CN112199803A - Cable group loop arrangement optimization method based on cultural gene algorithm - Google Patents

Cable group loop arrangement optimization method based on cultural gene algorithm Download PDF

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CN112199803A
CN112199803A CN202010904357.8A CN202010904357A CN112199803A CN 112199803 A CN112199803 A CN 112199803A CN 202010904357 A CN202010904357 A CN 202010904357A CN 112199803 A CN112199803 A CN 112199803A
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陈泽铭
牛海清
艾嘉伟
颜天佑
唐兴佳
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South China University of Technology SCUT
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Abstract

The invention discloses a cultural genetic algorithm-based cable group loop arrangement optimization method, which comprises the following steps of: s1, establishing a finite element model for coupling simulation of the cable group multi-physical field; s2, calculating the core temperature and the metal sheath induced voltage of each cable in the cable group; s3, establishing a mathematical model of an optimization problem which takes the phase sequence and the horizontal position of each loop cable as optimization variables, takes the induced voltage of the metal sheath not exceeding the standard value as a constraint condition and takes the minimum temperature of the highest core of the cable as an objective function; s4, converting the established finite element model into a function script form by taking the phase sequence and the position as input variables; and S5, optimizing the cable group loop arrangement mode by adopting a cultural gene algorithm. The optimization method has a good optimization effect, and is beneficial to reducing the temperature of the wire cores of the cable group, so that the carrying capacity of the cable group is improved.

Description

Cable group loop arrangement optimization method based on cultural gene algorithm
Technical Field
The invention relates to the technical field of power cables, in particular to a cultural gene algorithm-based cable group loop arrangement optimization method.
Background
In order to save urban land and meet huge electric energy requirements of urban areas, actual cable engineering is usually laid for a multi-loop cluster, the cable cluster may have the conditions of multiple voltage levels, load currents, different segment lengths and the like, and complex electromagnetic association and heat conduction relations exist among cables, so that the optimization of the arrangement mode of the multi-loop cable cluster has certain difficulty. At present, the calculation theory and method about multi-physical-field coupling are basically complete, and the multi-physical-field coupling modeling of complex cabling is already complete by utilizing a numerical calculation method, so that the arrangement mode of cables is urgently needed to be further optimized by combining an intelligent optimization algorithm on the basis, the advantages of cable group cabling are fully exerted, and the economic and safe operation of the cables is ensured.
Disclosure of Invention
The invention aims to solve the defects in the prior art, and provides a method for optimizing the loop arrangement of a cable group based on a cultural genetic algorithm.
The purpose of the invention can be achieved by adopting the following technical scheme:
a method for optimizing the loop arrangement of a cable group based on a cultural genetic algorithm comprises the following steps:
s1, establishing a finite element model of the multi-physical-field coupling simulation of the cable group according to the basic parameters of the cable group and the laying environment thereof;
s2, calculating the temperature of each cable core and the induced voltage of the metal sheath in the cable group based on the finite element model of the multi-physical-field coupling simulation of the cable group;
s3, establishing a mathematical model of an optimization problem which takes the phase sequence and the horizontal position of each loop cable as optimization variables, takes the induced voltage of the metal sheath not exceeding the standard value as a constraint condition and takes the minimum temperature of the highest core of the cable as an objective function;
s4, converting the finite element model of the cable group multi-physics coupling simulation into a function script form by taking the phase sequence and the position as input variables;
and S5, optimizing the phase sequence and the horizontal position of each loop cable by adopting a cultural gene algorithm.
Further, in step S1, a finite element model of two-dimensional magneto-thermal-mechanical multi-physical field coupling simulation is established according to the cable structure and position of the cable group, the surrounding environment condition of the cable group, and parameters thereof.
Further, in step S2, based on the finite element model of the cable group multi-physical field coupling simulation, the temperature field distribution of the cable group and the induced voltage of the metal sheath along the three-phase cable of each loop are calculated, and then the maximum value of the core temperature of the cable group and the maximum value of the induced voltage of the metal sheath are calculated.
