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Building and Environment 67 (2013) 111e128

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Building and Environment

journal homepage: www.elsevier .com/locate/bui ldenv

Building demand-side control using thermal energy storage underuncertainty: An adaptive Multiple Model-based Predictive Control(MMPC) approach

Sean Hay Kim*

Autodesk, Inc., San Rafael, CA 94903, USA

a r t i c l e i n f o

Article history:Received 6 March 2013Received in revised form24 April 2013Accepted 8 May 2013

Keywords:MPCMultiple modelsAdaptive controlUncertaintyFuzzy modelMMPC

* Tel.: þ1 415 940 2011.E-mail address: seanhay.kim@autodesk.com.

0360-1323/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.buildenv.2013.05.005

a b s t r a c t

This study investigates the demand-side control enhancement of TES though comparing the benchmarkcontrol strategies and newly-suggested adaptive MMPC designed to handle uncertainty in an adaptivefashion. Evaluations are performed through closed-loop simulations of an actual test building that iscalibrated with real data and weather. While typical MPC centralizes computational burden (due to aprovision for disturbances) on optimization through a single model, the adaptive MMPC distributes suchburden (with less complexity) to multiple local models and optimizations in advance, then the onlinesupervisory controller selects or interpolates the most adequate local models and control policies for thecurrent conditions, thereby provides an effective global control policy for the entire operation regime.Building Energy Model (BEM) is used to construct local models for the adaptive MMPC, which enablesmore semantically feasible and acceptable model calibrations through which practitioners would obtainmore model fidelity. This approach not only alleviates real time computation load, but also still achievesthe desired performance. Evaluation results show that the adaptive MMPC outperforms the storagepriority control and also ensures a near-optimal performance in load shifting under various uncertaintysituations, including depreciation scenarios and unmeasured disturbance scenarios.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

The demand-side control employs technical measures to alterthe system load profile in order to synchronize demand and supplyprofiles in a fashion that demand and supply stakeholders bothfavor. The primary objective of the demand-side control is to reducethe variability and level net demand, since large variations in thepower demand are more of a strain on the power grid such asdecreasing load factor. A driving force of the demand-side control atindividual buildings is, therefore, often a utility rate incentive: bothutility providers and customers prefer shifting the energy demandtoward the lower utility rate period as much as possible. Mutualbenefits are lower operating costs for customers and lower infra-structure investments for utility providers.

A successful demand-side control depends in part on howaccurately the building power demand is forecasted during theplanning control horizon, thus appropriate (and various, if neces-sary) demand-side control measures should be placed proactively

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in a harmonized fashion. Mechanical thermal energy storage (TES)under rate incentives is a well-established technical instrument ofthe demand-side control that can be selected for an individualbuilding [1e3]. In particular, Model-based Predictive Controls(MPCs) for TES have demonstrated solid performance [1,3]. Atypical output of the MPC for TES is a supervisory control portfoliothat manipulates charge and discharge rates of TES in accordancewith operation schedules of other cooling plants. In reality, how-ever, the MPCs are grounded in the prediction through simulationsusing specific building and system models under a specific forecastscenario. When unmeasured disturbances intervene, seriousunderperformance can result.

Several recent MPC studies actively deal with uncertaintyissues: one category is to enhance forecast accuracy, in particularfor weather and occupancy information, using online weatherforecasts [4,5] and instantaneous occupancy measurement andoccupancy prediction model [6,7]. The other category is the use ofadvanced algorithms and/or processes in formulating MPCs such asusing stochastic constraints in optimization [5,8] and real timeoptimization [9].

Most existing MPC formulations are based on a single modelapproach, where optimization handles disturbances while the

1 Demand charge can be levied with or without TOU. Typically TES is known tobe very efficient for offsetting demand charges occurring once per billing period.However, this study emphasizes a full extent of the load shifting capability of TES,which will be more highlighted with TOU on a daily basis.

S.H. Kim / Building and Environment 67 (2013) 111e128112

model describes the system dynamics that update the state. A mainlimitation of this approach is that larger computational complexityis loaded on optimization for a provision for unmeasured distur-bance, and thus the estimated state can differ from the actual statewhen the recalculated MPC is deployed if calculation time is longeror delayed.

Instead of centralizing the disturbance provision in a singlecontrol structure, adaptive control strategies are feasible alterna-tives, which distribute the burden and then chooses adequatecontrol parameters and/or control structures during online controlas conditions change due to disturbance [10]. For instance, pre-setcontrol logics such as lookup tables can be pre-built by offlineoptimization, thus relives real time computations [11]. If models areused as control structure, which is able to preserve system dy-namics (vs. simplified rules), more precise adaptations are enabledin a timely manner.

This study suggests a special class of adaptive control strategies,referred to as Multiple Model-based Predictive Control (MMPC). Amotivation of MMPC is that, for many complex engineering prob-lems, control problems that involve transitions between knownoperating regimes are readily handled by a multi-model approach[12]. In the adaptive MMPC, a bank of candidate models (andcontrollers) can be specified a priori. Then, a supervisory controllerselects the most adequate model for the current condition and/orsynthesizes them. For each model, a suitable controller can bepreviously designed off-line.

The selection of a suitable model to represent system dynamicsis a crucial step. A number of multiple model control schemes havebeen reported; in particular, in the process engineering domain[13e17]. A majority of nonlinear models used in the multi-modelapproach for HVAC control includes TakagieSugeno (TeS) fuzzymodels [18,19]. The value function-based approach to schedulemultiple controllers [20] expands an applicability of the adaptivescheduling: the value function is obtained by solving the dynamicprogramming using closed-loop simulation and a functionapproximator. An advantage of this approach is that adaptivescheduling is not limited to a specific type of model or controller.

