Anthony R. Florita1

e-mail: anthony.florita@nrel.gov

Larry J. Brackney

Electricity, Resources, and Building

Systems Integration Center,

National Renewable Energy Laboratory,

Golden, CO 80401

Todd P. OtanicarDepartment of Mechanical Engineering,

The University of Tulsa,

Tulsa, OK 74104

Jeffrey RobertsonDepartment of Mechanical Engineering,

Loyola Marymount University,

Los Angeles, CA 90045

Classification of CommercialBuilding Electrical DemandProfiles for Energy StorageApplicationsCommercial buildings have a significant impact on energy and the environment, being re-sponsible for more than 18% of the annual primary energy consumption in the UnitedStates. Analyzing their electrical demand profiles is necessary for the assessment ofsupply-demand interactions and potential; of particular importance are supply- ordemand-side energy storage assets and the value they bring to various stakeholders inthe smart grid context. This research developed and applied unsupervised classificationof commercial buildings according to their electrical demand profile. A Department ofEnergy (DOE) database was employed, containing electrical demand profiles represent-ing the United States commercial building stock as detailed in the 2003 CommercialBuildings Consumption Survey (CBECS) and as modeled in the EnergyPlus buildingenergy simulation tool. The essence of the approach was: (1) discrete wavelet transfor-mation of the electrical demand profiles, (2) energy and entropy feature extraction (abso-lute and relative) from the wavelet levels at definitive time frames, and (3) Bayesianprobabilistic hierarchical clustering of the features to classify the buildings in terms ofsimilar patterns of electrical demand. The process yielded a categorized and more man-ageable set of representative electrical demand profiles, inference of the characteristicsinfluencing supply-demand interactions, and a test bed for quantifying the impact ofapplying energy storage technologies. [DOI: 10.1115/1.4024029]

Introduction

Progress has been made in the awareness and implementationof renewable energy systems in a movement toward a sustainableand clean energy future. However, a large opportunity exists forenergy efficiency from an integrated, systems engineering per-spective. Commercial buildings in particular can benefit fromenhanced interactions with the electrical grid; commonly researchinterest lies in the optimization of indoor environmental quality orsingle building energy/cost performance. Recognizing that energyefficiency extends beyond building-site boundaries, building oper-ators can work with utilities and/or third-parties to use the build-ing as an asset in various forms of load shifting. Largely neglectedin many building-as-an-island performance analyses, suchresearch and demonstration projects are scarce but necessary ingrowth toward the smart grid.

With commercial buildings being responsible for more than18% of the annual primary energy consumption in the UnitedStates, there are opportunities for various stakeholders to benefit.The appropriate incentive signaling will trigger their active partic-ipation in whole-system efficiency and allow utilities to defer cap-ital investments while maintaining operational predictability.Quantifying the shared value among stakeholders is a crucialmissing element. Concerns have also been voiced about uncertain-ties in securing the raw energy resources needed to maintain“business as usual,” energy conversion emissions leading to harm-ful environmental impacts, and the intelligent dispatch of renew-able energy technologies within the energy infrastructure.

Energy storage has been identified as a vital yet largelyneglected support for bridging many engineered systems that are

orchestrated and optimized for multiple objectives. Proper andcost-effective energy storage can be building or utility scale. Con-founding the issue is the increased adoption of on-site renewablegeneration equipment in commercial buildings, such as photovol-taic (PV) panels or wind turbines, because the building acts asboth a generator and consumer of electricity. Furthermore, higherlevels of renewable penetration with intermittent generation ag-gravate whole-system instability because supply is not wellmatched to demand. Thus, understanding whole-system interac-tions and mobilizing energy storage for superior dispatch of gen-eration equipment are both essential. Ongoing research seeks agreater functional understanding between commercial buildingsand the electrical grid.

Literature Review

With focus placed on commercial buildings as an asset forwhole-system energy efficiency within the larger electrical gridcontext, the examination of literature followed suit. The naturalshared value in this supply-demand system can be expressed inmonetary terms. By placing the true value (cost) of unit energyconversion on unit energy pricing the utilities incentivize demandresponse. With proactive energy management this saves consum-ers utility costs and generators inefficient expenditures. A numberof building-related studies addressed these points in variousforms. Investigations of building thermal energy storage havemostly focused on thermal mass control and chilled water or icestorage. Electrochemical storage can also be helpful for renewabletechnologies and load shifting applications, but due to its rela-tively high cost current applications are in their infancy.

