CN105305442A - Multi-target intelligent power distribution network self-healing recovery method based on quantum genetic algorithm - Google Patents

Multi-target intelligent power distribution network self-healing recovery method based on quantum genetic algorithm Download PDF

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CN105305442A
CN105305442A CN201510852370.2A CN201510852370A CN105305442A CN 105305442 A CN105305442 A CN 105305442A CN 201510852370 A CN201510852370 A CN 201510852370A CN 105305442 A CN105305442 A CN 105305442A
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邓立华
刘娟
费峻涛
蔡昌春
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Changzhou Campus of Hohai University
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Abstract

The invention discloses a multi-target intelligent power distribution network self-healing recovery method based on a quantum genetic algorithm. The method uses a node-layered forward and backward substitution method for flow calculation and uses a quantum genetic algorithm for self-healing recovery reconstruction of multiple targets of a power distribution network. The quantum genetic algorithm utilizes qubits to encode chromosomes and uses quantum revolving doors to adjust the chromosomes, so that in a relatively small population scale, the algorithm quickly converges to a global optimal solution. Island determination in the reconstruction is achieved by means of flow calculation, and the dimension of an infeasible solution is lowered. With power distribution network losses and switch action frequency as reconstruction targets, the method achieves comprehensive optimization of multiple targets and has practical value.

Description

Multi-target intelligent power distribution network self-healing recovery method based on quantum genetic algorithm
Technical Field
The invention relates to a multi-target intelligent power distribution network self-healing recovery method based on a quantum genetic algorithm, in particular to a method for reconstructing the multi-target intelligent power distribution network self-healing recovery by adopting the quantum genetic algorithm after an intelligent power distribution network fails, and belongs to the technical field of power system control.
Background
The distribution network is composed of overhead lines, distribution transformers, switches and other facilities, and plays an important role in distributing electric energy in the power network. The power distribution network generally adopts closed-loop design and open-loop operation, and the operation structure of the power distribution network is radial. The R/X of the power distribution network is larger due to the fact that the line diameter of the power distribution line is smaller than that of the power transmission line, and convergence of a power flow algorithm commonly used in the power transmission network is difficult to guarantee when power flow calculation of the power distribution network is carried out.
The intelligent power distribution network is mainly characterized by having a complete self-healing function, and needing to reduce the influence of power grid faults on users as much as possible and simultaneously ensure the economic operation of the power distribution network. After the distribution network breaks down, the network structure of the distribution network is changed by adjusting the states of the section switch and the contact switch, and the purposes of self-healing recovery and optimized operation of the distribution network are achieved. The self-healing recovery reconstruction problem of the power distribution network is a multi-objective, multi-dimensional, multi-constraint and multi-period nonlinear combined optimization problem. The method for reconstructing the power grid of the power distribution network after the fault by adopting a quick and effective method is a key problem of self-healing recovery control of the intelligent power distribution network.
At present, methods for self-healing recovery and reconstruction of a power distribution network are numerous and can be basically divided into four types, namely a mathematical analysis method, an optimal flow mode algorithm, a branch exchange method and an artificial intelligence algorithm. The greedy search is performed by the mathematical analysis method, time is consumed, the problem of the power distribution network is treated as a pure mathematical problem when the method is applied, and the actual problem requirement in the reconstruction process of the power distribution network is not considered. The optimal flow mode algorithm time is increased along with the network scale, the loops are mutually influenced when the optimal flow mode is solved, the switching sequence influences the result, the state of a to-be-determined switch can be determined only through multiple distribution network load flow calculations, and the calculation efficiency is greatly reduced. In the process of reducing the network loss, the branch exchange method does not ensure that the reconstruction scheme reaches the optimal or approximately optimal state, lacks the global optimality in the mathematical sense and is easy to converge on the local optimal solution. Parameters in the artificial intelligence algorithm are difficult to determine and the search time is long.
