Assessment of power distribution system losses and mitigation through optimally placed D-STATCOM

Abstract

In general, power distribution losses are a crucial issues in the power industry. Although this is a global concern however this study is conducted in a Gesuba town 15 kV power distribution system consisting of 19 distribution transformers with total demand of 2.522 MW. High loss factor and less voltage stability issues are one of the most challenging issues in the town. A backward/forward sweep load flow analysis was utilized to analyze the system with application of particle swarm optimization (PSO) algorithm to find the kVAR size and the location of distribution static compensator (D-STATCOM) for objective of reducing power loss and improving the voltage profile. From the assessment, the critical bus is found as bus #6 with the optimal size of about 986 kVAR. From the data analysis, the average load factor (L_F) and loss factor (L_SF) are found as 47.013% and 11.71%, respectively. The town’s voltage-dependent load model is developed. A load flow analysis revealed that the average bus voltage magnitude before and after D-STATCOM integration is about 0.9148 pu and 0.9767 pu, respectively, with active power loss of 461.6203 kW and 179.2530 kW. It can be deduced from this analysis that the developed model appropriately represents the actual system, thus indicating that it would be advantageous for the utility to consider investing in implementing the proposed approach to achieve better performance.

Keywords:

• Backward/forward sweep
• distribution-STATCOM
• particle swarm optimization
• power losses
• voltage profile

Reviewing Editor:

• Ai Qingsong, Wuhan University of Technology, Wuhan, CHINA
• Chen Kun, Wuhan University of Technology, Wuhan, CHINA

Subjects:

• Science
• Earth Sciences
• Earth Sciences
• Geochemistry
• Engineering Technology
• Technology
• Engineering & Technology
• Systems & Control Engineering
• Control Engineering
• Social Sciences
• Economics, Finance, Business & Industry
• Industry & Industrial Studies
• Energy Industries & Utilities
• Electrical Power Industries

1. Introduction

1.1. Background of the study

The distribution system is one of the main part of the power system and controls the supply of electricity to customers. As electricity is transported on transmission lines, it experiences electrical losses. As the length of the transmission line increases, the loss increases and varies with the amount of power being transported. Average losses may vary from year to year due to network usage cycles, network configuration, and load profile shape and reactive power support level.

Two important aspects of loss study are loss and load factors. Electrical system losses are high in peak load conditions. Therefore, factors that represent the relationship between maximum loss and average loss help to determine the losses of an electrical system. Consumer devices are often designed to operate at specific voltages. However, some devices in the distribution system do not meet their rated limit (0.95 ≤ V ≤ 1.05 pu). Therefore, it can consume a large amount of current, which leads to a large voltage difference and power loss in the network. As a result, reaching acceptable voltage level in the distribution system is a challenging task.

Assessment of power system losses and its mitigation is an essential aspect of maintaining a reliable and efficient energy network. A thorough assessment of these losses involves identifying the sources and quantifying their magnitude. This requires advanced modeling techniques, data analysis and measurement tools to accurately evaluate factors, such as line resistance and reactive power consumption. Once the sources of losses are determined, appropriate mitigation strategies can be implemented. These include improving transformer designs for higher efficiency, implementing voltage control measures to reduce reactive power consumption.

Reducing power system losses can lead to improved voltage stability, ensuring that consumers receive a consistent and uninterrupted supply of electricity. Therefore, investing in the assessment and mitigation of power system losses is not only beneficial for economic and environmental reasons but also for the overall reliability and functionality of the energy network. Reducing losses can also create additional capacity that avoids large capital investments in new distribution infrastructure.

The problem of losses can be solved by appropriate VAR management at proper location. Some of these devices are capacitor banks, SVCs, distribution STATCOMs (D-STATCOMs), which is the main concern of this study. The most widely used custom power devices (CPDs) used as VAR management devices are distribution static compensator (DSTATCOM), static synchronous series compensator (SSSC), dynamic voltage restorer (DVR) and unified power quality conditioner (UPQC). As it delivers effective reactive power, the D-STATCOM is the most appropriate device among these devices. D-STATCOM has better ability to provide fast and continuous response during inductive and capacitive mode compensation (Kazmi et al., 2020).

Today, computer models are used to analyze load flows. The utility can benefit from having a consistent way to measure, compare and evaluate distribution system losses. This gives the regulators confidence that proper allocation is being made to utilities, cost-effective approaches to utilities to reduce system waste, and allows utilities to document energy savings so energy efficiency claims can be properly recognized. Due to nonlinearity of power system, the optimization algorithms are highly recommended to be applied for analyzing a system under different loading conditions. The particle swarm optimization (PSO) algorithm is utilized for this study. This algorithm is selected due to its less memory requirement, less programming complexity, application popularity in distribution system (Eberhart & Kennedy, 1995). The backward/forward sweep algorithm (because it is better than other algorithms in terms of unbalanced loading and high R/X ratio in the distribution system) (Petridis et al., 2021) is used for load flow analysis.

