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Determining penetration limit of central PVDG topology considering the stochastic behaviour of PV generation and loads to reduce power losses and improve voltage profiles

2020; Institution of Engineering and Technology; Volume: 14; Issue: 14 Linguagem: Inglês

10.1049/iet-rpg.2019.1376

1752-1424

Mohamed Saad Suliman, Hashim Hizam, Mohammad Lutfi Othman,

Smart Grid Energy Management

IET Renewable Power GenerationVolume 14, Issue 14 p. 2629-2638 Research Article Free Access Determining penetration limit of central PVDG topology considering the stochastic behaviour of PV generation and loads to reduce power losses and improve voltage profiles Mohamed Saad Suliman, Department of Electrical and Electronic Engineering, Faculty of Engineering, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, MalaysiaSearch for more papers by this authorHashim Hizam, Corresponding Author hhizam@upm.edu.my Department of Electrical and Electronic Engineering, Faculty of Engineering, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia Advanced Lightning, Power & Energy Research (ALPER), Faculty of Engineering, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, MalaysiaSearch for more papers by this authorMohammad Lutfi Othman, orcid.org/0000-0003-0382-8666 Department of Electrical and Electronic Engineering, Faculty of Engineering, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia Advanced Lightning, Power & Energy Research (ALPER), Faculty of Engineering, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, MalaysiaSearch for more papers by this author Mohamed Saad Suliman, Department of Electrical and Electronic Engineering, Faculty of Engineering, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, MalaysiaSearch for more papers by this authorHashim Hizam, Corresponding Author hhizam@upm.edu.my Department of Electrical and Electronic Engineering, Faculty of Engineering, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia Advanced Lightning, Power & Energy Research (ALPER), Faculty of Engineering, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, MalaysiaSearch for more papers by this authorMohammad Lutfi Othman, orcid.org/0000-0003-0382-8666 Department of Electrical and Electronic Engineering, Faculty of Engineering, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia Advanced Lightning, Power & Energy Research (ALPER), Faculty of Engineering, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, MalaysiaSearch for more papers by this author First published: 02 October 2020 https://doi.org/10.1049/iet-rpg.2019.1376 AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat Abstract Distributed generation (DG) has rapidly increased due to many technical, environmental and economical benefits. One of the DG application challenges is to find a proper area to incorporate the DG associated to a particular location. In this study, a central photovoltaic distributed generation (PVDG) topology is proposed to distribute the optimal sizes to the optimal locations. Uncertainties of load demand and renewable power generation are also taken into consideration of the optimisation problem. This study determines the deterministic and probabilistic penetration limits based on the distribution network topologies, considering the PVDG significant impact on active power losses reduction and voltage profiles improvement. The effectiveness of the proposed topology was validated on 33- and 69-bus distribution networks adopting Monte Carlo simulation method, Newton-Raphson load flow method and biogeography based optimisation. From the results, the voltage profiles, active power loss reduction, DG capacity required and penetration limit have shown better performances on the central PVDG topology over the bus dedicated PVDG topology. 1 Introduction Due to environmental, economical and governmental benefits, there has been increasing interests in renewable energy integration in power systems. The International Renewable Energy Agency has declared in the Renewable Capacity Statistics 2019 report that the world's total installed capacity of solar photovoltaic (PV) generation has increased from 22 to 480 GW. The off-grid capacity is increased from 0.3 to 3 GW between 2009 and 2018, respectively [1]. The growth rate of solar PV installed capacity indicates the reliability and efficiency of its output power. However, this power generated from PV is still a subject of research and development from applicability perspective. Despite the off-grid applications, the impact of solar PV integration in the distribution networks is a subject that requires further investigations. The integration of solar PV distributed generation (PVDG) in the