The quantum genetic algorithm is a method combining quantum computation and a genetic algorithm. The quantum computing realizes the parallel computing of the quantum by utilizing the superposition, entanglement and coherence of the quantum. Quantum Genetic Algorithm (QGA) based on qubits and quantum state enrolment properties. QGA represents chromosome by using quantum bit coding, and evolution search is completed by using quantum gate effect and quantum gate updating, so that optimization solution of target is realized. Compared with the traditional genetic algorithm, the quantum genetic algorithm of the dynamic rotation angle adjusting mechanism can quickly converge to the global optimal solution under a smaller population scale, and has the characteristic of strong global optimization capability. The application of the quantum genetic algorithm in the self-healing recovery aspect of the multi-target intelligent power distribution network is still blank.
Disclosure of Invention
In order to solve the technical problems, the invention provides a multi-target intelligent power distribution network self-healing recovery method based on a quantum genetic algorithm.
In order to achieve the purpose, the invention adopts the technical scheme that:
the multi-target intelligent power distribution network self-healing recovery method based on the quantum genetic algorithm comprises the following steps,
step one, initialization;
determining a switch combination before a fault and a fault switch circuit;
determining a population size n, the number m of quantum bits and an evolution algebra gs, wherein in self-healing recovery of the power distribution network, m represents the number of switches, namely branch lines, n represents the number of reconstruction schemes, and the population Q containing n individuals is { Q ═ Q }1,q1,…,qnWherein q isjJ is the jth individual in the population, 1,2, …, n;
the ith qubit is |0>Amplitude of probability ofThe ith qubit is |1>Amplitude of probability ofIndicating that all states are superimposed with the same probability at the time of initial search;
step two, defining an evolution algebra t as 1;
step three, quantum collapse;
generated by quantum collapse of population Q (t)p (t), an observation is made of Q (t) to obtain a set of determined solutions p ( t ) = { x 1 t , x 2 t , ... x n t } ;
Wherein,the observed value of the jth chromosome of the t generation has m quanta bits in total, and is a binary string with the length of m; (ii) a
Step four, modifying p (t) to meet the requirements that the fault bit is 0 and no island exists;
step five, carrying out load flow calculation by adopting a node layering forward-backward substitution method, calculating the network loss value of each group of the current generation, and storing the network loss values meeting the constraint conditions;
step six, constructing a multi-target comprehensive fitness function FZ by taking the network loss and the switching action times of the power distribution network as targets, evaluating the fitness values of all individuals of the population, and storing a reconstruction scheme with the minimum FZ in the current generation;
step seven, updating the population by using a quantum gate according to the value of the FZ;
the updating process comprises the following steps:
q j t + 1 = G ( t ) × q j t
wherein,is the jth individual in the population of the t generation,is the jth individual in the population of the t +1 th generation, G (t) is the quantum gate of the t generation,
G ( t ) = c o s θ ( t ) - s i n θ ( t ) s i n θ ( t ) cos θ ( t )
where θ is the rotation angle of the quantum gate, and θ is Δ θ × s (α)ii) Δ θ is a coefficient related to the convergence speed of the algorithm, s (α)ii) As a function of the direction of quantum rotation;
step eight, t is t + 1;
and step nine, judging whether t is less than gs, if so, turning to step three, and if not, ending.
The observation process is that a random number r between 0 and 1 is generated, ifThen getOtherwise getIs the probability that the observed value of the ith qubit in the jth chromosome of the tth generation is 0. .
The procedure of load flow calculation by adopting a node hierarchical forward-backward substitution method is as follows,
the voltage of a head end node and the power of a tail end node of the known power distribution network are calculated by taking a branch as a calculation unit; setting all node voltages as rated voltages, calculating voltage loss of each branch and current value on each branch according to node power from a last node to a first node backward section by section, and then carrying out back substitution to obtain power of a first node, which is a back substitution process; then, according to the voltage of the first node, the power of the first node and the voltage loss of each branch circuit, the voltage value of each node is obtained by forward pushing the first node to the last node section by section, which is a forward pushing process; and repeating the calculation, wherein the number of iterations is added until the voltage deviation of each node is within an allowable range.
The island judgment can be realized by means of node traversal in load flow calculation; after load flow calculation, the total number of nodes with the voltage value of the initial voltage equal to the number of root nodes is a sufficient condition that no island exists in the network structure after reconstruction.
