Competitive Equilibrium in Microgrids With Dynamic Loads
CoRR(2024)
摘要
In this paper, we consider microgrids that interconnect prosumers with
distributed energy resources and dynamic loads. Prosumers are connected through
the microgrid to trade energy and gain profit while respecting the network
constraints. We establish a local energy market by defining a competitive
equilibrium which balances energy and satisfies voltage constraints within the
microgrid for all time. Using duality theory, we prove that under some
convexity assumptions, a competitive equilibrium is equivalent to a social
welfare maximization solution. Additionally, we show that a competitive
equilibrium is equivalent to a Nash equilibrium of a standard game. In general,
the energy price for each prosumer is different, leading to the concept of
locational prices. We investigate a case under which all prosumers have the
same locational prices. Additionally, we show that under some assumptions on
the resource supply and network topology, locational prices decay to zero after
a period of time, implying the available supply will be more than the demand
required to stabilize the system. Finally, two numerical examples are provided
to validate the results, one of which is a direct application of our results on
electric vehicle charging control.
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