Thermal mass control harnesses the inherent thermal capaci-tance of the building for load shifting through supervisory controlof zone temperature set points and existing heating/cooling equip-ment. Lee and Braun [1] experimentally evaluated various strat-egies for a five-hour demand-limiting period; reductions in peak

1Corresponding author.Contributed by Solar Energy Division of ASME for publication in the JOURNAL OF

SOLAR ENERGY ENGINEERING. Manuscript received July 27, 2012; final manuscriptreceived January 31, 2013; published online June 11, 2013. Assoc. Editor: Gregor P.Henze.

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cooling load up to 30% were reported with minimal disturbance tooccupant comfort. A simulation study by Henze et al. [2] investi-gated the sensitivity of parameters governing the building thermalmass control process and developed a model predictive controlenvironment for optimizing cost savings.

Exploiting the sensible heat of a water body has long been astrategy for implementing thermal storage. A tank system can beintegrated into a building’s existing hydronic equipment, and findsits greatest use on campuses because of the economy of scale.Bahnfleth and Joyce [3] showed improvements in a university’scooling plant efficiency and achieved demand cost savings with anearly 17; 000 m3 stratified chilled-water storage. Sohn et al. [4]shifted 3MW of electrical demand from on- to off-peak for anArmy installation using stratified chilled-water storage.

With ice storage the energy stored in latent form is a magnitudegreater than the amount in an equal volume of chilled water, i.e.,per unit volume the “cool” energy stored is about 83:3 MJ=m3

with ice and about 8:3 MJ=m3 with liquid water. This can be cru-cial for commercial building applications where space is usuallylimited. Furthermore, with storage limitations the control of sys-tems is of upmost importance for the most (cost) effective loadshifting. Henze [5] surveyed research in the control of ice thermalenergy storage, including conventional, near-optimal, and optimalcontrol. Braun [6] developed a near-optimal control method forcharging and discharging an ice storage system in the presence ofreal-time pricing; the simplified method was shown to be within2% of the optimal solution.

Energy storage for intermittency issues and the integration ofrenewable energy has become increasingly important, especiallyfor utility-scale applications. Wind- and solar-generated electric-ity continually constitutes a larger portion of state renewable port-folio standards. Cavallo [7] addressed these concerns in thediscussion of electrochemical, flywheel, compressed air, andhybrid utility energy storage approaches; harnessing commercialbuildings as a capacitive element was not considered. Moreover,lacking need for energy conversion, electrochemical energy stor-age appears attractive to utilities. Kempton and Tomic [8] consid-ered vehicle-to-grid power, which employs electric-drive vehicles(e.g., battery, fuel cell, or hybrid) to interact with specific electricmarkets. Strategies and business models were considered, havingrepercussions for commercial buildings as plug-in electricvehicles become more common.

Methodology

This research developed and applied unsupervised classificationof commercial buildings according to their electrical demand pro-file. The nonstationary nature of such a time series embeds diurnalswings from occupancy cycles and contains both higher frequency(e.g., hour-to-hour) and lower frequency (e.g., seasonal) electricaldemands associated with weather and climate, respectively. ADepartment of Energy (DOE) commercial building database [9]was employed. The database contains hourly electrical demandprofiles representing the United States commercial building stockas detailed in the 2003 Commercial Buildings Consumption Sur-vey (CBECS) [10] and as modeled in the EnergyPlus buildingenergy simulation tool [11] for a typical meteorological year.Griffith et al. [12] described how the whole-building simulationtool was used for bottom-up modeling of the entire United Statescommercial building sector. Results from the 4820 modelsshowed good overall agreement with measured site-energy useintensity.

As fully detailed in following sections, the data were processedin three primary steps. The first step was to perform a discretewavelet transformation on each electrical demand profile. Thesecond step was to extract unique and descriptive energy and en-tropy features (absolute and relative) from each wavelet level atdefinitive time frames. The third step was the application ofBayesian probabilistic hierarchical clustering of the features toclassify the buildings in terms of similar patterns of electrical

demand. The process yielded a categorized and more manageableset of representative demand profiles, inference of the characteris-tics influencing supply demand interactions, and a test bed forquantifying the impact of applying energy storage technologies.