The constraint condition is that,
and (3) load flow calculation constraint: the power and voltage after each structural change are required to meet the load flow calculation;
and (3) line capacity constraint: sk≤smax
Node voltage constraint: vmin≤Vk≤Vmax
And (3) network topology constraint: the reconstructed power distribution network is also of a tree structure, and the generation of a ring network is not allowed;
wherein s iskAnd smaxRespectively, a calculated value of the power flowing through branch k and a maximum allowable value of the line capacity, VminAnd VmaxRespectively, a lower limit value and an upper limit value of the node voltage.
The multi-objective comprehensive fitness function FZ is,
FZ=K×s×f
wherein, K is a weight factor, s is the number of switching actions in the reconstruction scheme, and f is the network loss value in the reconstruction scheme.
The invention achieves the following beneficial effects: the method adopts a node-layered forward-backward substitution method to perform load flow calculation, adopts a quantum genetic algorithm to perform multi-target self-healing recovery reconstruction of the power distribution network, and has practical value; the quantum genetic algorithm adopts a quantum bit encoding chromosome and a quantum revolving door to realize the adjustment of the chromosome, so that the global optimal solution is quickly converged under a smaller population scale; island judgment in reconstruction is carried out by means of load flow calculation, and the dimension of an infeasible solution is reduced; and the network loss and the switching action times of the power distribution network are taken as reconstruction targets, so that multi-target comprehensive optimization is realized.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a diagram of an IEEE three-feeder 16-node radial network
FIG. 3 is a diagram of a network structure for optimal self-healing recovery reconstruction after No. 5 line fault
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
The quantum genetic algorithm is a probability optimization algorithm based on the quantum computing principle, and uses a novel encoding mode based on quantum bits, namely a pair of complex numbers is used for defining a quantum bit. A qubit, also called a qubit, is the smallest unit of information storage in a quantum genetic algorithm, and a qubit can represent not only two states 0 and 1, but also any superposition state between the two states, i.e. a qubit may be in |0> or |1>, or an intermediate state between the two, i.e. different superposition states of |0> and |1>, and the states of the qubit are represented as follows:
wherein,for the state of the qubit, α and β for qubits are |0 respectively>And |1>And the normalization condition is satisfied:
i|2+|βi|2=1(i=1,2,…,m)
therein,. mu.gαi|2Representing the probability that the observed value of a quantum state is 0, | βi|2Representing the probability that the observed value of the quantum state is 1, and m is the number of qubits.
Probability amplitude of a qubit is [ α ]]TThen, the probability amplitude of m qubits can be expressed as:
q = α 1 α 2 ... α m β 1 β 2 ... β m
assuming a population size of n, the chromosomes thereof are represented by qubits Q ═ Q1,q1,…,qnWherein q isjFor j-th individual in the population, j is 1,2, …, n, the quantum logic gate selects quantum gate G to update the population, namely:
G ( t ) = c o s θ ( t ) - s i n θ ( t ) sin θ ( t ) cos θ ( t )
wherein, theta is the rotation angle of the quantum gate, and the value is as follows:
θ=Δθ×s(αii)
wherein, s (α)ii) Δ θ is a coefficient related to the convergence speed of the algorithm as a function of the direction of the quantum rotation.
The quantum gate process is as follows:
q j t + 1 = G ( t ) × q j t
wherein t is an evolution algebra,is the jth individual in the population of the t generation,is the jth individual in the population of the t +1 generation, and G (t) is the quantum gate of the t generation.
The quantum genetic algorithm applies the probability amplitude expression to the coding of the chromosome, and has more parallelism and diversity than the traditional genetic algorithm; and evolution search is completed by using quantum gate updating, conversion between any superposition states can be realized, population diversity can be better kept, and search efficiency is higher.
The updated look-up table for the design quantum gate is shown in table one:
look-up table for table-quantum gate
The design idea of the first table is as follows: the quantum gate is to ensure that the algorithm converges rapidly to chromosomes with better fitness, such as: x at position i of the current chromosomei0, the corresponding position of the optimal individual in the population is biIf the fitness function f (x) is 1i)≤f(bi) In order to converge to a chromosome with better fitness, the probability of taking 1 needs to be increased, i.e., | α needs to be decreasedi|2Value, increase value | βi|2At this time if (α)ii) In the first and third quadrants, then theta rotates counterclockwise if (α)ii) In the second and fourth quadrants, then θ rotates clockwise. In the same way, the values of the rotation angles under other conditions can be analyzed.
