Planning of an LVAC Distribution System with Centralized PV and Decentralized PV Integration for a Rural Village

: Energy demand is continuously increasing, leading to yearly expansions in low-voltage (LV) distribution systems integrated with PVs to deliver electricity to users with techno-economic considerations. This study proposes and compares different topology planning strategies with and without PVs in a rural area of Cambodia over 30 years of planning. Firstly, the optimal radial topology from a distribution transformer to end-users is provided using the shortest path algorithm. Secondly, two different phase balancing concepts (i.e., pole balancing and load balancing) with different phase connection methods (i.e., power losses and energy losses) are proposed and compared to ﬁnd the optimal topology. Then, the integration of centralized (CePV) and decentralized PV (DePV) into the optimal topology is investigated for three different scenarios, which are zero-injection (MV and LV levels), no sell-back price, and a sell-back price. Next, the minimum sell-back price from CePV and DePV integration is determined. To optimize phase balancing, including the location and size of PV, an optimization technique using a water cycle algorithm (WCA) is applied. Finally, an economic analysis of each scenario based on the highest net present cost (NPC), including capital expenditure (CAPEX) and operational expenditure (OPEX) over the planning period, is evaluated. In addition, technical indicators, such as autonomous time and energy, and environmental indicator, which is quantiﬁed by CO 2 emissions, are taken into account. Simulation results validate the effectiveness of the proposed method.


Introduction
As the population grows and people's lifestyles change, the electricity demand continues to increase each year. New ways to improve the performance of the power grid are being explored by researchers to meet these needs. However, one of the challenges faced by the power system is the presence of single-phase loads in low-voltage (LV) distribution networks, which creates an imbalance and requires an effective strategy for load balancing. Moreover, the integration of renewable energy sources, such as solar photovoltaic (PV) systems, into a grid can also cause some issues, such as voltage rise and reverse power flow [1]. Therefore, it is crucial to find suitable solutions to improve the electrical technology in LV distribution networks to enhance the system's reliability, quality, and economics [2][3][4].
Many studies relevant to LV distribution system planning and operation are addressed in the literature review. To rebuild the radial topology in LV distribution systems, the authors [5,6] have applied the shortest path algorithm to optimize the radial structure, including the shortest cables. Power phase balancing is key to reducing power loss and improving service quality in low-voltage networks; the authors [7] have used the genetic reduction and voltage improvement. The best method is then determined based on several performance indicators (energy loss and energy purchase) and economic analysis (CAPEX, OPEX, and NPC). The second research gap relates to the integration of PV systems into the grid, which involves the flow of reverse power into the MV grid only, along with a fixed sell-back price. However, this study proposes the scenario of PV integration into the grid (LV and MV), which includes a scenario of zero injection into the grid (LV and MV) and a scenario of PV injection into the grid by proposing a sensitivity of sell-back prices. The economic analysis and technical performance are considered to find the best from each scenario.
The following are the novelty and contributions of this study: • Provide a planning tool for the LV distribution network with PV integration that is applicable to developing countries; • Provide a possible scenario for PV injection into the grid that aligns with current and future regulations; • Develop a tool using optimization solvers that allows distribution network planners to evaluate the LV topologies and the impact of PV integration on networks; • Analyze the techno-economic viability of PV integration in an LV distribution network For this reason, this study proposes planning of LVAC distribution networks with integration of CePV and DePV considering the shortest length of lines, phase balancing, and hosting PV capacity with techno-economic aspects over the planning study of 30 years through a case study in a rural area in Cambodia. Firstly, different concepts for topologies and phase balancing are proposed. Then, the integration of CePV and DePV into the optimal topology is studied. Next, the economic analysis and comparison of proposed methods by taking into account the capital expenditure (CAPEX), operational expenditure (OPEX), and net present cost (NPC) are investigated. Technical indicators such as autonomous time and energy and an environmental indicator represented by the quantity of CO 2 emissions are also considered. The rest of this study is organized as follows: Section 2 describes details of the proposed method, algorithm development, and case study; Section 3 presents the simulation results, and discussion; and Section 4 provides the conclusion and future work.

