Optimizing Techno-Economic Framework of REGs in Capacitive Supported Optimal Distribution Network

Abstract

This study describes the optimization of Distribution Network Structure (DNS) by altering sectionalizing and tie-switches with Reactive Power Injections (RPI) through optimal nodes under three load variations considering five different cases in Electric Distribution Networks (EDNs) to reduce Energy Loss (E_Loss), thereby achieving Economic Benefit (EB), which is the first step process. This approach yields EBs only to some extent. To achieve a greater reduction in E_Loss, enhancing bus voltage profile and to achieve additional EBs, this study examines the incorporation of Renewable Energy Generations (IREGs) into the optimal EDNs with reactive power support. The optimal energy has been purchased from the Independent Power Producers (IPPs). Besides, the Levy Flight Mechanism (LFM) integrated Seagull Optimization Algorithm (SOA) has been applied to solve the Economic Based Objective Function. The effectiveness of the developed methodology has been validated using IEEE 33-bus and a real 74-bus Myanmar EDN. The reductions in E_Loss achieved by LFM-SOA have been compared with those of other existing methods in the literature for all the cases. The results reveals that the developed methodology efficiently achieves more EBs ($) for all the cases by optimizing DNSA with and without RPIs and IREGs.

1. Introduction

At the outset, it is notable that roughly 30% of the collective power losses within Electric Distribution Networks (EDNs) of utilities across France, Germany, and the UK are exclusively attributed to the low voltage grids [1]. Likewise, in India, significant strides have been made in mitigating T&D losses through reforms in the electric power sector. As a result, in the fiscal year 2001–02, the overall Power Loss (P_Loss) dropped from 37% to 24.6% [2]. Network power losses can express how efficiently Distribution Network Operators (DNOs) supply electric energy to their consumers, which is considered to be the most critical performance indicator for evaluating EDN.

Conversely, the continual increase in energy demand and the swift depletion of resources in conventional power generation and transmission networks place mounting pressure on DNO to enhance the overall performance and guarantee the optimal operation of EDN. Most EDNs are generally formed as radial type, consisting of sectionalizing and tie-switches. Some of the standard methods to alleviate the Energy Loss (E_Loss) with enhancement in bus voltage profile are Distribution Network Structure Alteration (DNSA), optimal conductor selection, power balancing, optimal Reactive Power Injection (RPI), and Integration of Renewable Energy Generation (IREG). However, researchers have focused more on independent or joined optimization of DNS, RPI, and IREG optimizations for the past four decades.

In the 1980s, DNSA optimization emerged as a traditional technique. It involved adjusting the feeder’s topological structure by manipulating the open/close positions of sectionalizing and tie-switches. This adjustment occurred during emergencies or normal operations, with a key condition that radiality structure must be maintained throughout the optimization process. Critical goals like reducing P_Loss/E_Loss, improving the bus voltage stability, distributing loads evenly throughout the network, increasing productivity, stimulating economic growth, and guaranteeing prompt service restoration during emergencies can all be accomplished by optimizing DNSA. Over the past four decades, a multitude of research papers have addressed and solved problems through the implementation of DNSA [3,4,5].

Likewise, some of the reactive power demand from the Main Energy Supply (MES) can be reduced by optimizing RPI at key locations close to the loads within the radial EDN. This optimization can result in decreased real and reactive power losses (P_Loss & Q_Loss), enhanced bus voltage profiles, reduced need for feeder capability release, alleviated loading on thermally constrained equipment, alleviated load congestion, and improved power factor of the MES. As a result, it is possible to deliver real power output to end consumers more effectively. They are maximizing EB hinges on several factors, including minimizing E_Loss, strategically purchasing capacitors based on appropriate sizing and managing their associated costs, and determining the optimal locations, and types of capacitors to be deployed at required buses. It is crucial to note that installing capacitors at non-optimal locations can counteract the intended goals. In EDNs, researchers have dedicated significant attention to the study of reactive power support over the past four decades, as evidenced by a surfeit of research papers [6,7,8,9,10,11,12,13,14].

The above-discussed papers [3,4,5,6,7,8,9,10,11,12,13,14] focused on the individual operation of either DNSA or RPIs, which are two techniques performing well in reducing E_Loss and improving the bus voltage profiles. RPI optimization alone is inadequate and only DNSA optimization does not help in solving the problem during heavy load variations in achieving E_Loss reduction efficiently with enhancement in the bus voltage profile. Optimizing RPI or DNSA individually will not achieve the minimum loss configuration [15]. In contrast, the combined operation of RPIs and DNS alteration is a feasible choice to increase the EB through E_Loss reduction and further enhancement in bus voltage profile compared to separate optimization of RPIs or DNS alteration. Simultaneously selecting optimal nodes for RPI and sizing them alongside DNSA constitutes a nonlinear, complex, combinatorial, and mixed-integer optimization problem involving integer and discrete variables. Therefore, achieving optimal positions and determining capacities for reactive power devices along with appropriate network restructuring, plays a vital part in the organization and management of EDN. Research articles on P_Loss/E_Loss reduction or operating cost minimization in EDN that take DNSA optimization and RPIs optimization into consideration are quite limited [15,16,17,18,19,20,21,22,23,24,25].

The four different algorithms used in [16] to optimize RPIs and simultaneously optimize DNSA with RPIs are MBBO, MBFBO, CS, and MIC. These optimization efforts reduce P_Loss and E_Loss, enhance voltage profiles, and increase EBs. In this work, typical IEEE 33 & PG&E 69-bus test systems have been used to assess the algorithms’ performance. In [17], optimization algorithms such as MBBO, BTLBO, and DDE have been engaged for optimal DNSA optimization and RPI optimization after DNSA considering the same IEEE 33 and PG&E 69-bus test systems. P_Loss reduction with bus voltage and branch current limits have been considered an objective function [17]. Ref [18] adopts Dingo Optimizer to investigate the RPI optimization simultaneous with DNSA considering IEEE 33 bus system. Application of mathematical programming-based optimization (i.e.,) Mixed-integer Linear Programming model to solve simultaneous optimal DNSA and RPIs in radial EDN which is recasting into a single MILP problem has been suggested in [19]. The proposed model has been solved using commercially available software. To prove the efficacy of the proposed methodology, seven test systems such as IEEE 33, PG&E 69, TPC 83, Indian 119, Brazil 136, practical 202 and 417 buses have been validated. In [20], the Modified Particle Swarm Optimization (MPSO) algorithm has been used to implement RPIs at optimal buses alongside DNSA. The objective is to minimize both active and reactive power losses while enhancing power factor and voltage profile. Adaptive Whale Optimization Algorithm (AWOA) based two-stage optimization approach using DNSA with and without optimal RPIs at three nodes to reduce P_Loss and operational cost in the EDN has been carried out in [21]. This paper considers the loss sensitivity index-based selection of optimal nodes for reactive power compensation. Real and reactive power compensation with DNSA under six cases using AGPSO as an optimization method has been analyzed in [22]. Optimization of RPIs, and DNSA under four different cases using PGSA as optimization tool has been suggested in [23]. Loss sensitivity factor has been utilized to find the most appropriate nodes for reactive power compensation. This work considers P_Loss reduction, voltage, and current violation parameters as objective function. BSSA as optimization technique, optimal allocation of RPIs with DNSA in EDN has been used in [24]. Similar to [23], the goal of [24] also focuses on lowering P_Loss while abiding by restrictions of bus voltage and line current infractions with reliability assessment. Three distinct scenarios have been studied in this paper such as DNSA after RPIs, RPIs after DNSA and simultaneous application of DNSA and RPIs. IEEE 33-bus and PG&E 69 bus test system have been taken to prove the efficacy of the proposed technique. P_Loss and capacitor investment cost minimization as objective optimal allocation and sizing of RPIs with/without DNSA using MTS-HSSA Algorithm has been proposed in [25]. Power loss index has been utilized to provide a good initial solution. Two balanced EDN (IEEE 33 & Indian 119) and one unbalanced EDN (123 bus) were taken to prove the credibility of the proposed optimization technique.

With the remarkable advancement in IREG technologies, their amalgamation with EDN is an elegant planning choice for EDN operators. From [26], it is evident that PV generation holds tremendous potential in India owing to the abundant availability of solar irradiation across most regions of the country. Minimizing E_Loss in the EDN with the integration of REG penetration is the main criterion for obtaining EB. Most EDN operators operate under regulations where the IREG is anticipated to function at a fixed power factor equal to one [27]. However, reactive power support assistance in EDNs has been recognized by certain EDN operators [27]. Many research works have reported IREGs in EDN for the last two decades [28,29,30,31,32]. However, studies such as [33,34,35,36,37,38] have demonstrated that the combined optimization of DNS, RPI, and IREG in EDN leads to even further improved performance compared to the individual or integrated optimization of any two methods. This improvement is achieved while ensuring the satisfaction of both equality and inequality constraints.

Hence, to achieve additional E_Loss reduction and more EBs, in this study, the focus is on the optimal allocation and sizing of REGs with unity power factor at two or three optimal locations within the reactive power supported optimal EDN, known to be the final phase of E_Loss reduction. On the other hand, higher REG penetration will create voltage problems, islanding, and protection issues. Therefore, this study considers the maximum penetration level of real power injection as 50% of the total real power demand plus E_Loss after RPI optimization with DNSA. However, there is no restriction on RPIs. This study uses a real 74-bus three-feeder EDN in Myanmar in addition to typical IEEE 33-bus test equipment to validate the efficacy of the suggested approach. The aim is to achieve a higher reduction in E_Loss, consequently leading to an increase in EB.

