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Item Open Access Determination of cost-reflective feed-in tariff for grid connected solar PV systems in Lesotho(National University of Lesotho, 2020) Kokome, Limpho; Hove, TawandaLesotho needs a feed-in tariff policy that can help accelerate integration of renewable energy in its electricity grid. In this study a method to determine the feed-in tariff for grid connected solar Photovoltaic (PV) systems was developed. The necessity to set different tariffs for different locations in terms of the solar PV array yield 𝑌 , and different tariffs for different installed capacities were examined. Location specific tariffs were examined because given a particular solar module, the array yield 𝑌 could vary with location because of different ambient temperature and radiation, while size specific tariffs were examined because solar PV systems have different specific costs for different system sizes. In order to determine the cost reflective feed-in tariff, the Levelized Cost of Electricity (LCOE) was used as the objective function. With this approach the feed-in tariff was set as the price for selling electricity that is reasonably above the unit cost of production. A custom spreadsheet model was used to calculate the solar PV array yield 𝑌 over Lesotho. This array yield was used to divide Lesotho into two regions, low yield regions, and high yield regions. Representative systems were chosen and the feed-in tariff for different solar PV installed capacities in both regions were determined. The study found that the feed-in tariff varies with location and system size as follows; System Category FiT ($/kWh) Low Array Yield Region High Array Yield Region 30 kWp Roof Mount 0.1778 0.1616 500 kWp Roof Mount 0.1597 0.1451 30 kWp Ground Mount 0.1740 0.1581 500 kWp Groun Mount 0.1453 0.1321 10 000 kWp Ground Mount 0.1138 0.1034 The study recommends a feed-in tariff that is both location and size specific. The feed-in tariff depends on duration of the tariff with shorter periods resulting in higher feed-in tariff. A 20-year duration of the feed-in tariff is therefore recommended by this study. The method used in this study to determine the feed-in tariff included the impact of inflation in the analysis and therefore a fixed feed-in tariff (that is not indexed to inflation) is recommended. The energy regulator, and the ministry responsible for energy policy setting can make use of this study in setting out feed-in tariff policy.Item Open Access Determinants of choice of household energy use in Lesotho(National University of Lesotho, 2020) Mothala, Matsoso; Mpholo, Moeketsi; Thamae, RetselisitsoeWith the need to achieve Sustainable Development Goals, modern clean household energy choice forms the basis for heeding this call. In developing countries, most of the population lives in rural areas and is characterized by high dependence on polluting biomass for cooking and heating while they rely predominantly on paraffin and candles for lighting. Women and children in developing countries spend an appreciable amount of time collecting the biomass, hence unable to carry out other development activities. The use of modern technologies such as solar home systems for lighting could help pupils study at night with adequate light and with no adverse effects on their health. Nevertheless, the determinants of household energy choice have not been studied in many developing countries including Lesotho, despite the potential benefits of such a study. This study uses the data collected by Lesotho’s Bureau of Statistics through a national household energy consumption survey of 2017, to develop a multinomial logistic regression to identify and analyze the determinants of the choice of household energy use. The results indicate that income, as predicted by the energy ladder model is statistically significant for the choice of clean energy fuels. But other socio-economic factors such as gender, education, household size, and settlement type also play an important role in the choice of clean energy choice. The role of gender in the choice of fuels used within a household is generally statistically insignificant. There is not a clear distinction of preference, on the choice of fuel, between male-headed households versus female-headed households. An increase in the education level of the household head is statistically significant in choosing cleaner fuels. This suggests that public policies should have a strong focus on improving formal and informal education to increase awareness of clean energy fuels and their benefits. Household size is negative and statistically significant for the choice of clean fuels over traditional fuels. Large households have enough labour that is required for the collection of traditional fuels. In rural settlements, electricity is hardly used for either cooking or water heating, it is used only for lighting. This suggests that policies, for economic reasons, should not focus on extending the grid to the rural areas but to promote domestic systems and micro-grids that provide enough electricity for lighting and household entertainment.Item Open Access Design of a standalone hybrid solar-wind system with pumped hydro storage along Likhaebaneng river in Quthing District, Lesotho(National University of Lesotho, 2024) Pitso, Khiba; Khaba, L; Makhele, MExtending the power grid to all villages in Lesotho, a country characterized by rugged terrain comprising mountains and hills, is nearly financially unfeasible. Consequently, the nation suffers from escalating poverty due to insufficient access to electrical energy. The most viable and sustainable solution to provide electricity to unelectrified areas is to harness the renewable resources abundant in such regions. However, many renewable energy technologies face intermittency issues because they