A multi-scale calibration approach for process-oriented aggregated building energy demand models

Accepted Manuscript

A Multi-Scale Calibration Approach for Process-Oriented Aggregated Building Energy Demand Models Z. Todd Taylor , Yulong Xie , Casey D. Burleyson , Nathalie Voisin , Ian Kraucunas PII: DOI: Reference:

S0378-7788(18)33095-0 https://doi.org/10.1016/j.enbuild.2019.02.018 ENB 9041

To appear in:

Energy & Buildings

Received date: Revised date: Accepted date:

9 October 2018 29 January 2019 17 February 2019

Please cite this article as: Z. Todd Taylor , Yulong Xie , Casey D. Burleyson , Nathalie Voisin , Ian Kraucunas , A Multi-Scale Calibration Approach for Process-Oriented Aggregated Building Energy Demand Models , Energy & Buildings (2019), doi: https://doi.org/10.1016/j.enbuild.2019.02.018

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Highlights 

BEND responds to changes in climate, population, and building technology.

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Once calibrated, BEND captures interannual changes in building energy

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consumption. 

BEND simulates changes in peak energy demand better than a statistical model.

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Aggregated building energy models need to be calibrated at the scale they will be

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applied.

Corresponding author address: Z. Todd Taylor, Pacific Northwest National Laboratory, PO Box 999/MS K1-90, Richland, WA 99352. E-mail: [email protected]. Phone: 509-375-2676.

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A Multi-Scale Calibration Approach for ProcessOriented Aggregated Building Energy Demand

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Models

Z. Todd Taylor, Yulong Xie, Casey D. Burleyson, Nathalie Voisin, and Ian

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Kraucunas

Pacific Northwest National Laboratory, Richland, Washington

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Revision Submitted to Energy and Buildings

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Abstract

Long-term energy planning relies largely on projections of future energy demand and

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hourly load profiles. Aggregate building models are increasingly being utilized to characterize the sensitivity of current and future building stocks to changes in climate,

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population, and building technology on city-to-regional-to-national scales. Due to

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challenges in the availability of data, those analyses have been limited to projection of energy demand at a single scale, usually state or country, while long-term planning power system models and production cost models might operate at different spatial scales such as energy regions which are focused on ensuring adequate generation infrastructure. We propose and evaluate a novel method to calibrate an aggregate building energy demand model (PNNL’s BEND model) against the best available data at the spatial scale of

ACCEPTED MANUSCRIPT 3 balancing authorities. This approach extends previous work on aggregated building energy demand by facilitating analysis of building energy demand across scales, in particular policy and operational decision-making scales. We show that the bias-corrected model estimates building electric loads reasonably well compared with estimates from a

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statistical model, but has the additional feature of flexibility across spatial scales. While the calibration approach is presently U.S.-centric and associated with U.S. energy

regions, it can be extrapolated to other worldwide regions with similar scale challenges between policy and operational implementation decision making. We discuss the

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significant challenges involved in formulating and calibrating a complex physical model based on simulations of roughly 100,000 individual buildings against available aggregate regional electric load data and highlight areas for potential future work and improved data

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Keywords

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collection.

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Aggregate building energy modeling, BEND, EnergyPlus, EIA, calibration, WECC

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Introduction Accurately representing electricity demand over a range of spatial and temporal scales is critical for long-term power system planning and operations. Future electricity

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demands are most often projected based on assumed changes in population, projected cooling and heating degree days (Franco and Sanstad 2007; Wang and Chen 2014; Bartos et al. 2016; Huang and Gurney 2016; Auffhammer et al. 2017), and sometimes assumed technology changes such as new building and appliance efficiency codes and the

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incorporation of demand response technologies (Northwest Power and Conservation Council’s 7th power plan 20161). Global integrated assessment models tend to

independently project the different components of aggregate electricity demand (Zhou et

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al. 2013). Those projections either are regression-based or leverage Building Energy Simulation (BES) models. Those projections are most often performed at the scales of the

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drivers of changes (e.g., states or countries for changes in population, climate zones for changes in temperature, or energy regions for some technology shocks). Those scale-

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specific projections can limit the analysis of combinations of changes in the various

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drivers and limit the translation of the projected changes into power system models such as unit commitment and economic dispatch, and grid expansion models for decision-

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making by utilities and investors.

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https://www.nwcouncil.org/energy/powerplan/7/plan/

ACCEPTED MANUSCRIPT 5 Since regression-based projections are inherently scale-specific, we focus more specifically on BES models such as EnergyPlus (Crawley et al. 2001), which are commonly used to design buildings, evaluate building codes, and assess the impacts of design differences and/or intelligent controls on average and peak energy demand from

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individual buildings or small sets of buildings. Recently, BES-based studies aimed at long-term planning have begun to emerge (Wang and Chen 2014; Dirks et al. 2015;

Burillo et al. 2017; Shen 2017), including novel advances in the use of BES to simulate

very large populations of buildings from city to regional scales. For example, Richman et

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al. (2014) used cloud computing to simulate over a million of individual houses in the city of Toronto, while Davila et al. (2016) used simulations of ~83,000 individual buildings to model energy demand in the city of Boston. Reinhart and Davila (2016)

