Faculty of Science and Technology

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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, Sebota
Lesotho 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.
Open Access
Afm, stm and sts studies of grain boundaries And ion-beam induced defects in MGB2
(Nova Science Publishers, 2001-06) Narayan, Himanshu; Narlikar, A. V.; Herrmann, P. S. P.; Samanta, S. B.; Gupta, Anurag; Kanjilal, D.; Muranaka, T.; Akimitsu, J.; Vijayaraghavan, R.
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Antimicrobial activity of the cyclic peptides, Cyclo(D-Phe-4I-Pro) and Cyclo(L-Phe-4I-Pro).
(2013) Qhola, P. J.; Milne, J.
Open Access
Antimicrobial wound healing properties of indigenous medicinal plants of Lesotho and the pharmacist's role in minor wound care
(2021) Hlokoane, O.K.; Sello, M.
Lesotho has a rich supply of indigenous medicinal plant resources. More than a dozen Lesotho medicinal plants have been used to treat minor wound infections among Basotho for over 100 years. The aim is to provide scientifi validation of their antimicrobial activities against microorganisms relevant to the skin. The anti-infective activities of plants are thought to be due to the presence of active phytochemicals in parts of the plants, especially phenolic compounds, anthraquinones, glycosides, and alkaloids. Although there is limited research that establishes the structure-activity relationship of those phytochemicals, there are reports that attributed the phytochemical constituents with the antimicrobial effcts through a variety of mechanisms ranging from inhibition of cytoplasmic membrane function, inhibition of energy metabolism to inhibition of bacterial nucleic acid synthesis. The role of the pharmacist is to provide medical information on these compounds to promote the safe use of herbal products and in combination with conventional medicines.
Open Access
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 Nchejane
We 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 transformations
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, Tawanda
Lesotho 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.
Open Access
Development of time-of-use tariffs
(National University of Lesotho, 2020) Mohasoa, Lebohang Edwin; Mpholo, Moeketsi; Eager, Dan; Thamae, Retselisitsoe
The 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 flatrate 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; offpeak, 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.
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Direct approach to a group classification problem: Fisher equation with time-dependent coefficients
(World Scientific Publishing, 2016) Molati, M.; Khalique, C. M.
We perform Lie symmetry analysis of a time-variable coefficient Fisher equation which models reaction–diffusion–convection phenomena in biological, chemical and physical systems. These time-dependent coefficients (model parameters or arbitrary elements) are specified via the direct integration of the classifying relations.
Open Access
Disrupting tumor vasculature with oncolytic viruses
(National University of Lesotho, 2022-03) Motlomelo, Phallang Albert
Cancer 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.
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An efficient linear numerical scheme for the Stefan problem, the porous medium equation and nonlinear cross-diffusion systems
(SPEKTRUM STU Publishing, 2017-12-29) Molati, M.; Murakawa, H.
This paper deals with nonlinear diffusion problems which include the Stefan problem, the porous medium equation and cross-diffusion systems. We provide a linear scheme for these nonlinear diffusion problems. The proposed numerical scheme has many advantages, namely, it is very easy-to-implement, the ensuing linear algebraic systems are symmetric, it requires low computational cost, the accuracy is comparable to that of the well-studied nonlinear schemes, the computation is much faster than the nonlinear schemes to obtain the same level of accuracy. In this paper, numerical experiments are carried out to demonstrate efficiency of the proposed scheme.
Open Access
Energy supply management system for Lesotho user interactive system
(National University of Lesotho, 2020) Mololo, Tsepo Phineas
There is inadequate energy data in Lesotho due to lack of data collection tools that would assist in collecting and storing data from supply through transformation to final use of each energy form. This report describes a development of a full web-based system that captures and stores energy products in database from various supply sources using Personal Home Page (PHP) programming language. This system is user interactive and allows specified users to insert and/or retrieve energy products from the database while other users can register into the system to view, query or fetch as well as download stored energy products data and system generated energy commodity account (ECA) and energy balance (EB) for a specified year. From the 2017 and 2018 energy data that has been inputted into the Energy Supply Management System (ESMS), an ECA and EB reports are generated for the energy supply part which is where the system’s emphasis is on. The report provides analysis on Lesotho’s energy supply mix which is mainly from biomass with 73% of the total supply for both 2017 and 2018, with almost no traces of renewable energy penetration for both years. The supply of petroleum fuel constitutes 19% and 18% for 2017 and 2018 respectively which indicates a significant contribution to the greenhouse gases (GHG) emissions to the environment. It further gives analysis from the system generated EB on Lesotho’s self-reliance on energy supply which shows 75% and 76% for 2017 and 2018 respectively from indigenous production mainly covered by unsustainable biomass used inefficiently by major population of Lesotho. The major portion of energy supply is from imports of electricity from Eskom and EDM, coal and coal products, petroleum fuel and liquefied petroleum gas from South African mines and refineries respectively which indicates Lesotho’s reliance on imports and hence less security of energy supply.
