# Research on Three-Phase Unbalanced Commutation Strategy Based on the Spotted Hyena Optimizer Algorithm

Authors: Yi Zhang; XianBo Sun; Li Zhu; ShengXin Yang; YueFei Sun
Journal: Complexity
 (2022)

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## Abstract

Aimed at that ubiquitous three-phase unbalance problem in low-voltage distribution networks, the spotted hyena optimizer (SHO) algorithm is used to optimize the commutation strategy of the three-phase load unbalance. A multitarget swapping mathematical model was designed, and the objective was quickly resolved by relying on the excellent commutation strategy of the SHO. Finally, a case analysis was carried out on the data of a station area in Enshi, Hubei Province, and the results verify this swapping strategy can effectively reduce the unbalance rate.


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## Body

## 1. Introduction

In the power system, the three-phase unbalance index is one of the important indicators in measuring power quality. The unbalanced three-phase current will reflect the neutral wire, not as neutral, which directly leads to a high energy loss, accounting for 50%–60% of the total in the distribution network [1, 2]. Under unbalanced conditions, the negative sequence current will produce a distorted magnetic field and harm the transformer. The unbalanced load will cause the transformer to output unevenly, reducing the capacity utilization rate and causing the motor to vibrate and heat, which is not conducive to the operation of precision instruments and equipment [3, 4]. However, a low-voltage distribution network adopts the three-phase and four-wire system that generally has three-phase unbalance problems [5]. Asymmetry of three-phase line parameters [6], uneven load time and space distribution, large-capacity single-phase load switching [7], and large-scale distributed renewable energy connected to the grid are the main factors leading to unbalance [8]. The essence of three-phase unbalance is three-phase load asymmetry [9]. Therefore, efforts to solve the problem of three-phase load unbalance are of great importance in making electrical equipment safe to operate and the economic operation of the power grid.To solve the three-phase unbalance problem, scholars have conducted extensive research. From the perspective of compensation, Zeng et al. [10] proposed a reactive power compensation device based on Y-type and △-type parallel to solve the problem [10]; Xiao et al. [11] proposed an active asymmetric energy absorption method to absorb asymmetric power [11]; Li et al. [12] proposed reactive power compensation equipment to comprehensively compensate for the lack of reactive power and three-phase unbalance [12]; and Ji et al. [13] considered comprehensive compensation for unbalanced equipment connected to coupling points [13]. From the perspective of grid structure optimization, Tang et al. [14] considered dynamic load planning, optimizing line loading, and using commutation switches to intervene [14], and Wu et al. [15] considered using linear models to reconstruct and compensate for the active distribution network [15]. Compensated and absorbed power can be effectively adjusted when the unbalance is light, but the effect is insignificant when the unbalance is severe and the efficiency is worse.Many experts and scholars use strategy swapping when considering the essence of unbalanced and comprehensive economic factors. Traditional manual commutation has poor timeliness that does not meet the current power supply needs, and many even cause short-term power outages. With the development of power electronics technology and control theory, related researchers have proposed using smart commutation switches. Fang et al. [16] proposed an unbalance real-time management scheme that uses intelligent commutation switches and intelligent control terminals [16]. Li et al. [17] analyzed the commutation strategy and considered using software to detect the phase by using an algorithm to control the work of the commutation switch [17]. Lu et al. [18] used the fuzzy c-means clustering algorithm to optimize the commutation strategy [18]. The above methods have made a positive contribution to improving the three-phase unbalance, but the minimum unbalance degree and the minimum commutation times often cannot be met at the same time. Therefore, the accuracy of how the commutation strategy not only can meet the minimum unbalance degree but also can reduce the commutation times still needs to be improved. Metaheuristic algorithm is an interesting and important field. The application of the original heuristic algorithm is very popular in engineering and science fields [19]. The spotted hyena optimizer (SHO) algorithm is used in engineering and science because of its superior search performance. Reference [20] applied SHO to image matching, which improved the matching accuracy. In reference [21], the improved SHO is used for PID parameter optimization in VAR, which enhances the diversity of search.This article comprehensively considers the number of commutations of the smart commutation switch and the unbalance of the power grid. It fully considers the redundancy of the power grid, allowing a certain amount of unbalance to have a certain time limit. The objective function in the commutation strategy has multiple parameters and constraints. To improve the accuracy of the results, a meta-heuristic algorithm, the spotted hyena optimizer (SHO) algorithm is used in this work. SHO algorithm not only can avoid local optimization and dimension disasters in multiparameter models but also has obvious advantages in convergence speed and global optimization ability. The algorithm has the advantages of less number of operations, faster search speed, and saving operation time and re-source space. The above method is used to analyze the data of the three-phase unbalance of a certain station in Enshi, Hubei Province. The conclusion is drawn by comparing the unbalance before and after commutation. The optimization strategy in this paper can effectively improve three-phase unbalance.


