# Methods Overview¶

The EEmeter provides multiple methods for calculating energy savings. All of these methods compare energy demand from a modeled counterfactual pre-intervention baseline to post-intervention energy demand. Some of these methods, including the most conventional, weather normalize energy demand.

These basic methods [1] rely on a modeled relationship between weather patterns and energy demand. The particular models used by the EEmeter are described more precisely in Modeling Overview.

## Modeling periods¶

For any savings calculation, the period of time prior to the start of any interventions taking place as part of a project we term the baseline period. This period is used to establish models of the relationship between energy demand and a set of factors that represent or contribute to end use demand (such as weather, time of day, or day of week) for a particular building prior to an intervention. The baseline becomes a reference point from which to make comparisions to post-intervention energy performance. The baseline period is one of two types of modeling period frequently occurring in the EEmeter.

The second half of the savings calculation concerns what happens after an intervention. Any post-intervention period for which energy savings is calculated is called a reporting period because it is the period of time over which energy savings is reported. A project generally has only one baseline period, but it might have multiple reporting periods. These are the second type of modeling period to frequent occur in the EEmeter.

The extent of these periods will, in most cases, be determined by the start and end dates of the interventions in a project. However, in some cases, the intervention dates are not known, or are ongoing, and must be modeled because they cannot be stated explicitly. We refer to models which account for the latter scenario as structural change models; these are covered in greater detail in Modeling Overview.

EEmeter structures which capture this logic can be found in the API documentation for eemeter.structures.

## Trace modeling¶

The relationship between energy demand and various external factors can differ drastically from building to building, and (usually!) changes after an intervention. Modeling these relationships properly with statistical confidence is a core strength of the EEmeter.

As noted in the background, we term a set of energy data points a trace, and a building or project might be associated with any number of traces. In order to calculate savings models, each of these traces must be modeled.

Before modeling, traces are segmented into components which overlap each baseline and reporting period of interest, then are modeled separately. [2] This creates up to $$n * m$$ models for a project with $$n$$ traces and $$m$$ modeling periods.

Each of these models attempts to establish the relationship between energy demand and external factors as it performed during the particular modeling period of interest. However, since the extent to which a model successfully describes these relationships varies significantly, these must be considered only in conjunction with model error and goodness of fit metrics Modeling Overview. Any estimate of energy demand given by any model fitted by the EEmeter is associated with variance and confidence bounds.

In practice the number of models fitted for any particular project might be fewer than $$n * m$$ due to missing or insufficient data (see Data sufficiency). The EEmeter takes these failures into account and considers them when building summaries of savings.

## Weather normalization¶

Once we have created a model, we can apply that model to determine an estimate of energy demand during arbitrary weather scenarios. The two most common weather scenarios for which the EEmeter will estimate demand are the “normal” weather year and the observed reporting period weather year. This is generally necessary because the data observed in the baseline and reporting periods occurred during different time periods with different weather – and valid comparisons between them must account for this. Estimating energy performance during the “normal” weather attempts to reduce bias in the savings estimate by accounting for the peculiarity (as compared to other years or seasons) of the relevant observed weather.

In an attempt to reduce the number of arbitrary factors influencing results, we only ever compare model estimates or data over that has occurred over the same weather scenario and time period. This helps (in the aggregate) to ensure equivalency of end use demand pre- and post-intervention.

## Savings¶

If the data and models show that energy demand is reduced relative to equivalent end use demand following an intervention, we say that there have been energy savings, or equivalently, that energy performance has increased.

Energy savings is necessarily a difference; however, this difference must be taken carefully, given missing data and model error, and is only taken after the necessary aggregation steps.

The equation for savings is always:

$$S_\text{total} = E_\text{b} - E_\text{r}$$

or

$$S_\text{percent} = \frac{E_\text{b} - E_\text{r}}{E_\text{b}}$$

where

• $$S_\text{total}$$ is aggregate total savings
• $$S_\text{percent}$$ is aggregate percent savings
• $$E_\text{b}$$ is aggregate energy demand as under baseline period conditions
• $$E_\text{r}$$ is aggregate energy demand as under reporting period conditions

Depending on the type of energy savings desired, the values $$E_\text{b}$$ and $$E_\text{r}$$ may be calculated differently. The following types of savings are supported:

### Annualized weather normal¶

The annualized weather normal estimates savings as it may have occurred during a “normal” weather year. It does this by building models of both the baseline and reporting energy demand and using each to weather-normalize the energy values.

$$E_\text{b} = \text{M}_\text{b}\left(\text{X}_\text{normal}\right)$$

$$E_\text{r} = \text{M}_\text{r}\left(\text{X}_\text{normal}\right)$$

where

• $$\text{M}_\text{b}$$ is the model of energy demand as built using trace data segmented from the baseline period.
• $$\text{M}_\text{r}$$ is the model of energy demand as built using trace data segmented from the reporting period.
• $$\text{X}_\text{normal}$$ are temperature and other covariate values for the weather normal year.

