# Design on Universal Circuit Breaker via Improved Gray Wolf Optimization Algorithm

Authors: Shuidong Dai; Kewen Xia; Lili Shi; Min Xie
Journal: Mathematical Problems in Engineering
 (2020)

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## Abstract

Miniaturization design of the universal circuit breaker is very necessary, but it is not enough to consider only the miniaturization in the design but also consider the energy consumption and breaking capacity of the universal circuit breaker. To this end, a comprehensive optimization design method in this paper is proposed and studied. Firstly, based on the analysis of the universal circuit breaker miniaturization model, combines with the universal circuit breaker’s low energy consumption model and high-segmentation model, a comprehensive optimization model for designing universal circuit breakers is constructed. Secondly, for the comprehensive model solution, an improved gray wolf optimization (GWO) algorithm is proposed, that is, a “cloud model” is introduced to balance the local search and global search capabilities to improve the convergence speed; also, a weight strategy is introduced to avoid falling into the local minimum, and simulations of typical test functions show that the improved algorithm is superior to other algorithms. Finally, the improved gray wolf optimization algorithm is applied to the comprehensive optimization design of universal circuit breakers. The experimental results show that the proposed comprehensive design method is feasible and improves the design accuracy and efficiency of the universal circuit breaker.


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## Body

## 1. Introduction

Under the new trend of rapid development of new energy and smart grids, the scale of the power supply and distribution market continues to expand, which requires higher and higher reliability and operation of power grid [1]. As common switchgear, universal circuit breakers are used to connect and disconnect current to protect electrical equipment and distribution lines from overcurrent damage and undervoltage damage due to short circuits [2]. With the increase of daily power consumption, the optimization requirements for universal circuit breakers are very strict to ensure the safe operation of the power grid [3]. Among them, the optimization of universal circuit breakers is mainly reflected in energy saving, high breaking, miniaturization, and communication [4, 5].In order to solve the problem of the large volume of the universal circuit breaker, the research on the miniaturization of the universal circuit breaker is very necessary. The miniaturization of the universal circuit breaker is mainly to study the contact system of the universal circuit breaker. The contact system is mainly used to break the fault circuit and connect the short-circuit current [6]. When the contact system starts to work, it will generate a large electric repulsive force. That is, it requires a very large contact pressure [7]. This, therefore, makes it difficult to meet the requirements of miniaturization. To meet the design requirements of miniaturization, it is necessary to optimize the design of contact springs and energy storage and improve the arc extinguishing chamber.If we only study the miniaturization of the universal circuit breaker, there will still be some problems. Therefore, when we study the miniaturization, we should also analyze the energy consumption and breaking capacity of the universal circuit breaker. In terms of low energy consumption of universal circuit breakers, one is to save energy and materials and the other is to protect the environment with low carbon. When the universal circuit breaker is in a normal working state, the loss of electrical energy is related to many factors: the number and resistance of contact resistances, phase-offset cosine, copper loss, and so on [8]. In the universal circuit breaker high breaking, the requirements of the universal circuit breaker breaking ability is strong, that is, the limit-breaking current of the universal circuit breaker is large. When there is a short circuit in the circuit, the current is too large. At this time, the universal circuit breaker protection circuit is required, otherwise it will cause a fire, the loss of people’s life and property, among which the rapid disconnection of the arc between the dynamic and static contacts is the key to improve the breaking capacity. It can be said that the shorter the arc stagnation time after the dynamic and static contacts are separated, the higher the breaking capacity [9]. Therefore, when we design the universal circuit breaker, three factors should be considered: miniaturization, low energy consumption, and high breaking. Comprehensive optimization of the universal circuit breaker will not only solve the problem of large volume and high energy consumption but also make the breaking capacity higher.In recent years, with the development of electrical characteristic simulation and digital design, the extensive application of the intelligent information processing algorithm has replaced the traditional design methods of experience and trial algorithm design. This has effectively improved the efficiency of engineering design [10–12]. For example, the particle-based Euclidean distance, improved particle swarm optimization (PSO) algorithm [13] for optimal design of permanent magnet synchronous motors, and improved fuzzy performance reliability algorithm in dynamic systems (PPR) had been employed [14].The APSO algorithm is an improved adaptive particle swarm optimization algorithm [15], which searches for particles following the optimal particles in the solution space and solves the shortcomings of slow convergence speed and easily to fall into the local optimum of the basic PSO algorithm. The cultural differential evolution algorithm (CDE) [16] combined the cultural algorithm and the differential evolution algorithm to solve the traditional differential evolution algorithm's slow convergence rate and easy to fall into the local minimum problem. Artificial bee colony algorithm (ABC) is a heuristic search technology based on swarm intelligence, which can mimic the foraging behavior of bees. Due to its advantages of few control parameters and strong global search ability, it is widely used in many fields, such as training neural networks [17], data clustering [18], business travel problems [19], and engineering optimization [20].The GWO algorithm [21] is a new algorithm proposed by Mirjalili et al. In 2004, its performance is superior to other algorithms [22]. However, the GWO algorithm has many defects. To solve these problems, Teng et al. [23] combined the PSO algorithm with the GWO algorithm and proposed a hybrid wolf optimization algorithm based on particle swarm optimization(PSO_GWO); they introduced the idea of particle swarm optimization algorithm into the GWO algorithm, and the individual optimal value and the population optimal value were combined to update the position information of the gray wolf individuals in order to retain the optimal position of the gray wolf individuals.In addition, the “cloud model” was proposed by Liu et al. [24], and it is mainly used to describe the conversion model between qualitative concepts and quantitative representations. This model can improve the convergence speed of optimization algorithms [25]. Using a weighting strategy and linear weighting can balance the relationship between global search ability and local search ability [26, 27].In summary, if the normal “cloud model” and weighting strategy are introduced into the GWO algorithm, the shortcomings of the basic GWO algorithm can be solved. The improved GWO algorithm is used to comprehensively optimize the design of the universal circuit breaker, which can enhance the performance of the GWO algorithm and improve the design efficiency of the universal circuit breaker. Therefore, studying the comprehensive design of universal circuit breakers based on intelligent optimization algorithms has important theoretical significance and practical value.


## 2. Universal Circuit Breaker Optimization Model

### 2.1. Universal Circuit Breaker Miniaturization Optimization Model

#### 2.1.1. Analysis of Universal Circuit Breaker Miniaturization

Under the normal working conditions of the universal circuit breaker, if the mass and volume of the energy storage spring can be minimized, the design goal of miniaturization of the universal circuit breaker can be achieved.The energy storage spring is located in the operating mechanism of the universal circuit breaker. The structure of the cylindrical coil spring is shown in Figure1.Figure 1
Structure of a cylindrical coil spring, whereH is the length of the spring, d is the spring wire diameter, D is the spring middle diameter, and t is the pitch of the spring.The volume of the spring wires is as follows:(1)Vs=π4nd2L,where n is the spring coil number and L is the expansion length of the spring wires.The mass formula of the springs is(2)M=π4ρ1d2L,where ρ1 is the spring density.The volume of the springs is(3)V=π4D2H.According to the design requirements of the universal circuit breakers, there are some relationships:(4)L=πn+2D,H=540d4D2+1.5d.The design of spring needs to combine the corresponding constraints, including stiffness constraints, strength constraints, and fatigue strength constraints. According to the different external forces and functions of the spring, the spring structure is designed reasonably with the constraint conditions:(1)
The constraint formula of the spring stiffness condition is(5)λmax=8PC3nGd=8PD3nGd4≥λmin,whereλmax is the maximum deformation of the spring, λmin is the minimum deformation of the spring, G is the shear modulus of the spring wire, and C is the aspect ratio of the spring.(2)
The static strength conditional constraint formula is(6)τmax=8KPmaxDπd3≤τ,whereτmax is the maximum shear strength, Pmax is the maximum working load, and K is the spring curvature coefficient.The spring curvature coefficient can be obtained by the spring winding ratio:(7)K=4C−14C−1+0.615C,C=Dd.(3)
The fatigue strength conditional constraint formula is(8)nca=τ0+0.75τminτmax≥nF,wherenca is the calculation safety factor, nF is the design safety factor, τ0 is the pulsating cyclic fatigue limit of the steel wires, and τmin is the minimum shear force in the springs.(4)
In order to avoid resonance phenomena during spring operation, it is necessary to construct an inequality relationship between the operating frequency of the spring and the frequency of external load changes, so the formula for the constraint condition of no resonance is(9)f=3.65×105dnD2≥10fr,wheref is the natural frequency of the spring, fr is the frequency of external load changes, and n is the effective number of turns.(5)
In order to maintain the stability of the spring during operation, it is necessary to limit the length-to-diameter ratio according to different working conditions of the spring. The stability condition constraint formula is(10)b=n−0.5d+1.1λmaxD.When both ends of the spring are fixed,b is required to be 5.3 or less; when one end is fixed and the other end is free to expand and contract, b is required to be 3.7 or less; when both ends of the spring are free to expand and contract, b is required to be 2.6 or less.(6)
The coil of the springs is constrained by theC:(11)4≤C=Dd≤9.


