A decentralised graph-based framework for electrical power markets

One of the main tools used to clear the electrical power market across the world is the DC optimal power flow. Nevertheless, the classical model designed for vertically integrated power systems is now under pressure as new issues such as partial information introduced by the deregulation process, scalability posed by the multiple small renewable generation units as well as microgrids, and markets integration have to be addressed. This dissertation presents a graph-based decentralised framework for the electricity power market based on the DC optimal power flow where Newton's method is solved using graph techniques. Based on this ground, the main principles associated to the solution of systems of linear equations using a proper graph representation are presented. Then, the burden imposed by the handling of rows and columns in its matrix representation when inequality constraints have to be enforced or not is addressed in its graph based model. To this end the model is extended introducing the notion of conditional links. Next, this model is enhanced to address the graph decentralisation by introducing the weak link concept as a mean to disregard some links in the solution process while allowing the exact gradient to be computed. Following, recognizing that the DC optimal power flow is a quadratic separable program, this model is generalised to a quadratic separable program model. Finally, an agent oriented approach is proposed in order to implement the graph decentralisation. Here the agents will clear the market interchanging some economic information as well as some non-strategic information. The main contribution presented in this document is the application of graph methods to solve quadratic separable optimisation problems using Newton's method. This approach leads to a graph model whose structure is well defined. Furthermore, when applied to the DC optimal power flow this representation leads to a graph whose solution is totally embedded within the graph as both the Hessian as well as the gradient information can be accessed directly from the graph topology. In addition, the graph can be decentralised by providing a mean to evaluate the exact gradient. As a result when applied to the DC optimal power flow, the network interconnectivity is converted into local intercommunication tasks. This leads to a decentralised solution where the intercommunication is based mainly on economic information.