The Seagull Optimization method (SOA) created in 2019 [39], is a fast, creative, reliable, and computationally efficient optimization method that has been used in this work. This algorithm draws inspiration from the migrating and attacking behaviors of seagulls. According to [39], it is evident that SOA offers several competitive advantages over other algorithms when applied to a range of practical engineering problems. This study proposes a modification to the SOA by integrating the LFM to solve the EBOF problem. The efficacy of the LFM-SOA has been recognized in minimizing E_Loss and EB through a two-stage optimization process. In the first stage, the optimization involves DNSA and RPI sequentially. IREGs are positioned at optimal nodes inside the reactive power supported optimal EDN in the second stage.

Considering the above-debated features, the work’s contribution includes (i) Evaluation of the impact of EBs against E_Loss reduction using RPI optimization with DNSA considering only two nodes for the standard IEEE 33 bus system, (ii) A new EBOF to maximize the EB using IREG in capacitive penetrated optimal EDN (iii) Suggestion of futuristic LFM-SOA in solving the EBOFs (iv) prologue of a new real 74 bus three feeder Myanmar EDN for RPI optimization with DNSA and IREG.

The full work has been segregated into 5 sections. Section 2 explains that the mathematical formulation starts with EBOFs and the necessary constraints to perform the optimal RPIs with DNS optimization and IREG. In Section 3, the suggested approach, LFM-SOA, is examined along with how well it can solve the EBOF issue. It includes a detailed discussion of the methodology along with its flowchart tailored for the EBOF problem. In Section 4, the simulations are conducted, and the results obtained are thoroughly analyzed and discussed. Finally, Section 5 concludes by summarizing the obtained results and provides references for further exploration.

2. Mathematical Description of the Problem Statement

The purpose of RPI optimization with DNSA and IREGs in the radial EDN is to maximize the EB by reducing E_Loss, reduction in capacitor investment cost, and REG Energy Purchase Cost (REGEPC) subject to the satisfaction of power balance constraints and inequality constraints. The mathematical representation of the objective function is as given by (1).

2.1. Objective Function

Maximize: Economic Benefit (MEB) = (EG)_A + (EG)_B

(1)

where (EG)_A relates to the EB achieved by optimizing DNSA with and without optimal RPIs under three different load levels and (EG)_B relates to the EB attained by optimal energy purchase (REGEP) from independent power producers (investor-owned type-I DG power plant) and energy loss reduction cost before and after IREG. where

$${\left(\mathrm{EG}\right)}_{\mathrm{A}}=[{\mathrm{K}}_{\mathrm{MES}} \times {\displaystyle \sum _{l=1}^{{\mathrm{N}}_{\mathrm{LL}}}{(\mathrm{T}}_{\left(l\right)}} \times {\left({{\displaystyle \mathrm{P}}}_{\mathrm{TL}}^{\mathrm{BCP}} - {{\displaystyle \mathrm{P}}}_{\mathrm{TL}}^{\mathrm{ACP}}\right)}_{(l)}\left)\right]-[{\mathrm{K}}_{\mathrm{CAP}} \times {\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{TCN}}{{\displaystyle \mathrm{Q}}}_{\mathrm{C}\left(\mathrm{j}\right)}}+({{\displaystyle \mathrm{K}}}_{\mathrm{OM}} \times \mathrm{TCN}\left)\right]$$

$${\left(\mathrm{EG}\right)}_{\mathrm{B}}=\left[\right({\mathrm{K}}_{\mathrm{MES}}-{\mathrm{K}}_{\mathrm{REG}}) \times {\displaystyle \sum _{l=1}^{{\mathrm{N}}_{\mathrm{LL}}}{{\displaystyle \mathrm{T}}}_{\left(l\right)}} \times {\displaystyle \sum _{\mathrm{c}=1}^{\mathrm{NREG}}{{\displaystyle \mathrm{P}}}_{\mathrm{REG}(\mathrm{c},l)}}]+[{{\displaystyle \mathrm{K}}}_{\mathrm{MES}}\times {\displaystyle \sum _{l=1}^{{\mathrm{N}}_{\mathrm{LL}}}{{\displaystyle (\mathrm{T}}}_{\left(l\right)}}{{\displaystyle \times ({{\displaystyle \mathrm{P}}}_{\mathrm{TL}}^{\mathrm{BIREG}}-{{\displaystyle \mathrm{P}}}_{\mathrm{TL}}^{\mathrm{AIREG}})}}_{\left(l\right)}\left)\right]$$

From (EG)_A and (EG)_B, it is understandable that K_MES, K_CAP, K_OM, and K_REG are the cost factors referring to the Main Energy Supply, Capacitor purchase, operation and maintenance, and REG energy purchase, respectively. PREG indicates the real power injection by the type—I DG (REGEP) in kW. ‘T’ indicates the time duration (hours) at l^th load level. N_LL, TCN, and NREG indicates the number of load levels, the total number of nodes that require reactive power support, and the total number of nodes for real power injections by REGs. BCP, ACP, BIREG, and AIREG denotes before and after capacitor placement and before and after IREGs.

2.2. Power Balance Constraints

Throughout the optimization process, the power flow equations in the EDN must be met. The following can be used to quantitatively express these equality constraints, which include the active and reactive power balancing constraints represented by two nonlinear recursive power flow equations:

$$Q_{\mathrm{MES}}-\sum Q_D+\sum _j^{\mathit{TCN}}{Q}_{C\left(j\right)}-Q_{\mathit{TL}}=0 (\mathrm{Cases} 2 \mathrm{to} 5)$$

(2)

$$P_{\mathrm{MES}}-\sum P_D+\sum _{c=1}^{\mathit{NREG}}{P}_{\mathrm{REG}\left(\mathrm{c}\right)}-P_{\mathit{TL}}=0 (\mathrm{Cases} 6, 7 \& 8)$$

(3)

2.3. Inequality Constraints

2.3.1. Reactive Power Compensation Limit

The total reactive power injection penetration limit can be stated as

$${\displaystyle \sum _j^{TCN}{Q}_{C(j)}}\le ({\displaystyle \sum Q_D}+Q_{TL})$$

(4)

The total capacity of the reactive power compensation should be lower than the total reactive power demand of the EDN plus Q_TL.

2.3.2. Real Power Compensation Limit

The Penetration limit of real power injection can be stated as

$${\displaystyle \sum _c^{NREG}{P}_{REG(c)}}\le (\lambda )\times (\sum P_D+P_{TL})$$

(5)

where λ indicates the penetration limit of the REG energy which lies between 0 and 1. In other words, the total capacity of the REGs should be less than that of the total real power demand of the EDN plus P_TL.

2.3.3. Real and Reactive Power Constraint Limit

The real and reactive power injection limit by the REG at c^th bus and capacitor at j^th bus can be stated as

$$\left.\begin{array}{c}{P}_{\mathit{REG}\left(c\right)}^{\min }\le P_{\mathit{REG}\left(c\right)}\le P_{\mathit{REG}\left(c\right)}^{\max }\\ Q_{C\left(j\right)}^{\min }\le Q_{C\left(j\right)}\le Q_{C\left(j\right)}^{\max }\end{array}\right\}$$

(6)

2.3.4. Bus Voltage Limitation

Node voltage range can be stated as \

$$V_{(c)}^{\min }\le V_{(c)}\le V_{(c)}^{\max }$$

(7)

After compensation, the node voltage magnitudes within the EDN must remain well within acceptable limits.

2.4. Radiality and Isolation Constraints

It is essential to keep the EDN in a radiality structure to stop excessive current flow. Therefore, to maintain radiality during DNSA, several limitations need to be considered. Choosing the appropriate switches for opening (Sectionalizing switches)/closing (tie-switches) requires lot of guidelines and protocols. Sectionalizing switches that contribute to a mesh network by being linked to the sources and not being a part of any loop have to stay closed.

Isolation Constraints: To guarantee a constant power supply to all loads, all nodes must stay energised and restarted throughout DNSA. As a result, no customers shall lose power during the reconfiguration process and all buses should stay connected.

2.5. Assumptions

In this study, the following assumptions are made:

(a)

EDNs considered here are supposed to be balanced.

(b)

Loads are modelled as a constant power model only.

(c)

Only type I REG is considered here which generates active power only (i.e.,) unity pf.

(d)

Under the power purchase agreement, the DNO procures power from IPPs. Consequently, costs associated with the purchase, installation, operation, and maintenance of REG equipment are not covered by this arrangement.

(e)

This work has not taken into account the feeder switch operation and maintenance cost which is considered to be negligible.

