
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)12699-0
10.1016/j.heliyon.2024.e36668
e36668
Research Article
Power flow control and reliability improvement through adaptive PSO based network reconfiguration
Tantu Ashenafi Tesfaye ashenafi.tesfaye02@wsu.edu.et
a⁎
Biramo Degu Bibiso degubbc69@gmail.com
b
a Wolaita Sodo University, Wolaita Sodo, Ethiopia
b Arba Minch University, Arba Minch, Ethiopia
⁎ Corresponding author. ashenafi.tesfaye02@wsu.edu.et
22 8 2024
15 9 2024
22 8 2024
10 17 e366686 5 2024
17 8 2024
20 8 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Ensuring stable power flow and reliable supply could maintain system security, improve system efficiency, minimize power loss, and reduce the risk of supply outage. Power flow management can be employed to enhance bus voltage and decrease power losses. The reliability of the system is critical for both the customers and the utility to ensure supply continuity and improved revenue. With the growing demand for reliable power supplies, it is crucial that utilities devote efforts to ensure a consistent power supply to meet customer needs. However, the frequent occurrence of power interruptions and the prolonged duration of interruption pose significant challenges to power distribution systems in the town of Wolaita Sodo. This study aims to explore power flow and reliability control through the utilization of optimal distribution network reconfiguration (DNR). The optimal placement of tie-switches (TS) to address the power flow and reliability issues is done through the adaptive particle swarm optimization (APSO) algorithm. With the help of APSO, five TS units achieved the reliability indices within the national standard boundary. The backward/forward sweep (BFS) and Markov chain-based Monte Carlo simulation (MCMCS) methods are used for load flow and reliability analysis. Through simulation, with integration of five TS, SAIFI decreases from a value of 557 to about 34, SAIDI decreases from 573.59h to about 43.87h and EENS decreases from 1835.5 MWh to about 140.38 MWh annually, active power loss decreases from 1631.15 kW to about 559.35 kW, the minimum bus voltage increases from 0.7537pu to 0.9502pu. Finally, the evaluation of the suggested algorithm variants is conducted by taking into account the duration it takes to respond, the level of convergence achieved, and the extent to which power loss is minimized.

Keywords

Adaptive PSO
BFS load flow
Distribution network reconfiguration
Markov chain MCS
Reliability analysis
==== Body
pmc1 Introduction

1.1 Background of the study

Distribution power flow control refers to the management of power flows within a distribution network to achieve voltage regulation, power loss minimization, and reliability improvement. It involves the use of various control devices, such as voltage regulators, capacitor banks, distributed static compensators (DSTATCOMs), and controllable loads, to actively influence the flow of power in the distribution system. By actively adjusting voltage levels at different points in the distribution system, power flow control can help to maintain voltages within acceptable limits, ensuring reliable and stable operation of the network.

Power outages can disrupt daily activities, inconvenience customers, and affect businesses, resulting in significant economic losses for businesses, industries, and individuals. Evaluation and improvement of the reliability of the distribution system are essential to ensure customer satisfaction, support economic prosperity, improve public safety, improve energy efficiency, reduce environmental impact, and comply with regulatory requirements.

Distribution network reconfiguration (DNR) involves altering the topology of the distribution system by changing the operational status of switches and reconfiguring the network layout to optimize system performance. Using optimization algorithms can help to explore and evaluate different network configurations that may involve altering the status of switches to open or close certain feeder sections, changing tie-line connections, or reconfiguring the network layout to achieve the defined objectives [1]. This study is intended to propose only the best position for the switches in order to improve the performance of the system. The radial topology should not be violated at any instance and also there should be supply line from substation to every bus in the system. Thus, no customer should be disconnected during the switching process.

Adaptive particle swarm optimization (APSO) is an extension of the traditional particle swarm optimization (PSO) algorithm that incorporates adaptive mechanisms to dynamically adjust its parameters during the optimization process to enhance its performance, robustness, and convergence speed. Using the APSO algorithm to optimize network reconfiguration, the system can dynamically adapt to changing load conditions and network configurations.

The selection criteria of the PSO algorithm are due to its simplicity, robust to local optima, adaptable to handle various types of optimization problems, potential computational speedup, easier to tune and computational efficiency, which make it suitable for solving high-dimensional optimization problems [2]. Its versatility and effectiveness make it a popular choice for solving optimization problems in various domains.

There are various power flow analysis methods. However, due to the high R/X ratio and unbalanced load issues of the distribution network, backward/forward sweep (BFS) based load flow analysis is determined as a compatible approach for distribution network load flow analysis [3]. Thus, the power flow is formulated using the BFS based approach.

Probabilistic methods for analyzing system reliability involve assessing the probability of outage occurrence in a system based on statistical analysis of component failure rates. Monte Carlo simulation (MCS) is a powerful tool for analyzing power system reliability [4]. Aggregating the outcomes of multiple simulations enables the estimation of the probability of system outages. However, accurately capturing dependencies in MCS can be challenging. Markov models (MC) offer a solution by allowing for the precise representation of dependencies and interactions between various components. By utilizing MC, dependencies can be captured more accurately, leading to improved reliability assessments and outage probability estimations.

By strategically adjusting the configuration based on real-time data and load conditions, the required power stability and reliability can be achieved. Through proper DNR, utilities can enhance overall reliability of the system and reduce energy losses and associated costs. The main focus of this study is to explore how to renovate and configure a reliable distribution system to achieve an effective solution.

This study focuses on jointly improving power flow and reliability for the Wolaita Sodo town distribution network. The power flow focuses on the bus voltage profile and power loss investigation. The network includes 113 distribution transformers that have a peak demand of about 7.4 MW by 2023 supplied from a single source. The power is supplied through AAC-95 and AAC-50 rated conductors having total lengths of about 32.33 km and 23.69 km throughout the town, respectively.

