1 Introduction

In recent years, electrical power systems are facing major challenges, as the demand for power systems is growing exponentially. Also, thermal power plants create a high levels of emission of pollutants that have numerous negative effects on the environment and human health in which increase investments of renewable energy sources could be seen as solution for sustainable energy [1, 2]. Therefore, the main attention is focused on distributed generation as they are providing many opportunities for the existing distribution system and becoming one of the key drivers of dealing with its issues [3]. DG units are defined as small-scale generating units installed at distribution systems near load centers. Photovoltaic (PV), Wind Turbine (WT), and fuel cell are taken here as resources of distributed generation [4].

Power loss minimizations, voltage profile enhancement, maximizing the system stability, and energy cost reduction during peak load are the main challenges facing distribution systems [5, 6].

Thereby, the integration of renewable DGs can be a good alternative to deal with these challenges. The decision about DG placement is taken by their owners and investors, depending on site and primary fuel availability or climatic conditions. Although the installation and exploitation of DGs to solve network problems have been debated in distribution networks, the fact is that, in most cases, the Distribution System Operator (DSO) has no control or influence about DG location and size below a certain limit. However, DG placement impacts critically the operation of the distribution network. Inappropriate DG placement may increase system losses and network capital and operating costs. On the contrary, optimal DG placement can improve network performance in terms of voltage profile, reduce flows and system losses, and improve power quality and reliability of supply. Within this context, many kinds of research have been focused on presenting new strategies of DG placement in recent years. Optimal placement of wind and solar-based DG units into distribution systems was shown in [7] utilizing a unique multi-objective Particle Swarm Optimization (PSO). For optimal positioning and sizing of DG-based renewable sources for diverse distribution systems, the Ant Lion Optimization Algorithm (ALOA) is proposed in [8].

Paper [9] proposed a new technique based on the Moth Flame Optimization (MFO) algorithm to optimally allocate the PV-DG units in (RDSs) and determine the optimal size of each unit in three IEEE RDSs. The author in [10] suggested a modified voltage index method to place and size the DG units to increase the voltage stability margin, with conditions of both not exceeding the buses’ voltage and staying within the feeder current restrictions. [11] used the proposed multi-objective chaotic salp swarm algorithm to identify the ideal size and location of photovoltaic in a radial distribution system to minimize total power losses, total voltage variation, and optimize the voltage stability index. In [12], the author suggested a new robust and effective hybrid PSOGSA optimization algorithm for detecting the ideal position of DG units with a practical size for decreasing system power losses and operating costs while also enhancing voltage stability.

The author in [13] has devised an appropriate approach for sizing and positioning a single PV-DG unit on a three-phase unbalanced radial distribution feeder. Also, [14] used a PSO technique to find the ideal size and location for single and multiple DGs, with the main goals being to improve the voltage profile and reduce active power losses.

In [15], the authors provided a DG placement and sizing strategy for reducing system losses, increasing voltage magnitude, and improving stability. Using loss improvement and loss reduction indices, multiple DG units have been placed. The author in [16] presents optimal PV-DG allocation with various target functions such as voltage profile enhancement and energy loss reduction. In [17], the author determines the location and sizing of multiple distributed generation (DG) units in the distribution network with a multi-objective technique in which the Loss Sensitivity Factor (LSF) determines the optimal placement of DGs and Invasive Weed Optimization (IWO) finds optimal sizing of the DGs. The Binary Particle Swarm Optimization and Shuffled Frog Leap (BPSO-SLFA) algorithms are used in [18] to discover the optimal location and size of the DGs, which can significantly reduce power loss and increase the voltage stability. For improving network loss reduction, voltage profile, and annual energy savings the author in [19] presented a Comprehensive Teaching Learning-Based Optimization (CTLBO) technique for the optimal allocation of DGs in radial distribution systems. The Multi-leader Particle Swarm Optimization (MLPSO) was used in [20] to determine the ideal positions and sizes of DGs to minimize active power loss. The authors in [21] proposed a hybrid optimization approach to handle the problem of DG unit siting and sizing. The multi-objective PSO algorithm to find the optimal locations and sizes of DGs to mitigate the total power loss, reduce line current, and boost the voltage profile of a radial distribution system is investigated in [22].

The authors in [23] used Ant Colony Optimization (ACO) algorithm approach for optimum sizing and siting of DGs sizing in a power distribution system. The ant lion optimizer (ALO) has been presented for assessing the optimal size of multiple DG units in a balanced radial distribution system in [24].