1.2. Statement of the problem

In the electric power system, power loss often occurs when the utilities supply electricity to the customer through the distribution line. Ideally, the active power loss should be as low as possible. However, the data collected showed that the average four-year active power loss in the study area was around 22.33% with an average voltage drop of 17.89%. This means that the difference between the power supplied from the main substation feeder to the town and the power sold is about 22.33%. The annual power loss is found as 23.47%, 20.72%, 23.45% and 21.68% in 2019, 2020, 2021 and 2022, respectively.

The main reasons arising for high power losses in the network are aging of conductors, poor voltage regulation due to absence of VAR supporting device, distance from main substation (30.6 km), electricity theft, and overloading of distribution transformers. Some transformers in the proposed study area are overloaded while some are lightly loaded.

Thus, in order to improve the system performance by reducing the losses and improving the bus voltage profile, PSO algorithm is developed using MATLAB source code for optimal sizing and to find a critical bus for placement of the proposed D-STATCOM in the system. Due to their popularity, the ant colony optimization (ACO) and whale optimization algorithm (WOA) are used for performance comparison with PSO algorithm.

1.3. Contribution of the study

The main objective of this study is to reduce the active power loss and to improve the bus voltage profile for Gesuba town 15 kV system by using D-STATCOM

1. The actual active power connected to each distribution transformer is measured using voltage and current values at 15-min intervals during peak load periods.

2. Since there is no recorded line impedance data at study area, the length between each distribution transformer is measured and the impedance is calculated for each branch.

3. Investigation of different classes of the distribution load and its modeling by considering the voltage-dependent load models.

4. The PSO algorithm is utilized to determine optimal potential of the proposed D-STATCOM. Also PSO is used to locate the critical bus in the system for D-STATCOM placement.

2. Literature review

2.1. Brief review of related works

Researchers have explored different ways to mitigate power losses and voltage deviation using D-STATCOM. Numerous authors have proposed application of nature‐inspired metaheuristic techniques for finding the optimal location and size of one or multiple D‐STATCOMs.

Balamurugan et al. (2018) studied optimal placement and sizing of D-STATCOM using the WOA for decreasing power loss and improving bus voltage in distribution networks. Here voltage stability index (VSI) is used to determine optimal location and WOA used to find the optimal size of D-STATCOM. Sundararaman et al. (2022) used BAT algorithm to find the optimal locations of required DGs for minimizing the power losses and maintaining the bus voltage profile of the systems by developing voltage stability indicator.

Yuvaraj et al. (2017) utilized cuckoo search algorithm (CSA) to determine the optimal size of DG and DSTATCOM to minimize power losses of the system subjected. A loss sensitivity factor (LSF) and VSI are applied to determine location of DG and DSTATCOM, respectively. Ali et al. (2017) have presented an ant lion optimization approach (ALOA) for optimal allocation of DGs for different distribution systems by using LSF to identify very weak buses for locating DGs.

Selim et al. (2018) have presented an allocation of DG units and D-STATCOM by proposing Sine–Cosine Approach (SCA) algorithm for optimal size of D-STATCOM and DG to reduce power loss in distribution network by considering VSI for selection of optimal site for DG integration. Sirjani (2018) proposed the use of PSO algorithm to find the optimal terminal for D‐STATCOM for minimum losses in the network. Oloulade et al. (2018) have presented an ACO algorithm to calculate the optimal placement, size and amount of D‐STATCOMs with incorporation of the cost of devices within the optimization process.

Gupta and Kumar (2018) proposed the utilization of a sensitivity approach by calculating the VSI for choosing the optimal location of the D‐STATCOM. Rezaeian‐Marjani et al. (2020) presented a probabilistic technique for optimal allocation of the D‐STATCOM for improving the voltage deviation index (VDI) and to decrease the D‐STATCOM expected installation cost in radial/mesh distribution networks. Hussain and Subbaramiah (2017) calculated the optimal size by mathematical modeling of D-STATCOM, to maintain the voltage magnitude as 1pu and to supply the required reactive power for compensation at the node where D-STATCOM is placed.

Farhoodnea et al. (2016) used Firefly algorithm to determine the optimal size and location of D-STATCOM. Bagheri Tolabi et al. (2015) proposed a hybrid ACO algorithm with fuzzy multi-objective approach combination for simultaneous placement of DG and D-STATCOM in the reconfigured network. Devabalaji and Ravi (2016) presented a bacterial foraging optimization (BFO) algorithm to find optimal size and location of DGs and DSTATCOM in radial distribution system. Thuan et al. (2021) presented an improved coyote optimization algorithm (ICOA) for distribution network reconfiguration (DNR) problem considering unbalanced load.

2.2. Identified research gaps

Substation and distribution transformers are the main components that account for the largest share of losses in the power distribution system. The utilities usually have that data at the substation transformer level, which many articles have applied for their studies to reduce system losses. However, insufficient research has been conducted on the loss data at the distribution transformer level.

The distribution loads were not classified in most of the reviewed articles, with researchers applying the loads without any modifications. It is essential to classify the distribution system loads based on their intended installation purpose. Consequently, this research was undertaken to analyze the classification of distribution transformers along with the development of a load model based on voltage dependency.

