Mathematical description for the measurement and verification of energy efficiency improvement

Insufficient energy supply is a problem faced by many countries, and energy efficiency improvement is identified as the quickest and most effective solution to this problem. Many energy efficiency projects are therefore initiated to reach various energy saving targets. These energy saving targets need to be measured and verified, and in many countries such a measurement and verification (M&V) activity is guided by the International Performance Measurement and Verification Protocol (IPMVP). However, M&V is widely regarded as an inaccurate science: an engineering practice relying heavily on professional judgement. This paper presents a mathematical description of the energy efficiency M&V problem and thus casts into a scientific framework the basic M&V concepts, propositions, techniques and methodologies. For this purpose, a general description of energy system modeling is provided to facilitate the discussion, strict mathematical definitions for baseline and baseline adjustment are given, and the M&V plan development is formulated as an M&V modeling problem. An optimal M&V plan is therefore obtained through solving a calculus of variation, or equivalently, an optimal control problem. This approach provides a fruitful source of research problems by which optimal M&V plans under various practical constraints can be determined. With the aid of linear control system models, this mathematical description also provides sufficient conditions for M&V practitioners to determine which one of the four M&V options in IPMVP should be used in a practical M&V project.