Real time optimal water allocation in the Orange River catchment in South Africa

Abstract

The planning and management of water resources systems often involve formulation and establishment of optimal operating policies and the study of trade-off between different objectives. Due to the intricate nature of water resources management tasks, several models with varying degrees of complexities have been developed and applied for resolving water resources optimisation and allocation problems. Nevertheless, there still exist uncertainties about finding a generally consistent and trustworthy method that can find solutions which are very close to the global optimum in all scenarios. This study presents the development and application of a new evolutionary multi-objective optimisation algorithm, combined Pareto multi-objective differential evolution (CPMDE). The algorithm combines methods of Pareto ranking and Pareto dominance selections to implement a novel generational selection scheme. The new scheme provides a systematic approach for controlling elitism of the population which results in the simultaneous creation of short solution vectors that are suitable for local search and long vectors suitable for global search. By incorporating combined Pareto procedures, CPMDE is able to adaptively balance exploitation of non-dominated solutions found with exploration of the search space. Thus, it is able to escape all local optima and converge to the global Pareto-optimal front. The performance of CPMDE was compared with 14 state-of-the-art evolutionary multi-objective optimisation algorithms. A total of ten test problems and three real world problems were considered in the benchmark of the algorithm. Findings suggest that the new algorithm presents an improvement in convergence to global Pareto-optimal fronts especially on deceptive multi-modal functions where CPMDE clearly outperformed all other algorithms in convergence and diversity. The convergence metric on this problem was several orders of magnitude better than those of the other algorithms. Competitive results obtained from the benchmark of CPMDE suggest that it is a good alternative for solving real multi-objective optimisation problems. Also, values of a variance statistics further indicate that CPMDE is reliable and stable in finding solutions and converging to Pareto-optimal fronts in multi-objective optimisation problems. CPMDE was applied to resolve water allocation problems in the Orange River catchment in South Africa. Results obtained from the applications of CPMDE suggest it represents an improvement over some existing methods. CPMDE was applied to resolve water allocation problems in the agricultural and power sectors in South Africa. These sectors are strategic in forging economic growth, sustaining technological developments and contributing further to the overall development of the nation. They are also germane in capacitating the South African government’s commitment towards equity and poverty eradication and ensuring food security. Harnessing more hydropower from existing water sources within the frontier of the country is germane in capacitating the South African Government’s commitment to reduction of the countries’ greenhouse gas emissions and transition to a low-carbon economy while meeting a national target of 3 725 megawatts by 2030. Application of CPMDE algorithm in the behavioural analysis of the Vanderkloof reservoir showed an increase of 20 310 MWH in energy generation corresponding to a 3.2 percent increase. On analysis of storage trajectories over the operating period, it was found that the real time analysis incorporating a hybrid between CPMDE and ANN offers a procedure with a high ability to minimize deviation from target storage under the prevailing water stress condition. Overall, the real time analysis provides an improvement of 49.32 percent over the current practice. Further analysis involving starting the simulation with a proposed higher storage volume suggests that 728.53 GWH of annual energy may be generated from the reservoir under medium flow condition without system failure as opposed to 629 GWH produced from current practice. This corresponds to a 13.66 percent increase in energy generation. It was however noted that the water resources of the dam is not in excess. The water in the dam is just enough to meet all current demands. This calls for proper management policies for future operation of the reservoir to guard against excessive storage depletions. The study herein also involved the development of a decision support system for the daily operation of the Vanderkloof reservoir. This provides a low cost solution methodology suitable for the sustainable operation of the Vanderkloof dam in South Africa. Adopting real time optimisation strategies may be beneficial to the operation of reservoirs. Findings from the study herein indicate that the new algorithm represents an improvement over existing methods. Therefore, CPMDE presents a new tool that nations can adapt for the proper management of water resources towards the overall prosperity of their populace.