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wrote review of urban-scale modeling efforts and more recent efforts include Chen et al. (2017) who developped CitiBES , a web-based data and computing platform focusing on

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energy modeling and analysis of a city's building stock to support district or city-scale efficiency programs. Tarroja et al. (2018) developped BES at the scale of the state of

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California to support state-scale long-term energy planning while PNNL (2011),

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Fernandez et al. (2017), Xie et al (2018a), and Dirks et al. (2015) focused on simulations at the electricity grid scales. Dirks et al. (2015) used an aggregate building energy model

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based on ~26,000 individual buildings to project the impact of future climate changes on total building energy. These studies are based on hundreds of thousands runs of EnergyPlus models that are designed to be representative of the total building stock over a given region, but were not formally calibrated against aggregated building energy demand. While prior work has convincingly demonstrated their utility, there has been

ACCEPTED MANUSCRIPT 6 little to no work exploring the scientific challenges of calibrating the output of these large populations of building simulations, particularly at multiple scales. Calibration is an important component of physical models, which are better suited to projecting future changes compared to statistical models that are typically trained on existing data and thus

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may not capture emerging patterns or non-linearities that are unlike the training

observations. The calibration of individual buildings in EnergyPlus and other BES

models against measured data at the building scale has been the subject of extensive

research (e.g., ASHRAE Guideline 14-2002; Reddy 2006; Lin and Hong 2013; Coakley

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et al. 2014; Fabrizio and Monetti 2015; Royapoor and Roskilly 2015; Sun et al. 2016; Glasgo et al. 2017) of which Ruiz and Bandera (2017) provide a nice review. These calibration studies have assessed BES effectiveness for retrofit applications, controls

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studies, and studies of specific building components and technologies at the scale of individual buildings. They do not necessarily support the assumption that the individual

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building calibration will automatically translate to larger scales when aggregating

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buildings.

In this paper we aim to understand and quantify the errors in the estimates of

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aggregated regional building energy demand, including both average and peak load, based on the aggregation of many individual building models that are designed to

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represent the true building stock over the region. We propose and evaluate a novel method to calibrate an aggregate building energy demand model at regional scales (multiple states and/or load balancing areas) against the best available data at the spatial scale of balancing authorities. This approach extends previous work on aggregated building energy demand by facilitating analysis of building energy demand across scales,

ACCEPTED MANUSCRIPT 7 in particular policy (i.e., states) and operational decision-making scales (i.e., input to power system models). The experiment provides a framework for better understanding how technology innovation and individual building calibration aggregates to larger scales for studying, for example, grid resilience or capacity expansion needs. We present a two-

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step calibration applied to Pacific Northwest National Laboratory’s Building ENergy

Demand (BEND) model (Dirks et al. 2015; Burleyson et al. 2017), a regional-scale BES modeling framework, over the Western Electricity Coordinating Council (WECC)

interconnection. We then evaluate the ability of the model to represent overall average

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energy and peak demand using a calibration-evaluation experiment over two years with

varying weather conditions (2007 and 2010). We close by discussing the data needed to expand on such calibration approaches with a focus on long-term capacity expansion

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Data and Models

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planning.

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Spatial and Temporal Domains

Our calibration experiment is performed over the WECC (Fig. 1). The WECC is

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split over three countries including two provinces in Canada (British Columbia and Alberta), portions of 11 states in the U.S. (Washington, Oregon, California, Idaho,

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Montana, Colorado, Wyoming, Nevada, Utah, New Mexico, Arizona) and the state of Baja California in Mexico. The WECC includes 29 balancing authorities in which the load must be balanced at all times by local generation first (Fig. 1d). The domain encompasses diverse climates and associated unique building insulation characteristics

ACCEPTED MANUSCRIPT 8 and the necessary reported data (discussed later) are readily available for most of the region. Based on the availability of both weather data to force the model and the target

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energy consumption data needed for calibration, we selected two calendar years with sizable weather differences (2007 and 2010) for our calibration-validation experiment. Figure 2 shows the population-weighted monthly-mean temperature for both years.

County-level populations used in the weighting were obtained from the U.S. Census

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Bureau’s “County Intercensal Tables” data (https://www.census.gov/data/datasets/timeseries/demo/popest/intercensal-2000-2010-counties.html; accessed 29-Feb 2016). On average, the WECC was generally warmer in 2007 than 2010, particularly during the spring and summer months. An analysis of the spatial variability of the changes in

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temperature confirmed that these year-to-year changes were observed broadly across the entire WECC (not shown). Based on this we expect a priori that building energy

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consumption will decrease in most of the WECC from 2007 to 2010.

