CN114977267A - Elasticity optimization method for power distribution network containing micro-grid - Google Patents

Elasticity optimization method for power distribution network containing micro-grid Download PDF

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CN114977267A
CN114977267A CN202210070189.6A CN202210070189A CN114977267A CN 114977267 A CN114977267 A CN 114977267A CN 202210070189 A CN202210070189 A CN 202210070189A CN 114977267 A CN114977267 A CN 114977267A
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distribution network
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power distribution
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姚艳
舒恺
周勋甜
康家乐
岑银伟
汪雅静
张帅
张志刚
江涵
宋弘亮
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Ningbo Electric Power Design Institute Co ltd
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Abstract

The invention relates to a method for elastically optimizing a power distribution network comprising a microgrid, which comprises the following steps: step S1, establishing a distribution network load model containing the micro-grid based on the distributed power supply and the grid load; step S2, mapping the elastic branch into the power distribution network, and reconstructing a load model of the power distribution network comprising the micro-grid; normalizing to obtain a single-target optimization function based on a power loss objective function, a voltage stabilization objective function and a branch elastic objective function; and S3, optimizing a single-target optimization function by adopting a discrete quantum particle group algorithm DQPSO based on decimal integer coding, and solving the reconstructed load model of the power distribution network containing the microgrid. Compared with the prior art, the invention meets the elastic optimal operation of the power distribution network system under different load states, and has the advantages of improving the elasticity value of the power distribution network system, reducing the network loss and improving the voltage stability.

Description

Elasticity optimization method for power distribution network containing micro-grid
Technical Field
The invention relates to the field of optimization of a power distribution network of a power system, in particular to an elastic optimization method of a power distribution network comprising a micro-grid.
Background
Along with social development, the demand on energy sources is larger and larger, the contradiction between environmental protection and energy utilization is increased day by day, and more distributed power sources are connected to a power distribution network. These distributed power sources, however, create problems such as power quality. The micro-grid can integrate all distributed power supplies into a power distribution network through a PCC, can realize flexible and efficient application of the distributed power supplies in the power distribution network, and can effectively provide power support for the power distribution network.
The power distribution network is usually designed in a closed loop and operated in an open loop mode, and section switches and a small number of interconnection switches are arranged among nodes in the power distribution network; reconfiguration of the distribution network requires changing the topology of the distribution network by changing the state of the switches. It is desirable to maintain stability of the node voltage and improve reliability by reducing power loss of the network. Since there may be many alternative switch combinations in the power distribution system, power distribution network reconfiguration is a complex combinatorial, irreducible optimization problem.
At present, a lot of researches on static reconstruction of a power distribution network are carried out by many researchers at home and abroad, but the actual load is time-sequential, and the consideration on the load time-sequence is not good.
The genetic algorithm is used as a discrete coding algorithm, can well process the multi-dimensional optimization problem, and is earlier used as an artificial intelligence algorithm to be applied to the feeder line reconstruction of the power distribution network; but the traditional genetic algorithm has the defects of high CPU overhead, complex coding and the like;
the PSO is an intelligent optimization algorithm technology, and has the advantages of easier parameter setting and less time consumption than a genetic algorithm; however, the conventional particle swarm algorithm generally adopts continuous coding, while the power distribution feeder reconstruction is a discrete problem and needs to adopt binary particle swarm coding. However, as the network expands and the dimension of the particle increases, the convergence speed of the particle is reduced, and even the optimal convergence result cannot be obtained.
In order to optimize the reconstruction of the distribution feeder, a distribution network elastic optimization method with high convergence rate needs to be designed, so that a distribution network system can operate elastically and optimally under different load states.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method for flexibly and optimally optimizing a power distribution network with a microgrid, wherein the power distribution network system can flexibly and optimally operate under different load states.
The purpose of the invention can be realized by the following technical scheme:
the invention provides a method for elastically optimizing a power distribution network containing a micro-grid, which comprises the following steps:
step S1, establishing a distribution network load model containing the micro-grid based on the distributed power supply and the grid load;
step S2, mapping the elastic branch into a power distribution network, and reconstructing a load model of the power distribution network containing the micro-grid; normalizing to obtain a single-objective optimization function based on the power loss objective function, the voltage stability objective function and the branch elasticity objective function;
and S3, optimizing the single-objective optimization function by adopting a discrete quantum particle group algorithm DQPSO based on decimal integer coding, and solving the reconstructed load model of the power distribution network containing the microgrid.