rely on natural resources with diurnal and seasonal patterns for power generation. Thus, it is necessary to consider complementary energy storage systems. The pumped hydropower plant emerges as a viable option for hybrid systems seeking efficient energy storage solutions. The present study examines the planning of a pumped hydroelectric power station situated in the Quthing district, Lesotho, utilizing the resources of the Likhaebaneng River, and the solar radiation and wind resources available in the area. The research site is positioned at Latitude -30.352244 and Longitude 28.160639, while the river under consideration boasts an average flow rate of 0.3 cubic meters per second and a gross head of 301 meters. The pumps, powered by both solar and wind power, are employed to pump water from the lower reservoir to the upper reservoir via a succession of 14 cascaded reservoirs. The turbine utilized for this generation process is the 5 kW Turgo turbine. In the study area, the average scaled annual solar insolation and wind speeds are measured at 5.19 kWh/m²/day and 4.85 m/s at 30 m above ground level (a.g.l), respectively. The hybrid optimization model for electric renewables (HOMER) software was employed to model, simulate, and optimize the hybrid system consisting of solar, wind, and hydropower. The chosen optimized system in this study, featuring a maximum wind power output of 3,000 kW and a maximum PV power output of 4,568 kW, demonstrated a Net Present Cost (NPC) of $46.48 million and a levelized cost of energy (LCOE) of $0.2053 per kWh, which is equivalent to M3.80 per kWh. The system annually generates 8,074,658 kWh from solar resources, constituting 58.2% of the total production. Additionally, 5,797,867 kWh per year is generated from wind resources, accounting for 41.8% of the solar / wind system's total annual energy production of 13,872,525 kWh while 2,228,537 kWh is generated from PHES annually with the efficiency of 84.15 %. The consumption amounts to 8,764,589 kWh per year, resulting in an excess energy production of 28.9%.Item Open Access Design and economic analysis of a solar thermal pre-cooling system for agro-produce cold chain in Lesotho(National University of Lesotho, 2023) Yengane, Mpho Lucas; Mpholo, M; Mokeke, SThe agricultural sector in Lesotho faces considerable challenges related to post-harvest losses. When fresh vegetables are exposed to field temperatures of up to 35°C, even for a short period, it can lead to compromised cold storage quality, shortening their shelf-life by 20 hours. These post-harvest losses amount to an estimated 30-40% of the harvest, exacerbating poor economic performance and poverty. Solar thermal cooling, leveraging Lesotho’s abundant solar energy resources (4.5-6.5 kWh/m2/day), holds great potential for solar-powered refrigeration. This research aims to design a solar thermal cooling system tailored to the specific needs of preserving fresh agricultural produce. Also, a comprehensive economic analysis, encompassing TRNSYS and MATLAB evaluations, is conducted to assess the system’s financial viability. The TRNSYS simulation determines optimal values for the coefficient of performance, solar fraction, collector efficiency, exergy efficiency, and primary energy savings, while the MATLAB economic analysis scrutinizes various key economic metrics, including levelized cost of energy, net present value, savings to investment ratio, and discounted pay-back period, to thoroughly evaluate the system’s performance and economic feasibility. The outcomes reveal that even at the lowest considered coefficient of performance value (0.5), the solar thermal absorption cooling system demonstrates a more cost-effective levelized cost of energy when compared to the average electricity cost for refrigeration in Lesotho. The proposed solar thermal cooling system incorporates evacuated tube collectors and an auxiliary boiler to effectively manage a cooling load of 7.318 kW, ensuring the preservation of fresh vegetables at a temperature of 6.1°C. The optimized system design entails the selection of a chiller with a coefficient of performance value of 0.8, a collector area of 12 m², and a hot storage volume of 0.2 m³. This configuration maximizes solar energy utilization, resulting in higher solar fraction values and improved energy efficiency. Remarkably, this optimized configuration yields the best values for levelized cost of energy ($0.085/kWh), net present value ($9,200), discounted pay-back period (12 years), and savings to investment ratio (achieving 1 in year 13). These findings unequivocally highlight the financial feasibility and profitability of the solar thermal cooling system, positioning it as a highly promising investment option for addressing refrigeration needs in Lesotho.Item Open Access Design and analysis for a feasibility study of a floating solar PV power system for Metolong Dam(National University of Lesotho, 2022) Moqulo, Rorisang Christopher; Thamae, Leboli Zak; Hove, TawandaOver the past years, an increasing capacity of floating solar photovoltaic (FSPV) technology utilizing water bodies to install solar power has been implemented, showing an alternative for countries where land use is constrained, land is not easily accessible, or land leasing is expensive. In addition to reducing land use competition, FSPV is promoted as a more efficient solar technology, bringing with it additional benefits such as reduced water evaporation and decreased algae growth. Based on previous field studies and industry insights, this study aims to analyse whether an FSPV project can be a feasible and cost-effective option for electricity generation and usage at Metolong Dam and water treatment works (WTW) located in Maseru district, Lesotho. Furthermore, PV module temperature analysis is another critical area, governing the efficiency performance of