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Formulaion of the BEND Model

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Details on the formulation of the BEND model are extensively documented in (Xie et al. 2018b). Here we summarize some of the key pieces necessary for

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understanding this study and in particular understanding how the formulation of the model leads to inherent uncertainties in the predictions it makes. The construction of BEND is similar to other abstraction methods used in aggregate building modeling (e.g., Dall’O’ et al. 2012; Davila et al. 2016; Österbring et al. 2016; Reinhart and Davila 2016). The base set of buildings are represented by four high-level characteristics: type, size, vintage, and location. We use a suite of 16 building types (11 commercial and five

ACCEPTED MANUSCRIPT 9 residential), 6 size bins, 7 vintage bins, and 15 sub-regions across the U.S. to account for regional diversity in the building stock. The details of these categories are given in Xie et al. 2018b. The various combinations of these four high-level features leads to 672 (e.g., 16×6×7) representative buildings in each of the 15 regions across the U.S. These

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representative buildings are then translated into prototype buildings that have the general architecture and footprint of the actual buildings they are meant to represent, but detailed information about the construction and operation of these buildings (e.g., insulation

levels, internal loads and schedules, mechanical systems, etc.) are inferred from the four

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high-level characteristics. The inferred parameters are derived from the Commercial

Buildings Energy Consumption Survey (CBECS; EIA 2003) and Residential Energy Consumption Survey (RECS; 2009) databases. Although the sample of representative and

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prototype buildings is large, there is inherent uncertainty in relying on a statistical subset of the true building stock in a given region, which we discuss in a later section.

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Another critical input for large scale BES models is the total number of buildings

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within each energy region. For the BEND model, each simulated building can be thought of as a representative sample of the many real buildings that make up the true building

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stock. When aggregating the output of an initial set of EnergyPlus runs, each simulated building must be weighted appropriately to reflect the number of actual buildings it

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represents. The CBECS and RECS databases contain weights that represent the number of similar buildings each surveyed building represents. These weights are aggregated and adjusted to mirror the simplifications inherent in aggregated building energy demand models (i.e., grouping buildings into sets based on type, size, vintage, and location), to account for the introduced variation in, for example, HVAC systems, and to reflect the

ACCEPTED MANUSCRIPT 10 changes in spatial scale when configuring the model for different regions. Uncertainty inevitably arises from propagating the weights, which are themselves statistical bestguesses based on survey data, through the pre-simulation setup of BEND.

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The 15 BEND regions in the U.S. are defined in terms of the intersection (overlapping counties) of Energy Information Agency (EIA) climate zones and

International Energy Conservation Code (IECC) climate zones (Fig. 1a, b). The set of

representative buildings in a BEND region must be matched with one or more weather

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stations that provide the external forcing for the simulations in these regions. Those

weather stations must be distributed appropriately in order to adequately capture climate variability. The selection of representative weather stations is as important as the selection of representative buildings in managing the tradeoff between computational

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burden and detailed coverage of weather in each region. This tradeoff was explored in a companion paper (Burleyson et al. 2017). Based on this prior analysis, we chose to use a

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total of 32 weather stations; four stations in each of the eight IECC climate zones in the

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WECC (Fig. 1a). After dropping two stations due to a lack of data, 30 stations were ultimately used to force the individual building models. Each county in the WECC is

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mapped to the closest weather station within the same IECC climate zone.

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Each prototype building in a given BEND region is simulated using forcing from

all of the weather stations that map to counties in that region. Spatially, the unique combination of weather stations and BEND regions, of which there are 50 in the WECC (Fig. 1c), form the smallest spatial unit in BEND. The unique combinations of weather stations and prototype buildings determines the total number of EnergyPlus simulations required. We refer to these unique combinations as simulation-ready building models.

ACCEPTED MANUSCRIPT 11 There are 96,307 simulation-ready building models in the WECC (Table 1). Each of the simulation-ready building models was simulated for both 2007 and 2010 using EnergyPlus version 7.2, with each simulation taking roughly two minutes of wall-clock

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time on PNNL’s supercomputer – a sizable but tractable computational burden. The relevant output of each of the 96,307 simulation-ready building models is an 8760-hour (one year) time series of electricity consumption for the simulated building. In each of the 50 spatial units the 8760-hour electricity consumption profiles produced by

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the many EnergyPlus runs were aggregated separately into residential and commercial profiles for both 2007 and 2010. The aggregation is a simple weighted sum across

buildings at each hour of the year using the building weights derived from CBECS and RECS. The aggregation leads to 50 pairs (commercial and residential) of 8760-hour

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consumption profiles for each of the two years, one pair for each of the 50 spatial units.

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The best available observational data for this analysis is electricity consumption at the spatial scale of balancing authorities (BAs; Fig. 1d and Table 2). An individual utility

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might operate under different BA regions and the reported load at the BA scale already takes into account the potential splitting of utility loads onto electricity management

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regions to ensure consistency. We obtained the reported load data for both years from the

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EIA. Two types of necessary data are available from the EIA for most BAs: hourly total electricity consumption (Federal Energy Regulatory Commission [FERC] Form No. 714 dataset; https://www.ferc.gov/docs-filing/forms/form-714/data.asp; accessed 14-Jun 2016) and monthly total electricity consumption segregated into residential, commercial, industrial, and “other” sectors (EIA Form 861M dataset; https://www.eia.gov/electricity/data/eia861m/; accessed 10-Jun 2016).