1.2 Statement of the problem

An inconsistent power supply not only hampers productivity and causes damage to machinery, but also requires additional maintenance and negatively impacts the reputation of industries in terms of product quality. The interruption of power has resulted in the cessation of production for customers in the city. As the three-year data revealed, System Average Interruption Frequency Index (SAIFI) of the town in 2021, 2022 and 2023 is found as 603, 519 and 557 respectively. Moreover, the total System Average Interruption Duration Index (SAIDI) is found to be about 649.39h, 492.16h, and 573.58h respectively. The aim of Ethiopian Electric Utility (EEU) is to reduce SAIFI and SAIDI to about 20 and 25h, respectively. However, the data for the Wolaita Sodo town interruption each year are considerably higher than the required limits. The estimated magnitude of bus voltage during peak load session is about 0.83pu, which is less than the intended value of 0.9pu as a national standard. The estimated active power loss as of 2022 and 2023 is found to be about 22.97 % and 22.3 %, respectively. The estimation of active power loss is achieved by calculating the discrepancy between the energy supplied to the town from the respective feeder in the substation and the energy sold within a specific year.

In the Wolaita Sodo town, ensuring a reliable power distribution has proven to be a highly challenging task due to several deficiencies like radial topology that is susceptible to faults and reduction of voltage profile as the bus goes far away the main feeder, the aging of system equipment and long-lasting fault location tracing mechanism further exacerbate the issue. This vulnerability to disturbances has greatly frustrated customers in daily activities. Unplanned power outages with extended outages have significantly impacted customer consumption patterns. Therefore, solving stability and reliability related problems remains a primary challenge in meeting the needs of customers.

Through DNR, the optimal placement of the Smart Switch (SS) can accommodate the intended objectives of the study. The PSO through an adaptive tuning approach is considered for this study to find the optimal DNR locations. With the state of improving power flow and reliability indices such as SAIFI, SAIDI and the Expected Energy Not Supplied (EENS) through DNR, the MATLAB software is utilized for proposed evaluation.

1.3 Contribution of the study

The main objective of this study is to improve the bus voltage profile, to reduce active power loss, and to improve the reliability of the proposed system through DNR. In doing so, the following activities are conducted.a) The PSO algorithm is adopted to determine optimal DNR switching locations.☑ PSO may converge to a suboptimal solution prematurely, especially in multimodal optimization problems. The diversity-preserving operator (DPO) method is introduced to encourage exploration of the search space even after convergence seems to have occurred, helping to escape local optima.

☑ PSO performance can be sensitive to its parameters. The Constriction Coefficient Approach (CCA) as one of the adaptive inertia weight control strategies is used to dynamically adjust the PSO parameter.

b) Based on the line data and load data provided, the BFS method is employed for load flow analysis due to its suitability for radial systems.

c) Modeling dependencies between system components can be challenging in MCS. Thus, the Markov model-based MCS (MCMCS) is used to capture these dependencies more accurately for reliability analysis.

2 Literature review

2.1 Review on reliability improvement

Kahouli et al. presented a genetic algorithm (GA) and PSO based DNR to reduce EENS and power losses [5]. Pedago et al. proposed selective version of the binary PSO (BPSO) algorithm for DNR while considering the sigmoid function to control the particle rate change [6]. Souifi et al. carried out research on DNR for a multi-objective problem that involved GA [7]. Jafari et al. introduced an optimal DNR solution using a combination of the wild goat algorithm (WGA) and the exchange market algorithm (EMA) to improve both reliability and power loss [8]. Kumar et al. presented PSO-based optimal DNR to improve system performance and reliability [9]. Ma et al. proposed a hybrid data-driven approach to assess power grid reliability [10]. Ramavat et al. discussed the status of battery storage technology and its effects on improving reliability [11]. Battery storage system is proposed for ensuring a consistent power supply and improving grid reliability [12]. Bokyo et al. presented the reliability improvement methods by integrating mini-grids into power system [13]. Recalde et al. introduced a sequential MCS-based PSO approach for reliability planning aimed at deploying wind, solar PV, and tidal energy in a distribution network [14]. Lopez et al. presented a mixed-integer second-order conic programming (MISOCP) model to solve the distribution system reconfiguration problem for reliability analysis [15]. Ray et al. proposed differential search algorithm (DSA) based switch placement in distribution system to improve the reliability [16]. Using the MCS technique, Ge et al. addressed the active distribution system reliability assessment (DSRA) problem at both low and high levels of DG dispersion [17].

2.2 Review on power flow improvement

Muluneh et al. presented application of PSO-based DSTATCOM for distribution system stability improvement [3]. Oloulade et al. explored the improvement of system performance using ant colony optimization (ACO) for optimal DSTATCOM placement and DNR [18]. Soheil et al. carried out research on dynamic DNR to improve reliability in the presence of distributed generation (DG) using a reinforcement learning method [19]. Shi et al. introduced a DNR with DG to enhance resilience of the system through outage management system strategy that incorporates post-fault analysis and optimal scheduling of DG [20]. Essallah et al. proposed PSO to optimize switch status, DG location and size for DNR and DG integration planning to minimize power loss and enhance voltage profile [21]. Sharma et al. used a modified PSO algorithm for optimal load flow analysis in a system with integrated DGs [22]. Abido introduced an improved PSO algorithm for optimal setting of optimal power flow (OPF) problem control variables [23]. Gad provided a systematic review on PSO algorithm and its applications [24]. A hybrid genetic PSO method is proposed in Ref. [25] to determine the optimal allocation of DGs. Adepoju et al. proposed application of PSO for optimal placement and sizing of DGs in the distribution network [26]. Eid introduced adaptation for PSO parameters for optimal allocation of the DG in the distribution network [27]. Ullah et al. proposed phasor-PSO for optimal placement and sizing of DGs [28].