solar cells. In this study, the initial approach entailed the modelling of the Metolong reservoir water temperature (using Microsoft Excel) due to insufficient water temperature data at a selected location (since simulation software does not have features for FSPV). Then water temperature was used to investigate the photovoltaic (PV) module temperature on water bodies. The optimal sizing and performance prediction of a proposed power plant was modelled using a set of mathematical equations in a spreadsheet application (Microsoft Excel) and PVSyst software. Both models were compared to analyse the difference in annual electricity generation. Then, an economic analysis was performed to showcase the Levelized Cost of Electricity (LCOE) and Net Present Value (NPV). Finally, an evaporation model was proposed with the objective to quantify the potential savings an FSPV could provide using the calculations adapted from the Penman-Monteith model. The results indicated that this FSPV power plant would significantly contribute to the reduction of carbon dioxide (CO2) emissions. The recommended FSPV, with total installed capacity of 7.8 MWp, would consist of 3 platforms with an installed power of 2.6 MWp each. The study reveals that the proposed FSPV energy generation system is about 3.4% higher than ground-mounted PV (GMPV) generation system predicted by the PVSyst software due to the cooling effect provided by water just below the panels. From the simulation results, the value of performance ratio (PR) comes out as 90%, and the capacity utilization factor (CUF) value is 15.21% with a total effective energy generation at the output of the array of 17,345 MWh per year. The system could meet up to 70% of load demand during a typical day in winter months at the selected facilities. The FSPV system could cost US$ 10 Million with a payback period of 13 years, where the largest contributors to this cost are related to the floating structures and anchoring system of this plant. The proposed FSPV plant will substantially reduce the cost of energy as the plant cost is expected to be considerably reduced based on the low LCOE of 36.4 $/MWh. The economic feasibility of a FSPV system on a Metolong reservoir was thus established, and may be considered an efficient use option for electricity generation in Lesotho. Additionally, the shading provided by the FSPV system can save up to 84,136 m3 of water annually. The annual reduction of greenhouse gas (GHG) emissions was analyzed and found to be 17,329 tCO2 per year. Future studies should include more in-depth research into factors such as the impact of substation upgrade costs, variable interest rates, economies and environmental impacts.Item Open Access Construction of a long-term hourly electricity demand curve and peak load using MAED-EL for Lesotho(National Manpower Development Secretariat, 2020) KenteAt the time that this study was undertaken, Lesotho Electrical Company (LEC) had no longterm hourly load curve forecast for electricity consumption. This makes it difficult for the utility to plan for future power plants and cost effective bilateral agreements as well as policy maker to make informed decision and for Independent Power Producers (IPPs) to be developed by investor. Therefore, this study aimed to construct a long-term hourly load curve for future electricity consumption in Lesotho starting with 2018 as the base year, followed by five-year long intervals from 2020 to 2040. The Model for Analysis of Energy Demand (MAED-EL) was used to calculate future hourly load curves for electricity and it uses the end-use approach when calculating the energy projections. Three scenarios were considered in this study to model possible trajectories of future electricity consumption, namely: Business-as-Usual (BAU), Low Economy Scenario (LE) and High Economy Scenario (HE). The annual growth rates of electricity consumption were estimated to be 4.3% for BAU, 2.4% for LE and 6.3% for HE. The projected peak demand for each scenario occurs during winter season (June to July). It was anticipated that the peak load will grow by 224% 123% and 54% for HE, BAU and LE scenarios from 2020 to 2040 while the energy consumption will increase by 223%, 122% and 53% for HE, BAU and LE from 2020 to 2040. The base load was predicted to grow from 58.77 MW,56.79 MW and 54.74 MW for HE,BAU and LE to 190.05 MW, 126.29 and 84.29 in for HE,BAU and LE respectevely in 2040 . Due to growth of electrical energy load the power deficit which was already high in 2018 at 94.44 MW would increase to 539.92 MW, 330.1 MW and 196.44 MW for HE, BAU and LE respectively in 2040. The Peak Load of the system was equal or above 75% of system peak load for 20% of the available time of the year.Item Open Access Cascading wind and solar pumping systems to recirculate water for pumped hydropower storage system at Letsa-La-Letsie dam(National University of Lesotho, 2024) Monyau, Marasi; Khaba, L; Makhele, MThis dissertation investigates the use of cascading wind and solar power pumping systems for recirculating water for pumped hydropower generation at Lets'a-la-Letsie in the Quthing district, Lesotho. The study's main goals are to identify optimal wind and solar resources for positioning wind turbines and solar panels; to design a solar/wind pumping system for recirculating water for pumped hydropower storage; and to design a hybrid system that considers the LCOE (least cost of energy) and system performance. The digital elevation, solar energy and wind energy potential maps, in conjunction with QGIS, were used to analyse the heads of the study regions, and TURBNPRO was used to estimate the power outputs and specifications of the selected Pelton turbine. The net head for Lets'a-la-Letsie was 157 metres. The design flow rate for Lets'a-la-Letsie was 0.06 m3/s. To provide water to the top reservoir, 19 