Open Access
Er1−yCayBa2Cu3−x(Fe, Zn)xO7−δ superconductors: a study of microstructure and resistive transitions in a dc magnetic field
(IOP Publishing Ltd, 2001-10-15) Chaudhuri, Sukalpa; Gupta, Anurag; Ganesan, V.; Das, I.; Kumar, Anil; Zaleski, A. J; Narayan, Himanshu; Narlikar, A. V.
We report an investigation of structure by x-ray diffraction, microstructure by atomic force microscopy (AFM) and broadening of resistive transitions in high dc magnetic fields (0–20 kOe) in Er1−yCayBa2Cu3−x(Fe, Zn)xO7−δ (y = 0.1, 0.2; and 0 x 0.20) ceramic superconductors. The XRD shows that the presence of Ca does not alter the known effect of Fe/Zn substitution on the structure of the pure (y = 0) system. Substitution of both Fe and Zn leads to a decrease in the grain size and micro-hardness. Interesting results were obtained on the influence of various dopants on the broadening of resistive transitions in dc magnetic fields, in general: (1) an increase in Ca content suppresses it; (2) Zn substitution has no effect; and (3) Fe substitution enhances it. We show that these results can be interpreted in terms of a thermally activated flux motion (TAFM), and the effect of various dopants on the properties like pinning barrier and anisotropy.
Open Access
Evaluation and optimisation of solar water pumping systems for Lesotho
(National University of Lesotho, 2020) Moholo, Itumeleng Moses; Hove, Tawanda
Water and energy are the key drivers of sustainable development, yet the world is facing severe energy and water crisis. Photovoltaic water pumping system (PVWPS) is a mature technology that conserves both energy and water for sustainable applications. However the wider application of this technology is affected by improper system designs wider application of this technology is affected by improper system designs, high initial costs lack and of predictability . This study aims to evaluate critical factors for optimal sizing and performance prediction of PVWPS at the least cost of pumping. First objective of this study is to develop the meteorological parameters interpolated grid data base for Lesotho. Solar and ambient temperature data are recorded for 0.25 ×0.25 longitude and latitude interval for the range 27.00 East to 30.00 East and 28.00 South to 31.00 South. The range defines the extreme longitude and latitude boundaries of Lesotho. Grid data is interpolated and implemented into the computer program, hence meteorological parameters variations are automatically read at any point in Lesotho. Another objective is to develop a flow-power function, which comprehensively takes into account the instantaneous variation of ambient temperatures and solar irradiance and their effect on the pump system flow-rate and the system resistance. The flow-power function expresses the flow output of the solar pumping system as a function of the dynamic variation of the photovoltaic array power output, for a given pump and pipe parameters. The PVWPS components namely, the pump; solar photovoltaic array; pipeline system and the water storage are sized in an integrated fashion. The model is especially suitable for long pipelines where the PV array power required to deliver a demanded daily volume of water significantly decreases as the pumping main pipe diameter is increased. From the factory gate to site of installation the relative specific costs of PV array, pump and pipe differ from place to place. As a final objective an economical optimum combination of these sub system components, which meet the required daily demand of water at the least cost of pumping, is attained. Applying a time-step balance of the hourly pump flow output with the hourly water demand also enables a more precise estimation of the required balancing storage, by applying the mass-balance-curve approach. This study shows; how does the time step variation in meteorological parameters for a specified water requirement affect PVWP systems design and efficiencies; and how can the different pump-pipe combinations of PVWP systems be optimized from an integrated system perspective to arrive at the least cost of pumping. The applied method is technical accurate for sizing and also more economical thus proves to be a significant improvement to the traditional simplified approach of sizing solar pumping systems. It can result in significantly reduced unit cost of pumping. In the case study for Tosing, Lesotho (27.90 longitude 30.36 latitude) potable water demand of 350m3/ day. The design overall system efficiency is 7.1% the required PV array power was reduced by 25.8 % and the required water storage capacity reduced by 50% when compared to their respective values prescribed by the traditional sizing method. Keywords: meteorological grid data base, dynamic variations, photovoltaic water pumping system (PVWPS), flow-power function, optimal sizing, least cost of pumping
Open Access
Formulating short-term electricity demand forecasting for Lesotho
(National University of Lesotho, 2020) Lefela, Lereko; Prof Thamae, L. Z.