#### 2.1.2. Miniature Universal Circuit Breaker Model Construction

Because the switching force required for the universal circuit breakers is larger, two nested springs are used to provide the closing force. The density of carbon steel wires and spring wires isρ1=7.8×103kg/m3, the shear elastic modulus of springs is g=8×104MPa, and the diameters of outer and inner layers of spring wires are d1 and d2, respectively. The numbers of effective rings are n1 and n2, respectively. The middle diameters are D1 and D2, respectively.The diameters of the springs, the numbers of effective rings, and the middle diameters are set as independent variables, that is,(12)x=d1,n1,D1,d2,n2,D2T=x1,x2,x3,x4,x5,x6T.The corresponding objective function can be established according to the mass and volume formula:(13)fx=ω1Mx+ω2Vx.From the above formula,(14)Mx=1.92×10−5x12x2+2x3+x42x5+2x6,Vx=423.9×x14+x44+1.18×x1x32+x4x62,where M(x) is the total mass of inner and outer springs, V(x) is the total volume of inner and outer springs, and ω1 and ω2 are the weight coefficients of mass and volume, respectively. Through experimental analysis, when ω1 = ω2 = 0.5, the mass and volume of the contact spring obtained are the smallest.


### 2.2. Low Energy Consumption and High-Breaking Optimization Model of Universal Circuit Breaker

#### 2.2.1. Low Energy Consumption Optimization Model for Universal Circuit Breakers

During the entire power transmission process of the low-voltage power distribution system, about 30 to 40% of the power is consumed. The function of transformers, motors, and main universal circuit breakers is also the main reason for energy consumption. In order to reduce power consumption, it is necessary to select the appropriate number and capacity of transformers according to the actual situation of the power load to ensure that it is in a low energy consumption area. In the process of power supply, it can reduce the energy consumption by providing appropriate supply voltage and increasing the power of the low-voltage distribution system accordingly.The calculation of the internal power consumption of the universal circuit breaker by the International Electrotechnical Standard is as follows [28]:(15)W=∑k=1k=pIn2Zcosφ,where p is the number of phases, k is the number of stages, In is the rated current (A) of the universal circuit breaker, Z=R+X, and cosφ is the phase deviation angle of the internal circuit.Since the effect of impedance is negligible, formula (15) can be simplified to(16)W=∑k=1k=pIn2Rcosφ,where the single-contact resistance calculation formula is(17)R=ρ2lS,where ρ2 is the resistivity. Generally, when the length l is constant, using a plurality of copper braids with a cross-sectional area to increase the cross-sectional area S, the resistance value R will decrease. The number of contacts is now t. When the number of contacts is greater than l, the total impedance is(18)1Z=∑i=2t1Ri=∑i=2t1R.When the amount of consumables for a single contact isv, the generalized objective function of the energy consumption of the universal circuit breaker can be established as(19)f1=∑k=1pIn2cosφ1∑i=2t1/R+r1klntv+r2k∑i=2t1R,where r1 and r2 are punishment factors, and the general value ranges from 0.02 to 0.2.


#### 2.2.2. Universal Circuit Breaker High-Breaking Optimization Model

Due to the action of the contact spring, the contact surface will undergo a certain deformation during the process of pressing the moving and static contacts. The resulting contact with the metal is achieved between a few scattered points. So, under microconditions, current flows through electrical contact. In order to facilitate the study, we consider the macroconditions, assuming that these scattered points are a plane, which results in the phenomenon of current contraction and concentration. This phenomenon causes the horizontal component of the current between the dynamic and static contacts to form an electromotive force [29, 30]. The force is called the Holm force and can be expressed as(20)FH=μ0i24πlnR1r,where i is the current passing through the contact, μ0 is the vacuum permeability, the value is 4π×10−7, R1 is the contact radius, and r is the contact point radius.The contact point radius is determined by factors such as contact pressure and contact material and can be expressed as(21)r=Fkπ⋅ξ⋅H,where Fk is the contact pressure, ξ is the contact coefficient and ranges from 0.3 to 0.6, and H is the Brinell hardness of the contact material, for example, the Brinell hardness of the silver material is 900 N/mm2.When the contact system is in the closed state, in addition to the Holm force caused by the current contraction, the electric repulsive force received by the dynamic and static contacts also has the Lorentz force generated by the conductive circuit of the contact.In order to facilitate analysis and research, the Lorentz force on the conductive circuit of the contact is regarded as the electromotive force between two finite parallel conductors, which can be approximately expressed as [31](22)FL=μ04πki2,where k is the loop coefficient.The loop coefficientk is related to the shape and length of the conductor and is inversely proportional to the distance between two finite parallel conductors. For two parallel finite-length linear conductors l1 and l2, the length of the parallel guide rod is L, the distance between the conductors is m, and the current flowing through the conductor is i. At this time, the loop coefficient k can be expressed as(23)k=2Lm.Substituting formula (23) into formula (22), the Lorentz force can be expressed as(24)FL=μ04π2Lmi2.Combining formulas (22) and (24), we can construct a mathematical model for the high breaking of a universal circuit breaker and find the maximum value of the electric force. In theory, it is the minimum value of the reciprocal of the electric force. Therefore, the following mathematical model is obtained:(25)f2=1β1μ0i2/4πlnR1/r+β2μ0/4π2L/mi2,where β1andβ2 are internal parameters of the universal circuit breaker, β1+β2=1, i is the current, R1 is the contact radius, and ξ is the contact coefficient.


### 2.3. Construction of Comprehensive Optimization Model for Universal Circuit Breaker

In the optimization design of the universal circuit breaker, we should not only consider the miniaturization of the universal circuit breaker but also consider the energy consumption and breaking capacity of the universal circuit breaker. Therefore, on the basis of the universal circuit breaker miniaturization model, we combined the universal circuit breaker’s low energy consumption model and high-segmentation model to construct a comprehensive optimization model for designing universal circuit breakers. The minimum mass and volume of the spring can be used as the optimization target.According to formulas (13), (19), and (25), and combining the relationships between them, we can get the overall optimization objective function as(26)f=ε1∑k=1pIn2cosφ1∑i=2t1/R+r1klntv+r2k∑i=2t1R+ε21β1μ0i2/4πlnR1/r+β2μ0/4π2L/mi2+ε3w114ρ1π2d2n+2D+w2πD22H,where ε1,ε2,andε3 are nonnegative weight coefficients in the objective function and ε1+ε2+ε3=1.In the comprehensive optimization design, for the three weight coefficients, an empirical method or a grid method can be used to select appropriate parameters.As can be seen from the objective function formula (26), this comprehensive model fully considers the factors that affect the low energy consumption of the universal circuit breaker, the factors that affect the breaking capacity, the factors that affect the miniaturization of the contact spring, and the energy consumption, breaking capacity, and miniaturization. The design parameters mainly include decreasing penalty factor, contact resistance value, number of contacts, amount of consumables, phase deviation angle of internal circuit, contact radius, contact coefficient, current, spring diameter, and effective number of spring turns.Because the constructed universal circuit breaker comprehensive model is a complex function, commonly used mathematical methods are difficult to solve it. For this reason, an intelligent optimization algorithm can be used to iteratively optimize it to find the optimal solution.


## 2.1. Universal Circuit Breaker Miniaturization Optimization Model

### 2.1.1. Analysis of Universal Circuit Breaker Miniaturization

Under the normal working conditions of the universal circuit breaker, if the mass and volume of the energy storage spring can be minimized, the design goal of miniaturization of the universal circuit breaker can be achieved.The energy storage spring is located in the operating mechanism of the universal circuit breaker. The structure of the cylindrical coil spring is shown in Figure1.Figure 1
Structure of a cylindrical coil spring, whereH is the length of the spring, d is the spring wire diameter, D is the spring middle diameter, and t is the pitch of the spring.The volume of the spring wires is as follows:(1)Vs=π4nd2L,where n is the spring coil number and L is the expansion length of the spring wires.The mass formula of the springs is(2)M=π4ρ1d2L,where ρ1 is the spring density.The volume of the springs is(3)V=π4D2H.According to the design requirements of the universal circuit breakers, there are some relationships:(4)L=πn+2D,H=540d4D2+1.5d.The design of spring needs to combine the corresponding constraints, including stiffness constraints, strength constraints, and fatigue strength constraints. According to the different external forces and functions of the spring, the spring structure is designed reasonably with the constraint conditions:(1)
The constraint formula of the spring stiffness condition is(5)λmax=8PC3nGd=8PD3nGd4≥λmin,whereλmax is the maximum deformation of the spring, λmin is the minimum deformation of the spring, G is the shear modulus of the spring wire, and C is the aspect ratio of the spring.(2)
The static strength conditional constraint formula is(6)τmax=8KPmaxDπd3≤τ,whereτmax is the maximum shear strength, Pmax is the maximum working load, and K is the spring curvature coefficient.The spring curvature coefficient can be obtained by the spring winding ratio:(7)K=4C−14C−1+0.615C,C=Dd.(3)
The fatigue strength conditional constraint formula is(8)nca=τ0+0.75τminτmax≥nF,wherenca is the calculation safety factor, nF is the design safety factor, τ0 is the pulsating cyclic fatigue limit of the steel wires, and τmin is the minimum shear force in the springs.(4)
In order to avoid resonance phenomena during spring operation, it is necessary to construct an inequality relationship between the operating frequency of the spring and the frequency of external load changes, so the formula for the constraint condition of no resonance is(9)f=3.65×105dnD2≥10fr,wheref is the natural frequency of the spring, fr is the frequency of external load changes, and n is the effective number of turns.(5)
In order to maintain the stability of the spring during operation, it is necessary to limit the length-to-diameter ratio according to different working conditions of the spring. The stability condition constraint formula is(10)b=n−0.5d+1.1λmaxD.When both ends of the spring are fixed,b is required to be 5.3 or less; when one end is fixed and the other end is free to expand and contract, b is required to be 3.7 or less; when both ends of the spring are free to expand and contract, b is required to be 2.6 or less.(6)
The coil of the springs is constrained by theC:(11)4≤C=Dd≤9.