Materials and Methods
This study proposes various approaches to optimizing the radial topology of an unbalanced LVAC distribution network integrating CePV and DePV in a rural area of Cambodia. This study has seven specific objectives: (1) to reduce the total cable usage of the LVAC network by using the shortest path; (2) to optimize power loss by using two algorithms for power phase balancing: pole balancing (PB) and load balancing (LB); (3) to propose methods for optimizing energy loss during 24-h by using two approaches: Method 1 (M1), which optimizes power phase balancing at peak load and then applies the load curve, and Method 2 (M2), which optimizes energy loss for power phase balancing during 24 h; (4) to study the impact of CePV and DePV integration in the system; and (5) to evaluate the economic performance of the LVAC distribution network with and without PV integration; (6) to study the reliability of the system by using the autonomous operation of time and energy for PV integration; and (7) to study the environmental indicators of systems that have CO 2 emissions and CO 2 emission reduction. Figure 1 provides a flowchart of the various stages used to achieve the research objectives of this study. The first step involves gathering input data such as coordinates (X, Y), load demands of households (P, Q), line impedance (Z), etc. The second step is to optimize the radial topology, which includes finding the shortest cable path and implementing power phase balancing to minimize power loss. The third step proposes methods for minimizing energy loss and comparing the proposed radial topologies. The fourth step examines the integration of CePV and DePV systems into the optimal LVAC distribution network, considering its optimal sitting and sizing using WCA based on the objective function of power loss and a voltage limit constraint. The fifth step investigates

Description Method and Algorithms
This section describes the shortest path method, power phase balancing concept, method for energy loss minimization, PV installation, economic analysis formulation, and several input parameters of this study.

Shortest Path
In low-voltage alternating current (LVAC) distribution systems, electricity is mostly distributed from a three-phase distribution transformer to households with single-phase or three-phase feeders along electrical poles and roads. The shortest path is a method that studies the design topology using a radial system and provides the shortest cable use for an LVAC distribution network [9]. The steps for designing this radial topology with the shortest cable length are outlined in a flowchart shown in Figure 2.

Description Method and Algorithms
This section describes the shortest path method, power phase balancing concept, method for energy loss minimization, PV installation, economic analysis formulation, and several input parameters of this study.

Shortest Path
In low-voltage alternating current (LVAC) distribution systems, electricity is mostly distributed from a three-phase distribution transformer to households with single-phase or three-phase feeders along electrical poles and roads. The shortest path is a method that studies the design topology using a radial system and provides the shortest cable use for an LVAC distribution network [9]. The steps for designing this radial topology with the shortest cable length are outlined in a flowchart shown in Figure 2. Calculate the distance between each household and all pols using the distance between two points on a coordinate system.

Store the households for each pole
Determine the shortest distance between poles required by each household.
end Figure 2. Flowchart of shortest path method.

Power Phase Balancing
This part focuses on designing the structure of the LVAC distribution network by using the power phase balancing concept, and it provides two different cases of the research, such as Case 1 (pole balancing-PB) and Case 2 (load balancing-LB) as given in Figure 3 [10]. The objective of these cases is to minimize power loss while respecting voltage and current constraints using WCA for nonlinear optimization purposes [19].
1. Pole balancing (PB): in this case, the concept of single-phase connection of electrical poles is proposed by randomizing its phase connection (possible phase connection of electrical poles: Phase A, B, or C), which is performed using WCA optimization with the objective function of power loss. 2. Load balancing (LB): focuses on random single-phases in households (it means that each household has selected the possible phase connections on Phases A, B, or C). It also has the same objective function as pole balancing and is implemented using WCA optimization.

Power Phase Balancing
This part focuses on designing the structure of the LVAC distribution network by using the power phase balancing concept, and it provides two different cases of the research, such as Case 1 (pole balancing-PB) and Case 2 (load balancing-LB) as given in Figure 3 [10]. The objective of these cases is to minimize power loss while respecting voltage and current constraints using WCA for nonlinear optimization purposes [19].