similar pumps are required. Each pump has a power control of 37 kW (kilowatts). The top reservoir volume was calculated to be 2700 m3. This study uses the HOMER Pro simulation software to illustrate the performance of the Lets'a-LaLetsie hybrid renewable energy system. The system's total load includes the school load, clinic load, residential load, pumping load, and commercial load. The proposed hybrid system design consists of a 5379 kW solar PV array, a 1500 kW wind turbine, a 1985 kW converter, and a battery model for a pumped storage with a maximum capacity of 4331 Ampere hours (Ah). The optimal system has an LCOE of $0.417/kWh (Maluti 7.61/kWh) . The average solar irradiation and wind speed are determined to be 5.26 kWh/m2/day and 4.77 m/s, respectively. The project would require an initial capital commitment of about $27.9 million (509 million Maluti), with a total NPC (Net present Value) of $39.6 million (720 million Maluti). The findings show that Lets'a-La-Letsie has enough sun resources as well as the topography for the construction of pumped hydropower storage facilities. However, the country lacks a legislative and commercial framework to support the development of pumped-storage power facilities.Item Open Access Baselining Lesotho's disaggregated energy factors, ratios and intensities for household energy demand forecasting(National University of Lesotho, 2024) Sekatle, Mosa Patricia; Thamae, Leboli ZakAbstract The approach that is traditionally employed for household energy demand forecasting in many countries, including Lesotho, has primarily focused on two levels of aggregation which are to disaggregate data into rural and urban settlements. This study introduces an approach which is tailored specifically for Lesotho’s unique context. It adopts a methodology that utilizes Lesotho’s four agro-ecological zones, providing four levels of disaggregation which are the Lowlands, Foothills, Mountains and the Senqu River Valley. Additionally, it incorporates Lesotho’s ten administrative districts which are Botha-Bothe, Leribe, Berea, Maseru, Mafeteng, Mohale’s Hoek, Quthing, Qacha’s Nek, Mokhotlong and Thaba-Tseka. They offer 10 levels of disaggregation in household energy demand consumption patterns. The adopted approach allows a more comprehensive understanding of how the households energy consumption behavior varies across different zones and districts of the country. The approach provides valuable insights into zone or district specific energy needs and challenges; thus, it will enhance the accuracy of energy demand forecasting thereby informing more effective and targeted energy policies and interventions in Lesotho. The method used to baseline the disaggregated data is the exploratory data analysis (EDA) based on the Household Energy Consumption Survey (HECS) which was conducted in 2017. It uses both graphical and non-graphical techniques to uncover the data behavior, to spot anomalies and to check the trends through the visual and statistical summaries. The findings of the study, using absolute values, indicate that during summer months, energy intensities per household in zones demonstrate high average intensity on fuel wood (168.4 kg/HH) and animal waste (148.7 kg/HH), and the low average intensity on LPG (6.8 kg/HH), paraffin (21.4 Ltr/HH), and electricity (69.8 kWh/HH). However, during winter months, fuel wood (165.5 kg/HH) and animal waste (147.0 kg/HH) have high intensities, while paraffin (30.8 Ltr/HH), aloe (39.2 kg/HH) and crop waste (62.9 kg/HH) have the lowest intensities. In the districts during summer months, animal waste (155.6 kg/HH) and fuel wood (144.1kg/HH) have the highest average intensities, while LPG (15.5 kg/HH) and paraffin (38.6 Ltr/HH) have the lowest. In winter months, animal waste (157.2 kg/HH) and fuel wood (152.1 Ltr/HH) show high intensities, while aloe (31.1 kg/HH) and LPG (44.1 kg/HH) take the lower energy intensities. Per capita energy consumption in zones during summer months shows shrubs (75.2 kg/cap) and fuel wood (50.2 kg/cap) with high intensities, while LPG (11.1 kg/cap) and paraffin (10.2 Ltr/cap) have the lowest. In winter months, animal waste and fuel wood have the most intensities of 45.6 kg/cap and 50.2 kg/cap respectively. In the districts, animal waste and fuel wood have high intensities of 44.8 kg/cap and 41.9 kg/cap, with the lowest in LPG (4.6 kg/cap) and paraffin (11.9 Ltr/cap) in summer, while in winter, fuel wood (46.9 kg/cap) has the highest and aloe (10.5 kg/cap) has the lowest intensity on average. Lesotho’s energy consumption patterns in agro-ecological zones and administrative districts are mostly influenced by socio-economic and infrastructure gaps, which are apparent in the variation of energy consumption among districts and the reliance on traditional fuels is less urbanized areas. The Lowland zone and the Maseru district dominate most of the energy consumption statistics due to their large populations, better topography, proximity to infrastructure and stronger economic activities. The data delineates that while there is a growing shift towards modern energy sources, significant portion of the population still remain dependent on traditional fuels, particularly in remote areas. 