Therefore, the loss information of distribution transformers is computed by using measured line voltage and current during peak load periods. A line parameters are recorded at every 15-min interval during peak load times (12 AM–8 AM and 6 PM–8 PM) over a period of one month for each available distribution transformer.

Thus, this study works on a problem of optimal placement of D-STATCOM by using the improved load model development approach with proposed PSO algorithm. Before conducting the load flow, the system’s load modeling was conducted and then the recorded data is further used for load flow analysis.

3. Methodology

3.1. Modeling of the proposed power system

3.1.1. Line parameters modeling

The Gesuba town power distribution system is provided from the Wolaita Sodo-I substation (about 30 km long) having substation transformer capacity of 25 MVA at 15 kV. It distributes electricity to consumers through distribution transformers that step down from 15 kV to 380 V with a frequency of 50 Hz. The distribution system consists of 20 node points and AAC50 type 15 kV rated 19 distribution lines (branches). The proposed system consists of one slack bus and 19 load buses. A single-line diagram of a proposed system is shown in Figure 1.

Figure 1. Single-line diagram for Gesuba town power distribution system.

The inductance of transmission line depends upon the material, dimensions and configuration of the wires themselves and length with the spacing between them. The wire manufacturers usually supply tables of resistance per unit length at common frequencies (50 Hz or 60 Hz) to determine the resistance from such tables. The impedance is calculated at a frequency of 50 Hz and at a length of one kilometer. Thus, the impedance, Z of conductor is given by (Hussein, 2000): (1) $$Z_a=R_a+j0.06283\mathrm{\text{ln}}\hspace{0.17em}\frac{D}{{\mathit{\text{GMR}}}_a}\mathrm{ }\mathrm{\Omega }/\mathrm{\text{km}}$$(1) where (2) $$D=\sqrt[3]{D_{\mathit{\text{ab}}}\mathrm{*}{D}_{\mathit{\text{bc}}}\mathrm{*}{D}_{\mathit{\text{ac}}}}$$(2)

Since the conductors that are used in distribution feeders are the strand conductors, the Geometric mean ratio (GMR) for stranded conductors is given by: (3) $${\mathit{\text{GMR}}}_a=K\mathrm{*}r$$(3) where K: the GMR factor, r: actual conductor radius, R: resistance of conductor i in Ω/km, D: distance between conductors in meter, D_ab: Distance between conductors a and b in meter, D_bc: Distance between conductor’s b and c in meter, and D_ac: Distance between conductors a and c in meter.

The values of diameter, GMR factor, resistance and reactance values with its strand number of AAC conductor and conductor parameters of the feeder shown in Table 1 (Hussein, 2000).

Table 1. Standard AAC conductor parameters.

Conductor parameters	AAC95	AAC50	AAC25
Nominal cross-sectional area (mm^2)	95	50	25
Actual cross section (mm^2)	93.27	49.48	24.2
Stranding and wire diameter (Nos/mm)	19/2.5	7/3.0	7/2.1
Overall diameter (mm)	12.5	9.0	6.3
Actual diameter (mm)	10.8975	7.9377	5.56
GMR (mm)	4.13	2.88	1.87
Conductor resistance at 20 °C (ohm/km)	0.3095	0.5786	1.181
Maximum current rating, at 35 °C (Amps)	324	219	145
Maximum current rating, at 50 °C (Amps)	245	168	105

The positive sequence impedance of the conductors is obtained by multiplying the impedance per kilometer by its length. The self-impedance of phase conductors for AAC50 type conductors is found as (Hussein, 2000): (4) $$Z_{50}=0.5785+j0.34702\mathrm{ }\mathrm{\Omega }/\mathrm{\text{km}}$$(4)

Since all the lines in the town are AAC50-rated bare 15 kV rated conductors, the value for impedance computation considered only AAC50 formula and the distance between each transformer is measured and then it is multiplied with the given formula in order to find the required impedance for line data that is used for load flow analysis.

By employing the proposed procedures, the line data for the proposed network is calculated. There are only 19 distribution transformers in a proposed town and the R and X values for each branch is also computed. The line and load data is shown in Table 2. The total peak demand of the town is found as about 2.522 MW and 1.23 MVar for active and reactive power, respectively. The actual demand is computed from the measured current and voltage values during peak load sessions and the power factor considered is 0.8.

Table 2. Line and load data of the proposed network.

Branches					Loads at receiving end
No.	From	To	R (ohm)	X (ohm)	PL (kW)	QL (kVar)
1	1	2	0.9722	0.5476	122.00	61.00
2	2	3	1.0159	0.6462	138.40	54.20
3	3	4	0.9106	0.4306	201.50	93.00
4	4	5	0.8423	0.5192	154.82	74.57
5	5	6	0.9071	0.8198	125.40	60.82
6	6	7	0.7114	0.7241	130.14	64.46
7	7	8	0.4229	0.5891	135.14	66.20
8	8	9	1.9871	0.5782	94.500	22.47
9	9	10	1.0787	0.7447	174.80	94.01
10	9	11	0.4242	0.5761	175.00	99.87
11	11	12	0.8984	0.3325	108.40	65.68
12	12	13	0.7546	0.4211	105.10	62.00
13	12	15	0.6235	0.5214	144.00	57.10
14	12	16	0.9245	0.7149	107.10	58.71
15	13	14	0.9238	0.9012	198.00	92.51
16	16	17	0.9054	0.8086	105.00	67.41
17	17	18	0.6891	0.7584	99.700	24.57
18	18	19	0.7607	0.8164	105.00	65.70
19	19	20	0.8093	0.8781	98.00	45.70
Total					2522.00	1229.98