### Gross predicted¶

The gross predicted method estimates savings that have occurred from the completion of the project interventions up to the date of the meter run.

$$E_\text{b} = \text{M}_\text{b}\left(\text{X}_\text{r}\right)$$

$$E_\text{r} = \text{M}_\text{r}\left(\text{X}_\text{r}\right)$$

where

• $$\text{M}_\text{b}$$ is the model of energy demand as built using trace data segmented from the baseline period.
• $$\text{M}_\text{r}$$ is the model of energy demand as built using trace data segmented from the reporting period.
• $$\text{X}_\text{r}$$ are temperature and other covariate values for reporting period.

### Gross observed¶

The gross observed method estimates savings that have occurred from the completion of the project interventions up to the date of the meter run.

$$E_\text{b} = \text{M}_\text{b}\left(\text{X}_\text{r}\right)$$

$$E_\text{r} = \text{A}_\text{r}$$

where

• $$\text{M}_\text{b}$$ is the model of energy demand as built using trace data segmented from the baseline period.
• $$\text{A}_\text{r}$$ are the actual observed energy demand values from the trace data segmented from the baseline period. If the actual data has missing values, these are interpolated using gross predicted values (i.e., $$\text{M}_\text{r}\left(\text{X}_\text{r}\right)$$).
• $$\text{X}_\text{r}$$ are temperature and other covariate values for reporting period.

## Aggregation rules¶

Because even an individual project may have multiple traces describing its energy demand, we must be able to aggregate trace-level results before we can obtain project-level or portfolio-level savings. Ideally, this aggregation is a simple sum of trace-level values. However, trace-level results are often littered with messy results which must be accounted for; some may be missing data, have bad model fits, or have entirely failed model builds. The EEmeter must successfully handle each of these cases, or risk invalidating results for entire portfolios.

The aggregation steps are as follows:

1. Select scope (project, portfolio) and gather all trace data available in that scope

2. Select baseline and reporting period. For portfolio level aggregations in which baseline and reporting periods may not align, select reporting period type and use the default baseline period for each project.

3. Group traces by interpretation

4. Compute $$E_\text{b}$$ and $$E_\text{r}$$:

1. Compute (or retrieve) $$E_\text{t,b}$$ and $$E_\text{t,r}$$ for each trace $$\text{t}$$.
2. Determine, for each $$E_\text{t,b}$$ and $$E_\text{t,r}$$ whether or not it meets criteria for inclusion in aggregation.
3. Discard both $$E_\text{t,b}$$ and $$E_\text{t,r}$$ for any trace for which either $$E_\text{t,b}$$ or $$E_\text{t,r}$$ has been discarded.
4. Compute $$E_\text{b} = \sum_{\text{t}}E_\text{t,b}$$ and $$E_\text{r} = \sum_{\text{t}}E_\text{t,r}$$ for remaining traces. Errors are propagated according to the principles in Error propagation.
5. Compute savings from $$E_\text{b}$$ and $$E_\text{r}$$ as usual.

### Inclusion criteria¶

For inclusion in aggregates, $$E_\text{t,b}$$ and $$E_\text{t,r}$$ must meet the following criteria

1. If ELECTRICITY_ON_SITE_GENERATION_UNCONSUMED, which represents solar generation, is available, and if solar panels were installed as one of the project interventions, blank $$E_\text{t,b}$$ should be replaced with 0.
2. Model has been successfully built.

## Error propagation¶

Errors are propagated as if they followed $$\chi^2$$ distributions.

## Weather data matching¶

Since weather and temperature data is so central to the activity of the EEmeter, the particulars of how weather data is obtained for a project is often of interest. Weather data sources are determined automatically within the EEmeter using an internal mapping [3] between ZIP codes [4] and weather stations. The source of the weather normal data may differ from the source of the observed weather data.

There is a jupyter notebook outlining the process of constructing the weather data available here.

 [1] Additional information on why this method is used in preference to other methods is described in the Introduction.
 [2] This is not quite true for structural change models. This is covered in more detail in Modeling Overview.
 [3] Available on github.
 [4] The ZIP codes used in this mapping aren’t strictly ZIP codes, they’re actually ZCTAs.