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Item 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.Item Error analysis for finite difference schemes(National University of Lesotho, 2024-07-23) Kotoane, BokangNumerical methods are widely used in modern computations to approximate solutions to dif- ferential equations. There are many types of numerical methods that can be considered, but in this project, finite difference methods are considered. The underlying concept required for development of numerical schemes is taken into consideration. Numerical schemes are devel- oped and error analysis is always carried out for each scheme and solutions are developed using those schemes. in finding numerical solutions θ = 0, θ = 1, and θ = 1 2 are considered and they represent different schemes. It is found that the Crank-Nicholson scheme is the best performing finite difference scheme.Item Using a field trip to investigate the development of biology students'knowledge on local wetland ecosystem birds(National University of Lesotho, 2024-07-24) Tenane, MakabeloThis study investigated the development of Grade 11 biology students’ knowledge of wetland birds with the use of a field trip. The three research questions guiding the study were: “What is the conception of Grade 11 biology students’ knowledge on birds found in Pitseng wetland ecosystem?”; “How does Grade 11 students’ knowledge of birds in Pitseng wetland develop with the use of field trip approach overtime?” and “What is the difference between the conception of male and female students on wetland birds if any?” The research involved 34 participants, and the research instruments for generating data were observation and open-ended questionnaire and a students’ field worksheet. The students’ knowledge was assessed within the ecological literacy framework. The analysis of data was both qualitative and quantitative descriptive. The findings revealed that students’ knowledge on wetland birds increased with the use of field trip overtime. The study concludes that field trip is an effective strategy for studying birds in the local ecosystem, and for developing students’ ecological literacy. It is recommended that the method should be used widely in the teaching of biology and that further research should explore its use in the study of birds, with focus on students’ ecological conceptions in schools located in different regions of the country, and the data be analysed in terms of other demographic variables, such as age and home background.Item Application of Lie Symmetry method in pricing Arithmetic Asian options(National University of Lesotho, 2024-06-23) Kubeletsane, Monts'uoe EdwardThis research investigates the application of Lie symmetry method to find analytic solutions for arithmetic Asian options, which are crucial financial derivatives for managing risk in various commodity markets. By employing a two state partial differential equation approach, the study uses Lie symmetry method to enhance option pricing models. The research involves finding determining equations, infinitesimal generators, and invariant solutions, as well as examining the influence of parameters such as volatility, interest rates, and time on option prices.Item The development of highly selective modified glassy carbon electrode on acted carbon-iron oxide/graphene foam for electrocatalytic oxidation of uric acid and dopamine(National University of Lesotho, 2023) Mpakanyane, TebohoThis research study explores the application of nanomaterial-modified glassy carbon electrodes (GCE) for the voltammetric determination of dopamine and uric acid. The GCE was fabricated with iron oxide, activated carbon, and graphene foam. Energy Dispersive X-ray Spectroscopy (EDS), Fourier Transform Infrared spectroscopy (FT-IR), X-ray diffraction Spectroscopy (XRD), and Scanning Electron Microscopy (SEM) were used to examine the microporous activated carbon, iron oxide spherical structure (Fe3O4) particles that were attached to the graphene foam sheets. A drop-dry method was used for electrode modification. AC-Fe3O4/GF/GCE was electrochemically interrogated in the ferrocyanide redox probe using cyclic voltammetry. The current intensity and the reversibility of the redox probe were enhanced in the presence of the electrochemical sensor. Differential pulse voltammetry technique (DPV) was employed for individual determination of uric acid under the optimized experimental conditions; pH 6, scan rate 50 mV s -1 , pulse width 0.05 s, pulse amplitude 0.05 V, and supporting electrolyte 0.1 M phosphate buffer solution. A detection limit of 2.55 µM was obtained with an analytical linear range of 5 - 1630 µM. All selected foreign species showed no significant interference with the electrochemical determination of uric acid. Furthermore, dopamine analysis was carried out on AC-Fe3O4/GF/GCE using DPV. The electrochemical sensing was also optimized at various analytical conditions and a detection limit of 1.47 µM was obtained in the linear dynamic range of 2.5 to 450 µM. Glucose, glutamic acid, l lysine, and ascorbic acid are a few of the interfering species that exhibited almost no impact on dopamine detection. In addition, the simultaneous determination of uric acid