3.1.2. Distribution transformers loss assessment

Since transformers are inductive in nature they consume the power with lagging power factor. But the key input for estimating distribution transformer energy loss is the transformer load that determines the power factor and energy consumed. The distribution transformer-rated capacity does not reflect their actual consumption. Therefore, there is no measured load record for distribution transformers when the feeder is supplying the energy.

Losses in distribution transformer are broadly classified as: (2) No load losses (L_O) is a constant load and its data is obtained from datasheet of the transformer manufacturer (2) Load loss (L_L) is a function of load current (I²R), and its data could be computed by using the recorded line current and the percentage impedance (%Z) of the transformer.

The total distribution system loss at a given period can be expressed as percentage of total input energy to the system and total energy sold and is computed as (Muluneh & Ashenafi, 2022): (5) $$\text{Total\hspace{0.5em}loss}=\frac{\text{Energy\hspace{0.5em}input}-\text{Energy\hspace{0.5em}sold}}{\text{Energy\hspace{0.5em}input}}\mathrm{*}100\mathrm{\%}$$(5)

The overall losses comprise both technical and non-technical components, with non-technical loss primarily being a result of energy theft and unpaid bills, while technical losses occur during the transmission of energy from the source to the consumer end.

However, the two important factors used under this study are load factor and loss factor for finding the loss level of each distribution transformer. The load factor (L_F) can be described as the average load divided by the maximum demand (peak load) observed during a specific period. The loss factor (L_SF) is defined as the mean power losses throughout a designated timeframe when compared to the losses recorded at peak demand.

The L_SF can be formulated as (Navarro & Rudnick, 2009): (6) $$L_{\mathit{\text{SF}}}=\mathrm{\alpha \hspace{0.17em}}\mathrm{*\hspace{0.17em}}{L}_F+(1-\alpha )L_F^2$$(6) where α is the coefficient and taken as 0.15 for this study as recommended in Bayliss and Hardy (2012). However, this value may be applicable or not for other different systems.

Based on the recorded current and power values for peak sessions, the L_F and L_SF are computed for each of the transformers in the network. From the data computation, the average distribution transformers L_F and L_SF are found as about 47.013% and 11.61%, respectively. As shown, the load factor is very low in the town and the main reason arising is the poor service availability in the town and also the loss factor is high.

3.2. Load flow analysis

3.2.1. Load modeling

In general, the distribution networks load can be classified into three distinct types: industrial, residential, and commercial loads. Considering practicality, this research methodology is well-suited for implementing load models that are reliant on voltage. By employing static load models, different consumer classifications are depicted for the purpose of measuring the effect of voltage-dependent load models on DSTATCOM sizing.

The categorization of distribution transformers in the town is done by separating them into three classes–commercial, residential, and industrial loads–to determine the appropriate class of installation. During the network investigation, out of 19 transformers 8 transformers are supplying only residential loads, 3 are only industrial, 5 are only commercial loads, and 3 are supplying mixed commercial and residential loads.

Field measurements are carried out on each distribution transformer for determining the load models. Real power, power factor, and voltage are determined through the use of a power analyzer. Here only voltage values are recorded for this study. Because it is arduous and time-intensive to record measurements for every transformer available in the network, only peak time measurements of all transformers are documented.

3.2.2. Load flow formulation

The load flow analysis acts as an essential prerequisite in the electrical power engineering industry to assess normal operation mode, contingency analysis, and outage security for electrical power systems; therefore, various algorithms are implemented when conducting load flow analysis on distribution systems. In power distribution systems, the presence of unbalanced load and a high R/X ratio make algorithms, such as Gauss–Seidel and Newton–Raphson ineffective in achieving convergence. A backward/forward sweep algorithm was subsequently developed according to findings from studies, enabling the evaluation of distribution systems with short simulation times and low memory requirements, even when dealing with a significant number of buses in the system (Petridis et al., 2021; Yalew et al., 2021).

Let us consider only two buses interconnected through a branch in a distribution system as depicted in Figure 2.

Figure 2. Simple two bus power system.

