Improving reliability of the power distribution system in Goma (DRC) using solar distributed generation

The existing power distribution system of the city of Goma in the Democratic Republic of the Congo has many problems, including the scarcity of electric energy, power unreliability, the low access rate of electrification, poor flexibility in the network topology, and lack of demand response, which lead to shedding of load, unbalancing and overloading the system. The reliability of the Goma power distribution system is very poor by international standards. The major cause of this is the lack of adequate energy supply to meet demand. To mitigate the power reliability problem, a solar-based distributed generation (DG) is modelled and evaluated in this study. Each feeder has been considered separately with an appropriately designed DG. The work has evaluated initial investment cost and life cycle cost of the investment to assess the feasibility of the proposed solution. Based on the unserved energy and electricity tariff, an economic analysis was conducted. The reliability indices are computed and the modelled solution is designed for each feeder in PV syst software and simulated using ETAP, whose simulation results show that the reliability can be improved by up to 76%. 
 


Literature review
Power distribution system reliability is a major consideration in system operation and planning and several studies have been conducted to improve the reliability indices of power distribution system networks. They suggest different techniques for improvements. Khounnouvong and Premrudeepreechacharn (2015) proposed protective equipment, such as recloser and switching for reliability improvement in an electrical distribution system. Rahmawati and Hariyanto (2015) studied the optimal placement of switches in a distribution system and conducted a cost/worth analysis of the reliability improvement method. Chandhra Sekharet al. (2017) presented the reliability parameters and reliability indices of the Indian electricity network and compared the indices to national standard. Gono et al. (2011) conducted an empirical reliability computation. Hossein and Arani (2015) considered a case study where reliability indices were computed, analysed and compared with the standard, while Xu (2019) used reliability tracking to identify the weak points at which DG could be incorporated to improve the system reliability. In Garamaw (2020), the power reliability of a city in Ethiopia was evaluated, using the potential impacts of DG units on mitigating the power system reliability problem of the network. Two cases were considered: DG installed at 15 kV feeders, and DG connected at low-voltage sites (15/0.4 kV).
Reliability assessment of renewable energy interfaced electrical distribution system considering the electrical loss minimisation was developed by Kumar et al. (no date), using the optimal location(s) and sizing(s) of the renewable energy sources (RESs), and incorporating a battery storage system. Jose and Jorge (2020) reviewed and classified the state-of-the-art of reliability assessment in a microgrid. It has been established that more research studies are needed to assess how new control strategies and information and communications technology impact DGs' reliability. Agrawal et al. (2020) suggested a suitable modification in existing reliability indices in order to make them more appropriate for underground distribution systems. They addressed a new methodology for the reliability evaluation of underground distribution systems by proposing dynamic failure rates of feeders and suggests network reconfiguration to enhance the reliability and performance of distribution systems. Ghulomzoda et al. (2020) studied the method of control using reclosers in Tajikistan with distributed small generation. Based on modified reclosers, a method of decentralised synchronisation and restoration of the grid normal operation after the loss of the main power source was proposed.
A combined power generation system constituted with DG, battery storage and electric vehicles in a microgrid was applied by Bai et al. (2015) to achieve a reliable evaluation of a distribution network with microgrids. A methodology to model charging load and discharging capacity of multiple electric vehicle batteries was developed. The reliability of the distribution system was improved, based on determining the optimal capacity according to an economic and reliability evaluation. A predictive based reliability analysis of an electrical hybrid distributed generation was presented by Fu et al. (2018). The effect of a battery bank, as an electrical storage system, was investigated on the reliability of a DG system that forms an EHDG with a photovoltaic (PV) system as the main source.
Many papers have discussed the design and integration of PV systems in a grid. Garamaw (2020) focused on the key technical issues and design optimisation of large solar power plants. Gonen (2007) designed and built a PV power system installed on a rooftop over an area of 50 m 2 with a power output of 6 kWp. The installation of PV was done with a slope of 6 o and produced around 10 006.7 kWh of electrical energy per year. It was connected to the grid without a battery and the investment included the cost of maintenance and life cycle costs over 25 years. Gono et al. (2011) performed a techno-economic analysis of a solar PV power plant installed to meet the energy demand of a building in Delhi. Hossein and Arani (2015) showed that energy savings on net consumption and maximum demand can be maximised via optimal sizing of the solar PVbattery system, using the MATLAB genetic algorithm tool. The study revealed that optimal sizing of the solar PV-battery system contributed to energy bill savings up to 20% of net consumption via solar PV self-consumption, 3% of maximum demand (MD) via MD shaving and 2% of surplus power supplied to grid via net energy metering in regard to the Malaysian electricity tariff scheme and cost of the overall system.