Electricity demand forecasting is an important process in the planning and operation of the electricity industry. Providing uninterrupted energy to consumers requires electricity demand to be predicted accurately. This study utilizes ABB Nostradamus short-term demand forecasting software, which accepts historical demand data, days of the week, time of the year and Lesotho public holidays for electricity demand forecasting. It produced day-ahead, week-ahead and hourahead electricity demand forecasting results with 3.06%, 4.06% and 5.09% accuracy. These MAPE results are close to or within the acceptable 5% accuracy for short-term demand forecasting, and provide crucial confidence levels for LEC to engage in power pool trading in the SAPP market for optimal power procurement. LEC utilizes bilateral agreements with LHDA, Eskom and EDM to supply the electricity demand. During the high demand season, bilateral imports from Eskom and EDM costs LEC around 3.27 Million US Dollars (M49 Million) which is twice the money incurred (1.60 Million US Dollars (M24 Million)) during the low demand season. Compared to the average SAPP DAM, IDM and FPM-W prices, Eskom’s 20 USc/kWh peak cost is higher than SAPP’s 12 USc/kWh DAM and IDM, and 13 USc/kWh FPM-W peak charges. Again, EDM’s 4 USc/kWh off-peak cost is higher than SAPP’s 3 USc/ kWh DAM, IDM and FPM-W off-peak charges. The study therefore recommends bilateral contracts use to meet intermediate demand of around 103 MW. For demand above 103 MW, utilizing SAPP market can assist to reduce bulk purchases costs.
Open Access
Formulating short-term electricity demand forecasting for Lesotho
(National University of Lesotho, 2020) Lefela, Lereko; Thamae, Leboli Zak
Electricity demand forecasting is an important process in the planning and operation of the electricity industry. Providing uninterrupted energy to consumers requires electricity demand to be predicted accurately. This study utilizes ABB Nostradamus short-term demand forecasting software, which accepts historical demand data, days of the week, time of the year and Lesotho public holidays for electricity demand forecasting. It produced day-ahead, week-ahead and hourahead electricity demand forecasting results with 3.06%, 4.06% and 5.09% accuracy. These MAPE results are close to or within the acceptable 5% accuracy for short-term demand forecasting, and provide crucial confidence levels for LEC to engage in power pool trading in the SAPP market for optimal power procurement. LEC utilizes bilateral agreements with LHDA, Eskom and EDM to supply the electricity demand. During the high demand season, bilateral imports from Eskom and EDM costs LEC around 3.27 Million US Dollars (M49 Million) which is twice the money incurred (1.60 Million US Dollars (M24 Million)) during the low demand season. Compared to the average SAPP DAM, IDM and FPM-W prices, Eskom’s 20 USc/kWh peak cost is higher than SAPP’s 12 USc/kWh DAM and IDM, and 13 USc/kWh FPM-W peak charges. Again, EDM’s 4 USc/kWh off-peak cost is higher than SAPP’s 3 USc/ kWh DAM, IDM and FPM-W off-peak charges. The study therefore recommends bilateral contracts use to meet intermediate demand of around 103 MW. For demand above 103 MW, utilizing SAPP market can assist to reduce bulk purchases costs.
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Graphene: Synthesis, Transfer, and Characterization for Dye-Sensitized Solar Cells Applications
(ACS Publications, 2013) Dodoo-Ahrin, D.; Fabiane, M.; Bello, A.
Large area graphene films with varying growth time thicknesses were synthesized by chemical vapor deposition (CVD) on copper foil and transferred to other substrates for characterization and photovoltaic applications. Scanning tunneling microscopy, Raman spectroscopy, and imaging show films with high crystallinity, low defect density, I2D/IG ratio of 0.52?2.26, and the presence of continuous graphene sheets with optical transparency of 75.7%?96.8%. The use of CVD graphene sheets as counter electrode in dye-sensitized solar cells was explored. The short circuit current density (Jsc), the open circuit current (Voc), the fill factor (FF), and the overall conversion efficiency under AM 1.5, 100 mW cm?2 illumination are 12.7 mA/cm2 57.5% and 3.8%, respectively.
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Growth of graphene underlayers by chemical vapor deposition
(AIP Publishing, 2013) Fabiane, M.; Khamlich, S.; Bello, A.