2.3 Identified research gap

The reviewed articles have shown that the use of D-FACTS, DGs, and DNR can improve both the power flow and the overall reliability of the system. However, the identified research gaps are outlined below.☑ Reliability modeling must be clearly executed as the crucial reliability indices SAIFI and SAIDI must be taken into account. Additionally, it is advantageous to assess the reliability aspect in conjunction with power flow analysis while considering the DNR.

☑ Although swarm-based optimization algorithms have been greatly influenced by the control parameter, many studies have not offered adequate techniques for adapting the control parameter values. Thus, the DPO-CCA-based PSO formulation is proposed under this study.

☑ MCS model is a powerful tool for analyzing power system reliability. It involves simulating the behavior of the system under each sample. However, capturing the dependencies in the MCS as challenging issue is not presented adequately in the literatures. Integrating the Markov models to MCS is proposed and considered here to capture dependencies and interactions between different components in order to have better accuracy.

3 Methodology

3.1 Modeling of the proposed power system

There are currently 113 distribution transformers operating in the city, supplied from a single source. The peak active power demand for the town is about 7.4 MW in 2023. The power is supplied through AAC-95 and AAC-50 rated conductors. Due to the time, budget and human resource constraint of recording measurements for each transformer in the network, only peak load session current and voltage measurements of all transformers are documented.1. Line impedance modeling

The impedance, Z, can be calculated at a given frequency (50Hz for this study) per unit length of a kilometer as shown in Equation (3.1) [29,30]:3.1 Z=R+j0.06283lnDGMRΩ/km

Where R: conductor resistance in Ω/km, GMR: Geometric mean ratio of conductor, D: distance between phase conductors that can be computed as given in Equation (3.2):3.2 D=DabxDbcxDac3

In the existing distribution line arrangement in the town, the lines are placed in horizontal spacing fashion due to the adherence to the EEU distribution network standard. According to the EEU standard for a 15 kV system, the minimum spacing between the phases is: Dab = 0.64m, Dbc = 0.51m, Dac = 1.15m. Therefore, D can be found as about 0.72135m. The GMR values can be assessed from Ref. [30]. Thus, the impedance for AAC-95 and AAC-50 bare conductors can be computed as given in Equation (3.3):3.3 Z95=0.3085+j0.32441Ω/kmZ50=0.5785+j0.34702Ω/km}

2. Load modeling

Active and reactive power data were obtained for each transformer by measuring voltage and current. These measurements were made over a period of six months during morning and evening sessions, specifically on working days of the week. The weekly average power data was accumulated to obtain the monthly average power data. The load data of the proposed study is modeled in this manner with consideration of power factor to be 0.85.

3.2 Load flow modeling

The load flow analysis is essential for identifying the operation state of the system. The higher ratio of R/X and the unbalanced loading condition of the distribution system make the conventional Gauss-Seidel (GS) and Newton-Raphson (NR) methods inappropriate for distribution system load flow analysis [31]. As a result, the BFS method as recommended in Ref. [3] is considered to determine the active power losses and node voltage profile.

The basic steps in the BFS load flow approach are [3].• Initialization of node voltage: Bus voltage magnitude of all nodes set as 1pu.

• Backward sweep process: This is mainly used to calculate the branch current.

• Forward sweep process: This process is used to calculate the bus voltage magnitude

• Convergence criteria: In successive iterations, if the maximum bus voltage mismatch is less than the specified tolerance, the solution is said to converge. Otherwise, the iteration continues until the maximum iteration count is reached.

3.3 Reliability modeling

Modeling the reliability of a distribution system involves assessing the ability of the system to provide continuous and reliable electrical power to customers. The MCS is a powerful tool for analyzing power system reliability.

System indices are calculated considering the frequency and duration of interruption for all customers connected to the system [32].☞ Average failures at the load point i, λi (failures per year) is given in Equation (3.4):

3.4 λi=∑j∈Nλe,j

☞ Duration of the annual outage at the load point i, Ti (hours per year) is given in Equation (3.5):

3.5 Ti=∑j∈Neλe,j.rij

Where λe,j is the average failures, N is the total number of elements whose fault will interrupt the load point i, rij is the failure duration at load point i due to failed element j.☞ Expected Energy Not Supplied Index, EENSi (MWh per year) is given as shown in Equation (3.6):

3.6 EENSi=Pi.Ti

Where Pi is the load prior to the interruption.☞ Average SAIDI (h/year) can be given by Equation (3.7):

3.7 SAIDI=∑TiTotalnumberofcustomersserved

☞ Average SAIFI (#/year) can be given by Equation (3.8):

3.8 SAIFI=∑λiTotalnumberofcustomersserved

☞ Cost of expected energy not supplied (EENSCOST) is given in Equation (3.9):

3.9 EENScost=∑Pi.Ti.Tarrif

According to the EEPCo marketing and sales process estimation manual, the general flat rate tariff of 0.04$/kWh is used to estimate EENScost for this study.

3.4 Markov models for MCS

Modeling dependencies and interactions between different components of the power system can be challenging. For example, failure of one component can affect the reliability of other interconnected components, but capturing these dependencies accurately in the MCS can be difficult. Using Markov models can help to capture dependencies and interactions between different components with more accuracy. To apply Markov processes for reliability analysis, the following assumptions are made.☑ The system should be repairable.

☑ The life span of the system units obeys an exponential distribution.