Discrete Wavelet Transformation. A common technique toextract time-frequency information from a signal is the windowedFourier transform, i.e., in transversing a signal, the Fourier trans-form is combined with a windowing function of appropriate widthto ensure the weakly stationary assumption. The width of the win-dow determines how time resolution is traded for frequency resolu-tion and vice versa, which is ultimately bounded by the Heisenberguncertainty principle. Wavelet methods partially overcome this li-mitation with multiresolution analysis. They have proven effectivein many signal analysis and engineering applications consideringnonstationary transients. Essential discrete wavelet theory and itsapplicability to the research problem are presented. The reader isreferred to Percival and Walden [13] for complete development.

The discrete wavelet transform (DWT) is mathematically statedas

f ðxÞ ¼X

i

Xj

ai;jwi;jðxÞ (1)

where i; j2 Z, wi;jðxÞ are the wavelet expansion functions, and ai;j

are the discrete wavelet transformation (DWT) coefficients off ðxÞ. The coefficients are calculated as

ai;j ¼ð1�1

f ðxÞwi;jðxÞdx (2)

The wavelet expansion functions are generated through scalingand translation of the mother wavelet

wi;jðxÞ ¼ 2�i=2wð2�ix� jÞ (3)

where i and j are the scaling and translation parameters, respec-tively. There are numerous mother wavelet families, e.g., Haar,Daubechies, etc. They are not unique and must satisfy a few mathe-matical conditions, the most notable being the multiresolutioncondition. Ensuring the multiresolution condition is satisfied allowsthe successive transformation of the signal at discrete time scale(� time-frequency) while allowing perfect reconstruction of theoriginal signal. A scale is the wavelet’s width at level j, an approxi-mate Fourier period or inverse frequency. High scale correspondsto a global view of the data (e.g., the yearly electrical demandprofile shape) and the low scale corresponds to detail information(e.g., hourly electrical demand fluctuations from heating, ventila-tion, and air-conditioning (HVAC) equipment operation).

Mallat [14] was the first to devise a fast and pyramidal algo-rithm, deriving the relationship to filter banks. Figure 1 showshow the DWT is computed in practice and as accomplishedherein. The J � level DWT can be calculated as

f0ðxÞ ¼X

k

a0;k/0;kðkÞ

¼X

k

aJþ1;k/Jþ1;kðxÞ þXJ

j¼0

djþ1;kwjþ1;kðxÞ(4)

with /ðxÞ being the scaling function, related to the mother waveletand where the coefficients a0;k, ajþ1;n, and djþ1;n are either knownor calculated from the previous wavelet level according to

ajþ1;n ¼X

k

aj;khðk � 2nÞ

djþ1;n ¼X

k

aj;kgðk � 2nÞ(5)

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At level j, the wavelet coefficients aj and dj are termed approxi-mation and detail coefficients, respectively. From the figure, interms of a filter bank, g and h are half band high-pass and low-pass filters with corresponding filter coefficients. In addition, thefigure illustrates that due to the filtering operation (at each level j)half the samples can be discarded according to the Nyquist crite-rion. Downsampling the signal by two (removing every other da-tum), denoted as # 2, leaves half the number of points and doublethe scale. Because the filter removes half the frequencies this canbe interpreted as losing half the information—the resolution of thesignal is halved. In general, the DWT analyzes the signal at differ-ent frequency bands, with different resolutions, by transformingthe signal into coarse approximation and detail information—thecoarse approximation is further filtered as possible.

Each level j of the DWT reduces the time resolution by halfsince the resultant time series is half the previous level’s numberof samples. The frequency resolution doubles since the signal’sfrequency band is half of the previous level’s bandwidth. Thisreduces the uncertainty in the frequency by half. As shown inFig. 1 the process is repeated until no more data points remain,with each process iteration sequentially named from level 1 to J.Each level’s bandwidth F is labeled to shows the reduction oftime resolution and increase in frequency resolution.

When the signal strongly correlates with a wavelet of particularscale and time, large amplitudes are observed. Figure 2 shows thefirst three levels of a DWT with the Daubechies-4 wavelet utilizedin this research; 13 decomposition levels are possible with the8760 data points of each electrical demand profile. The bottom-most subplot is an example of a yearly (sampled hourly) electricalpower demand profile x½n�.

