Power Flow Management: Solvability Condition for a System with Controllable and Fluctuating Devices

Renewable energy sources such as wind power or photo-voltaic power are environmental-friendly, but the fluctuation of the output power can affect the stability and quality of power network due to their intermittent nature. From such point of view, a power flow control is introduced which assigns power levels for controllable power devices and connections between power devices to absorb the power fluctuations caused by fluctuating devices. While, the system controller needs to handle various aspects such as transient behavior, latency of system control, cost efficiency etc., the issue whether the system has a feasible solution or not is one of the most important issues. In the paper, we discuss solvability conditions for a system which includes both controllable and fluctuating power devices (i) with given power generation and consumption levels of fluctuating devices, and (ii) with any power level of fluctuating sources and loads. Hence, the ultimate objective is to design a system which has robustness against power fluctuations caused by fluctuating devices.