The P_ij and Q_ij are the real and reactive power flows between buses i and j, respectively, and it can be formulated as (Muluneh & Ashenafi, 2022; Yalew et al., 2021): (7) $$\left.\begin{array}{c}{P}_{\mathit{\text{ij}}}=P_j+P_{\mathit{\text{loss}},\mathit{\text{ij}}}\\ Q_{\mathit{\text{ij}}}=Q_j+Q_{\mathit{\text{loss}},\mathit{\text{ij}}}\end{array}\right\}$$(7)

The expression for the current passing through buses i and j can be represented as: (8) $$I_{\mathit{\text{ij}}}=\frac{P_{\mathit{\text{ij}}}-j{Q}_{\mathit{\text{ij}}}}{V_j\mathrm{\angle }{-\alpha }_j}$$(8)

Additionally, the line current flow can be formulated as: (9) $$I_{\mathit{\text{ij}}}=\frac{V_i\mathrm{\angle }{\alpha }_i-V_j\mathrm{\angle }{\alpha }_j}{R_{\mathit{\text{ij}}}+j{X}_{\mathit{\text{ij}}}}$$(9)

Through the analysis of Equations (7)(7) $$\left.\begin{array}{c}{P}_{\mathit{\text{ij}}}=P_j+P_{\mathit{\text{loss}},\mathit{\text{ij}}}\\ Q_{\mathit{\text{ij}}}=Q_j+Q_{\mathit{\text{loss}},\mathit{\text{ij}}}\end{array}\right\}$$(7) and (8)(8) $$I_{\mathit{\text{ij}}}=\frac{P_{\mathit{\text{ij}}}-j{Q}_{\mathit{\text{ij}}}}{V_j\mathrm{\angle }{-\alpha }_j}$$(8) , it becomes apparent that: (10) $$V_i^2-V_i{V}_j\mathrm{\angle }\left({\alpha }_j-{\alpha }_i\right)=\left(P_{\mathit{\text{ij}}}-j{Q}_{\mathit{\text{ij}}}\right)\left(R_{\mathit{\text{ij}}}+j{X}_{\mathit{\text{ij}}}\right)$$(10)

After separating the real and imaginary parts in Equation (9)(9) $$I_{\mathit{\text{ij}}}=\frac{V_i\mathrm{\angle }{\alpha }_i-V_j\mathrm{\angle }{\alpha }_j}{R_{\mathit{\text{ij}}}+j{X}_{\mathit{\text{ij}}}}$$(9) , we can have: (11) $$\left.\begin{array}{c}{V}_i{V}_j\hspace{0.17em}\mathrm{\text{cos}}\hspace{0.17em}\left({\alpha }_j-{\alpha }_i\right)=V_i^2-\left(P_{\mathit{\text{ij}}}{R}_{\mathit{\text{ij}}}+Q_{\mathit{\text{ij}}}{X}_{\mathit{\text{ij}}}\right)\\ V_i{V}_j\hspace{0.17em}\mathrm{\text{sin}}\hspace{0.17em}\left({\alpha }_j-{\alpha }_i\right)=Q_{\mathit{\text{ij}}}{R}_{\mathit{\text{ij}}}+P_{\mathit{\text{ij}}}{X}_{\mathit{\text{ij}}}\end{array}\right\}$$(11)

After squaring Equation (10)(10) $$V_i^2-V_i{V}_j\mathrm{\angle }\left({\alpha }_j-{\alpha }_i\right)=\left(P_{\mathit{\text{ij}}}-j{Q}_{\mathit{\text{ij}}}\right)\left(R_{\mathit{\text{ij}}}+j{X}_{\mathit{\text{ij}}}\right)$$(10) and adding up them, we could have: (12) $$V_j^2=V_i^2-2\mathrm{*}\left(P_{\mathit{\text{ij}}}{R}_{\mathit{\text{ij}}}+Q_{\mathit{\text{ij}}}{X}_{\mathit{\text{ij}}}\right)+\frac{1}{V_i^2}\left(R_{\mathit{\text{ij}}}^2+X_{\mathit{\text{ij}}}^2\right)\left(P_{\mathit{\text{ij}}}^2+Q_{\mathit{\text{ij}}}^2\right)$$(12)

By employing mathematical calculations, one can establish the real and reactive power losses in the following manner (Prakash & Lakshminarayana, 2016): (13) $$\left.\begin{array}{c}{P}_{\mathit{\text{loss}},\mathit{\text{ij}}}=I_{\mathit{\text{ij}}}^2{R}_{\mathit{\text{ij}}}=\frac{1}{V_j^2}\left(P_{\mathit{\text{ij}}}^2+Q_{\mathit{\text{ij}}}^2\right)R_{\mathit{\text{ij}}}\\ Q_{\mathit{\text{loss}},\mathit{\text{ij}}}=I_{\mathit{\text{ij}}}^2{X}_{\mathit{\text{ij}}}=\frac{1}{V_j^2}\left(P_{\mathit{\text{ij}}}^2+Q_{\mathit{\text{ij}}}^2\right)X_{\mathit{\text{ij}}}\end{array}\right\}$$(13)

By adding all line losses, the total real and reactive power losses of a network are computed as: (14) $$\left.\begin{array}{c}{P}_{\mathit{\text{loss}},\mathit{\text{ij}}}=\sum _{k=1}^{N_{\mathit{\text{br}}}}{P}_{\mathit{\text{loss}},\mathit{\text{ij}}}\\ Q_{\mathit{\text{loss}},\mathit{\text{ij}}}=\sum _{k=1}^{N_{\mathit{\text{br}}}}{Q}_{\mathit{\text{loss}},\mathit{\text{ij}}}\end{array}\right\}$$(14)

When verifying for convergence, if the error value goes over the set tolerance limit, another iteration is executed. In contrast, if the error value falls below the tolerance factor, the iterative process halts and exhibits the convergence result.

