# Energy Savings Calculation Methodology

The Energy Performance Forecasting Tool (Forecasting Tool) enables users to evaluate the potential energy savings from building retrofit projects. To accomplish this it uses actuarial forecasts, not simulations or models. Users will be able to:

• Identify energy conservation measures (ECMs) for a particular building that yield acceptable post-retrofit performance
• Identify buildings in the user's portfolio that, for pre-selected ECMs, will yield acceptable post-retrofit performance

It is important to note that the buildings being evaluated for retrofit performance are the user's buildings, not the buildings in the DOE Buildings Performance Database. Below is a scenario that explains how the Forecasting Tool provides an actuarial basis for such evaluation:

Suppose retrofits for a building are being considered. First, the Forecasting Tool queries all buildings with similar characteristics and climate. Suppose the query returns a set of buildings S with N buildings A1,A2, ..., AN. For specificity, consider monthly electricity usage. And let E1,E2, ...,EN be their electricity use for a given month. Assuming N is reasonably large, a probability density function (PDF), Ppre(E), for the energy use (per unit floor area) can be constructed. If the energy use of the building A is known, one can locate this building on the PDF. If certain retrofits are applied to the building, the building characteristics will change, so call this hypothetical building A'. One can now query the database to get a set S' with N' buildings resulting in a PDF Ppost(E). The sets S and S' need not be, and in general will not be the same.

The PDF for the energy savings is now given by a convolution:

Psavings = ∫ dxpre.dxpost Ppre(xpre).Ppost(xpost).δ(xpre — xpost — x)

This PDF allows an analysis of the financial risk in investing in this retrofit. For example, the probability that the savings will be less than a certain minimum acceptable value is a measure of the risk.

The basic idea of the Forecasting Tool is to extract the peer group for a given building. All members of the peer group share certain important characteristics of energy use. These characteristics can be categorized as fixed and have the ability to be retrofitted. For residential buildings the fixed characteristics are:

• Size
• Age
• Type (Single-Family, Multi-Family, etc.)
• Heating fuel and system type
• Cooling system type
• Climate in which the building is located

The retrofit characteristics are:

• Window type
• Attic and wall insulation
• Heating and cooling system efficiencies

This list is not exhaustive. One can add characteristics to the list such as window-to-floor-area ratio, whether the building has a basement, crawl space, or slab-on-grade, etc.

The user enters these characteristics for a building to be evaluated. An input that can take continuous values (such as floor area) is specified through a range rather than a single number. These ranges should be small enough that all buildings within this range (after normalization for square footage) can be considered peers.

The user also enters the characteristics of the post-retrofit building. The Forecasting Tool queries the database and performs the necessary convolution to provide the probability distribution of energy savings. This can be combined with the financial information for investment decisions. The evaluation can be done for each fuel, for each month.

Building energy performance is determined by a large number of parameters, more than are listed above. As the DOE Buildings Performance Database grows, it is expected that one will specify more of these parameters and in a narrower range and still get a statistically valid peer group size.

Commercial buildings are particularly challenging with a large number of characteristics especially with heating and cooling systems and lighting configurations. The building characteristics inputs were selected to be applicable to a broad range of buildings without requiring excessive amount of information for the building. Future work is planned to account for differences in the characteristics of the members within the peer group.