Constrained optimisation procedure for evaluating cyclic loading of power transformers

The paper reports new developments in computational methods for evaluating the normal cyclic rating (NCR) and long-term emergency rating (LTER) of transformers. It makes two major improvements to the procedures given in the international standard in the subject: IEC354. One improvement derives from an interpretation of NCR and LTER formulations as a constrained optimisation procedure. Starting from a given load profile, the procedure maximises transformer loading levels subject to constraints formed from maximum values of permissible internal temperatures and of a defined insulation ageing factor. The second advance is based on a separation of variables in the evaluation of the integral which gives the relative ageing factor. This measure makes major savings in the computing overheads of practical evaluations. The two developments together lead to reliable procedures for NCR or LTER evaluations in practice as encountered in a power authority or utility. They can be relied on to give a solution without user intervention. Convergence to a solution is independent of the transformer thermal characteristics relevant to rating studies and of the loading profiles for which they are carried out. The results summarise some of the studies used in validating a comprehensive software system that implements the procedures which the paper reports. The new procedures have been tested and compared with existing procedures for many practical cases and found to achieve significant advantage, sometimes dramatically so