The common steps of reliability analysis for the given system are.☑ Build transition diagram of the system: This includes defining the state of the system and drawing the transition diagram according to the failure and repair process.

☑ Formulate the state transition model: This includes defining the Markov chain and formulating the state transition equations.

☑ Compute reliability indices: Based on the state transition equations and initial states of the system, compute the reliability indices with application of Laplace transformation.

As the number of system components increases, the complexity of the state of the system also increases. Therefore, the two-state system model could have insufficient capability to meet the reliability analysis requirement [33]. Therefore, three-state Markov model is applied to evaluate the reliability of the proposed system. The three states are: State 0: Normal operating state, State 1: Partial Operating State and State 2: Failure state.

The failure and repair rate of the system are represented as λ and μ respectively and Δt represents a very short time interval. Fig. 1 shows the transition diagram of three states.Fig. 1 Transition diagram of a three-state system.

Fig. 1

Thus, based on Fig. 1, the state transition equations of the system can be derived. The probabilities of different working state are represented as: Ψ0→Normal operational state, Ψ1→Partial operational state and Ψ2→Failure state.

The three working state instantaneous transition probabilities from one state to another state can be given in Equation (3.10):3.10 [Ψ0(t+Δt)Ψ1(t+Δt)Ψ2(t+Δt)]=[1−(λ1+λ2)Δtμ1Δtμ2Δtλ1Δt1−μ1Δt0λ2Δt01−μ2Δt][Ψ0(t)Ψ1(t)Ψ2(t)]

According to the state transition map of the system as shown in Fig. 1, the state transition can be modeled as shown in Equation (3.10).

The instantaneous normal operating state transition, Ψ0 at time t, can be derived as shown in Equation (3.11):3.11 Ψ0(t)=μ1μ2λ1μ2+λ2μ1+μ1μ2−λ1(λ1+μ1−μ2)(λ1+μ1)[(λ2+μ2)−(λ1+μ1)]e−(λ1+μ1)t−λ2(λ2+μ2−μ1)(λ2+μ2)[(λ1+μ1)−(λ2+μ2)]e−(λ2+μ2)t

The instantaneous partial operating state transition, Ψ1 at time t, can be derived as shown in Equation (3.12):3.12 Ψ1(t)=λ1μ2λ1μ2+λ2μ1+μ1μ2+λ1(λ1+μ1−μ2)(λ1+μ1)[(λ2+μ2)−(λ1+μ1)]e−(λ1+μ1)t

The instantaneous failure operating state transition, Ψ2 at time t, can be derived as shown in Equation (3.13):3.13 Ψ2(t)=λ2μ1λ1μ2+λ2μ1+μ1μ2+λ2(λ2+μ2−μ1)(λ2+μ2)[(λ1+μ1)−(λ2+μ2)]e−(λ2+μ2)t

As t→∞, the steady-state probability of all states can be expressed as shown in Equation (3.14):3.14 Ψ0(∞)=μ1μ2λ1μ2+λ2μ1+μ1μ2Ψ1(∞)=λ1μ2λ1μ2+λ2μ1+μ1μ2Ψ2(∞)=λ2μ1λ1μ2+λ2μ1+μ1μ2}

By differentiating and taking the Laplace transform of Equation (3.10), the state transition can be derived as shown in Equation (3.15):3.15 sΨ0(s)−Ψ0(0)=−(λ1+λ2)Ψ0(s)+μ1Ψ1(s)+μ2Ψ2(s)sΨ1(s)−Ψ1(0)=λ1Ψ0(s)+μ1Ψ1(s)sΨ2(s)−Ψ2(0)=λ2Ψ0(s)+μ2Ψ2(s)}

ConsideringΨ(s)=(SI−A)−1Ψ(0)

Where, the term (SI−A) is shown in Equation (3.16):3.16 SI−A=[s+λ1+λ2−μ1−μ2−λ1s+μ10−λ20s+μ2]

The inversion required to find Ψ(s) can be given as shown in Equation (3.17):3.17 (SI−A)−1=[as−bs+λ1+μ1−cs+λ2+μ2].H

WhereH=[(s+μ1)(s+μ2)μ1(s+μ2)μ2(s+μ1)λ1(s+μ2)(s+λ1+λ2)(s+μ2)−λ2μ2λ1μ2λ2(s+μ1)λ2μ1(s+λ1+λ2)(s+μ1)−λ1μ1]

Applying the partial fraction, Ψ(s) can be given as shown in Equation (3.18):3.18 Ψ(s)=as[μ1μ2λ1μ2λ2μ1]+bs+λ1+μ1[−λ1(λ1+μ1−μ2)λ1(λ1+μ1−μ2)λ1λ2]+cs+λ2+μ2[−λ2(λ2+μ2−μ1)λ1λ2λ2(λ2+μ2−μ1)]

Using the adverse Laplace, Ψ(t) can be calculated as shown in Equation (3.19):3.19 Ψ(t)=a[μ1μ2λ1μ2λ2μ1]+b[−λ1(λ1+μ1−μ2)λ1(λ1+μ1−μ2)λ1λ2]e−(λ1+μ1)t+c[−λ2(λ2+μ2−μ1)λ1λ2λ2(λ2+μ2−μ1)]e−(λ2+μ2)t

Where a, b, and c are constants whose values are computed as shown in Equation (3.20):3.20 a=1(λ1+μ1)(λ2+μ2)b=1(λ1+μ1)[(λ2+μ2)−(λ1+μ1)]c=1(λ2+μ2)[(λ1+μ1)−(λ2+μ2)]}

While insuring that: ∑i=0nΨi(t)=1.

Where n is the total number of states in the system.