Preferably, the distributed power supply in the step S1 includes a fan output and a photovoltaic output; the wind speed which is met by the output of the fan follows the weibull distribution; the photovoltaic output adopts a photovoltaic power generation random model.
Preferably, the modeling process of the fan output is as follows:
Figure BDA0003481797840000021
wherein, P w Is the actual output power of the fan, P wr Rated power for the fan; v. of ci And v co Respectively cutting in wind speed and cutting out wind speed for the fan; v is the actual wind speed, obeys the weibull distribution of two parameters, and the probability density function is as follows:
Figure BDA0003481797840000022
where k and c are the shape parameter and the scale parameter, respectively.
Preferably, the photovoltaic output adopts a photovoltaic power generation random model, and the photovoltaic actual output power P PV Obeying to a Beta distribution, its probability density function is:
Figure BDA0003481797840000023
wherein R is pV Is the photovoltaic maximum output power; Γ (·) is a Γ function; alpha and Beta are Beta distribution shape parameters, are related to the solar irradiance, and take values thereofThe photovoltaic installation position is different.
Preferably, the modeling process of the grid load is as follows:
P L ＝a(t)P NL +(1-a(t))P EV
wherein, P L Is the load at time t; p NL For normal loading, compliance is expected to be μ NL Standard deviation of σ NL Normal distribution of (2); p EV A (t) is a load ratio coefficient;
the load P at time t L The probability density function of (a) is:
Figure BDA0003481797840000031
wherein, mu L,t And σ L,t Respectively is a load P L Expected value and standard deviation of.
Preferably, the charging load P EV A charging load random model is adopted, and the expression is as follows:
Figure BDA0003481797840000032
wherein, mu EV Is the expected value of the charging load; lambda [ alpha ] EV The coefficient of variation of the charging load is characterized by the ratio of the standard deviation to the absolute value of the expected value.
Preferably, in the step S2, the elastic branch is mapped into the power distribution network, and a load model of the power distribution network including the microgrid is reconstructed, specifically: based on the power angle characteristics of the branches, the power distribution network is mapped into an elastic mechanical network, the states of the branches and the nodes are correspondingly and synchronously changed in real time, and network topology optimization is converted into branch elasticity, so that a power distribution network load model containing the micro-grid is reconstructed.
Preferably, the mapping process of the power distribution network to the elastic mechanical network is as follows:
calculating the transmission active power of the branch as follows:
Figure BDA0003481797840000033
wherein, U i 、U j The voltage of a first node i and the voltage of a last node j of the alternating current branch are respectively; x L Is branch reactance, delta ij Is the phase angle difference of the node voltage;
branch transmission active power P L The first order incremental equation of (a) is:
Figure BDA0003481797840000034
coefficient of line elasticity K L The actual power angle characteristic of the branch is embodied, and the expression is as follows:
Figure BDA0003481797840000035
wherein, Δ P L Is active power P L First order increment of, delta ij Phase angle difference delta of node voltage ij First order increments of (d);
the branch elasticity objective function is then:
Figure BDA0003481797840000036
wherein, U i 、U j The voltage of a first node i and the voltage of a last node j of the alternating current branch are respectively delta ij The phase angle difference of two ends of the line is shown, and N is the total number of network nodes; x l Is the branch reactance.
