1. Introduction
Power system planning in most developing countries is associated with several challenges due to the non-linear relationship between the increasing population and power generation, low reliability on capital investment, dispersed utilities, etc. [
1]. Gross deficiency in power generation has driven many developing countries to forced load shedding to ensure that the meager generated power reaches the considerable population. In such a context, power system operators are concerned about active power control, which is invariably associated with the frequency stability [
2], and rarely consider reactive power control, which is associated with voltage stability [
3]. Furthermore, the rotor, frequency and voltage stability control are essential components of a reliable power system [
4].
The Nigerian power network (NGP) comprised approximately twenty-six power plants with a combined optimal power generation of slightly more than seven thousand megawatts (7000 MW) [
5], which are provided hydro and thermal power plants [
6]. This generated power serves a population of more than two hundred million (200,000,000) people [
7]. The NGP is faced several crises, including insufficient generation of electric power to match the demand [
8,
9], overstretched transmission lines and support, [
10] and the inability to withstand transient conditions [
11]. The average number of the recorded power outages, both partial and total, in the NGP every year is alarming [
12], and there seems to be no end in sight with respect to addressing this increasing figure. The high rate of blackouts in Nigeria has driven many small-scale businesses out of operation [
13], and the few remaining companies operate at a high cost of production due to the increase in prices of alternative sources of fuel, for example, diesel, gas, etc. Hence, there is a need to develop a tool to identify the weak buses and lines that are vulnerable to voltage collapse, which could lead to a national blackout.
The framework of this research is to (1) develop a new voltage stability pointer (NVSP) for evaluation of voltage stability, (2) train the NVSP with the support vector machine using a medium Gaussian kernel classification toolbox in a MATLAB environment and (3) adapt it to the Nigerian power network to classify it into two classes, i.e., stable and unstable. The lines and buses under the unstable classification will be flagged as vulnerable.
2. Related Work
The effort of the Nigerian government to increase the power generation capacity of the country has not yielded satisfactory results despite the considerable capital investment in the power sector over the years. According to the World Bank Energy Progress Report, only 55.4 percent of the Nigerian population had access to electricity in the year 2020 [
7]. The geographical structure of the transmission lines in Nigeria is shown in
Figure 1.
The load demand is predicted to reach 50,000 MW by the year 2035 [
6]. However, there little effort has been made to date to scale up the generation capacity to meet this future demand. The recorded cases of power outages in the NGP between January and June 2022 are estimated to be five [
14]. This number is high compared to other developed nations [
7]. The variation in load demand is among the factors that affect the power network stability [
15]. Ramirez-Gonzalez M. et al. [
16] studied contingencies in a power network and their effects on security. A convolutional neural network was used to allocate power injection stations in the power network, with the result proving the effectiveness of the proposed method.
Similarly, Abdulkareem A. et al. [
10] suggested that the NGP topology be changed from a radial to ring structure to minimize losses and voltage instability. The TCN annual technical report also set a goal to achieve this transition before the year 2030 [
6]. However, such a transition will be time-consuming and cost-intensive, and a solution is urgently required before it can be implemented. In addition, Obi P. I. et al. [
17] presented a technique to improve the NGP with static Var compensators to fulfill the voltage quality requirements. However, this technique is regarded as a short-term solution to the lingering problem faced by the Nigerian power grid. Moreover, Adebayo et al. [
18] proposed two methods to identify vulnerable buses in a power network. The first method was achieved through the maximum loading limit technique, and the other was based on the configuration of the power network. The NGP 24-bus and IEEE 30-bus systems were used to evaluate the proposed method. The critical buses were strengthened with FACTS components. Simulation results showed that optimal placement of a compensating device could improve the voltage profile. In [
19], a stability concept for power systems based on the frequency control of synchronous machines was presented. The system was tested with various loading patterns, and the results were compared with conventional synchro-converter models.
In a research paper presented by Kasis A. et al. [
20], a technique was evaluated to solve the problem associated with fluctuations of renewable energy sources and the effects on power stability. Multiple possibilities for frequency dynamics were modeled, considering the variability of the inherent power supply. The results showed the immunity of the power stability to a high-frequency cycle. A surge in renewable power penetration in power distribution networks might result in overvoltage at network buses in the absence of an effective control mechanism. Heidari Yazdi et al. [
21] proposed a method to regulate voltage magnitude based on the load demand. Power demand usually varies; therefore, means to compensate for the peak consumption period is necessary. An overvoltage resulting from excessive reactive power injection was considered and addressed for a stable power system.