Moreover, as t→0, Ψ0→1, Ψ1 and Ψ2→0. On other hand as t→∞, the probability of the system under normal (Ψn) and abnormal (Ψa) working state can be given as shown in Equation (3.21):3.21 Ψn=Ψ0(∞)=μ1μ2λ1μ2+λ2μ1+μ1μ2Ψa=Ψ1(∞)+Ψ2(∞)=λ1μ2+λ2μ1λ1μ2+λ2μ1+μ1μ2}

Let Ψ denote the probability of failure of a system and xi be an indicator variable that states:{x0=0ifthesystemisnormalworkingstatex1=1ifthesystemispartialworkingstatex2=2ifthesystemisfailurestate

The probability of system failure can be estimated as shown in Equation (3.22):3.22 Ψ=1N∑i=1Nxi

Where N is the number of sample systems state.

For a large sample size, the unbiased sample variance can be given as shown in Equation (3.23):3.23 V(x)=1N∑i=1N(xi−Ψ)2

The accuracy level of MCS is given by as shown in Equation (3.24):3.24 α=1−ΨNΨ

The MCS creates fluctuating convergence. Thus, the large number of samples (N) is usually used to decrease the error bound [34]. The random number generation is common in MCS. The basic requirements for random number generation are.☑ Uniformity: Random numbers must be distributed uniformly [0, 1].

☑ Independence: Correlation between random numbers should be minimum.

☑ Long period: It should take a long period to repeat the number.

The Weibull-distributed random number generation is utilized for this study. Its PDF can be formulated as [34] shown in Equation (3.25):3.25 f(x)=βαβ[xβ−1](e[−(xα)β])

Where 0≤x<∞, α, and β > 0.

Using the inverse transform, the CDF is given as shown in Equation (3.26):3.26 U=1−e[−(xα)β]

Thus, the random variate can be computed as shown in Equation (3.27):3.27 X=α(−lnU)1β

Thus, important steps for generating Weibull-distributed random variates are.• Step 1: Generate a uniformly distributed random number sequence [0, 1].

• Step 2: Calculate the random variate X using Equation (3.27).

Fig. 2 demonstrates the process of conducting reliability analysis for the proposed system using the MCMCS technique.Fig. 2 System reliability analysis based on MCMCS

Fig. 2

3.5 Adaptive PSO formulation

PSO is a population-based optimization algorithm inspired by the social behavior of flocks of birds or schools of fish. Some of its advantages are simplicity, efficiency, robustness, flexibility, parallelism, application diversity [2]. While offering these advantages, it is important to note that no single optimization algorithm is universally superior to all others. The choice of algorithm might depend on factors such as problem characteristics, computational resources, and user expertise. It is always advisable to experiment with hybrid techniques to find the most suitable one for a particular problem. To do that, DPO and CCA techniques are introduced to increase the performance of PSO.

3.5.1 Objective functions and constraints

The objective functions (fitness) for this study are to improve bus voltage profile, reduce power loss (Ploss), and improve system reliability (SAIFI, SAIDI). These are formulated as shown in Equation (3.28):3.28 F1=min∑PlossF1=min∑|Vref−Vactual|F3=w1SAIFISAIFIt+w2SAIDISAIDIt}

Where SAIFIt, SAIDIt are the target values and the weighting values w1+w2 = 1. According to EEU, SAIFIt and SAIDIt are 20 and 25h respectively.

The constraints considered are.a. Power balance constraint: Power generated should be capable of supplying demand capacity and the system losses as formulated in Equation (3.29).

3.29 Psubstation=Pload+Ploss

b. Voltage bus constraint: Bus voltage magnitude should not be violated as formulated in Equation (3.30).

3.30 Vmin≤Vbus+Vmax

According to EEU, the maximum and minimum voltage magnitude is in the range of 1.1 and 0.90 (±10 %).c. Average failure rate and repair time: Average failure rate and repair time should be reachable as given in Equation (3.31).

3.31 λk,min≤λk≤λk,maxrk,min≤rk≤rk,max}

The average failure rate and repair time of kth element are denoted as λk and rk respectively. On the other hand, λk,min and rk,min represent the minimum reachable values for the failure rate and repair time of the kth element, λk,max and rk,max indicate the maximum allowable failure rate and repair time, respectively.d. Radial structure: To maintain the radial topology, the following criteria should not be violated:✓ Number of active lines (NL) must be one less than the number of buses (NB) as shown in Equation (3.32).

3.32 NL=NB−1

✓ The number of open switches must be equal with the total number of meshes as formulated in Equation (3.33).

3.33 Sop=Nloop

✓ The network must not have isolated nodes and the distance between node n and the substation node must be finite as formulated in Equation (3.34).

3.34 d(n,nsubstation)<∞,∀n≠nsubstation

3.5.2 DPO-based PSO formulation

In the PSO process, particles might converge to a local optimum and fail to explore other regions of the search space in the case of large systems. Thus, the DPO is introduced to encourage exploration of the search space even after convergence seems to have occurred, helping to escape local optima. DPO-PSO is an extension of the traditional PSO algorithm aimed at maintaining diversity among the solutions explored during the optimization process. This extension is particularly useful in scenarios where the search space is multi-modal with multiple optimal solutions.

To reach an optimal global solution, the particles move iteratively in search space, and the position vector Xi and the velocity vector, Vi of the particle i at tth iteration are updated as [2] shown in Equation (3.33):3.35 Vit+1=ωVit+c1r1(Pbest,it−Xit)+c2r2(Gbestt−Xit)Xit+1=Xit+Vit+1}

Where ω is the inertia weight parameter, r1 and r2 are random numbers [0, 1], c1 and c2 are social and cognitive learning factors, Pbest and Gbest are the best personal and global objective function (fitness) values as given in Equation (3.28).

