Mixed integer linear programming for unit commitment and load dispatch optimisation
Abstract
The objective of solving the unit commitment and environmental economic load dispatch problem (UCEELD) for power utilities is to minimise the overall operational cost associated to power generation, while optimising the utilisation of natural resources. Power generation scheduling is however not a simplistic process as a multitude of aspects needs to be considered such as aging infrastructure, stringent emissions legislation, operational limitations and aligning base load with peaking station's scheduling. Apart from the financial objective, the optimisation problem is also focused on meeting the forecasted load demand of the power grid in an attempt to prevent grid instabilities. The intricacy of the scheduling and resource allocation process is significantly increased when a large power grid such as South Africa's grid is considered. Given the magnitude and complexity of the problem, a mathematical optimisation model was developed in this thesis applying mixed integer linear programming (MILP) as formulation technique and a commercial solver known as Cplex to obtain a proven global optimal solution to the mentioned problem. Specific emphasis was applied in using MILP instead of literature defined heuristic methods as these methods are not able to guarantee proven optimal solutions. Provided the nonlinearity of the UCEELD problem, the technique of piecewise linear approximation using binary variables were applied to linearise the nonlinear aspects of the problem with the aim of applying the MILP formulation. For the purpose of this thesis, only thermal, hydro and pumped storage generating technologies were considered for optimisation. The contributions of this thesis were towards developing a realistically sized UCEELD model using MILP with the aim of incorporating the model into the production environment. Modeling contributions include the addition of thermal generation water consumption into the model objective function and incorporating stochasticity to the production model. The computational results provided in the thesis are based on the data obtained from a realistically sized power generation utility containing 98 thermal, 8 hydro and 6 pumped storage generating units. The model verification results confirmed that the proposed model is able to solve the optimisation problems accurately with the model response being as expected. From the validation results, it is observed that the proposed UCEELD MILP model is able to solve a realistically sized model to proven optimality within 44 minutes. A data handling tool comprising of a graphical user interface is also proposed to improve data acquisition, processing and incorporation into the optimisation model as well as interpretation thereof. The development of the UCEELD MILP model allows power utility management to effectively perform strategic decision-making within a short time frame to allow the optimisation of overall operational costs.
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