Reliability indices
Reliability can be taken as the ability of a system to perform its required function with specified conditions in a time interval. It is also the percentage of time a voltage source is uninterrupted (Williset al., 2009). Reliability indices are found to consider the downtime and uptime of a component or element.
Most reliability indices are average values of a particular reliability characteristic for a given system. The indices for distribution analysis include customer-oriented indices and load-or energy-oriented indices.

Customer-oriented indices System average interruption frequency index (SAIFI):
This index, in units of 1/C/a, shows the number of sustained interruptions that a given or average number of customers are facing during a specified period (Power and Energy Society, 2012). It is calculated as in Equation 1.
where λ is the failure rate at load point i, N is the total number of customers interrupted at load point i, and N is the total number of customers at load point i.

System average interruption duration index (SAIDI):
This index, in units of h/C/a, represents the total duration of interruption that a certain number of customers are facing during the period (Power and Energy Society, 2012) and calculated as in Equation 2.
where U is the restoration time in minutes, N is the total numbers of customers interrupted, and N is the total numbers of customers. where U is the restoration time in minutes, N is the total number of customers interrupted, and λ is the failure rate at load point i.
where N 0 is the number of interruptions, and N is the total number of customers interrupted.
Average service availability index (ASAI): This index indicates a period of time (often in percentage) that a customer has power provided during one year (or other defined reporting period). It is the ratio of the total number of customer hours that service was available during a given period to the total customer hours demanded (Power and Energy Society, 2012), and calculated as in Equation 5.
where ℎ time period understudy in an hour, U is the restoration time, in an hour, N is the total number of customers interrupted at load point I, and N is the total number of customers served.

Average service unavailability index (ASUI):
This index is the probability of having loads unsupplied and it is the complementary value to the ASAI (Power and Energy Society, 2012), and is calculated as in Equation 6.

Load and energy-oriented indices
Energy not supplied index (ENS): This index, in units of MWh/a, is the amount of unserved energy or the energy not delivered to the customers in a given period (Power and Energy Society, 2012) and expressed as in Equation 7.
where (i) is the average load.

Average system interruption frequency index (ASIFI):
The calculation of this index is based on load rather than customers affected. ASIFI is sometimes used to measure distribution performance in areas that serve relatively few customers that have relatively large concentrations of load, predominantly industrial/commercial customers (Power and Energy Society, 2012), as expressed in Equation 9.

= (9)
Average system interruption duration index (ASIDI): The calculation of the ASIDI is based on load rather than customers affected (Power and Energy Society, 2012), as expressed in Equation 10.

Description of the case study
The Société Nationale d'Electricité (SNEL) network is the main supplier in Goma and covers 18% electrification access rate of the city. A 70kV transmission line is extended from Ruzizi to Goma substation. The distribution system in the city has primary voltages of 15 kV and 6.6 kV and it is stepped down to 380 and 220 V for the customer level. It has one substation, with an installed power of two transformers working alternately as 2  10 MVA / 110-70 kV/15kV ratings and one thermal power plant with 1.1 MVA rating but not used due to its high fuel cost. Its topology is radial, as shown in Figure 1, and contains five feeders. Table 1 describes several power transformers, the total installed capacity for each feeder, as well as conductor size. Table 2 gives the frequency and duration of interruptions due to non-momentary and planned interruptions in the existing grid of SNEL in Goma, while Figures 2 and 3 show the planned and momentary interruptions of each feeder of each year in the distribution system from the recorded data of the SNEL substation from June 2018 to May 2020.       Figure 4 shows the frequency of interruptions for each cause as well as its duration classified for each feeder and it gives also the percentage of each cause of interruption in the system. Based on Figure 4, the percentage contributions of each cause of interruptions of the total frequency and duration of interruptions of each feeder and the overall system are analysed. Thus, load shedding (permutation of feeders) is the greatest cause of interruptions (33% of them) and its long duration is due to the scarcity of electric energy produced. Overload is the second-largest cause of interruption (22%) in the system -often due to the high customer demand and the inability of the system to meet it.
As the demand for energy is much greater than the supply and cannot be easily controlled, a power limiter has been installed at the beginning of the high voltage transmission line to ensure that Goma's network does not exceed its predefined portion. Interruptions caused by the power limiter in the network account for 17% of all interruptions, 7% represents some human error occurring in the exploitation of the network, atmospheric discharges account for 5%, and frequency corrections account for 4%. Other causes represent 13% of all interruptions, including birds, component failure, insulator perforation, poles damaged by cars, and burned wires.
Based on the recorded data for interruption between 2018 and 2020, the reliability indices for each feeder are calculated as shown in Table 3. Figures 5 and 6 illustrate the comparison of the commonly used reliability indices SAIFI and SAIDI, which are the major indicators of the level of reliability. Figure 7 shows all calculated reliability indices of Line 1, from which it can be seen that some indices are not visible, due to the higher value of certain indices.    The economic impact of poor reliability of SNEL's distribution system, based on the highlighted descriptions and analysis, is shown in Table  4. The economic evaluation of the reliability shows the cost of an outage at the utility side illustrated in Equation 12. Utility outage costs include the loss of revenue for energy not supplied, and the increased maintenance and repair costs to restore power to the customers affected. The maintenance and repair costs can be quantified by Equation 11 (Gonen, 2007).
where is the labour cost for each repair and maintenance action, and is the replacement or repair cost. Therefore, the total utility cost for an outage is expressed in Equation 12.
where is the energy not supplied. In the expected energy not supplied (EENS) index, energy per customer unit time is defined by Equation 13.
where is the total number of elements in the distribution system, L i is the average load at load point , r ij is the failure duration at point i due to component j, and λ ij is the failure rate at load point i due to component j.