In an effort to solve problems associated with power network configuration, Narimani et al. [
22] proposed a novel method of analyzing several contingency problems associated with the architecture of the network. This was achieved through a graph theory approach that identifies different power components responsible for contingency, especially between two successive contingencies. The results showed that the proposed method could rapidly identify multiple contingencies. In the same vein, Randey A et al. [
23] proposed a network reconfiguration technique for NGP to secure the network from a possible grid collapse and thereby improve the voltage profile. Contingency analysis resulted suggested that the redistribution of notable generators to defined voltage set-points would reduce power outages.
In a paper presented by Nkan et al. [
24], several compensative devices were investigated with the aim of combining two similar controllers. The method was tested on NGP in the power system analysis toolbox (PSAT) in MATLAB. Analysis results showed that the combination of similar compensating devices could reduce power losses to a considerable extent. Some NGP buses are currently operating below their standard rated voltage [
25] as a result of overload and congestion, with no adequate plan for contingency. Moreover, Liu S. et al. [
26] presented a study on the dynamism of a stability point in a power network through the injection of noise and time delay. The aim of this method is to improve the integrity of the power network in a smart grid. The authors assessed the effect of noise on power system stability.
The power stability problem has recently received attention from many researchers, and efforts are being made to address the problems associated with power stability. Alnasseir et al. [
27] addressed the power stability problem by introducing a static synchronous compensator (STATCOM) and a thyristor-controlled series capacitor (TCSC). The two compensators were assessed independently, and their results were compared. The results showed that the TCSC is relatively effective in securing power stability. Similarly, Calma E. and Pacis M. [
28] studied voltage stability indices for different states of operation in a power system. The proposed approach involved an artificial neural network, and the Newton–Raphson power flow was employed in the MATLAB environment. The results demonstrated the feasibility of the proposed approach, especially compared with other machine learning techniques in terms of assessing the voltage stability of a power network. In addition, Collados-Rodriguez et al. [
29] analyzed the effect of power electronics components on power system stability. Several cases of stability were evaluated to assess the minimum power generation expected to ensure power network security with the installation of compensative components. The stability indices considered for the evaluation were frequency and voltage, which were sufficient to identify the vulnerable lines in the network [
2,
3].
The effect of harmonics on power stability cannot be overemphasized [
30]. Abirami and Ravi [
31] recommended a technique to reduce harmonic distortion, especially with the advent of electric car charging stations in the distribution network. They suggested that a shunt capacitive filter be connected in parallel with dynamic loads in a radial distribution network. Simulation results revealed that adequate control of harmonic could enhance the power quality delivery to end consumers. Similarly, Zaheb H. et al. [
32] investigated the effect of inductive load dynamics on various voltage stability indices. The researchers emphasized the suitability of these indices for online application. The obtained results were used to classify the indices in terms of their ability to assess, formulate and analyze the voltage stability.
The NVSP proposed in this study was developed to (a) verify the voltage stability status of the Nigerian power network, (b) assess the vulnerability of each transmission line to voltage instability, (c) flag unstable lines and buses and (d) suggest a reactive power injection station. With this approach, it is expected that the outcome of this research will help to tame the frequent power outages in the NGP, and thus, improves the economic viability of the country.
5. Conclusions
In this paper, we presented a novel voltage stability index, the NVSP, for the classification of the 28-bus NGP, 330 kV transmission lines and buses. The classification was based on the vulnerability of each line to voltage collapse for the base and contingency cases. The results presented in
Table 1 show that the Ikeja-west–Benin line was the only unstable line in the base case, with an NVSP index value of 0.9672 and a voltage magnitude of 0.997 (p.u). However, the problem was remedied by the installation of a STATCOM at the Ikeja-west bus, which improved the voltage stability of the line to an NVSP index value of 0.7621, as presented in
Figure 8, with the voltage magnitude enhanced to 1.023 (p.u). A contingency analysis was carried out to evaluate the loadability of the P-Q buses of the 28-bus, 330 kV NGP. The Gombe, Jos and Kano P-Q buses were ranked as the most critical buses, with a maximum reactive power limit of 100.9 MVar, 142.9 MVar and 210.9 MVar, respectively. The most stable P-Q buses are Aja, Alaoji, Aladja and Akangba, with a maximum reactive power limit of 6005.58 MVar, 3820.2 MVar, 2972.4 MVar and 2,0508 MVar, respectively. Furthermore, the results obtained in this research show that (1) the installation of injection substations close to the flagged points will reduce the number possible blackouts, especially at Gombe, Jos and Kano buses; (2) increasing the power generation capacity from the Shiroro plant will also help to prevent the P-Q buses at these critical buses from operating close to their maximum capacity limit; and (3) the load at the P-Q buses for the critical buses—Gombe, Jos and Kano—could be optimally shed, especially during peak load hours, to maintain the stability of the NGP.