As compared to the Fourier transform, the time localization ofthe frequencies will not be lost with the DWT; however, the timeresolution is dependent on the level. Furthermore, more informa-tion in the signal resides at higher frequencies and this is wheretime localization is more precise because of more samples. At lowfrequencies the frequency resolution is better but has low time re-solution because of the limited number of samples. Frequencybands (i.e., scales) of little importance will have low amplitudesand in many cases can be discarded with a small loss of informa-tion. It should be noted that only a portion of the temporal infor-mation from the DWT was used herein because of the nature ofunsupervised classification (described below); however, the DWT

was selected over Fourier methods so ongoing research could fur-ther harness time-frequency information in perturbation studies ofindividual buildings or building classes—allowing more focusedstudies of electrical demand at critical time periods for the devel-opment of functional relationships.

Feature Extraction. Successfully classifying the commercialbuilding according to their electrical demand profiles rested on theexpressivity and the independence of the features extracted fromthe various wavelet levels. Reducing the dimensionality of fea-tures is crucial for any classification algorithm because of the“curse of dimensionality.” A number of statistics and/or metricswere considered, but the following signal energy and entropy fea-tures were found most informative for inferences and effectivewithin clustering algorithms. Furthermore, due to the broad natureof the supply-demand research concerning (commercial) building-grid interactions the primary focus was: (1) how energy consump-tion/demand is patterned and (2) the extent of disorderednessfrom patterned behavior. Classification results will allow specifi-cation of energy storage technologies according to where the sig-nal energy lies and for smoothing disorderedness during criticaltime periods of electrical power demand.

Relative Wavelet Energy. With the wavelet coefficients deter-mined, termed cj½k� here for generality, the signal energy at eachresolution level j ¼ 1; 2;…; n was

Ej ¼X

k

jcjðkÞj2 (6)

The total signal energy was calculated as

Etotal ¼k x½k� k2¼X

j

Xk

jcjðkÞj2 ¼X

j

Ej (7)

For each resolution level the relative wavelet energy was calcu-lated as

Ej;rel ¼Ej

Etotal

(8)

This ratio indicates the relative wavelet energy contained in eachtime scale resolution.

As illustrated in Fig. 3, a histogram fEjg for each commercialbuilding was plotted to compare and contrast the electricaldemand profile components for each wavelet level. For classifica-tion purposes all possible wavelet levels were considered—13separate signal energy features were extracted from each commer-cial building’s electrical demand profile. The signal energy

Fig. 1 The discrete wavelet transformation (DWT) performedusing a filter bank for multiresolution analysis of the electricaldemand profiles

Fig. 2 The first three levels of a DWT using the Daubechies-4wavelet: the magnitude at a given time indicates the correlationstrength at that level; units are not included for visual clarity

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features were informative because of their relative sense, i.e.,building size (correlating with demand magnitude) and climate(geographic) influences were effectively considered but standar-dized. From the figure, building #1 had more pronounced relativewavelet energy in level 4 and the latter wavelet levels; level 4roughly corresponds to diurnal variations and levels 12 and 13with seasonal imbalance. In comparison, building #4820 con-tained more relative wavelet energy in the middle wavelet levels(i.e., levels 5 through 9). Observing the original demand profilesignals, only seasonal imbalances were obvious.

Total Wavelet Entropy. Shannon entropy provided a measureof information contained in the signal

HwtðEÞ ¼ �X

j

Ej;rel � ln½Ej;rel� (9)

In this context it measured the degree of signal disorder, providinginformation about the underlying dynamical processes. Well-ordered signals are more predictable and can be represented witha fewer number of wavelet levels. Complex signals, usually em-bedded with stochastic influences, are less predictable and a largernumber of wavelet levels are required for representation. Shannonentropy provided a means for quantifying these observations andits calculation was termed the total wavelet entropy of a givenelectrical demand profile.

The frequency plot of Fig. 4 represents the total wavelet en-tropy for all 4820 commercial building electrical demand profiles.That is, HwtðEÞ is one feature extracted for classification purposesfrom each commercial building’s yearly electrical demand profile.From the database, the minimum, median, and maximum total

wavelet entropies of 1.072, 1.865, and 2.433 were obtained forbuildings #1040, #3827, and #1361, respectively. Furthermore,seasonal total wavelet entropies (i.e., winter, spring, summer, andfall—defined by solstices and equinoxes) were extracted as fourseparate features.