### 2.1.2. Miniature Universal Circuit Breaker Model Construction

Because the switching force required for the universal circuit breakers is larger, two nested springs are used to provide the closing force. The density of carbon steel wires and spring wires isρ1=7.8×103kg/m3, the shear elastic modulus of springs is g=8×104MPa, and the diameters of outer and inner layers of spring wires are d1 and d2, respectively. The numbers of effective rings are n1 and n2, respectively. The middle diameters are D1 and D2, respectively.The diameters of the springs, the numbers of effective rings, and the middle diameters are set as independent variables, that is,(12)x=d1,n1,D1,d2,n2,D2T=x1,x2,x3,x4,x5,x6T.The corresponding objective function can be established according to the mass and volume formula:(13)fx=ω1Mx+ω2Vx.From the above formula,(14)Mx=1.92×10−5x12x2+2x3+x42x5+2x6,Vx=423.9×x14+x44+1.18×x1x32+x4x62,where M(x) is the total mass of inner and outer springs, V(x) is the total volume of inner and outer springs, and ω1 and ω2 are the weight coefficients of mass and volume, respectively. Through experimental analysis, when ω1 = ω2 = 0.5, the mass and volume of the contact spring obtained are the smallest.


## 2.1.1. Analysis of Universal Circuit Breaker Miniaturization

Under the normal working conditions of the universal circuit breaker, if the mass and volume of the energy storage spring can be minimized, the design goal of miniaturization of the universal circuit breaker can be achieved.The energy storage spring is located in the operating mechanism of the universal circuit breaker. The structure of the cylindrical coil spring is shown in Figure1.Figure 1
Structure of a cylindrical coil spring, whereH is the length of the spring, d is the spring wire diameter, D is the spring middle diameter, and t is the pitch of the spring.The volume of the spring wires is as follows:(1)Vs=π4nd2L,where n is the spring coil number and L is the expansion length of the spring wires.The mass formula of the springs is(2)M=π4ρ1d2L,where ρ1 is the spring density.The volume of the springs is(3)V=π4D2H.According to the design requirements of the universal circuit breakers, there are some relationships:(4)L=πn+2D,H=540d4D2+1.5d.The design of spring needs to combine the corresponding constraints, including stiffness constraints, strength constraints, and fatigue strength constraints. According to the different external forces and functions of the spring, the spring structure is designed reasonably with the constraint conditions:(1)
The constraint formula of the spring stiffness condition is(5)λmax=8PC3nGd=8PD3nGd4≥λmin,whereλmax is the maximum deformation of the spring, λmin is the minimum deformation of the spring, G is the shear modulus of the spring wire, and C is the aspect ratio of the spring.(2)
The static strength conditional constraint formula is(6)τmax=8KPmaxDπd3≤τ,whereτmax is the maximum shear strength, Pmax is the maximum working load, and K is the spring curvature coefficient.The spring curvature coefficient can be obtained by the spring winding ratio:(7)K=4C−14C−1+0.615C,C=Dd.(3)
The fatigue strength conditional constraint formula is(8)nca=τ0+0.75τminτmax≥nF,wherenca is the calculation safety factor, nF is the design safety factor, τ0 is the pulsating cyclic fatigue limit of the steel wires, and τmin is the minimum shear force in the springs.(4)
In order to avoid resonance phenomena during spring operation, it is necessary to construct an inequality relationship between the operating frequency of the spring and the frequency of external load changes, so the formula for the constraint condition of no resonance is(9)f=3.65×105dnD2≥10fr,wheref is the natural frequency of the spring, fr is the frequency of external load changes, and n is the effective number of turns.(5)
In order to maintain the stability of the spring during operation, it is necessary to limit the length-to-diameter ratio according to different working conditions of the spring. The stability condition constraint formula is(10)b=n−0.5d+1.1λmaxD.When both ends of the spring are fixed,b is required to be 5.3 or less; when one end is fixed and the other end is free to expand and contract, b is required to be 3.7 or less; when both ends of the spring are free to expand and contract, b is required to be 2.6 or less.(6)
The coil of the springs is constrained by theC:(11)4≤C=Dd≤9.


## 2.1.2. Miniature Universal Circuit Breaker Model Construction

Because the switching force required for the universal circuit breakers is larger, two nested springs are used to provide the closing force. The density of carbon steel wires and spring wires isρ1=7.8×103kg/m3, the shear elastic modulus of springs is g=8×104MPa, and the diameters of outer and inner layers of spring wires are d1 and d2, respectively. The numbers of effective rings are n1 and n2, respectively. The middle diameters are D1 and D2, respectively.The diameters of the springs, the numbers of effective rings, and the middle diameters are set as independent variables, that is,(12)x=d1,n1,D1,d2,n2,D2T=x1,x2,x3,x4,x5,x6T.The corresponding objective function can be established according to the mass and volume formula:(13)fx=ω1Mx+ω2Vx.From the above formula,(14)Mx=1.92×10−5x12x2+2x3+x42x5+2x6,Vx=423.9×x14+x44+1.18×x1x32+x4x62,where M(x) is the total mass of inner and outer springs, V(x) is the total volume of inner and outer springs, and ω1 and ω2 are the weight coefficients of mass and volume, respectively. Through experimental analysis, when ω1 = ω2 = 0.5, the mass and volume of the contact spring obtained are the smallest.


## 2.2. Low Energy Consumption and High-Breaking Optimization Model of Universal Circuit Breaker

### 2.2.1. Low Energy Consumption Optimization Model for Universal Circuit Breakers

During the entire power transmission process of the low-voltage power distribution system, about 30 to 40% of the power is consumed. The function of transformers, motors, and main universal circuit breakers is also the main reason for energy consumption. In order to reduce power consumption, it is necessary to select the appropriate number and capacity of transformers according to the actual situation of the power load to ensure that it is in a low energy consumption area. In the process of power supply, it can reduce the energy consumption by providing appropriate supply voltage and increasing the power of the low-voltage distribution system accordingly.The calculation of the internal power consumption of the universal circuit breaker by the International Electrotechnical Standard is as follows [28]:(15)W=∑k=1k=pIn2Zcosφ,where p is the number of phases, k is the number of stages, In is the rated current (A) of the universal circuit breaker, Z=R+X, and cosφ is the phase deviation angle of the internal circuit.Since the effect of impedance is negligible, formula (15) can be simplified to(16)W=∑k=1k=pIn2Rcosφ,where the single-contact resistance calculation formula is(17)R=ρ2lS,where ρ2 is the resistivity. Generally, when the length l is constant, using a plurality of copper braids with a cross-sectional area to increase the cross-sectional area S, the resistance value R will decrease. The number of contacts is now t. When the number of contacts is greater than l, the total impedance is(18)1Z=∑i=2t1Ri=∑i=2t1R.When the amount of consumables for a single contact isv, the generalized objective function of the energy consumption of the universal circuit breaker can be established as(19)f1=∑k=1pIn2cosφ1∑i=2t1/R+r1klntv+r2k∑i=2t1R,where r1 and r2 are punishment factors, and the general value ranges from 0.02 to 0.2.


### 2.2.2. Universal Circuit Breaker High-Breaking Optimization Model

Due to the action of the contact spring, the contact surface will undergo a certain deformation during the process of pressing the moving and static contacts. The resulting contact with the metal is achieved between a few scattered points. So, under microconditions, current flows through electrical contact. In order to facilitate the study, we consider the macroconditions, assuming that these scattered points are a plane, which results in the phenomenon of current contraction and concentration. This phenomenon causes the horizontal component of the current between the dynamic and static contacts to form an electromotive force [29, 30]. The force is called the Holm force and can be expressed as(20)FH=μ0i24πlnR1r,where i is the current passing through the contact, μ0 is the vacuum permeability, the value is 4π×10−7, R1 is the contact radius, and r is the contact point radius.The contact point radius is determined by factors such as contact pressure and contact material and can be expressed as(21)r=Fkπ⋅ξ⋅H,where Fk is the contact pressure, ξ is the contact coefficient and ranges from 0.3 to 0.6, and H is the Brinell hardness of the contact material, for example, the Brinell hardness of the silver material is 900 N/mm2.When the contact system is in the closed state, in addition to the Holm force caused by the current contraction, the electric repulsive force received by the dynamic and static contacts also has the Lorentz force generated by the conductive circuit of the contact.In order to facilitate analysis and research, the Lorentz force on the conductive circuit of the contact is regarded as the electromotive force between two finite parallel conductors, which can be approximately expressed as [31](22)FL=μ04πki2,where k is the loop coefficient.The loop coefficientk is related to the shape and length of the conductor and is inversely proportional to the distance between two finite parallel conductors. For two parallel finite-length linear conductors l1 and l2, the length of the parallel guide rod is L, the distance between the conductors is m, and the current flowing through the conductor is i. At this time, the loop coefficient k can be expressed as(23)k=2Lm.Substituting formula (23) into formula (22), the Lorentz force can be expressed as(24)FL=μ04π2Lmi2.Combining formulas (22) and (24), we can construct a mathematical model for the high breaking of a universal circuit breaker and find the maximum value of the electric force. In theory, it is the minimum value of the reciprocal of the electric force. Therefore, the following mathematical model is obtained:(25)f2=1β1μ0i2/4πlnR1/r+β2μ0/4π2L/mi2,where β1andβ2 are internal parameters of the universal circuit breaker, β1+β2=1, i is the current, R1 is the contact radius, and ξ is the contact coefficient.