While many existing cases of MPC use simplified first principlemodels or data-driven black-box models, this study suggests usinga detailed engineering model, developed based the laws of physicsconcerning heat and mass transfer and various fluid flows, andvalidated by modeling experts. This type of model is often called aBuilding Energy Model (BEM), which includes TRNSYS [21]. Bene-fits of using BEM for MPC include:

i) Model and configuration parameters of a BEM possess phys-ical meaning, thus calibrations against real buildings andvalidation of the BEM can be more semantically feasible andacceptable. Also, sensor data can be incorporated much morereadily and directly when updating the system state duringMPC deployment [9].

ii) With the increasing popularity of a Building InformationModel (BIM) in the design practice, construction of a BEM thatoffers adequate resolutions and details, from the initial designphase to the operation phase, becomes feasible in a moreseamless fashion; thus, modelers become relieved of con-cerns over model fidelity.

iii) Particularly for MMPC, training and tuning multiple modelsmust be conducted for quality assurance. Extreme operationdata is often required to ensure model robustness (i.e., modelaugmentation), in particular for the data-driven black boxmodels. However, an acquisition of the extreme operationdata is often not available for buildings (such as extremeambient temperature beyond the average and twice theaverage internal heat gains) since extreme weather and

occupancy, the primary contributors affecting the building inextreme conditions, are highly infrequent and not control-lable in order for the modeler to obtain quality training data.Indeed, many MMPC studies reported in literature collectsuch data by exercising the validated analytical model withthe controlled configuration. This study seeks to uncover anopportunity for directly using BEM.

A known disadvantage of using BEM for MPC, however, is itsrelatively slow simulation speed [9,11], compared to the simplifiedfirst principle models and data-driven black-box models. However,due to its increased computation power, in particular with cloudand parallel computing support, BEM is expected to bemore readilyand widely accepted in the building control domain.

As this study has been initialized by a need of practitioners forthe enhanced building demand-side controls under various typesof uncertainty, this study aims to first propose a prototype of theadaptive MMPC for TES using BEM. Then its performance is eval-uated, with respect to optimal MPC and a traditional (rule-based)storage priority control, against a test building for which TES con-trol is designed in accordance with a planned new time of use(TOU) tariff with higher rate incentives.1

The organization of this study is as follows: Section 2 discussesthe operation of TES and MPC formulation. Section 3 describestheory, algorithms and development process of the adaptive MMPCfor TES. Section 4 introduces the implementation of the adaptiveMMPC through a case study. Section 5 describes evaluation sce-narios and benchmark MPCs and reports on the performance ofMPC strategies.

2. The Model-based Predictive Control (MPC) for TES

This section introduces control features for operating TES anddescribes how the typical MPC for TES is formulated.

2.1. Operation of TES

A principle of operating the TES for demand-side control is theload shifting that takes advantage of rate incentives betweenhigher and lower power rates of a given day: to store chilled me-dium in the TES during the least expensive period of the day (off-peak), and to release it during the most expensive period of the day(on-peak).

As the TES serves the building’s thermal demand only during alimited period of a day, a separated and smaller-sized TES chiller isoften favored: the dedicated TES chiller is designated to serve theTES charging load, while the main chiller serves the rest of thebuilding demand after a designated portion of the demand is metby the discharged cooling energy from the TES according to Equa-tion (1).

_Qmain:chiller ¼ _Q load � udk (1)

where _Qmain:chiller denotes the chiller cooling demand, _Q load de-notes the observed building demand, and uk denotes the rate of theenergy transfer to or from the TES, while the superscript d denotesdischarging.

Control variable uk of TES can be divided into i) charging rate ofenergy from the TES chiller to the TES ðuckÞ, and ii) discharging rate

Fig. 1. Block diagram of typical MPC for TES.

S.H. Kim / Building and Environment 67 (2013) 111e128 113

of energy from the TES to the building cooling demand ðudkÞ for anytime interval k. They are subject to their own constraints:

0 � uck � uc:max (2-1)

0 � udk � ud:max (2-2)

where uc.max and ud.max denote the maximum charging and dis-charging rates of energy set by physical system constraints,respectively. Charge and discharge rates depend on the availablethermal energy inventory and the current thermal demand. Theavailable energy inventory of the TES for any time interval k (xk) isthen described as follows:

xkþ1 ¼ xk þ uckDt (3-1)

xkþ1 ¼ xk � udkDt (3-2)

xmin � xkxfull

� xmax (3-3)

where xfull denotes the state that the maximum volume of thechilledmediummeets the full capacity of the TES (CAPTES); and xminand xmax denote the minimum % and maximum % of the energyinventory, respectively. These boundary conditions are employed inorder to account for the heat transfer limitations of the TES andchiller cooling capacity constraints. For instance, when the energyinventory approaches the bottom, a mixing effect accelerates a lossof cooling capacity of the TES. Thus xmin and xmax are set to 0.1 and0.9, respectively [2].

Fig. 2. The execution horizon (EH) can be as long as the planning horizon (PH). ThePCH denotes the preconditioning horizon.

2.2. Process model and control objective of the MPC for TES

Demand-side control utilizing thermal inventory pursuesminimizing the HVAC operating cost, which includes both the on-peak and off-peak electricity use terms (to represent the powerdemand of customers) and their utility rates (to represent thepreferences of power suppliers). The objective function is formu-lated as:

minU⏞J U; x tð Þð Þwhere J ¼ ∑

N

k¼1Pe kð Þre kð ÞΔt (4)

where Dt denotes the time interval; N denotes the number of thetime intervals for the planning horizon; Pe(k) denotes the totalelectricity use for the time interval k (kWh); re(k) denotes the costper unit of electricity for the time interval k ($/kWh).

The MPC employs the model that accounts for the behavior ofthe building and systems within the control scope as a predictioninstrument through which the MPC can make a predictive controlsolution. As depicted in Fig.1, it also takes their initial states and themeasured disturbances for the planning horizon. The optimizeremployed in developing the MPC then provides the optimum so-lution meeting the objective function. Fig. 2 describes that theresulting control solution is deployed only for the execution hori-zon, which is typically shorter than or equivalent to the length ofthe planning horizon. The shorter the execution horizon is, thecloser the MPC is to the real time control.

The operation cost can be minimized when TES is chargedduring the cheapest period of a day just as much as needed for theon-peak demand and then it is depleted while serving the on-peakdemand. Then operation of the main chiller is minimized duringon-peak hours as well.