## 2. Commutation Strategy Analysis

### 2.1. Three-Phase Unbalance Concept

Three-phase unbalance means that the amplitude of the three-phase voltage (current) is not equal, or the phase difference is not 2/3π. The voltage of the normal three-phase power supply system is symmetrical, and the sequence of A, B, and C phases is 120°, as shown in Figure 1.Figure 1
Three-phase voltage phasor diagram: (a) ideal three-phase voltage vector and (b) unbalanced three-phase voltage vector.
(a)(b)Three-phase voltage phases are described with the following mathematical formula:(1)U˙A=U˙ejφ,U˙B=U˙ejφ−2π/3,U˙C=U˙ejφ−4π/3.Operatorα is introduced as follows:(2)α=ej2π/3=−12+j32,α2=ej4π/3=−12−j32,α3=ej2π=1,where 1+α+α2=0 and α4=α. If these conditions are not met, they are called unbalanced systems.By aiming at the three-phase unbalance problem, this paper determines the current unbalance. The unbalance rate is expressed as follows:(3)ρ=Imax−IavIav×100%.Here,ρ is the three-phase current unbalance rate, Imax is the maximum value of the three-phase current, and Iav is the average value of the three-phase current: Iav=I_A+I_B+I_C/3.


### 2.2. Three-Phase Unbalance in Engineering

Within the power supply area of Enshi, Hubei Province, there are three-phase unbalance problems in transformer areas. Figure2 shows the real-time data of the three-phase current in a transformer area from 18: 00 to 24: 00 on February 25, 2021. It was recorded every 15 minutes. The current of phase C is significantly higher than that of phase B. As shown in Figure 3, the time-varying curve of the unbalance rate is shown. The unbalance rate of the station area is higher than 15% most of the time, and it can reach 98.72% in the most serious case. Since no reasonable and effective treatment method has been found, the local engineer solves it by cutting the load for a short time, affecting the reliability of the power supply (data source: State Grid of Hubei Enshi).Figure 2
Three-phase current.Figure 3
Three-phase current unbalance rate.


### 2.3. Implementation of the Commutation Strategy

Swapping uses electrical equipment to evenly redistribute the unbalanced three-phase load and change the heavy phase load to a light phase. The traditional mechanical commutation device takes a long time to replace the phase, which will quickly cause power loss. An intelligent commutation switch is a real-time, online device to solve three-phase unbalance. The main controller sends a commutation action through a General Packet Radio Service (GPRS) wireless signal to each distributed commutation switch. Power electronic devices replace traditional mechanical switches. The commutation time is less than 0.01 s and will not affect the load to achieve the purpose of seamless commutation.As shown in Figure4, the commutation switch was connected to the main distribution network by the three-phase and four-wire system, with single-phase output to the user, which lays a structural foundation for commutation. Various load types are distributed in the station area, including single-phase, three-phase, and mixed users. The commutation switch is also installed in a targeted distributed manner. The commutation switch monitors the user’s power consumption and sends it to the main controller in real time. The master controller adopts different commutation control strategies according to the unbalance rate, commutation times, unbalanced duration, and other factors in the station area. Therefore, considering the switch life of the devices, the frequency of swapping switch and commutation should be minimized as far as possible; the unbalance rate of three-phase current shall be as low as possible; short time unbalance can be tolerated,; and the main controller program needs to establish a multiobjective commutation mathematical model.Figure 4
Station area commutation switch topology.


#### 2.3.1. Minimum Commutation Times

Ifn commutation switches are installed in the station area, a single commutation switch is defined as di. The matrix D is composed of all commutation switches:(4)D=d1,d2,d3,…dn.Total commutation switch time in the station areaσ is defined as follows:(5)σ=∑indi.The minimum commutation time is defined as the objective functionα1 as follows:(6)α1=minσ.