1 This approach provides critical information for policymakers, enabling them to develop more accurate energy demand forecasts and design targeted interventions. The study’s results can guide strategic energy planning to address Lesotho’s specific energy needs, promoting energy access and efficiency while transitioning towards cleaner energy sources. The insights gained from this research lay the foundation for future studies to build more sophisticated, localized energy models that better reflect the dynamics of Lesotho.Item Open Access An optimization approach for the economic dispatch incorporating renewable energy resources into the LEC power sources portfolio(National University of Lesotho, 2022) Rateele, Thato Nchakha; Thamae, Leboli ZakElectricity demand in Lesotho has been constantly rising over the past years and has greatly surpassed the main domestic generation of 72 MW hydropower station in ‘Muela, which only supports a monthly average of 58% of the load and the deficit is imported from South Africa and Mozambique through fixed bilateral contracts. Although these contracts are regarded as uninterruptable as transmission paths are secured in advance, they come with heavy reliability premium costs endured by electricity utility, Lesotho Electricity Company (LEC). With the abundant renewable energy sources in Lesotho, Independent Power Producers (IPPs) could be invited to erect wind farms and solar photovoltaics (PV) plants to increase local energy security and diversify LEC power sources. Because electrical power networks must be secure, reliable, and cost-effective, the study developed a power dispatching approach that includes solar PV and wind generators to aid 'Muela meet demand and be backed by imports. According to the analysis, main grid imports are minimized by 22.3% with the introduction of 50 MW Ha-Ramarothole solar PV and by 40.2% with wind farms (24 MW Masitise and 34 MW Lets'eng) working with 'Muela. A 59.7% minimization is obtained by combining solar PV at 50 MW, wind farms at 58 MW, and 'Muela at 72 MW. Furthermore, the study used the Monte Carlo approach to simulate generation adequacy analysis in order to establish the monthly average expected demand not supplied (EDNS) and loss of load probability (LOLP). The EDNS never drops below 0 MW, while the LOLP only reaches a minimum of 52% for all scenarios evaluated, according to generation adequacy analysis of all local generators. Finally, the study assessed the influence of renewable energy absorption on LEC in terms of costs in procuring power locally and from imports using the South African Power Pool (SAPP) Markets: Day Ahead Market (DAM), Forward Physical Market (FPM) weekly and monthly. Since DAM yearly cost of energy is approximately half that of FPM weekly and monthly, it has been shown to be the most cost-effective market to procure under for renewables penetrations. Additionally, the cost of electricity anticipated to be incurred while purchasing from solar at 50 MW, ‘Muela, and DAM is around LSL 45 million less expensive than the fixed bilateral contracts. As a result, minimization of imports and their cost can be effectively accomplished with DAM because the total cost of energy (local prices plus DAM pricing) significantly reduces the potential expenses.Item Open Access Analysis of the categories of the sustainability dimensions to achieve sustainable mini-grids(National University of Lesotho, 2023) Maema, Tanki Alfred; Mpholo, MTaking into consideration the rise of mini-grids globally, their important contribution in reaching the universal access to energy goal, and the uneconomic costs of national grid extension to certain areas, it is only befitting that mini-grids are studied extensively. This study intends to find the variables of a sustainable mini-grid and what makes a mini-grid sustainable, analysed and identifies the sustainability of the different models of mini-grids and finally finds which mini-grid business model is sustainable and is better suited Lesotho in order to raise the countries electricity access and better the populations livelihoods. The study assesses the categories of four (the community-owned, private, Public-Private Partnership (PPP), and utility business models) sustainability dimensions of mini-grids across selected countries with similar conditions to Lesotho. It shows that for a mini-grid to survive throughout its lifetime it has to adequately satisfy the economic, environmental, institutional, social, and technical sustainability dimensions. The developer-consumer and the multi-tier frameworks developed by James Knuckle (2016) and the World Bank (2015) respectively were used in the assessment of the categories of sustainability dimensions for all four mini-grid business models. With the help of the frameworks, the study findings show that the PPP and private mini-grids proved to be the closest models to sustainability in all the assessed categories and dimensions failing in the cash recovery and affordability categories respectively. They are followed by community mini-grids which fall back on some categories ( cash recovery,tariff coverage of the operations and maintenance and tariff setting) for this reason are not sustainable. The PPP model has similar operations to utility mini-grids, as suggested by the frameworks, but has proven to be slightly better in a few categories. Utility minigrids are the furthest from sustainability of the studied mini-grids. They failed in the cash recovery category, failed to have tariffs covering their O&M cost, have low tariff settings and have limited power supplied to their customers. From the already existing research on mini-grid models in Lesotho, suggestions are provided for Lesotho and its upcoming mini-grids. The study shows that a combination of private and community mini-grids is found to be the best uptake provided there are subsidies to help people afford the cost-reflective tariffs.Item Open Access Analysis of the viability of using solar thermal energy for Maluti Mountain Brewery(National University of Lesotho, 2021) Lillane, Malillane; Hove, Tawanda; Mpholo, MIt has been established by literature that there is worldly movement towards renewable energy usage because of global warming. Solar energy among many is one form of renewable energy that can be used to reduce conventional energy usage. This study realized an opportunity to reduce the conventional energy (coal) use at Maluti Mountain Brewery (MMB); a brewery in Lesotho by