For each particle, P, in the tth iteration, Pit, the new particle Pit+1 is generated by updating position and velocity according to Equation (3.35). By combining Pit and Pit+1, the new particle Pnew,it+1 having position, Xnew,it+1 and velocity Vnew,it+1 can be generated as shown in Equation (3.360:3.36 Xnew,it+1={Xit+1,ifrand[0,1]<ρXit,otherwiseVnew,it+1=Vit+1}

Where ρ is the predefined probability and it is found that 0.73 for this study resulted better performance.

The greedy selection of the particle can be given as shown in Equation (3.37):3.37 Pit+1={Pnew,it+1,iff(Pnew,it+1)≤f(Pit+1)Pit+1,otherwise

Where f(.) is the fitness function (Equation (3.28)).

The main steps to be followed for DPO-based PSO are shown in Algorithm 1.Algorithm 1 Proposed DPO-PSO algorithm1. Initialize each article in the swarm;

2. Initialize Pbest and Gbest;

3. While iter < Max_Iter do

4.  For i = 1 to N do

5.  Calculate velocity of particle i according to eqn (3.35) (i);

6.  Update position of particle i according to eqn (3.35) (ii);

7.  Calculate the fitness value (eqn. (3.28)) of particle i;

8.  Iter = Iter+1;

/* DPO mechanism*/

9  Generate a new particle according to eqn (3.36);

10.  Calculate the fitness value (eqn. (3.28)) of new particle i;

11.  Select best one according to eqn. (3.37);

12.  Update Pbest and Gbest;

13.  End

14.  End

	

3.5.3 CCA based PSO formulation

The one drawback of the PSO algorithm is that its performance can be sensitive to its parameters and dependent on them. The CCA as an adaptive inertia weight control strategy used to dynamically adjust the PSO parameter during the optimization process. In this technique, the inertia weight is calculated on the basis of a constriction coefficient that is used to balance the cognitive and social components of the particle's velocity.

The inertia weight parameter can be modeled as shown in Equation (3.38):3.38 ω=ωmax−(ωmax−ωminMaxIter)Iter

According to Ref. [35], the CCA to ensure stable convergence of the PSO algorithm is given by as shown in Equation (3.39):3.39 Vit+1=Π[ωVit+c1r1(Pbest,it−Xijt)+c2r2(Gbestt−Xit)]

Where, Π can be formulated as shown in Equation (3.40)3.40 Π=22−φ−φ2−4φ,φ=c1+c2

To guarantee stability, φ ≥ 4. However, as φ increases, Π deceases and this could result in decreased diversification with slow response. Thus, adaptation of Π by introducing the control parameters is proposed here.

Updating velocity can be performed as shown in Equation (3.41):3.41 Vit+1=Πt+1[ωVit+c1r1(Pbest,it−Xijt)+c2r2(Gbestt−Xit)]

Where, Πt+1 can be formulated as shown in Equation (3.42)3.42 Πt+1=[1−(IterMaxIter)ξ]rand[0,1]

Here ξ is used to adjust the rate of velocity reduction. If ξ is large, it will slow down the reduction of Π, thus reducing the speed and losing the balance of exploration and exploitation. If ξ is so small, the algorithm might pre-maturely converge, thus resulting in the trapping of local optima. Through various experiments, the value of ξ is considered to be 3 for this study.

It is worth mentioning that the second term in equation (3.41) represents the cognitive part, where the particle changes its velocity based on its own knowledge, and the third term represents the social part, where the particle changes its velocity based on social adaptation.

3.6 Overall proposed procedures

To maintain a DNR, the suggested solution algorithm includes the subsequent switching operational sequences.☑ The initial operation involves opening the switch.

☑ If the radial network structure is compromised by closing a switch (Equation (3.33)), that particular switch could result in a node receiving power from two directions.

☑ If inter-loops persist after previous step, one switch in the loop is randomly opened.

☑ To maintain a radial network structure, only one switch is allowed to be open in each mesh. Thus, the total number of open switches is equal to the total number of meshes (Equation (3.34)).

☑ To prevent any feeder section from being left out of service, a switch that is not part of any mesh must be closed (Equations 3.32, 3.33)).

The main steps to be followed for the proposed algorithm are shown in Algorithm 2.Algorithm 2 Proposed DPO-CCA-based PSO algorithm1. Initialize each particle in the swarm; Pbest and Gbest;

2. While iter < Max_Iter do

3.  For i = 1 to N do

4.  Calculate velocity of particle i according to eqn (3.35) (i);

5.  Update position of particle i according to eqn (3.35) (ii);

6.  Calculate the fitness value (eqn. (3.28)) of particle i;

7.  Iter = Iter+1;

/* DPO and CCA mechanism*/

8  Calculate constriction coefficient according to eqn (3.42)

9.  Update velocity of particle i according to eqn (3.41)

10.  Update position of particle i according to eqn (3.35) (ii);

11.  Generate a new particle according to eqn (3.36);

12.  Calculate the fitness value (eqn. (3.28)) of new particle i;

13.  Select best one according to eqn (3.37);

14.  Update Pbest and Gbest;

15.  End, End

	

The aim of this study is to identify the optimal DNR that minimizes power losses, bus voltage deviation, and reliability indices, all while adhering to a specific set of constraints. With these goals in mind, DNR points can be obtained by analyzing network connectivity. The network topology changes scheme subroutine to determine tie-switches that placed in each mesh of the network is shown in Fig. 3.Fig. 3 Flow chart of the distribution network topology update.