2.6. Electrical Distribution Network Power Flow (EDNPF)

To analyze the steady-state performance of EDN and for proper planning of power transfer in the modern EDN, it is mandatory to carry out PF analysis which is one of the most common computational procedures used at the time of solving the optimization problem. High speed and low storage requirements, simplicity, flexibility, ease of programming, and high reliability are the key parameters to be considered for the satisfactory performance of an EDNPF. Due to the radial configuration of the EDN with a high R/X ratio and the challenges associated with handling power balance equations, it has been recognized in previous published works that conventional PF methods such as Gauss-Seidel, Newton-Raphson, and Fast Decoupled PF, commonly used for Transmission networks, may not be suitable for radial EDNs. These methods often require significant time and numerous iterations to converge [40,41]

To ensure accurate results, this study adopts a robust, fast, flexible, and computationally efficient EDNPF method. This method is based on a recursive function and utilizes a linked-list data structure specifically designed for power flow analysis [35]. The author leverages the tree-like structure of the EDN by efficiently utilizing dynamic data structures. The integration of IREGs into the EDN leads to a change in the direction of power flow, transitioning from unidirectional to bidirectional. The state of the EDN becomes critical to a greater extent and there is a significant increase in complexity as well. Though EDNPF [42] is not intended to solve radial EDNs with REGs, however the same EDNPF has been further developed in [43], which can solve radial EDNs with IREG. This EDNPF [43] has been utilized in this work to solve the EOF. A mathematical formulation of EDNPF can be found in [22].

3. Proposed Methodology for the Chosen Problem (LFM-SOA)

Optimizing problems with numerous variables and constraints presents inherent complexities, often resulting in suboptimal solutions when employing classical numerical methods. In contrast, Swarm-based Optimization Algorithms provide a more accessible approach to address such challenges, necessitating less intricate parameterization than evolutionary algorithms. Nevertheless, attaining optimal outcomes requires striking a delicate balance between exploration and exploitation within the search space. This paper briefly discusses the rationale behind adopting Swarm-based Optimization Algorithms, particularly focusing on the development of LFM-SOA, and presents its mathematical modeling approach.

The avian family Laridae encompasses diverse species, with seagulls among its notable members. These birds exhibit a broad spectrum of masses and lengths and possess a sophisticated diet comprising insects, fish, reptiles, amphibians, earthworms, and more. Predominantly adorned with white feathers, seagulls display remarkable adaptations in their feeding behaviors. They employ tactics such as dispersing breadcrumbs and emitting rain-like noises with their feet to attract fish and earthworms. Notably, seagulls possess a unique pair of glands above their eyes, specifically evolved to flush out salt by opening their bills, allowing them to drink both fresh and saltwater.

Seagulls are known for their gregarious nature, often forming colonies where they harness their cunning to locate and capture prey. During migration, a critical aspect of their behavior involves identifying the most abundant food sources to sustain their energy needs. This migratory and foraging behavior can be delineated into several key tasks: (i) Adjusting initial positions to avert collisions among individuals. (ii) Migrating in cohesive groups, following the trajectory of the fittest individual, thereby optimizing chances of survival. (iii) Utilizing the fitness of select individuals to inform and update the initial placements of the group. In addition, seagulls have a characteristic corkscrew gait, especially while attacking migrant birds as they pass across aquatic bodies of water. These complex behaviors can be conceptualized and modeled as an objective function to be optimized, offering insights into the adaptive strategies employed by these avian predators. See [18] for a depiction of the conceptual model illustrating these seagull behaviors.

3.1. SOA Mathematical Formulation

Seagull’s two natural behaviors (migration and attacking) are formulated as mathematical modeling which has been discussed in this section

3.1.1. Exploration—Migration Behaviour

In the simulation of seagull migration, three key conditions were meticulously considered to ensure the smooth navigation of the flock:

Preventing collisions: To address the risk of collisions with neighboring seagulls, a novel variable “A” was introduced into the Equation (8) and (9). This addition enhances the calculation of the new search agent position, thereby minimizing the likelihood of mid-air collisions and ensuring the flock’s safety [39].

$${{\displaystyle \overrightarrow{C}}}_S=\mathrm{A} \times {{\displaystyle \overrightarrow{P}}}_S(X)$$

(8)

$$\mathrm{A}={{\displaystyle f}}_C - (\mathrm{X} \times ({{\displaystyle f}}_C÷{{\displaystyle Max}}_{iteration}))$$

(9)

In which X = 0, 1, 2………… Max. _iteration

${{\displaystyle \overrightarrow{C}}}_S$—the search agent’s role (does not overlap with another search agent)

${{\displaystyle \overrightarrow{P}}}_S$—The search agent’s current location

X—represents the latest version,

A represents how a search agent navigates a specific search space.

${{\displaystyle f}}_C$—Managing the frequency of variable A, which is a linear drop from f_c to 0 (f_c is set to 2) [39] contains a thorough explanation of f_c’s sensitivity analysis.

Moving in the direction of the best neighbor: Following the avoidance of neighbor-to-neighbor collisions, the search agents proceed to move in the direction of the best neighbor. This strategic adjustment enables the flock of seagulls to capitalize on the guidance provided by the most optimal individual within their vicinity, enhancing their overall migration trajectory and efficiency.

$${{\displaystyle \overrightarrow{M}}}_S=\mathrm{B} \times ({{\displaystyle \overrightarrow{P}}}_{bS}(X)-{{\displaystyle \overrightarrow{P}}}_S(X))$$

(10)

where—M_S is the search agent’s (P_S) position about the ideal search agent P_bs.

B—To guarantee that exploitation and exploration are fairly balanced, the behaviour is random and is calculated as

B = 2 × A² × rd          (‘rd’ is a random number between 0 and 1.)

(11)

Stay close to the top searcher: Lastly, the search agent changes its viewpoint regarding which search agent is best [39].

$${{\displaystyle \overrightarrow{D}}}_S=|{{\displaystyle \overrightarrow{C}}}_S+{{\displaystyle \overrightarrow{M}}}_S|$$

(12)

where ${{\displaystyle \overrightarrow{D}}}_S$ indicates the distance between the search agent and the optimal agent (i.e., the seagull with the lowest fitness score).

3.1.2. Exploitation—Attacking Behaviour

The operation seeks to draw attention to the extensive background and sophisticated knowledge that underpin the search process. During migration, seagulls exhibit dynamic adjustments in their attack angle and speed, showcasing their adaptive capabilities. Utilizing a combination of wing movements and body weight adjustments, seagulls maintain their airborne position with precision and finesse. However, as described in [39], the predator assumes a characteristic spiral-like pattern in the air during predatory attacks, moving with amazing quickness and precision over the x, y, and z planes.

$$x^{\prime }=r_s\times \cos (k)$$

(13)

$$y^{\prime }=r_s\times \sin (k)$$

(14)

$$z^{\prime }=r_s\times k$$

(15)

$$r_s=u\times e^{kv}$$

(16)

where ‘r_s’ indicates the radius of each spiral turn and “k” stands for a random value that is uniformly distributed between 0 and 2. The variables “u” and “v” define the spiral’s configuration, and “e” stands for the natural logarithm’s base. Equations (13) through (16) are used to calculate the search agent’s updated position, as shown in (17).

$${{\displaystyle \overrightarrow{P}}}_S(X)=({{\displaystyle \overrightarrow{D}}}_S\times x\prime \times \mathrm{y}\prime \times \mathrm{z}\prime )+{{\displaystyle \overrightarrow{P}}}_{bs}$$

(17)

where P_s(x) saves the best solution and updates the position of other search agents.

3.2. Incorporation of LFM into SOA

To address the drawbacks of SOA, like premature convergence and subpar performance, a new approach called LFM has been introduced. LFM dynamically adjusts the position of search elements to strike a better balance between exploration and exploitation within SOA. By optimizing the search agent’s location, capacitor size, and the structure of key components like EDN and IDG, LFM enhances the algorithm’s effectiveness. Additionally, incorporating LPDF-determined jump sizes improves exploration, reducing the risk of getting stuck in local optima. Equation (18) illustrates the updated position using LFM. This approach shows promise in improving convergence and solution quality compared to traditional SOA methods.

$${{\overrightarrow{\mathrm{P}}}_{\mathrm{S}}(\mathrm{x}) }_{\mathrm{new}} = \mathrm{levy} (\alpha , \beta , \gamma , \Delta )$$

(18)

where the position of the Levy distribution (∆), the flat parameter (α), the symmetry parameter (β), and the empirical standard deviation (γ) are all mentioned. The value assigned to “α” is derived from [44].

The optimization process begins with a randomly formed population, where search agents continuously adjust their positions throughout the iteration process, aiming to identify the best solution. While ‘A’ drops linearly from its initial value to zero, key variables like ‘B’ enable a progressive shift from exploration to exploitation. Figure 1 provides the flowchart describing the LFM-SOA algorithm and the steps in the optimization procedure.

3.3. Application of LFM-SOA for the Chosen Problem

The steps involved in the LFM-SOA are discussed below:

Step 1: Initialize the seagull population (pop) and reset the parameters f_c, u, v, k, number of iterations, and dimension of variables. Create the initial seagull populations based on the arrangement of variables provided in

Table 1. Typical values and arrangement of Solution Vectors (SVs)—All cases.