preheating the boiler make up water. The boiler at MMB is serviced by condensate (70°C) and the cold water from the tap. The cold makeup water mixes with the condensate prior to the being carried into the boiler and thus reducing the efficiency of the boiler. This is because the boiler in turn demands a lot of coal to heat up the boiler feed water. A retrofitted solar thermal system into the existing system at MMB was done. This system was aimed at preheating the cold make up water before it mixes with the hot condensate in order to avoid the makeup water from reducing the condensate temperature. An Excel based model was made in order to design a solar thermal system that is cost effective and technically viable. The designed system is an active solar thermal system composed of evacuated tube collector with the EPD of 18 kWh/$), collector area of 80 m2 which was decided upon by the required maximum storage tank temperature of 100 °C. The storage tank size of the system was found to be 2110 Liters. A tank of such size could not be found on the market; therefore, a 2500 Liters storage tank would be ideal for the purpose. The actual collector area decided upon according to the collector aperture area of 2.998 was found to be 81 m2. The system was found to be able to preheat 54% of the makeup water (12 % of the boiler feed water is the makeup water). The amount of coal used by MMB would be reduced by 11% and therefore saving the company as the NPVSS is positive, amounting to $25044 for over 20 years.Item Open Access Analysis of Quthing River and Letseng-la-Letsie for hydropower potential(National University of Lesotho, 2020) Lekhanya, Liteboho; Khaba, L; Makhele, MThis dissertation presents the analysis of Quthing River and Letseng-la-Letsie for hydropower potential in Quthing district in Lesotho. Electrical power deficit in the country is more prominent in rural areas like Quthing District. This calls for assessment of electrical sources in the vicinity of rural area load centers to inform policies for electrical production so as to curb power deficit problem. Mountain Rivers like Quthing River with steep slopes or gradients naturally provide good head which needs to be assessed along with its flow rates. Furthermore elevated dams like Letseng-la-Letsie can also provide a natural good head which needs to be assessed alongside with its discharge rates. The assessment was carried out by employing catchment area method to asses flow rates since the abstraction points of the study areas were ungaged and lacks data. The maps in association with QGIS were used to evaluate heads of the study areas and lastly TURBNPRO was used to determine power outputs from the study areas. The resultant net head for Quthing River was found to be 164.15 m while the net head for Letsengla-Letsie was 159.23 m. The design flow rate of Quthing River was found to be 0.58 m3/s while that of Letseng-la-Letsie was 0.116 m3/s. The results from TURBNPRO showed that the power output for Quthing River turbine was 815 kW while the power output for Letseng-la-Letsie turbine was 221 kW. Using typical hydro-electric generators efficiency of 99% and typical capacity factor for Africa of 0.49, the capacity from Quthing River was found to be 807 kW with annual energy of 3.46 MWh. The capacity for Letseng-la-Letsie was found to be 0.22 MW with annual energy of 0.95 MWh.Item Open Access Adaptive, robust, and fault-tolerant control strategies for grid-connected renewable energy systems(National University of Lesotho, 2024) Nkhabu, Tsitso; Makhele, Molefe; Mokeke, SebotaLesotho is currently facing a power generation-demand imbalance. The 2023/24 annual report by the Lesotho Electricity and Water Authority highlights a peak demand of 222.12 MW, which is nearly three times the country’s installed generation capacity of 74.7 MW. Consequently, the nation relies on costly power imports from Mozambique and South Africa to cover the shortfall. To address this issue, Lesotho plans to integrate renewable energy sources, specifically wind and solar, into its national grid. However, integrating these low-inertia and intermittent renewable power sources introduces grid stability challenges, as they are vulnerable to disturbances like load changes or grid faults. This research focused on designing control strategies capable of not only adjusting system voltage to accommodate uncertainties from power system dynamics, internal changes, and external disturbances but also stabilizing the system under small disturbances. The analysis was conducted on a grid-connected 38 MW wind power plant, using five control strategies: Constant Voltage (Const. V), Constant Reactive Power (Const. Q), Constant Power Factor (Const. cosɸ), Voltage Droop based on Reactive Power (voltage Q-droop), and voltage droop based on reactive power in the q-axis (voltage Iq-droop). These strategies were evaluated for their adaptability, robustness, and fault tolerance under two operational scenarios: variations in wind speed and fluctuations in the Point of Connection (POC) bus voltage. With a three-phase short circuit created and cleared on the high voltage (HV) bus bar, all control strategies are within a 5 % voltage deviation upon service restoration and fault clearance within a period of 0.015 seconds. A Supervisory Control and Data Acquisition (SCADA) system was designed for the monitoring and control of the wind power plant. Determined from the closeness of the HV bus voltage to the POC voltage, the most adaptive control strategy is used for each operation scenario, taking into account the wind speed as well as the POC voltage. It was observed that the evaluation by the SCADA system is consistent with the result obtained from the DIgSILENT PowerFactory software. For further exploration, research is recommended for the implementation of Artificial Neural Networks (ANNs) in machine learning to accommodate any wind speed and POC voltage levels for the control strategies under investigation.Item Open Access A chemical process design for green hydrogen production through water electrolysis in Lesotho(National University of Lesotho, 2024) Ramaisa, Tsepiso Angelina; Thamae, TimothyThis research addresses the pressing need for process design models that are specifically adapted to Lesotho's distinct resource profile, particularly its vast hydroelectric capacity. At present, there is a noticeable gap in process models designed for green hydrogen production that take into account the unique energy conditions of Lesotho. To address this shortcoming, the study presents a detailed chemical process design for hydrogen production through water electrolysis, utilizing Lesotho’s renewable energy. The process model developed includes detailed mass balances to ensure precise quantification of material flows. Critical process parameters, including molar and mass fractions as well as stream molar flow rates, are defined to accurately describe the system, providing a solution that is specifically optimized for Lesotho's energy resources. The key unit operations, including separators, mixers and an electrolyser, are carefully modelled. Separators are used for phase separation and component purification, while mixers are designed to efficiently combine process streams. The electrolyser, central to the process, is modelled according to the electrochemical reactions which take place and mass transfer considerations. To ensure accurate phase equilibrium calculations, the Rachford-Rice equations are applied. Additional equations are formulated to characterise equipment performance and to address system constraints, such as product purity requirements. The developed model serves as a tool for enhancing hydrogen production and assessing overall process efficiency. It offers a framework for examining how different operating conditions and design parameters affect system performance. Future research should focus on incorporating renewable energy sources like wind and solar to diversify and enhance the sustainability of hydrogen production in Lesotho. Performing comprehensive energy balances will offer deeper insights into the system's efficiency and potential for optimization. Moreover, including economic and environmental assessments will provide a more thorough evaluation of the commercial feasibility of green hydrogen production in the country. These suggestions not only address current gaps but also lay the groundwork for developing a more integrated and scalable model for green hydrogen production, which could be applied to other regions with similar renewable energy resources, supporting both regional and global efforts towards sustainable energy transitions.Item Open Access ACE One cookstove(National University of Lesotho, 2021) Qoola, Thato; Thamae, Timothy; Berg, DominikThe study was conducted to evaluate the performance of ACE One cook stove which is manufactured by African Clean Energy (ACE) in Lesotho by assessing the performance of different solid biomass fuels within the stove. Pellets, pine wood, corn cobs and cow dung provided by ACE were used in this study where cooking time, energy consumption, heat transfer, combustion temperature and particulate matter emissions were assessed. The heating values were determined using Proximate Analysis, the values ranged from 13.43 MJ/kg for cow dung to 17.65 MJ/kg for corn cobs. Measurement of air pollutants were performed using mobile air quality monitor and combustion temperature measurements were performed using infrared thermometer. The temperature was measured for each fuel and the highest temperature was found when using wood, about 460 °C, followed by corn cobs with 370 °C, pellets with 340 °C and cow dung with 290 °C. However, the pellets had the most sustained heat compared to other fuels. Using wood and corn cobs transferred heat faster due to their big flame and raised the temperature of the water quickly. When using wood, water in a pot gained 610 kJ in 9 minutes, with corn cobs, pellets and cow dung, energy gained was 410 kJ, 350 kJ and 240 kJ respectively. Water Boiling Tests (WTB) results showed that the use of cow dung required much more fuel and an extended cooking time compared to other fuels. The second WBT using a different mass to test refuelling showed that refuelling slowed the cooking process. When burning the fuels in a closed room, the PM2.5 emissions for all the fuels were above 425 µg/m3, which was considered as hazardous level. Cow dung emitted more particles than other fuels during combustion which lasted longer in a room. The pellets showed the lowest emissions of them all in both open and closed room. In a closed room, the highest value for the pellets was 800 µg/m3 while other fuels had reached 999.9 µg/m3. The values obtained when burning the fuels in an open room had shown a significant decrease in emissions, 60.3 µg/m3 for pellets, 144.7 µg/m3 for wood, 234.2 µg/m3 for corn cobs and 612.4 µg/m3. The study further assessed the performance of the charging system that comes along with the stove. The power dissipated by the solar panel in this study was less than its rated power. The highest value from 4 experiments done one different days was 8.57 W. Time taken to charge the stove with a wall charger was shorter than using a solar panel. Using the battery of the stove to charge a cell phone has shown high power usage but using it for powering LED lamp has shown to be discharging the battery at a very slow rate.Item Open Access Analytical solutions to the arithmetic asian options pricing model using lie symmetry methods(National University of Lesotho, 2025-07) Kubeletsane, Monts’uoe Edward; Nchejane, Ngaka JohnThis dissertation explores the use of Lie symmetry methods to find analytical