and dopamine was conducted successfully. They have been determined by differential pulse voltammetry, and the modified electrode exhibited a linearity relationship over a wide range of uric acid concentrations from 2.5 to 450 μM, with a detection limit of 1.75 μM, (s/n = 3). A linear trend for the current response for dopamine concentrations ranging from 5 to 400 μM, with a detection limit of 2.7 μM, has also been obtained. The results, therefore, demonstrated the sensor’s superior electrocatalytic activity and its high selectivity for dopamine and uric acid even when some foreign species were present. The average V recoveries from the real sample analyses of the urine samples showed that the proposed sensor could be put to use in the real sample analysis. The developed electrode was generally found to be highly selective and sensitive toward uric acid and dopamine. It has achieved better sensing performances with a very low detection limit, wider linear ranges, and short analysis times as compared to most previously reported modified electrodes for the same analytes. Furthermore, the developed electrode was validated successfully for real sample analysis in biological fluids. The proposed methods have many attractive features, such as low cost, simplistic electrode preparation procedure, easy renewability, long-term usability, and rapid analysis. The developed electrode also displayed good repeatability and selectivity towards interfering substances. It is a promising modified electrode for the electrochemical detection of other electroactive important compounds in biological systems.Item Nonlinear acoustics in medical ultrasound(National University of Lesotho, 2023-06) Sekhesa, ThekoIn this work, an approximate solution for the 1-Dimensional Westervelt equation is found. This is done primarily using a numerical approximation method called Finite Di erence Method. The rst part of this work is to approximate the solution in regions of the domain where the nonlinearities are negligible. The second part of this work is to approximate a solution in regions of the domain where the nonlinearities are non-negligibleItem Rehabilitation of Katse dam mini-hydropower plant(National University of Lesotho, 2022-04) Thamae, Ntoampe WThe Katse Dam Mini-Hydropower station was designed to generate and supply electricity to auxiliary systems without connecting to the grid. This would increase the dam power supply and reliability thereby reducing the electricity bill incurred on the Lesotho Highland Water Project (LHWP) for operations. However, to date, the Mini-Hydropower station is not fully operational. In this study, the decommissioned Katse Dam Mini-Hydropower plant’s rehabilitation is evaluated. Three significant activities characterized this rehabilitation process. The upgrading of electro-mechanical equipment or damaged parts, using condition assessment filters. Uprating is explored by flow duration plots for the possibility of increasing plant capacity. Lastly, the capacity dispatch (Integration) is studied intensively with computer software package (DigSilent Power Factory), for grid integration alternatives. In general, electrical equipment is the plant's most vulnerable to fatigue. Mechanical equipment is moderately damaged, with governor and guide bearing systems standing out. Assessment of the potential of the plant’s capacity increase revealed that the reservoir compensation flow regime resulted in minimum design values of head and discharge being fulfilled 96% of the time. The Katse Dam load capacity is met 90% of the time, while the maximum single machine power is exceeded 84% of the time. The Mini-Hydropower stable response to dam load growth and decline without a grid was shown in the grid integration option. However, there was a substantial deviation to a sudden loss of grid without load shedding, and the local bus voltage dropped below 6% tolerance. The findings of this investigation demonstrated the need for this plant to be rehabilitated. All the necessary tests on relevant components point to the goals of the plant and the necessity for restoration. According to the economic study, implementing this project will result in a 9- year return on investment and a 2.02 MWh annual energy guarantee, which is 54% of the yearly energy consumption of the auxiliary systemsItem Estimating hydropower generation potential of the Metolong dam(National University of Lesotho, 2022-10) Moerane, Mokhothu EmmanuelMetolong dam is located 30 km east of Maseru town, with the dam retaining wall built inside the Phuthiatsana River. The purpose of the dam is to supply portable water to Maseru, Roma Mazenod, Morija and Teyateyaneng. The Instream Flow Requirement (IFR) given post Metolong dam construction and meant to sustain life downstream of the dam was used to estimate how much hydropower can be generated from IFR. Even though the study is aimed at assessing the hydropower generation potential of the dam, it did not address the sedimentation rate occurring inside the dam per year and how much storage capacity is lost due to sedimentation. Microsoft excel spreadsheet is used to estimate how much electricity can be generated from IFR and to examine how the water temperature affects