Congestion Control and Optimal Size of a Photovoltaic Device Using Multiverse Optimization Technique

For the safety of the power network, each grid needs to operate within stability limits. The grid might be congested, due to the lack of compatible generators and transmitters. Congestion could be triggered by unexpected events like power outage, sudden increase of load demand, and tool failure. The incidence of congestion in the energy program disturbs the grid, and causes more outages to interconnected systems. Frequent outages pose a serious threat to the power system: the tools will be damaged, and the power quality will be undermined. To cope with the threat, the energy program for the grid must be able to rectify congestion instantly.

The voltage of the congested grid can be stabilized with many compensation devices, or distribution generation (DG) unit. Focusing on bus sensitivity and wind availability, Suganthi et al. [1] discussed how to control congestion in the grid of wind farms: a differential evolution (DE)-based strategy was proposed to reduce transmission line congestion by rescheduling generators and constructing additional wind farms, and an updated mutation operator was introduced to improve the performance of the strategy. Remha et al. [2] examined the ideal location and size of DG units in radial distribution networks, and optimized the two parameters through three latest techniques: injecting active power, injecting reactive power, and injecting both powers. To choose the best site for DG units, Arief and Nappu [3] defined the tangent vector of the continuation power flow (CPF) method as the differential change ratio of voltage to load, and iteratively estimated the DG size in each place until the grid reaches the stable state.

Inspired by cosmological concepts like white hole, blackhole, and wormhole [4], Mirjalili et al. [5] tried to reduce grid voltage by integrating a wind turbine with a squirrel cage induction generator, and adopted the CPF method to locate wind farms and stabilize static voltage. Based on the 24h power demand, Sharma et al. [6] tested the reliability of the hourly load shapes of IEEE-30 and IEEE-57 bus systems, compared the results of flower pollination algorithm (FPA)-DE hybrid optimization with those of DE optimization, and confirmed the excellence of both strategies in congestion reduction. Using a modified IEEE-39 bus New England test system, Gope et al. [7] attempted to minimize congestion cost and enhance system safety through congestion management with and without a pump storage hydro unit (PSHU), and proposed a congestion management method based on bus sensitivity and generator sensitivity; the former was adopted to determine the location of wind farms [8]. Focusing on the optimal power flow (OPF) problem, Hooshmand et al. [9] established an objective function to minimize generator fuel and emission penalty cost, combined the bacterial foraging (BF) algorithm with the Nelder-Mead (NM) approach to solve the OPF problem, and optimized the size and position of thyristor-controlled series capacitor (TCSC) by minimizing the cost of generation, emissions, and the device.

Kashyap and Kansal [10] hybridized the firefly algorithm with DE optimization, and proved that the hybrid approach can efficiently handle congestion in a deregulated market by rescheduling generators, while satisfying both technical and economic constraints. Nappu et al. [11] discussed the concepts, technical challenges, and methods for alternate redispatch mechanism, formulated a locational management price scheme based on an optimization strategy for congestion control. Thangalakshmi and Valsalal [12] suggested that, in a deregulated power system, the independent system operator (ISO) faces the difficult task of managing transmission line congestion, and took account of the economic factors of most congestion management solutions. Verma and Mukherjee [13] put forward a generator rescheduling strategy based on ant lion optimizer (ALO), a novel algorithm inspired by the hunting mechanism of ant lions, to manage grid congestion. The effectiveness of the strategy was verified on modified IEEE 30-bus, modified IEEE 57-bus, and modified IEEE 118-bus, under the security constraints of load bus voltage and line loading impact. The strategy was found to outperform several modern optimization algorithms. Khatavkar et al. [14] improved the branch loading index of the grid by reducing losses, and enhancing voltage stability.

To solve the dynamic direct current (DC) optimal power flow (DDCOPF) problem, Dehnavi and Abdi [15] identified the ideal buses with such indices as power transfer distribution factors (PTDFs), and available transfer capability (ATC), and demonstrated the merits of their identification method: reducing line congestion, increasing benefits of consumers and ISO, improving load curve features, preventing line outages and blackouts, and enhancing grid dependability. For cost-free mitigation of grid congestion, Vijayakumar [16] took flexible alternating current (AC) transmission system (FACTS) as a cost-free method, optimized the positions of TCSC and unified power flow controller (UPFC) to relieve grid congestion, and introduced the genetic algorithm (GA) to solve the complex objective function in congestion management. Reddy and Singh [17] offered two distinct ways to find a suitable position for UPFC: one is based on sensitivity, and the other is based on pricing. The sensitivity-based approach aims to reduce the overall loss of the system. Ravindrakumar and Chandramohan [18] obtained a set of Pareto optimal solutions for grid congestion alleviation by the non-dominated sorting genetic algorithm II (NSGA-II).