Preferably, in step S2, a single-objective optimization function is obtained through normalization based on the power loss objective function, the voltage stabilization objective function, and the branch elasticity objective function, and the specific process is as follows:
1) establishing a power loss objective function, wherein the expression is as follows:
Figure BDA0003481797840000041
wherein, U i 、P i And Q i The voltage, the active power and the reactive power of the branch with a branch head node i are respectively; n is the number of branches, which is the same as the total number of network nodes; r is i The resistance of the ith branch of the power distribution network; k is a radical of i Is a binary variable, k i 0,1 denotes that switch i is open or closed;
2) establishing a voltage stabilization objective function, wherein the expression is as follows:
U stabl ＝4[(XP j -RQ j ) 2 +(XQ j +RP j )U i 2 ]/U i 4
wherein, U stabl The voltage stability index of the branch is represented by i at the first node and j at the last node; r, X are the resistance and reactance of the branch, respectively; p j 、Q j Respectively the active power and the reactive power flowing into the end node j; u shape i The voltage amplitude of a branch initial node i is obtained; the maximum voltage stability index in all the branches is the voltage stability index of the power distribution network system;
3) the single-objective optimization function obtained by normalization is:
Figure BDA0003481797840000042
wherein f is ploss 、U stabl 、f kl Respectively a power loss objective function, a voltage stability objective function and a branch elasticity objective function, f 1 、f 2 、f 3 Respectively obtaining a power loss value, a voltage stability value and a branch elasticity value of a power distribution network load model containing the micro-grid before reconstruction; lambda [ alpha ] 1 、λ 2 、λ 3 The weighting factors representing power loss, voltage stability and branch elasticity, respectively.
Preferably, in the step S3, the discrete quantum particle group algorithm DQPSO particle position updating expression is:
Figure BDA0003481797840000043
Figure BDA0003481797840000044
Figure BDA0003481797840000045
wherein, X id (t +1) is the d-dimensional position of the t +1 th iteration particle i; mbest (t) is the average optimal position of the ith particle in the population of the t iteration, P id (t) is the current best position of the t-th iteration particle i; m is the number of particles in the population, and D is the particle dimension; p id (t) is the current best position of the t-th iteration particle i, P gd (t) is the global optimum position of the t-th iteration particle i,
Figure BDA0003481797840000051
is the interval [0,1]Random numbers uniformly distributed therein; beta is the coefficient of contraction and u is the interval [0,1 ]]Random numbers, X, distributed uniformly within id (t) is the d-dimensional position of the t-th iteration particle i.
Compared with the prior art, the invention has the following advantages:
1) according to the dynamic reconfiguration optimization method taking the system elasticity optimization as the sub-target, the topological structure of the power distribution network is optimized according to the load, meanwhile, the searching capability of particles is enhanced based on the quantum-behaved particle swarm algorithm, and the corresponding decimal integer coding mode is designed, so that the system can operate elastically and optimally under the condition of different load states, the elasticity value of the original power distribution network system can be effectively improved, the network loss is reduced, and the voltage stability is improved;
2) the power distribution network is mapped into the elastic mechanical network, the power distribution networks reflecting the power angle characteristics are mapped into the elastic mechanical network one by one on the basis of the rule that the active power flow direction of the power grid follows from the generator to the load, and the elasticity of the branch is increased by optimizing the topology of the network;
3) the discrete quantum particle group algorithm DQPSO with stronger global optimization capability is adopted, and the decimal integer code is applied to the quantum particle group algorithm QPSO to perform elastic optimization on the power distribution network, so that the active loss of a power distribution network system is reduced, and the voltage stability is improved;
4) the distributed power supply DGs are integrated by the micro-grid and are connected into the power distribution network through the public coupling point, so that the distributed power supply is flexibly and efficiently applied to the power distribution network, and the power support can be effectively provided for the power distribution network.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a flow chart of a method in an embodiment;
FIG. 3 is a topology structure diagram of a 33-node distribution network;
FIG. 4 is a load graph in the example;
FIG. 5 is a wind power output and photovoltaic output diagram in an embodiment;
FIG. 6 is a comparative graph of the elasticity before and after optimization of a power distribution system including a microgrid in an embodiment;
FIG. 7 is a graph of node voltage simulation results before and after network topology optimization in an embodiment.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, shall fall within the scope of protection of the present invention.
Aiming at the problem of power distribution network reconstruction, the invention comprehensively considers the network loss, the voltage stability and the branch elasticity, converts a multi-objective function into a single-objective optimization function by a normalization method, and adopts a discrete quantum particle swarm algorithm (DQPSO) to solve the problem of feeder reconstruction under different distributed power supplies.