the electricity projections. The results show that the dam has the capacity to produce 65kW from In-stream flow requirement (IFR) in April, as a month with the highest IFR and 7 kW in September, as a month with the lowest IFR. These power production figures are studied together with the water temperature in three scenarios to observe the effects of water temperature on power production. The outcome is that they seem to have no significant effect. The power production is based on when a Radial flow PAT (Pump As Turbine) of 0.6 efficiency and generator of 0.955 efficiency are attached at IFR release point. The dam head ranges between 23 m – 44 m for IFR, with water releases of 0.01 m3/s – 0.3 m3/s. This power can be used for distributed generation or net metering by the Water and Sewage Company (WASCO). The financing of the project is not expected to exceed $50 000 given the condition of the already installed penstock at the recovery period of less than 4 years factoring in fluctuations of power brought by those of IFR for environmental purposes downstream of Metolong dam.Item Determining cost-effective integration renewable energy resource plan for Lesotho (2022-2040)(National University of Lesotho, 2022-07) Nzemene, Tsoarelo NelsonThe renewable energy potential for Lesotho has been sufficiently studied with only a limitation of which specific places could such energy be derived. The country does not have an integrated renewable energy plan (IRP) to help direct its efforts to address the problem of energy insecurity, low energy supply and over 50 percent dependence on electricity imports from South Africa and Mozambique. Most of the resources have been spent haphazardly and unprofitably in a bid to address access to energy problem. The objective of this study is to create an IRP that responds to cost effectiveness in Lesotho for 2022 to 2040 and to identify suitable places for renewable energy generation using Geographic Information System (QGIS) capabilities in order to increase the baseload capacity for Lesotho. These objectives were achieved by evaluating the existing renewable energy resources, especially solar and wind by determining suitable places for power generation to meet the ever-growing demand. This was achieved by first establishing the aggregated forecast electricity demand using the existing studies and this forecast formed the basis for envisaged future power demand for Lesotho. For example, the electricity demand is projected to reach 350MW in 2040. Secondly, proximity analysis results of the resource base to the grid, primary road infrastructure and substations at 3.5km and 15km buffer zones were done to determine suitable areas for renewable energy generation. The identified places were examined and the amount of energy that could be generated from them was estimated and evaluated. The findings showed that a total of 310MW added into the main grid cumulatively from both wind and solar resources from 2022 to 2040 would result in electricity supply independence for the country. The cheapest option in a generation was given first priority in terms of when to enter into the generation stream to meet the existing demand during scheduling in the determination of the optimum IRP. The study recommends a progressive reduction of imports since they can serve as safety buffers of the electricity network in the event hydropower is not sufficiently developed. The energy policy, renewable energy policy and other energy supply and demand instruments will be profited by this study.Item Design and analysis for a feasibility study of a floating solar PV power system for Metolong Dam(National University of Lesotho, 2022-06) Moqulo, Rorisang ChristopherOver 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 impactsItem An otimization approach for the economic dispatch incorporating renewable energy resources into the LEC power sources portfolio(National University of Lesotho, 2022-06) Rateele, Thato NchakhaElectricity 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 allscenarios 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 The development of highly selective modifies glassy carbon electrode on activated carbon-iron oxide/graphene foam for electrocatalytic oxidation of uric acid and dopamine(National University of Lesotho, 2023) Mpakanyane, LitebohoThis research study explores the application of nanomaterial-modified glassy carbon electrodes (GCE) for the voltammetric determination of dopamine and uric acid. The GCE was fabricated with iron oxide, activated carbon, and graphene foam. Energy Dispersive X-ray Spectroscopy (EDS), Fourier Transform Infrared spectroscopy (FT-IR), X-ray diffraction Spectroscopy (XRD), and Scanning Electron Microscopy (SEM) were used to examine the microporous activated carbon, iron oxide spherical structure (Fe3O4) particles that were attached to the graphene foam sheets. A drop-dry method was used for electrode modification. AC-Fe3O4/GF/GCE was electrochemically interrogated in the ferrocyanide redox probe using cyclic voltammetry. The current intensity and the reversibility of the redox probe were enhanced in the presence of the electrochemical sensor. Differential pulse voltammetry technique (DPV) was employed for