Distribution power markets: detailed modeling and tractable algorithms
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The increasing integration of renewable generation presents power systems with economic and reliability challenges, mostly due to renewables' volatility, which cannot be effectively addressed with business-as-usual practices. Fortunately, this is concurrent with rising levels of Distributed Energy Resources (DERs), including photovoltaics, microgeneration and flexible loads like HVAC loads and electric vehicles. DERs are capable of attractive time-shiftable behavior and of transacting reactive power and reserves in addition to real power. If DER capacity is optimally allocated among these three products, distribution network and economic benefits can be realized and renewable-related challenges can be mitigated, enabling increased renewable integration safety limits. In order to achieve optimal DER scheduling, this thesis proposes the formulation of a spatiotemporal marginal-cost based distribution power market and develops and implements tractable clearing algorithms. First, we formulate a centralized market clearing algorithm whose result is the optimal DER real power, reactive power and reserves schedules and the optimal nodal marginal costs. Our market formulation develops for the first time detailed and realistic models of the salient distribution network variable costs (transformer degradation, voltage sensitive loads) together with distribution network constraints (voltage bound constraints, that reflect distribution network congestion and AC load flow), and intertemporal DER dynamics and capabilities. However, the centralized algorithm does not scale, motivating the use of distributed algorithms. We propose two distributed algorithms: • A fully distributed algorithm that relies on massively parallel DER and distribution line specific sub-problem solutions, iteratively coordinated by nodal price estimates which promote and eventually enforce nodal balances. Upon convergence, nodal balances hold and optimal marginal costs are discovered. We further existing practices by using local penalty updates and stopping criteria that significantly reduce communication requirements. • A novel, partially distributed formulation in which DERs self-schedule in parallel based on centrally calculated price estimates, resulting from a load flow calculation. Nodal balances hold during all iterations. Finally, we are, to the best of our knowledge, the first to study voltage-constrained distribution market instances cleared with distributed methods. We decrease the deviation of marginal costs from their optimal values using first order optimality conditions and use voltage barrier functions for speedier convergence.