On the annual wave energy absorption by two-body heaving WECs with latching control J.C.C. Henriques a, * , M.F.P. Lopes b , R.P.F. Gomes a , L.M.C. Gato a , A.F.O. Falcão a a IDMEC, Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais,1049-001 Lisboa, Portugal b Wave Energy Centre, Av. Manuel da Maia,1049-001 Lisboa, Portugal article info Article history: Received 13 October 2011 Accepted 31 January 2012 Available online 23 March 2012 Keywords: Wave energy Time domain Latching control Threshold unlatching time Two-body system Cummins equations abstract Although the latching control strategy has been recognized as an important mean of increasing the efficiency of one-body point-absorbing wave energy converters (WECs), its effectiveness in two-body floating point-absorbers has been questioned in some studies. The current work investigates the increase in annual absorbed energy achieved with a simple threshold unlatching control strategy when applied to a generic two-body heaving WEC. The WEC performance is evaluated for a set of sea-states characteristic of the wave climate off the Portuguese west coast. To achieve this computationally intensive task, a new high-order numerical method for the solution of the Cummins equations is presented and used. This approach is based on a polynomial representation of the solution, whose coefficients are computed using a continuous least-squares approximation. The code has been parallelized and computations were performed at the IST cluster. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction The energy extraction by offshore WECs is, in general, obtained through the relative motion of two or more parts of the converter. The moving parts may have relative motion in translation modes, as in the Wavebob [1] and the IPS Buoy [2], or the relative rotation between parts of the converter, as the case of SEAREV [3]. Other particular cases, as devices connected directly to the seabed and bottom mounted oscillating water columns can be seen as partic- ular cases of the first one, where the second body (the earth) has infinite mass. The two-body problem in heave is very relevant in the scope of offshore wave energy conversion. This problem has been studied by a number of authors both theoretically [4,5] and numerically [6e9]. The latching control technique, first proposed by [10] for one- body systems, consists in locking the body motion when its velocity vanishes and releasing it such that ideally the velocity becomes in phase with the excitation force during the unlatched part of the cycle. Under certain conditions, a significant increase in the energy extraction can be achieved, when compared with the non-controlled case. This strategy can be adapted for the relative motion of two-body systems, using the relative velocity as reference. The possibility offered by latching control of achieving larger efficiencies over a broad range of incident frequencies can signifi- cantly improve the device economics. Moreover, the efficiency gain is larger at frequencies smaller than the device resonance frequency, which may result in a substantially smaller device for the same wave energy absorption capability [11]. The practical application of the latching strategy raises several problems, mainly related to the need of fast response of mechanical and/or hydraulic components. The study of this strategy for one-body systems has been quite extensive including successful experimental investiga- tions [12e15]. The utilization of latching control in two-body heaving systems has been justifiably questioned (see e.g. [16]) because the two bodies keep moving as one-body after latching, which makes the system less efficient as the dynamics becomes different from what was idealized in one-body latching control. However, the effect of this is dependent on the mass ratio of the two bodies. In the limiting case, when the mass of one of the bodies increases to infinity, the gain from latching control increases since the system becomes equivalent to a floater reacting against the seabed [4]. This paper examines the influence of the relative mass of the two bodies on the latching control efficiency for a given annual wave climate. * Corresponding author. Tel.: þ351 218417296. E-mail addresses: joaochenriques@ist.utl.pt (J.C.C. Henriques), mlopes@wave- energy-centre.org (M.F.P. Lopes), ruigomes@ist.utl.pt (R.P.F. Gomes), luis.gato@ ist.utl.pt (L.M.C. Gato), antonio.falcao@ist.utl.pt (A.F.O. Falcão). Contents lists available at SciVerse ScienceDirect Renewable Energy journal homepage: www.elsevier.com/locate/renene 0960-1481/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2012.01.102 Renewable Energy 45 (2012) 31e40