individual determination of uric acid under the optimized experimental conditions; pH 6, scan rate 50 mV s-1, pulse width 0.05 s, pulse amplitude 0.05 V, and supporting electrolyte 0.1 M phosphate buffer solution. A detection limit of 2.55 µM was obtained with an analytical linear range of 5 - 1630 µM. All selected foreign species showed no significant interference with the electrochemical determination of uric acid. Furthermore, dopamine analysis was carried out on AC-Fe3O4/GF/GCE using DPV. The electrochemical sensing was also optimized at various analytical conditions and a detection limit of 1.47 µM was obtained in the linear dynamic range of 2.5 to 450 µM. Glucose, glutamic acid, l-lysine, and ascorbic acid are a few of the interfering species that exhibited almost no impact on dopamine detection. In addition, the simultaneous determination of uric acid and dopamine was conducted successfully. They have been determined by differential pulse voltammetry, and the modified electrode exhibited a linearity relationship over a wide range of uric acid concentrations from 2.5 to 450 μM, with a detection limit of 1.75 μM, (s/n = 3). A linear trend for the current response for dopamine concentrations ranging from 5 to 400 μM, with a detection limit of 2.7 μM, has also been obtained. The results, therefore, demonstrated the sensor’s superior electrocatalytic activity and its high selectivity for dopamine and uric acid even when some foreign species were present. The average recoveries from the real sample analyses of the urine samples showed that the proposed sensor could be put to use in the real sample analysis. The developed electrode was generally found to be highly selective and sensitive toward uric acid and dopamine. It has achieved better sensing performances with a very low detection limit, wider linear ranges, and short analysis times as compared to most previously reported modified electrodes for the same analytes. Furthermore, the developed electrode was validated successfully for real sample analysis in biological fluids. The proposed methods have many attractive features, such as low cost, simplistic electrode preparation procedure, easy renewability, long-term usability, and rapid analysis. The developed electrode also displayed good repeatability and selectivity towards interfering substances. It is a promising modified electrode for the electrochemical detection of other electroactive important compounds in biological systems.Item Disrupting tumor vasculature with oncolytic viruses(National University of Lesotho, 2022-03) Motlomelo, Phallang AlbertCancer is a disease caused by accumulation of phenotype-altering genetic mutations in somatic cells, which results in abnormal growth of a ected cells. Among many cancer therapies that are currently under clinical investigation, virotherapy, which uses viruses called oncolytic viruses (OVs) that specif- ically replicate in cancerous cells while sparing normal cells, has recently become one of the promising therapeutic approaches that aim to destroy cancer cells. The aim of this study is to understand the dynamics of disrupting tumor vasculature and tumor endothelium with OVs. The model is developed based on the modeling techniques that lead to a system of ordinary di erential equations (ODEs). Qualitative analysis, non-dimensionalization and stability of ODEs are performed. We also derive the steady states of the model and investigate their stability. Interestingly, our results show that there are two stable points and one non-stable point from which we found that the treatment is successful if the viral clearance rate is larger than the lysis rate. The simulations further show that oncolytic virotherapy is successful when both burst size and lysis rate are large, and fails whenever both are small.Item Mathematical modelling of natural killer (NK) cells recruitment in oncolytic virotheraphy(National University of Lesotho, 2020-12) Senekal, Noma SusanNatural killer (NK) cells are known to constitute a major part of innate immunity against tumors and viral infections. Upon successfull viral entry into the tumor microenvironment (TME) or tumor, NK cells may however prematurely kill infected tumor cells and oncolytic viruses (OV), which then results in reduced overall e cacy of oncolytic virotherapy. In this thesis, we examine the e ects of NK cell recruitment within the TME during tumor treatment with OV. To achieve this, we devised and analyzed a simple mathematical model that describes the dynamic interactions of the tumor cells, OV and NK cells based on currently available preclinical and clinical literature. In particular, a central goal of this work is to investigate and characterize therapeutic conditions under which the synergistic balance between OV-induced NK responses and required viral cytopathicity may or may not result in a successful treatment. Interestingly, we found that NK cell recruitment to the TME must take place neither too early nor too late in the course of OV infection so that treatment will be successful. Notably, we also found that NK cell responses are most in uential at either early (partly because of rapid response of NK cells to viral infections or antigens) or later (partly because of