Bayesian Energy Measurement and Verification Analysis

Abstract

Energy Measurement and Verification (M&V) aims to make inferences about the savings achieved in energy projects, given the data and other information at hand. Traditionally, a frequentist approach has been used to quantify these savings and their associated uncertainties. We demonstrate that the Bayesian paradigm is an intuitive, coherent, and powerful alternative framework within which M&V can be done. Its advantages and limitations are discussed, and two examples from the industry-standard International Performance Measurement and Verification Protocol (IPMVP) are solved using the framework. Bayesian analysis is shown to describe the problem more thoroughly and yield richer information and uncertainty quantification results than the standard methods while not sacrificing model simplicity. We also show that Bayesian methods can be more robust to outliers. Bayesian alternatives to standard M&V methods are listed, and examples from literature are cited.

A Practical Guide to Gaussian Process Regression for Energy Measurement and Verification within the Bayesian Framework

“…The metering instrument used to create the energy usage dataset for the case study in Section 2 has an inherent uncertainty of 1%. The GP treats the inputs to the training set (the pre-intervention energy usage data) not as point estimates, but as random points with known distribution (known mean and variance) [4,16]. This is referred to as probabilistic programming and is a powerful approach since it automatically allows for well-defined quantification of the uncertainties [4].…”

“…Carstens et al [4] rightfully points out that the traditional frequentist approach for obtaining well-defined uncertainty can lead to misinterpretation of the uncertainty it conveys. This creates an opportunity for the use of nonlinear Gaussian Process (GP) regression within the Bayesian paradigm for quantifying uncertainties in the M&V process [5].…”

“…This creates an opportunity for the use of nonlinear Gaussian Process (GP) regression within the Bayesian paradigm for quantifying uncertainties in the M&V process [5]. The probabilistic nature of Bayesian models means that uncertainty is well defined [4]. GP regression can therefore provide true confidence in the calculated savings of energy efficiency projects and in that way provide more bankable figures and reliable retrofit campaigns.…”

“…Another attractive property of the Bayesian paradigm is that little knowledge of the underlying energy model is necessary, thus reducing the induced error associated with the model [8]. The Bayesian paradigm allows the data to "speak for itself", thus largely eliminating the modelling error in M&V [4,9].…”

“…The GP is part of the Bayesian paradigm since both rely on the construction of a prior distribution. Rather than allocating a specific energy model (or function) to the data regression, the GP regresses data in a non-parametric, yet certain, way (see Rasmussen and Williams [10], Carstens et al [4] and Figure 1). Figure 1 illustrates the structure of a typical GP algorithm for use in energy savings quantification.…”