Further, in step S3, the mathematical model of the optimization problem is established as follows:
min Tmax(X)
s.t.X＝[a1,a2,...,an,l1,l2,...,ln]
Ush(X)<Ud
l1,l2,...,ln∈Ωl
a1,a2,...,an∈Ωa
in the formula, n is the number of the tunnel cable loops; x is a decision variable vector of the problem, and comprises n sequence variable values and n position variable values; t ismax(X) and Ush(X) the maximum value of the temperature of the cable core and the maximum value of the induced voltage of the metal sheath of the cable which are calculated by the finite element model are respectively related to a decision variable X; u shapedInducing a voltage value for a cable metal sheath allowed in engineering design; lnAnd anPosition variables and phase sequence of the nth loop, respectivelyA variable; omegaaIs the range of phase sequence variables; omegalThe range of locations for the looped cable that are allowed for engineering is related to the length of the cable holder and the overall outer diameter of the cable.
Further, in the step S4, the finite element model of the cable group multi-physics field coupling simulation is converted into a function script form by a software joint simulation method with the phase sequence variable and the position variable as inputs and the maximum value of the cable core temperature, the maximum value of the metal sheath induced voltage and the maximum value of the circulating current as outputs.
Further, the step S5 is as follows:
s51, encoding the phase sequence variables on phase sequence chromosomes in a bit string encoding mode, and encoding the position variables on position chromosomes in a real number encoding mode, so that population individuals are formed by two chromosomes;
s52, initializing the population and setting the interval omegaaAnd ΩlGenerating phase sequence chromosome and position chromosome, and constructing population individual X ═ a1,a2,...,an,l1,l2,...,ln]；
S53, selecting an fitness function for judging the fitness of the chromosome to the target, the jth individual XjHas an adaptation value of fj＝-Tmax(Xj) (ii) a Wherein T ismax(Xj) The maximum value of the temperature of the cable core calculated by the finite element model;
s54, sorting the population according to the size of the adaptive value, intercepting the individual with better adaptive value as the intelligent agent, starting a local search algorithm near the intelligent agent to search the nearby better solution, and realizing the local optimization of the intelligent agent of each generation;
s55, selecting: calculating the adaptive value of each individual and the probability of the adaptive value of each individual to be reserved to filial generations, and randomly selecting the individuals according to the probability to form a filial generation population;
s56, crossing: randomly exchanging part of gene positions of chromosomes of two individuals in the population according to the cross probability to generate a new gene combination;
s57, mutation: randomly selecting variant individuals and variant gene positions according to the variant probability, and generating new individuals by replacing original genes with randomly generated variant genes;
and S58, judging the generated new generation group, outputting the temperature solution with the optimal adaptation value and the corresponding optimal individual if the population evolution algebra reaches the maximum, otherwise updating the population, and returning to the step S53 to perform the iterative calculation of the next generation.
Further, the process of step S54 is as follows:
s541, defining the intelligent agent as an individual with a higher adaptation value in the population, and setting the threshold value of the intelligent agent in the population to be 0.6, namely selecting 40% of the individuals in the population before the adaptation value as the intelligent agent;
s542, calculating Euclidean distances among all agents in the population, and calculating the kth generation population PkMiddle intelligent agent
Figure BDA0002660873050000041
And
Figure BDA0002660873050000042
the calculation formula of Euclidean distance of (1):
Figure BDA0002660873050000043
wherein L is the variable number of the problem space, namely the total length of the chromosome;
Figure BDA0002660873050000044
and
Figure BDA0002660873050000045
are respectively xlUpper and lower bounds of (a);
s543, calculating agent xjSparse distance to all other individuals, the sparse distance defined as agent xjShortest euclidean distance to all other individuals:
Figure BDA0002660873050000046
wherein popsize is population number.