As shown in fig. 1, the method for flexibly optimizing a power distribution network including a microgrid according to the present embodiment includes the following steps:
step S1, establishing a distribution network load model containing the micro-grid based on the distributed power supply and the grid load; the distributed power supply comprises fan output and photovoltaic output;
the fan output modeling process comprises the following steps:
Figure BDA0003481797840000061
wherein, P w For actual output power of the fan, P wr Rated power for the fan; v. of ci And v co Respectively setting a cut-in wind speed and a cut-out wind speed for the fan; v is the actual wind speed, obeys the weibull distribution of two parameters, and the probability density function is as follows:
Figure BDA0003481797840000062
where k and c are the shape parameter and the scale parameter, respectively.
Photovoltaic output adopts a photovoltaic power generation random model, and the actual photovoltaic output power P PV Obeying to a Beta distribution, its probability density function is:
Figure BDA0003481797840000063
wherein R is pV Is the photovoltaic maximum output power; Γ (·) is a Γ function; alpha and Beta are Beta distribution shape parameters, are related to sunlight irradiance, and have values which are different along with different photovoltaic installation positions.
Step S12, the modeling process of the power grid load is as follows:
P L ＝a(t)P NL +(1-a(t))P EV
wherein, P L Is the load at time t; p NL For normal loading, compliance is expected to be μ NL Standard deviation of σ NL Normal distribution of (2); p EV For charging load, a (t) is the duty ratio coefficient；
The load P at time t L The probability density function of (a) is:
Figure BDA0003481797840000071
wherein, mu L,t And σ L,t Respectively is a load P L Expected value and standard deviation of.
The charging load P EV A charging load random model is adopted, and the expression is as follows:
Figure BDA0003481797840000072
wherein, mu EV Desired value, lambda, of the overall charging load for an electric vehicle EV The coefficient of variation of the overall charging load of the electric automobile is characterized by the ratio of the standard deviation to the absolute value of the expected value.
Step S2, mapping the elastic branch into the power distribution network, and reconstructing a load model of the power distribution network comprising the micro-grid; normalizing to obtain a single-target optimization function based on a power loss objective function, a voltage stabilization objective function and a branch elastic objective function;
the elastic branch mapping method is based on mechanical analysis, and the states of the branches and the nodes correspond to each other in real time and change synchronously; mapping the power distribution network into an elastic mechanical network based on the similarity between the power angle characteristic of the branch and the tensile force elongation characteristic of the spring in physics; in order to make the addition of active power and the superposition rule of vector force the same, all branches are regarded as vertical directions in the embodiment, and at this time, the distribution networks reflecting the characteristics of power angles can be mapped into elastic network networks in mechanics one by one, so that the elasticity of the branches is increased by optimizing the topology of the networks.
The mapping process described above is as follows:
1) calculating the transmission active power of the branch as follows:
Figure BDA0003481797840000073
wherein, U i 、U j The voltage of a first node i and the voltage of a last node j of the alternating current branch are respectively; x L Is branch reactance, delta ij Is the phase angle difference of the node voltage;
branch transmission active power P L The first order incremental equation of (a) is:
Figure BDA0003481797840000074
2) coefficient of line elasticity K L The actual power angle characteristic of the branch is embodied, and the expression is as follows:
Figure BDA0003481797840000075
wherein, Δ P L Is active power P L First order increment of, delta ij Phase angle difference delta of node voltage ij First order increments of (d);
3) the maximum branch elasticity objective function is then:
Figure BDA0003481797840000076
wherein, U i 、U j The voltage of a first node i and the voltage of a last node j of the alternating current branch are respectively delta ij The phase angle difference of two ends of the line is shown, and N is the total number of network nodes; x l Is a branch reactance;
in step S2, based on the power loss objective function, the voltage stabilization objective function, and the branch elastic objective function, a single-objective optimization function is obtained through normalization, and the specific process is as follows:
1) establishing a power loss objective function, wherein the expression is as follows:
Figure BDA0003481797840000081
wherein, U i 、P i And Q i The voltage, the active power and the reactive power of the branch with a branch head node i are respectively; n is the number of branches, which is the same as the total number of network nodes; r is i The resistance of the ith branch of the power distribution network; k is a radical of i Being binary variables, k i 0,1 denotes that switch i is open or closed;
2) establishing a voltage stabilization objective function, wherein the expression is as follows:
U stabl ＝4[(XP j -RQ j ) 2 +(XQ j +RP j )U i 2 ]/U i 4
wherein, U stabl The voltage stability index of the branch is represented by i at the first node and j at the last node; r, X are the resistance and reactance of the branch, respectively; p j 、Q j Respectively the active power and the reactive power flowing into the end node j; u shape i The voltage amplitude of a first node i of the branch circuit is;
when the system is broken down, the voltage stability degree of the power distribution network system can be judged according to the distance between the weak branch in the system and the critical value. The maximum voltage stability index in all branches is the voltage stability index of the power distribution network.