1.
Pole balancing (PB): in this case, the concept of single-phase connection of electrical poles is proposed by randomizing its phase connection (possible phase connection of electrical poles: Phase A, B, or C), which is performed using WCA optimization with the objective function of power loss.

2.
Load balancing (LB): focuses on random single-phases in households (it means that each household has selected the possible phase connections on Phases A, B, or C). It also has the same objective function as pole balancing and is implemented using WCA optimization. Calculate the distance between each household and all pols using the distance between two points on a coordinate system.

Store the households for each pole
Determine the shortest distance between poles required by each household.
end Figure 2. Flowchart of shortest path method.

Power Phase Balancing
This part focuses on designing the structure of the LVAC distribution netwo using the power phase balancing concept, and it provides two different cases o research, such as Case 1 (pole balancing-PB) and Case 2 (load balancing-LB) as giv Figure 3 [10]. The objective of these cases is to minimize power loss while respe voltage and current constraints using WCA for nonlinear optimization purposes [19 1. Pole balancing (PB): in this case, the concept of single-phase connection of elec poles is proposed by randomizing its phase connection (possible phase connecti electrical poles: Phase A, B, or C), which is performed using WCA optimization the objective function of power loss. 2. Load balancing (LB): focuses on random single-phases in households (it mean each household has selected the possible phase connections on Phases A, B, or also has the same objective function as pole balancing and is implemented WCA optimization.

Methods for Energy Loss Minimization
This point focuses on minimizing energy loss by proposing two different methods [20]. These methods are performed by taking into account a load profile to study the energy performance per day, and it is also implemented for the PB and LB concepts.

1.
Method 1: It investigates how to minimize power loss at peak load, and after that, a topology is given for PB and LB at peak load. Additionally, a load profile is performed on this method to attain the energy loss for a day. Figure 4a presents the process of Method 1 as a flow chart.
Step 1 begins with the input of coordinates, peak demands of the household, line impedances, and a load profile.
Step 2 involves choosing either case pole balancing or load balancing to simulate peak load in this step.
Step 3 checks to see if the time is less than 24 h.
Step 4 changes bus data based on its load profile.
Step 5 obtains new bus data for a given period (t) in hours.
Step 6 involves running backward-forward load flow to calculate power loss, voltage, and current.
Step 6 then loops back to Step 2 until a certain condition is met. The final step involves calculating the energy loss.

2.
Method 2: It is a technique that focuses on reducing energy loss during the load profile of a power system using PB and LB to optimize the distribution and balancing of power. This can help to reduce energy costs and improve the efficiency of the power system. Figure 4b shows the flowchart for method 2, which is also used for both PB and LB. The first step involves inputting data such as coordinates (X, Y), peak household demands, line impedances (Z), and a load profile. The second step has case pole and load balancing and selects one to test in this method. The third step is a random phase connection (x) for 24 h. The fourth step focuses on testing LV topology for load profile and x-phase connection by performing load flow (BWFW) to obtain power loss, voltage profile, and current during each hour over 24 h. The fifth step provides a formula to calculate energy loss by summing the power loss of each hour and multiplying it by 1 h. Lastly, WCA optimization is performed to find the smallest energy loss until this condition is met.

PV System Installation
Integrating a PV installation into LVAC distribution networks can offer significant benefits in terms of reduced energy costs and environmental impact [21,22]. In this study, two concepts of PV integration are proposed: a centralized PV system, which is installed at MV/LV transformers (CePV), and a decentralized PV system (DePVs), which is installed on the rooftops of households and then integrates into the LV grid as given in Figure 5. In Cambodia, the policy is that the total size of PV systems that can be connected to the grid cannot exceed 50% of the transformer size or demand contract in kW [23], which is calculated by multiplying the kVA rating transformer by 0.9 (i.e., power factor). To figure out the size of the PV system, we need to know the transformer's size in kW instead of kVA due to the power factor. For instance, if a transformer is 160 kVA, we can convert it to kW using a power factor of 0.9, resulting in a transformer size of 144 kW. Therefore, the size of the PV system that can be connected to the grid would need to be 72 kW, which is half of the transformer size in kW. To clarify, the total size of CePVs that can be installed is 72 kW, and the same total size of DePVs can also be installed. Since DePVs are installed in individual households, this study aims to use a water cycle algorithm (WCA) to optimize the location, size, and number of PV systems in the LVAC distribution network. This analysis is based on the voltage limit of each bus and power loss reduction to ensure that the PV systems operate efficiently and safely within the grid. Furthermore, in this section, we propose three scenarios for both CePV and DePV; which are zero injection to the grid; PV injection with no sell-back price; and PV injection with a sell-back price.   In this study, the WCA is used to solve the problem formulation. The ob function and constraints were defined in the mathematical Equations provided in ( However, since the analysis of this study is evaluated at the hourly level, shor violations may exist for voltage and current at the minute level.