distribution networks shall be under optimal utilisation term which considers the impact of variety of aspects such as DG rating, purpose, power delivery area, technology, environmental impact, mode of operation and penetration level [2]. The use of DG sources could be due to different purposes, namely improvement of power quality and voltage profile, loss reduction, reducing investment and operation costs. Finding the optimal DG size and location are fundamentals to achieve the optimal DG utilisation. Specifying the power delivery area is a major aspect in the optimal utilisation analysis as well as the DG technology utilised. The DG technology is a wide term that necessitates technical analysis and description. The classification of the DGs by their energy production to the network are as follows [3]: type I DG capable of injecting reactive power only, type II DG capable of injecting active power only, type III DG capable of injecting active and reactive power, and type IV DG capable of injecting active power and absorb reactive power. Grid-connected DGs are usually equivalent to PQ, PV and PI nodes for power flow calculation. There are only PQ, PV nodes and balance nodes in the traditional distribution network, and there are PI nodes in the distribution network with distributed generation. However, the PI node is usually be transformed into PQ node during the power flow calculation [3]. The environmental impact plays a significant role in every electrical power system, the derating factors of all electromechanical equipments occur against the altitude, humidity, ambient temperature and so on [4]. Moreover, the stochastic nature contribution from PV generators adds other factors like direct normal irradiance, diffuse horizontal irradiance, global horizontal irradiance of specified longitude and latitude [4]. The stochastic nature and intermittency of solar PVDG contribute the uncertainties to the network power flow. In addition, the chances of minimum load demand coincide with the peak PV generation. Or, the chances of peak load demand coincide with the minimum PV generation, consequently the relative penetration level will be affected as time-series function [5]. Thus, the study defines the penetration limit as a function of time, which models the PVDG and the load behaviour at a certain point of time as a ratio of PVDG output power to the actual power consumed at that particular time. 2 Literature review Determination of optimal size and location of DG units is fundamental aspect of DG optimal utilisation. The lack of obligation in optimal utilisation technical aspects may directly leads to reverse power flow, network power loss, power quality problems, voltage variation and frequency violation. Recently, the optimal sizing and allocation of DG units was investigated using different optimisation techniques. Stud krill herd algorithm was employed in [6] to optimally allocate DG units for voltage deviation and power loss reduction. Kumawat et al. [7] have solved the DG sizing and placement problem using particle swarm optimisation (PSO) to minimise energy loss. War optimisation [8] was presented to reduce power loss. Ant lion optimisation algorithm was used to optimally allocate PV and wind turbine (WT) by minimising active power loss [9]. In [10], the linearised power flow formulation was used to investigate the probabilistic nature of output power for wind DG and its impact in terms of voltage improvement and loss reduction in distribution systems. Genetic algorithm (GA) was used to optimally allocate and size DG units to minimise voltage deviation and real power losses [11]. Dragonfly algorithm [12] was used to optimally allocate DG units and maximisation of benefits in distribution networks. PSO with constriction factor approach (PSO–CFA) to enhance loading capacity by optimally allocating DG units was proposed in [13]. Hybrid of ant colony optimisation and artificial bee colony algorithm (ACO–ABC) [14] and modified teaching learning based optimisation (MTLBO) [15] were employed to optimally allocate DG units for voltage profile improvement and power loss reduction. New analytical approach has been evolved in [16] to minimise power losses. Biogeography based optimisation (BBO) method has been proposed in [17] to find optimal location and sizing of PVDG units to reduce power losses while maintaining voltage profile and voltage harmonic distortion at the standards limit. Their proposed logarithm had been demonstrated against the GA, PSO algorithm and the artificial bee colony algorithm (ABC). As a result, it promises to provide better solution quality and accuracy with faster convergence over the applied methods. Modelling DG and load demand uncertainties along with