solutions for arithmetic Asian options; path-dependent financial derivatives widely used for risk management in commodity markets. The pricing problem is formulated as a partial differential equation (PDE) involving the asset price, time, and the running average of the asset price. Lie symmetry analysis is applied to the PDE to compute its infinitesimal generators, determine an optimal system of one-dimensional sub-algebras, and perform symmetry reductions. Each reduced PDE obtained through this process also admits further symmetries, allowing for successive reductions and the construction of exact invariant solutions. Techniques such as Riccati reductions and the Frobenius method are employed to solve the resulting ordinary differential equations (ODEs). The study further examines the influence of key financial parameters (volatility, interest rate, and time to maturity) on the structure and behavior of the pricing solutions. The findings contribute to the theoretical understanding of Asian option pricing and provide analytical benchmarks for validating numerical approaches.Item Open Access Symmetry analysis of the parabolic system for european option pricing with liquidity shocks(National University of Lesotho, 2025) Moreboli, Bonang; Nchejane, Ngaka John; Poka, Wetsi DavidWe address the knowledge gap between financial theory and practice by developing a framework to analyse European option pricing under liquidity shocks, which reduce market completeness and challenge traditional models like Black–Scholes. To tackle this, we undertake a Lie symmetry analysis of a coupled system designed to model European options subject to liquidity shocks. The system consists of a degenerate parabolic equation and another is a first-order nonlinear ordinary differential equation (ODE) in time with no spatial derivatives. Our analysis has uncovered the parabolic system’s Lie symmetry group and infinitesimal generators. We have then proceeded to investigate the system dynamics by constructing commutative tables that illustrate the relationships between the vector fields under study and the one-dimensional optimal system of symmetry subalgebras associated with the initial equation. Employing similarity reductions, we have applied the Lie symmetry methodology to decompose the system into several nonlinear ordinary differential equations (ODEs) corresponding to each symmetry subalgebra. Finally, we present obtained invariant solutions through simulations as 2D and 3D graphs.Item Open Access Solving the barrier options model with linear time-dependent volatility numerically(National University of Lesotho, 2025-07) Phate, Seeiso; Nchejane, Ngaka JohnThe main purp ose of this work is to approximate the solution of the barrier option pricing model whose evolution is described in terms of partial differential equation called Black-Scholes model. In this model, we consider volatility as a linear function of time. This is done primarily using a numerical approximation technique by the name of finite difference method. We consider Crank Nicolson scheme and forward difference scheme in time derivative to discretize the model and represent it as a tridiagonal matrix. Furthermore, we analyse the stability of the discretized model using Von Neumann stability analysis. We finally find the numerical solution to find key insights and the implications.Item Open Access Solving the barrier options model with linear time-dependent volatility by symmetry analysis(National University of Lesotho, 2025-07) Kometsi, Relebohile Veronecca; Nchejane, Ngaka JohnThis project aims to solve the barrier options model with linear time-dependent volatility, described as a Partial Differential Equation (PDE) using symmetry analysis. The only PDE to be considered will be the Black-Scholes model. Firstly, we use Lie symmetry to find symmetries of our model from our determining equations. Once the symmetries are found, they will b e picked at random to form characteristic equations needed to find invariant solutions. Lastly, the solutions will b e interpreted and graphed.Item Open Access Lie Symmetry analysis of partial differetial equations associated with the Westervelt Model in non-linear acoustics(National University of Lesotho, 2024-06-27) Sekhesa, Theko MartinSound-wave propagation in compressible media has significant non-linearities. It is for this reason, that modelling such phenomena necessitates a partial differential equation that considers these non-linear effects. That is where the Westervelt model comes into action, it is a non-linear partial differential equation used to model the propagation of high finite amplitude sound waves in non-linear acoustics, i.e., sonar systems, medical ultrasound imaging and non-destructive testing. The propagation of such waves takes place in non-linear media that exhibit thermal and viscous characteristics, e.g. human tissue. Two equations that represent the Westervelt model are considered in this work, the first one is the usual equation that has the dissipative term as the third-order temporal derivative. The second equation is where the linear wave relation has been inserted for the dissipative term. Symmetry analysis is performed on each of the models individually. This involves generating an over-determined system of linear homogeneous partial differential equations, which is solved to get the Lie point symmetries. Then, with the aid of the adjoint and commutator tables, an optimal system of sub-algebras is found and used in the similarity reductions to get the invari- ant sub-models. One-parameter Lie point groups are constructed, followed by exact invariant solutions for the sub-models, with the modified simple equation method applied to find some solitary wave solutions. Lastly, simulations in terms of 2D and 3D graphs representing the in- variant solutions are presented.