•
Objective function In this study, the WCA is used to solve the problem formulation. The objective function and constraints were defined in the mathematical Equations provided in (1)-(3). However, since the analysis of this study is evaluated at the hourly level, short-term violations may exist for voltage and current at the minute level.

•
Objective function • Subjective to: where P loss is total active power loss in kW, V i is the voltage at i bus in pu, I line is the current of each line in kA, and I max_line is the maximum current of each line in kA.

Economic Analysis
• CAPEX, OPEX, and NPC This section presents the formulas used to measure the cost of the proposed method, including capital expenditure (CAPEX) and operating expenditure (OPEX) [3,4,24]. CAPEX stands for capital expenditure and includes the initial cost of acquiring and installing the equipment essential for the project, such as cables (C cable ), PV modules (C PV ), and PV inverters (C inverter ). It also covers the cost of replacing components (C replacement ), for example, the replacement cost of the inverter, which must be replaced after 15 years.
where C cable is the cost of total cable in k$, C PV is the cost of PV modules in k$, C inverter is the cost of inverter in k$, and C replacement is the cost of replacement in k$. OPEX refers to the ongoing costs associated with operating and maintaining the system. It includes the cost of purchasing energy from the MV (medium voltage) grid as well as any costs related to selling energy to households and back to the grid from PV injection. O&M (operations and maintenance) costs, which include maintaining the PV components and other equipment that make up the system, are also included in OPEX.
where C EnergySold is the cost of energy sold in k$, C EnergyPurchased is the cost of energy purchased in k$, C O&M is the cost of operation and maintenance in k$, i is the real discount rate [%], and T is the index of the year. The net present cost (NPC) equation is a way to calculate the total cost of a project or system, taking into account both the capital expenditure (CAPEX) and operating expenditure (OPEX). It helps project developers and investors evaluate a project's financial viability. In short, the NPC equation is a crucial tool for assessing a project's profitability and making informed decisions.
The real discount rate is a percentage that shows how much future cash flows are worth today after accounting for inflation. The real discount rate is expressed as in (7).
where, i is the nominal discount rate [%], and f is the expected inflation rate [%].

Autonomous Operation Time, Energy, and CO 2 Emissions
Grids are considered autonomous based on two factors [4]: (1) their ability to operate independently from the main grid for a certain amount of time (autonomous time expressed as a percentage (8)); and (2) the amount of energy they produce from their own solar panels compared to the total amount of energy needed by the main grid (autonomous energy expressed as a percentage (9) The total CO 2 emissions from energy use depend on how much carbon dioxide is released into the air when we generate and use energy, as provided by Equation (10) [4].
where, i sources is an index of production types (i.e., one for PV and two for grid), N sources is the number of sources production types (i.e., two types), LCCO 2i sources is life-cycle CO 2 emissions in kg/kWh for source, and is the total energy produced from each source over the project in kWh.