As shown in fig. 1, the multi-target intelligent power distribution network self-healing recovery method based on the quantum genetic algorithm includes the following steps:
step one, initialization;
determining a switch combination before a fault and a fault switch circuit;
determining a population size n, the number m of quantum bits and an evolution algebra gs, wherein in self-healing recovery of the power distribution network, m represents the number of switches, namely branch lines, n represents the number of reconstruction schemes, and the population Q containing n individuals is { Q ═ Q }1,q1,…,qnWherein q isjJ is the jth individual in the population, 1,2, …, n;
the ith qubit is |0>Amplitude of probability ofThe ith qubit is |1>Amplitude of probability ofMeaning that all states are superimposed with the same probability at the initial search.
And step two, defining an evolution algebra t as 1.
And step three, quantum collapse.
P (t) is generated by quantum collapse of the population Q (t), namely, Q (t) is observed once to obtain a set of determined solutions p ( t ) = { x 1 t , x 2 t , ... x n t } ;
Wherein,i.e., the observed value of the jth chromosome, is a binary string of length m,namely, the observed value of the jth chromosome of the tth generation has m quanta in total, and is a binary string with the length of m.
The observation process is that a random number r between 0 and 1 is generated, ifThen getOtherwise getIs the probability that the observed value of the ith qubit in the jth chromosome of the tth generation is 0.
And step four, modifying p (t) to meet the requirements that the fault bit is 0 and no island exists.
Islanding means that there is one or several nodes that are not connected to a power node or are connected to a branch containing a power node, i.e. a power-loss node.
And step five, performing load flow calculation by adopting a node hierarchical forward-backward substitution method, calculating the network loss value of each group of the current generation, and storing the network loss values meeting the constraint conditions.
The procedure of load flow calculation by adopting a node hierarchical forward-backward substitution method is as follows,
the voltage of a head end node and the power of a tail end node of the known power distribution network are calculated by taking a branch as a calculation unit; setting all node voltages as rated voltages, calculating voltage loss of each branch and current value on each branch according to node power from a last node to a first node backward section by section, and then carrying out back substitution to obtain power of a first node, which is a back substitution process; then, according to the voltage of the first node, the power of the first node and the voltage loss of each branch circuit, the voltage value of each node is obtained by forward pushing the first node to the last node section by section, which is a forward pushing process; and repeating the calculation, wherein the number of iterations is added until the voltage deviation of each node is within an allowable range.
The distribution network is usually designed by distributing N feeders with N interconnection switches, so that the whole system operates in an open loop, and therefore, the condition that the network is open-loop is that only N switches are opened after reconstruction. On the premise of ensuring that the total number of opened switches in the network is equal to the number of interconnection switches, if an isolated island exists, a closed loop must exist, and if no isolated island exists, no closed loop must exist, so that when the total number of opened switches is equal to the number of interconnection switches and no isolated island network exists, the network is a closed loop-free network. Therefore, island judgment can be realized by means of node traversal in load flow calculation; after load flow calculation, the total number of nodes with the voltage value of the initial voltage equal to the number of root nodes is a sufficient condition that no island exists in the network structure after reconstruction.
The constraints are as follows:
and (3) load flow calculation constraint: the power and voltage after each structural change are required to meet the load flow calculation;
and (3) line capacity constraint: sk≤smax
Node voltage constraint: vmin≤Vk≤Vmax
And (3) network topology constraint: the reconstructed power distribution network is also of a tree structure, and the generation of a ring network is not allowed;
wherein s iskAnd smaxRespectively, a calculated value of the power flowing through branch k and a maximum allowable value of the line capacity, VminAnd VmaxRespectively, a lower limit value and an upper limit value of the node voltage.
And step six, constructing a multi-target comprehensive fitness function FZ by taking the network loss and the switching action times of the power distribution network as targets, evaluating the fitness values of all individuals of the population, and storing the reconstruction scheme with the minimum FZ in the current generation.
The multi-objective comprehensive fitness function FZ is,
FZ=K×s×f
wherein, K is a weight factor, s is the number of switching actions in the reconstruction scheme, and f is the network loss value in the reconstruction scheme.