#### 2.3.2. The Smallest Unbalance Degree of a Three-Phase Current

The effective value of current flowing through each commutation switch isI1, I2, I3…, In. The current RMS matrix I collected by all commutation switches is(7)I=I1,I2,I3…,In.The phase of the commutation switch is defined aski, and i can be 1, 2, or 3. The numbers 1, 2, and 3, respectively, represent the commutation switch in the power supply of phases A, B, and C, such as k1 indicates the commutation switch output for phase A power, so the vector-matrix K of the state of the commutation switch is(8)K=k1,k2,k3…,kn.The sum current of each phase can be indicated by the product of the commutation switch on the phase and the corresponding current as follows:(9)KI=IAIBIC.Using the formula (3) as the judgment standard, the minimum degree of the objective function of three-phase current unbalance is defined as followsα2:(10)α2=minρ.Consider the redundancy of the power grid, avoid unnecessary commutation, and set the trigger condition; the unbalance is greater than 15%; and the duration is greater than 10 minutes:(11)ρ>15%∩​t>10min.The total objective function is established as follows:(12)fit=α1+βα2.whereα1 represents the minimum commutation time, and in the range of [0, N]; α2 represents the minimum three-phase current unbalance rate, and in the range of 0,100%. Because α1 and α2 have different orders of magnitude, α2’s absolute value is much less than α1. In order to adjust the weight when using the spotted hyena algorithm to solve the function, the adjustment value is introduced as β, and α1 and α2 are weighted fit similar control. When analyzing the established commutation objective function, the method directly determines the effectiveness of the commutation strategy. Considering the convergence speed and the ability of global optimization, this paper uses the SHO algorithm to solve the function model and give an optimal commutation strategy.


## 2.1. Three-Phase Unbalance Concept

Three-phase unbalance means that the amplitude of the three-phase voltage (current) is not equal, or the phase difference is not 2/3π. The voltage of the normal three-phase power supply system is symmetrical, and the sequence of A, B, and C phases is 120°, as shown in Figure 1.Figure 1
Three-phase voltage phasor diagram: (a) ideal three-phase voltage vector and (b) unbalanced three-phase voltage vector.
(a)(b)Three-phase voltage phases are described with the following mathematical formula:(1)U˙A=U˙ejφ,U˙B=U˙ejφ−2π/3,U˙C=U˙ejφ−4π/3.Operatorα is introduced as follows:(2)α=ej2π/3=−12+j32,α2=ej4π/3=−12−j32,α3=ej2π=1,where 1+α+α2=0 and α4=α. If these conditions are not met, they are called unbalanced systems.By aiming at the three-phase unbalance problem, this paper determines the current unbalance. The unbalance rate is expressed as follows:(3)ρ=Imax−IavIav×100%.Here,ρ is the three-phase current unbalance rate, Imax is the maximum value of the three-phase current, and Iav is the average value of the three-phase current: Iav=I_A+I_B+I_C/3.


## 2.2. Three-Phase Unbalance in Engineering

Within the power supply area of Enshi, Hubei Province, there are three-phase unbalance problems in transformer areas. Figure2 shows the real-time data of the three-phase current in a transformer area from 18: 00 to 24: 00 on February 25, 2021. It was recorded every 15 minutes. The current of phase C is significantly higher than that of phase B. As shown in Figure 3, the time-varying curve of the unbalance rate is shown. The unbalance rate of the station area is higher than 15% most of the time, and it can reach 98.72% in the most serious case. Since no reasonable and effective treatment method has been found, the local engineer solves it by cutting the load for a short time, affecting the reliability of the power supply (data source: State Grid of Hubei Enshi).Figure 2
Three-phase current.Figure 3
Three-phase current unbalance rate.


## 2.3. Implementation of the Commutation Strategy

Swapping uses electrical equipment to evenly redistribute the unbalanced three-phase load and change the heavy phase load to a light phase. The traditional mechanical commutation device takes a long time to replace the phase, which will quickly cause power loss. An intelligent commutation switch is a real-time, online device to solve three-phase unbalance. The main controller sends a commutation action through a General Packet Radio Service (GPRS) wireless signal to each distributed commutation switch. Power electronic devices replace traditional mechanical switches. The commutation time is less than 0.01 s and will not affect the load to achieve the purpose of seamless commutation.As shown in Figure4, the commutation switch was connected to the main distribution network by the three-phase and four-wire system, with single-phase output to the user, which lays a structural foundation for commutation. Various load types are distributed in the station area, including single-phase, three-phase, and mixed users. The commutation switch is also installed in a targeted distributed manner. The commutation switch monitors the user’s power consumption and sends it to the main controller in real time. The master controller adopts different commutation control strategies according to the unbalance rate, commutation times, unbalanced duration, and other factors in the station area. Therefore, considering the switch life of the devices, the frequency of swapping switch and commutation should be minimized as far as possible; the unbalance rate of three-phase current shall be as low as possible; short time unbalance can be tolerated,; and the main controller program needs to establish a multiobjective commutation mathematical model.Figure 4
Station area commutation switch topology.


### 2.3.1. Minimum Commutation Times

Ifn commutation switches are installed in the station area, a single commutation switch is defined as di. The matrix D is composed of all commutation switches:(4)D=d1,d2,d3,…dn.Total commutation switch time in the station areaσ is defined as follows:(5)σ=∑indi.The minimum commutation time is defined as the objective functionα1 as follows:(6)α1=minσ.