Case Study
This study on low-voltage distribution systems selected a rural village in Sandek commune, Batheay district, Kampong Cham Province, Cambodia as shown in Figure 6 [9]. The village has a total of 22 electrical poles and 107 households. Electrical power is supplied using a 22/0.4-kV transformer with a capacity of 160 KVA placed at the first pole, with a total power of 43 kW in the initial year. The mainline and secondary lines have conductor sizes of 120 mm 2 and 4 mm 2 , respectively. These details were used to model the low-voltage distribution system in the village and evaluate its performance.
where, i is the nominal discount rate [%], and f is the expected inflation rate [%].
2.1.7. Autonomous Operation Time, Energy, and CO2 Emissions Grids are considered autonomous based on two factors [4]: (1) their ability to operate independently from the main grid for a certain amount of time (autonomous time expressed as a percentage (8)); and (2) the amount of energy they produce from their own solar panels compared to the total amount of energy needed by the main grid (autonomous energy expressed as a percentage (9)).
The total CO2 emissions from energy use depend on how much carbon dioxide is released into the air when we generate and use energy, as provided by Equation (10) where, sources i is an index of production types (i.e., one for PV and two for grid), sources N is the number of sources production types (i.e., two types), emissions in kg/kWh for source, and is the total energy produced from each source over the project in kWh.

Case Study
This study on low-voltage distribution systems selected a rural village in Sandek commune, Batheay district, Kampong Cham Province, Cambodia as shown in Figure 6 Figure 7 shows how much solar power was produced in p.u. over a year. This information came from software called HOMER Pro. The software used data from NASA for solar radiation [25]. Figure 8 was used to obtain a PV curve and a normalized load curve. The PV curve was determined by averaging the solar power generated over a year. The load curve at the site is based on the measurement using a power quality analyzer Fluke 435 series II. It is worth noting that these curves were assumed to remain constant during the planning period, which means that the same curves were used for simulations covering different periods (such as the 1st year, 2nd year, or up to the 30th year). Figure 7 shows how much solar power was produced in p.u. over a year. This information came from software called HOMER Pro. The software used data from NASA for solar radiation [25]. Figure 8 was used to obtain a PV curve and a normalized load curve. The PV curve was determined by averaging the solar power generated over a year. The load curve at the site is based on the measurement using a power quality analyzer Fluke 435 series II. It is worth noting that these curves were assumed to remain constant during the planning period, which means that the same curves were used for simulations covering different periods (such as the 1st year, 2nd year, or up to the 30th year).

Tariff Payment for MV Feeders and Households in Rural Areas
Electricity is purchased from a medium voltage (MV) feeder and supplied to rural areas as part of this research study. Two different electricity tariffs between MV and LV are considered in this study; the distributor is paid based on monthly meter readings from the MV/LV transformer, and the households are charged a monthly payment for their electricity usage. This payment structure is designed to cover the costs of purchasing and distributing electricity while also ensuring that the electricity remains affordable and  Figure 7 shows how much solar power was produced in p.u. over a year. This information came from software called HOMER Pro. The software used data from NASA for solar radiation [25]. Figure 8 was used to obtain a PV curve and a normalized load curve. The PV curve was determined by averaging the solar power generated over a year. The load curve at the site is based on the measurement using a power quality analyzer Fluke 435 series II. It is worth noting that these curves were assumed to remain constant during the planning period, which means that the same curves were used for simulations covering different periods (such as the 1st year, 2nd year, or up to the 30th year).

Tariff Payment for MV Feeders and Households in Rural Areas
Electricity is purchased from a medium voltage (MV) feeder and supplied to rural areas as part of this research study. Two different electricity tariffs between MV and LV are considered in this study; the distributor is paid based on monthly meter readings from the MV/LV transformer, and the households are charged a monthly payment for their electricity usage. This payment structure is designed to cover the costs of purchasing and distributing electricity while also ensuring that the electricity remains affordable and

Tariff Payment for MV Feeders and Households in Rural Areas
Electricity is purchased from a medium voltage (MV) feeder and supplied to rural areas as part of this research study. Two different electricity tariffs between MV and LV are considered in this study; the distributor is paid based on monthly meter readings from the MV/LV transformer, and the households are charged a monthly payment for their electricity usage. This payment structure is designed to cover the costs of purchasing and distributing electricity while also ensuring that the electricity remains affordable and reliable for rural communities. The tariff rates for the distributor and household electricity usage in Cambodia are provided in Tables 1 and 2, respectively, according to the relevant regulations [26].

