Optimal Design and Performance Analysis of Multiple Photovoltaic with Grid-Connected Commercial Load

This study aimed to evaluate the potential of integrating Photovoltaic (PV) with commercial load and examine the impact on distribution networks. To estimate the hourly PV output power, 13 years of historical weather data were used. Furthermore, a beta probability density function was modeled to handle large amounts of data and generate a 24-hour predicted PV curve. Particle Swarm Optimization (PSO) was used to determine the location and size of multiple PV units, ranging from 1 to 3. PV performance was tested on IEEE 33-bus and 69-bus test systems using time-varying commercial load, with power loss index (PLI) set as the objective function. PV penetration level was also calculated. The results showed a significant power loss reduction and PV penetration levels when 3 PV units were integrated into the system compared to a single PV unit. Specifically, the power loss reduction improved from 32.71% to 45.37% and 43.80% to 48.08%, producing PV penetration levels of 43.08% and 40.15% in 33-bus and 69-bus systems, respectively. The results indicated that the integration of multiple PV units was better than the single PV integration. The proposed model using PSO determined the impact of considering weather-dependent PV generation simultaneously with time-varying loads. It also provided knowledge to model the optimal location and sizing of multiple PV units in the distribution networks based on the generated solar irradiance patterns.

Commercial load; Historical weather data; Power loss; PV penetration; Particle swarm optimization

Problem Formulation

2.1. Solar PV Modelling

Thirteen years of hourly weather satellite data (Solcast, 2018) were used to forecast the average hourly irradiance and PV output power as well as evaluate the potential of PV integration with commercial loads in Malaysia (30821N, 1014113E). The location of Malaysia near the equatorial makes it a perfect opportunity to utilize abundant solar energy resources, with an average annual irradiance of 4-5 kWh/m²/day (Mohammad, Al-Kayiem, and Aurybi, 2020). The historical data collected were divided into 24-hour segments, each with solar irradiance measured at specific hours. The mean (µ) and standard deviation  for each hour were calculated based on the irradiance data collected hourly over the 13 years. This facilitated the determination of the probability of solar irradiance for each hour and the estimation of PV output. The Beta-PDF f(s) is expressed using equation (1) as follows (Atwa et al., 2010):

where  is a random variable for solar irradiance measured in (kW/m²),  is a gamma function,  and  both parameters of equation (6) are derived using mean, µ and standard deviation,  respectively using equation (2)  (Atwa et al., 2010):

The probability of solar irradiance,  in the limits of and during a specific hour (t=1) can be obtained using equation (3)  (Atwa et al., 2010):

2.2. PV Module Output

PV power is significantly influenced by temperature, climate and geographical factors, and solar irradiance. The output of PV_NET module,  is expressed as a function of solar irradiance as follows (Atwa et al., 2010):

where is the number of PV modules, and  is the fill factor that depends on solar irradiance. The total expected PV output power at a given hour, at , is derived using (3) and (4), which relies on the irradiance  and the characteristic of the modules given by equation (5)-(8) is expressed by the following expression equation (9) (Ali et al., 2018):

2.3. Load Modelling

The following equations (10)-(11) express the new active and reactive distribution load demand  and  at a respective bus integrated with time-varying commercial loads in a given period (t) equation (Atwa et al., 2010):

2.4. Distribution Bus System

        This study used a standard IEEE 33-bus and 69-bus test system, with each distribution bus having different load power and system losses. The rated voltage for both systems was 100 MVA and 12.66 kV. The total load demand and base power losses for 33-bus were 3.715 MW, 2.300 MVAr, and 211.20 kW, 143.03 kVAr, respectively. The total load demand and base power losses for 69-bus were 3.800 MW, 2.690 MVAr, and 224.95 kW, 102.14 kVAr, respectively (Kakueinejad et al., 2020; Nawaz and Tandon, 2018). Furthermore, both bus systems were assumed to serve as distribution power stations for commercial load areas, meaning that all connection points were considered commercial consumers. This study was limited to using historical weather data based on collected solar irradiation, acknowledging that the power output might vary depending on solar irradiation at a specific location. It was assumed that the distribution grid was connected to the commercial load areas.

