1. Introduction
Voltage stability (VS) is a major focus of modern power system (PS) utility companies. Therefore, VS is the ability of systems to keep the voltage profile stable when undergoing large or small disturbances. Different means have been used to improve the voltage profile in modern PS, such as battery storage systems and distributed energy resources (DER) [
1,
2,
3,
4]. The increase in the infrastructure and load demand rate leads to the high utilization of PS energy equipment. This has made systems experience voltage instability that has led to blackouts in some parts of the world, destruction of some businesses and daily activities, and increased power loss. Based on this problem, this study is motivated by identifying the weak bus that could cause a blackout in a system and reducing system transmission loss, which is caused by a shortage of reactive power (RP), which significantly affects the quality of energy delivery to the consumer end. Environmental and economic factors are two leading causes for establishing a new transmission line (TL). As the load increases, the system is heavily loaded, and maintaining stability becomes difficult; thus, the system operates close to the instability point [
5,
6,
7,
8]. Evaluation of system stability is based on the node/bus voltage profile. Presently, there are numerous techniques for finding system stability. The line voltage stability index (LVSI) [
9], a simplified voltage stability index (SVSI) [
10], L-index [
11], a global voltage stability index (GVSI) [
12], etc. Some classical voltage stability assessments and various techniques have been proposed for weak bus identification in power system networks. Some of them are genetic algorithms based on support vector machine (GA-VSM) [
13], ant colony (AC) [
14], electric cactus structure (ECS) [
15], and network response structural characteristic (NRSC) [
16].
A shortage of RP in a PS network causes a tremendous waste of electricity in the distribution system, resulting in extra emission of carbon and power generation cost. Therefore, reducing losses in transmission line networks (TLN) is essential for system safety. However, the best way to reduce losses in TLs of PS networks is RP optimization (RPO). Two methods used in solving the RPO problem are traditional and evolutionary algorithms. Traditional methods include the Newton–Raphson (NR) method, interior point methods, quadratic programming, and linear programming [
17]. Recently, evolution algorithms have been used to solve RPO problems, such as the hybrid pathfinder algorithm (HPFA) [
18], hybrid PSO (HPSO-PFA) [
17], modified PFA (mPFA) [
19], chaotic krill herd [
20], ant lion optimizer (ALO) [
21], the tree seed algorithm (TSA) [
22], and the improved pathfinder algorithm (IPFA) [
23]. However, PSO is good in search capacity and has less programming than others [
17].
Harish et al. used the fast voltage stability index (FVSI) and line stability index (
) to identify the location of flexible alternating current transmission system (FACTS) devices along with PSO, artificial bee colony (ABC), and the hybrid genetic algorithm (H-GA) to find the sizing of the FACTS devices [
24]. Also, a novel method for strengthening PS stability was proposed by Jaramillo et al. [
25]. FVSI was used to identify the node on which the SVC should be installed under an N-1 scenario. It was reported that the result obtained could reestablish the FVSI in each contingency before the outage [
25]. The voltage collapse critical bus index (VCCBI) [
26], L-Index, voltage collapse proximity index (VCPI), and modal analysis [
27], which are part of voltage stability indices (VSI), were used to identify weak/vulnerable buses in electrical power systems. Power loss reduction was made using a hybrid loop-genetic-based algorithm (HLGBA) [
28], the Jaya algorithm (JAYA), diversity-enhanced (DEPSO), etc. [
29].
This research considers the identification of critical nodes and loss reduction, which serve as merit over the previous work mentioned above. FVSI and
were used to find the critical node in the system based on load flow (LF) results from MATLAB 2018b software (MathWorks, Inc., Natick, MA, USA). FVSI and
were chosen because of their efficiency in identifying the weak/vulnerable bus (i.e., the fastness of FVSI and the accuracy of
) [
30]. The critical node was determined by the value of the indices (i.e., FVSI and
). When the indices value reaches unity or is close to unity, that node is the critical node of the system. The reactive powers of all the load buses were increased one after the other to determine the maximum RP on each of the load buses/nodes. Also, each line’s value of FVSI and
was computed to determine the load-ability limit on each load bus. The ranking was carried out based on the indices value of each node; hence, the node with the highest indices values is the system’s critical bus. This bus contained the smallest RP when the load bus was varied. The identified node needs reactive power support to avoid voltage collapse. Also, enhanced PSO (EPSO) was used to minimize the PS network loss along with PSO variants that have been developed by previous research, such as PSO-based time-varying acceleration coefficients (PSO-TVAC) [
31], random inertia weight PSO (RPSO), and PSO based on success rate (PSO-SR) [
32]. To overcome the premature convergence of PSO, the chosen EPSO was applied, and it uses neighborhood exchange to share more information with the other best individual (neighborhood) to improve itself, which makes it more efficient in getting a prominent solution (i.e., exploitation stage) to optimizing the objective function. The novelty of this research and this paper’s contribution is that each particle learns from its own personal and global positions in the PSO algorithm in the social cognitive system. Apart from personal experience and better information received from the search areas, it is advisable to share with better individuals to enhance or improve itself. Therefore, a new acceleration constant (
is added to the original PSO equation, making obtaining the best solution more efficient. Also, additional
gives the swarm the capability to reach the exploitation stage, which helps to overcome the premature convergence of PSO. However, this paper has contributed by (1) comparing different PSO variants and EPSO for power loss reduction; (2) identifying the power system critical node for the perfect operation of generators to avoid breakdown.
The rest of the paper is structured as follows:
Section 2 presents the problem formulation of voltage stability indices and RPO, and
Section 3 discusses the PSO, its variants, and EPSO. The results and discussion are presented in
Section 4, and the conclusion and future work is the last section.
5. Conclusions and Future Work
The role of PS operations is to ensure a stable voltage at the consumer end. Unfortunately, the PS failed to meet the desired goal due to generator failures and losses in the TL. This work applied EPSO to reduce the real power loss and other PSO variants. FVSI and were used to identify the critical bus and to learn the stressfulness of the lines in a PS. For the IEEE 9 bus system, bus 8 is the critical node, and the lines connected to it are the most stressful lines of the system. It has the lowest value of RP of 240 MVar, and one of the indices reaches unity (1). Node 14 was the critical node in the IEEE 14 bus system, and the lines connected to it experienced voltage instability. EPSO was used to reduce/diminish the actual/real power loss on the IEEE 9 and 14 bus systems. The loss was reduced from 9.842 MW to 7.543 MW for EPSO and 7.608 MW, 7.602 MW, 7.589 MW, and 7.600 MW for PSO, RPSO, PSO-TVAC, and PSO-SR, respectively, for the IEEE 9 bus system. Also, the losses on the IEEE 14 bus system were reduced from 13.775 MW (the base case) to 12.253 MW for EPSO and 12.263 MW, 12.259 MW, 12.260 MW, and 12.261 MW for PSO, RPSO, PSO-TVAC, and PSO-SR, respectively. The result shows that the EPSO algorithm gives a better loss reduction than other techniques and PSO variants in the literature. This indicates that EPSO is suitable for improving grid voltage quality, thereby suggesting that the technique will be a valuable tool for PS engineers in the planning and operation of electrical PS networks. This work recommends applying EPSO to other metaheuristic algorithms to form a hybrid method to solve engineering problems and some standard IEEE benchmark functions. Also, the computation time should be improved in future work.