### 2.3.2. The Smallest Unbalance Degree of a Three-Phase Current

The effective value of current flowing through each commutation switch isI1, I2, I3…, In. The current RMS matrix I collected by all commutation switches is(7)I=I1,I2,I3…,In.The phase of the commutation switch is defined aski, and i can be 1, 2, or 3. The numbers 1, 2, and 3, respectively, represent the commutation switch in the power supply of phases A, B, and C, such as k1 indicates the commutation switch output for phase A power, so the vector-matrix K of the state of the commutation switch is(8)K=k1,k2,k3…,kn.The sum current of each phase can be indicated by the product of the commutation switch on the phase and the corresponding current as follows:(9)KI=IAIBIC.Using the formula (3) as the judgment standard, the minimum degree of the objective function of three-phase current unbalance is defined as followsα2:(10)α2=minρ.Consider the redundancy of the power grid, avoid unnecessary commutation, and set the trigger condition; the unbalance is greater than 15%; and the duration is greater than 10 minutes:(11)ρ>15%∩​t>10min.The total objective function is established as follows:(12)fit=α1+βα2.whereα1 represents the minimum commutation time, and in the range of [0, N]; α2 represents the minimum three-phase current unbalance rate, and in the range of 0,100%. Because α1 and α2 have different orders of magnitude, α2’s absolute value is much less than α1. In order to adjust the weight when using the spotted hyena algorithm to solve the function, the adjustment value is introduced as β, and α1 and α2 are weighted fit similar control. When analyzing the established commutation objective function, the method directly determines the effectiveness of the commutation strategy. Considering the convergence speed and the ability of global optimization, this paper uses the SHO algorithm to solve the function model and give an optimal commutation strategy.


## 2.3.1. Minimum Commutation Times

Ifn commutation switches are installed in the station area, a single commutation switch is defined as di. The matrix D is composed of all commutation switches:(4)D=d1,d2,d3,…dn.Total commutation switch time in the station areaσ is defined as follows:(5)σ=∑indi.The minimum commutation time is defined as the objective functionα1 as follows:(6)α1=minσ.


## 2.3.2. The Smallest Unbalance Degree of a Three-Phase Current

The effective value of current flowing through each commutation switch isI1, I2, I3…, In. The current RMS matrix I collected by all commutation switches is(7)I=I1,I2,I3…,In.The phase of the commutation switch is defined aski, and i can be 1, 2, or 3. The numbers 1, 2, and 3, respectively, represent the commutation switch in the power supply of phases A, B, and C, such as k1 indicates the commutation switch output for phase A power, so the vector-matrix K of the state of the commutation switch is(8)K=k1,k2,k3…,kn.The sum current of each phase can be indicated by the product of the commutation switch on the phase and the corresponding current as follows:(9)KI=IAIBIC.Using the formula (3) as the judgment standard, the minimum degree of the objective function of three-phase current unbalance is defined as followsα2:(10)α2=minρ.Consider the redundancy of the power grid, avoid unnecessary commutation, and set the trigger condition; the unbalance is greater than 15%; and the duration is greater than 10 minutes:(11)ρ>15%∩​t>10min.The total objective function is established as follows:(12)fit=α1+βα2.whereα1 represents the minimum commutation time, and in the range of [0, N]; α2 represents the minimum three-phase current unbalance rate, and in the range of 0,100%. Because α1 and α2 have different orders of magnitude, α2’s absolute value is much less than α1. In order to adjust the weight when using the spotted hyena algorithm to solve the function, the adjustment value is introduced as β, and α1 and α2 are weighted fit similar control. When analyzing the established commutation objective function, the method directly determines the effectiveness of the commutation strategy. Considering the convergence speed and the ability of global optimization, this paper uses the SHO algorithm to solve the function model and give an optimal commutation strategy.


## 3. Solution of the Objective Function of Commutation Strategy

### 3.1. SHO Algorithm

SHO algorithm is a new metaheuristic algorithm based on the social activities and hunting methods of the spotted hyena, proposed by Dhiman in 2017 [22, 23]. In the SHO, individuals trust their peers and their excellent ability to identify prey for optimization activities. This way makes the population finds the optimal prey efficiently. The optimization method of the SHO algorithm is mainly divided into four steps: surrounding, hunting, attacking, and searching. The above behaviour can be expressed by the mathematical model.


