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Integration of distributed renewable energy sources (D- RES) has been introduced as a viable solution to offer cheap and clean energy to customers in decentralized power system. D- RES can offer local generation to flexible customers based on their servicing deadline and constraints, benefiting both D- RES owners and customers in terms of providing economic revenue and reducing the cost of supplied energy. In this context, this paper proposes a dynamic matching framework using model predictive control (MPC) to enable local energy sharing in power system operation. The proposed matching framework matches flexible customers with D- RES to maximize social welfare in the matching market, while meeting the customers' servicing constraints prior to their deadline. Simulations are conducted on a test power system using multiple matching algorithms across different load and generation scenarios and the results highlighted the efficiency of proposed framework in matching flexible customers with the appropriate supply sources to maximize social welfare in the matching market. 

The current practice of discrete-time electricity pricing starts to fall short in providing an accurate economic signal reflecting the continuous-time variations of load and generation schedule in power systems. This paper introduces the fundamental mathematical theory of continuous-time marginal electricity pricing. We first formulate the continuous-time unit commitment (UC) problem as a constrained variational problem, and subsequently define the continuous-time economic dispatch (ED) problem where the binary commitment variables are fixed to their optimal values. We then prove that the continuous-time marginal electricity price equals to the Lagrange multiplier of the variational power balance constraint in the continuous-time ED problem. The proposed continuous-time marginal price is not only dependent to the incremental generation cost rate, but also to the incremental ramping cost rate of the units, thus embedding the ramping costs in calculation of the marginal electricity price. The numerical results demonstrate that the continuous-time marginal price manifests the behavior of the constantly varying load and generation schedule in power systems. 

In this paper, we first introduce a variational formulation of the Unit Commitment (UC) problem, in which generation and ramping trajectories of the generating units are continuous time signals and the generating units cost depends on the three signals: the binary commitment status of the units as well as their continuous-time generation and ramping trajectories. We assume such bids are piecewise strictly convex time-varying linear functions of these three variables. Based on this problem derive a tractable approximation by constraining the commitment trajectories to switch in a discrete and finite set of points and representing the trajectories in the function space of piece-wise polynomial functions within the intervals, whose discrete coefficients are then the UC problem decision variables. Our judicious choice of the signal space allows us to represent cost and constraints as linear functions of such coefficients, thus, our UC models preserves the MILP formulation of the UC problem. Numerical simulation over real load data from the California ISO demonstrate that the proposed UC model reduces the total dayahead and real-time operation cost, and the number of ramping scarcity events in the real-time operations.