The calculation formula of the network loss is that,
f = Σ k = 1 n I k 2 * R k
wherein R iskIs the resistance of branch k, IkIs the current of branch k.
The calculation formula of the number of switching actions is as follows,
S = Σ i = 1 m | t i ′ - t i |
wherein, ti' and tiRespectively are the reconstructed switch states before and after the reconstruction of the distribution network,ti0 denotes switch off, ti1 indicates that the switch is closed.
Step seven, updating the population by using a quantum gate according to the value of the FZ;
the updating process comprises the following steps:
q j t + 1 = G ( t ) × q j t
wherein,is the jth individual in the population of the t generation,is the jth individual in the population of the t +1 th generation, G (t) is the quantum gate of the t generation,
G ( t ) = c o s θ ( t ) - s i n θ ( t ) s i n θ ( t ) cos θ ( t )
where θ is the rotation angle of the quantum gate, and θ is Δ θ × s (α)ii) Δ θ is a coefficient related to the convergence speed of the algorithm, s (α)ii) As a function of the direction of quantum rotation;
step eight, t is t + 1;
and step nine, judging whether t is less than gs, if so, turning to step three, and if not, ending.
To further explain the method, taking an IEEE three-feeder 16-node radial network diagram as shown in fig. 2 as an example, where switches 10, 7, and 14 are interconnection switches and are in an open state, a line 5 is tried to be selected and failed, and at this time, nodes 4 and 6 lose power, the running program finds 23 sets of fault recovery schemes that can satisfy the power flow constraint condition, where the multi-objective comprehensive optimal is the 21 st set, the optimal self-healing recovery reconstruction network structure diagram is shown in fig. 3, the results are derived, and the first four sets of optimization results are shown in table two.
Table two self-healing recovery reconstruction result
Scheme(s) 1 2 3 4
Switch 1 1 1 1 1
Switch 2 1 1 1 0
Switch 3 1 1 1 1
Switch 4 1 1 1 1
Switch 5 0 0 0 0
Switch 6 1 1 1 1
Switch 7 1 1 1 1
Switch 8 1 1 0 0
Switch 9 1 1 1 1
Switch 10 0 1 0 1
Switch 11 1 1 1 1
Switch 12 1 1 1 1
Switch 13 1 1 1 1
Switch 14 1 0 1 14
Switch 15 0 0 1 1
Switch 16 1 1 1 1
Value of loss of network 0.0939 0.0942 0.0947 0.0950
Switch operation number 4 4 4 4
Multiple objective function value 0.1339 0.1342 0.1347 0.1350
The power distribution network reconstruction scheme found by the method is based on the minimum network loss serving as a main optimization target, and is additionally provided with a target optimization function with the minimum switching action times, and the optimization target of the algorithm considers the factors with the minimum switching action times in the actual operation of the power distribution network, so that the method is more practical.
The quantum genetic algorithm adopts a quantum bit coding chromosome and a quantum revolving gate to realize the adjustment of the chromosome, so that the global optimal solution can be quickly converged under a smaller population scale, and the global optimal solution can be obtained when the general evolution algebra is 3; island judgment in reconstruction of the method is realized by means of load flow calculation, and the dimension of an infeasible solution is reduced; according to the method, the network loss and the switching action times of the power distribution network are taken as reconstruction targets, and multi-objective comprehensive optimization is realized.