The construction of a new industrial system in the form of a photovoltaic power plant is a major long-term investment, and in this sense, determining the location is a critical point on the road to the success or failure of an industrial system. One of the main objectives in industrial site selection is finding the most appropriate site with desired conditions defined by the selection criteria [25, 26].

In this paper, PV location and size are chosen and implemented, based on land plot availability, proper site conditions, and cost budgetary and there is no luxury for a modification. Hence, this case under these constraints had been studied. The grid performance when connecting the PV-DG unit to each bus across the transmission line to find the optimally connected bus considering the available transfer capacity (ATC) of the bus line was analyzed.

The PV-DG unit fragmentation into small units to be connected to all buses is applied for higher grid performance. The remainder of this paper is arranged as follows: Sect. 2 presents the IEEE 15 bus system modeling based on MATLAB environment, Sect. 3 studies the grid performance under restricted specific size and location of PV-DG unit integration. Section 4 studies the PV-DG unit fragmentation into small equal units connected to all buses. Finally, Sect. 5 demonstrates the conclusion.

2 IEEE-15 Bus System

IEEE test grids are common in the research community. IEEE 15-bus11 kV redial distribution system has characteristics of a long grid lightly loaded requiring the application of voltage regulators to satisfy voltage standards which is similar structures of medium voltage system in Egypt. Hence, the grid performance enhancement study in this paper is tested in the IEEE 15-bus system.

A single line diagram of the standard IEEE 15 bus test system is shown in Fig. 1. The IEEE-15 bus system has a total load of 1226.4 KW and 1251.11 KVAR. The transmission line data and load data to be used to form the test system model are given in Table 1 [27].

Fig. 1
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Single line diagram of 15-bus radial distribution system

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Table 1 Transmission line data for IEEE 15 bus system
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The IEEE-15 bus system is simulated using MATLAB/Simulink environment as shown in Fig. 2. The per-unit voltages values and load powers for the IEEE-15 bus system using Simulink are shown in Table 2. Table 3 shows the IEEE-15 bus system efficiency. It was observed from Tables 2 and 3 that the test system has low efficiency and low buses voltages in which this paper studies the enhancement of these values. Figure 3 shows the voltages profile of the IEEE-15 bus system.

Fig. 2
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Simulink model of IEEE 15 bus system

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Table 2 Voltages and power flow data of IEEE 15-bus system
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Table 3 Total demand, losses and generation
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Fig. 3
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Voltages profile of IEEE-15 bus system

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3 PV-DG Connected to the System

In general, all types of distributed generation (DG) have a significant effect on reducing real power losses, operating costs, and enhancing voltage stability. Regarding PV-DG, there are a lot of design criteria related to sizing, location, and available land plot for installation. In this research, the PV-DG unit is integrated into the IEEE-15 bus system test grid with restricted specific size and location to study the grid performance and how to enhance it. The size of PV-DG unit 400 kW is selected to be in the range of 25% of the system load which represents a huge percent value of the system under this study. Also, the PV-DG unit location is selected to be beside bus1 as a restricted placement in which the best brightness of the sun, and the least weather factors.

The PV-DG unit consists of four PV arrays delivering each a maximum of 100 kW at 1000 W/m2 sun irradiance. A single PV array block consists of 64 parallel strings where each string has 5 Sun Power SPR-315E modules connected in series.

Each PV array is connected to a DC/DC converter (average model). The outputs of the boost converters are connected to a common DC bus of 500 V. Each boost is controlled by individual Maximum Power Point Trackers (MPPT). The MPPTs use the “Perturb and Observe” technique to vary the voltage across the terminals of the PV array to get the maximum possible power. A three-phase Voltage Source Converter (VSC) converts the 500 V DC to 260 V AC and keeps the unity power factor. A 400 kVA 260 V/11 kV three-phase coupling transformer is used to connect the converter to the grid as in Fig. 4.

Fig. 4
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PV-DG unit block diagram

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Load flow analysis is carried out with PV-DG unit 400KW interconnected at bus 1 as shown in Fig. 5. Load powers and voltages profile of IEEE-15 bus system is shown in Table 4. Table 5 shows the system efficiency after PV-DG unit penetration.

Fig. 5
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PV-DG unit connected to the IEEE-15 bus system

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Table 4 Voltages and power flow data with PV-DG penetration
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Table 5 Total demand, losses and generation with PV-DG penetration
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By comparing the system efficiency 95.6% when the PV-DG at bus 1 and without PV-DG 95.4%, the efficiency was slightly better in the PV-DG penetration. On the other hand, there is a significant enhancement in the voltages profile as shown in Fig. 6.