#### 3.1.1. Surrounding

Spotted hyenas hunt their prey by being familiar with its location. The mathematical model of this behaviour is as follows:(13)D⟶h=B⟶⋅PP⟶x−P⟶x,(14)P⟶x+1=Pp⟶x−E⟶⋅Dh⟶.Here,D⟶h is the physical distance between the target group and the spotted hyena unit, PP⟶ is the location of prey, P⟶x is the individual location for spotted hyenas, B⟶ is the disturbance vector, and E⟶ is the convergence factor, and the formula is as follows:(15)B⟶=2r1,(16)E⟶=2h⟶⋅r2−h⟶,(17)h⟶=5−5tT.Here,r1 and r2 are the random vector and value in [0, 1] intervals, respectively; t is the current number of iterations; T is the maximum number of iterations; and h⟶ decays linearly from five to zero as the number of iterations increases.


#### 3.1.2. Hunting

Spotted hyenas live in groups. The trusted network composed of unit companions is a reliable basis for hunting; the specific formula is as follows:(18)D⟶h=B⟶⋅PP⟶x−P⟶k,(19)P⟶k=Ph⟶−E⟶⋅Dh⟶,(20)Ch⟶=Pk⟶+Pk+1⟶+⋯+Pk+N⟶.Here,Ph⟶ represents the location of the best spotted hyena individual, P⟶k indicates the location of other spotted hyenas, N represents the number of spotted hyenas, and Ch⟶ represents the cluster of N optimal solutions.(21)N=countnosPh⟶,Ph+1⟶,Ph+2⟶,…,+Pk⟶+M⟶.Here,M⟶ has a random vector value in [0.5, 1] intervals; after M⟶nos is added, the numbers define the number of solutions and calculate all the candidate solutions.


#### 3.1.3. Attacking

When the convergence factor isE⟶<1, the spotted hyena population attacks the prey. The specific formula for attacking the prey is as follows:(22)P⟶x+1=Ch⟶N.Here,P⟶x+1 will save the location of the optimal spotted hyena and update the location of others.


#### 3.1.4. Searching

Spotted hyenas are mostly located in the optimal solution clusterCh⟶, and the spotted hyena population indicates the location of the cluster to search for prey. When the convergence factor is E⟶>1, the spotted hyena will disperse and conduct a global search to find more suitable prey; when the convergence factor is E⟶<1, the spotted hyena population attacks the prey; and B⟶ also provides the prey with random weight to avoid the population falling into the local optimal solution.


### 3.2. Solution of the Model

So far, the solution model of the full text has been established. Firstly, the main process of the model of minimum current unbalance and minimum commutation times is as follows:(1)
According to the defined commutation switch matrix, calculate the total commutation time to obtain equation (5) and objective function equation (6).(2)
According to the current matrix defined in equations (7)–(9), calculate the current imbalance according to equation (3) to obtain the objective function (10).(3)
The main controller at the secondary side of the transformer continuously calculates the electrical parameters at the secondary side and compares them with the target limit value. Once the set conditions are exceeded, the SHO algorithm will be started according to the established final objective function (12).(4)
According to the final commutation matrix generated by the SHO algorithm, the minimum commutation times and minimum unbalance degree are calculated to meet the power quality requirements of the power grid.Then, the spotted hyena algorithm is applied to solve the commutation objective function model. The solving steps of the spotted hyena algorithm are as follows:(1)
Initialize the spotted hyena population. Generate the random matrix Dn (n = 1, 2, …, n), according to the equation (4), and generate a random number from [0, 3]. If the switch belongs to the value range of [0, 1], it is phase A output; if the number belongs to [1, 2], it is phase B output; if the number belongs to [2, 3], it is phase C output.(2)
Define initialization parameters. DefineB⟶, h, N, and the maximum iterations according to equations (15), (17), and (21).(3)
Calculate the fitness of each individual.Ph⟶ = the best search, and Ch⟶ = the group or cluster of all far optimal solutions. According to equation (12), calculate the weight of commutation times and three-phase current unbalance.(4)
A set of optimal solutions is determined according to equations (20) and (21).(5)
Update the position of the population according to equation (22). Update h, B, E, and N.(6)
Check whether the individuals in the population exceed the boundary and adjust them.(7)
Calculate the fitness of each individual after population renewal.(8)
Update the previous optimal positionPh with the new optimal solution by equations (18) and (19).(9)
Judge whether the iteration termination conditions are met. If satisfied, the optimal solution is output; otherwise, return to execution (4) until optimization is completed.The flow chart is presented in Figure5.Figure 5
Flowchart of phase-change solution.


## 3.1. SHO Algorithm

SHO algorithm is a new metaheuristic algorithm based on the social activities and hunting methods of the spotted hyena, proposed by Dhiman in 2017 [22, 23]. In the SHO, individuals trust their peers and their excellent ability to identify prey for optimization activities. This way makes the population finds the optimal prey efficiently. The optimization method of the SHO algorithm is mainly divided into four steps: surrounding, hunting, attacking, and searching. The above behaviour can be expressed by the mathematical model.