antitumoral ability of NK cells) stages of oncolytic virotherapy. The model further predicts that: (a) an NK cell response augments oncolytic virotherapy only if viral cytopathicity is weak; (b) the recruitment of NK cells modulates tumor growth; and (c) the depletion of activated NK cells within the TME enhances the probability of tumor escape in oncolytic virotherapy. Taken together, our ndings demonstrate that OV infection is crucial, not just to cytoreduce tumor burden, but also to induce potent NK cell response necessary to achieve complete or at least partial tumor remission. Furthermore, our modeling framework supports combination therapies involving NK cells and OV which are currently used in oncolytic immunovirotherapy to treat several cancer types.Item Techno-economic analysis and policy design for PV electricity net-metering systems in Lesotho(National University of Lesotho, 2021-04) Moleko, Lebohang AlbertLesotho imported 65% of its electricity from Electricidade de Moçambique (EDM) and Electricity Supply Commission (ESKOM) in 2019/2020 (Lesotho Electricity Company (LEC), 2020). This is higher as compared to 59% in 2018/2019 ( Lesotho Electricity and Water Authority (LEWA), 2019). This shows that there is an increasing demand, but stagnant generation capacity hence the ne e d for the security for the supply of electricity in Lesotho. Studies have shown that the interconnection of Solar Photovoltaic (PV) systems to the grid can reduce electricity imports amongst others. The objective of my study is to design optimum grid-connected solar PV systems for residential, commercial, industrial and institutional purposes; predict the system field performance and d o a cost-benefit analysis on net metering. Optimal PV system is designed using the Typical Meteorological Year data closest to Maseru. PV power and inverter power outputs are calculated for each hour of the given typical year. The different load profiles from the utility are also used. Net metering policy options guidelines are designed such that PV electricity is sold to the grid at the utility retail price with no PV capacity cap for net metered systems. The benefits from net metered PV systems are calculated. These are from surplus sales, avoided energy savings and peak shaving in the billing period of 12 months. The results show that with the current electricity tariffs, the PV system that gives the net electricity payments of zero at the end of the billing period for commercial and industrial customers results in negative NPV values which indicate that the system is not acceptable. On the contrary, the net-metered residential PV system offers the profitability index of 2.7643 at the discount rate of three percent (3%) which is very attractive for investment on the customer‟s perspective. The internal rate of return of the project is thirteen percent (13%). Based on these results, it is concluded that with the current tariff settings for residential customers, only the residential PV net metering is technically and economically viable. As for the commercial and industrial activities, PV net metering is technologically viable but not economically viable. The changes in some variables such as dropping of solar PV systems‟ capital and the increase in energy charges to $0.0423 and $0.039 for commercial and industrial customers respectively, can make the systems acceptable. The reasonable Net Present Value (NPV) values are likely to increase the adoption rate of electricity net metering. H o w e v e r , to attract more investment into the net-metering system, the interest rate of the investment should always be greater than the inflation rate. The larger 12 the range between the two, the more attractive the investment can be.Item Modelling and optimization of micro grids for rural areas in Lesotho(National University of Lesotho, 2021-05) Fonya, Thabo SamuelThe study analysed different types of hybrid micro grids system configurations and found out the following to be both technically and economically viable: (a) PV with Levelised Cost of Electricity (LCOE) of R4.64/kWh, (b) PV/Wind of R5.03/kWh, (c) PV/Wind/Generator at R5.16 /kWh and lastly (d) PV/Generator of R4.80/kWh. These viable system configurations have more than 93.1 % renewables. All four technically and economically viable system configurations were found to be more sensitive to either price of diesel or inflation rate. As diesel price increased from R13.00/litre to R15.00/litre, LCOE increased from R5.15/kWh to R5.24/kWh. As inflation rate changed from 5.00 % to 6.50%, LCOE decreased from R4.64/kWh to R4.42/kWh. The most suitable system configuration has been found to both technically and economically viable is solar/generator with LCOE of R4.80/kWh and lower carbon emissions of 4843 kg/yr greenhouse gas emissions. For this solar/generator, NPV is R940 994.00, IRR is 18%, while ROI is 15.5% and payback period is 5.81 years. Any hybrid micro grid system that had hydro component in its system configuration was found to be not viable due to the high capital cost which contributed to high LCOE. The high cost of the system configuration that included the hydro component had been brought about by the high cost of civil works for erecting diversion