CN108173265B - Power distribution network reconstruction method based on linearized power flow - Google Patents
Power distribution network reconstruction method based on linearized power flow Download PDFInfo
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Abstract
The invention provides a power distribution network reconstruction method based on linearized power flow, and belongs to the technical field of power system operation control. Firstly, establishing a power distribution network reconstruction model consisting of a target function and constraint conditions; respectively converting the target function and the constraint condition, and converting the original model into a mixed integer quadratic programming model; and solving the converted model to obtain the opening and closing state variables of each branch, and performing corresponding opening and closing actions according to the solving result to realize network reconstruction. The method is high in calculation speed and good in convergence, and is suitable for being applied to scenes such as real-time network reconstruction of the power distribution network.
Description
Technical Field
The invention relates to a power distribution network reconstruction method based on linearized power flow, and belongs to the technical field of power system operation control.
Background
The distribution network is an important component of an electric power system, and compared with a transmission network with a looped network running, the distribution network is generally in a disconnected state during running although the distribution network is provided with a looped link, and the network running structure is radial. Thus, in power distribution networks, changes in network architecture are fundamental and important means for carrying out various power distribution network applications.
The network reconstruction of the power distribution network is a method for optimizing various power distribution network operation indexes including minimum network loss, load balance and the like by adjusting and controlling a network structure, and achieves a specific purpose through opening and closing of branches in the network and change of the network structure.
A network reconstruction model of a power distribution network belongs to the problem of nonlinear programming of mixed integers, and all possible network structures grow exponentially along with the number of the branch circuits which can be broken in the whole network, so that the problem of NP difficulty is solved. Therefore, efficient solution of power distribution network reconstruction through an approximate model is needed.
The conventional power distribution network reconstruction method has heuristic algorithms such as genetic algorithm and the like, a feasible solution is obtained by searching all possible reconstruction schemes, the defects are that the optimal solution is difficult to obtain, and algorithm parameters are required to be adjusted to adapt to new conditions when the operation conditions change.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a power distribution network reconstruction method based on linear trend. The method takes the current state of the current power grid as a reference point, approximates the nonlinear terms in the current equation to obtain a linear three-phase current model, and quickly obtains a network reconstruction scheme by solving a mixed integer quadratic programming problem. The method is high in calculation speed and good in convergence, and is suitable for being applied to scenes such as real-time network reconstruction of the power distribution network.
The invention provides a power distribution network reconstruction method based on linearized power flow, which is characterized by comprising the following steps of:
(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, IijCurrent of branch ij, rijIs the branch ij resistance;
(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, xijThe 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 ofnodeIs the number of all nodes in the system, NrootThe 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 ofgk、pkmActive power of branch gk and km, q, respectivelygk、qkmReactive 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, pij,max,qij,maxThe upper limit of active power and the upper limit of reactive power of the branch ij are 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, zgkIs a three-phase impedance matrix of branch gk, which is a symmetrical complex matrix of 3 × 3 representing the conjugate of the complex number, vkAnd vgRepresenting the voltages of node k and node g, i, respectivelygkRepresenting the current, s, of branch gkgkRepresents the power of branch gk;
(1-2-5) node voltage upper and lower limit constraints, wherein the expression is as follows:
vk,min≤|vk|≤vk,max
in the above formula, vk,min,vk,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, | vg|2，|vk|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 isgkAnd XgkAre 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 branchijAnd 0 represents that the branch ij is opened, 1 represents that the branch ij is closed, and corresponding switching action is carried out according to the solving result to realize network reconstruction.
The invention has the characteristics and beneficial effects that:
according to the method, a power distribution network reconstruction model is established, nonlinear branch voltage equations in the model are subjected to first-order expansion linearization at reference point power, integer variables and continuous variables are decoupled, and a mixed integer nonlinear programming problem which is difficult to solve is converted into a mixed integer quadratic programming problem to be solved. Therefore, the power distribution network reconstruction method is high in calculation speed and good in convergence, can ensure the optimality of results compared with a heuristic algorithm, and is suitable for being applied to scenes such as real-time network reconstruction of a power distribution network.
Drawings
FIG. 1 is a block diagram of the overall flow of the method of the present invention.
Detailed Description
The invention provides a power distribution network reconstruction method based on linearized power flow, which is further described in detail below with reference to the accompanying drawings and specific embodiments.
The invention provides a power distribution network reconstruction method based on linearized power flow, aiming at the network characteristics of radial operation and three-phase imbalance of a power distribution network, the overall flow is shown in figure 1, and the method comprises 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 objective of power distribution network reconstruction is generally selected to minimize network loss, and the expression of a model objective function is as follows:
in the above formula, IijCurrent of branch ij, rijIs the branch ij resistance;
(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, xijThe 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 ofnodeIs the number of all nodes in the system, NrootIs the number of root nodes (feeders) 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 ofgkAnd pkmActive power of branch gk and km, q, respectivelygkAnd q iskmReactive 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 node arbitrarily selected in the power distribution network, 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, pij,max,qij,maxRespectively the upper limit of active power and the upper limit of reactive power of a branch node k;
(1-2-4) branch voltage equation constraint, wherein the expression is as follows:
in the above formula, the first and second carbon atoms are,
the division points are shown, v, I and s are all in the form of three-dimensional column vectors representing voltage, current and power, respectively, of the three phases, zgkIs a three-phase impedance matrix of the branch gk, which is a symmetrical complex matrix of 3 × 3, the subscript g represents the node number of the head end of the branch, the subscript k represents the node number of the tail end of the branch, the ×, represents the conjugate of the complex number, vkAnd vgRepresenting the voltages of node k and node g, i, respectivelygkRepresenting the current, s, of branch gkgkRepresenting the power of branch gk.