### 3.1.1. Surrounding

Spotted hyenas hunt their prey by being familiar with its location. The mathematical model of this behaviour is as follows:(13)D⟶h=B⟶⋅PP⟶x−P⟶x,(14)P⟶x+1=Pp⟶x−E⟶⋅Dh⟶.Here,D⟶h is the physical distance between the target group and the spotted hyena unit, PP⟶ is the location of prey, P⟶x is the individual location for spotted hyenas, B⟶ is the disturbance vector, and E⟶ is the convergence factor, and the formula is as follows:(15)B⟶=2r1,(16)E⟶=2h⟶⋅r2−h⟶,(17)h⟶=5−5tT.Here,r1 and r2 are the random vector and value in [0, 1] intervals, respectively; t is the current number of iterations; T is the maximum number of iterations; and h⟶ decays linearly from five to zero as the number of iterations increases.


### 3.1.2. Hunting

Spotted hyenas live in groups. The trusted network composed of unit companions is a reliable basis for hunting; the specific formula is as follows:(18)D⟶h=B⟶⋅PP⟶x−P⟶k,(19)P⟶k=Ph⟶−E⟶⋅Dh⟶,(20)Ch⟶=Pk⟶+Pk+1⟶+⋯+Pk+N⟶.Here,Ph⟶ represents the location of the best spotted hyena individual, P⟶k indicates the location of other spotted hyenas, N represents the number of spotted hyenas, and Ch⟶ represents the cluster of N optimal solutions.(21)N=countnosPh⟶,Ph+1⟶,Ph+2⟶,…,+Pk⟶+M⟶.Here,M⟶ has a random vector value in [0.5, 1] intervals; after M⟶nos is added, the numbers define the number of solutions and calculate all the candidate solutions.


### 3.1.3. Attacking

When the convergence factor isE⟶<1, the spotted hyena population attacks the prey. The specific formula for attacking the prey is as follows:(22)P⟶x+1=Ch⟶N.Here,P⟶x+1 will save the location of the optimal spotted hyena and update the location of others.


### 3.1.4. Searching

Spotted hyenas are mostly located in the optimal solution clusterCh⟶, and the spotted hyena population indicates the location of the cluster to search for prey. When the convergence factor is E⟶>1, the spotted hyena will disperse and conduct a global search to find more suitable prey; when the convergence factor is E⟶<1, the spotted hyena population attacks the prey; and B⟶ also provides the prey with random weight to avoid the population falling into the local optimal solution.


## 3.1.1. Surrounding

Spotted hyenas hunt their prey by being familiar with its location. The mathematical model of this behaviour is as follows:(13)D⟶h=B⟶⋅PP⟶x−P⟶x,(14)P⟶x+1=Pp⟶x−E⟶⋅Dh⟶.Here,D⟶h is the physical distance between the target group and the spotted hyena unit, PP⟶ is the location of prey, P⟶x is the individual location for spotted hyenas, B⟶ is the disturbance vector, and E⟶ is the convergence factor, and the formula is as follows:(15)B⟶=2r1,(16)E⟶=2h⟶⋅r2−h⟶,(17)h⟶=5−5tT.Here,r1 and r2 are the random vector and value in [0, 1] intervals, respectively; t is the current number of iterations; T is the maximum number of iterations; and h⟶ decays linearly from five to zero as the number of iterations increases.


## 3.1.2. Hunting

Spotted hyenas live in groups. The trusted network composed of unit companions is a reliable basis for hunting; the specific formula is as follows:(18)D⟶h=B⟶⋅PP⟶x−P⟶k,(19)P⟶k=Ph⟶−E⟶⋅Dh⟶,(20)Ch⟶=Pk⟶+Pk+1⟶+⋯+Pk+N⟶.Here,Ph⟶ represents the location of the best spotted hyena individual, P⟶k indicates the location of other spotted hyenas, N represents the number of spotted hyenas, and Ch⟶ represents the cluster of N optimal solutions.(21)N=countnosPh⟶,Ph+1⟶,Ph+2⟶,…,+Pk⟶+M⟶.Here,M⟶ has a random vector value in [0.5, 1] intervals; after M⟶nos is added, the numbers define the number of solutions and calculate all the candidate solutions.


## 3.1.3. Attacking

When the convergence factor isE⟶<1, the spotted hyena population attacks the prey. The specific formula for attacking the prey is as follows:(22)P⟶x+1=Ch⟶N.Here,P⟶x+1 will save the location of the optimal spotted hyena and update the location of others.