Figure 1 The normalized commercial load curve (Jamahori, Abdullah and Ali, 2023)

2.5. Load Flow Analysis

Assuming 2 buses,  and  k+1 connected through branch i, the following formula equation (12)-(13) was used to calculate the active, P_Loss(i)  and reactive,  Q_Loss(i) branch power loss between 2 buses (Ali et al., 2018):

where R_ij is the branch resistance and X_ij is the branch reactance between 2 buses. The base case (without PV) hourly active and reactive power injection across any branches at each period can be calculated as a summation of effective k + 1^th   bus power, load demand power, and power losses at K + 1 bus as follows equation (14)-(15) (Ali et al., 2018):

 

where P_i, and Q_(I) are the active and reactive power injections between 2 buses, with P_D(ij) and Q_D(ij) as the actual load power between both buses. The total power losses,  TP_LOSS(i) before PV integration are a summation of both losses given by equation (16) derived from equation (12) and equation (13):

 

The addition of a new power source affected the load flow in the distribution system. Therefore, the new active, P_DNEW(k+1) and reactive,  Q_DNEW(K+1) power injections at k +1 bus, where PV is installed, are as follows equation (17)-(18) (Ali et al., 2018):

where P_D(K+1) and Q_D(K+1) are the actual active and reactive load power at the effective bus, while P_PV and Q_PV are the active and reactive power generation from PV. Q_PV is a function of P_PV with a fixed power factor, therefore, where  a is positive (+) when PV injects reactive power and negative (-) when it consumes reactive power, and  is an operating power factor of PV unit at bus k + 1.

Assuming the solar PV unit is installed at  bus, the hourly active,  and reactive,  power injection across branch  at each period can be calculated as follows equation (19)-(20) (Jamahori, Abdullah and Ali, 2023):

2.7. Particle Swarm Optimization (PSO)

PSO algorithm-based random particle generation aimed to achieve the best value of the fitness function by updating the position and velocity. The basic principle of PSO works by using the swarm's knowledge and experience to randomly direct particles across the search space to find the best local and global solution, g_best  based on their personal best solution, p_best. The particles change by updating position and velocity using a weighted acceleration, ?, at each iteration to accelerate toward the fitness function. PSO updates each particle by comparing the best fitness to the current . Assuming the new generation of fitness is superior to the current , newly generated fitness replaces  solution. Finally, the best global solution for any particle,  is selected by comparing all particles' fitness. The flowchart of the optimization framework using PSO is shown in Figure 2.

Figure 2 The flowchart of the optimization framework using PSO

PSO parameters were selected based on initial suggestions from the year of development (1995), which proposed limiting the population size to 20-50 particles. Larger swarms typically improved the efficiency of the method for more complicated problems and practical applications. While significantly smaller swarm sizes were suggested for the majority of PSO variants regarding unimodal problems, hundreds of particles/swarms would still perform optimally. PSO parameters for the integration of multiple PV are shown in Table 1.

Table 1 PSO Parameters for integration of multiple PV

3.1.  Optimal Location and Size of Multiple PV units

The simulation result for multiple PV integrations with commercial load users in IEEE 33-bus and IEEE 69-bus are summarized in Tables 2 and 3, respectively. Based on the optimization, the results showed that the optimal PV sizing for the commercial load users differed significantly in both distribution networks. This was mainly due to the optimal location and power demand in each bus system.

Tabel 2 Summary of multiple PV optimization results in IEEE 33-Bus

Tabel 3 Summary of multiple PV optimization results in IEEE 69-Bus

For IEEE 33-bus, the optimal PV integration for a single PV was at bus 6 with a size of 4.57 MW, while 2 PV units were at bus 12 and 30, respectively, with a size of 1.71 MW and 2.08 MW. The optimal location and sizing of 3 PV units were at bus 14, 24, and 30, with PV sizes of 1.41 MW, 1.75 MW, and 1.75 MW, respectively. In IEEE 69-bus, the optimal PV integration for a single PV was at bus 61 with the size of 3.35 MW, while 2 PV units were at buses 18 and 61, respectively, with the size of 0.99 MW and 3.19 MW. The optimal location and sizing of 3 PV units were at buses 11, 17, and 61, with PV sizes of 0.91 MW, 0.72 MW, and 3.04 MW, respectively. The cumulative PV sizes for 1, 2, and 3 PV units were 4.57 MW, 3.79 MW, and 4.91 MW, respectively, for IEEE 33-bus and 3.35 MW, 4.18 MW, and 4.67 MW, respectively, for IEEE 69-bus. The results showed that the average total PV size was larger when integrated with commercial load users in 33-bus compared to 69-bus system.

Figure 3 presents the expected PV output from Equation (9) and commercial demand consumption for both systems using Equations (10) and (11). Furthermore, maximum PV production and load consumption occurred concurrently during the day, following the solar PV production, which peaked at noon and was low in the morning and evening.

Figure 3 Expected PV output with commercial demand (a) IEEE 33-Bus; and (b) IEEE 69-Bus

Since the system operated as an integrated grid system, the grid served the remaining load consumption when PV power was unavailable or insufficient to supply the load. On the other hand, the highest PV output was observed when 3 PV units were integrated into both bus systems. The expected PV output was lowest with 2 PV in 33-bus and 1 PV unit in 69-bus system. While the varying lowest PV size between both buses did not affect the overall power losses, it affected the overall PV penetration. Further discussion on PV penetration level and power loss reduction was provided in the next sub-section.