Fig. 3

In a DNR study using APSO, each particle represents a potential candidate configuration in the system. Here is how the APSO algorithm works in the context of DNR.☑ Initialization: Initially, a population is generated randomly within the search space.

☑ Particle (X): It is a candidate solution represented by a d-dimensional vector where d is the number of optimized parameters. Each particle represents a possible DNR, which includes the status (open or closed) of switches at various locations. The particle encodes the switching states of the switches, defining which lines are open and which are closed.

☑ Population: It is set of n particles at time t, i.e. Pop(t) = [X1(t), …, Xn(t)]T.

☑ Fitness Evaluation: Fitness of each particle is evaluated as per Equation (3.28).

☑ Adaptation Mechanism: Incorporate adaptive mechanisms within the PSO algorithm.

☑ Velocity and position update: Update the velocity and position using APSO equations.• Each particle iteratively updates its velocity and position in the search space according to its own experience (Pbest) and the social-collective experience of the swarm (Gbest).

• This adjustment is guided by the equations of the APSO algorithm (Equation (3.36) up to 3.42), which aim to explore promising regions of the search space while exploiting the best solutions found so far.

• Updating is based on the fitness evaluations (Equation (3.28)) until convergence criteria are attained.

☑ Solution extraction: Extract the best performing particle(s) representing the optimal DNR that determine the switching actions to achieve the defined objectives.

The steps to follow for an optimal DNR with the proposed algorithm are shown in Fig. 4. The main steps are summarized as follows.Fig. 4 Network reconfiguration using proposed APSO.

Fig. 4

Step 1 Input power loss and disconnected branch set of reconfiguration as initial solution

Step 2 Close the disconnected branch and open its neighborhood branches in the loop.

Step 3 Is there load between closed and disconnected switches?

• If yes, go to step 4.

• Else, disconnect the next branch according to the search direction and go to step 4.

Step 4 Do the newly generated network satisfy operating constraints?

• If yes, add these switches to network and go to step 5

• Else, discard these switches and go to step 5

Step 5 Have all loops been searched?

• If yes, go to step 6.

• Else, go to the next loop and return to step 2

Step 6 Select the network with minimum objective function values in switches set.

• If fitness value is same as last iteration, output the results.

• Else, go to step 2

4 Results and discussion

The initial control parameters of the PSO algorithm are given in Table 1. The number of dimensions represent the required number of tie-switches within the system. Identification of loops is done through network modeling, where loops are identified based on the connectivity of network branches.Table 1 Initial PSO control parameters and tie-switches for DNR.

Table 1Parameters	Values	
Number of particles	10	
Number of iterations	50	
Acceleration coefficients (c1 and c2)	[2.2, 2.2]	
PSO momentum (wmax and wmin)	[1.2, 0.3]	
Dimensions (DNR loops)	5	
Initial tie-switches locations	[114,115,116 117 118]	

The five new tie-switches locations to be considered initially are [114,115,116 117 and 118]. For the proposed objectives, the system must first be reconfigured. The proposed APSO algorithm is utilized for DNR by using MATLAB software. The number of tie switches in the system should not be greater than that of the number of meshed loops.

Initially, the proposed power distribution network is made to have five meshed-loops, and the normally closed (NC) switches in each loop are shown in Table 2. These NC switches are considered as lines (branches) in the given loop. The single line diagram of the existing system with initial tie-switches before proposed reconfiguration is shown in Fig. 5.Table 2 Initial loops and normally closed switches.

Table 2Loop 1: 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 114	
Loop 2: 35, 36, 37, 38, 46, 47, 48, 49, 50, 51, 52, 53, 115	
Loop 3: 54, 55, 59, 64, 65, 66, 67, 68, 116	
Loop 4: 69, 70, 71, 72, 80, 85, 86, 87, 88, 89, 90, 91, 92, 93, 117	
Loop 5: 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 118	

Fig. 5 Layout of the existing system before reconfiguration with initial TSs.

Fig. 5

The initial and optimal DNR points are shown in Table 3. Thus, based on the resulting optimal tie-switches locations, the network configuration is modified, and BFS and MCMCS are analyzed.Table 3 Initial and optimal DNR points for proposed objectives.

Table 3Loop	Initial switches	Opening switches	Tie-switch location	
#	From bus	To bus	Length (m)	From bus	To bus	Length (m)	From bus	To bus	Length (m)	
1	18	31	642	27	28	773	18	28	971	
2	39	54	403	50	51	442	39	54	390	
3	17	69	981	66	67	909	17	69	882	
4	70	94	520	93	94	484	67	94	508	
5	98	110	604	106	107	204	98	110	604	

Various combinations of loops are repeatedly examined by simulation of the system. The optimal candidate DNR points are presented in Table 4.Table 4 Optimal combination of tie-switches and reliability.

Table 4

As shown in Table 4, the tie-switch combination of case three resulted in the best result than other combinations. Through repeated examination and analysis of power loss, bus voltage profile, and reliability, the final proposed network configuration is presented in Fig. 6.Fig. 6 Layout of the reconfigured distribution network.

Fig. 6

4.1 Bus voltage profile

The BFS load flow is carried out using the network peak demand data. From six-month peak session field measurement data, the minimum and average bus voltage magnitudes ever recorded are found to be about 0.7447pu and 0.9157pu, respectively. From the initial case load flow analysis, the minimum and average bus voltage magnitudes are found to be about 0.7537pu and 0.9037pu, respectively. These values with proposed DNR based load flow analysis are found to be approximately 0.9502pu and 0.9674pu, respectively.

From bus #66 up to #110 the bus voltage magnitude is less than the national standard of 0.90pu for both field data and initial case load flow analysis. Fig. 7 shows the bus voltage profile for all buses during each scenario.Fig. 7 Bus voltage profile during each scenario.

