Control For Energy and Sustainability

EPSRC Programme Grant

Energy Flow in Interconnected Systems

    Professor Jan Willems (K.U. Leuven)
    Cambridge University Engineering Department, Lecture Room 5
    Friday 05 February 2010, 14:00-15:00

Abstract. We examine what is meant by the power and the energy which a physical system exchanges with its environment. The systems which we consider interact through terminals, as wires for electrical circuits, and pins for mechanical devices. Associated with each terminal, there are variables through which the system interacts with its environment. For circuits, these variables are current and potential, and for (one-dimensional) mechanical systems, position and force. Systems are interconnected by sharing variables at the interconnected terminals. We define a port as a set of terminals that satisfy certain conditions, which we call the port-Kirchhoff laws. For ports, and only for ports, we define the power and the energy which flows into a system. Since a port involves more than one terminal, power and energy are not `local’, but involve `action at a distance’. Moreover, we cannot speak about the power and the energy flow along any set of terminals. We discuss the nature of ports for electrical and mechanical systems, and derive an expression for energy that is not frame dependent. We end by proving that a connected RLC circuit forms a 1-port. This implies that in open systems energy rarely flows between subsystems along the interconnected interface.