3) The single-objective optimization function obtained by normalization is:
Figure BDA0003481797840000082
wherein f is ploss 、U stabl 、f kl Respectively a power loss objective function, a voltage stability objective function and a branch elasticity objective function, f 1 、f 2 、f 3 Respectively obtaining a power loss value, a voltage stability value and a branch elasticity value of a power distribution network load model containing the microgrid before reconstruction; lambda [ alpha ] 1 、λ 2 、λ 3 The weighting factors representing power loss, voltage stability and branch elasticity, respectively, are set to 0.3, 0.3 and 0.4 in this embodiment.
Step S3, as shown in fig. 2, optimizing a single-objective optimization function by using a discrete quantum particle group algorithm DQPSO based on decimal integer coding, and solving a reconstructed load model of the power distribution network including the microgrid, the specific process is as follows:
1) initializing power distribution network parameters, determining the capacity and installation nodes of the micro-grid, and performing integer coding on the ring network;
2) initializing a discrete quantum particle group algorithm, judging the feasibility of a solution, and randomly generating an initial population according to a search space;
3) judging the feasibility of the solution, and calculating the fitness of the feasible solution;
4) and updating the population information until the termination condition is met, and outputting an optimization result.
The expression for updating the positions of the particles in the population information is as follows:
Figure BDA0003481797840000091
Figure BDA0003481797840000092
Figure BDA0003481797840000093
wherein, X id (t +1) is the d-dimensional position of the t +1 th iteration particle i; mbest (t) is the average optimal position of the ith particle in the t iteration population, P id (t) is the current best position of the t-th iteration particle i; m is the number of particles in the population, and D is the particle dimension; p is id (t) is the current best position of the t-th iteration particle i, P gd (t) is the global optimum position of the t-th iteration particle i,
Figure BDA0003481797840000094
is the interval [0,1]Random numbers uniformly distributed in the interior; beta is the coefficient of contraction and u is the interval [0,1 ]]Random numbers, X, distributed uniformly within id (t) is the d-dimensional position of the t-th iteration particle i.
Next, the validity of the method of the present invention is verified by taking a 33-node power distribution network system as an example.
Fig. 3 shows a topological structure diagram of a 33-node power distribution network system, and fig. 4 shows a 12.66kV radial power distribution network system of 33-node buses. The switch comprises 5 interconnection switches and 32 section switches, wherein 1 to 32 are normally closed switches, and 33 to 37 are normally open switches. All tie and section switches are considered as candidates for reconfiguration.
Verification one: in order to verify the performance of the discrete quantum particle group algorithm DQPSO algorithm, the method is compared with a genetic algorithm GA, a particle swarm algorithm PSO and a discrete particle swarm algorithm DPSO in the aspect of feeder line reconstruction.
The algorithm parameters are set as follows: the overall scale is 50, and the maximum iteration number is 1000; for the DPSO, the maximum and minimum values of the weighting values are 0.9 and 0.4, respectively, and the learning factors c1 and c2 are both 2.0. The crossover rate and the variation rate of the genetic algorithm GA were set to 0.8 and 0.15, respectively.
The results are shown in Table 1.
TABLE 1
Figure BDA0003481797840000095
Figure BDA0003481797840000101
The results obtained by the four algorithms are the same for a 33-node power distribution network system without a microgrid. The method adopts a discrete quantum particle group algorithm DQPSO to converge after 16 iterations.
And (5) verifying:
and adding a microgrid into the power distribution network, wherein the distributed power supply parameters of the microgrid are set in the table 2.