Thereby the supervisory control performance of TES highlydepends on an accurate building demand forecast during controlhorizon and a reactive discharge charge to the demand profile. Aslong as the observed demand is within an effective range of theforecasted demand, the optimizer modulates charging and dis-charging rates that result in the optimal performance.

TheMPC for TES first finds the optimized Qdischarge that meets onthe estimated building demand bQ load while minimizing bQmain chillerfor the planned discharge horizon (Equation (5-1)), and then itdetermines Qcharge that includes Qdischarging and QTES.loss (Equation(5-2)).

Qdischarge ¼Zdischarge:end

discharge:start

�_Q load � _Qmain chiller

�dt

¼ bQ load � bQmain chiller (5-1)

Qcharge ¼ QTES chiller ¼ Qdischarge þ QTES:loss (5-2)

Eventually the MPC delivers the control portfolio composed ofuck and udk for time interval k.

During the charging period, the TES chiller provides the fixed uckto the TES by regulating the chiller supply temperature (Tchw) ac-cording to

Tchw ¼ TTES �uck

3cmccp(6-1)

_QTES chiller ¼ uck ¼ 3cmccpðTTES � TchwÞ (6-2)

S.H. Kim / Building and Environment 67 (2013) 111e128114

where 3c denotes the charging heat transfer effectiveness for theflow rate mc.

During the discharging period, the energy flow leaving the TESis modulated by a three-way control value for the fixed udk in orderto maintain the required load supply temperature (Tcoil). However,if the discharge energy flow udk is less than _Q load ðudk < _Q loadÞ, thenthe main chiller should provide the supplemental cooling energy_Qmain chiller according to

_Qmain chiller ¼ _Q load � udk ¼ mdcpðTcoil � TchwÞ (7)

Operation of the main chiller during on-peak hours is thus oneof the primary reasons that escalate the HVAC operation cost,which should be minimized in the demand-side control.

Inmanycases, a root cause for theunderperformingdemand-sideMPC using TES is, therefore, that the building demand prediction forthe planning horizon is not as accurate as requireddinherently, thisis due to the unmeasured disturbance originating from uncertaintyin model and external model inputs. A classical resolution in usingMPC is to carry out successive short-term execution horizonsthroughwhich theMPC is able to frequently update the current stateand introduces new external information upon operation regimechanges, while a sufficiently long planning horizon for each execu-tion horizon is still secured, such that the MPC corrects thediscrepancybetween themeasured state and thepredicted state andthen provides the updated control solutions.

An intention of this study is to suggest a new perspective for theMPC that utilizes multiple models formulated during the planninghorizon based on the premise that uncertainty in model andexternal inputs is reasonably bounded (i.e., the bounded forecastaccuracy), thus operation regime change is bounded as well. Inmultiple model scheme, each model possess own operation rangeanalyzed a priori and a set of local operation ranges composes theglobal operation range. Therein it assumes the selection and/orsynthesis of control policies, each of which is (sub) optimal to eachlocal model, can offer a near-optimal (at least effective) global so-lution for the global operation range. Therefore theMMPC for TES isexpected to provide appropriate control solutions online whichcorrespond to the transient building demand (i.e., adaptation),rather than calculating new control solutions through the singleglobal model at every update.

3. The adaptive Multiple Model-based Predictive Control(MMPC) for TES

A major motivation for the multiple model scheme is that asingle model can be so complex to account for non-linear behaviorthat is frequently observed when the system shifts between oper-ation regimes. Multiple local modeling can be simpler than singleglobal modeling according to the assumption that there are lessrelevant phenomena and simpler interactions in local models [12].Thus scheduling or interpolating multiple control policies canalleviate the curse-of-dimensionality associated with a large controlaction space, which is often the case for developing a supervisorycontrol that should consider all the operation regimes.

3.1. Hierarchical multiple-model scheme

A block diagram of the MMPC considered in this study has atwo-level control framework as depicted in Fig. 3. In the lower level,each local model is built for single operating regime of all the re-gimes that the global system encompasses. Local control policy ui isgenerated for a local model distinctive from other local models. Inthe higher level, the fuzzy supervisory scheduler determines theweight for each of the local control policies based on the identifier

for the distinctive condition of each local model. Then weightedlocal control policies are summed up and then delivered as theglobal control output u. The control output at each time step is usedfor the control action at next time step. The unmentioned compo-nents depicted in Fig. 3 will be described in Section 3.4 and 3.5.

Each local model has the same structure but operates indifferent conditions. A priori knowledge for the expected operationconditions often suggests clues in identifying distinctive localoperation regimes for the local model. At the same time, however,the imprecise and qualitative nature of the a priori analysis oftencannot make an explicitly quantified classification. Fuzzy modelinghas been known as a machine-side correspondence for human in-telligence that can complement the shortcomings of the a priorianalysis while it transforms the imprecise and qualitative knowl-edge into the stochastic representation of the information. Thisstudy uses fuzzy clustering and fuzzy C-Means clustering algorithmto identify local models per operation regime and also to quantifyrule sets andmembership function between driving factors and theresulting classification, which will be further discussed in Section3.2 and Section 3.3, respectively.

3.2. Fuzzy clustering and rule set

Fuzzy clustering allocates a single data set into one or moreclusters by means of the “membership function” specifying thestrength of the association between the single data set and a certaincluster; such that “clustered” data sets present homogenousbehavior. The membership function is typically expressed throughthe fuzzy partition matrix g, an element of which (yij) denotes thedegree of the association for a single data set to a fuzzy cluster; itcan be calculated by projecting each point of the input and output(i, o) onto the input vector I and output vector O through thepartition matrix g.

First of all, the fuzzy clustering needs to derive fuzzy rule sets.Fuzzy rule sets are derived by projecting the clusters onto the axisplane. The projected cluster pattern indicates the profile of thefuzzy rule (e.g., linear or ellipsoid) and spacing between clusters.Generic fuzzy rule sets can be formulated according to:

Ri : if i1 is Ak i1ð Þi and i2 is Ak i2ð Þ

i ;…; and iN is Ak iNð Þi then Oj Ið Þ

¼ ωioi for oi ¼ f ii; ai; bið Þ(8)

where i denotes the rule number; j denotes the cluster number; Ndenotes the number of input and output variables; ii denotes the ithinput vector in I ¼ {i1, ., iN}; oi denotes the ith output vector inO¼ {o1,., oN}; Ai denotes the antecedent range for input I; k(i1),.,k(iN) denote linguistic expressions about where ii is located in therange of Ai; ui denotes the member function expressed by the fuzzyweight; f(i; ai, bi) denotes a model between ii and oi with modelparameters ai and bi; and Oj(I) denotes the rule consequents.