Optimization	No. of Variables	Switch Status & Bus Details	Solution Vectors Range
			IEEE 33-Bus EDN	Real 74-Bus Myanmar EDN
D N S A	5 (X1 to X5)	Tie-Switch Nos. 33 to 37/ 74 to 78	0—Tie-switch Open 1—Tie-switch closed
	5 (X6 to X10)	Feeder Switch Nos. 2 to 33/2 to 74	If the Tie-switch closed (i.e., 1), the respective feeder switch in that particular loop should be opened
Capacitor (RPI)	2 + 2 (X1 to X4)/3 + 3 (X1 to X6)	Bus Nos. 2 to 33/2 to 74	0.1–0.75 MVAr (‘L’ Load) 0.3–1.5 MVAr (‘M’ Loads) 0.5–2.0 MVAr (‘H’ Loads)	0.2–1.0 MVAr (‘L’ Load) 0.2–1.5 MVAr (‘M’ Load) 0.5–2.0 MVAr (‘H’ Load)
R EG (type I)	2 + 2 (X15 to X18)/3 + 3 (X17 to X22)	Bus Nos. 2 to 33/2 to 74	0.3–0.8 MW (‘L’ Load) 0.6–1.5 MW (‘M’ Load) 0.9–2.5 MW (‘H’ Load)	0.3–1.5 MW (‘L’ Load) 0.5–2.0 MW (‘M’ Load) 0.4–3.0 MW (‘H’ Load)
			Total penetration limit (λ) of EGs should be ≤50% for both the test systems for each load level as mentioned in Equation (5)

, which includes details related to the location and size of capacitors, switch configurations, and optimal REG buses with their capacities.

Step 2: Generate the initial search agents randomly, ensuring compliance with all constraints from Equations (2) to (7).

Step 3: Utilize the EDNPF algorithm discussed in [42,43] to calculate system parameters such as P_Loss/E_Loss and bus voltage profiles for all buses associated with each generated search agent. Evaluate the fitness of the initial positions of the seagulls randomly, determining the best search agent position for the first iteration.

Step 4: Assessing the fitness values of (1) across several individuals, will allow you to determine the overall optimum value by comparing the fitness values of individuals within the existing seagull population. Find the present population’s global best values.

Step 5: If the maximum number of iterations is reached, conclude the operation, and display the objective function value related to the optimal structure of EDN, optimal capacitors/REG buses, and their optimal sizing. Otherwise, repeat the steps from 2 to 5.

3.4. Parameter Arrangements to Solve the EOF

The utilization of LFM-SOA to solve the EBOF, as depicted in (1), involves determining the placement and capacity of capacitors (non-discrete) with and without DNSA. Additionally, it encompasses the allocation and sizing of REGs in the reconfigured capacitive-supported EDN to achieve EBs based on E_Loss reduction. The different solution vectors for eight scenarios are outlined in Table 1.

Only particles that meet all constraints are considered for the initial population. Table 1 provides the minimum and maximum values of capacitors (kVAr) for two or three optimal buses, as well as the minimum and maximum values for REGs for two or three optimal buses. The change in variable parameters can be determined by substituting the eight case studies into Equation (18) when particles transition from their current positions to new positions. The newly generated variables obtained at the end of each iteration will replace previous, poorer vectors. Until the allotted number of iterations is reached, this iterative procedure is continued. Parameters like agent size and the number of iterations are set to 800 and 80, respectively, for both test systems.

4. Case Study Details, Simulations and Discussions

The first test system considered here is a renowned IEEE 33-bus system under Before Optimization (BO) condition as depicted in Figure 2. The parameter details for the standard IEEE 33-bus system have been sourced from ref. [45]. It has 37 edges, 33 buses, and 5 looping branches. The apparent power supplied to this network totally under 50%, 100%, and 160% load levels are (1906.29 + j 1183.049), (3926 + j 2443.135), and (6547.4843 + j 4090.22) kVA respectively including losses. The apparent power losses under BO are (48.79 + j33.049), (211 + j 143.135) and (603.4843 + j 410.22) kVA respectively. The minimum node voltages recorded are 0.954, 0.9038, and 0.836 p.u. respectively for three load variations. For this test system, two optimal nodes each for IREGs and RPIs are considered.

The next test system under consideration is a brand-new, real, three-feeder, 74-bus Myanmar EDN, whose BO structure is depicted in Figure 3. Line and bus data can be accessible from [46]. It has 74 buses, 73 edges, and 5 looping branches. The total apparent power supply fed to this network under 75%, 100%, and 125% load levels are (5056.541 + j 3406.3139), (6786.8685 + j 4575.7065) and (8541.8858 + j 5763.7683) kVA respectively including losses. The real and reactive power losses under BC are (93.791 + j 71.0639), (169.8685 + j 128.7065) [39] and (270.5858 + j 205.0183) kVA respectively. The minimum node voltages recorded are 0.96, 0.946, and 0.9317 p.u respectively under three load variations (75%, 100% and 125%). Three optimal nodes have been considered in this test system for real and reactive power compensation.

All nodes in the examined EDN are regarded as load nodes, except node no. 1. After Optimization (AO), the permissible range for node voltages is between 0.95 p.u. and 1.05 p.u. Eight distinct scenarios are examined to assess the efficacy of the selected algorithm in maximizing EB ($) by minimizing E_Loss and capacitor investment costs and maximizing REGEPC of REGs. The annual cost of capacitors ($/kVAr) and their fixed O&M cost ($/location) are taken as $0.5 [47] and $620 [48], respectively. The MES energy cost (K_MES) and REGEPC (K_REG) are taken as $0.05/kWh and $0.034246575/kWh (converted from $300/kW) [49] respectively. Out of the total duration in a year, 2190, 4745, and 1825 h are considered for Light, medium, and heavy load variations, respectively. The simulation has been developed and carried out in MATLAB R2021a installed in a 4th Gen. Intel i5 processor with 8 GB RAM (windows 8.1 OS). The MATLAB programming has been designed such that simultaneous optimization of all the three load variations for each case has been done one after the other with the condition that the optimal nodes selected by LFM-SOA for real and reactive power compensation should be the same for all the three load variations. However, for capacitor cost evaluation and EB achievement, the total highest capacitor sizes (heavy load level) pertaining to cases 2 to 5 (discussed below) have been taken, and regarding real power injection (cases 6 to 8), the EB has been calculated subject to satisfaction of Equation (13).

Case 1: The initial condition of DNSA, as depicted in Figure 2 and Figure 3, to demonstrate the EB achieved after reducing E_Loss.

Case 2: RPI optimization at two/three optimal nodes in the EDN-BO (Figure 2 and Figure 3) has been conducted to illustrate the impact of reactive power compensation on reducing the E_Loss, capacitor investment costs, and EB.

Case 3: Optimal DNSA has been performed on reactive power compensated network (Case 2) to evaluate the impact of E_Loss reduction and max. EB attainment beyond case 2.

Case 4: To investigate the role of RPIs in obtaining additional EBs after case 1, optimal capacitor allocation and sizing at two or three ideal nodes have been carried out.

Case 5: Assessing the E_Loss reduction, capacitor investment cost, EB, and optimal structure of the EDN in comparison to cases 3 and 4 has been done by performing RPIs at two/three optimal nodes concurrently with DNSA in the EDN-BO has been performed.

Case 6 to 8: Placement and capacity determination of DGs (type I) in the reactive power injected reconfigured EDN (i.e.,) allocation of DGs at two/three optimal nodes after cases 3, 4, and 5 respectively have been performed to examine the result of REGEP based E_Loss reduction and EBs with enhancement in node voltages.

4.1. Findings and Discussions—IEEE 33 Bus Prototype System

The IEEE 33-bus system’s specifics have already been covered. The performance of IEEE 33 test EDN using LFM-SOA for cases 1 through 5 under three different load variations have been shown in

Table 2. Performance of LFM-SOA—IEEE 33 Bus system—All load levels.

Load	Case	PLoss(kW)	ELoss (kWh)	% ELoss Reduction	Cap. (kVAr) Details	Switches Open	Vmin (p.u)	Δ ELoss Cost ($)	Cap. Cost ($)	EB ($)
50%	BC	48.79	106,850.1	-----	-----	33–34–35–36–37	0.954	-----	-----	0
	1	30.07	65,853.3	38.3685	-----	7–14–9–32–28	0.972516	2049.84	-----	2049.84
	2	33.856	74,144.64	30.61	178 (12) 487 (30)	33–34–35–36–37	0.96425	1635.273	332.5	1302.773
	3	21.095	46,198.05	56.764	178 (12) 487 (30)	7–14–9–32–28	0.981309	3032.6	332.5	2700.1
	4	21.038	46,073.22	56.8805	157 (12) 516 (30)	7–14–9–32–28	0.981815	3038.844	336.5	2702.344
	5	21.012	46,016.28	56.9338	146 (9) 529 (30)	7–13–9–32–28	0.982041	3041.691	337.5	2704.191
100%	BC	211.004	1,001,213.98	-----	-----	33–34–35–36–37	0.9038	-----	-----	0
	1	125.628	596,104.86	40.4618	-----	7–14–9–32–28	0.943635	20,255.45	-----	202,455.45
	2	141.78	672,746.1	32.807	463 (12) 1044 (30)	33–34–35–36–37	0.9314	16,423.394	753.5	15,669.894
	3	85.803	407,135.23	59.3358	463 (12) 1044 (30)	7–14–9–32–28	0.963214	29,703.94	753.5	28,950.44
	4	85.14	403,657.15	59.682	488 (12) 1169 (30)	7–14–9–32–28	0.96546	29,860.28	828.5	29,031.78
	5	84.96	403,135.2	59.7354	597 (9) 1072 (30)	7–13–9–31–28	0.965492	29,903	834.5	29,068.5
160%	BC	603.4843	1,101,358.85	-----	-----	33–34–35–36–37	0.836	-----	-----	0
	1	340.45	621,321.25	43.586	-----	7–14–9–32–28	0.906793	24,001.88	-----	24,001.88
	2	389.468	710,779.1	35.4634	747 (12) 1686 (30)	33–34–35–36–37	0.883015	19,528.987	1216.5	18,312.487
	3	227.712	415,574.4	62.2671	747 (12) 1686 (30)	7–14–9–32–28	0.940030	34,289.222	1216.5	33,072.722
	4	226.82	413,946.5	62.415	708 (12) 1792 (30)	7–14–9–32–28	0.941964	34,370.62	1250	33,120.62
	5	226.641	413,619.825	62.4446	681 (9) 1816 (30)	7–13–9–32–28	0.9424	34,386.95	1248.5	33,138.45

. After case 1, (i.e.,) DNSA in BO state, the E_Loss reduction obtained under three load variations ranges between 38% and 43.5% when all the five tie-switches (33 to 37) are closed against openings of 7, 14, 9, 32, and 28. Following the case 1, the improvements in bus voltages under three load variations (50%, 100% and 160%) compared to BO are 0.018516 p.u., 0.039835 p.u., and 0.070793 p.u., respectively. From

Table 3. Consolidated results LFM-SOA—Case 1 to 5—IEEE 33 Bus system.