Relative Wavelet Entropy. Signal disorder in a relative sensewas calculated as

HwtðEbjEaÞ ¼ �X

j

Ej;rel;b � lnEj;rel;b

Ej;rel;a

� �(10)

Distinctness of commercial building electrical demand behaviorwas quantified through this relative wavelet entropy calculation.

Fig. 3 Two typical building electrical demand profiles and their relative wavelet energycomparison

Fig. 4 Frequency plot of total wavelet entropy for each of the4820 commercial buildings

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Two different varieties of relative wavelet entropy were consid-ered: the outer calculation, which relatively compared independ-ent entropy distributions, and the inner calculation, whichexamined local entropy distributions relative to the signal itself.For the outer version, the relative wavelet entropy was condition-ally calculated against the minimum, median, and maximum totalwavelet entropies and used as three separate extracted features.For the inner version, the relative wavelet entropy was condition-ally calculated against the time-sequential seasonal total waveletentropy, i.e., springjwinter, summerjspring, falljsummer, andwinterjfall, and used as four separate extracted features.

Classification Feature Set. In total 25 features were extractedfrom each electrical demand profile—those found in testing tomost effectively distinguish clusters—and an approximate balanceof extracted signal energy and entropy features was noted. Thisincludes 13 relative wavelet energy features, five total wavelet en-tropy features (one yearly and four seasonally), and seven relativewavelet entropy features (three moment-based and four season-ally). The Bayesian hierarchical clustering algorithm summonedthe feature set for the purposes of classifying the commercialbuilding electrical demand profiles.

Bayesian Probabilistic Hierarchical Clustering. Hierarchicaldata clustering is usually a bottom-up agglomerative algorithmand a common method for unsupervised learning or classification.Typically, a distance metric is specified to assess the relative“closeness” of clusters and a threshold measure is used for stop-ping the clustering process. Each datum (or feature vector) is ini-tially its own cluster and then the two closest clusters areiteratively merged. The process yields a final number of clusters(or classes) of data containing similar features. Although choosingdefinitive features is difficult, the task of specifying meaningfuldistance and threshold metrics presents further obstacles. Theselimitations can be partially overcome with data standardization,bootstrapping (resampling) methods, and clever project-specificmetric definitions.

Difficulties with the classical approach have been overcomewith recent advances. Heller and Ghahramani [15] employed thepowerful Bayesian perspective for probabilistic hierarchical clus-tering, where marginal likelihoods are used in assessing whichclusters to merge and to avoid overfitting the problem; this wasthe chosen approach for the unsupervised classification problemexamined in this research. Advantages of the approach are sum-marized in four main points: (1) a probabilistic model is definedsolely through data and used for computing the predictive distri-bution of (unseen) data for cluster inquiries, (2) a model-based cri-terion is used to assess whether or not to merge clusters instead ofad-hoc distance measures, (3) Bayesian hypothesis testing is usedin decision making: whether to merge clusters or not and the depthof the tree, and (4) the algorithm is fast and has been proven towork with real-world (biological) data.

Using the Bayesian approach, all data (feature vectors) are ini-tially their own cluster (subtree) and two hypotheses are consid-ered in the cluster merging process. For data in a possible clusterDc, the first hypothesis Hc

1 is that all data were generated, inde-pendent and identically distributed (IID), from the same probabil-istic model pðxjhÞ, where parameter h is unknown. A priordistribution over the model parameters need to be specified,pðhjbÞ, with hyperparameter b; a prior represents a priori knowl-edge of the parameter, but if it is unknown a uniform distributionis used. The probability of Dc underHc

1 is calculated as

pðDcjHc1Þ ¼

ðpðDcjhÞpðhjbÞdh

¼ð Y

xðiÞ2Dc

pðxðiÞjhÞ

24

35pðhjbÞdh (11)

This model-based criterion evaluates the degree-of-plausibilitythat some data belong to a given cluster. The alternative hypothe-sis Hc

2 is that the data Dc have two or more clusters in it. Theprobability of the data under Hc

2 is a product over the subtrees Ti

and Tj. Synthesizing the data probabilities under both Hc1 and Hc

2,it can be shown that the marginal probability of the data in a treeTk (recursively defined) is

pðDcjTkÞ ¼ pðHc1ÞpðDcjHc

1Þþ ð1� pðHc

1ÞÞpðDijTiÞpðDjjTjÞ (12)