TABLE 2
Figure BDA0003481797840000102
The locations of the microgrid grid-tie installations and the capacity of the 33-node power distribution network system are shown in table 3. The microgrid handles PQ nodes (where node active power P and reactive power Q are given). The convergence accuracy is set to 10e-6, the lower limit of each dimension particle is set to 1, and the upper limits are respectively 10,7,15,21 and 11.
TABLE 3
Microgrid numbering Grid-connected node Active power (kW) Power factor
1 3 50 0.8
2 6 100 0.9
3 24 200 0.9
4 29 100 1
Fig. 4 is a load diagram in the example. Fig. 5 is a wind power and photovoltaic force diagram in the embodiment. FIG. 6 is a comparison graph of elasticity before and after optimization of a load system of a power distribution network comprising a microgrid. FIG. 7 is a graph of node voltage simulation results before and after network topology optimization in an embodiment. The reconstruction results and the node voltage amplitudes before and after reconstruction are shown in table 4.
TABLE 4
Figure BDA0003481797840000103
According to simulation results, after the discrete quantum particle swarm algorithm DQPSO is adopted to perform elastic optimization on a power distribution network system containing a microgrid, the active loss of the power supply network system is reduced, and the voltage stability is improved to a certain extent.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications and substitutions can be easily made by those skilled in the art within the technical scope of the invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (10)

1. The method for elastically optimizing the power distribution network comprising the micro-grid is characterized by comprising the following steps of:
step S1, establishing a distribution network load model containing the micro-grid based on the distributed power supply and the grid load;
step S2, mapping the elastic branch into a power distribution network, and reconstructing a load model of the power distribution network containing the micro-grid; normalizing to obtain a single-target optimization function based on a power loss objective function, a voltage stabilization objective function and a branch elastic objective function;
and S3, optimizing a single-target optimization function by adopting a discrete quantum particle group algorithm DQPSO based on decimal integer coding, and solving the reconstructed load model of the power distribution network containing the microgrid.
2. The method for flexibly optimizing the power distribution network including the microgrid of claim 1, wherein the distributed power sources in the step S1 comprise a fan output and a photovoltaic output; the wind speed which is met by the output of the fan follows the weibull distribution; the photovoltaic output adopts a photovoltaic power generation random model.
3. The method for flexibly optimizing the power distribution network comprising the microgrid according to claim 2, wherein the modeling process of the fan output is as follows:
Figure FDA0003481797830000011
wherein, P w For actual output power of the fan, P wr Rated power for the fan; v. of ci And v co Respectively setting a cut-in wind speed and a cut-out wind speed for the fan; v is the actual wind speed, obeys the weibull distribution of two parameters, and the probability density function is as follows:
Figure FDA0003481797830000012
where k and c are the shape parameter and the scale parameter, respectively.
4. The method according to claim 2, wherein the photovoltaic output adopts a photovoltaic power generation stochastic model, and the photovoltaic actual output power P is the photovoltaic actual output power P PV Obeying to a Beta distribution, its probability density function is:
Figure FDA0003481797830000013
wherein R is pV Is the photovoltaic maximum output power; Γ (·) is a Γ function; alpha and Beta are Beta distribution shape parameters, are related to sunlight irradiance, and have values which are different along with different photovoltaic installation positions.
5. The method according to claim 2, wherein the modeling process of the grid load is as follows:
P L ＝a(t)P NL +(1-a(t))P EV
wherein, P L Is the load at time t; p NL For normal loading, compliance is expected to be μ NL Standard deviation of σ NL Normal distribution of (2); p EV A (t) is a load ratio coefficient;
the load P at time t L The probability density function of (a) is:
Figure FDA0003481797830000021
wherein, mu L,t And σ L,t Respectively is a load P L Expected value and standard deviation of.
6. The method for flexibly optimizing the power distribution network comprising the microgrid according to claim 5, characterized in that the charging load P EV A charging load random model is adopted, and the expression is as follows:
Figure FDA0003481797830000022
wherein, mu EV Is the expected value of the charging load; lambda [ alpha ] EV The coefficient of variation of the charging load is characterized by the ratio of the standard deviation to the absolute value of the expected value.