Design of solar distributed generation
Around 76% of interruptions are caused by lack of energy produced, as demonstrated by the difference between the installed capacity and average power transmitted through transmission lines of each feeder, as shown in Table 5. Based on the power not served (Table 5), the capacity of the powerplant, the area, number of PV module needed, inverter capacity and converter size of each feeder were sized, as shown in Table 6. These steps have been considered when sizing the system (Nwaigwe et al., 2019;Diantari, 2016).
i) Calculate total Watt-hours per day needed from the PV modules.
ii) Size the PV modules. iii) Calculate the total Watt-peak rating needed for PV modules. iv) Calculate the number of PV panels for the system. PV syst software has been used to verify and ensure that the results given in Table 6 were calculated properly. Figure 8 shows the way the system has been configured in the software. In Figures 9-12, different reports of system design of each feeder have been given and described.

Cost of investment
The total capital cost includes the cost of the PV array, cost of the inverters, cost of the step-up transformers, and the balance of system equipmentwhich includes the cost of electrical wiring, meter, protections, junction boxes, cabinets, switchgear, combiners, fuses, breaker and other non-electrical components, and the cost of civil work and structure. The assumed cost of each component is shown in Table 7. Table 8 describes the investment cost. The study does not consider storage, as it has been conducted for grid connected system; therefore cost related to storage will not be given. Transfomer (USD/kWp) 20 Balance of system equipment USD/kWp) 74 Civil work (USD/kWp) 165 According to Stapleton and Neill (2012) and Renewable Energy Agency, 2019, the maintenance and operational costs per year generally account for 1-2% of the total cost of investment, which includes the cost of purchased components. Therefore, in the present study, 1% as maintenance and operation has been considered. Table 9 shows the cost of maintenance and operation for each feeder, and the total capital cost.    Life cycle cost (Lcc) will be calculated considering the initial investment costs (C) and the maintenance and operational ( & ) long-term costs (Stapleton and Neill, 2012;Diantari, 2016), as shown in Equation 14.

= + & (14)
It is assumed that the solar PV power plant has 25 years of life, based on expected PV lifespan. The discount rate (i) that is used to calculate the present value in this study is 8% (Villafuerte and al. (2019). This value is chosen based on the actual interest rate bank loans in DRC. Actual value of the maintenance and operational costs during the project life of 25 years is calculated, based on Stapleton and Neill (2012) and Diantari (2016), as shown in Equation 15.
With the initial investment cost (C) and the calculation of the actual maintenance and operational ( & ), life cycle costs for solar to be built during the project life of 25 years is shown in Table 10 for each feeder.
Based on the local radiation and output power found in Table 6 at the power transformer side, the annual energy that can be produced by solar PV power plant is calculated using Equation 16, and sale of electricity after 25 years is given by Equation 17. Both are represented in Table 11.
Based on the life cycle cost of the investment shown in Table 10 and the sale of electricity described in Table 11, it is seen that the project leads to profit. The life cycle cost of Line 1 is USD 18 149 098.96 and the sale of electricity for Line 1 gives USD 39 089 800.4, while the lifecycle cost of Line 5 is USD 12 174 955 and its sale of electricity gives USD 5 384 517. It could be argued that the sale of electricity of Line 5 leads to a loss, but this is compensated for by the sale of electricity of other lines. Figure 13 shows the comparison between the life cycle cost of each line and its sale of electricity.