Case	Case 1	Case 2	Case 3	Case 4	Case 5
ELoss (kWh)/B O value	1,283,279.41/2,209,422.93	1,457,669.84/2,209,422.93	868,907.685/2,209,422.93	864,009.02/2,209,422.93	862,771.3/2209,422.93
% ELoss reduction	41.91789	34.02486	60.67264	60.894	60.95
ELoss reduction cost ($)	46,307.176	37,587.6545	67,025.75	67,270.7	67,332.585
Capacitor details (kVAr)	----	747 (12) 1686 (30)	747 (12) 1686 (30)	708 (12) 1792 (30)	681 (9) 1816 (30)
Capacitor inv. cost ($)	----	2456.5	2456.5	2490	2488.5
EB ($)	46,307.176 (41.91789%)	35,131.1545 (31.8012%)	64,569.25 (58.44897%)	64,780.7 (58.6404%)	64,844.1 (58.6978%)

it is apparent that an overall E_Loss decrease and EB of about 42% and $46307, respectively is evidenced. The proposed methodology achieves a better performance than [3,4,5,20,21,22,23,24,25]. However, the bus voltage improvement is found to be less compared to [3,5,21,23]. By referring [3], it is observed that the P_Loss reduction achieved by LFM-SOA is more than 6% under light load variations. However, under 100% load, the P_Loss reduction achieved by [3] is 5.4482% more than LFM-SOA which is unrealistic and also practically not feasible considering previously published research articles.

Next case 2, by RPIs optimization through two nodes, the E_Loss reduction achieved under three load variations are 30.61%, 32.807%, and 35.4634% respectively with the reactive power penetration of 58.6956%, 72.565%, and 67.85%. For 50%, 100% and 160% load, the minimum bus voltage has increased by 0.01025 p.u., 0.0276 p.u., and 0.047015 p.u., respectively. From Table 3, it is observed that the overall E_Loss reduction and EB obtained under case 2 are 34.02486% and $35131.1545, respectively.

The results achieved by LFM-SOA under three load levels have been compared with other methods which are tabulated in

Table 4. Comparison of Case 2—IEEE 33-bus system—All load levels.

Ref.	Cap. Details (kVAr)/(Bus)	PLoss (kW)/(PLoss − BC)	Vmin (p.u) @18	ELoss Reduction Difference (kWh)	Capacitor Cost ($)	Capacitor O & M Cost	EB ($)
50% Load Level
Clonal [6]	150 (12) 100 (24) 600 (30)	32.0895/47.0709	0.9678	32,809.266 (31.8273%)	425	$1860	−644.54
Analytical [7]	300 (14) 250 (30) 170 (32)	33.04/47	0.9734	30,572.4 (29.702%)	360	$1860	−691.38
G W O [8]	300 (5) 150 (12) 300 (29)	32.42/47.07	0.9694	32,083.5 (31.124%)	375	$1860	−630.825
W C A [8]	300 (5) 150 (12) 300 (29)	32.43/47.07	0.9687	32,061.6 (31.103%)	375	$1860	−631.304
P B O A [9]	125 (13) 72 (28) 162 (29)	35.03134/48.7968	0.966	30,146.357 (28.1%)	179.5	$1860	−532.182
M P S O [20]	850 (7 Nodes)	33.469/47.2	0.9668	30,070.89 (29.091%)	425	$4340	−3261.4555
LFM-SOA	178 (12) 487 (30)	33.856/48.79	0.966	32,705.46 (30.608%)	332.5	$1240	+62.773
100% Load Level
S C A [10]	500 (12) 1050 (30)	141.89/210.99	0.931	327,879.5 (32.75%)	775	$1240	14,378.98
S C A [11]	350 (14) 1000 (30)	142.551/210.988	0.93	324,733.565 (32.4364%)	675	$1240	14,321.68
CF-PSO [12]	465 (12) 1035 (30)	141.86/211	0.9303	328,069.3 (32.767%)	750	$1240	14,413.465
P S O [13]	450 (12) 1050 (30)	136.76/202.67	0.9357	312,742.95 (32.5208%)	750	$1240	13,647.15
E P S O [13]	900 (11) 900 (31)	135.42/202.67	0.9329	319,101.25 (33.182%)	900	$1240	13,815.06
G T O [14]	300 (14) 600 (24) 1050 (30)	132.4256/202.6771	0.9368	333,343.3675	975	1860	13,832.168
M P S O [20]	2000 (7 Nodes)	142.21/202.4	0.94043	285,601.55 (29.738%)	1000	$4340	8940.1
LFM-SOA	463 (12) 1044 (30)	141.75/211	0.9314	328,591.25 (32.82%)	753.5	$1240	14,436.063
160% Load Level
Clonal [6]	550 (12) 100 (24) 1050 (30)	393.2709/575.3682	0.8528	332,327.57 (31.6488%)	850	$1860	13,906.38
Analytical [7]	840 (14) 650 (30) 520 (32)	384/575.36	0.9	349,232 (33.2592%)	1005	$1860	14,596.6
G W O [8]	1200 (5) 450 (13) 1200 (29)	364.82/575.36	0.8982	384,235.5 (36.593%)	1425	$1860	15,926.78
W C A [8]	1050 (5) 600 (12) 1050 (29)	368.56/575.36	0.8982	377,410 (35.9427%)	1350	$1860	15,660.5
LFM-SOA	747 (12) 1686 (30)	389.468/603.4843	0.883015	390,576.1 (35.46311%)	1216.5	$1240	17,072.3

. Under 50% load, it is evident that the E_Loss reduction and capacitor sizings obtained by the proposed method is better than [6,7,8,9,20]. Because of the lower O&M costs associated with capacitors, the proposed method achieves more EB. The penetration of RPIs by the proposed method is less compared to [6,7,8,20]. By comparing the bus voltage improvement with [6,7,8,9,20], LFM-SOA optimizes less enhancement in bus voltage because of a smaller number of compensations. Considering 100% load variations and from Table 4, it is obvious that the performances of LFM-SOA is found to be better than [10,11,12,13,14,20] in reaching EB. The penetration of RP in [11,12,13] are less compared to LFM-SOA. However, the difference is meagre only. However, the bus voltage improvement is better than [10,11,12,13,14,20]. Though [13,14,20] yields more enhancement in node voltage, the BO value is more than the BO value of the load flow used here. A min. and max. EB of $22.518 [12] and $5495.963 [20] have been observed. Under 160% load, the E_Loss minimization is better than [6,7,8] and also a minimum EB of $1145.52 has been evidenced compared to [8(GWO)]. Bus voltage improvement is found to be less than [6,7,8]. It is understood from Table 4 that LFM-SOA achieves more EB under all load variations. Still the bus voltage improvement is less compared to [6,7,8,9,10,11,12,13,14,20] due to reactive power support at a smaller number of optimal nodes.

Case 3 (i.e.,) DNSA after case 2 achieves, E_Loss reduction difference of more than 26% under three load variations are evidenced. Similarly, the improvement in bus voltages is found to be 0.017059, 0.031814 and 0.057015 p.u. respectively. The difference in EB yields by DNSA after case 2 are $1397.327, $13,280.546, and $14,760.235 respectively considering three load levels. By viewing Table 3, an overall E_Loss reduction and EB difference of 26.64778% and $29,438.0955 have been evidenced. The performance comparison of LFM-SOA under scenarios 3 to 5 with 100% load levels is shown in

Table 5. Comparison of Case 3 to 5—IEEE 33-Bus system—100% Load level.