3.3. PSO formulation

The PSO is one of the swarm intelligence algorithms introduced by J. Kennedy and E. Russell from social animal characters being inspired by the concept of schooling fish and flocking birds (Eberhart & Kennedy, 1995). Due to its ease of implementation, highly precise solution, and fast convergence, PSO has gained significant popularity in solving practical problems. The flowchart of PSO algorithm is shown in Figure 3.

Figure 3. Flowchart for the proposed PSO algorithm.

3.3.1. Objective function

The objective (fitness) functions considered for this study are system branch active power losses and the VDI. These are formulated as shown below.

a) Power losses: The fitness function is formulated to minimize the power losses of the electrical distribution network by the following equation (Prakash & Lakshminarayana, 2016): (15) $$F_1=\mathrm{\text{min}}\left(P_{\mathit{\text{loss}}}\right)$$(15) where (16) $$\left.\begin{array}{c}{P}_{\mathit{\text{loss}}}=\sum _{i=1}^{N_{\mathit{\text{br}}}}{I}_i^2{R}_i \\ P_{\mathit{\text{loss}}}=\sum _{i=1}^{N_{\mathit{\text{br}}}}\left[\frac{P_i^2+Q_i^2}{V^2}{R}_i\right]\end{array}\right\}$$(16) where N_br is the total number of branches; I_i is the current that flow branch i, R_i is the resistance of branch i, P_i, and Q_i is the active and reactive power flow of branch i, and V is the receiving end bus voltage magnitude.

b) Voltage profile: The VDI can be formulated as (Muluneh & Ashenafi, 2022): (17) $$F_2=\left|\frac{V_{\mathit{\text{ref}}}-V_i}{V_{\mathrm{\text{max}}}-V_{\mathrm{\text{min}}}}\right|\mathrm{*}100\mathrm{\%}$$(17) where V_ref is reference voltage (i.e. 1) and V_i is actual voltage of ith bus, V_max and V_min are maximum and minimum bus voltage tolerance values (1.05 and 0.95 pu).

3.3.2. Constraints

a) Power balance constraint: The consumed power of the network should be equal to the generated power of the system as given by Muluneh and Ashenafi (2022) and Prakash and Lakshminarayana (2016): (18) $$\left.\begin{array}{c}{P}_G=\sum _{m=1}^{N_{\mathit{\text{br}}}}{P}_{\mathit{\text{loss}},m}+\sum _{i=1}^{N_b}{P}_{\mathit{\text{load}},i}\\ Q_G+\sum _{j=1}^{N_d}{Q}_{\mathit{\text{stat}},j}=\sum _{m=1}^{N_{\mathit{\text{br}}}}{Q}_{\mathit{\text{loss}},m}+\sum _{i=1}^{N_b}{Q}_{\mathit{\text{load}},i}\end{array}\right\}$$(18) where P_G and Q_G are substation active and reactive power, P_loss and Q_loss are active and reactive line losses, P_load and Q_load are active and reactive loads, Q_stat,j is reactive power injected by the D-STATCOM and N_d denotes numbers of D-STATCOM.

b) Voltage constraint: The bus voltages should be within allowable limits and expressed as: (19) $$V_{\mathrm{\text{min}}}\le V_i\le V_{\mathrm{\text{max}}}\mathrm{ }i\in N_b$$(19) where V_min and V_max are the minimum and maximum voltages at ith node and it is considered as 0.95 pu and 1.05 pu, respectively.

c) D-STATCOM reactive power constraint: Constraint of D-STATCOM reactive power injection capacity is given by: (20) $$Q_{\mathit{\text{stat}},\mathrm{\text{min}}}\le Q_{\mathit{\text{stat}},i}\le Q_{\mathit{\text{stat}},\mathrm{\text{max}}}\mathrm{ }i\in N_b$$(20)

A generalized approach to be followed by PSO algorithm to solve the fitness function for D-STATCOMs sizing as shown in Figure 7 can be illustrated as follows:

• Step 1: Read the network data such as line data, and load data

• Step 2: Execute the load flow analysis algorithm

• Step 3: Calculate bus voltages and power losses

• Step 4: Initialize the PSO algorithm

• Step 5: Define inputs of the PSO algorithm and determine fitness function

• Step 6: Create the initial population and compute fitness function

• Step 7: Check whether constraints are satisfied or not

  • Step 8: If not satisfied, go to Step 6

  • Step 9: If constraints are satisfied, print the solutions achieved.

4. Results and discussions

4.1. Developed load model of the study area

In mathematical notation, from the collected data and by using the curve fitting approach, the voltage-dependent load model for the proposed distribution system study area can be depicted as (Claeys et al., 2021): (21) $$\left.\begin{array}{c}{P}_k=P_{\mathit{\text{nk}}}{\left(\frac{V_k}{V_n}\right)}^{\alpha }\\ Q_k=Q_{\mathit{\text{nk}}}{\left(\frac{V_k}{V_n}\right)}^{\beta }\end{array}\right\}$$(21) where P_k and Q_k are real and reactive power at bus k, P_n, and Q_n are active and reactive power at nominal bus voltage at bus k, V_k and V_n are actual and nominal voltage values, α and β are real and reactive power exponents.

