This paper analyses the performance of a real heat pump plant via methods of entropy generation minimization or finite-time thermodynamics. The analytical relations between heating load and pressure ratio, and between coefficient of performance (COP) and pressure ratio of real closed regenerated Brayton heat pump cycles coupled to constant- and variable-temperature heat reservoirs are derived. In the analysis, the irreversibilities include heat transfer-irreversible losses in the hot- and cold-side heat exchangers and the regenerator, the non-isentropic expansion and compression losses in the compressor and expander, and the pressure drop loss in the pipe and system. The optimal performance characteristics of the cycle may be obtained by optimizing the distribution of heat conductances or heat transfer surface areas among the two heat exchangers and the regenerator, and the matching between working fluid and the heat reservoirs. The influence of the effectiveness of regenerator, the effectiveness of hot- and cold-side heat exchangers, the efficiencies of the expander and compressor, the pressure recovery coefficient and the temperature of the heat reservoirs on the heating load and COP of the cycle are illustrated by numerical examples. Published in 1999 by John Wiley & Sons, Ltd.