The first term considers the hypothesis that there is a single clusterin Dc, and the second term sums over all other clusterings of datain the tree. Bayes’s theorem is applied to determine the posteriorprobability of the merged hypothesis

pðHc1jDcÞ ¼

pðHc1ÞpðDcjHc

1ÞpðHc

1ÞpðDcjHc1Þ þ ½1� pðHc

1Þ�pðDijTiÞpðDjjTjÞ(13)

The quantity pðHc1jDcÞ is used to decide which two trees to merge

and the final structure of the hierarchy; the tree is cut at pointswhere pðHc

1jDcÞ < 0:5. That is, p ¼ 0:5 is the division between“yes” and “no” for the cutting of the tree. The Bayesian hierarchi-cal clustering algorithm is efficient, basing clustering solely onthe probability of observed data features.

Results

This research was programmed in a publicly available computa-tional environment [16] using publicly available data [9] for theunsupervised classification of commercial buildings based solelyon their electrical demand profile. Using the methodology out-lined, the initial dataset of 4820 buildings was reduced into 114classes for a compression of greater than 97%. The processyielded a categorized and more manageable set of representativeelectrical demand profiles, inference of the characteristics influ-encing supply-demand interactions, and a test bed for quantifyingthe impact of applying energy storage technologies.

Due to the large number of buildings (4820) the results of theclustering were nearly impossible to represent in the classic den-drogram format. Nonetheless Fig. 5 presents the complete cluster-ing process, while neglecting inclusion of the building labels dueto significant overlap, so the reader might visualize the 4820 build-ings merging into the final 114 classes according to the extractedfeatures. Figure 6 displays a limited portion of the full dendrogram,classes 8 and 9, demonstrating the merging hierarchy of the build-ings within the class. The red dashed lines on the dendrogram rep-resent merges that the clustering algorithm does not make, whilethe number displayed represents the log odds for merging.

Manual inspection of each class represented a significant chal-lenge. Each building has tens of thousands of variables and pa-rameters, and significant results may be overlooked. Because ofthis challenge, the approach taken herein utilized graphical techni-ques for the sake of presentation, as well as simplifications appro-priate to the CBECS data [10] utilized. That is, only high-levelcharacteristics within each class were considered for condensedresults presentation and for the demonstration of general resultshelpful for this article. For illustration purposes, three primarycharacteristics were focused on to demonstrate a subset of possi-ble inferences, as well as to show relevant characteristics influenc-ing the classification: the climate, the principal building activity,and the building size. Finally, a simple example is given to exem-plify one of many possible ways the identified building classesmight be utilized with respect to energy storage analysis.

The Influence of Climate. The first characteristic that wasinvestigated for its influence on the classification of buildings was

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the climate region. The CBECS database utilizes five climateregions based on the number of cooling and heating degree days(CDD and HDD, respectively). Figure 7 shows the heat map basedon the climate zone used in the modeling and the resulting classes.The darkest red (or gray in print) rectangles represent classes witha very small number or zero buildings for the given climate regionbeing represented in the class, while white (or bright yellow) rep-resents a class with a large number of buildings from a given cli-mate zone. For the sake of discussion, focus was placed on a fewclasses to demonstrate the results of the technique. For example,classes 48 and 90 are highly represented by buildings from cli-mate zones 4 and 1, respectively, whereas, classes 72 and 103 aremost represented by buildings in zones 3 and 1, respectively, butalso were significantly represented in other climates.

From the heat map it can be seen that climate zone does notnecessarily represent a strong driver for classification. Thisimplies that energy storage control strategies might apply irre-spective of climate and are modified solely by magnitude to

ensure coverage of signal energy and entropy features. The caveatto this line of thinking is that the utility rate structure for a givenbuilding will vary across the country and will drive the energystorage control strategy. However, it is feasible that multiplebuildings serviced at a given bus might be analyzed for energystorage opportunities and the appropriate demand profile fromeach respective class could simply be added. Overall the heat mapshowed climate regions associated with specific classes did notdemonstrate any conclusive patterns. A variety of reasons withinthe modeled database could lead to this: First, multiple weatherfiles were used to model buildings within a given climate zone[12]. This leads to more variety in weather within a given climatezone. Second, differing building sizes and types could lead to sig-nificantly different operating patterns within a given climate zone.

