Modelling power systems in a long-term power shortage

This thesis proposes and analyses decision support models for power systems operating in chronic power shortage conditions. Mostly these power systems exist in Sub-Saharan Africa, but other countries, for example Pakistan, Nepal, Cambodia and Bangladesh, suffer from similar problems. The thesis is structured in three parts looking at demand forecasting, distribution level load shedding and national level power rationing. First, we develop methods to forecast the electrical load on a power system conditional on a policy of load shedding. Our methods are based on the Linear Gaussian State Space Model and the Kalman Filter. Conventional time series forecasting methods cannot be applied in a power system operating in a state of chronic load shedding because the observed demand is determined both by the latent unsuppressed demand and by the load shedding decisions of the Distribution System Operator. We demonstrate the accuracy of these forecasting methods on a dataset from a Nigerian electricity distribution company. In addition, these models have potential to improve estimates of the latent demand for electricity compared to existing methods that rely on unreliable proxy variables or 'bottom-up' calculations that are difficult to verify. Next, we formulate an optimization problem to help Distribution System Operators incorporate probabilistic demand forecasts such as those developed in this thesis into their planning of load shedding. Our problem is closely related to a stochastic variant of the classic "knapsack problem" with random item "weights". We extend the literature on this problem to study the case where the item weights are given by a stochastic process which is only observed after an item is included in the knapsack. Our computational experiments provide evidence that the theoretical benefits of planning ahead are not realized in practice. It seems that for realistic range of stochastic demand processes a robust policy can be derived by an approach that only considers immediate costs and benefits. Finally, we study the problem of balancing supply and demand at the national level. We develop an AC Optimal Power Flow model with endogenous load shedding and use this to quantify the trade-off between maximizing the total amount of power delivered and distributing the available power between regional distribution companies in a fairer way. Our model represents the situation in the Nigerian power system in which the system operator minimizes load shedding, subject to exogenous proportional power supply targets for different regions. We explore how the level of permitted deviation from the target and the time period over which this target is to be achieved affects the level of load shedding. The use of an AC power flow model complicates the problem but is necessary because voltage constraints are often binding in highly stressed transmission networks in countries like Nigeria.