With the widespread use of power electronic devices, modern distribution networks are turning into flexible distribution networks (FDNs), which have enhanced active and reactive power flexibility at the transmission-distributioninterface (TDI). However, owing to the stochastics and volatility of distributed generation, the flexibility can change in real time and can hardly be accurately captured using conventional discrete-time (DT) assessment methods. This paper first proposes the notion of continuous-time (CT) TDI active and reactive flexibility and establishes its mathematical model. This model comprehensively considers the flexible devices in the FDN and the impact of uncertainty of photovoltaic power generation and load. In particular, a novel direction-factor-based metric is proposed to model CT-TDI PQ flexibility. Moreover, an efficient solution method is designed to address the difficulties in handling the infinite dimension of CT model and the complexity of biobjectivity from assessing both active and reactive flexibility to be assessed. The solution successfully transforms the infinite dimensional optimization into a finite dimensional problem and effectively explores the PQ plane in a parallel pattern. Case studies show that the method can more effectively assess the realtime TDI flexibility of an FDN relative to conventional DT counterparts, and also reveals the impact of the relevant factors, such as penetrations of flexible devices and levels of uncertainty.
This article investigates the autonomous demand response (ADR) in a building microgrid incorporating photovoltaic (PV) generation and plug-in electric vehicles. Two operation models are introduced in this article to enhance the self-utilization of PV power: 1) mixed integer programming (MIP)-based optimization model; and 2) the game theoretic model. To avoid the disadvantages of MIP-based centralized optimization in a decentralized approach, a non-cooperative ADR game framework is formulated based on the proposed virtual cost mechanism for each player to help in selecting the optimal consumption strategy coordinately. The existence of the unique Nash equilibrium which coincides with the optimal solution of the MIP-based operation model is proved. In addition, an iterative algorithm is developed to determine the equilibrium solution for the ADR game. Simulation results verify that the non-cooperative game-based ADR program is effective in improving the utilization of PV energy and benefits to microgrid systems. INDEX TERMS Autonomous demand response (ADR), building microgrid, plug-in electric vehicles, game theory, self-utilization, photovoltaic (PV).
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