weir for the micro grid power station.Item Application of lie symmetrics to solving fractional black-scholes option pricing model in financial mathematics(National University of Lesotho, 2022-10-21) Ramoeletsi, Realeboha; Kaibe, Bosiu, Ngaka NchejaneWe perform Lie symmetry analysis to the fractional Black-Scholes option pricing model whose price evolution is described in terms of a partial di erential equation (PDE). As a result, new complete Lie symmetry group and in nitesimal generators of the one-dimensional fractional Black-Scholes pricing model are derived. Furthermore, we compute a family of exact invariant solutions that constitute the pricing models for the Black-Scholes model using the associated in nitesimal generators and the corresponding similarity reduction equations. Using known solutions, more solutions are generated via group point transformationsItem Investigating viability of using solar(National University of Lesotho, 2021-04) Lesenyeho, Tabempe Edgar; Hove, TawandaSelection of the solar thermal collector using the energy per dollar matrix, prevailing interest rate and the prevailing inflation rate is of paramount importance for decision-making for investment in solar-assisted biodigesters. This paper presents a comprehensive computer-based excel model on investigating the viability of using solar thermal energy for optimizing the biogas yields in Lesotho. The excel based model is used to analyze both the thermal and economic performance of the solar-assisted biogas digester.The model determines solar thermal performance,solar thermal collector size, solar storage size, as well as the surface area over which the heat losses occur in both the solar water heater and biodigester tank.It will further look into economic analysis of the system. In order to ensure maximum benefits, sizing of the solar thermal system has been carried out to give the optimum solution. Simulations have been performed on an hourly time step. Comparison of production of biogas with solar thermal energy and production of biogas without solar thermal energy were undertaken to find the effects of temperature on the production of biogas. It was found that the production of biogas is optimum at the mesophilic temperatures of 180 C to 300 C. Different collectors, both evacuated tube collectors and flat plate collectors which are valued by Solar Ratings & Certificate Corporation are ranked using energy per dollar matrix. The Sun power evacuated tube collector is the best collector used for system design since it has high energy per dollar of 25.3 kWh and low heat loss parameters. The Net Present Value is the objective function to optimize for the solar thermal system. The optimum collector area to deploy for 5𝑚3 biodigester is 16𝑚2, the optimum solar storage tank of 800 liters is required. The total cost of buying the collector and the solar storage tank is $1744.In Lesotho 1𝑚3 of biodigester requires a solar v thermal collector area of about 3𝑚2.The optimum collector area gives a maximum Net Present Value of $1854.Moreover, the biogas produced is 396𝑚3 per annum with the percentage increase of extra biogas as 11.5% per annum. The project is economically viable with a Net Present Value of $1854, an Internal Rate of Return of 10.36%, a Payback period of 9 years, and a Benefit-Cost Ratio of 2.01. The project lifetime is 20 years.Item Development of time-of-use-tariffs(National University of Lesotho, 2020-07) Mohasoa, Lebohang Edwin; Mpholo, Moeketsi, Dan, Retselisitsoe Eager, ThamaeThe electricity consumption profile varies during any 24-hour period, but the electricity pricing policy for Lesotho Electricity Company (LEC) does not reflect this fluctuation as it employs flat-rate tariffs across all customer categories. This fails to adequately capture the costs exerted on the electricity network by each customer at a certain period. To address this problem, time-of-use (ToU) tariffs are determined in this study, while ensuring revenue neutrality for the utility before any load shifting. Implementation of a comprehensive ToU based pricing model could be an effective mechanism to reflect the costs imposed on the network by customers and therefore encourage customers to engage in load adjustment. The Gaussian mixture model has been utilized to determine ToU time-periods and prices. The time-periods are divided into different periods; off-peak, standard, and peak periods. Different customer categories have different durations of time- periods. This is attributed to the observed load profiles of different customer categories. Furthermore, different customer categories have different prices per period resulting in different price ratios. Possible load-shifting scenarios of 5% and 10% have resulted in a reduction in customer energy bills of 2.6% and 5.2%, respectively. While, the LEC bulk energy savings translated to 13 GWh and 30 GWh for the two load-shifting scenarios, respectively. Key words:Item Analysis of the viability of using thermal energy for Maluti Mountain Brewery(National University of Lesotho, 2021-04) Lillane, Malillane; Mr. Hove, Tawanda; Dr. Mpholo, MoeketsiIt 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.
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