Input Parameters
This section provides several input data used for simulating and analyzing the economic evaluation of the project. Table 3 [3,[27][28][29][30] provides the input parameters, including load growth, the nominal discount rate, the expected inflation rate, the prices of PV panels, the prices of inverters, the prices of cables, etc. These data points are important for accurately modeling the financial performance of the project and assessing its economic viability over its expected lifetime [3,27,28]. Additionally, inputs of life-cycle CO 2 emissions for two types of sources (grid and PV) are provided in this section [29,30].

Optimal Radial Topology
In this study, four different strategies to build the LVAC distribution system for 30 years of operation were proposed. The costs and performance of each method were compared, and the results were presented in Table 4. The best method for a radial power system was found to be M2-LB (method two load balancing). It was found that this method has the highest NPC of 55.003 k$, including the OPEX of 68.199 k$. Additionally, it was observed that this method performs well in terms of energy loss (189.274 MWh), energy purchased (7425.564 MWh), minimum voltage of 0.910 pu, and CO 2 emissions of 2970.226 tons. Therefore, the M2-LB method is the most effective and efficient way to build the LVAC radial topology, as in this case study.  Figure 9 shows the cash flow for the M2-LB method. It displays the costs for CAPEX, OPEX, and NPC for each year. From the first to the third year, the NPC cost is negative, which means the project needs to spend money during these years. However, from the fourth to the thirtieth year, the NPC is positive, which means the project generates profit during these years. In Figure 10, the best topology for radial topology and power phase balancing is shown using the M2-LB method. This method ensures that each household's phase connection follows the load-balancing concept.

Scenario 1: Zero Injection
The information presented in Table 5 shows the results of the zero-injection grid scenario, comparing different cases such as the base case without PV (i.e., M2-LB), Case 1 with a CePV zero injection MV grid, Case 2 with a DePV zero injection MV grid, and Case 3 with a DePV zero injection LV grid. The table indicates that the base case without PV has the highest NPC of 55.003 k$, which means it is the most cost-effective system among all the cases studied. Therefore, the topology without PV is the best option for this particular scenario of zero injection.
For PV integration, Case 2, which involves autonomous operation using solar energy, displays the best system in terms of energy and CO2 emission reductions compared to Case 1 and Case 3. This means the system performs better when it can operate autonomously using solar energy, resulting in lower CO2 emissions.

Scenario 1: Zero Injection
The information presented in Table 5 shows the results of the zero-injection grid scenario, comparing different cases such as the base case without PV (i.e., M2-LB), Case 1 with a CePV zero injection MV grid, Case 2 with a DePV zero injection MV grid, and Case 3 with a DePV zero injection LV grid. The table indicates that the base case without PV has the highest NPC of 55.003 k$, which means it is the most cost-effective system among all the cases studied. Therefore, the topology without PV is the best option for this particular scenario of zero injection. For PV integration, Case 2, which involves autonomous operation using solar energy, displays the best system in terms of energy and CO 2 emission reductions compared to Case 1 and Case 3. This means the system performs better when it can operate autonomously using solar energy, resulting in lower CO 2 emissions. Figure 11 displays the cost of each case, which has CAPEX, OPEX, NPC, and the cost of energy purchased. The base case has lower CAPEX and OPEX costs than Cases 1, 2, and 3. However, the base case has a profit with a higher NPC of $55.003 k$ compared to Cases 1, 2, and 3. In addition, the base case spends the most money on purchasing energy, with a cost of 898.493 k$, compared to Cases 1, 2, and 3. Figure 11. The bar graph for the cost of scenario 1. Table 6 presents the results of scenario 2, which includes three different cases: the base case without PV, Case 1 with CePV, and Case 2 with DePV. This study concludes that the base case without PV is the best scenario because it has the highest NPC of 55.003 k$ compared to the other scenarios. This suggests that for this particular LVAC distribution network, the most cost-effective option is to not use solar power and stick with the base case.  For PV integration, both Case 1 and Case 2 provide the same percentage of autonomous operation time and energy at 36% and 59%, respectively. However, Case 2 shows better CO 2 emission reductions than Case 1 and the base case, indicating that the system performs better when it can operate autonomously and results in lower CO 2 emissions.

