Introduction – motivation
Imagine you’re trying to figure out how outside air temperature (OAT) and time-of-week affect energy consumption in a building. With a “common sense” approach, you’d need to test each factor separately—keeping all other variables constant while changing just one. But in the real world, things don’t work that neatly. Inputs like OAT and time-of-week change simultaneously, creating a noisy, messy dataset.
To illustrate this, we’ll use a real-world dataset showing main electricity consumption (kW) alongside OAT (°C). Even at a quick glance, it’s clear that energy use increases during the summer—most likely due to cooling loads. But let’s dig deeper.
In the traditional workflow, analysts often begin by plotting a scatter chart of OAT against energy consumption, using monthly or weekly averages using methods such as degree days or ASHRAE changepoint. However, evaluation of aggregated data does not provide any insight into intraday energy consumption profile. So you need to analyse hourly data. But when we move to hourly data, variability skyrockets, see chart below. For instance, at an OAT of 26 °C during a typical workday, observed consumption can swing anywhere from 60 kW to 130 kW. With such a wide range, pinpointing expected usage becomes nearly impossible without accounting for more than just temperature.
Energy use isn’t driven solely by temperature – it also follows a time-of-week schedule (office hours, weekends, nights). Hot afternoons often coincide with peak operating hours, making it difficult to untangle these overlapping influences. Simply comparing “temperature vs. load” merges two distinct patterns together.
This is where machine-learning models like TOWT come in. By simultaneously fitting both time-of-week and temperature effects, the model learns, for example, that a 30 °C Tuesday at 3 PM will draw more energy not only because it’s hot (cooling demand) but also because it’s mid-afternoon on a workday (higher occupancy).
A helpful analogy is listening to an orchestra. To the untrained ear, it’s a single wall of sound. But experienced listeners can pick out individual instruments, rhythms, and harmonies. TOWT does the same with energy data: it separates overlapping signals so we can understand them in isolation.
Technical detail part
The original concept was introduced by Price in “Methods for Analyzing Electric Load Shape and its Variability” (Lawrence Berkeley National Laboratory Report LBNL-3713E, May 2010) https://eta-publications.lbl.gov/sites/default/files/LBNL-3713E.pdf Since then, it has been widely adopted—cited in numerous academic papers and implemented in open-source tools like RMV2.0 (LBNL), NMECR (kW Engineering), and OpenDSM (formerly OpenEEmeter). It’s also a core part of the CalTRACK Methods and features in several commercial tools, including our own at Energy Twin.
At Energy Twin, we’ve built on the original idea, developing several extensions to make the model more useful in real-world applications—especially where high granularity and robustness are essential.
Weather dependency
Let’s focus on one of those key influences: weather dependency.
Once the TOWT model has separated schedule and temperature effects, we can extract the pure weather-dependent load. This final step reveals how much additional energy consumption is driven specifically by outdoor temperature, plotted separately for occupied and unoccupied days.
By breaking down these intertwined effects, we gain a much clearer understanding of how weather truly impacts energy consumption – a crucial insight when moving from simpler, monthly models to more granular hourly or daily analyses, just compare the graph above with the hourly scatter plot data.
Time-of-Week Dependency
When working with TOWT (Time-Of-Week and Temperature) models, it’s just as important to account for time dependent load – patterns driven not by weather, but by routine. These time-of-week (TOW) driven variations reflect predictable behaviors: office occupancy, operational schedules, or equipment cycles. They repeat week after week, regardless of outdoor conditions.
When modeling the time dependent load – each hour of the week (or 15-minute, 5-minute interval) is treated as a distinct category, allowing the model to capture patterns in energy consumption independently of weather influences. These are typically related to occupancy, schedules, or equipment cycles.
For those who want to dig a bit deeper into the technical side…
To represent these categorical time periods numerically, one-hot encoding (OHC) is used. Using this technique, we transform each time interval into a binary vector where only the element corresponding to the current time slot is set to 1 and all the others are 0. These vectors serve as independent variables in the resulting regression model, enabling it to learn separate baseline consumption levels for each time period. This article provides a clear illustration of how one-hot encoding works, along with simple examples. https://www.geeksforgeeks.org/ml-one-hot-encoding/
Granularity – How precise should your time model be?
The TOWT model reflects multiple levels of temporal granularity, depending on the available data and the desired resolution of analysis. Time-of-week OHC can be constructed at different intervals—such as hourly, 15-minute, or even 5-minute.
Choosing the appropriate resolution is a tradeoff between capturing time-sensitive variability and maintaining model stability. As you can see in graph above, moving from hourly to 15-minute granularity makes a significant difference, revealing much finer operational patterns – such as short-duration spikes or control system behavior.
Variants of TOW Modeling
Each building may require a different definition of the TOW structure, depending on how complex its operational schedule is and how much historical data is available. For facilities with consistent, predictable usage, a simple approach – such as a single daily profile repeated across the week – might be sufficient. But this isn’t suitable for most commercial buildings, which tend to follow more varied routines. A more common approach is the typical TOWT, which assigns a separate profile to each day of the week, allowing the model to reflect different usage on weekdays versus weekends. For even higher fidelity, the model can incorporate custom day types – such as holidays, maintenance periods, or seasonal shutdowns – by adding binary indicators or grouping time slots differently.
Conclusion
The Time-of-Week and Temperature (TOWT) model has become a widely recognized and trusted approach for detailed energy consumption modeling. One of its greatest strengths lies not just in its predictive accuracy, but in its transparency.
Unlike many black-box machine learning models—such as neural networks—that may yield high performance but little interpretability, TOWT offers clear, explainable parameters. These include distinct components for weather-dependent loads and time-of-week-dependent loads, which provide valuable insights into the underlying behavior of a building. In essence, you’re not just getting a forecast—you’re gaining a deeper understanding of how and why a building consumes energy the way it does.
This interpretability is critical in real-world energy analytics, where decision-makers need to justify savings, uncover inefficiencies, and tailor operational strategies based on specific drivers. For example, knowing how much of a building’s load is due to weather (e.g., cooling demand) versus operational schedules (e.g., peak working hours) enables targeted energy-saving measures.
Thanks to its balance between statistical rigor and practical insight, TOWT remains a cornerstone method for analysts, auditors, and engineers working on high-resolution, actionable energy models.