ACCEPTED MANUSCRIPT 12 While there were nominally 29 BAs in the WECC during our years of study, our analysis focuses on the 19 BAs for which hourly load data was available for our target years. Collectively, these 19 BAs cover roughly 85% of the population of the WECC and roughly 80% of the total simulated demand, so we do not expect our exclusion of the 10

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small (by population and load) BAs to influence our overall results or conclusions. The

unavailability of disaggregated hourly load data (i.e., hourly energy demand segregated into residential, commercial, and industrial loads) is a key obstacle for both the

calibration of BEND as well as other efforts to estimate aggregate building energy

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demand. Absent such data, we used the monthly disaggregated load data to split the

hourly total electricity consumption into residential, commercial, industrial, and other components using the simplifying assumption that the load fraction for each of these

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components does not change throughout the month or by time of day. An evaluation of the sectoral disaggregation of the EIA target data is included in Section S1 of the

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Supplemental Material.

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The BEND simulation results need to be scaled to match the spatial scale of the BAs before analyzing bias in the model. Generally speaking, the 50 spatial units of

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BEND have no direct spatial mapping to BAs. However, both the BEND spatial units and the BAs can be considered aggregations of counties. Therefore, we used counties as an

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intermediate spatial unit to convert between the spatial scales in BEND and the spatial scales of the BAs that provide our target data. Counties are a useful intermediate scale because they have clearly defined boundaries and many useful related datasets (e.g., population) are available at the county level. Because population is a major driver of building energy demand, county-level populations were used to proportionally distribute

ACCEPTED MANUSCRIPT 13 the aggregated commercial and residential load profiles to all of the counties that make up each spatial unit in BEND. Once the load profiles were disaggregated to the county level, a simple summation of loads from each county in a given BA generated the base data product for our bias correction analysis: a pair of commercial and residential hourly

Calibration-Validation Approach

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load profiles for each BA that can be evaluated against the target data from the EIA.

Aggregated building energy demand models such as BEND simulate a large

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number of individual building models that are combined and weighted so as to represent the true building stock in a given area. When individual buildings are modeled with EnergyPlus, accurate model inputs could, at least theoretically, be derived from the actual

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buildings involved - known building construction characteristics, equipment and mechanical systems installed, operation schedules, and occupant behaviors. Likewise, the

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actual energy consumption of those buildings could, at least theoretically, be available from building management systems, monitoring sensors, loggers and recorders, or, in

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aggregate form, from utility billing data. Additionally, it is relatively straightforward to

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identify a nearby weather station that represents the actual weather conditions that a single individual building is experiencing. The key challenge of calibrating an aggregate

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model like BEND is that most of these data are not available for the entire set of simulated buildings or for the region(s) of interest. Aggregate building models have particular features that require unique treatment

for devising a calibration approach. These largely stem from the fact that they blend a physically-based model (EnergyPlus) with a high-level formulation that is statistical in

ACCEPTED MANUSCRIPT 14 nature. Despite careful formulation, the simplifying assumptions made during the setup of aggregate BES naturally lead to differences between the simulated and observed building loads. There are at least four clear sources of bias:

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1) Relying on a statistical subset of buildings to represent the whole building stock in a region: Because it is impossible to simulate all real buildings in a given region, aggregate BES relies on abstract representative buildings designed to mirror the characteristics of the true building stock. Although the sample of representative

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buildings is large, on the order of 100,000 unique EnergyPlus building models, it is still a statistical abstraction and thus subject to representativeness issues. Similarly, because the representative building stock is informed by the large-scale CBECS and RECS databases, there are uncertainties in the total number of real

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buildings that each representative building is meant to represent.

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2) The necessity of up- or downscaling from spatial scales for which input data are available to the scales needed for calibration and decision-making: Because the

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formulation of the model requires input data on multiple spatial scales that do not map directly to the best available spatial scales for calibration, BES and BEND in

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this case relies on a simiplifed scaling approach using population to cross up or

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down a broad range of spatial scales.

3) The need to adequately represent regional weather variability while maintaining a tractable number of weather stations and simulations: Unlike traditional building modeling in which the weather forcing file attached to the simulation can be imagined as being co-located with the simulated building, as an aggregate regional model BEND’s fidelity depends on selecting an appropriate number of

ACCEPTED MANUSCRIPT 15 representative weather stations in order to adequately capture natural climate variability, variability that is baked into the observed building loads against which BEND is judged, within a simulated region.

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4) The lack of perfect baseline data against which to calibrate the aggregate model: Data that capture aggregate regional building loads with appropriate segregation by sector (e.g., residential, commercial, etc.) are often hard to find, incomplete, or not directly comparable. As such there are limited targets to calibrate the model

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and ensure it generates the right answer for the right reason.

Rather than addressing or quantifying these sources of bias independently, we opted for the more straightforward approach of lumping all sources of bias together and correcting the finished product. We used a simple scaling approach to correct these

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biases. For each BA, separate scaling factors were derived for the residential and

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commercial consumption profiles in BEND on both a monthly and hourly basis using the 2007 EIA data. Scaling factors were calculated as the ratios between the EIA target data

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and the BEND output for each month and hour. We did not include separate scaling factors by daytype (e.g., day of week) because the explicit schedules used to drive the

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energy simulations largely capture the weekday-weekend load differences and we wished

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to avoid over-specifying the calibration with a huge number of scalars. A total of 288 (12 months × 24 hours) scaling factors were calculated for each of the residential and commercial profiles in each BA. The scaling factors are derived following Eq. 1:

[Eq. 1]