## 2.2.1. Low Energy Consumption Optimization Model for Universal Circuit Breakers

During the entire power transmission process of the low-voltage power distribution system, about 30 to 40% of the power is consumed. The function of transformers, motors, and main universal circuit breakers is also the main reason for energy consumption. In order to reduce power consumption, it is necessary to select the appropriate number and capacity of transformers according to the actual situation of the power load to ensure that it is in a low energy consumption area. In the process of power supply, it can reduce the energy consumption by providing appropriate supply voltage and increasing the power of the low-voltage distribution system accordingly.The calculation of the internal power consumption of the universal circuit breaker by the International Electrotechnical Standard is as follows [28]:(15)W=∑k=1k=pIn2Zcosφ,where p is the number of phases, k is the number of stages, In is the rated current (A) of the universal circuit breaker, Z=R+X, and cosφ is the phase deviation angle of the internal circuit.Since the effect of impedance is negligible, formula (15) can be simplified to(16)W=∑k=1k=pIn2Rcosφ,where the single-contact resistance calculation formula is(17)R=ρ2lS,where ρ2 is the resistivity. Generally, when the length l is constant, using a plurality of copper braids with a cross-sectional area to increase the cross-sectional area S, the resistance value R will decrease. The number of contacts is now t. When the number of contacts is greater than l, the total impedance is(18)1Z=∑i=2t1Ri=∑i=2t1R.When the amount of consumables for a single contact isv, the generalized objective function of the energy consumption of the universal circuit breaker can be established as(19)f1=∑k=1pIn2cosφ1∑i=2t1/R+r1klntv+r2k∑i=2t1R,where r1 and r2 are punishment factors, and the general value ranges from 0.02 to 0.2.


## 2.2.2. Universal Circuit Breaker High-Breaking Optimization Model

Due to the action of the contact spring, the contact surface will undergo a certain deformation during the process of pressing the moving and static contacts. The resulting contact with the metal is achieved between a few scattered points. So, under microconditions, current flows through electrical contact. In order to facilitate the study, we consider the macroconditions, assuming that these scattered points are a plane, which results in the phenomenon of current contraction and concentration. This phenomenon causes the horizontal component of the current between the dynamic and static contacts to form an electromotive force [29, 30]. The force is called the Holm force and can be expressed as(20)FH=μ0i24πlnR1r,where i is the current passing through the contact, μ0 is the vacuum permeability, the value is 4π×10−7, R1 is the contact radius, and r is the contact point radius.The contact point radius is determined by factors such as contact pressure and contact material and can be expressed as(21)r=Fkπ⋅ξ⋅H,where Fk is the contact pressure, ξ is the contact coefficient and ranges from 0.3 to 0.6, and H is the Brinell hardness of the contact material, for example, the Brinell hardness of the silver material is 900 N/mm2.When the contact system is in the closed state, in addition to the Holm force caused by the current contraction, the electric repulsive force received by the dynamic and static contacts also has the Lorentz force generated by the conductive circuit of the contact.In order to facilitate analysis and research, the Lorentz force on the conductive circuit of the contact is regarded as the electromotive force between two finite parallel conductors, which can be approximately expressed as [31](22)FL=μ04πki2,where k is the loop coefficient.The loop coefficientk is related to the shape and length of the conductor and is inversely proportional to the distance between two finite parallel conductors. For two parallel finite-length linear conductors l1 and l2, the length of the parallel guide rod is L, the distance between the conductors is m, and the current flowing through the conductor is i. At this time, the loop coefficient k can be expressed as(23)k=2Lm.Substituting formula (23) into formula (22), the Lorentz force can be expressed as(24)FL=μ04π2Lmi2.Combining formulas (22) and (24), we can construct a mathematical model for the high breaking of a universal circuit breaker and find the maximum value of the electric force. In theory, it is the minimum value of the reciprocal of the electric force. Therefore, the following mathematical model is obtained:(25)f2=1β1μ0i2/4πlnR1/r+β2μ0/4π2L/mi2,where β1andβ2 are internal parameters of the universal circuit breaker, β1+β2=1, i is the current, R1 is the contact radius, and ξ is the contact coefficient.


## 2.3. Construction of Comprehensive Optimization Model for Universal Circuit Breaker

In the optimization design of the universal circuit breaker, we should not only consider the miniaturization of the universal circuit breaker but also consider the energy consumption and breaking capacity of the universal circuit breaker. Therefore, on the basis of the universal circuit breaker miniaturization model, we combined the universal circuit breaker’s low energy consumption model and high-segmentation model to construct a comprehensive optimization model for designing universal circuit breakers. The minimum mass and volume of the spring can be used as the optimization target.According to formulas (13), (19), and (25), and combining the relationships between them, we can get the overall optimization objective function as(26)f=ε1∑k=1pIn2cosφ1∑i=2t1/R+r1klntv+r2k∑i=2t1R+ε21β1μ0i2/4πlnR1/r+β2μ0/4π2L/mi2+ε3w114ρ1π2d2n+2D+w2πD22H,where ε1,ε2,andε3 are nonnegative weight coefficients in the objective function and ε1+ε2+ε3=1.In the comprehensive optimization design, for the three weight coefficients, an empirical method or a grid method can be used to select appropriate parameters.As can be seen from the objective function formula (26), this comprehensive model fully considers the factors that affect the low energy consumption of the universal circuit breaker, the factors that affect the breaking capacity, the factors that affect the miniaturization of the contact spring, and the energy consumption, breaking capacity, and miniaturization. The design parameters mainly include decreasing penalty factor, contact resistance value, number of contacts, amount of consumables, phase deviation angle of internal circuit, contact radius, contact coefficient, current, spring diameter, and effective number of spring turns.Because the constructed universal circuit breaker comprehensive model is a complex function, commonly used mathematical methods are difficult to solve it. For this reason, an intelligent optimization algorithm can be used to iteratively optimize it to find the optimal solution.


## 3. Intelligent Optimization Algorithm Design

### 3.1. Basic Gray Wolf Optimization Algorithm

Wolves belong to a fairly intelligent group of animals in nature. They are mainly gregarious. They hunt and kill prey by tracking, hunting, encircling, and finally attacking the target. Generally speaking, the gray wolf population is 5 to 12 as a whole. They live together and hunt together.The hierarchical mechanism of the population in the gray wolf optimization algorithm is very strict, as shown in Figure2.Figure 2
Schematic diagram of the gray wolf hierarchy.In Figure2, the head wolf at the top of the pyramid is called α. Its main function is to make decisions about hunting behavior, habitat, and food distribution. It is not necessarily the best wolf, but it is the best leader. The wolf on the second level of the pyramid is called β. If α is missing from the wolf pack, then β is the successor and helps to make a decision. At the third level of the pyramid is δ, which listens to the instructions of α and β and is mainly responsible for reconnaissance and alerting. Among them, α and β, which are less adaptable, will be reduced to δ. The wolf pack at the bottom of the pyramid is called ω, which is mainly responsible for balancing the internal relationships of the population and obeying other wolf packs. This strict hierarchical mechanism can make the gray wolf hunt the prey more efficiently [32].According to the gray wolf's hierarchy, we can think thatα represents the optimal solution, β represents the superior solution, δ represents the suboptimal solution, and ω is the candidate solution set, which is converted into a mathematical model. The updated formula can be obtained as(27)D=C⋅Xpt−Xt,Xt+1=Xpt−A⋅D,where D is the distance between the gray wolf and the prey, C is the coefficient, Xp is the position of the prey, t is the number of iterations, X is the position of the gray wolf individual, and A is the coefficient.The relationship between the coefficientsA and C can be obtained from the following formula:(28)A=2a⋅r1−a,(29)C=2r2,where r1 and r2 represent random numbers on [0, 1] and a is the convergence factor.As the number of iterations increases,a will linearly decrease from 2 to 0; the closer a is to 2, the stronger the global search ability, to avoid falling into a local optimal solution; the closer a is to 0, the stronger the local search ability, which will accelerate convergence.In formula (28), when A>1 , the gray wolf population expands the search range and can search for better prey, which is a global search. When A<1, the gray wolf population’s enclosing circle shrinks and belongs to local search.When the gray wolf determines the position of the prey and surrounds the target, it is generally led by the head wolf, that is, the optimal solutionα, and the position of the prey by the optimal solution β and the suboptimal solution δ, and then the position information of the wolf group is updated. The update formula is as follows:(30)Dα=C1Xα−Xt,Dβ=C2Xβ−Xt,Dδ=C3Xδ−Xt,where Xα is the current position of α, Xβ is the current position of β, Xδ is the current position of δ, C1, C2, and C3 represent random vectors, and X(t) represents the current position of the gray wolf.The definition of the length and direction of theω wolf's advance towards α, β, and δ wolves is(31)X1=Xα−A1⋅Dα,X2=Xβ−A2⋅Dβ,X3=Xδ−A3⋅Dδ.The final position where gray wolfω can be obtained is(32)Xt+1=X1+X2+X33.