The Influence of Building Type. The second characteristicinvestigated was based on the principal building activity. The

Fig. 5 Dendrogram of the clustering process for the United States commercial building stock: visualization of the 4820buildings merging into the final 114 clusters (building classes) according to the 25 features extracted from the electrical demandprofiles; for visual clarity building labels not included.

Fig. 6 Limited portion of dendrogram (with focus on clusters 8 and 9) demonstrating merging hierarchy; dashed lines aremerges not made, while the number displayed indicated log odds for merging

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CBECS database classifies buildings based on their major usagewith such categories as office space, retail, and inpatient healthcare to name a few. It can be seen in Fig. 8 that building type oftenleads to selection of a load profile for a given class. For example,classes 71 and 104 are predominantly filled with buildings usedfor inpatient health care. It is of interest to determine if principalbuilding activity is so dominant why these two clusters are notmerged into the same cluster. A reason will be addressed in thenext subsection. Additionally classes 48 and 91 were not domi-nated by one building type but share a variety of building types,but these classes were made up of buildings primarily from oneclimate zone. On the other hand, offices, which are also the largest

set of buildings by building type within the database, were domi-nant in a variety of classes. Interestingly the majority concentra-tions were located in adjacent classes, demonstrating their likelyappearance in higher level merges. Although the Bayesian hier-archical clustering routing does not consider these merges to behighly probable, it did indicate the potential for similar behavior.

The Influence of Building Size. Square footage was also ahighly revealing result, particularly when the discussion includesthe effects listed in the previous section. For example it was notedthat classes 71 and 104 were primarily made of buildings used for

Fig. 7 Clustering heat map based on United States climate zones: CBECS uses five climate regions based on cooling and heatingdegree days. Darkest rectangles represent a cluster with a small number of buildings (or zero), while white rectangles representa cluster with a large number.

Fig. 8 Clustering heat map based on principal building activity: CBECS classifies buildings according to their major usage,e.g., office, retail, etc. Darkest rectangles represent a cluster with a small number of buildings (or zero), while white rectanglesrepresent a cluster with a large number.

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inpatient health care but were not merged. When this result wascombined with Fig. 9 it could be seen that these two classes werenot merged because of the difference in square footage. Class 71was primarily made of smaller health care buildings with class104 being made up of the largest two square footage categories inthe data set; the difference in classification is likely attributed tovastly different HVAC equipment, even though the (standardized)occupancy and usage patterns of the buildings are similar. Turningthe attention to classes 48 and 91 again, it can be seen that theseclasses were made up of mixed results based on square footage.

Perceived Use of the Commercial Building Classes. It shouldbe noted the unsupervised classification represents only the first-level, top-down approach to uncovering functional relationshipbetween a building electrical demand and its governing parame-ters and/or variables. The identified classes of commercial build-ing according to their demand profile have two perceived useswith respect to demand response and/or energy storage.� Unit commitment and dispatch models are used to determine

scheduling for start up and/or shut down of power plants in asystem area of interest, i.e., usually across multiple states. Mixedinteger programming is used to solve the commitment problemwith forecast weather and demand, with each unit having uniquecharacteristics and constraints (e.g. up and down times, ramprates, scheduled maintenance, etc.), and the solution is modifiedand dispatched on a shorter horizon according to updated andhopefully more accurate information. Since even percentageimprovement in demand forecasting can save tens of millions ofdollars on a yearly basis, there is a great need to better understandelectrical demand at a particular distribution bus and better predictit. The aggregation of the appropriate building demand profileclasses, where perhaps transmission is constrained and, thus,power is costly, can provide a starting point for further analysis.This can help in decision making with respect to demand responseincentives or the addition of energy storage.� On a building level the understanding of how building param-

eters and/or variables influence the demand profile is incomplete.The unsupervised approach was helpful for uncovering correla-tions and natural grouping. It is noted that the bottom-up, deter-ministic modeling and simulation approach used to produce thecommercial building demand profiles [12], albeit the state-of-the-art [11], provided only an estimation of nominal behavior and

neglects considerable uncertainty. However, it is the authors’belief that since the database [9] was derived from an elaboratestatistical analysis of the building stock [10], it provided a goodstarting point for this research. It is apparent there are uncountablecombinations of data analyses and regressions that could be per-formed to better understand functional relationships—even with-out considering the uncertainty of each parameter and/or variableor the accuracy of the simulation models themselves. Further-more, it is apparent building-level thermal perturbations (e.g.,thermal energy storage and release) will influence the demandprofile and any given building might shift classes.