We present a simple and very convincing approach to visualizing that subsequent layers of graphene grow between the existing monolayer graphene and the copper catalyst in chemical vapor deposition (CVD). Graphene samples were grown by CVD and then transferred onto glass substrates by the bubbling method in two ways, either direct-transfer (DT) to yield poly (methyl methacrylate) (PMMA)/graphene/glass or (2) inverted transfer (IT) to yield graphene/PMMA/glass. Field emission scanning electron microscopy (FE-SEM) and atomic force microscopy (AFM) were used to reveal surface features for both the DT and IT samples. The results from FE-SEM and AFM topographic analyses of the surfaces revealed the underlayer growth of subsequent layers. The subsequent layers in the IT samples are visualized as 3D structures, where the smaller graphene layers lie above the larger layers stacked in a concentric manner. The results support the formation of the so-called �inverted wedding cake�stacking in multilayer graphene growth.
Open Access
Integration of solar heating systems in the textile industry
(National University of Lesotho, 2024) Leseeka, Litheba Catherine
Currently, fossil fuels are the mostly used source of thermal energy in the industrial sector in Lesotho. They provide the necessary heat for different industrial processes across a range of temperatures. Within the sector, the textile industry is a significant consumer of thermal energy, particularly for the wetting processes that require large amounts of hot water. As global concerns about climate change and global warming intensify, industries are required to reduce their carbon footprint and transition to cleaner and sustainable energy sources. This study investigated the techno-economic viability of integrating solar water heating systems at the Vishan Clothing Laundry facility in Maseru, Lesotho, using T*SOL simulation software. The study focused on three main points: solar thermal system design, performance analysis and evaluating the economic aspects of the proposed system. To determine the most efficient system for meeting the laundry’s hot water needs, six separate simulations were conducted for a comprehensive comparative analysis. From the simulations, the optimally designed system consists of Dimas SA RADIANT RSV 25 flat-plate collectors at 30° inclination angle with a collector area of 1,980 m2 and a storage tank with a capacity of 130 m3. This configuration achieves an efficiency of 54%, and a solar fraction of 89%, indicating a significant contribution from solar energy to the overall hot water production. The economic analysis under two different financing approaches shows that the system is economically viable. The proposed system under equity financing has a capital return time of 7 years, a positive net present value (NPV) of M 13,981,755, an internal rate of return (IRR) at 16.88% and cost of solar energy at M 0.831/kWh. Under equity-debt financing, the proposed system has a capital return time of 7.9 years, and amortization period of 10.3 years, a positive NPV of M 12,983,854, an IRR at 18.78% and cost of solar energy at M 0.872/kWh. These financial indicators demonstrate the economic feasibility and potential profitability of integrating solar heating systems in the textile industry. The study further highlights the need for further research to refine the system design and improve its performance. Most importantly, the study emphasizes the necessity of conducting in-depth energy audits to accurately determine the thermal energy demand of the facility. Such audits can probably provide more precise data, ensuring that the designed system can adequately meet the thermal energy demand of the laundry facility.
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Laboratory assessment of insecticidal properties of Tagetes minuta crude extracts against Brevicoryne brassicae on cabbage
(Journal of Entomology and Nematology, 2013) Phoofolo, M. W.; Mabaleha, S.; Mekbib, Sissay Bekele
The cabbage aphid, Brevicoryne brassicae is one of the most serious insect pests of cabbage in Lesotho. Chemical insecticides for efficient control of this pest are often unaffordable for resource-poor farmers. As a first step in a search for effective pest management techniques that can be affordable and easily available to these farmers, the aphicidal activities of Tagetes minuta crude extracts were evaluated against the cabbage aphid. A comparison was made on lethal and sub-lethal effects of T. minuta crude extracts from acetone, methanol, water and a mixture of acetone/methanol/water (7:7:1, v:v). The solvent system that produced the most toxic extract was the mixture, followed by methanol and water, whereas acetone produced the least toxic extract. The sub-lethal effect on cabbage aphid fecundity was well described by linear regression equations that showed significant reduction in fecundity as the concentration of crude extracts increased. The extract from the mixture solvent system had the strongest effect on fecundity.
Open Access
Lie group analysis and invariant solutions of a pseudo-parabolic partial differential equation modelling solvent uptake in polymeric solids
(2020-09-21) Khati, Maile; Prof. Molati, M
The main purpose of this work is to perform Lie group analysis of a pseudo-parabolic partial di erential equation modelling solvent uptake in polymeric solids. Three di erent sub-models for constitutive laws for the di usion coe cient and the viscosity will be considered. Once the symmetries have been determined, they will be used to nd groupinvariant solutions for the optimal systems of one-dimensional subalgebras obtained and where possible, exact solutions will be obtained.

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