### 3.2. Improved Gray Wolf Optimization Algorithm

Due to the shortcomings of the gray wolf optimization algorithm, such as slow convergence speed, low solution accuracy, and easily to fall into local minimum, we propose to improve the GWO algorithm.Aiming at the shortcoming of GWO algorithm, the cloud model is introduced adjusting the size of the convergence factora according to the fitness of the gray wolf individual. The main role of a is to balance the local search and global search capabilities and avoid falling into the local optimal solution.The adjustment strategy ofA can be based on the idea of golden section. In the k-th iteration, n gray wolf individuals in the gray wolf population are sorted from small to large according to the fitness value, and then the fitness value of the gray wolf population is defined. The golden section is(33)fgoldenk=ffloor0.618∗nk.At this time, the gold fitness ofn1 gray wolf individuals with fitness greater than fgoldenk is fbetterk=ffloor0.618∗n1k and the gold fitness of n2 gray wolf individuals with fitness less than a is fworsek=ffloor0.618∗n2k. According to the two dividing lines fbetterk and fworsek, the gray wolf divided into 3 subgroups. If the fitness value m of the current gray wolf individual i is greater than n, it means that some gray wolf individuals are close to the optimal solution, which accelerates the local convergence speed. It is not necessary to perform a global search. At this time, a=0. If the fitness fik of the gray wolf individual i is less than fworsek, the global search capability is enhanced and a=2. If fworsek<fik<fbetterk, the convergence factor a now is as follows:(34)a=2−2×e−fik−EX2/2En′2,where EX is the expected value, En is the entropy value, and He is the super entropy value. The expressions are as follows:(35)EX=fbestk,En=fbetterk−fbestkb2,He=Enb2,where b1=b2=2 and En′=normrndEn,He.During the iterative process, theω wolf is approaching the three wolves α, β, and δ, and it is easy to fall into a local minimum. Therefore, formula (32) is linearly weighted, that is, a weighting strategy is introduced to avoid falling into local minima:(36)Xt+1=w1X1+w2X2+w3X33.Here,(37)w1=X1X1+X2+X3,w2=X2X1+X2+X3,w3=X3X1+X2+X3.After introducing the cloud model and weight strategy, the improved GWO algorithm is named cloud model-weight GWO algorithm (CW-GWO).The specific implementation steps of the CW-GWO algorithm are as follows:Step 1: initialize the population. Set the relevant parameter values, the number of populations, the maximum number of iterations, and so on.Step 2: calculate the gray wolf’s individual fitness and record the first three values of individual fitness, and the positions areXα, Xβ, and Xδ.Step 3: calculate the distances of other individuals in the wolf pack toXα, Xβ, and Xδ and update the positions of the wolf pack individuals according to formula (36)Step 4: update the value of the convergence factora and other parameter values using the principle of the cloud model.Step 5: find the fitness values of all individuals, compare them with the values during the last iteration, select the best three positions as the next generation to continue searching, and check whether it has reached the end of the algorithm. If the maximum number of iterations is reached, stop the calculation and output the optimal position; if not, continue from Step 2.


### 3.3. Performance Test and Analysis of CW-GWO Algorithm

To verify the feasibility and effectiveness of the algorithm, classic test functions are used. To avoid accidents, four different types of classic test functions were selected for the analysis of the CW-GWO algorithm. Test function expressions are shown in Table1 So, for experimental. environment: a Windows 10 system, processor model Intel (R) Core (TM) i5-5200U, main frequency 2.20GHZ, memory 4.0 GB, MATLAB R2015b, was usedIn MATLAB software, the parameters are set as follows: the dimension D to 2 and the number of populations to 50, and the experiment is repeated 20 times to obtain the average value of the optimal value.Table 1
Classic test function.
Function nameExpressionSearch intervalThe optimal valueSpheref1x=∑i=1Dxi2[−100, 100]0Schwefel2.22f2x=∑i=1Dxi−∏i=1Dxi[−100, 100]0Rosenbrockf4x=∑i=1D100⋅xi+1−xi22+xi−12[−2.048, 2.048]0Schafferf7x=0.5+sin2∑i=1Dxi2−0.5/1.0+0.001∑i=1Dxi22[−100, 100]0


#### 3.3.1. Sphere Function

Under the same initial conditions, the global optimal value is searched by the APSO algorithm, ABC algorithm, CDE algorithm, and CW-GWO algorithm, and its iterative curve is shown in Figure3.Figure 3
Iterative simulation diagram of sphere function optimization.As can be seen from Figure3, after introducing the “cloud model” and weighting strategy, the improved CW-GWO algorithm has the highest solution accuracy, 100 iterations, reaching 4.292e − 103; it will not fall into the local optimal solution, and other algorithms cannot obtain the highest accuracy.


#### 3.3.2. Schwefel2.22 Function

Under the same initial conditions, the global optimal value is searched by the APSO algorithm, ABC algorithm, CDE algorithm, and CW-GWO algorithm, and its iterative curve is shown in Figure4.Figure 4
Schwefel2.22 function optimization iterative simulation diagram.As can be seen from Figure4, the improved CW-GWO algorithm achieves a solution accuracy of 0.01 during 8 iterations, but it is still iterating, reaching the highest accuracy at the 99th iteration, with a solution accuracy of 2.301e − 51 and a solution accuracy ratio. Other algorithms are higher.


#### 3.3.3. Rosenbrock Function

Under the same initial conditions, the global optimal value is searched by the APSO algorithm, ABC algorithm, CDE algorithm, and CW-GWO algorithm, and its iterative curve is shown in Figure5.Figure 5
Iterative simulation diagram of Rosenbrock function optimization.For the Rosenbrock function, if the dimension is 2 or 3 dimensions, it represents a unimodal function, and if it is more than 3 dimensions, it represents a multimodal function. It can be seen from Figure5 that the CW-GWO algorithm has better performance and the highest accuracy, reaching 2.624e − 05.


#### 3.3.4. Schaffer Function

Under the same initial conditions, the global optimal value is searched by the APSO algorithm, ABC algorithm, CDE algorithm, and CW-GWO algorithm, and its iterative curve is shown in Figure6.Figure 6
Schaffer function optimization iterative simulation graph.For the Schaffer multimodal function, when the 16th iteration is reached, the global optimal value obtained by the CW-GWO algorithm is 0, and its solution accuracy is the highest compared with other algorithms.Because the minimum value of these test functions is all 0, the minimum value of the test result is equal to the error. The test results of each algorithm are shown in Table2.Table 2
Comparison of test function simulation results.
Function nameAlgorithmNumber of iterationsNumber of iterations at optimal valueRunning time (s)Minimum valueFall into local optimumThe most accurateSphereCW-GWO1001000.08874.292e − 103YCDE100990.16437.271e − 18ABC100950.27870.01962YAPSO1001000.13293.765e − 11Schwefel2.22CW-GWO100990.10232.301e − 51YCDE100990.22811.06e − 8ABC100830.36210.3716YAPSO1001000.15371.549e − 05RosenbrockCW-GWO1001000.10272.624e − 105YCDE100990.18578.386e − 16ABC100940.32200.03416YAPSO1001000.14956.897e − 09SchafferCW-GWO100160.10820YYCDE100990.14851.821e − 15ABC100850.26330.00012APSO1001000.14315.3e − 14Through the above classic functional simulation tests, the proposed CW-GWO algorithm is reliable, and its accuracy and speed are better than those of several other algorithms.


## 3.1. Basic Gray Wolf Optimization Algorithm

Wolves belong to a fairly intelligent group of animals in nature. They are mainly gregarious. They hunt and kill prey by tracking, hunting, encircling, and finally attacking the target. Generally speaking, the gray wolf population is 5 to 12 as a whole. They live together and hunt together.The hierarchical mechanism of the population in the gray wolf optimization algorithm is very strict, as shown in Figure2.Figure 2
Schematic diagram of the gray wolf hierarchy.In Figure2, the head wolf at the top of the pyramid is called α. Its main function is to make decisions about hunting behavior, habitat, and food distribution. It is not necessarily the best wolf, but it is the best leader. The wolf on the second level of the pyramid is called β. If α is missing from the wolf pack, then β is the successor and helps to make a decision. At the third level of the pyramid is δ, which listens to the instructions of α and β and is mainly responsible for reconnaissance and alerting. Among them, α and β, which are less adaptable, will be reduced to δ. The wolf pack at the bottom of the pyramid is called ω, which is mainly responsible for balancing the internal relationships of the population and obeying other wolf packs. This strict hierarchical mechanism can make the gray wolf hunt the prey more efficiently [32].According to the gray wolf's hierarchy, we can think thatα represents the optimal solution, β represents the superior solution, δ represents the suboptimal solution, and ω is the candidate solution set, which is converted into a mathematical model. The updated formula can be obtained as(27)D=C⋅Xpt−Xt,Xt+1=Xpt−A⋅D,where D is the distance between the gray wolf and the prey, C is the coefficient, Xp is the position of the prey, t is the number of iterations, X is the position of the gray wolf individual, and A is the coefficient.The relationship between the coefficientsA and C can be obtained from the following formula:(28)A=2a⋅r1−a,(29)C=2r2,where r1 and r2 represent random numbers on [0, 1] and a is the convergence factor.As the number of iterations increases,a will linearly decrease from 2 to 0; the closer a is to 2, the stronger the global search ability, to avoid falling into a local optimal solution; the closer a is to 0, the stronger the local search ability, which will accelerate convergence.In formula (28), when A>1 , the gray wolf population expands the search range and can search for better prey, which is a global search. When A<1, the gray wolf population’s enclosing circle shrinks and belongs to local search.When the gray wolf determines the position of the prey and surrounds the target, it is generally led by the head wolf, that is, the optimal solutionα, and the position of the prey by the optimal solution β and the suboptimal solution δ, and then the position information of the wolf group is updated. The update formula is as follows:(30)Dα=C1Xα−Xt,Dβ=C2Xβ−Xt,Dδ=C3Xδ−Xt,where Xα is the current position of α, Xβ is the current position of β, Xδ is the current position of δ, C1, C2, and C3 represent random vectors, and X(t) represents the current position of the gray wolf.The definition of the length and direction of theω wolf's advance towards α, β, and δ wolves is(31)X1=Xα−A1⋅Dα,X2=Xβ−A2⋅Dβ,X3=Xδ−A3⋅Dδ.The final position where gray wolfω can be obtained is(32)Xt+1=X1+X2+X33.