A Classified Building Energy Storage Example. An exampleis given on how a building class might be used to aid the energystorage design for a particular building. The first step would be toexamine all buildings within that class to better understand possi-ble trends. When examining a single commercial building for theapplication of energy storage, one might be interested in a specificenergy storage technology, have a good understanding of the ap-proximate storage capacity needed, and optimize the designaccording to a particular utility rate structure to save operatingcosts.

The representative commercial building demand profile fromclass #1 (scaled by the magnitude of peak demand from the firstbuilding in the class) is considered for the month of July. In addi-tion, on-site PV panels were added such that the solar fraction wasequal to unity if all energy can be stored, i.e., the total energyneeded to operate the building was equal to the PV production butthe supply and demand do not necessarily match. Figure 10 showsthe building demand profile, the PV production, and the hourlydifference, respectively. The necessity for storage is evident dur-ing periods when PV production is high but the building demandis low; this is especially notable on the weekends. This is a prob-lem of a “highly energy efficient building” where simply addingan abundant amount of PV without regard to the whole system ef-ficiency leads to problems. That is, it is possible the power peaksflowing back into the grid make the whole-system efficiencyworse. Furthermore, the utility is only going to buy power back ata fraction of what it charges for the same quantity.

To capture the energy spillage back onto the grid, a genericenergy storage was considered. Simple on/off control to (or from)the storage was based on the hourly difference between building

Fig. 9 Clustering heat map based on square footage. Darkest rectangles represent a cluster with a small number of buildings(or zero), while white rectangles represent a cluster with a large number.

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demand and PV production. The parameters of interest were: (1)the energy storage size as a fraction of the worst-case design stor-age capacity and (2) the maximum charging/discharging rate perhour as a fraction of the design storage capacity. The design stor-age capacity (J) was specified as the greatest diurnal differencebetween building demand and PV production during the month ofJuly, i.e., the theoretical ability to store all excess production onthe worst-case July day. The maximum charging/discharging rateparameter allowed the design storage capacity to go from emptyto full in one hour or vice versa. Charging and discharging effi-ciencies were assumed to be 90%. Temperature degradations werenot considered. Although the parameters were for a generic stor-age, they represent a range of electrochemical storagetechnologies.

From Fig. 11 it is shown that the net energy spillage to the gridwas more sensitive to the rate of charging/discharging than thestorage size. In both cases, at fractions above approximately 0.50,the solution does not change. With an adequate storage size(� 0:35 design capacity) and charging/discharging rate (� 0:2max rates) only 35% of the PV production was sent to the gridand not utilized on site. The maximum (monthly) demand fromthe grid is also a big concern for building operators because of theexpensive charges associated with its peak magnitude; it wasinteresting to see how much the storage influences peak demand.From the figure, the storage allowed demand savings of 12.5%without dedicated control. In all energy storage studies utility ratestructures will have a profound influence, and those results offeredhere are solely to illustrate classification results.

Conclusions

Overall the heat maps presented in Figs. 7 through 9 demon-strated the validity of the technique to classify similar buildingsthat one might expect to have indistinguishable electrical demands,as well as shed light on unexpected classes. The two-way andpotentially higher interactions these figures reveal showed the chal-lenging nature of such a technique but also demonstrated howdynamic building usage can be. This technique and the results pre-sented here represented just the first level of analysis and demon-strated the need for further research within the identified buildingclasses. Particularly, the investigation will be extended to look atthe impact of weather from a more detailed level and the impact ofthe air-conditioning equipment used. Additionally, investigating ifsignificant variations in classification occur when real weather dataare used, versus typical meteorological year data, is of concern.Furthermore, observing what happens to the load profiles when alarge suite of advanced technologies, including various on-site gen-erators and energy storage technologies, are included is of greatinterest. These impacts in particular are highly relevant to the intel-ligent integration of commercial buildings with renewable genera-tion and energy storage capabilities.

Acknowledgment

T.P.O. and J.R. would like to acknowledge the DOE FaST pro-gram for the opportunity to conduct this research, and would liketo thank National Renewable Energy Laboratory (NREL) for con-tinued support in pursuit of this topic.

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Fig. 11 Energy spillage and peak demand savings as a func-tion of energy storage parameters

Fig. 10 The building demand profile, on-site PVE generation and difference forthe month of July

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