From the recorded data, by considering 15 kV as a nominal voltage, V_n and nominal kVA rating of the each distribution transformer, the parameters α and β values for different load models as recommended in Claeys et al. (2021) are modified to make it compatible with the proposed power distribution system as shown in Table 3.

Table 3. Load types and their exponent values.

Load type	α	β
Commercial load	1.43	3.17
Residential load	0.86	3.94
Industrial load	0.28	4.61

This model parameters only represent the case study area currently connected load system. The overall regression performance of the proposed curve fitting model is found as about 99.63% having RMSE, R-squared and p value of 0.073, 99.592% and 0.0022, respectively.

4.2. Bus voltage without and with D-STATCOM

For conducting the proposed study, the following control parameters of the PSO algorithm implementation are presented as shown in Table 4. The PSO control parameters are varied and checked for several times and the values resulted in better convergence (improvement of the system performance) are presented here.

Table 4. Control parameter value of PSO.

Total number of swarm size: 50	Iteration count: 50
PSO parameters, c1 = 1.5, c2 = 2.2	PSO inertia (wmax, wmin): wmax = 1.2, wmin = 0.3

With the proposed control parameters, the convergence plot is presented as shown in Figure 4. And with help of the PSO parameters, the optimal DSTATCOM capacity and location are found as about 985.7 kVAR and bus #6, respectively (Figure 5).

Figure 4. Block diagram of the proposed study.

Figure 5. Convergence graph of PSO algorithm.

The bus voltage profile for actual measured values, before and after D-STATCOM-based compensation is presented as shown in Table 5. The actual values represent the bus voltage values for only peak load sessions. The integration of about 986 kVAR-sized D-STATCOM at bus six (6) resulted in an enhancement of the bus voltage magnitude for all buses in the system.

Table 5. Bus voltage magnitude (pu) before and after compensation.

Measured		Load flow result
Bus No	Vbus actual	Vbus before	Vbus after
1	1	1	1
2	0.9852	0.9848	0.988
3	0.9658	0.9691	0.9761
4	0.9426	0.9566	0.9663
5	0.9373	0.9454	0.9582
6	0.9185	0.9330	1.0003
7	0.9248	0.9235	0.9947
8	0.9125	0.9176	0.9919
9	0.9044	0.9004	0.9787
10	0.9008	0.8991	0.9775
11	0.9062	0.8959	0.9772
12	0.8977	0.8902	0.9734
13	0.8758	0.8887	0.9721
14	0.8911	0.8874	0.9709
15	0.8793	0.8896	0.9729
16	0.9015	0.8868	0.9704
17	0.8838	0.8841	0.9679
18	0.8744	0.8826	0.9665
19	0.8752	0.8813	0.9654
20	0.8368	0.8807	0.9648
Average	0.9107	0.9148	0.9767

The average bus voltage magnitudes for actual measurement, load flow before and load flow after compensation are found as about 0.9107 pu, 0.9148 pu and 0.9767 pu, respectively. The minimum bus voltage magnitudes are found as 0.8368 pu, 0.8807 pu and 0.9582 pu for actual, load flow before and after compensation. Moreover, the resulting bus voltage profile comparison is presented in Figure 6.

Figure 6. Comparison of bus voltage profile with compensation.

4.3. Line losses without and with D-STATCOM

After conducting the proposed load flow at 25 MVA and 15 kV base power and voltage, the line losses of each branch are selected and presented as shown in Table 6. As shown injection of proposed optimal reactive power to the system significantly reduced both active and reactive power losses of each branch.

Table 6. Line losses before and after compensation.

Branch			Active power loss		Reactive power loss
No	From	To	Without	With	Without	With
1	1	2	81.8809	32.7215	46.1201	19.8719
2	2	3	78.0433	29.0597	49.6423	18.9575
3	3	4	62.8772	23.3316	29.7331	11.7182
4	4	5	48.8876	18.1072	30.1347	11.6601
5	5	6	45.4222	16.7184	41.0508	15.2345
6	6	7	31.2804	11.9059	31.8389	12.0952
7	7	8	16.0587	6.7635	22.3698	8.9107
8	8	9	63.9542	23.2636	18.6092	7.6909
9	9	10	0.4673	0.1977	0.3226	0.1365
10	9	11	9.3810	4.6393	12.7402	5.8350
11	11	12	14.6106	6.9924	5.4074	3.4068
12	12	13	0.9849	0.4114	0.5496	0.2296
13	12	15	0.1680	0.0703	0.1405	0.0587
14	12	16	3.5156	2.7662	2.7186	2.4338
15	13	14	0.4981	0.2080	0.4859	0.2029
16	16	17	2.1467	1.1949	1.9172	1.0992
17	17	18	0.8679	0.6617	0.9552	0.6981
18	18	19	0.4671	0.1946	0.5013	0.2089
19	19	20	0.1084	0.0452	0.1177	0.0490
Total loss			461.6203	179.2530	295.3549	120.4975

The total active power loss before and after the proposed compensation is found as about 461.6203 kW and 179.253 kW, respectively, and the total reactive power loss is reduced from 295.3549 kVAR to 120.4975 kVAR with D-STATCOM integration. The comparison of active power loss for each branch is shown in Figure 7.