## 3.2. Improved Gray Wolf Optimization Algorithm

Due to the shortcomings of the gray wolf optimization algorithm, such as slow convergence speed, low solution accuracy, and easily to fall into local minimum, we propose to improve the GWO algorithm.Aiming at the shortcoming of GWO algorithm, the cloud model is introduced adjusting the size of the convergence factora according to the fitness of the gray wolf individual. The main role of a is to balance the local search and global search capabilities and avoid falling into the local optimal solution.The adjustment strategy ofA can be based on the idea of golden section. In the k-th iteration, n gray wolf individuals in the gray wolf population are sorted from small to large according to the fitness value, and then the fitness value of the gray wolf population is defined. The golden section is(33)fgoldenk=ffloor0.618∗nk.At this time, the gold fitness ofn1 gray wolf individuals with fitness greater than fgoldenk is fbetterk=ffloor0.618∗n1k and the gold fitness of n2 gray wolf individuals with fitness less than a is fworsek=ffloor0.618∗n2k. According to the two dividing lines fbetterk and fworsek, the gray wolf divided into 3 subgroups. If the fitness value m of the current gray wolf individual i is greater than n, it means that some gray wolf individuals are close to the optimal solution, which accelerates the local convergence speed. It is not necessary to perform a global search. At this time, a=0. If the fitness fik of the gray wolf individual i is less than fworsek, the global search capability is enhanced and a=2. If fworsek<fik<fbetterk, the convergence factor a now is as follows:(34)a=2−2×e−fik−EX2/2En′2,where EX is the expected value, En is the entropy value, and He is the super entropy value. The expressions are as follows:(35)EX=fbestk,En=fbetterk−fbestkb2,He=Enb2,where b1=b2=2 and En′=normrndEn,He.During the iterative process, theω wolf is approaching the three wolves α, β, and δ, and it is easy to fall into a local minimum. Therefore, formula (32) is linearly weighted, that is, a weighting strategy is introduced to avoid falling into local minima:(36)Xt+1=w1X1+w2X2+w3X33.Here,(37)w1=X1X1+X2+X3,w2=X2X1+X2+X3,w3=X3X1+X2+X3.After introducing the cloud model and weight strategy, the improved GWO algorithm is named cloud model-weight GWO algorithm (CW-GWO).The specific implementation steps of the CW-GWO algorithm are as follows:Step 1: initialize the population. Set the relevant parameter values, the number of populations, the maximum number of iterations, and so on.Step 2: calculate the gray wolf’s individual fitness and record the first three values of individual fitness, and the positions areXα, Xβ, and Xδ.Step 3: calculate the distances of other individuals in the wolf pack toXα, Xβ, and Xδ and update the positions of the wolf pack individuals according to formula (36)Step 4: update the value of the convergence factora and other parameter values using the principle of the cloud model.Step 5: find the fitness values of all individuals, compare them with the values during the last iteration, select the best three positions as the next generation to continue searching, and check whether it has reached the end of the algorithm. If the maximum number of iterations is reached, stop the calculation and output the optimal position; if not, continue from Step 2.


## 3.3. Performance Test and Analysis of CW-GWO Algorithm

To verify the feasibility and effectiveness of the algorithm, classic test functions are used. To avoid accidents, four different types of classic test functions were selected for the analysis of the CW-GWO algorithm. Test function expressions are shown in Table1 So, for experimental. environment: a Windows 10 system, processor model Intel (R) Core (TM) i5-5200U, main frequency 2.20GHZ, memory 4.0 GB, MATLAB R2015b, was usedIn MATLAB software, the parameters are set as follows: the dimension D to 2 and the number of populations to 50, and the experiment is repeated 20 times to obtain the average value of the optimal value.Table 1
Classic test function.
Function nameExpressionSearch intervalThe optimal valueSpheref1x=∑i=1Dxi2[−100, 100]0Schwefel2.22f2x=∑i=1Dxi−∏i=1Dxi[−100, 100]0Rosenbrockf4x=∑i=1D100⋅xi+1−xi22+xi−12[−2.048, 2.048]0Schafferf7x=0.5+sin2∑i=1Dxi2−0.5/1.0+0.001∑i=1Dxi22[−100, 100]0


### 3.3.1. Sphere Function

Under the same initial conditions, the global optimal value is searched by the APSO algorithm, ABC algorithm, CDE algorithm, and CW-GWO algorithm, and its iterative curve is shown in Figure3.Figure 3
Iterative simulation diagram of sphere function optimization.As can be seen from Figure3, after introducing the “cloud model” and weighting strategy, the improved CW-GWO algorithm has the highest solution accuracy, 100 iterations, reaching 4.292e − 103; it will not fall into the local optimal solution, and other algorithms cannot obtain the highest accuracy.


### 3.3.2. Schwefel2.22 Function

Under the same initial conditions, the global optimal value is searched by the APSO algorithm, ABC algorithm, CDE algorithm, and CW-GWO algorithm, and its iterative curve is shown in Figure4.Figure 4
Schwefel2.22 function optimization iterative simulation diagram.As can be seen from Figure4, the improved CW-GWO algorithm achieves a solution accuracy of 0.01 during 8 iterations, but it is still iterating, reaching the highest accuracy at the 99th iteration, with a solution accuracy of 2.301e − 51 and a solution accuracy ratio. Other algorithms are higher.


### 3.3.3. Rosenbrock Function

Under the same initial conditions, the global optimal value is searched by the APSO algorithm, ABC algorithm, CDE algorithm, and CW-GWO algorithm, and its iterative curve is shown in Figure5.Figure 5
Iterative simulation diagram of Rosenbrock function optimization.For the Rosenbrock function, if the dimension is 2 or 3 dimensions, it represents a unimodal function, and if it is more than 3 dimensions, it represents a multimodal function. It can be seen from Figure5 that the CW-GWO algorithm has better performance and the highest accuracy, reaching 2.624e − 05.


### 3.3.4. Schaffer Function

Under the same initial conditions, the global optimal value is searched by the APSO algorithm, ABC algorithm, CDE algorithm, and CW-GWO algorithm, and its iterative curve is shown in Figure6.Figure 6
Schaffer function optimization iterative simulation graph.For the Schaffer multimodal function, when the 16th iteration is reached, the global optimal value obtained by the CW-GWO algorithm is 0, and its solution accuracy is the highest compared with other algorithms.Because the minimum value of these test functions is all 0, the minimum value of the test result is equal to the error. The test results of each algorithm are shown in Table2.Table 2
Comparison of test function simulation results.
Function nameAlgorithmNumber of iterationsNumber of iterations at optimal valueRunning time (s)Minimum valueFall into local optimumThe most accurateSphereCW-GWO1001000.08874.292e − 103YCDE100990.16437.271e − 18ABC100950.27870.01962YAPSO1001000.13293.765e − 11Schwefel2.22CW-GWO100990.10232.301e − 51YCDE100990.22811.06e − 8ABC100830.36210.3716YAPSO1001000.15371.549e − 05RosenbrockCW-GWO1001000.10272.624e − 105YCDE100990.18578.386e − 16ABC100940.32200.03416YAPSO1001000.14956.897e − 09SchafferCW-GWO100160.10820YYCDE100990.14851.821e − 15ABC100850.26330.00012APSO1001000.14315.3e − 14Through the above classic functional simulation tests, the proposed CW-GWO algorithm is reliable, and its accuracy and speed are better than those of several other algorithms.


## 3.3.1. Sphere Function

Under the same initial conditions, the global optimal value is searched by the APSO algorithm, ABC algorithm, CDE algorithm, and CW-GWO algorithm, and its iterative curve is shown in Figure3.Figure 3
Iterative simulation diagram of sphere function optimization.As can be seen from Figure3, after introducing the “cloud model” and weighting strategy, the improved CW-GWO algorithm has the highest solution accuracy, 100 iterations, reaching 4.292e − 103; it will not fall into the local optimal solution, and other algorithms cannot obtain the highest accuracy.


## 3.3.2. Schwefel2.22 Function

Under the same initial conditions, the global optimal value is searched by the APSO algorithm, ABC algorithm, CDE algorithm, and CW-GWO algorithm, and its iterative curve is shown in Figure4.Figure 4
Schwefel2.22 function optimization iterative simulation diagram.As can be seen from Figure4, the improved CW-GWO algorithm achieves a solution accuracy of 0.01 during 8 iterations, but it is still iterating, reaching the highest accuracy at the 99th iteration, with a solution accuracy of 2.301e − 51 and a solution accuracy ratio. Other algorithms are higher.


## 3.3.3. Rosenbrock Function

Under the same initial conditions, the global optimal value is searched by the APSO algorithm, ABC algorithm, CDE algorithm, and CW-GWO algorithm, and its iterative curve is shown in Figure5.Figure 5
Iterative simulation diagram of Rosenbrock function optimization.For the Rosenbrock function, if the dimension is 2 or 3 dimensions, it represents a unimodal function, and if it is more than 3 dimensions, it represents a multimodal function. It can be seen from Figure5 that the CW-GWO algorithm has better performance and the highest accuracy, reaching 2.624e − 05.