Ref.	Cap.(kVAR) Details	Switch Status	PLoss (kW)/(PLoss − BO)	Vmin (p.u)	Difference in ELoss Reduction (kWh)	Cap. Cost ($)	Capacitor O & M Cost	EB ($)
CASE 3
M B B O [16]	750 (27) 450 (30) 600 (24)	7–11–34–36–28	83.469/202.677	0.9559	565,641.96 (58.8168%)	900	$1860	25,522.1
C S [16]	300 (8) 750 (30) 600 (23)	8–5–37–30–12	95.6628/202.677	0.9704	507,782.38 (52.8%)	825	$1860	22,704.12
M I C [16]	750 (27) 150 (2) 750 (24)	9–25–14–33–37	97.6377/202.677	0.95	498,411.48 (51.826%)	825	$1860	22,235.574
M B F B O [16]	900 (5) 600 (27) 750 (2)	8–37–14–7–36	97.3076/202.677	0.95	499,977.8 (51.98885%)	1125	$1860	22,013.89
A G P S O [22]	450 (12) 600 (24) 1050 (30)	6–14–9–32–37	84.1986/211.04	0.9607	601,672.643 (60.103%)	1050	$1860	27,173.63
P G S A [23]	450 (8) 300 (13) 300 (19) 150 (27) 600 (30)	8–10–13–31–37	101.037/202.7	0.9412	482,390.935 (50.1544%)	900	$3100	20,119.55
B S S A [24]	600 (6) 600 (24) 600 (33)	11–27–33–36–34	105.9175/202.6771	0.95	459,124.302 (47.7407%)	900	$1860	20,196.215
LFM-SOA	463 (12) 1044 (30)	7–14–9–32–28	85.803/211	0.96322	594,059.76 (59.335%)	753.5	$1240	27,709.488
CASE 4
MBBO [17]	300 (12) 300 (25) 300 (20)	33–14–11–25–37	110.616/202.677	0.95	436,829.445 (45.4225%)	450	$1860	19,531.47
DDE [17]	300 (33) 600 (30) 900 (3)	7–13–8–36–28	111.86/202.677	0.96114	430,926.665 (44.8088%)	900	$1860	18,786.33
BTLBO [17]	150 (13) 300 (29) 900 (30)	7–13–8–36–28	115.6684/202.677	0.9554	412,855.81 (42.9297%)	675	$1860	18,107.79
A G P S O [22]	600 (12) 450 (24) 900 (30)	7–14–9–32–37	83.304/211	0.9626	605,917.52 (60.5194%)	975	$1860	27,460.876
P G S A [23]	450 (8) 300 (13) 300 (19) 150 (27) 600 (30)	8–13–19–27–30	87.872/202.7	0.9422	544,858.86 (56.649%)	900	$3100	23,242.943
B S S A [24]	100 (19) 600 (23) 100 (30)	7–14–30–35–37	115.7382/202.6771	0.95	412,525.0805 (42.8953%)	400	$1860	18,366.254
G W O [31]	472 (24), 1100 (30) 579 (21)	7–14–9–32–37	93.29/202.66	0.9555	518,960.65 (53.967%)	1075.5	$1860	23,012.53
LFM-SOA	488 (12) 1169 (30)	7–14–9–32–28	85.14/211	0.96546	597,205.7 (59.648%)	828.5	$1240	27,791.785
CASE 5
D O A [18]	512 (8) 714 (29) 495 (30)	7–17–11–27–34	103.65/202.6	0.9530	469,517.75 (48.84%)	860.5	$1860	20,755.39
M I L P Mod [19]	400 (8) 550 (24) 950 (30)	7–14–9–32–37	92.65/ 202.67	0.9583	522,044.9 (54.2853%)	950	$1860	23,292.245
M P S O [20]	900 (7 Nodes)	7–34–11 32–28	100.69/202.4	0.9549	482,613.95 (50.252%)	450	$4340	21,820.7
A W O A [21]	400 (24) 250 (25) 150 (30)	37-close 25-open	97.415/169.95	------	344,178.58 (42.6802%)	400	$1860	14,948.93
B S S A [24]	600 (19) 600 (30) 600 (33)	7–11–17–34–37	104.5116/202.6771	0.95732	465,795.3 (48.4344%)	900	$1860	20,529.765
MTS-HSSA [25]	650 (30) 350 (25) 200 (31)	8–9–17–32–37	91.01/202.66	0.962	529,779.25 (55.0923%)	600	$1860	24,028.9625
G W O [31]	533 (24), 957 (30) 445 (8)	7–14–9–32–37	92.59/202.66	0.9595	522,282.15 (54.3126%)	967.5	$1860	23,286.6075
LFM-SOA	597 (9) 1072 (30)	7–13–9–31–28	84.96/211	0.965492	598,059.8 (59.7346%)	834.5	$1240	27,828.49

. From Table 5, it is evident that LFM-SOA achieved more P_Loss reduction/EB than [16,22,23,24]. Though the E_Loss reduction achieved by [22] is better than LFM-SOA, EB achieved by LFM-SOA is more by $535.858. On the other hand, the bus voltage improvement is superior to [16] (CS). It has been reported that LFM-SOA performs better than [16,22,23,24].

Under three load levels, the LFM-SOA performance under scenario 4 (i.e.,), RPIs at two ideal nodes after case 1 results in an E_Loss reduction difference of about 19%. Though the E_Loss reduction under case 4 considering three load variations is more than case 3, the difference is minuscule. Compared to case 3, the bus voltage improvement is superior. From Table 3, it is noticeable that the difference in EB between case 3 and case 4 is $211.45 only. Considering Case 4 and from Table 5, it is apparent that the LFM-SOA yields more E_Loss reduction.

Optimization of RPIs at two nodes simultaneously with DNSA under BO condition considering case 5 yields better performance in E_Loss reduction, bus voltage improvement, and more EB compared to cases 3 and 4 which is apparent from Table 2 and Table 3. However, the difference is 0.03% to 0.05% only. It is observed that the difference in total RPI values under case 5 is more than cases 3 and 4 for 50% and 100% load variations. By screening Table 5 and by comparing the performances yielded by LFM-SOA with [18,19,20,21,24,25,38], the E_Loss reduction, bus voltage improvement, and EB are found to be better. The minimum and maximum differences in EBs achieved are $3799.5275 [25] and $12879.56 [21].

Table 6. Performance of LFM-SOA—Case 6 to 8—IEEE 33 Bus system—All load levels.

Load	Case	DG Details (kW)	PLoss (kW)	ELoss (kWh)	Extra ELoss(kWh) Reduction Gained	Total ELoss Reduction	DGEP Cost ($)	Vmin (p.u)
50%	6	434 (9) 497 (29)	5.7124	12,510.156	33,687.894/72.92%	88.292%	69,825.05	0.99189
	7	325 (12) 606 (29)	5.275	11,552.25	34,520.97/74.926%	89.1884%	69,825.05	0.98737
	8	323 (15) 608 (29)	5.054	11,068.26	34,943.64/75.947%	89.6413%	69,825.05	0.99028
100%	6	848 (9) 1020 (29)	22.571	107,099.4	300,035.84/73.694%	89.303%	303,550.22	0.984298
	7	827 (12) 1041 (29)	21.7976	103,429.61	300,559.7/74.398%	89.67%	303,550.22	0.978983
	8	875 (15) 993 (29)	21.46	101,827.7	301,307.5/74.741%	89.8294%	303,550.22	0.978768
160%	6	947 (9) 2052 (29)	55.297	100,917	314,653.73/75.716%	90.837%	187,437.64	0.96163
	7	1090 (12) 1909 (29)	54.21	98,933.25	314,995/76.1%	91.0172%	187,437.64	0.96671
	8	1054 (15) 1943 (29)	51.853	94,631.72	319,077.5/77.121%	91.4077%	187,312.635	0.975077

shows how well LFM-SOA performs in reducing E_Loss beyond cases 3 to 5 while taking type I DGs into account at two nodes. As previously pointed out, for cases 3 to 5, shown in Table 1, the penetration of DGs (after reactive power compensation in the optimal EDN) has been limited to 50%. Further E_Loss reduction gained under cases 6, 7, and 8 is from 73% to 77% compared to cases 3 to 5 considering all three load variations. As a result, the overall E_Loss decrease has improved between 88% to 91%. From Table 6 it is noticeable that the enhancement in bus voltage is maximum under case 6 (50% and 100%) and case 8 (160%) compared to other two.

Table 7. Consolidated results—Case 6 to 8—IEEE 33 Bus system—All Load levels.

Parameter		Case 6	Case 7	Case 8
Total ELoss (kWh)—BC		2,209,422.93/$110,471.15
Total ELoss(kWh)—before DG allocation		868,907.685	864,009.02	862,771.3
Total ELoss (kWh)—after DG allocation		220,526.58	213,915.112	207,527.685
% extra ELoss reduction		74.62025	75.24157	75.9464
% Total ELoss reduction		90.0188	90.318	90.60715
Cost saving ($)—ELoss reduction—after REGEP	50% load	1684.395	1726.05	1747.4
	100% load	15,001.79	15,027.984	15,065.375
	160% load	15,732.869	15,750.66	15,949.405
Cost Saving ($)–after REGEP	50% load	32,119.5	32,119.5	32,119.5
	100% load	139,632.78	139,632.78	139,632.78
	160% load	86,221.115	86,221.115	86,163.61
EB ($)—ELoss after REGEP		32,419.056	32,504.7	32,762.18
EB ($) by REGEPC		257,973.76	257,973.76	257,916.25
EB ($)—RPI Optimization		64,569.25	64,780.7	64,844.1
Total net EBs ($)		354,962.045	355,259.16	355,522.53

displays the EB obtained under cases 6 to 8. The total EB difference between cases 6 and 8 and between 7 and 8 are $560.47 and $263.38, respectively. The REGEPC for cases 6 and 7 is slightly greater than 8. This is because of 2 kW difference in REGEP. The difference in E_Loss reduction based EBs under cases 6 to 8 are minuscule. Finally, by screening

Table 8. Comparison of Case 8—IEEE 33 Bus system—All Load levels.