S544, calculating agent xjSparsity of, sparsity ofDegree is defined as normalized to [0,1 ]]Sparse distance of (2):
Figure BDA0002660873050000047
wherein the agentsize is the number of agents;
s545, randomly generating a plurality of offspring agent populations O in the neighborhood search radiuskThe neighborhood search radius of each agent is r _ agentj＝sjXr, progeny population size of popsize _ agentj＝sjXpopsize, where r is the primordial population PkThe search radius of (a);
s546, calculating an intelligent agent population OkAnd mixing with the original population to re-select more excellent individual update population, and keeping the population number before and after local search unchanged, namely Pk＝U(Pk×Ok) Wherein the operator U (P)k×Ok) Is defined as a set PkAnd OkThe union set is sorted according to the adaptive value from large to small, the part with larger adaptive value is intercepted, and the number of the intercepted elements and the set P are keptkThe same;
further, in step S55, a roulette wheel selection strategy is adopted.
Further, in step S56, a single point crossing strategy is applied to both chromosomes, and the selected crossing probability is 0.85.
Further, in step S57, a single point mutation strategy is applied to both chromosomes, and the selected mutation probability is 0.1.
Compared with the prior art, the invention has the following advantages and effects:
(1) the method simulates the running condition of the cable group by using a finite element simulation method, calculates the temperature of the core of the cable, the induced voltage of the metal sheath and the circulating current, and has higher calculation precision compared with an analytic calculation method;
(2) the method converts the established finite element model into a form of a functional script which can be compiled, applies an optimization algorithm to solve the optimized arrangement model of the cable group, and has higher calculation efficiency and optimization effect;
(3) the invention adopts the culture gene algorithm, performs combined optimization on the phase sequence variable and the position variable, and has higher optimization effect compared with the genetic algorithm.
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FIG. 1 is a schematic flow chart of a cable group loop arrangement optimization method based on a cultural genetic algorithm, disclosed by the invention;
FIG. 2 is a schematic diagram of the laying of a cable group according to an embodiment of the present inventioniThe horizontal position variable of the ith loop cable represents the shortest distance value from the ith loop cable to the wall in mm; a isiIs the phase sequence variable of the ith loop cable;
FIG. 3 is a flow chart of a cultural genetic algorithm for joint optimization of cable phase sequence positions in an embodiment of the present invention;
FIG. 4 is a diagram of the convergence of the optimization algorithm in an embodiment of the present invention;
fig. 5 is a diagram of seven-loop tunneling cable sizing in an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, 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 derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Examples
In this embodiment, a cable group laid in a tunnel in the Guangzhou city area is taken as a research object, as shown in fig. 5, which is a schematic flow chart of an optimization method for loop arrangement of a cable group based on a cultural genetic algorithm disclosed by the present invention, and the method includes the following steps:
s1, establishing a tunnel laying cable group multi-physical field coupling model according to the tunnel structure parameters and the cable group parameters;
in step S1, a two-dimensional magneto-thermal-path multi-physical field coupling model is established according to the actual multi-loop tunneling cable group parameters.
S2, calculating the core temperature, the induced voltage of the metal sheath and the circulation value of the tunnel laying cable group based on the tunnel laying cable group multi-physical field coupling model;
in step S2, based on the finite element model of the cable group multi-physical field coupling simulation, the temperature field distribution of the cable group and the induced voltage of the metal sheath along the three-phase cable of each loop are calculated, and further the maximum value of the core temperature of the cable group and the maximum value of the induced voltage of the metal sheath are calculated.
S3, establishing an optimization problem which takes the minimum highest core temperature of the cable group as an objective function, the phase sequence and the horizontal position of each loop cable group as optimization variables and the induced voltage of the metal sheath not exceeding a standard value as a constraint condition;
in step S3, in conjunction with fig. 2, the mathematical model is established as follows:
min Tmax(X)
s.t.X＝[a1,a2,...,an,l1,l2,...,ln]
Ush(X)<Ud
l1,l2,...,ln∈Ωl
a1,a2,...,an∈Ωa
in the formula, n is the number of the tunnel cable loops; x is a decision variable vector of the problem, and comprises n sequence variable values and n position variable values; t ismax(X) and Ush(X) the maximum value of the temperature of the cable core and the maximum value of the induced voltage of the metal sheath of the cable which are calculated by the finite element model are respectively related to a decision variable X; u shapedInducing a voltage value for a cable metal sheath allowed in engineering design; lnAnd anRespectively is a position variable and a phase sequence variable of the nth loop; omegaaIs the range of phase sequence variables; omegalThe range of locations for the looped cable that are allowed for engineering is related to the length of the cable holder and the overall outer diameter of the cable.