3.3. Fuzzy C-Means (FCM) algorithm to identify the membershipfunction

Consider a finite set of data Z ¼ {z1,., zn}, which consists of theinputs and output. The data set Z is divided into C clusters {Z1, .,ZC}. Each cluster Zi (i ¼ 1, ., C) corresponds to single operationrange of the global operation rage. Clusters {Z1, ., ZC} are deter-mined by a partition matrix g according to

g ¼ �yij�i i ¼ 1;.;C j ¼ 1;.;n (9)

In Equation (9), yij is a numeric value in [0, 1] and represents thedegree to which an element zj belongs to the ith cluster.

Fig. 3. Block diagram of the supervisory MMPC for TES.

S.H. Kim / Building and Environment 67 (2013) 111e128 115

Number of clusters and allocation of data set to each cluster aredetermined by a given criterion that optimizes the objective func-tion of the Fuzzy C-Means (FCM) algorithm [22]:

J�yij;4k

� ¼XCi¼1

Xnj¼1

ymij����zj � 4i

����2 m > 1 (10)

wherem denotes exponential weight for the degree of fuzziness ofthe partition matrix; jjzj � 4kjj denotes the Euclidean distance be-tween zj and the cluster center 4k.

To solve Equation (10), yij (for fixed 4k where i ¼ 1, ., C) iscalculated using Equation (11).

yij¼

1����zj�4i����2!1=m�1

Pck¼1

1�����zj�4k

����2!1=m�1 i¼1;.;C; j¼1.;n (11)

The FCM algorithm continually finds the minimum J(yij, 4k) untiljjU(iþ1) � U(i)jj < ˛where i denotes the iteration step and ˛ denotesthe termination criterion between [0, 1].

3.4. Fuzzy adaptive scheduling of multiple control policies

The idea of the gain scheduling [23] has motivated the adaptivescheduling; that is, the scheduling variables select or interpolateamong a priori constructed controllers. First, the controller sched-uling problem discussed in this study can be formulated as thefollowing state transition equation:

xtþ1 ¼ f ðxt ;utÞ (12)

where xt denotes the state vector and ut denotes the control actionvector at time t.

The scheduler for time interval t finds the control policy uj bysearching a set of candidate control policies U. It finds theminimumcost for the current state xt and future states only over the candi-date control policies U according to

minuj˛U

hf�xt ;ujðxtÞ

�þ J*ðxtþ1Þi

(13)

where f denotes a single-time interval cost.The cost function J* represents the desired state holding the

minimum cost in future time steps described as:

J*ðxtÞ ¼XPHk¼ t

f�xk;uk

�(14)

where PH denotes the number of time steps in the (future) plan-ning horizon.

The single-time interval cost f(xk,uk) is typically obtained usingthe quadratic criterion according to

f�xk;uk

� ¼ ðrkþ1 � ykþ1Þ2 (15)

where r denotes the reference, y denotes the output, i.e., yk ¼ h(xk).During online control, the evaluation of the cost J* requires

model f and h. However, running the system model real-time forthe evaluation of the cost J* within the sampling time frame maynot be always feasible. The proposed adaptive scheduler approxi-mates the control policy ut in the absence of a real-time runningmodel bymeans of searching for the local model, the state of whichhas the most similarity with the observed state.

Equation (16) conceptualizes this mechanism; it searches for thepre-stored states that are adjacent to the observed state xq. The pre-stored states are obtained offline by running closed-loop simula-tions with a number of nominal control policies that are (sub)optimal for the limited local operating conditions, but a collectionof which represents the global operating condition. Then theapproximated cost function ~J is calculated by adding up theweighted cost functions of the nominal neighborhood states xj.Since nominal local control policies are (sub) optimal to the oper-ation range of the corresponding nominal local model, their costfunctions are already minimized. Therefore, the closer the querystate xq is to the neighborhood nominal state xj, the smaller the costfunction J* is.

S.H. Kim / Building and Environment 67 (2013) 111e128116

J*ðxÞ ¼ minuq˛UðxqÞ

hf�xq;uq

�þ~J�f�xq;uq

��i~J�xq� ¼ PNðxqÞ

xj3jqJ�xj� (16)

where xj denotes a nominal neighborhood state that is adjacent tothe query state xq; N(xq) denotes the set of xj, thus xj˛N(xq); 3jq

denotes the dissimilarity between the nominal neighborhood statexj and the query state xq (between 0 and 1).

The proposed adaptive scheduler then calculates the controlpolicy uq through interpolating the locally optimized control pol-icies uj per the corresponding dissimilarity 3jq. The dissimilarity 3isconceptually defined as

3c ¼ ����xc � xq���� (17)

where xc denotes the state of the local cth model, and jja� bjj de-notes the Euclidean distance between states a and b.

The primary driver for the dissimilarity is attributed to distur-bances. In general, the disturbance w holds both measured andunmeasured characteristics, thus the overall disturbance can beestimated as bwk. As they can be considered a biased term for themodel input, different degrees of estimated disturbances can berepresented in the following state transition equation with an ad-ditive input disturbance.

xt ¼ f ðxt�1;ut�1Þ þ bwt�1 (18)

If the system contains a significant time delay such as buildings,the disturbance observed at time t often causes the state to deviatefrom the nominal state in future time steps with a significant timedelay. Therefore, if the disturbance bwt is observable at time t, thedissimilarity 3c can be rewritten by adding the estimated distur-bance bw into the state vector according to

3ct ¼

�������xct ; bwct�T � �xqt ; bwq

t�T ������ (19)

Note that the state and disturbance are assumed to be observable.The membership function u delivered from the fuzzy clustering

eventually serves as the dissimilarity 3. The membership functiondetermines the degree of the overlap between local models andthus the degree of the overlap between local control policies. Themembership function also smoothly transitions between controlpolicies and thus avoids kicks when the system behavior shifts fromone regime to another regime. As noted, regime shifting can beidentified by “observing” the state x and disturbance w, which canbe called the observer s. Then the incremental control variable Duis aggregated according to the membership function of theobserver s:

ut ¼ ut�1 þ Du ¼ ut�1 þXCi¼1

uiðsÞDuit (20)

whereui denotes themembership function of the observer s for thecontrol policy formulated for the ith local model.

