Browsing by Subject "optimisation"

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    Mathematics for Economists
    (2014-08-21) Eyal, Katherine
    This resources consists of comprehensive notes, tutorials and solutions for Honours level economics. Material covered includes linear algebra, comparative statics, optimisation, integration and differential equations and systems of difference and differential equations, eigenvalues, complex numbers. These notes, tutorials and solutions cover the basic tools and applications in order to prepare the student for the study of Macroeconomics, Microeconomics and Econometrics at an intermediate and advanced level.
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    Open Access
    Optimal placement and effect of a wind farm on load flow and protection systems in a municipal distribution network
    (2019) Martin, Mogamat Noer; Awodele, Kehinde O.
    Much research has been done on the effects of distributed generation on network characteristics. However, little research has been done on the effects of this distributed generation on current network protection schemes. An IPP has approached a South African municipality regarding the connection of a wind farm that would be connected to the municipality’s existing grid. This presented a unique opportunity to simulate and study the impact and effect that this wind farm would have on a real-life network in terms of network operation and protection schemes. This also presents the possibility of connecting the wind farm in a different configuration, possibly resulting in better network operation at a lower cost. The network optimisation in this research was done using the probability-based incremental learning (PBIL) and differential evolution (DE) optimisation techniques. These algorithms were programmed and modelled according to the desired IPP wind farm requirements using the MATLAB and MATPOWER simulation packages. The networks used in these algorithms were modelled in the text-based MATPOWER format. This research goes on to study a modified 14-bus IEEE test network in terms of network characteristics and protection performance so that an idea of the performance of the optimisation algorithms can be obtained. Protection data for the IEEE network was not available. The network was thus graded for use in this study. The research then continues to model the existing and proposed network configuration, and proposes various other points of connection to the municipal network using the PBIL and DE algorithms. These studies were conducted using the DIgSILENT PowerFactory simulation package, with the networks and protection data being modelled in this package. Network and protection performance results were recorded for each case in both networks under study. The results show that in the case of the modified IEEE network, the DE algorithm provides a better solution in terms of improving power losses while the PBIL algorithm provides a better solution in terms of improving the voltage profile. In the case of the municipality network, the DE algorithm provides the best performance, with the DE result managing to reduce power losses by 83.89% compared to the current and proposed network configurations. The overall voltage profile was also seen to improve by over 23%. The research also found that the change in fault level for the various cases are minimal. This is due to the limitation in fault current contribution imposed by the use of an inverter system connecting the wind farm to the grid. This means that, as the results shows, network grading is not very much affected by the addition of the wind farm connections. However, it is seen that the municipal network is not optimally graded in the base case. Finally, it is also seen that, though not often used in research, the MATPOWER package works well as a network simulation tool. A costing analysis was also conducted and shows that the DE solution is the most cost-effective solution, in addition to being the best-performing solution. The study recommends that the results produced by the DE algorithm be implemented instead of the proposed implementation. The municipal network should also be regraded and new protection settings should be implemented.
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    Open Access
    Optimising opportunities for the expansion of the central chronic medicines dispensing and distribution programme in South Africa
    (2026) Carmichael, Grace; Silal, Sheetal
    Background: The Central Chronic Medicines Dispensing and Distribution (CCMDD) programme was introduced in South Africa to try to alleviate the overextension of primary health-care clinics in South Africa. This programme allows patients to collect repeat medicine prescriptions for chronic conditions from a pick-up point to reduce traffic through clinics. Since its inception in 2016 the success of the programme has not been assessed and a data-driven expansion plan has not been developed. This study aims to answer the question of whether the programme has been successful in reducing clinic head-counts and provides guidance to decision makers on where new pick-up points should be introduced in the country. Methods: To assess the impact of the programme on country-wide clinic headcounts, an interrupted time series analysis was performed using both an ARIMA model and a linear regression model fitted using generalised least squares. To determine the optimal wards to introduce pick-up points in so as to best reduce clinic headcounts, a location- allocation optimisation was performed with the objective of allocating to wards with the highest clinic headcounts. All analyses were conducted in R and Gurobi was the optimisation software used. Results: Both the ARIMA and regression model indicated that clinic headcounts have been steadily decreasing (from a starting total headcount of 8 362 953) at an average rate of about 7000-8000 patients per month since the introduction of the programme and up until March 2020. The ARIMA estimate for this slope change is: -7188.03 (CI: [-11254.01 ; -3122.05]), and the regression estimate is: -8174 (CI: [-11254.01 ; -3122.0]). The two different models do not agree on the initial drop in patient numbers when the programme was initially introduced. While there is not strong evidence that there is an initial decrease (intercept estimate), the slope change is similar between the two models, indicating that the headcounts have been gradually decreasing since programme introduction. The location-allocation optimisation produced a model that decision- makers can use to help guide the expansion of the programme. This model indicates that 500 additional pick-up points are a good amount to be able to reduce headcounts from the majority of clinics in the country under most scenarios. Conclusions Clinic headcounts in South Africa have reduced since the introduction of the CCMDD programme, however, there is still room for programme expansion. This expansion should be guided by the model presented in this study but also by practical considerations of programme decision-makers.