## 3.1.4. Searching

Spotted hyenas are mostly located in the optimal solution clusterCh⟶, and the spotted hyena population indicates the location of the cluster to search for prey. When the convergence factor is E⟶>1, the spotted hyena will disperse and conduct a global search to find more suitable prey; when the convergence factor is E⟶<1, the spotted hyena population attacks the prey; and B⟶ also provides the prey with random weight to avoid the population falling into the local optimal solution.


## 3.2. Solution of the Model

So far, the solution model of the full text has been established. Firstly, the main process of the model of minimum current unbalance and minimum commutation times is as follows:(1)
According to the defined commutation switch matrix, calculate the total commutation time to obtain equation (5) and objective function equation (6).(2)
According to the current matrix defined in equations (7)–(9), calculate the current imbalance according to equation (3) to obtain the objective function (10).(3)
The main controller at the secondary side of the transformer continuously calculates the electrical parameters at the secondary side and compares them with the target limit value. Once the set conditions are exceeded, the SHO algorithm will be started according to the established final objective function (12).(4)
According to the final commutation matrix generated by the SHO algorithm, the minimum commutation times and minimum unbalance degree are calculated to meet the power quality requirements of the power grid.Then, the spotted hyena algorithm is applied to solve the commutation objective function model. The solving steps of the spotted hyena algorithm are as follows:(1)
Initialize the spotted hyena population. Generate the random matrix Dn (n = 1, 2, …, n), according to the equation (4), and generate a random number from [0, 3]. If the switch belongs to the value range of [0, 1], it is phase A output; if the number belongs to [1, 2], it is phase B output; if the number belongs to [2, 3], it is phase C output.(2)
Define initialization parameters. DefineB⟶, h, N, and the maximum iterations according to equations (15), (17), and (21).(3)
Calculate the fitness of each individual.Ph⟶ = the best search, and Ch⟶ = the group or cluster of all far optimal solutions. According to equation (12), calculate the weight of commutation times and three-phase current unbalance.(4)
A set of optimal solutions is determined according to equations (20) and (21).(5)
Update the position of the population according to equation (22). Update h, B, E, and N.(6)
Check whether the individuals in the population exceed the boundary and adjust them.(7)
Calculate the fitness of each individual after population renewal.(8)
Update the previous optimal positionPh with the new optimal solution by equations (18) and (19).(9)
Judge whether the iteration termination conditions are met. If satisfied, the optimal solution is output; otherwise, return to execution (4) until optimization is completed.The flow chart is presented in Figure5.Figure 5
Flowchart of phase-change solution.