Although there is no generally prescribed guide to selectobserver variables e rather it depends on the a priori knowledgeper application domain e fuzzy clustering often suggests a set ofcandidate observer variables and/or even an insight for the domainexpert to choose the right observer.

3.5. Development procedure of the adaptive MMPC for TES

The adaptive MMPC for TES is developed through the followingsteps:

Step 1: Construct a stub system model and calibrate the stubmodel. It is worth noting that while model calibration focuseson reducing biases in model parameters, precision andrandomness in model parameters and inputs can still be sig-nificant sources of disturbance. In general, calibration compli-ance codes specify a calibration tolerance such as CV-RMSE of�30% [24], �25% [25], and �20% [26] for hourly data. Moredetails about calibrating BEMs are found [27,28].Step 2: Prepare the training and verification input andoutput data set that consists of uncertainty sources for thedisturbance w, which are assumed to be primary drivers forvarious operation conditions and regime change. It is wellknown that the primary uncertainty sources causing theobserved demand varying from the forecasted demand includeweather, building operation, internal heat gain variation, freshair fraction, and infiltration [43]. Monte-Carlo simulations canbe used to quantify uncertainty sources to obtain the data set.The training data set will be used for fuzzy clustering (Step 3),while the verification data set will be used for offline learning(Step 8).Step 3: Perform fuzzy clustering as described in Section 3.3.Step 3-1: Run the Fuzzy C-Means (FCM) algorithm for theoffline training data set using an initial number of clusters Co asdescribed in Section 3.3. The clustering algorithm outputs thefuzzy partition matrix g and the cluster center matrix 4.Step 3-2: Determine the observer s. Each element yij of thepartition matrix g indicates which state and/or disturbancevariables (i.e., observer variables) can be premise variables thatare able to identify distinctive operation regimes. Selectedobserver variables should be cross-validated with respect to thea priori knowledge for the known factors sensitive to the output.Step 4: Tune each local model with the values of the observervariables located in the cluster center. Determine the fuzzyrule sets and the membership function ui for ith local model.

Each cluster becomes the operation range of each local model.Local models can thus be identified through tuning model pa-rameters with the values of the observer variables located in thecluster center.Determine the rule parameters and the membership function ui

in Equation (8). The membership function ui can be tuned tosatisfy the objective function (Equation (10)) through iteratingthe fitting of all the data into Oj(I); such that the iteration stopswhen:

Root Mean Square Error ðRMSEÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1N

XNk¼1

cok � ok

�2vuut < ˛

(21-1)

bo ¼PC

i¼1 uiD boiPCi¼1 ui

(21-2)

where k denotes the iteration step and ˛ denotes the terminationcriterion between [0, 1]; N denotes the number of simulation datapoints.If the condition in Equation (21) cannot be met, revisit Step 3 andadjust the number of clusters C.

Fig. 5. Three internal heat gain forecast scenarios include IHG-85%, IHG-100%, IHG-115%. Two ambient temperature forecast scenarios include W1 (nominal weatherforecast) and W2 (with higher max. tem). The varying occupancy scenario (MD) rep-resents a typical meeting day. Occupants have intensive meetings in the morning andearly afternoon, and then occupancy drops below the nominal in the late afternoon.The shaded area denotes on-peak hours.

S.H. Kim / Building and Environment 67 (2013) 111e128 117

Step 5: Offline optimization: identify Model-based PredictiveControls (MPCs) for each local model.

Develop optimal local control policies using MPCs for each localmodel using the objective function described in Equation (4).Note that robustness of the MPC is secured when the local MPCoperates only within its pre-determined operation boundary.

Step 6: Use of Kalman Filter for estimating the state using theobserver. A Kalman filter can be used to produce a statisticallyoptimal estimate of the observer variable. Details about appli-cations of Kalman filters for the observer can be found in Refs.[5,17].Step 7: Compute the global system control output. Firstcompute the system control signal Du of each local model andthen aggregate them according to the membership function ui.

The incremental control Du for the global system can be ob-tained through:

Du ¼PC

i¼1 uiDuiPCi¼1 ui

(22)

Compute the global system control output using u(t þ 1) ¼u(t) þ Du.

Fig. 4. Control process for TES of the building S. Control variables (in red) include the charging and discharging energy transfer rate of the TES. (For interpretation of the referencesto color in this figure legend, the reader is referred to the web version of this article.)

S.H. Kim / Building and Environment 67 (2013) 111e128118

Step 8: Offline learning. A successful scheduling of local modelsin the model bank depends on i) quality calibration of the stubmodel, ii) identifying critical sources of disturbances, iii) aneffective range of the disturbance bwt which is expected to beobserved during online control, and iv) adequate spacing be-tween membership functions that enables the observer to pre-cisely locate the local model and also enables the local controloutputs to smoothly transit to each other. Ideally the objectivefunction of MPC should be formed into a Lyapunov function forthe closed-loop system to guarantee system stability. In practice,although this requirement is generally relaxed for stable sys-tems with slow dynamics such as buildings [5], this step re-quires that the global control output that interpolates multiplelocal control policies in various circumstance should be verifiedwith respect to the desired control output (i.e., the referencecontrol).