Discussion
When applying solar DG to a power plant, the interruption frequency as well as duration will be reduced, as shown in Table 12 and Figures 13 and 14, considering the same load and same number and category of customer. The frequencies of interruptions and durations of interruptions of Line 1 are reduced by 72% and 86% respectively. The frequency and duration of interruptions of Line1 are 478.8 interrup- tions per year and 177.932 hour per year respectively. When the line is fed using solar DG, the frequency of interruptions is reduced to 135.8 per year. The duration of interruptions of Line 1 is 177.97 hours per year, but when the line is fed using solar DG, this is reduced to 26.08 hours per year. The reliability indices of the designed distributed generation system are calculated, with results given in Table 13, which shows reliability indices calculated using the predicted frequency and duration of interruptions of the designed grid system using solar photovoltaic DG. The SAIFI value of the overall system is reduced by using it.
The SAIDI value of the overall system is reduced as shown in Figure 15 and, therefore, the reliability of the existing network is improved. SAIDI improvement is higher than SAIFI because the causes leading to more hours of the outages were solved using DG.

Simulation of reliability analysis
The distribution model of the existing grid shown in Figure 17 is done to verify the calculated reliability indices values. Figure 18 shows the simulation model of the designed system. The system model is an overhead line, using step-down power transform-ers, with loads categorised considering residential load, commercial load, and industrial load. The summary report provides a listing of reliability indices for the overall system of distribution model of the existing network. The report presented in Table 14 describes the values of the reliability indices of the overall system such as SAIFI, SAIDI, CAIDI, ASAI, ALIFI, and ALIDI of the existing network. This simulation result verifies that the prediction of the values of each reliability index shown in Table 3 is done properly. It proves that the reliability of the existing network is very poor and has to be improved. For instance, from the simulation report shown, it can be seen that the SAIFI is 326.6100 interruptions per customer per year and SAIDI is 1319.8180 hours per customer per year, which verifies that the prediction of SAIFI and SAIDI in Table 13 is done properly.  Figure 17 verify the mathematically calculated values given in Table 3. Additional to this, the summary report gives the values of expected customer outage cost (ECOST), expected energy not supplied (EENS), and interrupted energy assessment rate (IEAR).
The summary report shown in Table 15 confirms that the reliability indices found using mathematical methods are correct. The result proves that the reliability of the system has been improved as it was calculated mathematically, as shown in Table  13. From the simulation summary report, we can see that SAIFI is 11.2 while is 12.2 in Table 13; SAIDI is 38.49 while it is 37.06 as calculated value. As SAIFI and SAIDI are based on how frequency interruptions and duration of the interruptions have been improved, it proves that the reliability the power distribution system has been improved.
The result found in ETAP software 16.0 for the overall system certifies that the predictive values were properly calculated. However, some values found by calculation are slightly different from the one obtained by simulation, such as AENS and EENS.

Conclusion
This research has shown that the reliability of Goma power distribution system is very poor, due to the lack of energy produced leading to scarcity of the energy in the city. The reliability has been improved using solar distributed generation, as the main cause of interruption was the lack of energy produced which resulted in demand exceeding supply. The average frequency of interruptions of Goma network is 364.87 interruptions per customer per year and the average duration of interruptions is 1478.7 hours per customer per year for the overall system, which have been improved to 12.247 for the system average interruption frequency index (SAIFI) and 37.067 for the system average interruption duration index (SAIDI). Investment cost was calculated based on the standard cost of each equipment, and the life cycle cost was calculated considering the discount rate in the cost of operational and maintenance for the designed system. Applying photovoltaic distributed generation has improved the reliability of the system by up to 76%.

Author contributions
G. Sengi was responsible for data curation, writing original draft preparation, writing the review and editing visualisation, methodology, investigation and resource organisation. E. Ntagwirumugara was responsible for visualisation, supervision of formal analysis, funding acquisition, writing the review and editing visualisation, project administration and resources.