Ref.	Switch Position	Details of DG (kW)	Cap. Details (kVAr)	PLoss (kW)/(PLoss − BC)	% PLoss Reduction
I G A [35]	33–9–35–36–37	370 (14) 575 (24) 519 (30)	200 (15) 200 (25) 500 (30)	2.78/47.06	94.0926
I P S O [35]	33–9–35–36–37	368 (14) 520 (24) 524 (30)	200 (14) 300 (24) 500 (30)	2.76/47.06	94.135
I T L B O [35]	33–9–35–36–37	371 (14) 540 (24) 527 (30)	200 (15) 300 (24) 500 (30)	2.74/47.06	94.1776
LFM-SOA	7–13–9–32–28	323 (15) 608 (29)	146 (9) 529 (30)	5.054/48.79	89.6413
I G A [35]	7–9–17–35–37	748 (14) 1079 (24) 1043 (30)	300 (15) 300 (25) 1100 (30)	11.59/202.67	94.2813
I P S O [35]	7–9–17–25–35	748 (14) 1003 (24) 1057 (30)	300 (14) 500 (24) 1000 (30)	11.12/202.67	94.51325
I T L B O [35]	7–9–17–35–37	744 (14) 1070 (24) 1048 (30)	300 (15) 500 (24) 1000 (30)	11.21/202.67	94.4688
B A [35]	14–24–33–35–36	1670 (6) 410 (9) 490 (32)	300 (11) 300 (26) 900 (30)	22.96/202.67	88.6712
C S O [35]	11–20–24–35–36	1690 (6) 630 (14) 710 (31)	1200 (7) 600 (3) 600 (33)	21.82/202.67	89.234
MRFOA [36]	7–8–9–17–27	841 (13), 1144 (30)	600 (30), 900 (9)	14.84/ 202.69	92.678
B P S O [37]	33–34–9–12–24	1000 (29) 1000 (33)	1270 (30) 480 (6)	22.46/208.5	89.2278
G W O [38]	05–35–14–17–26	1050.1 (9) 1174.7 (25) 717.8 (33)	450 (9) 600 (29) 600 (30)	12.14/202.5	94.001
LFM-SOA	7–13–9–31–28	597 (9) 1072 (30)	875 (15) 993 (29)	21.45/211	89.834
I G A [35]	7–34–9–36–28	845 (14) 1122 (24) 1072 (30)	300 (15) 300 (25) 1200 (30)	64.79/575.27	88.74
I P S O [35]	7–34–9–36–28	831 (14) 1005 (24) 1128 (30)	300 (14) 600 (24) 1200 (30)	62.53/575.27	89.13
I T L B O [35]	7–34–9–36–28	823 (14) 1070 (24) 1068 (30)	300 (15) 600 (24) 1200 (30)	63.26/575.27	89.00
LFM-SOA	7–13–9–32–28	1054 (15) 1943 (29)	681 (9) 1816 (30)	51.853/603.4843	91.4077%

, it is seen that the maximum difference in E_Loss reduction achieved by LFM-SOA under light load level is 4.5363% less than [35]. Under 100% load, the performance of LFM-SOA is better, compared to [35,37] (BA & CSO). However, the performance of other algorithms in [35] (IGA, IPSO, ITLBO), [36,38] are found to be better than LFM-SOA. Under 160% load, the E_Loss reduction achieved by LFM-SOA is 2.6677%, greater than [35] (IGA, IPSO, ITLBO).

It is apparent from Table 8 that, the performance of [35,36,37,38] is better compared to LFM-SOA under 50% and 100% load variations which are because of high penetration of REGs and capacitors compared to LFM-SOA and also the number of compensation nodes are three in [35,36,37,38]. It is to be noted that the performance of LFM-SOA under 160% load level is better than [35]. From the above discussions, it is clear that, LFM-SOA achieves a better performance than other methods. Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9 shows the node voltages considering cases from BC to 8

4.2. Results and Discussions—Real Three Feeder 74 Bus Myanmar EDN

This practical EDN’s specifications have already been discussed. The impact of LFM-SOA in optimizing the cases from BC to 8 is covered from

Table 9. Performance of LFM-SOA—Case BC to 5—Real 74 Bus system.

Load	Case	PLoss (kW)	ELoss (kWh)	% ELoss Reduction	Capacitor Details (kVAr)	Switches Open	Vmin (p.u)	Δ ELoss Cost ($)	Capacitor Cost ($)	EB ($)
75%	BC	93.791	205,402.29	-----	-----	74–75–76–77–78	0.96	-----	-----	-----
	1	73.281	160,485.39	21.8677	-----	31–49–76–42–50	0.975623	2245.845	-----	2245.74
	2	67.152	147,062.88	28.4025	621 (26) 447 (46) 736 (65)	74–75–76–77–78	0.97098	2916.97	2762	154.97
	3	54.74	119,880.6	41.636	621 (26) 447 (46) 736 (65)	31–48–76–41–50	0.981133	4276.08	2762	1514.08
	4	54.653	119,690	41.729	707 (26) 656 (64) 334 (68)	31–49–76–42–50	0.981033	4285.611	2708.5	1577.11
	5	53.99	118,238.1	42.4358	437 (25) 367 (38) 903 (66)	31–48–76–42–50	0.98181	4358.21	2713.5	1644.71
100%	BC	169.8685	806,026.03	-----	-----	74–75–76–77–78	0.946	-----	-----	-----
	1	131.92	625,960.4	22.34	-----	31–49–76–42–50	0.96727	9003.28	-----	9003.28
	2	118.68	563,136.6	30.1342	897 (26) 716 (46) 1275 (65)	74–75–76–77–78	0.96312	12,144.472	3304	8840.472
	3	97.746	463,804.77	42.4578	897 (26) 716 (46) 1275 (65)	31–49–76–39–50	0.97914	17,111.06	3304	13,807.06
	4	96.538	458,072.81	43.169	1250 (26) 714 (64) 735 (68)	31–49–76–42–50	0.97580	17,397.66	3209.5	14,188.16
	5	95.303	452,212.735	43.896	796 (25) 492 (38) 1419 (66)	31–48–76–42–50	0.976852	17,690.665	3213.5	14,477.165
125%	BC	270.5858	493,819.085	-----	-----	74–75–76–77–78	0.9317	-----	-----	-----
	1	208.754	380,976.05	22.851	-----	31–49–76–42–50	0.958804	5642.15	-----	5642.15
	2	188.356	343,749.7	30.3895	1137 (26) 851 (46) 1513 (65)	74–75–76–77–78	0.952943	7503.47	3610.5	3892.97
	3	153.602	280,323.65	43.2335	1137 (26) 851 (46) 1513 (65)	31–49–76–39–50	0.973887	10,674.77	3610.5	7064.27
	4	152.415	278,157.375	43.6722	1309 (26) 755 (64) 1202 (68)	31–49–76–42–50	0.969943	10,783	3493	7290
	5	151.11	275,775.75	44.1545	1028 (25) 656 (38) 1752 (66)	31–47–76–43–50	0.969822	10,902.167	3578	7324.167

,

Table 10. Consolidated Results—LFM-SOA—Case 1 to 5—Real 74 Bus system.

Case	Case 1	Case 2	Case 3	Case 4	Case 5
Total ELoss (kWh) reduction/BC value	1,167,421.84/1,505,247.405	1,053,949.18/1,505,247.405	864,009.02/1,505,247.405	855,920.185/1,505,247.405	846,226.585/1,505,247.405
% ELoss reduction	22.4432	29.98166	42.6	43.1375	43.7816
Total ELoss cost ($)/ BC ELoss value ($)	58,371.092/75,262.37	52,697.46/75,262.37	43,200.45/75,262.37	42,796/75,262.37	42,311.33/75,262.37
Capacitor details (kVAr)/(bus no.)	-----	1137 (26) 851 (46) 1513 (65)	1137 (26) 851 (46) 1513 (65)	1309 (26) 755 (64) 1202 (68)	1028 (25) 656 (38) 1752 (66)
Capacitor cost ($)	-----	3610.5	3610.5	3493	3578
Net EB ($)	16,891.278	18,954.41	28,451.42	28,973.37	29,373.04
% Net EB	22.4432	25.18444	37.803	38.4965	39.0275

,

Table 11. Performance of LFM-SOA–Case 6 to 8–Real 74 Bus Myanmar system.

Load	Case	DG Details (kW)	PLoss (kW)	ELoss (kWh)	Extra ELoss (kWh) Reduction Gained	Total % ELoss Reduction	REGEPC ($)	Vmin (p.u)
75%	6	688 (26) 783 (38) 1018 (67)	15.616	34,199.04	85,681.56/71.472%	83.35	186,675.13	0.988144
	7	580 (25) 686 (35) 1222 (67)	13.495	29,554.05	90,136.02/75.307%	85.6116	186,600.13	0.988145
	8	835 (26) 427 (38) 1226 (68)	12.489	27,350.91	90,887.19/ 76.868%	86.684	186,600.13	0.988148
100%	6	751 (26) 737 (38) 1832 (67)	24.305	115,327.225	348,477.55/75.1345%	85.692	539,500.39	0.984133
	7	686 (25) 805 (35) 1829 (67)	22.707	107,744.7	350,328.1/ 76.4786%	86.6326	539,500.39	0.984136
	8	911 (26) 736 (38) 1672 (68)	21.145	100,333	351,879.71/77.8128%	87.552	539,337.89	0.984139
125%	6	482 (26) 998 (38) 2675 (67)	38.837	70,877.52	209,446.125/74.7168%	85.647	259,687.69	0.980093
	7	988 (25) 680 (35) 2486 (67)	36.963	67,457.48	210,700/75.7485%	86.34	259,625.19	0.980095
	8	959 (26) 1222 (38) 1970 (68)	33.355	60,872.88	214,902.88/77.9267%	87.673	259,437.69	0.9801

and

Table 12. Consolidated results of LFM-SOA—Case 6 to 8—Real 74 Bus system.

