The variation of efficiency with size, and the economic choice of electrical machinery

Abstract

The paper consists roughly of two parts—an examination of the efficiency of electrical machinery of varying sizes, and an application of the results to the problem of economic choice. In the former section it is shown that wherever there is more than one kind of loss a large machine will have a higher efficiency than a small one, by an amount which is roughly predicable. It is further shown that this efficiency can be maintained with little or no diminution when the machine is suitably under-run, depending on the kinds and proportions of the losses. This makes it possible to calculate the cost of improving the efficiency of a given service to any required degree through the employment of larger plant than is physically necessary.Applying this to the selection of apparatus to fulfil a given service at the least total cost, the cases considered are squirrelcage induction motors, small d.c. motors and single-phase transformers. Placing all items on an annual basis, the rates of change of the various charges with reference to the frame size are worked out for a range of sizes in each of the three cases. These rates of change form an index by which the most economical size can readily be estimated for any conditions of service, and the method of doing this is fully explained in the paper.The results suggest that where the hours of service are long or energy is expensive a far larger or more efficient machine is justified than would normally be employed. Where such improved efficiency is proposed, the method here developed makes it possible to calculate the particular degree of improvement which is economically justified in any case. Such a calculation should be an essential feature of the design (or failing this, the selection) of all apparatus for long-hour service.