S4, converting the established finite element model into a function script form by taking the phase sequence and the position as input variables;
in step S4, the established finite element model is converted into a form of a programmable function script by a software co-simulation method, with the phase sequence and position as input variables and the maximum temperature of the cable core, the maximum value of the induced voltage of the metal sheath, and the maximum value of the circulating current as output variables.
And S5, optimizing the loop arrangement mode of the tunnel cable group by adopting a cultural gene algorithm.
In step S5, the method includes the steps of:
s51, encoding the phase sequence variables on phase sequence chromosomes in a bit string encoding mode, and encoding the position variables on position chromosomes in a real number encoding mode, so that population individuals are formed by two chromosomes;
s52, initializing the population and setting the interval omegaaAnd ΩlGenerating phase sequence chromosome and position chromosome, and constructing population individual X ═ a1,a2,...,an,l1,l2,...,ln]；
S53, selecting an fitness function for judging the fitness of the chromosome to the target, the jth individual XjHas an adaptation value of fj＝-Tmax(Xj) (ii) a Wherein T ismax(Xj) The maximum value of the temperature of the cable core calculated by the finite element model;
and S54, sorting the populations according to the adaptive values, and intercepting the individuals with better adaptive values as the intelligent agents.
Starting a local search algorithm near the agent to search a better solution near the agent, so as to realize local optimization of the agent of each generation;
in this embodiment, the specific process of step S54 is as follows:
s541, defining the intelligent agent as an individual with a higher adaptation value in the population, and setting the threshold value of the intelligent agent in the population to be 0.6, namely selecting 40% of the individuals in the population before the adaptation value as the intelligent agent;
s542, calculating Euclidean distances among all agents in the population, and calculating the kth generation population PkMiddle intelligent agent
Figure BDA0002660873050000081
And
Figure BDA0002660873050000082
the calculation formula of Euclidean distance of (1):
Figure BDA0002660873050000083
wherein L is the variable number of the problem space, namely the total length of the chromosome;
Figure BDA0002660873050000084
and
Figure BDA0002660873050000085
are respectively xlUpper and lower bounds of (a);
s543, calculating agent xjSparse distance to all other individuals, the sparse distance defined as agent xjShortest euclidean distance to all other individuals:
Figure BDA0002660873050000086
wherein popsize is population number.
S544, calculating agent xjSparsity defined as normalized to [0,1 ]]Sparse distance of (2):
Figure BDA0002660873050000087
wherein the agentsize is the number of agents;
s545, randomly generating a plurality of offspring agent populations O in the neighborhood search radiuskThe neighborhood search radius of each agent is r _ agentj＝sjXr, progeny population size of popsize _ agentj＝sjXpopsize, where r is the primordial population PkThe search radius of (a);
s546, calculating an intelligent agent population OkAnd mixing with the original population to re-select more excellent individual update population, and keeping the population number before and after local search unchanged, namely Pk＝U(Pk×Ok) Wherein the operator U (P)k×Ok) Is defined as a setPkAnd OkThe union set is sorted according to the adaptive value from large to small, the part with larger adaptive value is intercepted, and the number of the intercepted elements and the set P are keptkThe same;
s55, selecting: calculating the adaptive value of each individual and the probability of the adaptive value of each individual to be reserved to filial generations, and randomly selecting the individuals according to the probability to form a filial generation population;
in step S55 of the present embodiment, a roulette selection strategy is employed;
s56, crossing: randomly exchanging part of gene positions of chromosomes of two individuals in the population according to the cross probability to generate a new gene combination;
in step S56 of this embodiment, a single-point crossing strategy is adopted for both chromosomes, and the selected crossing probability is 0.85;
s57, mutation: randomly selecting variant individuals and variant gene positions according to the variant probability, and generating new individuals by replacing original genes with randomly generated variant genes;
in step S57, a single point mutation strategy is applied to both chromosomes, and the selected mutation probability is 0.1;
and S58, judging the generated new generation group, outputting the temperature solution with the optimal adaptation value and the corresponding optimal individual if the population evolution algebra reaches the maximum, otherwise updating the population, and returning to the step S53 to perform the iterative calculation of the next generation.