network reconfiguration is hosting capacity enhancement techniques. Several hosting capacity enhancement and assessment methods have been overviewed in [18] to define the hosting capacity in modern power systems with DG units as transactive approach to integrate the distribution networks with different types of energy systems. In [19], uncertainty of load and renewable generation as well as distribution network reconfiguration is taken in the optimisation problem to maximise annual cost savings and minimise active power loss. DG units and soft open points have been allocated in [20] to active distribution networks with network reconfiguration to investigate total active losses. In [21], WT and PV-based DG units were allocated in time-varying distribution networks by carrying out probabilistic load flow (PLF) analysis, Monte Carlo simulation (MCS) and the point estimate methods. Comparison between the Weibull and Gumbel probability distribution functions (PDF) was presented in [22] to predict wind speed and wind power output considering DG in distribution systems. PLF was presented in [23]. In [24], various uncertainties presence of distribution generation in distribution networks was studied considering MCS to carry out PLF. Maya and Jasmin [25] have considered the PV output power uncertainty and seasonal load variation in the simulation study. In [26], probabilistic modelling for solar irradiation, wind speed uncertainty and electrical load demand using beta, Weibull and normal PDFs were proposed. Based on the literature survey, it is noted that considering loads and generation uncertainty necessitate a PLF to be executed along with the deterministic load flow (DLF). All the reviewed studies have investigated the allocation of DG units directly next to the optimum location as bus dedicated DG, while it is possible that some distribution network operators may not find the proper space to allocate the PVDG in that location. Therefore, central PVDG (CPVDG) has been proposed to be incorporated to distribute the consolidated optimum sizes to the optimum locations. 2.1 Paper organisation The contribution is mentioned in Section 3, while the problem formulation is described in Section 4. Section 5 presents the methods. The described model is applied on two case study distribution networks, and the simulation results are presented and discussed in Section 6. Finally, conclusions are outlined in Section 7. 3 Contributions The contributions of this study are threefold: Determining the optimal size and location of CPVDG in distribution networks. Investigate the integration impact of CPVDG on distribution networks. Uncertainty of loads and PV generations are considered in the optimisation problem. 4 Problem formulation The concern of this study is the optimal integration of CPVDG using BBO method, where the generation and load uncertainties are considered. That necessitates a PLF based on MCS method to improve voltage profiles and minimise active power losses in the distribution network (1) where F is an objective or fitness function and is the total active power losses in kW. The function is subjected to the following voltage constraint: (2) where is the voltage at node i in p.u. DG penetration level definition considered in the study is the ratio of the power amount injected by DG in the network to the network load amount [3] (3) 5 Methods The study compares the bus dedicated DG topology versus central DG topology to determine the DG penetration limit of distribution network based on finding the optimal size and location of PVDG units, by modelling the generation and loads uncertainty. The optimal size and location of bus dedicated PVDG units shall be optimised to be incorporated as consolidated CPVDG which distribute the optimal power to the optimal locations. Thus, the study finds the optimal size and location of bus dedicated PVDG, then optimise the consolidated size at the identified CPVDG location to reduce active power losses and improve voltage profiles. 5.1 Biogeography-based optimisation method The theory of Island Biogeography primarily focuses on the distribution of species among neighbouring habitats based on the mathematical models of extinction and migration of species [27]. Fundamentally, the geographical areas that are well suited as residences for biological species are said to have a high habitat suitability index (HSI). Features that correlate with HSI include factors such as rainfall, diversity of vegetation, diversity of topographic features, land area and temperature. The variables that characterise habitability are called suitability index variables (SIVs). SIVs can be considered as the independent variables of the habitat, and HSI can be the dependent variable