For every data set zk of the verification data set, its cost functionshould be evaluated by the following:

JðzkÞ ¼ minuk˛U

hfðzk;ukÞ þ~Jðf ðz;uÞÞ

i(23)

The cost function J(zk) can be minimized when the controlvector uk is closer to the reference control vector urk, which is theoptimal outcome of the MPC for the singleton model identifiedby the verification data set zk. It is obtained according to:

urk ¼ argminurkbfuðtþjjtÞgjþHc�1

j¼t

J�zkðtÞ;urk

�(24)

In the ith iteration step, the control error ei is evaluated by thefollowing equation for every verification data set zk.

ei ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1N

XNk¼1

�uk � urk

�2vuut (25)

The iteration is repeated until the control error converges withthe convergence criteria R. For each iteration, the number of

Fig. 6. Coil load data clustered per operation scenario from 12 to 5 pm of the index day. Red cinterpretation of the references to color in this figure legend, the reader is referred to the

clusters, spacing between membership functions, and/or pa-rameters of the membership function can be readjusted forsmaller control error, which often requires revisiting Step 3.

Step 9: Online control. The adaptive MMPC can be deployed attime t as defined by the following optimization problem:

ut ¼ argminu˛U

hfðxt ;utÞ þ~Jðf ðx;uÞÞ

i(26)

4. Case study

A three-story office building located in Metro Atlanta, GA (calledthe building S), is built using TRNSYS [21]. This building has un-dergone numerous retrofits. Also, due to the nature of the ITconsulting firm that currently occupies this building, occupancylevels and the subsequent lighting and equipment operation levelsfrequently deviate from the norm.

The facility manager plans to change the current utility plan to anew TOU plan with a higher rate incentive ($0.129/kWh from 12 to7pm during weekdays in summer seasons and $0.032/kWh duringother hours), through which a load-shifting control strategy uti-lizing TES is expected to offer an economic benefit.

4.1. Computer model of the building S

Each floor consists of eight zones comprising 24 zones total.Each floor area is about 4161 m2 in which the core zone occupies2980 m2. The fenestration ratio is around 38% for each façade.Central cooling plants include the existing centrifugal main chiller(nominal capacity 1200 kW), a new centrifugal TES chiller (nominalcapacity 600 kW), and a new TES (nominal capacity 6000 kWh).Themain chiller has a constant coefficient-of-performance (COP) of3, which is an outcome of the calibration. It is also assumed that TESchiller has a COP of 3. A combinational operation between the mainchiller and the TES serves the coil load for fan coil units (with fan

ircles denote cluster centers. Note that clustered data are sampled at every 30 min. (Forweb version of this article.)

Fig. 8. Control error e when the number of clusters varies between 3 and 11 and thestandard deviation of the membership function varies from CoV of 3%e15%.

S.H. Kim / Building and Environment 67 (2013) 111e128 119

efficiency of 0.33). The set point temperature is set to 24 �C duringoccupied hours (7 ame5 pmweekday), otherwise released to 35 �C.

Fig. 4 illustrates the supervisory control process for TES. Asdescribed in Section 2, control variables for TES include chargingand discharging energy transfer rate of TES.

Only daily total building electricity use, hourly chiller electricityuse, andmonthly gas use data are available to calibrate the building Smodel for the calibration base year. Unfortunately there is no sub-metered data for lighting and equipment electricity use. With atypical office building operation and lighting and equipmentschedule and real weather data in 2008 acquired from Ref. [29], thebuilding S model has been calibrated according to the signatureanalysis [27], which presents graphical deviations betweenmeasured and simulated energy consumption as a function ofaverage dry bulb temperature. With the system configuration in2008 (with only the main chiller), the peak occupancy density iscalibrated to 0.1 person/m2; the peak lighting power density iscalibrated to 17 W/m2; and the peak equipment power density iscalibrated to 12.75W/m2. The COP of the main chiller is calibrated to3. Other parameters have been slightly modified from the designconditions or default values and then presented as the base value inTable A1eA5. The CV-RMSE for the chiller electricity use based onhourly data was calculated as 21.5% and the CV-RMSE for the totalbuilding electricity use using daily datawas calculated as 10.5%, bothof which are compatible with the ASHRAE tolerance of 30% [24].

4.2. Sources of uncertainty

To account for times of varying occupancy levels and depen-dently varying lighting and equipment uses due to the nature of ITconsulting companies, variations of �15% are accounted for inoperation schedules; three daily occupancy profiles and corre-sponding LPD and EPD profiles (Internal heat gain profiles of IHG-85%, IHG-100%, and IHG-115%) are assumed based on facilitymanagers’ opinions, as Fig. 5 depicts.

Kim and Augenbroe have shown that, in general, the NDFD XML[4] (based on the online weather forecast by the National DigitalForecast Database) outperforms the EWMAwith absolute deviation

Fig. 7. TES control for each local model includes charging and discharging profiles for each

modification [30] (based on the location-specific historical weatherrecords) in forecasting sporadic characteristics of weather [4]. Theyrecommend using multiple weather scenarios for MPCs to dealwith sporadic uncertainty in the weather forecast more adequately.Both forecasts were collected for a typical summer day, namely theindex day. In Fig. 5, the abs.dev.EWMA projects a typical summerday in the building location (W1), whereas the NDFD-XML projectshigher max temperature (W2).

Forecasted operation scenarios for the index day therefore consistof combinations between daily internal heat gain profiles and dailyweather forecast profiles, as Equation (27) describes. Note that the

time interval. The shaded area denotes the on-peak hours (from 12 to 7 pm weekday).

Fig. 9. The membership function of the coil load observer at 3 pm of the index day with the weather forecast W1.

S.H. Kim / Building and Environment 67 (2013) 111e128120

nominal operation scenario W1-IHG-100% consists of the nominalweather forecast W1 and the internal heat gain forecast IHG-100%.X

¼ fW1;W2g�fIHG�85%; IHG�100%; IHG�105%g (27)

Sources of uncertainty in the model and surrounding configu-ration are listed in Table A1eA5 in the Appendix. For each source,the range of variation for each source has been assessed from ref-erences. Note that uncertainty sources for building thermal de-mand (Table A1eA4 and outside air fraction in Table A5) anduncertainty sources in operating FCUs (Table A5 and Table 5 of Ref.[43]) are used for clustering (Section 4.3).