Parameter		Case 6	Case 7	Case 8
Total ELoss (kWh)–BC		1,505,247.408/75,262.37
Total Energy (kWh)—before DGEP		864,009.02	855,920.185	846,226.585
Total Energy (kWh)—after DGEP		220,403.79	204,756.24	188,556.81
% ELoss reduction		74.49	76.077	77.718
% Total ELoss reduction		85.35764	86.39717	87.4734
Total ELoss cost ($)		11,020.19/75262.37	10,237.812/75,262.37	9427.8405/75,262.37
Cost saving ($)— ELoss reduction	75% load	4284.1	4506.8	4544.36
	100% load	17,423.9	17,516.4	17,594
	125% load	10,472.3	10,535	10,745.14
Cost Saving ($)— by DGEP	75%load	85,870.366	85,835.866	85,835.866
	100% load	248,169.612	248,169.612	248,094.86
	125% load	119,456.1	119,427.313	119,341.1
Total DGEP Cost ($)		985,863.21	985,725.71	985,375.71
EBs ($)—ELoss after DGEP		32,180.26	32,558.2	32,883.5
EBs ($)—by REGEPC		453,496.078	453,433.48	453,272.48
EBs ($)—RPI optimization		28,451.42	28,973.37	29,373.04
Total net EBs ($)		514,128.41	514,965.37	515,529.02

. Under case 1 and from Table 9, it is evident that the E_Loss has decreased by 21.8677%, 22.34%, and 22.851%, respectively, with the bus voltage enhancement of 0.015623, 0.02127, and 0.027104 p.u. considering 75%, 100%, and 125%, loads respectively, by opening sectionalizing switches 31, 42, 49, and 50 against closing four out of five tie-switches (except switch number 76). From Table 10, it is seen that under case 1 (i.e.,) by DNSA in the BO condition, the overall E_Loss reduction and EB achieved are 22.4432% and $16891.278 respectively. By comparing case 1 with [34] under 100% load, it is identified that out of five tie-switches, only one tie-switch (No.78) has been closed besides the opening of one sectionalizing switch (No.69). The E_Loss reduction achieved by [34] is 18.977% only (i.e.,) the E_Loss has been reduced from 805,552.007 to 652,682.342 kWh. The enhancement in bus voltage is 0.01831 p.u.

Under case 2 (i.e.,) optimal RPIs at three optimal nodes in the BO condition, the E_Loss has reduced by 28.4025%, 30.1342%, and 30.39% respectively for three load variations with RP penetration of 53.275%, 63.6555%, and 61.405%. The bus voltage improvement after case 2 has been acknowledged as 0.01098, 0.01712 and 0.021243 p.u respectively. From Table 10, the E_Loss reduction and net EB are 29.98166% and $18,954.41.

Next the debate is based on the joint operation of DNSA with RPIs under cases 3 to 5. Case 3 (i.e.,) DNSA after case 2 yields an extra E_Loss reduction of 13.2335%, 12.3236%, and 12.844% respectively compared to case 2 (75%, 100%, and 125% loads) respectively by closing 4 out of 5 switches (except switch number 76). Bus voltage improvement of 0.010153, 0.01602 and 0.020944 p.u. respectively beyond case 2 is noticed. The EB by DNSA after case 2 is $1359.11, $4966.588 and $3171.3. From Table 10, it is obvious that an overall E_Loss reduction difference of 12.61834% beyond case 2 with EB of $9497.01 is evidenced.

The effect of RPIs after case 1 (i.e.,) case 4 yields an extra E_Loss reduction of 19.8613%, 20.829%, and 20.8212% beyond case 1 with reactive power support of 50.222%, 59.6557% and 57.4922% has been acknowledged. The bus voltage improvement after case 4 seems to be 0.00541, 0.00853 and 0.011139 p.u respectively. From Table 10, an overall E_Loss reduction difference of 20.6943% compared to case 1 with a net EB of $12,082.092 which is perceptible.

From Table 9 and Table 10, the simultaneous operation of DNSA with RPIs at three optimal nodes in the BO condition yields, a better performance compared to cases 3 and 4 considering E_Loss reduction, bus voltage improvement and EBs. However, the difference is minuscule. From Table 10, it is witnessed that the difference between cases 3 & 5 and 4 & 5 in E_Loss reduction and net EBs are 1.2245% and 0.6% and $922 and $400 respectively.

Similar to the IEEE 33 bus test system, this real test system has also undergone real power injection at three optimal nodes to achieve further E_Loss reduction, bus voltage improvement, and EBs. Table 11 and Table 12 reveals the performance of type I REGs (cases from 6 to 8) after the combined operation of DNSA with RPIs (i.e.,) the effect of real power compensation after cases 3 to 5. Cases 6 to 8 yields further E_Loss reduction difference between 71% and 78% compared to cases 3 to 5 with real power penetration of exactly 50% for all three load variations and cases.

Thus, the total E_Loss reduction reached from 83% to 88%. The bus voltage also reached beyond 0.988 (LL), 0.984 (ML), and 0.98 (HL). Finally, Table 12 exposes the overall EB after cases 6 to 8. The overall extra E_Loss reduction achieved under cases 6 to 8 is between 74.5% and 77.7% compared to cases 3 to 5. Thus, the total E_Loss reduction has reached around 87.7%. By DGEP at three optimal nodes, an EB of around $486K is noticed. However, the difference between case 6, 7 and 8 are below $200 and below $500 respectively. Thus, the total overall EB attained is found to be around $515K. These results proved the efficacy of LFM-SOA in achieving higher E_Loss reduction thereby maximum attainment of EBs. Figure 10, Figure 11, Figure 12, Figure 13, Figure 14 and Figure 15 reveals the bus voltage performances from cases BC to 8 under three load variations.

5. Conclusions

This work proposes applying the well-known evolutionary algorithm LFM-SOA to minimize E_Loss. It has been used for both separate and joint optimization of DNSA with RPIs at two or three optimal nodes under five different cases. Furthermore, to show the robustness of the developed algorithm in achieving more E_Loss reduction and further EBs, IREGs (type I) at two/three optimal nodes in the reactive power supported optimal EDN (after scenarios 3 to 5) have been performed. To estimate the proficiency of the proposed model and method, this work adopts standard IEEE 33-bus, and a new real 74-bus three-feeder Myanmar EDN have been applied. It is appropriate to consider load variations based on investigation and hence this study takes three load variations such as 50%, 100%, and 160% for IEEE 33 bus EDN and 75%, 100%, and 125% load variations for real 74-bus three feeder Myanmar EDN. The key findings, which are highly intriguing, are enumerated below.

1. By optimizing DNSA and RPIs, an E_Loss reduction of around 42% and 32% respectively for IEEE 33 bus test system and around 22% and 30% respectively for Myanmar 74 bus test system have been yielded. Regarding EBs, $46,307 and $35,131 respectively have been achieved by optimizing DNSA and RPIs at two nodes for IEEE 33 bus test system and $16,891 and $18,954 respectively for Myanmar 74 bus test system have been achieved.

2. An overall E_Loss reduction and EB of 60.95% and $64,844.1 have been achieved by simultaneous optimization of RPIs with DNSA for the standard IEEE 33 bus system. For a real 74-bus three-feeder Myanmar EDN, the overall E_Loss reduction and EBs are 43.7816% and $29,373.04 respectively.

3. By the incorporation of REGs (two/three) in the optimal reactive power supported EDN, further E_Loss reduction from 73% to 77% is evidenced compared to cases 3 to 5, around 29% and 33% respectively beyond optimization of RPIs and DNSA (between case 5 and case 8) for IEEE 33 bus test system and Myanmar 74 bus test system have been witnessed. Thus, the total E_Loss reduction has moved up to 91% for IEEE 33 bus system and up to 77.7% for real 74-bus Myanmar EDN. Around 29% and 33% of extra E_Loss reduction have been yielded by optimizing IREGs at two/three optimal nodes in the reactive power supported optimal network. Thus, the maximum EB has reached beyond $350K for the IEEE 33-bus test system and more than $500K for real 74-bus Myanmar EDN respectively.

4. From the results, it is understood that the difference in EB between cases 3 to 5 and cases 6 to 8 are minuscule and are estimated below $1500 only for both EDNs.

According to the data above, LFM-SOA optimizes real and reactive power injections through ideal nodes with DNSA, resulting in higher EBs and E_Loss decrease. Comparing LFM-SOA’s performance with other optimization methods, three key metrics were examined: Reduction of E_Loss, bus voltage profile, and EBs (IEEE 33 bus system). To resolve radial EDN planning and operation issues, the suggested methodology is therefore more appropriate and an effective algorithm as well.