Solving large-scale transmission network problems
Beşik, Deniz (2014) Solving large-scale transmission network problems. [Thesis]
Electricity is supplied by generators to meet the demand of the customers through the transmission lines. The flow-based optimization models in the literature seek for optimal generation cost while satisfying the demand and the physical constraints of the network. However, electricity transmission can be disrupted by exogenous factors such as weather conditions, terrorist attacks, human and operational errors or voltage drop due to line losses. These factors can generate a risk in the system leading to unmet demand of customers. Furthermore, this risk increases when the distances between the generators and the demand points becomes larger. In this thesis, we propose an electric network optimization model which emphasizes the risk arising from the long distance electricity transmission. In an electric network, if generators satisfy the demand in their vicinity, the arising risk from long distance electricity transmission can be reduced. In this regard, we use a path-based electric network optimization model where the objective is to minimize a risk function based on the path lengths and the flows. This risk function is obtained by incorporating a path length dependent risk coefficient into the convex quadratic generator cost function. Our work differs from the works in the literature as we consider such at risk function. To solve the resulting model, we employ column generation. However, column generation is not applicable when the objective function is convex quadratic. Therefore first, the convex quadratic function is approximated by a piece-wise linear convex function. However, the linear programming equivalent of this model causes a row-wise increase. This increase would cause to change the given solution approach. Thus second, an equivalent linear programming model without a row-wise increase is presented. The resulted model is solved with standard column generation and the numerical results are obtained for example networks.
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