An electrical analogy for the Pentland Firth tidal stream power resource

Abstract

Several locations in the Pentland Firth, UK, have been earmarked for the deployment of separate farms of tidal turbines. However, recent numerical modelling suggests that these farms will be inter-dependent and that they must work together to optimize their collective performance. To explain this inter-dependence, in this paper we develop an electrical circuit analogy to describe flow through the Pentland Firth, in which parallel connections in the circuit represent different sub-channels formed by the islands of Swona, Stroma and the Pentland Skerries. The analogy is introduced in stages, beginning with turbines placed in a single channel, then turbines placed in a sub-channel connected in parallel to another sub-channel, and finally more complicated arrangements, in which turbines are installed both in parallel and in series within a multiply connected channel. The analogy leads to a general formula to predict the tidal power potential of turbines placed in a sub-channel connected in parallel to another sub-channel, and a predictive model for more complicated multiply connected channel arrangements. Power estimates made using the formula and predictive model (which may be applied using only measurements of the undisturbed natural tidal hydrodynamics) are shown to agree well with numerical model predictions for the Pentland Firth, providing useful insight into how to best develop the resource.