## 3.3.4. Schaffer Function

Under the same initial conditions, the global optimal value is searched by the APSO algorithm, ABC algorithm, CDE algorithm, and CW-GWO algorithm, and its iterative curve is shown in Figure6.Figure 6
Schaffer function optimization iterative simulation graph.For the Schaffer multimodal function, when the 16th iteration is reached, the global optimal value obtained by the CW-GWO algorithm is 0, and its solution accuracy is the highest compared with other algorithms.Because the minimum value of these test functions is all 0, the minimum value of the test result is equal to the error. The test results of each algorithm are shown in Table2.Table 2
Comparison of test function simulation results.
Function nameAlgorithmNumber of iterationsNumber of iterations at optimal valueRunning time (s)Minimum valueFall into local optimumThe most accurateSphereCW-GWO1001000.08874.292e − 103YCDE100990.16437.271e − 18ABC100950.27870.01962YAPSO1001000.13293.765e − 11Schwefel2.22CW-GWO100990.10232.301e − 51YCDE100990.22811.06e − 8ABC100830.36210.3716YAPSO1001000.15371.549e − 05RosenbrockCW-GWO1001000.10272.624e − 105YCDE100990.18578.386e − 16ABC100940.32200.03416YAPSO1001000.14956.897e − 09SchafferCW-GWO100160.10820YYCDE100990.14851.821e − 15ABC100850.26330.00012APSO1001000.14315.3e − 14Through the above classic functional simulation tests, the proposed CW-GWO algorithm is reliable, and its accuracy and speed are better than those of several other algorithms.


## 4. Comprehensive Optimization Design of Universal Circuit Breaker

### 4.1. Comprehensive Optimization Design Steps of Universal Circuit Breaker

The comprehensive optimization design steps of the universal circuit breaker based on the intelligent optimization algorithm are as follows:Step 1: according to the design requirements of the universal circuit breaker, the parameters that need to be designed are determined, such as the decreasing penalty factor, the contact resistance value, the number of contacts, the number of consumables, the phase deviation angle of the internal circuit, the contact radius, the contact coefficient, the current, spring diameter, and the effective number of spring turns.Step 2: the universal circuit breaker miniaturization model, low energy consumption model, and high-breaking model are built, respectively.Step 3: the comprehensive optimization model of the universal circuit breaker is constructed, and the determination of the coefficient can be selected by the empirical method or the grid method.Step 4: according to the objective optimization function, a fitness function is established.Step 5: the intelligent optimization algorithm is used for iterative optimization to obtain the parameter values of the comprehensive design of the universal circuit breaker.


### 4.2. Experiment and Analysis

In order to verify the comprehensive optimization effect of the universal circuit breaker, the following two experimental studies are mainly performed on the universal circuit breaker of the model HSW6 series. The improved CW-GWO algorithm is used to optimize the design and the parameters such as decreasing penalty factor, contact resistance value, and contact parameters such as number of consumables, phase deviation angle of internal circuit, contact radius, current, spring diameter, and effective number of spring turns. For comparative analysis, the APSO algorithm, ABC algorithm, and CDE algorithm are used for optimization design.


#### 4.2.1. Experiment 1

The parameter settings are as follows:(a)
Miniaturization: the value range of the spring diameter is 0.4∼3 mm, the value range of the working circle is 8∼20, the middle diameter of the spring is 3∼25 mm, the safety factor of the spring design is 1.5, the forced vibration frequency is 4 Hz, and the minimum deformation is 0.1, which is 1000 N/mm2. The maximum working load of the spring is 70 N, and the minimum working load of the spring is 30 N.(b)
Low energy consumption: decreasing coefficient of penalty factor, ranging from 0.02 to 0.2; single-contact resistance value ranging from 9 to 30; the phase deviation angle of the internal loop value ranging from 0.3 to 0.6; the number of contacts ranging from 11 to 20; consumable value range is 70∼125 kg; phase level, 3 phases; rated current is 2000 A.(c)
High breaking: there are 3 variables in total, among which the current ranges from 1000 to 4000 A, the contact radius ranges from 3 to 5 mm, and the phase deviation angle of the internal loop ranges from 0.3 to 0.6. Contact pressure is 2 N.According to the comprehensive design model formula (26) of the universal circuit breaker, it is designed as a fitness function with coefficients of 0.3, 0.4, and 0.3, respectively. Four algorithms, APSO, ABC, CDE, and CW-GWO, are used for optimization. The fitness function is shown in Figure 7, and the optimization results are shown in Table 3.Figure 7
Experiment 1, the universal circuit breaker comprehensive model optimization iteration curve.Table 3
Optimal design parameter values of the universal circuit breaker in experiment 1.
Optimal parameterThe optimal valueSpring diameterd (mm)0.8Number of working circlesn15.28Spring middle diameterD (mm)4.6Diminishing penalty factorsr1,r2(r1=r2)0.02, 0.02Single-contact resistanceR (μΩ)18Phase angle of internal loopcosφ0.3Number of contacts15Consumables (kg)90Currenti (A)2000Contact radiusR1 (mm)3Contact coefficientξ0.59As can be seen from Figure7, when the comprehensive model of the universal circuit breaker is optimized, the fitness function value obtained by the CW-GWO algorithm is the best and the convergence speed is the fastest. It can be seen from Table 3 that under the requirements of low energy consumption and high segmentation, the miniaturization effect is relatively ideal.


#### 4.2.2. Experiment 2

The parameter settings are as follows:(a)
Miniaturization: the value range of the spring diameter is 0.8∼3 mm, the value range of the working circle is 5∼20, the middle diameter of the spring is 6∼30 mm, the safety factor of the spring design is 1.5, and the forced vibration frequency is 4 Hz. The minimum deformation is 0.1, which is 1000 N/mm2. The maximum working load of the spring is 40 N, and the minimum working load of the spring is 20 N.(b)
Low energy consumption: decreasing coefficient of the penalty factor, ranging from 0.02 to 0.2; single-contact resistance value ranging from 11 to 28; the phase deviation angle of the internal loop value ranging from 0.3 to 0.32; number of contacts ranging from 7 to 20; consumable value range is 90∼150 kg; phase level, four phases; and rated current is 3000 A.(c)
High breaking: there are 3 variables in total, among which the current ranges from 1000 to 4000 A, the contact radius ranges from 0.8 to 5 mm, and the phase deviation angle of the internal loop ranges from 0.3 to 0.6. Contact pressure is 6 N.According to the comprehensive design model formula (26) of the universal circuit breaker, it is designed as a fitness function with coefficients of 0.3, 0.4, and 0.3, respectively. Four algorithms, APSO, ABC, CDE, and CW-GWO, are used for optimization. The fitness function is shown in Figure 8, and the optimization results are shown in Table 4.Figure 8
Experiment 2, the universal circuit breaker comprehensive model optimization iteration curve.Table 4
Optimal design parameter values of the universal circuit breaker in experiment 2.
Optimal parameterThe optimal valueSpring diameterd (mm)0.8Number of working circlesn8Spring middle diameterD (mm)6Diminishing penalty factorsr1,r2 (r1=r2)0.02, 0.02Single-contact resistanceR (μΩ)16Phase angle of internal loopcosφ0.3Number of contacts15Consumables (kg)115Currenti (A)2230Contact radiusR1(mm)5Contact coefficientξ0.498It can be seen from Figure8 that when the comprehensive model of the universal circuit breaker is optimized, the function fitness value obtained by the CW-GWO algorithm is the best and the convergence speed is also the fastest. It can be seen from Table 4 that under the requirements of low energy consumption and high segmentation, the miniaturization effect is also ideal.In summary, the comprehensive optimization design method of universal circuit breakers proposed in this paper is feasible and can obtain high-performance parameter indicators of universal circuit breakers and greatly improve the design accuracy and efficiency of universal circuit breakers.


## 4.1. Comprehensive Optimization Design Steps of Universal Circuit Breaker

The comprehensive optimization design steps of the universal circuit breaker based on the intelligent optimization algorithm are as follows:Step 1: according to the design requirements of the universal circuit breaker, the parameters that need to be designed are determined, such as the decreasing penalty factor, the contact resistance value, the number of contacts, the number of consumables, the phase deviation angle of the internal circuit, the contact radius, the contact coefficient, the current, spring diameter, and the effective number of spring turns.Step 2: the universal circuit breaker miniaturization model, low energy consumption model, and high-breaking model are built, respectively.Step 3: the comprehensive optimization model of the universal circuit breaker is constructed, and the determination of the coefficient can be selected by the empirical method or the grid method.Step 4: according to the objective optimization function, a fitness function is established.Step 5: the intelligent optimization algorithm is used for iterative optimization to obtain the parameter values of the comprehensive design of the universal circuit breaker.


## 4.2. Experiment and Analysis

In order to verify the comprehensive optimization effect of the universal circuit breaker, the following two experimental studies are mainly performed on the universal circuit breaker of the model HSW6 series. The improved CW-GWO algorithm is used to optimize the design and the parameters such as decreasing penalty factor, contact resistance value, and contact parameters such as number of consumables, phase deviation angle of internal circuit, contact radius, current, spring diameter, and effective number of spring turns. For comparative analysis, the APSO algorithm, ABC algorithm, and CDE algorithm are used for optimization design.