∑ ∑

{

{

}

ACCEPTED MANUSCRIPT 16 Where EIA and BEND represent the hourly load time series of a year from the EIA reported values and the BEND simulated values; type is the type of the load (residential or commercial), m is the month index from 1 to 12, h denotes the hour of day from 1 to

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24, and d represents the day index from 1 to the number of days in a given month. To evaluate the fidelity of this calibration approach, the scaling factors developed from the 2007 data were then applied to the 2010 BEND simulation to generate calibrated results for comparison with the corresponding 2010 EIA target data. This involves a

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simple multiplication between the scaling factors and the 2010 BEND output by month and hour. Our calibration-validation approach is functionally similar to separating data into training and evaluation subsets, a common approach in statistical modeling. It was

assumed that there was no significant change in the building stock between the two years,

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although we acknowledge that changing economic conditions may have influenced the

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between-year load differences in ways that BEND is unable to directly capture. We also constructed a simple statistical model, a LOESS regression that related

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the observed temperatures in 2007 to the observed residential and commercial building loads for each BA, which we use to benchmark the calibrated version of BEND. The

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statistical model is taken as a representative, albeit simplified, example of a more typical

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approach to predicting aggregate building energy demand. The comparison with the statistical model is described in more detail in Section 3.4.

Results Uncalibrated Energy Demand

ACCEPTED MANUSCRIPT 17 An initial analysis of the uncalibrated version of BEND shows both the promise and shortcomings of the uncalibrated model. Figure 3 shows a comparison of the uncalibrated BEND estimate of the total monthly building load, the sum of the residential and commercial building loads, to the EIA target data for a single BA (BA 16; Arizona

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Public Service Co. [AZPS]). Throughout this section we use this single BA as an

illustrative example. The results for other BAs are similar and are included in the Supplemental Material. In the case of BA 16, the uncalibrated version of BEND

overestimates the total building load in all months. This is characteristic of the majority

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of the BAs, although several produce underestimates or only small differences.

The scaling factors quantify the magnitude of the bias. Figure 4 shows the commercial and residential scaling factors by month and hour for BA 16. There are

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obvious systematic biases as a function of both time of year (represented by month) and time of day. BEND’s estimates for commercial buildings substantially exceed the

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reported loads while the residential estimates are substantially lower than the reported

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data. The scaling factors of all 19 BAs with adequate data are shown in Figs. S8-S9 in the Supplemental Material. Although there are notable and apparently systematic biases in all

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BAs, this is somewhat expected given the assumptions made in constructing the model. It does not mean that BEND does not have the ability to predict changes in energy demand

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associated with different weather and climate patterns, which is the key quantity that we are ultimately interested in. Calibrated Energy Demand To evaluate the usefulness of a simple scaling factor, in which the calibration is agnostic to the specific sources of the systematic biases, the scaling factors calculated

ACCEPTED MANUSCRIPT 18 from the 2007 data were applied to the raw BEND residential and commercial hourly energy profiles for the year 2010. These calibrated hourly profiles were aggregated and analyzed to obtain annual energy totals and peak loads to be compared against the target EIA values for 2010. Table S1 gives the EIA-reported and BEND-estimated annual total

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electricity consumption and peak demand for each of the BAs. The relative biases of the BEND estimates, expressed as percentages relative to the target data, are also calculated and are shown in Fig. 5.

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From Table S1 and Fig. 5 we can see that the BEND estimates of the annual total electricity consumption have a mean absolute bias of 2.6%, a maximum positive bias of 7.3%, and a maximum negative bias of 7.4% across all 19 BAs. The relative biases of BEND estimates of peak demand are larger, ranging from a 22.1% overestimation in BA

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135 to a 4.6% underestimate in BA 53. On average, BEND’s peak load is overestimated by 7.4%, a similar magnitude bias as the 6.5% average underestimate using the LOESS

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model. The date of the peak demand in BEND was identified within ±1 day of the EIA

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peak demand in 12 of the 19 BAs. By contrast, the statistical model was able to identify peak demand within ±1 day in eight of the BAs. Section S3 of the Supplemental Material

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gives additional details comparing the performance of BEND with the statistical model.

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So far we have focused on common uncertainty indices such as the mean bias

error (MBE) and normalized mean bias errors (NMBE). Another common metric is the Coefficient of Variation of Root Mean Square Error (CV[RMSE]), which measures the variability of the errors. The American Society of Heating, Refrigerating and AirConditioning Engineers (ASHRAE) Guide 14 recommends Mean Bias Error (MBE) values within ± 5% and CVRMSE values below 10% (see, for example, Garrett and New,

ACCEPTED MANUSCRIPT 19 2016). Ruiz and Bandera (2017) also provide a review of those metrics and how they have been used in various energy demand model analyses. The average CVRMSE across all balancing authorities was 9.9%, meaning that on an hour-by-hour basis BEND simulated an aggregate building energy demand bias of less than 10%. The maximum

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CVRMSE value, ~16%, occurred in the El Paso Electric Company (EPE) balancing

authority. In general, the CVRMSE metric closely resembles the map of peak demand

biases shown in Fig. 5b, largely due to the metrics’ inherent sensitivity to larger biases

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(not shown).