4.3. Identification of local models and local controllers

Recall from the process model for TES (Equations (5-1) and (5-2)) that a successful TES control depends on an accurate predic-tion of total on-peak cooling demand and a responsive discharge ofthe stored cooling energy for varying cooling demand. Thus it is

Fig. 10. The membership function of the coil load observer a

reasonable that local models are identified for the distinctive rangeof cooling demand variations.

Practically, though, time variant cooling demand cannot beobserved; instead, the coil load for FCUs (depicted in Fig. 4) isobservable through monitoring temperature sensors and flowmeters for the flow-in and flow-out of a FCU. Therefore, clusteringdata were collected for uncertainty sources for the coil load of FCUssuch as supply air temperature, water flow rate, and fan efficiency,as well as external and internal disturbances that are known to bedominant drivers of the cooling demand variation.

From the set of 192 simulation runs (Monte Carlo samplings of 32sets are collected for each of the six operation scenarios), approxi-mately 10,000 data points were collected for the training data. Asampling time of 0.5 h is used. An initial intention was to find anycorrelations between specification and process parameters inbuilding and HVAC system components and operation scenarios,such as the cooling tower efficiency depends on the web-bulbtemperature. After several trials for different clustering configura-tions and evaluations, however, the FCM algorithm verifies the a

t 3 pm of the index day with the weather forecast W2.

Fig. 11. TheW3 denotes the actual observed ambient temperature for the index day. Itsweights against the two forecast W1 and W2 are calculated by Kalman filter.

S.H. Kim / Building and Environment 67 (2013) 111e128 121

priori knowledge that clusters for coil loads are distinctive peroperation scenario, as shown in Fig. 6, which depicts the clusteringresults from 12 pm to 5 pm. Although outside air rate, externalconvective heat transfer coefficient, ground albedo, glazing U-valueand SHGC, core zone capacitance, FCU fan efficiency, FCU supply airtemperature, and roof U-value are observed as sensitive factors tocoil load, coil load variations by these factors are observed as stillbeing anchored to the individual operation scenario. For instance,although higher outside air rate results in higher coil load in oneoperation scenario, it is not remarkably higher than the coil loadresulting from the operation scenario with higher ambient temper-ature and/or higher internal gain. The cluster analysis using the FCMalgorithm therefore implies that a reasonable clustering for coil loadsdepends on the realistic ranges of operation scenarios and theeffective spacing between operation scenarios (thus the number ofclusters), such that each local model can be distinctly identified foreach operation range by each scenario.

Although both weather and internal heat gain scenarios areprimary drivers in varying coil load, the weather scenario is moreimpactful than the internal heat gain scenario, and it is also directlyobservable by monitoring weather variables through an on-siteweather station. Thus, ambient temperature is added to theobserver, yielding the following definition for the observer s.

st ¼hxcoil Loadt ; wamb:tem

t

i(28)

where xt denotes the observed coil load at time t andwt denotes theobserved ambient temperature at time t.

Parameters of each local model were tuned with the values ofparameters for the cluster center. The operation scenario of eachlocal model was set with the corresponding weather scenario andinternal heat gain scenario. Initial membership functions were thenbuilt with the normal distribution with mean and standard devia-tion of coil loads distributed in each cluster.

Local MPCs were developed for each local model according toEquation (4).ModelCenter [31]was used for the optimization engine.It is worthy to note that the computer complexity of optimization for

Table 1Configurations of the depreciation scenario where each parameter represents wear and

Nominal

A. Energy sensitive building elements and HVAC&R equipmentExtWall.U-value (W/m2 K) 0.462ExtWall.Solar absorptance 0.65Roof.U-value (W/m2 K) 0.292Roof.Solar absorptance 0.6SlabFloor.U-value (W/m2 K) 0.289Glazing.U-value (W/m2 K) 1.76Glazing.SHGC 0.65Outside air rate (ACH) 1.24Infiltration (ACH) 0.3Chiller COP coefficient 3.00Chilled water supply temperature (�C) 6.67Chilled water loop temperature differential (�C) 5.5Condenser water loop temperature differential (�C) 5.5FCU cooling supply air temperature (�C) 12.7FCU total fan efficiency 0.33Pump efficiency 0.77B. Thermal zones and external environmentSouthZone. Capacitance (kJ/K) 9799EastZone. Capacitance (kJ/K) 9799NorthZone. Capacitance (kJ/K) 9799WestZone. Capacitance (kJ/K) 9799CoreZone. Capacitance (kJ/K) 98893External convective heat transfer coefficient hf hfInternal convective heat transfer coefficient (ceiling) (kJ/h-m2 K) 1.8Internal convective heat transfer coefficient (floor) (kJ/h-m2 K) 10.8Internal convective heat transfer coefficient (interior wall) (kJ/h-m2 K) 9Ground albedo 0.17

nominalmodel under nominal scenario (i.e., without a considerationof uncertainty) is often trivial [5]. As noted, typical MPC carries onmultiple execution horizons, which are intentionally designed to beshorter than the planning horizon. However, the adaptive MMPCpresented in this study considers the planning horizon and theexecution horizon of a 24 h period to demonstrate its robustnessagainst unmeasured disturbances, namely the longest executionhorizon case (although shorter execution horizons may still bechosen). The MMPC is designed to have the preconditioning horizon(PCH) from 6 pm to 8 pm and the planning horizon (PH) from 8 pmto next day 8 pm. Thus the execution horizon (EH) is designed tostart at 8 pm.When theMPC starts a closed-loop simulation at 6 pm,themodelermakes sure that actual thermal state at 6 pm is explicitlyassigned to the simulation.

TES charging control requires the prediction of the totaldischarge during on-peaks, which obviously depends on the pre-dicted on-peak coil load. Until occupied hours begin and thus the

tear conditions and inherently varying physical factors.

model Depreciated model Remark

1.755 Wear and tear; least insulation0.77 Wear and tear [32]1.328 Wear and tear; the least insulation0.72 Wear and tear [32]0.99 Wear and tear; the least insulation5.74 Performance drops to a single pane glazing0.951.5 Wear and tear; 20% higher0.6 Wear and tear [38]2.73 Wear and tear; 9% less9.3 Wear and tear; 40% higher6 Wear and tear; 10% higher6.6 Wear and tear; 20% higher14 Wear and tear; 10% higher0.27 Wear and tear; 20% lower0.6 Wear and tear [40]

16,678 The greater interior capacitance [33]16,67816,67816,678168,3171.2 hf The greater coefficients [32e36]2.881814.70.3

Table 2Total HVAC electricity use (on-peak and off-peak ratio in parenthesis) and total HVAC operation cost of the MMPC, optimal MPC and storage priority control in the forecastedscenarios.