Figure 7. Active power loss comparison for each branch.

The loading and loss factor of each distribution transformer in the study area are assessed and the values are presented as follows in Table 7. The one-month 15-min interval actual energy consumption of peak load sessions is recorded and the maximum consumption occurred during this session is observed. Table 7 shows the connected peak and average demand (in kVA) of each transformer for computation of the load and loss factors.

Table 7. Load and loss factor of distribution transformers.

Actual record			Computed
Trafo No	Speak	Savg	LF	LSF
1	136.4	92.72	0.6797	0.1713
2	148.6	112.54	0.7571	0.1995
3	221.9	146.42	0.6598	0.1643
4	171.8	95.1	0.5534	0.1289
5	139.4	32.19	0.2310	0.0427
6	145.2	27.24	0.1876	0.0334
7	150.5	33.81	0.2247	0.0413
8	97.1	54.37	0.5597	0.1309
9	198.5	10.66	0.0537	0.0085
10	201.5	161.46	0.8013	0.2165
11	126.7	57.06	0.4502	0.0979
12	122	42.46	0.3480	0.0704
13	154.9	26.59	0.1717	0.0302
14	122.1	120.12	0.9835	0.2926
15	218.5	189.42	0.8667	0.2427
16	124.8	95.01	0.7615	0.2012
17	102.7	2.73	0.0266	0.0041
18	123.9	17.18	0.1387	0.0237
19	108.1	51.51	0.4763	0.1055
Average			0.4701	0.1161

As shown in Table 7, the average loading and loss factors of the system transformers are found as about 0.4701 (47.01%) and 0.1161 (11.61%), respectively. This loss factor can be attributed solely to the loading of distribution transformers and does not take into account the branch losses. The load and loss factor are depicted in Figure 8.

Figure 8. Load and loss factors for each transformer.

As shown in Figure 8, out of 19 transformers, only seven (7) transformers are loaded higher than 60%, which could have better efficiency. This poor loading state of the transformers could lead the system less performing and low revenue generation. The main reason arising for poor utilization is due to long network outage state in the town.

4.4. Comparison of the algorithms

Table 8 shows the convergence performance (computation time, D-STATCOM size and resulting loss) for each proposed cases (base case, PSO, ACO and WOA cases). The reason for choosing ACO and WOA for comparison with PSO is due to their growing popularity for optimal system compensation.

Table 8. Comparison of the proposed optimization algorithms.

Scenario	Comp time	DSTATCOM size	Ploss (kW)	Qloss (kVar)
Without case	0.1011	–	461.6203	295.3549
PSO case	0.0630	986 kVAR	179.2530	120.4975
ACO case	0.0840	1062 kVAR	207.5100	136.7860
WOA case	0.0910	1141 kVAR	215.6500	127.2170

From Table 8, we could observe that PSO-based DSTATCOM integration within a system performed best than other approaches. The optimal kVAR of DSTATCOM using PSO algorithm is lower than ACO and WOA cases. The computational time of PSO is faster than ACO and WOA. From system loss comparison, we could observe that the PSO has better performance than ACO and WOA algorithms.

5. Conclusions

The distribution transformers loading and loss assessment could help the utility for improved revenue generation and also improved customer satisfaction. Under this study, each distribution loading state and the loss factor are assessed through field measurement of current, voltage and power measurements through 15-min interval during peak load sessions only for one month. From the recorded data, the voltage dependency of the proposed system loading state was assessed and the load model was developed.

Due to unbalanced loading and higher R/X ratio of distribution system, the backward/forward sweep algorithm was employed for load flow analysis in MATLAB software by considering 25 MVA and 15 kV base power and voltage. With help of PSO algorithm, the optimal location and kVAR capacity was determined for the proposed D-STATCOM incorporation. Comparison of PSO convergence is conducted with ACO and WOA algorithms, in which the PSO performed better. Moreover, the voltage profile of all buses was found within the IEEE-315 standard limits (0.95≤ V ≤ 1.05 pu) when the proposed D-STATCOM was incorporated optimally within the system.

As a future study, the following points should be considered:

• Field data records considered only peak load sessions and this might be not enough to describe the transformers loading state. Thus, the full day-long loading state should be considered.

• The voltage-dependent load model is developed for the proposed system. However, the frequency variation effect is not studied and might be added in future study directions.

• The dynamic loading state of the system is not considered under this study and might be added in the future.

Disclosure statement

The authors declare no conflicts of interest regarding the publication of this article.

Data availability statement

The line data and load data used to support the findings of this study are included within the article.

Additional information

Funding

This work was carried out as routine research and as such, the authors did not receive any funding support or grant for this work.