as shown in migration curve of Fig. 1. Fig. 1Open in figure viewerPowerPoint Migration curve Habitats with a high HSI tend to have a large number of species, while those with a low HSI have a small number of species. Habitats with a high HSI have many species that emigrate to nearby habitats, simply by virtue of the large number of species that they host. Habitats with a high HSI have a low species immigration rate because they are already nearly saturated with species. Therefore, high HSI habitats are more static in their species distribution than low HSI habitats. By the same token, high HSI habitats have a high emigration rate; the large number of species on high HSI islands have many opportunities to emigrate to neighbouring habitats (This does not mean that an emigrating species completely disappears from its home habitat; only a few representatives emigrate, so an emigrating species remains extant in its home habitat, while at the same time migrating to a neighbouring habitat.). While habitats with a low HSI have a high species immigration rate because of their sparse populations. This immigration of new species to low HSI habitats may raise the HSI of the habitat, because the suitability of a habitat is proportional to its biological diversity. However, if a habitat's HSI remains low, then the species that reside there will tend to go extinct, which will further open the way for additional immigration. Due to this, low HSI habitats are more dynamic in their species distribution than high HSI habitats [28]. To find the optimal size and location for the case study systems BBO algorithm is chosen which offers better solution quality and accuracy with faster convergence, over the GA, the PSO algorithm and the ABC [17]. The algorithm has two main operations to migrate the species between the habitats: migration operation and mutation operation [28]. The algorithm parameters are shown in Table 1. Table 1. BBO algorithm parameters Parameters Set to E maximum migration rates 1 I maximum immigration rates 1 maximum mutation rate 0.1 probability 1 EKR elite keeping ratio 0.2 size population number 50 maximum iteration number 100 5.2 Optimal size and location of PVDG using BBO The optimal size and location of PVDG is subjected to the main objective function (4) of minimising the active power loss. The total active power loss of the distribution network is evaluated by summing all power losses value at each branch of the system with n nodes as per (5) (4) (5) 5.3 Optimal size and location of CPVDG The optimal size and location of CPVDG follow the identification of optimal number, size and location of PVDG units. These primary resulted values shall be consolidated in one added bus called CPVDG as depicted in Fig. 2. The identification process of the optimal CPVDG location is based on two criteria. First, next to the highest DG capacity to avoid high transmission losses. Second, at the centre of the optimal buses locations, where there is the lowest transmission admittance value to avoid transmission losses. Fig. 2Open in figure viewerPowerPoint CPVDG connected to the optimum locations 5.4 Solar PVDG modelling Considering PVDG will add several prevailing uncertainties to the grid complexity due to its stochastic nature from the random solar irradiances. The PV output power is directly dependent on the solar irradiance which follows bimodal distribution for the same hour of a typical day in each season [29]. The solar irradiance for each hour of the day is modelled by the beta PDF based on our historical data for the selected site. The historical satellite data have been collected for 1 year from [30]. The data stored contains solar irradiance for every hour in a period of one year. Thus, 8760 solar irradiance data is 365 irradiance level data for each hour in a typical day of the year, as shown in hourly solar irradiation spectrum (Fig. 3). Fig. 3Open in figure viewerPowerPoint Hourly solar irradiation spectrum To obtain the beta PDF used which model the randomness of solar irradiance, a day is split into 24 h as a time segment, every one hour has its own solar irradiance PDF which has been divided into periods (states). It is assumed that each hour has 20 states with step of 0.05 kW/m2 as illustrated in Figs. 4 and 5. The mean µ and standard deviation σ have been calculated from the historical data to find the size parameter β and shape parameter α values as demonstrated in (6)–(9) and Fig. 4 [29] (6) where S is the solar irradiance (kW/m2), is the beta distribution function of s, and β is the size parameter and α is the shape parameter. Fig. 4Open in figure viewerPowerPoint PDF for solar irradiance at hours 8, 11 and 14 Fig. 5Open in figure viewerPowerPoint PDF for solar