(1-2-5) node voltage upper and lower limit constraints, wherein the expression is as follows:
vk,min≤|vk|≤vk,max
in the above formula, vk,min,vk,maxRespectively, the lower and upper voltage limits of node k.
(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;
because the voltage per unit value of each node in the power distribution network is approximate to 1, the square of the branch current is approximate to the square sum of the active power and the reactive power of the branch, namely, 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, | vg|2，|vk|2Representing the square of the voltage magnitude at node g and node k, respectively.
In order to linearly approximate the branch voltage equation, a reference state is selected, and in actual operation, the current state of the power system can be used as the reference state, and the value of the reference state is denoted by a superscript 0, and includes:
a voltage value representing the reference state of node g,
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 isgkAnd XgkAre 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;
integer variable x appears in power distribution network node power balance constraintgk,xkmContinuous variable p with powergk,pkm,qgk,qkmThe form of multiplication, such a non-linear form of the product of different variables, increases the difficulty of solving the optimization model. The node power balance constraint is therefore rewritten as follows:
the branch power constraint is rewritten, and the expression is as follows:
for the linearized branch voltage equation in (2-2), when line i-j is disconnected, the voltage across the disconnected branch should not have a direct relationship, so relaxation is performed using the large M method, rewritten as:
m represents a positive number large enough to be more than one hundred times the normal voltage amplitude, so if branch g-k is open (x)ijIs 0) then MijMore than one hundred times the normal voltage amplitude, such that | vg|2-|vk|2Is limited to normal voltage amplitudeBetween one hundred times and minus one hundred times the magnitude of the normal voltage, this constraint can always be satisfied, corresponding to no direct restriction between the node voltages across the open branch. If branch gk is closed (x)gk1) the above constraint is equivalent to a linearized branch voltage equation.
(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, can be efficiently solved by various commercial solvers such as Gurobi, Cplex and the like by using a branch-and-bound method, and the result obtained by solving is that the opening and closing state variable x of each branch isijAnd when the branch i-j is disconnected at 0 and the branch ij is closed at 1, the corresponding switching action can be carried out according to the solving result 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, IijCurrent of branch ij, rijIs 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, xijThe 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 ofnodeIs the number of all nodes in the system, NrootThe 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 ofgk、pkmActive power of branch gk and km, q, respectivelygk、qkmReactive 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,qij,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, zgkIs a three-phase impedance matrix of branch gk, which is a symmetrical complex matrix of 3 × 3 representing the conjugate of the complex number, vkAnd vgRepresenting the voltages of node k and node g, i, respectivelygkRepresenting the current, s, of branch gkgkRepresents the power of branch gk;
(1-2-5) node voltage upper and lower limit constraints, wherein the expression is as follows:
vk,min≤|vk|≤vk,max
in the above formula, vk,min,vk,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, | vg|2，|vk|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 isgkAnd XgkAre 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 branchij0 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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| CN109066674A (en) * | 2018-09-28 | 2018-12-21 | 国网天津市电力公司 | Reconstruction method of power distribution network based on the full Smoothing Newton Method of Constraints |
| CN109256772B (en) * | 2018-10-16 | 2020-09-01 | 清华大学 | Convex optimization solving method for optimal cut-off of power transmission network of power system |
| CN109473980B (en) * | 2018-11-30 | 2023-11-03 | 中国电力科学研究院有限公司 | Reconstruction method and system of power distribution network |
| CN109713694A (en) * | 2019-01-25 | 2019-05-03 | 南方电网科学研究院有限责任公司 | Network dynamic reconstruction method for three-phase asymmetric power distribution network |
| CN111130118B (en) * | 2020-01-09 | 2021-02-02 | 清华大学 | Optimal power flow calculation method of power system based on piecewise linearization |
| CN112542838B (en) * | 2020-11-26 | 2023-01-03 | 云南电网有限责任公司 | Three-phase power flow linearization method for power distribution network based on support vector regression |
| CN113364054B (en) * | 2021-05-17 | 2024-04-30 | 国家电网有限公司 | Power distribution network interval network reconstruction model optimization method based on second order cone relaxation method |
| CN113949063B (en) * | 2021-10-25 | 2024-08-27 | 国网天津市电力公司电力科学研究院 | Fault isolation and recovery reconstruction method for power distribution network |
| CN114156867B (en) * | 2021-11-11 | 2024-04-09 | 国网北京市电力公司 | Optimization method and device for power distribution network interval network reconstruction model |
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