Similar energy consumption and peak demand statistics were also calculated by season and are shown in Table S2 and Figs. 6-7. The relative biases in seasonal total energy consumption are comparable to the annual estimates, with an average bias smaller

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than 1% and only one case larger than 10%. The relative biases of the seasonal peak demand estimates are greater than those on an annual basis, ranging from a 17%

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underestimate to a 37% overestimate. This is unsurprising since peak estimates come

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from a single day and hour’s load, while seasonal and annual loads benefit from the cancelling effects of averaging across many days and hours. BEND was somewhat better

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at identifying the seasonal peak demand days during spring and fall compared to summer and winter. This may be a result of the year-to-year variations in weather extremes being

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more pronounced in the very hot and very cold months compared to the milder swing seasons.

Figure 8 shows the distributions of the relative biases of hourly loads for both years and all BAs. Each box-and-whisker plot shows the median of its data as a horizontal line within the box. The box extends outward to the first and third quartiles,

ACCEPTED MANUSCRIPT 20 meaning the box holds 50% of the data. The whiskers extend to the last data point within 1.5 times the inter-quartile range of the median. Data beyond 1.5 interquartile ranges are plotted separately. Both years are shown because although the monthly (and hence annual) sums of the 2007 BEND estimates are constrained to match the target data via

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our calibration approach, the scaling approach does not prohibit significant differences in individual hourly load estimates. Several observations can be made from Fig. 8. First,

most of the biases are within +/-15% (see dashed lines). Second, the magnitudes of the variation in biases are comparable between 2007 and 2010, which suggests that the

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calibration technique performs similarly for both the calibration and verification years. Third, while the median biases in 2007 are all close to zero, as would be expected

because the calibration coefficients were developed on the 2007 data, the median biases

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in 2010 deviate from zero and the deviations are substantial for some BAs. The monthly, seasonal, and annual aggregates of both total energy consumption

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and peak demand for the entire WECC during 2010 from the BEND estimates and the

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EIA target data are given in Table 3. BEND’s total annual energy consumption exceeds the EIA baseline by 1.8%. At seasonal and monthly levels BEND’s estimates show biases

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ranging from near zero to a seasonal maximum of 2.9% during the spring and a monthly maximum of 3.8% during November. These relative biases are similar in magnitude to

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most of the biases at the BA level (Tables S1-S2). In almost every case, BEND’s energy and peak demand estimates for the whole WECC are higher than the EIA baseline. Annually, BEND’s peak demand is biased high by 6.1%, while seasonal estimates range between 6.1% and 10.9% and monthly estimates between 2.5% and 10.9% larger than the recorded data. The date of the peak demand in the WECC was estimated correctly by

ACCEPTED MANUSCRIPT 21 BEND for the annual peak, for 75% of the seasonal peaks, and for 66% of the monthly peaks. Capturing Changes in Energy Demand

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The primary purpose of the two-year experiment was to determine how well BEND, which is based on a first-principles approach to simulating energy and peak loads, can be calibrated to match observed data across two different weather years. Figure 9

shows how BEND’s estimation of the change in building loads between 2007 and 2010

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compares to the observed change from the EIA reported loads. If there were perfect

correlation between the calibrated BEND estimates and the observed data then all of the BAs would fall along the 45° line. Encouragingly, most of the BAs fall close to the 45° line, indicating that, after calibration, BEND is largely able to adequately capture changes

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in total building loads due to year-to-year variations in weather. However, a few BAs

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show substantial deviations. Figure 9 also shows a similar comparison of the change in annual peak demand between 2007 and 2010. There is clearly more scatter in the data for

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peak loads compared to annual consumption. This is not unexpected and likely arises from the greater volatility of peak loads in response to extreme weather events, the

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stronger influence of weather station selection on weather variability that contributes to

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peak loads, and because the calibration methodology itself is dependent on aggregate load ratios and does not try to explicitly correct for errors in peak demand. An analysis of temperature biases at the time of peaks loads showed a clear relationship between the magnitude of temperature biases in the model and the magnitude of the peak load biases. Correlations between the two biases ranged from 0.25-0.82 with a mean value of 0.55. When BEND or other similar models “feel” the wrong weather on days with extreme

ACCEPTED MANUSCRIPT 22 temperatures, that will directly, perhaps even linearly, translate into biases in their representations of peak demands. This relationship at least partly explains why some of the BAs fell well off of the 1:1 line in Fig. 9b.

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Comparison Against a Statistical Model As a mechanism to objectively validate the predictive accuracy of BEND against more commonly used methods and to generally evaluate the calibration approach, we

developed a simple regression model that also predicted year-to-year changes in building

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loads. We used a LOESS statistical model, a nonparametric fitting method based on

locally-weighted regression smoothing to model building energy use (the EIA target data) against weather data (temperature) from the year 2007. Unique regression models were created for each BA. The regression models were then applied to the 2010 weather data

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to estimate the building energy consumption by hour and meteorological season. The

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2010 loads estimated from the regression models were compared against the corresponding BEND loads to highlight qualitative differences between the two

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approaches.