irradiance at hour 16 The size and shape parameters [29] were calculated using (7) (8) The solar irradiance probability at any specific hour can be calculated by (9) where is the solar irradiance probability at specific hour and is the beta distribution function of s. The solar DG used in the study is unity power factor solar DG model as per the recommendation of IEEE 1547 current standard; PV inverters are not permitted to supply reactive power to the grid [31]. The solar module is Astronergy 370 W STAR II CHSM72M. The characteristics of the module [32] are listed in Table 2. It is classified as a medium-scale PVDG. The number of modules shall be considered based on the required power identified by the algorithm for the distribution system. The module characteristics that affect the module output power are demonstrated in the following equations: (10) (11) (12) (13) (14) where and are the cell temperature (°C) and ambient temperature (°C), respectively, is the nominal operating temperature of the cell (°C), S is the solar irradiance in kW/m2, I, and are the output current of the PV module in A, current at maximum power point, and short-circuit current in A, respectively, and are the current and volt temperature coefficients in A/°C and V/°C, respectively, V, and are the output voltage of the PV module (V), open-circuit voltage (V) and voltage at maximum power point (V), respectively, FF, N and are the fill factor, number of modules and output power of the PV module (W). Table 2. PV module characteristic [32] CHSM72M-HC series 370 W Parameters Specifications V oc, V 47.64V I sc, A 9.80 A V mpp, V 39.71V I mpp, A 9.32 A K v, mV/°C −13.4345 K a, mA/°C 0.42415 N OT, °C 46 Since the solar irradiance is weather and time dependent, different periods have different PDFs, for example for the given solar irradiance hour 14 the expected output power or average output power is calculated using (14) and plotted in Fig. 6. The total expected power for this particular hour with respect to the 20 periods associated are calculated using the area under the curve of that period which is 161.81 W. For the period of 1 h, the module is expected to produce output power of 161.81 Wh. Fig. 6Open in figure viewerPowerPoint Expected output of a PV module at hours 14 5.5 Load uncertainty modelling There are plenty of uncertainties in power system variables such as load demand. The load demand in the power system is classified into two components [33]. First, the deterministic component is dependent on several factors such as time of the day, type of the day and weather conditions. Second, the stochastic component, which is a direct result of the consumer behaviour. The stochastic model of load demand is considered as independent random variables modelling. This model is able to capture the randomness of these data analysis, where the statistical load curves for particular time are summed to have variation around its mean. The stochastic nature of load demand at this study is following normal distribution function modelling [19, 24] which is common to consider the load as normally distributed with a mean value and standard deviation. The mathematical modelling of normal distribution PDF is represented as (15) where is the PDF and x is the load randomness. are the mean load value and standard deviation, respectively. The probabilistic nature of the load demand at each bus in the distribution system is incorporated into the load flow analysis. Load demand at each bus is assumed to be random variables with normal distribution [24, 33] as depicted in (16) and (17). Fig. 7 shows the power demand samples of the real and reactive profiles at the 24th bus, Fig. 8 shows the mean value of active and reactive load demand. Power demand PDF samples of 24th bus are depicted in Fig. 9 (16) (17) Fig. 7Open in figure viewerPowerPoint Real and reactive power load at 24th bus Fig. 8Open in figure viewerPowerPoint Mean real and reactive power demand profile 6 Results and discussions This section presents simulation results obtained from BBO algorithm for both bus dedicated PVDG integration. Central PVDG topology incorporation on the 12.66 kV, 33-bus radial distribution network [34] has 32 branches with total load of 3.715 MW and 2.3 MVAR as shown in Fig. 10. The second case study is the 12.66 kV, 69-bus radial distribution network [35], which has 68 branches with total load of 3.802 MW and 2.694 MVAR as shown in Fig. 11. The simulation result shows the effectiveness of the proposed topology for voltage profiles improvement and loss minimisation in radial distribution networks. In this study, a DLF using Newton Raphson method and PLF using MCS has been carried out to consider the uncertainty of stochastic load