### 4.2.1. Experiment 1

The parameter settings are as follows:(a)
Miniaturization: the value range of the spring diameter is 0.4∼3 mm, the value range of the working circle is 8∼20, the middle diameter of the spring is 3∼25 mm, the safety factor of the spring design is 1.5, the forced vibration frequency is 4 Hz, and the minimum deformation is 0.1, which is 1000 N/mm2. The maximum working load of the spring is 70 N, and the minimum working load of the spring is 30 N.(b)
Low energy consumption: decreasing coefficient of penalty factor, ranging from 0.02 to 0.2; single-contact resistance value ranging from 9 to 30; the phase deviation angle of the internal loop value ranging from 0.3 to 0.6; the number of contacts ranging from 11 to 20; consumable value range is 70∼125 kg; phase level, 3 phases; rated current is 2000 A.(c)
High breaking: there are 3 variables in total, among which the current ranges from 1000 to 4000 A, the contact radius ranges from 3 to 5 mm, and the phase deviation angle of the internal loop ranges from 0.3 to 0.6. Contact pressure is 2 N.According to the comprehensive design model formula (26) of the universal circuit breaker, it is designed as a fitness function with coefficients of 0.3, 0.4, and 0.3, respectively. Four algorithms, APSO, ABC, CDE, and CW-GWO, are used for optimization. The fitness function is shown in Figure 7, and the optimization results are shown in Table 3.Figure 7
Experiment 1, the universal circuit breaker comprehensive model optimization iteration curve.Table 3
Optimal design parameter values of the universal circuit breaker in experiment 1.
Optimal parameterThe optimal valueSpring diameterd (mm)0.8Number of working circlesn15.28Spring middle diameterD (mm)4.6Diminishing penalty factorsr1,r2(r1=r2)0.02, 0.02Single-contact resistanceR (μΩ)18Phase angle of internal loopcosφ0.3Number of contacts15Consumables (kg)90Currenti (A)2000Contact radiusR1 (mm)3Contact coefficientξ0.59As can be seen from Figure7, when the comprehensive model of the universal circuit breaker is optimized, the fitness function value obtained by the CW-GWO algorithm is the best and the convergence speed is the fastest. It can be seen from Table 3 that under the requirements of low energy consumption and high segmentation, the miniaturization effect is relatively ideal.


### 4.2.2. Experiment 2

The parameter settings are as follows:(a)
Miniaturization: the value range of the spring diameter is 0.8∼3 mm, the value range of the working circle is 5∼20, the middle diameter of the spring is 6∼30 mm, the safety factor of the spring design is 1.5, and the forced vibration frequency is 4 Hz. The minimum deformation is 0.1, which is 1000 N/mm2. The maximum working load of the spring is 40 N, and the minimum working load of the spring is 20 N.(b)
Low energy consumption: decreasing coefficient of the penalty factor, ranging from 0.02 to 0.2; single-contact resistance value ranging from 11 to 28; the phase deviation angle of the internal loop value ranging from 0.3 to 0.32; number of contacts ranging from 7 to 20; consumable value range is 90∼150 kg; phase level, four phases; and rated current is 3000 A.(c)
High breaking: there are 3 variables in total, among which the current ranges from 1000 to 4000 A, the contact radius ranges from 0.8 to 5 mm, and the phase deviation angle of the internal loop ranges from 0.3 to 0.6. Contact pressure is 6 N.According to the comprehensive design model formula (26) of the universal circuit breaker, it is designed as a fitness function with coefficients of 0.3, 0.4, and 0.3, respectively. Four algorithms, APSO, ABC, CDE, and CW-GWO, are used for optimization. The fitness function is shown in Figure 8, and the optimization results are shown in Table 4.Figure 8
Experiment 2, the universal circuit breaker comprehensive model optimization iteration curve.Table 4
Optimal design parameter values of the universal circuit breaker in experiment 2.
Optimal parameterThe optimal valueSpring diameterd (mm)0.8Number of working circlesn8Spring middle diameterD (mm)6Diminishing penalty factorsr1,r2 (r1=r2)0.02, 0.02Single-contact resistanceR (μΩ)16Phase angle of internal loopcosφ0.3Number of contacts15Consumables (kg)115Currenti (A)2230Contact radiusR1(mm)5Contact coefficientξ0.498It can be seen from Figure8 that when the comprehensive model of the universal circuit breaker is optimized, the function fitness value obtained by the CW-GWO algorithm is the best and the convergence speed is also the fastest. It can be seen from Table 4 that under the requirements of low energy consumption and high segmentation, the miniaturization effect is also ideal.In summary, the comprehensive optimization design method of universal circuit breakers proposed in this paper is feasible and can obtain high-performance parameter indicators of universal circuit breakers and greatly improve the design accuracy and efficiency of universal circuit breakers.


## 4.2.1. Experiment 1

The parameter settings are as follows:(a)
Miniaturization: the value range of the spring diameter is 0.4∼3 mm, the value range of the working circle is 8∼20, the middle diameter of the spring is 3∼25 mm, the safety factor of the spring design is 1.5, the forced vibration frequency is 4 Hz, and the minimum deformation is 0.1, which is 1000 N/mm2. The maximum working load of the spring is 70 N, and the minimum working load of the spring is 30 N.(b)
Low energy consumption: decreasing coefficient of penalty factor, ranging from 0.02 to 0.2; single-contact resistance value ranging from 9 to 30; the phase deviation angle of the internal loop value ranging from 0.3 to 0.6; the number of contacts ranging from 11 to 20; consumable value range is 70∼125 kg; phase level, 3 phases; rated current is 2000 A.(c)
High breaking: there are 3 variables in total, among which the current ranges from 1000 to 4000 A, the contact radius ranges from 3 to 5 mm, and the phase deviation angle of the internal loop ranges from 0.3 to 0.6. Contact pressure is 2 N.According to the comprehensive design model formula (26) of the universal circuit breaker, it is designed as a fitness function with coefficients of 0.3, 0.4, and 0.3, respectively. Four algorithms, APSO, ABC, CDE, and CW-GWO, are used for optimization. The fitness function is shown in Figure 7, and the optimization results are shown in Table 3.Figure 7
Experiment 1, the universal circuit breaker comprehensive model optimization iteration curve.Table 3
Optimal design parameter values of the universal circuit breaker in experiment 1.
Optimal parameterThe optimal valueSpring diameterd (mm)0.8Number of working circlesn15.28Spring middle diameterD (mm)4.6Diminishing penalty factorsr1,r2(r1=r2)0.02, 0.02Single-contact resistanceR (μΩ)18Phase angle of internal loopcosφ0.3Number of contacts15Consumables (kg)90Currenti (A)2000Contact radiusR1 (mm)3Contact coefficientξ0.59As can be seen from Figure7, when the comprehensive model of the universal circuit breaker is optimized, the fitness function value obtained by the CW-GWO algorithm is the best and the convergence speed is the fastest. It can be seen from Table 3 that under the requirements of low energy consumption and high segmentation, the miniaturization effect is relatively ideal.


## 4.2.2. Experiment 2

The parameter settings are as follows:(a)
Miniaturization: the value range of the spring diameter is 0.8∼3 mm, the value range of the working circle is 5∼20, the middle diameter of the spring is 6∼30 mm, the safety factor of the spring design is 1.5, and the forced vibration frequency is 4 Hz. The minimum deformation is 0.1, which is 1000 N/mm2. The maximum working load of the spring is 40 N, and the minimum working load of the spring is 20 N.(b)
Low energy consumption: decreasing coefficient of the penalty factor, ranging from 0.02 to 0.2; single-contact resistance value ranging from 11 to 28; the phase deviation angle of the internal loop value ranging from 0.3 to 0.32; number of contacts ranging from 7 to 20; consumable value range is 90∼150 kg; phase level, four phases; and rated current is 3000 A.(c)
High breaking: there are 3 variables in total, among which the current ranges from 1000 to 4000 A, the contact radius ranges from 0.8 to 5 mm, and the phase deviation angle of the internal loop ranges from 0.3 to 0.6. Contact pressure is 6 N.According to the comprehensive design model formula (26) of the universal circuit breaker, it is designed as a fitness function with coefficients of 0.3, 0.4, and 0.3, respectively. Four algorithms, APSO, ABC, CDE, and CW-GWO, are used for optimization. The fitness function is shown in Figure 8, and the optimization results are shown in Table 4.Figure 8
Experiment 2, the universal circuit breaker comprehensive model optimization iteration curve.Table 4
Optimal design parameter values of the universal circuit breaker in experiment 2.
Optimal parameterThe optimal valueSpring diameterd (mm)0.8Number of working circlesn8Spring middle diameterD (mm)6Diminishing penalty factorsr1,r2 (r1=r2)0.02, 0.02Single-contact resistanceR (μΩ)16Phase angle of internal loopcosφ0.3Number of contacts15Consumables (kg)115Currenti (A)2230Contact radiusR1(mm)5Contact coefficientξ0.498It can be seen from Figure8 that when the comprehensive model of the universal circuit breaker is optimized, the function fitness value obtained by the CW-GWO algorithm is the best and the convergence speed is also the fastest. It can be seen from Table 4 that under the requirements of low energy consumption and high segmentation, the miniaturization effect is also ideal.In summary, the comprehensive optimization design method of universal circuit breakers proposed in this paper is feasible and can obtain high-performance parameter indicators of universal circuit breakers and greatly improve the design accuracy and efficiency of universal circuit breakers.


## 5. Conclusions

By using the gray wolf optimization algorithm to study the optimal design of the universal circuit breaker, we can draw the following conclusions.Firstly, in the miniaturization design of the universal circuit breaker, the energy consumption and breaking capacity of the universal circuit breaker must be considered. Therefore, based on the analysis of the miniaturization model, a low energy consumption model and a high-segmentation model are combined to construct a universal circuit breaker synthesis optimization model.Secondly, in the study of the gray wolf optimization algorithm, in order to overcome the slow convergence speed, the introduction of the cloud model can balance the local search and global search capabilities and the introduction of the weighting strategy can avoid local minima. Therefore, an improved gray wolf optimization algorithm (CW-GWO) based on the cloud model and weight strategy is proposed.Finally, the improved gray wolf optimization algorithm is applied to the optimization solution of the comprehensive model of the universal circuit breaker, and the high-performance parameter indicators of the universal circuit breaker can be obtained. The experimental results show that the method proposed in this paper is practical and greatly improves the design accuracy and efficiency of the circuit breaker.



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*Source: 8071057-2020-05-27.xml*