In this embodiment, the convergence condition of the algorithm is shown in fig. 4, compared with the traditional genetic algorithm, in this embodiment, the cultural genetic algorithm has a better optimization effect, the positions and the phase sequence arrangement modes of the tunnel cables before and after optimization are shown in table 1, the optimization result is shown in table 2, the maximum temperature of the cables is reduced by 3.77% after the optimization, the induced voltage of the metal sheath is reduced by 7.94%, the total circulating current loss of the metal sheath is reduced by 15.49%, the average circulating current value is reduced by 3.62%, all indexes are reduced, and the optimization effect is good.
TABLE 1 Cable arrangement before and after optimization
Figure BDA0002660873050000091
Figure BDA0002660873050000101
TABLE 2 Cable parameter Table before and after optimization
Parameter(s) Before optimization After optimization Percentage reduction
Maximum core temperature/. degree.C 90.36 86.952 3.77％
Maximum value of induced voltage/V 64.2 59.1 7.94％
Total circulation loss/(W/m) 267.76 226.273 15.49％
Mean circulating current value/A 110.71 106.71 3.62％
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (10)

1. A method for optimizing the loop arrangement of a cable group based on a cultural genetic algorithm is characterized by comprising the following steps:
s1, establishing a finite element model of the multi-physical-field coupling simulation of the cable group according to the basic parameters of the cable group and the laying environment thereof;
s2, calculating the temperature of each cable core and the induced voltage of the metal sheath in the cable group based on the finite element model of the multi-physical-field coupling simulation of the cable group;
s3, establishing a mathematical model of an optimization problem which takes the phase sequence and the horizontal position of each loop cable as optimization variables, takes the induced voltage of the metal sheath not exceeding the standard value as a constraint condition and takes the minimum temperature of the highest core of the cable as an objective function;
s4, converting the finite element model of the cable group multi-physics coupling simulation into a function script form by taking the phase sequence and the position as input variables;
and S5, optimizing the phase sequence and the horizontal position of each loop cable by adopting a cultural gene algorithm.
2. The method as claimed in claim 1, wherein in step S1, a finite element model of two-dimensional magneto-thermal-mechanical coupling simulation is established according to the cable structure and position of the cable group, the surrounding environment condition of the cable group and its parameters.
3. The method as claimed in claim 1, wherein in step S2, based on the finite element model of the cable group multi-physical field coupling simulation, the temperature field distribution of the cable group and the induced voltage of the metal sheath along the three-phase cables of each loop are calculated, and then the maximum value of the core temperature of the cable group and the maximum value of the induced voltage of the metal sheath are calculated.
4. The method for optimizing the loop layout of a cable cluster based on a cultural genetic algorithm as recited in claim 1, wherein the mathematical model of the optimization problem established in step S3 is as follows:
min Tmax(X)
s.t.X＝[a1,a2,...,an,l1,l2,...,ln]
Ush(X)<Ud
l1,l2,...,ln∈Ωl
a1,a2,...,an∈Ωa
in the formula, n is the number of the tunnel cable loops; x is a decision variable vector of the problem, and comprises n sequence variable values and n position variable values; t ismax(X) and Ush(X) the maximum value of the temperature of the cable core and the maximum value of the induced voltage of the metal sheath of the cable which are calculated by the finite element model are respectively related to a decision variable X; u shapedInducing a voltage value for a cable metal sheath allowed in engineering design; lnAnd anRespectively is a position variable and a phase sequence variable of the nth loop; omegaaIs the range of phase sequence variables; omegalThe range of locations for the looped cable that are allowed for engineering is related to the length of the cable holder and the overall outer diameter of the cable.
5. The method as claimed in claim 1, wherein in step S4, the finite element model of the multi-physics coupling simulation of the cable group is converted into a function script form by a software co-simulation method with the phase sequence variable and the position variable as inputs and the maximum temperature of the cable core, the maximum induced voltage of the metal sheath and the maximum circulating current as outputs.
