端节点编号，*代表复数的共轭，v_k和v_g分别表示节点k和节点g的电压，i_gk表示支路gk的电流，s_gk表示支路gk的功率。In the above formula,

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

(1-2-5) The upper and lower limit constraints of the node voltage are expressed as follows:

v _k,min ≤|v _k |≤v _k,max

In the above formula, v _k,min , v _k,max are the lower and upper voltage limits of node k, respectively.

(2) transform the model established in step (1); the concrete steps are as follows:

(2-1) Transform the objective function of the distribution network reconstruction 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 a reference state, and linearize the branch voltage equation constraints;

Taking the conjugate of both sides of the branch voltage equation and multiplying it with the original constraint expression, we get:

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

代表节点g参考状态的电压值，

分别代表支路gk参考状态的有功功率和参考状态的无功功率In order to linearize the branch voltage equation, a reference state needs to be selected. 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:

is the voltage value representing the reference state of node g,

Represents the active power and the reactive power of the reference state of the branch gk, respectively

The Taylor expansion of the quadratic term can be obtained:

是3×1的向量，取值如下式所示，diag表示将向量转化为对角矩阵：Among them, R _gk and X _gk are both 3 × 3 matrices,

is a 3 × 1 vector, the value is shown in the following formula, diag means to convert the vector into a diagonal matrix:

和

是阻抗参数，表达式如下：In the above formula,

and

is the impedance parameter, the expression is as follows:

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

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

Rewriting 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 across the disconnected branch should not have a direct relationship, so the big M method is used to relax, and it is rewritten as:

M represents a large enough positive number, and the magnitude 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 minus one hundred times the normal voltage amplitude, this constraint is always satisfied, which is equivalent to disconnecting the node voltage across the branch There are no direct restrictions in between. The above constraint is equivalent to the linearized branch voltage equation if the branch gk is closed (x _gk is 1).

(3) solving the model transformed by 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 _Gurobi , Cplex and other commercial solvers using the branch and bound method. Represents that branch ij is open, and 1 represents that branch ij is closed, and corresponding switching actions can be performed according to the solution results to realize network reconstruction.

Claims (1)

1. A power distribution network reconstruction method based on linearized power flow is characterized by comprising the following steps:

(1) establishing a power distribution network reconstruction model, wherein the model consists of a target function and constraint conditions; the method comprises the following specific steps:

(1-1) determining an objective function of a power distribution network reconstruction model;

the reconstruction of the power distribution network aims at minimizing network loss, and the expression is as follows:

in the above formula, I_ijCurrent of branch ij, r_ijIs a branch ij resistor；

(1-2) determining constraint conditions of the power distribution network reconstruction model, specifically as follows:

(1-2-1) radial operation constraint of the power distribution network, wherein the expression is as follows:

in the above formula, x_ijThe method comprises the following steps that (1) an open-close state variable of any branch ij in the power distribution network is represented, wherein 0 represents open and close, and 1 represents close; n is a radical of_nodeIs the number of all nodes in the system, N_rootThe number of root nodes in the system;

(1-2-2) power balance constraint of the nodes of the power distribution network, wherein the expression is as follows:

in the above equation, the first equation represents the balance of the active power of the node k, and the second equation represents the balance of the reactive power of the node k; p is a radical of_gk、p_kmActive power of branch gk and km, q, respectively_gk、q_kmReactive power for leg gk and leg km respectively,

is the active load of the node k and,

is the reactive load of node k; wherein k is a randomly selected node, g is the number of the upstream node of the node k, and m is the number of the downstream node of the node k;

(1-2-3) branch power constraint, the expression is as follows:

in the above formula, the first and second carbon atoms are,_pij,max,q_ij,maxthe upper limit of active power and the upper limit of reactive power of branch ij respectively；

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

in the above formula, the first and second carbon atoms are,

representing the dot 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_gkIs a three-phase impedance matrix of branch gk, which is a symmetrical complex matrix of 3 × 3 representing the conjugate of the complex number, v_kAnd v_gRepresenting the voltages of node k and node g, i, respectively_gkRepresenting the current, s, of branch gk_gkRepresents the power of branch gk;

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

v_k,min≤|v_k|≤v_k,max

in the above formula, v_k,min,v_k,maxThe lower and upper voltage limits of node k, respectively;

(2) converting the model established in the step (1); the method comprises the following specific steps:

(2-1) converting a target function of the power distribution network reconstruction model;

and the square of the branch current is approximate to the square sum of the active power and the reactive power of the branch, so that the objective function is converted into:

(2-2) selecting a reference state, and linearizing the branch voltage equation constraint;

conjugate is taken from two sides of a branch voltage equation and is point-multiplied with an original constraint expression to obtain:

in the above formula, | v_g|²，|v_k|²Represents the square of the voltage amplitude of the node g and the node k respectively;

selecting a reference state, the value of which is indicated by a superscript 0, wherein

The voltage representing the reference state of the node g,

and

respectively representing the active power of the reference state and the reactive power of the reference state of the branch gk;

taylor expansion of the quadratic term yields:

wherein R is_gkAnd X_gkAre all a matrix of 3 × 3 a,

the vector is 3 × 1, and the value is shown as the following formula, diag indicates that the vector is converted into a diagonal matrix:

in the above formula, the first and second carbon atoms are,

and

is an impedance parameter, the expression is as follows:

(2-3) decoupling the integer variable and the continuous variable;

the power balance constraint of the power distribution network nodes is rewritten, and the expression is as follows:

the branch power constraint is rewritten, and the expression is as follows:

and (3) relaxing the linearized branch voltage equation obtained in the step (2-2) by using a large M method, and rewriting as follows:

in the above formula, M is a positive number;

(3) solving the model transformed in the step (2);

after the conversion in the step (2), the target function of the model is expressed as follows:

the constraints are as follows:

the converted model is a mixed integer quadratic programming model, and the model is solved to obtain the open-close state variable x of each branch_ij0 represents the branch ij open, 1 represents the branchAnd closing the path ij, and performing corresponding switching action according to the solving result to realize network reconstruction.

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