In conclusion, the method adopts the node-layered forward-backward substitution method to perform the load flow calculation, adopts the quantum genetic algorithm to perform the multi-target self-healing recovery reconstruction of the power distribution network, and has practical value.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (6)

1. The self-healing recovery method of the multi-target intelligent power distribution network based on the quantum genetic algorithm is characterized by comprising the following steps of: comprises the following steps of (a) carrying out,
step one, initialization;
determining a switch combination before a fault and a fault switch circuit;
determining a population size n, the number m of quantum bits and an evolution algebra gs, wherein in self-healing recovery of the power distribution network, m represents the number of switches, namely branch lines, n represents the number of reconstruction schemes, and the population Q containing n individuals is { Q ═ Q }1,q1,…,qnWherein q isjJ is the jth individual in the population, 1,2, …, n;
the ith qubit is |0>Amplitude of probability ofThe ith qubit is |1>Amplitude of probability ofIndicating that all states are superimposed with the same probability at the time of initial search;
step two, defining an evolution algebra t as 1;
step three, quantum collapse;
p (t) is generated by quantum collapse of the population Q (t), namely, Q (t) is observed once to obtain a set of determined solutions p ( t ) = { x 1 t , x 2 t , ... x n t } ;
Wherein, the observed value of the jth chromosome of the t generation has m quanta bits in total, and is a binary string with the length of m;
step four, modifying p (t) to meet the requirements that the fault bit is 0 and no island exists;
step five, carrying out load flow calculation by adopting a node layering forward-backward substitution method, calculating the network loss value of each group of the current generation, and storing the network loss values meeting the constraint conditions;
step six, constructing a multi-target comprehensive fitness function FZ by taking the network loss and the switching action times of the power distribution network as targets, evaluating the fitness values of all individuals of the population, and storing a reconstruction scheme with the minimum FZ in the current generation;
step seven, updating the population by using a quantum gate according to the value of the FZ;
the updating process comprises the following steps:
q j t + 1 = G ( t ) × q j t
wherein,is the jth individual in the population of the t generation,is the jth individual in the population of the t +1 th generation, G (t) is the quantum gate of the t generation,
G ( t ) = c o s θ ( t ) - s i n θ ( t ) s i n θ ( t ) cos θ ( t )
where θ is the rotation angle of the quantum gate, and θ is Δ θ × s (α)ii) Δ θ is a coefficient related to the convergence speed of the algorithm, s (α)ii) As a function of the direction of quantum rotation;
step eight, t is t + 1;
and step nine, judging whether t is less than gs, if so, turning to step three, and if not, ending.
2. The multi-target intelligent power distribution network self-healing recovery method based on the quantum genetic algorithm as recited in claim 1, wherein: the observation process is that a random number r between 0 and 1 is generated, ifThen getOtherwise get Is the probability that the observed value of the ith qubit in the jth chromosome of the tth generation is 0.
3. The multi-target intelligent power distribution network self-healing recovery method based on the quantum genetic algorithm as recited in claim 1, wherein: the procedure of load flow calculation by adopting a node hierarchical forward-backward substitution method is as follows,
the voltage of a head end node and the power of a tail end node of the known power distribution network are calculated by taking a branch as a calculation unit; setting all node voltages as rated voltages, calculating voltage loss of each branch and current value on each branch according to node power from a last node to a first node backward section by section, and then carrying out back substitution to obtain power of a first node, which is a back substitution process; then, according to the voltage of the first node, the power of the first node and the voltage loss of each branch circuit, the voltage value of each node is obtained by forward pushing the first node to the last node section by section, which is a forward pushing process; and repeating the calculation, wherein the number of iterations is added until the voltage deviation of each node is within an allowable range.
4. The multi-target intelligent power distribution network self-healing recovery method based on the quantum genetic algorithm, according to claim 3, is characterized in that: the island judgment can be realized by means of node traversal in load flow calculation; after load flow calculation, the total number of nodes with the voltage value of the initial voltage equal to the number of root nodes is a sufficient condition that no island exists in the network structure after reconstruction.
5. The multi-target intelligent power distribution network self-healing recovery method based on the quantum genetic algorithm, according to claim 3, is characterized in that: the constraint condition is that,
and (3) load flow calculation constraint: the power and voltage after each structural change are required to meet the load flow calculation;
and (3) line capacity constraint: sk≤smax
Node voltage constraint: vmin≤Vk≤Vmax
And (3) network topology constraint: the reconstructed power distribution network is also of a tree structure, and the generation of a ring network is not allowed;
wherein s iskAnd smaxRespectively, a calculated value of the power flowing through branch k and a maximum allowable value of the line capacity, VminAnd VmaxRespectively, a lower limit value and an upper limit value of the node voltage.
6. The multi-target intelligent power distribution network self-healing recovery method based on the quantum genetic algorithm as recited in claim 1, wherein: the multi-objective comprehensive fitness function FZ is,
FZ=K×s×f
wherein, K is a weight factor, s is the number of switching actions in the reconstruction scheme, and f is the network loss value in the reconstruction scheme.
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