Fig. 6
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Voltages profile without/with PV-DG at bus1

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Despite just penetrating a PV-DG unit to the system at a restricted location beside Bus1 enhances the performance as shown in Fig. 6 and as clarified in Table 5, this research studies all available connections between PV-DG unit and all buses to find higher grid performance and to be realistic under restricted conditions.

3.1 Optimal Bus to be Connected to PV- DG Unit Through Transmission Line

In this case, the PV-DG unit beside Bus1 is connected to each bus, keeping in consideration the Available transfer capacity ATC of the existing test grid network for how transmission lines can bear the PV-DG surpluses or not. Hence, only available buses numbers 1, 2, 3, 4, 6, and 11 can be connected to the PV-DG unit with transmission lines as shown in Fig. 7. Also, the transmission line data for these connections between available buses and PV-DG unit are shown in Table 6.

Fig. 7
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IEEE-15 bus system with available connected buses with PV-DG unit

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Table 6 Transmission Line Data for PV-DG connected to system available buses
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In this case, Table 7 shows the results of all buses voltages when connecting the PV-DG unit to each available bus in which connecting the PV-DG unit to bus no. 11 gives the optimal voltage profile. Figure 8 shows the IEEE-15 bus test grid performance regarding voltage profile in the cases of the grid without PV-DG, grid with PV-DG connected to bus 1, and grid with PV-DG connected to bus 11 through the transmission line.

Table 7 Voltages buses with connecting PV-DG unit to available buses through TL
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Fig. 8
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Voltage profile performance of IEEE-15 bus test grid

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Also, the results shown in Table 8 indicate a better enhancement in the system efficiency 96.6% when connecting the PV-DG unit to bus no. 11 comparing the system efficiency 95.6% when the PV-DG at bus 1 and without PV-DG 95.4%.

Table 8 Total demand, losses, and generation with PV-DG unit connected to bus 11
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4 PV-DG Unit Fragmentation into Small Units

The idea of PV-DG unit fragmentation into small units comes to mind for enabling all buses to be connected with part of PV-DG instead of only one bus which in turn enhance logically the performance and overcome the problem of the available transfer capacities of the existing transmission line network that can bear the PV-DG surpluses or not. Hence, the study of PV-DG unit fragmentation into small units had been occurred by dividing the PV-DG unit into 14 equal parts and connecting to each loaded bus with transmission line data as shown in Fig. 9 and Table 9.

Fig. 9
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IEEE-15 bus system with PV-DG unit fragmentation

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Table 9 Transmission line data for PV-DG unit fragmentation connected to system buses
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In this case, Table 10 shows the results of all buses voltages when connecting the 14 equal parts of the PV-DG unit to the 14 buses as shown in Fig. 9 through appropriate transmission lines which indicate a valuable voltage profile comparing the previous cases: grid without PV-DG, grid with PV-DG connected to bus 1, and grid with PV-DG connected to bus 11 through the transmission line and as shown in Fig. 10.

Table 10 Voltages buses with PV-DG unit fragmentation connection through TL
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Fig.10
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Voltage profile performance of IEEE-15 bus test grid at different cases

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In the meantime, results shown in Table 11 indicate a significant enhancement in the system efficiency of 99.4% in this case comparing the system efficiency 96.6% when connecting the PV-DG unit to bus no. 11 and the system efficiency 95.6% when the PV-DG at bus 1 and without PV-DG 95.4%.

Table 11 Total demand, losses and generation with PV-DG unit fragmentation into 14 units
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5 Conclusion

In this paper, the size and placement of PV-DG unit in radial distribution systems were previously determined and implemented as a constrain in which normally connected to the nearest ordinary bus. The major purpose of this study is to investigate how grid performance can be improved under these constrain. This investigation was carried out using an IEEE 15 bus system in a MATLAB environment. The research studies the grid performance when connecting a PV-DG unit to each bus across a transmission line to determine the best-linked bus considering the network lines' available transfer capacity (ATC). The network lines ATC made a limitation to specific numbers of available connected buses to the PV-DG unit under this study. Simulation results indicate that connecting the PV-DG unit to bus no. 11 gives a better voltage profile and an enhancement in the system efficiency comparing connecting at bus 1 as the nearest ordinary bus. To overcome the availability of PV-DG unit connections to specifically limited buses due to network ATC, the obtained results proved that the PV-DG unit fragmentation into small units at the same place and connecting them to all buses give optimal voltage profile and the best system efficiency reach 99.4% comparing connecting PV-DG unit at bus 1 as a nearest ordinary bus 95.6%. The work will be verified using the Hardware in the Loop (HIL) paradigm in which considered as a future work.