On optimal investment strategies for energy conservation

Abstract

This paper focuses on the problem of optimal time-phasing of investments in energy conservation. We determine the optimal time-phased investment strategy under the assumption that incremental investment can be made at any time without cost penalty. The results of the analysis are compared with the more practical approach of making all conservation investments at one time. We find, for a number of realistic cases, that there are only minor differences (typically 10% or less) between the two strategies in terms of present value. Accordingly, we conclude that a strategy of erring on the side of early investment in energy conservation measures is often justified. The analysis of the optimal time phasing for conservation investments involves the Kuhn-Tucker conditions, and is developed in detail in an appendix to the paper. The final form is quite simple when the amount of energy used annually by a system decreases exponentially with capital investment in conservation. We have found that the exponential form provides a good fit to a number of cases reported in the literature. For the exponential form and for relevant ranges of paramenters, the optimal investment strategy consists of an initial investment in conservation, followed by a constant investment per year up to a cut-off time ( t 2) less than the lifetime of the system ( T), after which no further investment is justified. The results of an analysis are presented in dimensionless graphical form for convenience of application. The analysis developed is directly relevant and applicable to situations in which an ensemble of conservation opportunities exists. An example would be when an entity (e.g. the Federal Government) is faced with installing conservation measures in a large number of buildings. The methodology developed may then be used to determine the optimal time phasing for each of a series of conservation measures.