Fig. 7

As shown in Fig. 7, the area between the 93rd and 110th bus is occupied by a Hospital and Industries that have installed voltage regulation equipment at their own expense. These devices, while not meeting the EEU standard utility scale requirements, do have some influence on the system but have been omitted from the load flow analysis in this research.

4.2 Power losses

According to the EEU Wolaita Sodo district estimate of active power loss as of 2023, the actual power loss of the network is found to be approximately 1650.29 kW (that is, 22.3 % of total generation). The initial load flow analysis of the case resulted in an active power loss of about 1631.14 kW. Although, after application of optimal DNR, the active power loss is found to be about 559.35 kW. The active power loss of each branch is presented in Fig. 8.Fig. 8 Active power loss of each branch before and after DNR.

Fig. 8

Based on Fig. 8, the branch with the highest active power loss is branch #54, which links bus #17 to #55, with a magnitude of about 170.1 kW. This occurrence may be attributed to its length within the system compared to other branches. By implementing the optimal DNR, the power loss can be significantly decreased from 170.1 kW to about 56.89 kW.

The reactive power loss values before and after application of the optimal DNR is found to be about 1448.2 kVAR and 455.03 kVAR respectively. The reactive power loss of each branch is presented in Fig. 9.Fig. 9 Reactive power loss of each branch before and after DNR.

Fig. 9

4.3 Reliability

After reconfiguring the network using the placement of the switches in their candidate locations in the system, the presentation of the reliability of the system with the application of MCMCS for each performance of the switch (TS) is presented as shown in Table 5.Table 5 Reliability indices under increasing TS.

Table 5Year	SAIFI	SAIDI (h)	EENS (MWh)	Ecost ($)	
Initial	557	573.59	1835.50	68,396.53	
One TS	203	211.57	1177.02	43,859.48	
Two TS	123	156.43	923.57	34,366.53	
Three TS	62	86.74	477.68	17,774.72	
Four TS	50	60.19	192.61	7167.12	
Five TS	34	43.87	140.38	5223.61	

As shown in Tables 5 and if five TS units are integrated within the distribution network, the resulting reliability can be summarized as follows.☞ The number of interruptions could decrease from 557 as of 2023 to 34 annually.

☞ The duration of interruptions could be reduced from 573.59h to about 43.87h.

☞ The energy lost due to sustained interruptions is decreased from 1835.5 MWh to about 140.38 MWh annually.

☞ The cost of energy lost due to sustained interruptions that the utility loses is decreased from 68,396.53$ to about 5223.61$ annually.

4.4 Performance comparison

Table 6 presents the performance of the proposed algorithm in terms of response time. The results demonstrate a notable enhancement for adaptive scenarios, specifically the DPO-PSO and CCA-PSO cases. However, it is worth noting that the proposed DPO-CCA-PSO algorithm surpasses the performance of other variants.Table 6 Comparison of variant PSO techniques.

Table 6Algorithms	Response time	Total Ploss (kW)	Iterations taken	
Basic-PSO	0.0201	567.15	39	
DPO-PSO	0.0163	560.02	27	
CCA-PSO	0.0188	566.43	34	
DPO-CCA-PSO	0.0104	559.35	21	

The performance of the algorithm under consideration in terms of active power loss is illustrated in Fig. 10. The DPO-CCA-PSO algorithm proposed achieved a convergence to an active power loss level of 559.35 kW after around 21 iterations, outperforming other variations in terms of both power loss reduction and response time.Fig. 10 Comparison of PSO algorithm variants regarding power loss.

Fig. 10

5 Conclusions

Improvement of the voltage profile, minimization of power loss and improvement of reliability are crucial objectives in power systems to ensure stable and reliable electricity delivery. This study investigated the APSO-based DNR for the Wolaita Sodo town distribution system. The proposed system includes 113 distribution transformers having a peak demand of about 7.4 MW. For load flow analysis, the base values of the system are considered 20MVA and 15 kV for power and voltage, respectively. To find the line impedance data, the mathematical modeling is considered using the measured length of each branch. Peak demand is calculated from measured voltage and current records during data collection periods.

The DNR was designed to improve the power flow and reliability of the system. The DPO-CCA-PSO method is utilized to determine the optimal locations of the tie-switches. Thus, the TS locations are determined and, subsequently, the system bus voltage, power loss, and reliability indices are computed. The BFS-based power flow analysis and MCMCS-based reliability analysis were implemented by using MATLAB. Finally, the performance of the proposed algorithm variants is assessed by considering factors such as response time, convergence, and reduction in power loss.

Data availability statement

Research data supporting the study's findings is provided as supplementary material.

CRediT authorship contribution statement

Ashenafi Tesfaye Tantu: Writing – original draft, Validation, Supervision, Software, Project administration, Methodology, Investigation, Formal analysis, Conceptualization. Degu Bibiso Biramo: Writing – review & editing, Visualization, Validation, Investigation.

Declaration of competing interest

The authors declare no competing interests.

Appendix A Supplementary data

The following is the Supplementary data to this article:Multimedia component 1

Multimedia component 1

Acknowledgement

The authors thank the technicians of the Wolaita Sodo town distribution network and the ECE department technical assistance staff of Wolaita Sodo University. As we wrap up the data collection period for six months, we wanted to take a moment to express our deepest gratitude for your invaluable contribution and unwavering dedication to ensuring the success of our study. We extend our sincere thanks for your hard work during this process. Your contributions have been indispensable, and we could not have accomplished what we have without you.

Appendix A Supplementary data to this article can be found online at https://doi.org/10.1016/j.heliyon.2024.e36668.
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