Scenario 2: Injection to the MV Grid without Sell-Back Price
In Figure 12, the costs of CAPEX, OPEX, NPC, and energy purchases for each case are presented. The base case shows lower CAPEX and OPEX expenses compared to Cases 1 and 2. However, it has a profile with a higher NPC of 55.003 k$ than Cases 1 and 2. Additionally, the base case incurs the highest cost for purchasing energy, totaling 898.493 k$. - 20 24 In Figure 12, the costs of CAPEX, OPEX, NPC, and energy purchases for each case are presented. The base case shows lower CAPEX and OPEX expenses compared to Cases 1 and 2. However, it has a profile with a higher NPC of 55.003 k$ than Cases 1 and 2. Additionally, the base case incurs the highest cost for purchasing energy, totaling 898.493 k$.  Figure 13 shows a bar graph comparing the cost of NPC and the payback period with and without CePV. CePV proposes that the sell-back price start at 10% to 200% of 0.118 $/kWh. For an explanation of the figure, as the sell-back price increases, the value of NPC also increases while the payback period decreases, as shown in the graph. To be profitable with CePV integration, compared to the NPC of topology without PV, the price of selling back electricity must be more than 110% of the price of buying electricity from the power grid ($0.118 per kWh), and the payback period starts at 11.5 years and decreases from there.  Figure 13 shows a bar graph comparing the cost of NPC and the payback period with and without CePV. CePV proposes that the sell-back price start at 10% to 200% of 0.118 $/kWh. For an explanation of the figure, as the sell-back price increases, the value of NPC also increases while the payback period decreases, as shown in the graph. To be profitable with CePV integration, compared to the NPC of topology without PV, the price of selling back electricity must be more than 110% of the price of buying electricity from the power grid ($0.118 per kWh), and the payback period starts at 11.5 years and decreases from there.   Figure 14 has a graph comparing the NPC and payback period without PV and with DePV. DePV studies selling electricity back at a price starting at 10% to 120% of 0.118 $/kWh. To make a profit with DePV integration, compared to the NPC of topology without PV, the selling price of electricity needs to be at least 110% higher than the cost of buying electricity from the power grid, and the payback period is decremented starting from 12 (year, month). • Strategy 2: Minimize the sell-back price to get the profit Figure 15 is a graph that displays the NPC and payback period of the CePV system at different sell-back prices. The graph demonstrates that for the CePV system to make a profit, it needs to sell the cost of electricity back to the grid at a price higher than 47% of the cost it pays to buy electricity from the grid, and the payback period decreases from a value of 29.6 (year, month), which is $0.118 per kWh.  Figure 14 has a graph comparing the NPC and payback period without PV and with DePV. DePV studies selling electricity back at a price starting at 10% to 120% of 0.118 $/kWh. To make a profit with DePV integration, compared to the NPC of topology without PV, the selling price of electricity needs to be at least 110% higher than the cost of buying electricity from the power grid, and the payback period is decremented starting from 12 (year, month).  Figure 14 has a graph comparing the NPC and payback period without PV and with DePV. DePV studies selling electricity back at a price starting at 10% to 120% of 0.118 $/kWh. To make a profit with DePV integration, compared to the NPC of topology without PV, the selling price of electricity needs to be at least 110% higher than the cost of buying electricity from the power grid, and the payback period is decremented starting from 12 (year, month). • Strategy 2: Minimize the sell-back price to get the profit Figure 15 is a graph that displays the NPC and payback period of the CePV system at different sell-back prices. The graph demonstrates that for the CePV system to make a profit, it needs to sell the cost of electricity back to the grid at a price higher than 47% of the cost it pays to buy electricity from the grid, and the payback period decreases from a value of 29.6 (year, month), which is $0.118 per kWh. • Strategy 2: Minimize the sell-back price to get the profit Figure 15 is a graph that displays the NPC and payback period of the CePV system at different sell-back prices. The graph demonstrates that for the CePV system to make a profit, it needs to sell the cost of electricity back to the grid at a price higher than 47% of the cost it pays to buy electricity from the grid, and the payback period decreases from a value of 29.6 (year, month), which is $0.118 per kWh. Energies 2023, 16, x FOR PEER REVIEW 17 of 19 Figure 15. CePV with sell-back prices. Figure 16 shows the graph of the NPC and payback period of DePV with the proposed percentage of the sell-back price. To make a profit, DePV needs to sell the cost of electricity back to the grid at a price higher than 48% of the cost it pays to buy electricity from the grid (which is $0.118 per kWh), and the payback period is decremented starting from 29.8 (year, month). To summarize, the first strategy, CePV and DePV, both need to sell electricity back at 110% of 0.118 $/kWh to make a profit compared to the NPC of the topology without PV. However, the second strategy shows that CePV is better than DePV because it has a lower sell-back price, starting at 47%. This means that investing in CePV gives a better return compared to investing in DePV. After simulation, notice that as the sell-back price increases, the value of NPC also increases while the payback period decreases.  Figure 16 shows the graph of the NPC and payback period of DePV with the proposed percentage of the sell-back price. To make a profit, DePV needs to sell the cost of electricity back to the grid at a price higher than 48% of the cost it pays to buy electricity from the grid (which is $0.118 per kWh), and the payback period is decremented starting from 29.8 (year, month).  Figure 16 shows the graph of the NPC and payback period of DePV with the proposed percentage of the sell-back price. To make a profit, DePV needs to sell the cost of electricity back to the grid at a price higher than 48% of the cost it pays to buy electricity from the grid (which is $0.118 per kWh), and the payback period is decremented starting from 29.8 (year, month). To summarize, the first strategy, CePV and DePV, both need to sell electricity back at 110% of 0.118 $/kWh to make a profit compared to the NPC of the topology without PV. However, the second strategy shows that CePV is better than DePV because it has a lower sell-back price, starting at 47%. This means that investing in CePV gives a better return compared to investing in DePV. After simulation, notice that as the sell-back price increases, the value of NPC also increases while the payback period decreases. To summarize, the first strategy, CePV and DePV, both need to sell electricity back at 110% of 0.118 $/kWh to make a profit compared to the NPC of the topology without PV. However, the second strategy shows that CePV is better than DePV because it has a lower sell-back price, starting at 47%. This means that investing in CePV gives a better return compared to investing in DePV. After simulation, notice that as the sell-back price increases, the value of NPC also increases while the payback period decreases.

