Theory of the Exploitation of Tidal Energy and Its Application to the Bay of Fundy

Abstract

Considerable progress has been made in the understanding of the concepts underlying the exploitation of tidal energy during the last 20 years; this progress has culminated in the actual construction of a tidal plant at the mouth of the Rance River near St. Malo, France. Since the Bay of Fundy is one of the largest reservoirs of tidal energy in the world, the theory of exploitation of tidal energy has been reviewed with a view to its application to the Bay of Fundy.The rate of change of the energy contained in an oscillating mass of water in a basin on a rotating earth can be written out using the equations of hydrodynamics. The concept of power transfer arises immediately, which enables one to follow the transit of power from one part of the basin to another. This makes it possible to establish a balance of the power present in the basin.Only the potential energy present in the tide can be profitably exploited, and it is obtained by enclosing part of the basin by a dam in which some turbines and pumps are imbedded, as well as some complementary sluices. The emptying and filling of the enclosed part of the basin through the turbines during the fall and rise of the sea leads to the production of energy. The upper bounds of the energy available in this way can be easily established and it can also be readily shown that the use of pumps increases the amount of energy available. The actual amount of energy drawn from the reservoir is limited by the smaller range of the tide inside the reservoir and the efficiency of the turbines. The timing and duration of the various operations involved in the operation of a tidal plant, pumping, generating power, opening or closing the sluices, waiting for a head to develop, can be studied quantitatively.For this purpose the type and number of fundamental operations are carefully studied and accurate definitions are given of them, permitting calculations on a number of possible sequences of operations up to 25 tidal periods. The number of possible sequences is very large and it is not possible to study all of these sequences individually.Under some circumstances a given sequence of operations for the actual times of starting and stopping the turbines, starting and stopping the pumps, opening and closing the sluices, waiting for a head, and the changes of level inside the reservoir can be calculated with the help of the calculus of variations. For instance, these quantities yield to systematic calculation if the plant is operated with the purpose of producing the maximum amount of energy. The calculus of variations, however, cannot help directly when other modes of operation are considered, such as operating the plant in such a way as to supply power only during peak demand.The response of the basin to the oscillating ocean will be altered after the construction of the reservoir needed for the operation of the tidal plant. This modification may be important when the plant draws considerable amounts of energy from the tide.With the help of the concepts developed it becomes an easy task to make a balance sheet for the tidal power present in the Bay of Fundy, restricting ourselves to M2, the main lunar semidiurnal constituent that is representative of average conditions. Many sites in the Bay of Fundy are found to be suitable for the generation of energy; some involve relatively simple engineering and yield modest amounts of energy such as the Digby site; others, such as the Minas Channel site, could yield very considerable amounts of energy but the engineering difficulties associated with their construction might prove prohibitive.