3.2. Impact on PV Penetration

PV penetration level is the total expected PV output (MW) ratio to the total load demand consumed during the day (MW). A high penetration level shows that PV production is sufficient to provide power to meet the load demand. PV penetration results are presented in Figure 4. Based on the results, PV penetration levels for 1, 2, and 3 PV units in 33-bus and 69-bus were 40.15%, 33.29%, 43.08%, and 28.72%, 35.90%, 40.15%, respectively.

Figure 4 Penetration level for multiple PV integration

The penetration level increased significantly with load demand in 69-bus as the number of installed PV increased, while the difference in penetration level between 1 PV and 3 PV in 33-bus was insignificant. The maximum PV penetration was recorded when 3 PV units were integrated with commercial load in 33-bus, and the least being 1 unit integrated into 69-bus system. As mentioned, the optimum size of PV was subjected to power loss minimization. Since power loss in the distribution system depended on the load of each model, the size of PV units in each case varied accordingly. The cumulative sizes of PV in MW for each load model considering single and multiple PV units for the two distribution systems are presented in Tables 2 and 3. For 33-bus system, the impact of 2 PV units on the total size of PV in MW was the most optimal compared to the installation of 1 and 3 PV units. On the other hand, for 69-bus distribution system, the impact of 1 PV unit on the total size of PV in MW was more optimal than the installation of 2 and 3 PV units. Therefore, the penetration of PV units in the distribution networks varied and depended on the size of PV in distribution networks.

3.3. Impact on Power Losses

The power loss for multiple PV integration in both buses is presented in Figure 5. The power loss reduction showed promising results after multiple PV units were integrated into both bus systems. Specifically, the power loss for 1, 2, and 3 PV units in 33-bus and 69-bus were 32.71%, 40.66%, 45.37%, and 43.80%, 47.40%, 48.08%, respectively. These power losses were influenced by the total PV generated during the day, the total load served at a specific hour, and the location and sizing of PV units. In addition, the load demand variations in each bus directly affected the location for PV installation. This could be attributed to the typical installation of PV near areas with the highest load demand and farther from the grid supply to ensure continuous power supply while minimizing voltage deviation and power loss. The reduction in power losses was more significant with multiple PV in 33-bus compared to 69-bus system. The installation of a third PV in 69-bus did not significantly reduce the total power losses. Therefore, 3 PV units were more optimal to be installed for 33-bus, and only 2 PV units were recommended for time-varying commercial users in 69-bus system, as the effect of the third PV could be neglected. This was because the rate of improvement in distribution system performance was primarily determined by the total size of PV units.

Figure 5 Power loss for multiple PV integration (a) IEEE 33-Bus; and (b) IEEE 69-Bus

       The optimal location and size of 1 to 3 PV units were determined based on proximity to areas with the highest load demand and distance from the grid supply. This ensured the additional sources from PV could continue to supply the load at a different location. The power losses with multiple PV were affected by the total PV generated during the day, the total load served at a specific hour, and the total PV sizing on the individual location. In addition, the load demand variations in different bus systems directly affected the location of installation. Integrating multiple PV units showed that beyond installing 2 PV units, there was no significant impact on 69-bus system. However, installing 3 PV was significant in addressing the load demand in 33-bus system. The reduction in power losses was more prominent within 33-bus compared to 69-bus system. The power loss was influenced by the supply of power to the distribution networks and depended on the size of PV units. Larger PV sizes corresponded with greater improvements in bus voltage magnitude. Nonetheless, inadequate PV sizing could lead to additional power losses and suboptimal improvement of bus voltage profiles.

In conclusion, this study showed that modeling multiple PV units with commercial load users at optimal size and location had varied impacts on the distribution system performance. Furthermore, the integration of multiple PV units outperformed single PV integration, resulting in improved power loss reduction from 32.71% to 45.37% and 43.80% to 48.08% in 33-bus and 69-bus systems, respectively. This integration produced PV penetration levels of 43.08% and 40.15% in the respective bus systems. The proposed model not only assessed the impact of considering weather-dependent PV generation alongside time-varying loads but also provided insights into modeling the optimal location and sizing of multiple PV units in distribution networks based on solar irradiance patterns. Moreover, this study showed the importance of considering load variations in designing a PV grid system to ensure optimal performance and efficiency. By accounting for variations in load demand, PV system could be appropriately sized to match varying load profiles, preventing overgeneration during low-demand periods and ensuring sufficient electricity generation during peak hours. This method maximized the utilization of renewable energy and helped to maintain grid stability and reliability, ensuring consistent voltage levels, balanced power flow, and the ability to respond swiftly to changes in demand or supply to minimize power losses. Therefore, considering load variations was essential for the successful and resilient operation of PV grid system.

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