Abstract
Often because of limitations in generation capacity of power stations, many developing countries frequently resort to disconnecting large parts of the power grid from supply, a process termed load shedding. This leaves households in disconnected parts without electricity, causing them inconvenience and discomfort. Without fairness being taken into due consideration during load shedding, some households may suffer more than others. In this paper, we solve the fair load shedding problem (FLSP) by creating solutions which connect households to supply based on some fairness criteria (i.e., to fairly connect homes to supply in terms of duration, their electricity needs, and their demand), which we model as their utilities. First, we briefly describe some state-of-art household-level load shedding heuristics which meet the first criteria. Second, we model the FLSP as a resource allocation problem, which we formulate into two Mixed Integer Programming (MIP) problems based on the Multiple Knapsack Problem. In so doing, we use the utilitarian, egalitarian and envy-freeness social welfare metrics to develop objectives and constraints that ensure our FLSP solutions results in fair allocations that consider the utilities of agents. Then, we solve the FLSP and show that our MIP models maximize the groupwise and individual utilities of agents, and minimize the differences between their pairwise utilities under a number of experiments. When taken together, our endeavour establishes a set of benchmarks for fair load shedding schemes, and provide insights for designing fair allocation solutions for other scarce resources.
Highlights
Energy is the key driver for growth in developing countries
A knapsack problem is one where a fixed-capacity knapsack is to be fitted with a set of items, each with its weight and value, in such a way that the knapsack holds the items with the highest values within its capacity [24]. This is often modelled as an optimization problem and solved using linear programming, where a combination of items are selected to maximize the value of items packed into the knapsack, subject to the knapsack’s capacity constraints
Thereafter, we discover from multiple studies that the appliances typically available in a home in Nigeria include lighting, televisions, electric fans, DVD players, washing machines, electric irons, air conditioners, refrigerators, sewing machine and water pumps [11,26,30,31, 44]
Summary
Energy is the key driver for growth in developing countries. many such countries face significant challenges in providing enough energy to power their industries and communities [20]. While load shedding will remain a common practice in developing countries for the near future, it is absolutely necessary to develop solutions which reduce unfairness in the system Such solutions will improve the general availability of electricity, present a better platform for fighting poverty, increase the welfare of individuals and enhance societal development. Against this background, this paper presents load shedding solutions that consider the heterogeneous electricity needs of households and uses these to fairly connect households to supply.
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