## 4. Case Analysis

Enshi City, Hubei Province, is located at the junction of Central and Western China. Most of the power supply areas are karst landforms. The power supply terminals are mainly single-phase users, which are scattered and disorderly, and the three-phase imbalance is not optimistic.To distinguish the above data, the monitoring data of a station area in Enshi, Hubei Province, on January 24, 2021, were selected for analysis. Suppose 21 commutation switches are installed within the station area, the phase sequence of each commutation switch and the effective values of the current flowing is shown in Table1.Table 1
Value of current before commutation.
Number123456789101112131415161718192021PhaseBAACCBCBACACACBCACACBCurrent (A)4.795.864.329.146.725.2310.627.126.7712.029.2110.214.328.53.678.727.567.335.029.474.21In Table1, the “number” represents the number of each commutation switch installed on the user; the “phase” represents the phase sequence of the output current of the commutation switch; and the “current” represents the effective value of the current flowing through the commutation switch. For example, number 1, phase B current 4.79 indicates that the number 1 commutation switch is flowing current from phase B, and the effective value is 4.79 A.Corresponding to the commutation mathematical model parameters, the number of commutation switches isn = 21, and the number of current measurements is n = 21. In the analysis of 21-unit load currents, the sum of three-phase currents at the transformer secondary side’s output end: ∑IA=43.06A, ∑IB=25.02A, ∑IC=82.73A, and the unbalance rate ρ=Imax−Iav/Iav×100%=64.57%, has far exceeded the allowable 15%. According to relevant standards, the unbalance is serious. If the unbalance state is continuously maintained, high energy loss will continue to occur and threaten the operation safety of electrical equipment in the station area. The intelligent commutation switch will take commutation measures and use the SHO to analyze the station data and quickly give the commutation strategy. Input the original data before commutation to the SHO algorithm, including the number of commutation switches, the phase sequence of commutation, and the effective value of the current.Step 1.
Code the current data collected by 21 commutation switches; phase “A, B, C” sequence is represented by the numbers “1, 2, 3,” respectively; and each current data is corresponding to the phase sequence to obtain 2 × 21 matrix.Step 2.
Bring 21 groups of phase sequence and current data into the SHO algorithm to start initialization and calculation.Step 3.
Set constraints. The SHO algorithm sets the trigger condition and unbalance atρ>15%; the duration is t>10min; and it takes the adjustment value as β=30.Step 4.
Based on the calculation method and steps designed above, the parameters for setting SHO are shown in Table2.
As the table shows, the “Search Agents”=30, and the “max iterations”=50. The “Lower bound” and the “upper bound” represent the three-phase sequence. The “dimension” takes the value 21, which means there are 21 sets of data. The SHO algorithm was used to optimize the commutation strategy and find the best commutation combination. To compare the advantages of SHO, we compare the fitness of the proposed SHO algorithm with particle swarm optimization (PSO) and whale optimization algorithm (WOA). The fitness convergence curves of the three algorithms are shown in Figure7. The fitness curve shows that the number of SHO iterations is better than PSO and WOA when solving the three-phase unbalanced commutation strategy problem, and the algorithm proposed has some advantages.Table 2
SHO parameter settings.
Search agentsMax iterationsLower boundUpper boundDimension30500321Figure 6
Fitness curve.Figure 7
Current comparison.Step 5.
The results are calculated, 1 × 21’s phase order matrixK'. After the number of iterations in the figure reaches 20 generations, the fitness curve converges; the commutation strategy was given; and the adjusted commutation matrix and switching phasor matrix are output as follows:(23)K′=1.235147,0,0.414848,0.296163,1.083751,1.565902,3,1.027106,2.318674,0.98336,1.446175,3,0,1.247804,1.143984,2.164118,0.750938,2.76022,0,3,1.668109.Step 6.
Translate the results. The commutation strategy given by the SHO algorithm is analyzed. The output switching phasor matrix is a group of decimal arrays with a number of 21, representing the switching phase sequence numbers of 21 commutation switches that are arranged in sequence. The value range is within the initialization population value field0,3 generated in step 1 of the SHO algorithm. The decimal is rounded up according to the initialization requirements. The value within the range of 0,1 is phase A; phase B is in the range of 1,2; and phase C is in the range of 2,3. Translate the matrix output by the SHO algorithm into a commutation command, as shown in Table 3.
According to the data in Table3, switch number four was changed from phase C to A; switch number five from phase C to B; switch number nine was changed from phase A to C; switch number ten from phase C to A; switch number eleven from phase A to B; and switch number fourteen was changed from phase C to phase B. Among the 21 commutation switches, only six switches function, so the commutation time is σ=6. After commutation, the sum of the three-phase current is: ∑IA=48.24A, ∑IB=45.24A, and ∑IC=53.12A, and the three-phase unbalance rate is ρ=I_max−I_av/I_av×100%=8.7%, and the result not only considers the minimum commutation times but also ensures the degree of the unbalance meets the requirements, which is the best choice.
The comparison of the three-phase effective current value and three-phase unbalance current rate before and after commutation are presented in Figures7 and 8. Before commutation, the phase B load is the light-load phase, and the current flowing through the secondary side of the transformer was 25.02 A. Phase C was a heavy-load phase with a current of 82.73 A, and phase A was relatively mild. The commutation strategy increased the phase B current to 45.24 A and shunted the phase C current to 53.12 A by switching the phase sequences of six commutation switches numbers four, five, nine, ten, eleven, and fourteen.
The unbalance of the three-phase current before commutation was 64.57%; afterward, it was 8.7%. The degree of unbalance was reduced by 56%. Therefore, the three-phase unbalance in the station distribution area improved significantly.Table 3
Current value after commutation.
Number123456789101112131415161718192021PhaseBAAABBCBCABCABBCACACBCurrent (A)4.795.864.329.146.725.2310.627.126.7712.029.2110.214.328.53.678.727.567.335.029.474.21Figure 8
Unbalance rate comparison.


## 5. Conclusions

Pointed at the common three-phase unbalance problem in the distribution network, this paper studies the commutation strategy of how an intelligent commutation switch proposes to optimize commutation strategy by using the SHO algorithm that analyzes and verifies the engineering example by using MATLAB and obtains the following conclusions: the SHO can find better fitness value, fast convergence speed, and strong optimization performance and can effectively improve the commutation strategy. The commutation strategy proposed in this paper considers the optimal solution of commutation times and the degree of unbalance, rapidity, and accuracy of optimization. This method controls the commutation switch better, makes the optimal commutation strategy for unbalanced the three-phase current, effectively reduces the three-phase current unbalance to less than 15%, achieves the purpose of improving the three-phase unbalance in the station area, and has strong engineering practice value.



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*Source: 2092421-2022-07-16.xml*