Conclusions
This research study compares different topologies with and without PV integration in rural areas of Cambodia over 30 years. The different radial topologies are evaluated and compared based on the shortest path method for minimizing cable length. Pole and load balancing techniques are developed to minimize power losses, improve voltage, and simulate methods for minimizing energy loss over 24 h. With a radial topology and phase power balancing, Method 2 with load balancing (M2-LB) has the highest NPC and is the best approach for radial topology. The study of systems with and without PV (CePV and DePV) integration into the optimal radial topology is also investigated; Scenario 1 is for zero injection into the grid, with three cases: CePV with zero injection into MV grid, DePV with zero injection to the MV grid, and DePV with zero injection to the LV grid. With this scenario, the base case is the highest NPC for the LVAC distribution network. Scenario 2 has three cases; PV injection into the MV grid without a sell-back price, and the base case without PV integration is the best case with the highest NPC. Next, Scenario 3 has two sell-back price strategies. Strategy 1 compares the topology without PV to the topology with PV to find the sell-back price to profit from CePV and DePV; upon comparing a topology without PV, the sell-back price should be at least 110% of 0.118 $/kWh. Strategy 2: Find the minimal sell-back price for CePV and DePV, in which the minimum sell-back price is also provided, which has the minimum sell-back price of 47% and 48% of 0.118 $/kWh for the cases of CePV and DePV, respectively, to generate profit from the project. In addition, autonomous operation and environmental indications are also provided. In conclusion, this study provides a planning tool for an effective economic analysis considering CAPEX, OPEX, NPC, voltage improvement, and environmental indicators in the LVAC distribution network with DePV-CePV integration. However, the integration of PV and storage into the low-voltage distribution system will be investigated in future work.