Mathematical description of the performance measurement and verification

Claimed savings of energy efficiency projects often need to be measured and verified. The measurement and verification (M&V) activities are guided by the International Performance Measurement and Verification Protocol in many countries. However, the M&V is largely believed to be an inaccurate science: an engineering practice with a lot of professional judgement. This paper presents a mathematical description of the M&V problem and thus casts into a scientific framework of the basic M&V concepts, propositions, techniques and methodologies. We start with a general description and modeling of energy systems, then introduce the idea of developing an M&V plan as an M&V modeling problem. M&V models are shown via examples to be established by analyzing physical laws, measured data, or stochastic processes. As an application of this framework, we provide sufficient conditions to choose the M&V options. Finally, we introduce a notion of optimal M&V design. It shows that an optimal M&V plan is a design process guided by fundamental principles of calculus of variation and optimal control systems.