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Figure 10 shows a comparison between BEND and the LOESS statistical regression for both energy consumption and peak demand for the WECC. The high bias

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of BEND shown in Table 3 is again apparent, but Fig. 10 also shows BEND’s biases to be similar in magnitude to those of the regression. While BEND’s peak demand estimates tend to be biased high, the LOESS regressions tend to underestimate peak demand by similar amounts. While we use a simple regression model as opposed to an operational model which are better fitted to available data, we demonstrate that BEND can have overall similar predictive accuracy with the advantage of being flexible in spatial scales;

ACCEPTED MANUSCRIPT 23 that is, consistent estimates can be provided for multiple aggregations of results to other scales such as states, energy regions, and counties.

Discussion and Conclusions

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The purpose of this paper was to introduce a novel calibration approach for

process-based aggregated building energy demand models with scalable results over a

range of spatial and temporal scales. Largely due to data availability constraints, a twoyear experiment was developed to quantify and characterize the biases in the energy

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demand as estimated by an aggregated energy demand model (BEND) over the western U.S. interconnect. The year 2007 was used for calibration and 2010 was used for evaluation. Comparing the calibrated 2010 run against the 2010 observed data illustrated

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the fidelity of the model and the utility of our calibration approach. Our conclusions are as follows:

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1) Aggregated energy building models need to be bias corrected. Relying on

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adequate calibration of an individual BES tool is insufficient. The uncalibrated version of BEND tends to systematically underestimate residential building loads

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and overestimate commercial building loads in most of the 19 balancing authorities (BAs) we studied. After calibration, BEND was able to generate

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estimates of annual total electricity consumption across all 19 BAs within 1% of the mean. Post-calibration biases in peak loads were both larger and more variable, ranging from -4.6% to +21.1%. BEND was able to identify the peak demand day in 2010 within ±1 day of the observed peak in 12 of the 19 BAs.

ACCEPTED MANUSCRIPT 24 Seasonal biases in total energy consumption were comparable to the annual estimates, with a mean bias smaller than 1% and only one BA larger than 10%. 2) A calibrated aggregated building energy demand model can be equivalent in

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performance to a simplified regression model, with the added benefit of flexibility in spatial scales for prediction purposes. The calibrated BEND model had comparable biases to a LOESS statistical model trained by relating 2007 temperatures to 2007 observed building loads.

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Although the calibration approach is simple, this is the first proposed approach to calibrating aggregate BES across multiple spatial scales. This study motivates the need for further research in this field, with an emphasis on improving the collection of data needed for calibration. We urge utilities and balancing authorities to expand the data they

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collect and share in order to make such calibration experiments easier to manage and

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resulting models more useful. Long-term energy planning relies on projection of drivers such as population change, climate change, regulatory changes as well as technology

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shocks such as demand response, appliance efficiency, and associated flexibility in building energy demand. More and better resolved data is required to fully understand the

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contribution of building energy demand to future total demand and for developing

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resilient energy systems. The emergence of scalable and realistic aggregated building energy demand

models are critical for long-term energy planning and further evaluating the sensitivity of seasonal and peak energy demand under variations in climate (via the weather forcing files), population and building stock (via the number and spatial distribution of

ACCEPTED MANUSCRIPT 25 buildings), and building technologies (via the parameters of the building technologies [e.g., HVAC systems]). While the calibration approach is presently U.S.-centric and associated with U.S.

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energy regions, it can be extrapolated to other worldwide regions with similar challenges between policy and operational implementation decision making scales. The key

challenges of extending this methodology to other regions involve the data to drive the method. Several key categories of data must be available for any region of interest,

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including a sufficiently detailed characterization of the building stock, observed hourly

electric load data to calibrate against, hourly weather files for the time periods of interest (including one or more years’ actual data for calibration and projected data for the future periods of interest), and adequate population (or other surrogate) data to allow up- and

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down-scaling of results to the regions/subregions of interest. With regard to building stock characterization, the RECS/CBECS data we used may now be the best available

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data for large U.S. regions, but non-U.S. regions and/or smaller regions (e.g., cities) will

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require specific local data on square footage capturing all major building types and vintages. Hourly electric load data separated by sector (residential, commercial,

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industrial/other) is not currently available for most regions, but as it becomes available it

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will greatly enhance our method’s ability to make useful projections for any region.

ACCEPTED MANUSCRIPT 26 Acknowledgments This research was supported by the U.S. Department of Energy, Office of Science, as part of research in the Multi-Sector Dynamics, Earth and Environmental System Modeling Program. Pacific Northwest National Laboratory is a multi-program national laboratory

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operated by Battelle for the U.S. Department of Energy under Contract DE-AC0576RL01830. A portion of the research was performed using PNNL Institutional

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Computing at Pacific Northwest National Laboratory.

Conflicts of Interest

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The authors declare no conflicts of interest involving this work.

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Tables and Figures Table 1. The total number of BEND prototype models, weather stations, and simulationready building models for each EIA climate zone in the WECC. The number of simulation-ready building models is the product of the number of prototype building models and the number of weather stations.