This paper handles overload through generator rescheduling, eliminating the need for load shedding, and proposes a new stochastic population-based algorithm called multiverse optimization (MVO). Through the test on an IEEE 30 bus system, our approach was proved suitable under two different congestion scenarios. The remainder of this paper is organized as follows: Section 2 carries out the CPF analysis; Section 3 examines the PV energy storage system; Section 4 introduces the MVO technique; Section 5 analyzes the IEEE 30 bus system; Section 6 connects the system with the PV tuned by MVO; Section 7 summarizes the strengths of MVO in congestion control.

The PV energy storage system is commonly called the distributed energy storage system. Studies have shown that the PV system is very stable, its proximity to load and decentralized structure. Since the solar radiation sometimes falls below zero, solar power alone cannot address the congestion problem. The energy generated by a PV device can be calculated by:

$S_{G}^{t}=S_{r}\left\{1+\left(T_{r}-T_{a}\right) \propto\right\} \times \frac{i_{r r}^{t}}{1000}$                   (1)

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Figure 2. Single line representation of the IEEE 30 node test network

The grid output is evaluated on an IEEE 30 node test network containing 6 generators and 20 loads, as well as a PV network. After continuous iterations, the PV network is placed at node 15 by the proposed algorithm. The grid is considered with and without PV power generation. With the growing load, the grid became congested. To ease the congestion, the PV network is integrated to the grid, enhancing the load capacity. Besides, the size of the PV network tuned by the MVO is optimized to improve the network performance (Figure 2).

5.1 PV analysis on voltage profile, active and reactive powers

Figure 3 shows the voltage profile of the unit without PV network. In this case, the highest voltage profile is obtained through iterations. The active and reactive power profiles of the unit without PV network are displayed in Figures 4 and 5, respectively. Figure 6 depicts the load capacity curve of the unit. Obviously, the highest load capacity is 2.9859. Table 1 lists the parameters of the unit without PV network. Table 2 shows the total generation and losses.

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Figure 3. Voltage profile of the unit without PV network

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Figure 4. Active power profile of the unit without PV network

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Figure 5. Reactive power profile of the unit without PV network

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Figure 6. Load capacity curve of the unit without PV network

Table 1. Parameters of the unit without PV network

Table 2. Total generation and losses of the unit without PV network

5.2 10% and 20% rises in load without PV system

Figure 7 shows the voltage profile of the unit without PV network with a load increase of 10%. In this case, the voltage peaked at 1. The active and reactive power profiles of the unit without PV network are displayed in Figures 8 and 9, respectively. Figure 10 depicts the load capacity curve of the unit. In this case, the highest load capacity is 1.8254. Table 3 lists the parameters of the unit without PV network with a load increase of 10%. Table 4 shows the total generation and losses in this case.

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Figure 7. Voltage profile of the unit without PV network-a load increase of 10%

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Figure 8. Active power profile of the unit without PV network-a load increase of 10%

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Figure 9. Reactive power profile of the unit without PV network-a load increase of 10%

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Figure 10. Load capacity curve of the unit without PV network a load increase of 10%

Table 3. Parameters of the unit without PV network-a load increase of 10%

Table 4. Total generation and losses of the unit without PV network-a load increase of 10%

In the absence of PV network, the voltage peaked at 1 if the load increased by 20%. In this case, the load capacity maximized at 1.2296. Table 5 lists the parameters of the unit without PV network with a load increase of 20%. Table 6 shows the total generation and losses in this case.

Table 5. Parameters of the unit without PV network-a load increase of 20%

Table 6. Total generation and losses of the unit without PV network-a load increase of 20%

This paper studies the congestion control of the grid through CPF simulation, and proposes an algorithm to acquire the full load capacity while minimizing active power losses. The test results show that the MVO approach outperforms other cases without PV network in terms of load capacity and active power losses. The MVO algorithm can optimize the size of PV, and rationalize the loading parameters, thereby ensuring grid safety and eliminating network congestion.