behaviour and the time varying of PV distributed generation as shown in Table 3. Fig. 9Open in figure viewerPowerPoint PDF of power demand samples for 24th bus Fig. 10Open in figure viewerPowerPoint IEEE 33-bus distribution network Fig. 11Open in figure viewerPowerPoint IEEE 69-bus distribution network Table 3. Base systems load flow calculation results Test system Load flow type Load flow technique Run number Losses mean µ, MW Losses standard deviation σ Generation mean µ, MW Generation standard deviation σ 33-bus probabilistic MC based on Newton Raphson 10,000 0.2039 13.79 3.921 134.75 33-bus deterministic Newton Raphson 1 0.2026 — 3.918 — 69-bus probabilistic MC based on Newton Raphson 10,000 0.2271 35.83 4.024 244.36 69-bus deterministic Newton Raphson 1 0.2249 — 4.027 — Fig. 12 demonstrates the PDF of active power loss from PLF, considering the uncertainty of stochastic load behaviour which observed to be 203.98 kW. The active power loss from the DLF is 202.68 kW. While the deterministic active power generation is 3917.68 kW. The probabilistic active power generation is 3921.3 kW as depicted in Fig. 13 for the 33-bus test system. The voltage profiles for the deterministic and PLF are depicted in Fig. 14. Fig. 12Open in figure viewerPowerPoint PDF of active power loss Fig. 13Open in figure viewerPowerPoint PDF of active power generation Fig. 14Open in figure viewerPowerPoint Voltage profiles for 33-bus system The active power loss from PLF of the 69-bus distribution system is 227.1 kW when considering the uncertainty of stochastic load behaviour. The active power loss from the DLF is 224.9 kW. While the deterministic active power generation is 4026.85 kW. The probabilistic active power generation is 4024.06 kW. The deterministic and PLF depict the voltage profiles in Fig. 15. Fig. 15Open in figure viewerPowerPoint Voltage profiles for 69-bus system To verify the effectiveness and feasibility of the applied BBO algorithm method in solving optimisation problem over other applicable algorithms in determining optimum location and size for the four simulated cases, and by increasing the number of candidate DG units to raise the problem complexity, the results are compared with PSO–CFA [13], ABC [36] and hybrid ACO–ABC [14] methods for 33-bus system. The 69-bus system has been simulated using BBO algorithm and compared with MTLBO [15] and ACO-ABC [14]. As shown in Tables 4 and 5, the proposed technique achieves better minimum active power generation and higher active power loss reduction. It proves that the applied method has good performances in obtaining high-quality solutions. Table 4. Comparison of the simulation results for IEEE 33-bus distribution network Simulation case Method Optimal location (bus number) DG optimal size, MW Total capacity, MW Power losses, MW 1 DG unit ABC 6 2.5775 2.5775 0.1050 PSO–CFA 6 2.5752 2.5752 0.1039 ACO–ABC 6 2.5753 2.5753 0.1039 BBO 6 2.5753 2.5753 0.1039 2 DG units ABC 6 1.9707 2.5464 0.0899 15 0.5757 PSO–CFA 14 0.7876 2.0363 0.0862 29 1.2487 ACO–ABC 13 0.8464 2.0052 0.0859 30 1.1588 BBO 30 1.1586 2.0050 0.0859 13 0.8464 3 DG units ABC 6 1.7569 3.1152 0.0792 15 0.5757 25 0.7826 PSO–CFA 10 1.0491 2.7326 0.0760 25 0.8786 33 0.8049 ACO–ABC 14 0.7547 2.9260 0.0714 24 1.0999 30 1.0714 BBO 14 0.7541 2.9247 0.0714 24 1.0993 30 1.0716 4 DG units ABC 6 1.0765 3.0884 0.0665 15 0.5757 25 0.7824 32 0.6538 PSO–CFA 13 0.7484 3.0213 0.0689 24 1.0759 28 0.5994 31 0.5976 ACO–ABC 7 0.9114 3.2000 0.0659 14 0.5858 24 0.9877 31 0.7151 BBO 7 0.9161 3.191 0.0659 14 0.5853 24 0.9809 31 0.7085 Table 5. Comparison of the simulation results for IEEE 69-bus distribution network Simulation case Method Optimal location (bus number) DG optimal size, MW Total capacity, MW Power losses, MW 1 DG unit MTLBO 61 1.8197 1.8197 0.08332 ACO–ABC 61 1.8726 1.8726 0.08319 BBO 61 1.8673 1.8673 0.08318 2 DG units MTLBO 17 0.5197 2.2517 0.071776 61 1.732 ACO–ABC 18 0.5309 2.3127 0.071657 61 1.7818 BBO 17 0.52833 2.30958 0.07164 61 1.78125 3 DG units MTLBO 11 0.4938 2.5447 0.069539 18 0.3784 61 1.6725 ACO–ABC 11 0.5597 2.6224 0.069429 21 0.3468 61 1.7159 BBO 11 0.53882 2.62418 0.06928 18 0.36694 61 1.71842 4 DG units BBO 11 0.57173 3.3223 0.06791 21 0.34329 50 0.69576 61 1.71151 After identifying the optimum number, size and location of DG units from BBO algorithm, all the DG unit capacities have been consolidated by optimising the total capacity of CPVDG as a single added bus. This CPVDG unit shall distribute and inject the consolidated optimum sizes to the optimum locations as demonstrated in Fig. 2. The process of identifying the optimum location of the CPVDG shall be based on two scenarios. First, the CPVDG shall be installed next to the bus with the highest DG capacity to avoid