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1 2042 11 22462

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# of Prototype Building Models # of Weather Stations # of Simulation-Ready Building Models

EIA Climate Zone 2 3 4 1869 2046 1896 11 8 14 20559 16368 26544

5 1729 6 10374

Total 9582 50 96307

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Table 2. The 19 balancing authorities (BAs) in the WECC with data available for calibration. BA Long Name

BA Short Name

16 18 33 53 72 73 84 99 106 116 121 124 125 129 132 135 136 138 155

Arizona Public Service Co. Avista Co. City of Tacoma, Dept. of Public Utilities El Paso Electric Co. Idaho Power Co. Imperial Irrigation District Los Angeles Department of Water and Power Nevada Power Co. NorthWestern Energy - Montana California Independent System Operator - Pacific Gas & Electric Portland General Electric Co. Public Service Co. of Colorado Public Service Co. of New Mexico Puget Sound Energy Sacramento Municipal Utility District California Independent System Operator - San Diego Gas & Electric Seattle City Light Sierra Pacific Resources Tucson Electric Power Co.

AZPS AVA TDPU EPE IDP IID LADWP NVP NWE-MT CISO-PGE PGE PS-CO PS-NM PSE SMUD CISO-SDGE SCL SPR TEP

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BA #

ACCEPTED MANUSCRIPT 37 Table 3. The monthly, seasonal, and annual total energy consumption and peak demand for the entire WECC from EIA reported data and BEND estimates in 2010. Dates shown in the far right columns are the month, day, and hour of the peak demand. Energy Consumption (MWh)

Peak Demand (MW)

EIA

BEND

Bias %

EIA

BEND

Bias %

Month

Jan

32784796

32686617

-0.3%

54635

56858

4.1%

Jan

Day

Hour

Month

7

19

Jan

7

18

EIA 28904921

0.1%

52613

54553

3.7%

Feb

9

19

Feb

9

20

31013742

31994828

3.2%

51703

56636

9.5%

Mar

9

20

Mar

9

22

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28862973

Apr

29389258

30135362

2.5%

47879

51978

8.6%

Apr

5

20

Apr

2

21

May

30887724

31764304

2.8%

50301

51577

2.5%

May

20

17

May

5

21

Jun

34057906

34742734

2.0%

67171

69894

4.1%

Jun

28

17

Jun

28

16

Jul

38460813

39063090

1.6%

72935

75618

3.7%

Jul

15

17

Jul

15

16

Aug

37619386

38403870

2.1%

72975

77416

6.1%

Aug

25

17

Aug

25

16

Sep

34081204

35254566

3.4%

66717

73961

10.9%

Sep

27

17

Sep

3

16

Oct

31642877

31502878

-0.4%

58033

60821

4.8%

Oct

1

16

Oct

1

15

Nov

31374749

32557239

3.8%

56708

61473

8.4%

Nov

29

19

Nov

24

19

Dec

33473705

33555270

0.2%

56831

60685

6.8%

Dec

30

19

Dec

30

19

DJF

95121474

95146808

0.0%

51703

56636

9.5%

Mar

9

20

Mar

9

22

MAM

91290724

93894494

2.9%

72975

77416

6.1%

Aug

25

17

Aug

25

16

JJA

110138105

112209694

1.9%

66717

73961

10.9%

Sep

27

17

Sep

3

16

SON

97098830

99314683

2.3%

56831

60685

6.8%

Dec

30

19

Dec

30

19

Annual

393649133

400565678

1.8%

72975

77416

6.1%

Aug

25

17

Aug

25

16

AC

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Annual

BEND

Feb

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Season

Hour

Mar

M

Month

Day

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Figure 1. County-level maps of the (a) IECC climate zones, (b) EIA climate zones, (c) smallest BEND spatial units, and (d) BAs in the WECC. The gray shaded regions in (d) map BAs without the necessary data for calibration.

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Figure 2. Annual cycle of the population-weighted monthly-mean temperature in the WECC during (solid line) 2007 and (dashed line) 2010.

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Figure 3. Total (residential + commercial) building electricity consumption in BA 16 for the (red lines) uncalibrated and (teal lines) calibrated versions of BEND. By definition the calibrated version of BEND exactly matches the reported EIA data for each month.

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Figure 4. Monthly and hourly scaling factors for the (top) commercial and (bottom) residential building loads in BA 16 based on the 2007 BEND simulation.

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Figure 5. Biases in the (a) annual energy consumption and (b) peak energy demand by BA for the calibrated 2010 BEND simulation. The gray shaded regions are BAs without the necessary data for calibration.

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Figure 6. Biases in the seasonal energy consumption by BA for the calibrated 2010 BEND simulation. The gray shaded regions are BAs without the necessary data for calibration.

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Figure 7. Biases in the seasonal peak energy demand by BA for the calibrated 2010 BEND simulation. The gray shaded regions are BAs without the necessary data for calibration.

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Figure 8. Distributions of hourly relative bias of the total (residential + commercial) building load in (red) 2007 and (teal) 2010 based on the calibrated BEND simulations and the EIA target data for each BA.

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Figure 9. Changes in the annual energy consumption (left) and annual peak energy demand (right) between 2007 and 2010 by BA based on the calibrated BEND simulations and the EIA target data.

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Figure 10. Seasonal and annual bias distributions in annual energy consumption and peak energy demand based on the (red) calibrated BEND simulations and (teal) LOESS regressions for 2010. Biases are computed with respect to the EIA target data.