7. The method according to claim 5, wherein in step S2, the elastic branch is mapped into the distribution network, and a load model of the distribution network with the microgrid is reconstructed, specifically: based on the power angle characteristics of the branches, the power distribution network is mapped into an elastic mechanical network, the states of the branches and the nodes are correspondingly and synchronously changed in real time, and network topology optimization is converted into branch elasticity, so that a power distribution network load model containing the micro-grid is reconstructed.
8. The method for elastic optimization of the power distribution network comprising the microgrid according to claim 7, wherein the mapping process of the power distribution network to the elastic mechanical network is as follows:
calculating the transmission active power of the branch as follows:
Figure FDA0003481797830000023
wherein, U i 、U j The voltage of a first node i and the voltage of a last node j of the alternating current branch are respectively; x L Is branch reactance, delta ij Is the phase angle difference of the node voltage;
branch transmission active power P L The first order incremental equation of (a) is:
Figure FDA0003481797830000024
coefficient of line elasticity K L The actual power angle characteristic of the branch is embodied, and the expression is as follows:
Figure FDA0003481797830000031
wherein, Δ P L Is active power P L First order increment of, delta ij Phase angle difference delta of node voltage ij First order increments of (d);
the branch elasticity objective function is then:
Figure FDA0003481797830000032
wherein, U i 、U j The voltage of a first node i and the voltage of a last node j of the alternating current branch are respectively delta ij The phase angle difference of two ends of the line is shown, and N is the total number of network nodes; x l Is the branch reactance.
9. The method according to claim 8, wherein in step S2, based on the power loss objective function, the voltage stabilization objective function, and the branch elasticity objective function, a single objective optimization function is obtained by normalization, and the specific process is as follows:
1) establishing a power loss objective function, wherein the expression is as follows:
Figure FDA0003481797830000033
wherein, U i 、P i And Q i The voltage, the active power and the reactive power of the branch with a branch head node i are respectively; n is the number of branches, which is the same as the total number of network nodes; r is i The resistance of the ith branch of the power distribution network; k is a radical of i Being binary variables, k i 0,1 denotes that switch i is open or closed;
2) establishing a voltage stabilization objective function, wherein the expression is as follows:
U stabl ＝4[(XP j -RQ j ) 2 +(XQ j +RP j )U i 2 ]/U i 4
wherein, U stabl The first node is i, and the last node is j; r, X are the resistance and reactance of the branch, respectively; p j 、Q j Respectively the active power and the reactive power flowing into the end node j; u shape i The voltage amplitude of a first node i of the branch circuit is; the maximum voltage stability index in all the branches is the voltage stability index of the power distribution network system;
3) the single-objective optimization function obtained by normalization is:
Figure FDA0003481797830000034
wherein, f ploss 、U stabl 、f kl Respectively a power loss objective function, a voltage stability objective function and a branch elasticity objective function, f 1 、f 2 、f 3 Respectively obtaining a power loss value, a voltage stability value and a branch elasticity value of a power distribution network load model containing the micro-grid before reconstruction; lambda [ alpha ] 1 、λ 2 、λ 3 The weighting factors representing power loss, voltage stability and branch elasticity, respectively.
10. The elasticity optimization method for the power distribution network including the microgrid according to claim 1, wherein in the step S3, the discrete quantum particle group algorithm DQPSO particle position updating expression is:
Figure FDA0003481797830000041
Figure FDA0003481797830000042
Figure FDA0003481797830000044
wherein, X id (t +1) is the d-dimensional position of the t +1 th iteration particle i; mbest (t) is the average optimal position of the ith particle in the population of the t iteration, P id (t) is the current best position of the t-th iteration particle i; m is the number of particles in the population, and D is the particle dimension; p id (t) is the current best position of the t-th iteration particle i, P gd (t) is the global optimum position of the t-th iteration particle i,
Figure FDA0003481797830000043
is the interval [0,1]Random numbers uniformly distributed therein; beta is the coefficient of contraction and u is the interval [0,1 ]]Random numbers, X, distributed uniformly within id (t) is the d-dimensional position of the t-th iteration particle i.
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