6. The method for optimizing the loop layout of a cable cluster based on a cultural genetic algorithm as recited in claim 1, wherein the step S5 comprises the steps of:
s51, encoding the phase sequence variables on phase sequence chromosomes in a bit string encoding mode, and encoding the position variables on position chromosomes in a real number encoding mode, so that population individuals are formed by two chromosomes;
s52, initializing the population and setting the interval omegaaAnd ΩlGenerating phase sequence chromosome and position chromosome, and constructing population individual X ═ a1,a2,...,an,l1,l2,...,ln]；
S53, selecting an fitness function for judging the fitness of the chromosome to the target, the jth individual XjHas an adaptation value of fj＝-Tmax(Xj) Wherein T ismax(Xj) Calculating the maximum value of the temperature of the cable core by using a finite element model;
s54, sorting the population according to the size of the adaptive value, intercepting the individual with better adaptive value as the intelligent agent, starting a local search algorithm near the intelligent agent to search the nearby better solution, and realizing the local optimization of the intelligent agent of each generation;
s55, selecting: calculating the adaptive value of each individual and the probability of the adaptive value of each individual to be reserved to filial generations, and randomly selecting the individuals according to the probability to form a filial generation population;
s56, crossing: randomly exchanging part of gene positions of chromosomes of two individuals in the population according to the cross probability to generate a new gene combination;
s57, mutation: randomly selecting variant individuals and variant gene positions according to the variant probability, and generating new individuals by replacing original genes with randomly generated variant genes;
and S58, judging the generated new generation group, outputting the temperature solution with the optimal adaptation value and the corresponding optimal individual if the population evolution algebra reaches the maximum, otherwise updating the population, and returning to the step S53 to perform the iterative calculation of the next generation.
7. The method for optimizing the loop layout of a cable cluster based on a cultural genetic algorithm as recited in claim 6, wherein the step S54 comprises the following steps:
s541, defining the individuals with higher fitness values in the population as the intelligent agents, and setting the threshold value of the intelligent agents in the population to be 0.6, namely selecting the individuals 40% before the fitness values in the population as the intelligent agents;
s542, calculating Euclidean distances among all agents in the population, and calculating the kth generation population PkMiddle intelligent agent
Figure FDA0002660873040000031
And
Figure FDA0002660873040000032
the calculation formula of Euclidean distance of (1):
Figure FDA0002660873040000033
wherein L is the variable number of the problem space, namely the total length of the chromosome;
Figure FDA0002660873040000034
and
Figure FDA0002660873040000035
are respectively xlUpper and lower bounds of (a);
s543, calculating agent xjSparse distance to all other individuals, the sparse distance defined as agent xjShortest euclidean distance to all other individuals:
Figure FDA0002660873040000036
wherein popsize is the population number;
s544, calculating agent xjSparsity defined as normalized to [0,1 ]]Sparse distance of (2):
Figure FDA0002660873040000041
wherein the agentsize is the number of agents;
s545, randomly generating a plurality of offspring agent populations O in the neighborhood search radiuskThe neighborhood search radius of each agent is r _ agentj＝sjXr, progeny population size of popsize _ agentj＝sjXpopsize, where r is the primordial population PkThe search radius of (a);
s546, calculating an intelligent agent population OkAnd mixing with the original population to re-select more excellent individual update population, and keeping the population number before and after local search unchanged, namely Pk＝U(Pk×Ok) Wherein the operator U (P)k×Ok) Is defined as a set PkAnd OkThe union set is sorted according to the adaptive value from large to small, the part with larger adaptive value is intercepted, and the number of the intercepted elements and the set P are keptkThe same is true.
8. The method for optimizing the circuit layout of a cable cluster based on cultural genetic algorithm as recited in claim 6, wherein the roulette selection strategy is adopted in step S55.
9. The method as claimed in claim 6, wherein in step S56, a single point crossing strategy is applied to both chromosomes, and the crossing probability is 0.85.
10. The method as claimed in claim 6, wherein in step S57, a single point mutation strategy is applied to both chromosomes, and the probability of mutation is 0.1.
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