Evaluation scenarios Nominal weather þ nominal internal heatgain (W1-IHG-100%)

Nominal weather þ lower internal heatgain (W1-IHG-85%)

Higher max. temperature þ higher internal heatgain (W2-IHG-115%)

Control strategies Optimal MPC MMPC Storage priority Optimal MPC MMPC Storage priority Optimal MPC MMPC Storage priority

Total HVAC electricityuse (kWh)

2715 (10%/90%) 2743(10%/90%)

2838(10%/90%)

2470(10%/90%)

2557(10%/90%)

2717 (11%/89%) 3942 (9%/91%) 3954(11%/89%)

3809 (17%/83%)

Total Cost ($) 112 (100%) 115 (103%) 118 (105%) 103 (100%) 106 (103%) 115 (112%) 161 (100%) 166 (103%) 182 (113%)

S.H. Kim / Building and Environment 67 (2013) 111e128122

coil load can be observed, ambient temperature is the only availableobserver variable. Thus the MMPC takes a control strategy that TESis charged at the base charge rate until the coil load is observed,presuming the internal heat gain scenario IHG-70% and theweather scenario chosen by the observed temperature. Then theadaptive charging becomes activated (namely, the charge on-demand) when the coil load becomes observable. The Kalman fil-ter that calculates statistically time variant optimal weight of theobserver with respect to the forecast, enables an advance sched-uling, thus it eventually accelerates the adaptation. The resultingMPC solutions for each local model are presented in Fig. 7.

For offline learning, verification data sets for 15 of typical summerdays in 2008 were recollected; these data sets include the sameportfolio of uncertainty sources used for initial clustering, but actualobserved values were used for weather scenarios. During offlinelearning of the membership function, the exercise range of internal

Fig. 12. Chiller load profiles, TES control, and HVAC electricity use profile of the MMPC, MPCmodel participation ratio of the MMPC per the observed coil load follows in the bottom.

heat gain scenario is extended from IHG-60% to IHG-140% as a pro-vision for extreme cases. Membership functions were tuned byvarying the number of clusters, and mean and standard deviation ofthe membership function, until the control error falls under thecriteria (Equation (25)). As shown in Fig. 8, nine clusters (i.e., 15%spacing in internal heat gain level) and standard deviation of 5% ofthe mean of coil loads in each cluster (i.e., Coefficient of variation of5%) resulted in the control error e of less than 0.05. An example ofmembership functions of the observed coil load for each weatherscenario at 3 pm of the index day is shown in Figs. 9 and 10.

5. Evaluations

Evaluation scenarios are chosen in an attempt to describe un-certainty situations as realistic as possible to which MPC is sus-pected to be vulnerable. The first type of those evaluation scenarios

and storage priority control in the lower-cooling-demand scenario W1-IHG-85%. Local

S.H. Kim / Building and Environment 67 (2013) 111e128 123

includes unexpected and sporadic variation of weather and internalheat gains caused by varying occupancy and corresponding re-actions. Also when MPC is formulated based on the building andsystem models, but calibrated only for practically available pa-rameters due to a lack of benchmark data or budget limits, they stillcan be vulnerable to model parameter uncertainty which can occurwhen the model does not fully represent the reality.

5.1. Benchmark control strategies

Performance of the adaptive MMPC will be compared to thefollowing benchmark strategies.

i) Optimal MPC: it is formulated according to the objectivefunction in Equation (4). It assumes a perfect prediction forweather and internal heat gains, and perfectlymatchingmodelparameters and configurations under each evaluation scenario.Therefore this benchmark implies theoretical performancetarget and its control profile denotes the reference control (ur).

ii) Storage priority control: it is one of the most typical TEScontrol strategies while chiller priority control can result inhigher operation costs than the case without TES under sometime-varying utility tariffs [2]. Based on the predicted base load,it discharges the cooling energy at a constant rate during on-peak. The main chiller serves the load difference if the

Fig. 13. Chiller load profiles, TES control, and HVAC electricity use profile of the MMPC, MPCmodel participation ratio of the MMPC per the observed coil load follows in the bottom.

observed load is greater than the predicted load. Thus as long asthe base load prediction is sufficiently accurate, the designatedload shifting is secured; this benchmark is the baseline strategyimplying practical performance target. In this example, the baseload is predicted for nominal scenario and nominal model.

5.2. Evaluation scenarios

This section describes the evaluation scenarios with more details.

i) Forecasted scenarios: Six operation scenarios S (Section 4.2)are the forecasted scenarioswhenMPC begins to be formulatedfor the planning horizon. While the scenario W1-IHG-85% isexpected to result in a lower cooling demand profile than thenominal scenario, the scenario W2-IHG-115% is expected toresult in a higher cooling demand profile than the nominalscenario. Also, in these forecasted scenarios it is assumed thatthere isnoparameteruncertainty inthemodel, systemdata,andprocess parameters of the test building (i.e., nominal model).

ii) Depreciation scenario: Depreciation scenario implies (boun-ded) theworst case scenariowhere the test buildingmaycontainaged components and worst performance values for varyingphysical parameters (e.g., larger convective heat transfer coef-ficient) and/or biased sensor readings formonitored processes,but which still fall under the nominal operation scenario

and storage priority control in the higher-cooling-demand scenario W2-IHG-115%. Local

Table 3Total HVAC electricity use (on-peak and off-peak ratio in parenthesis) and total HVAC operation cost of theMMPC, optimal MPC, and storage priority control in the depreciationscenario and the unmeasured disturbance scenarios W2-IHG-MD and W3-IHG-MD.

Evaluation scenarios Depreciated model þ nominal scenario(W1-IHG-100%)

Higher max. temperature þ meetingday (W2-IHG-MD)

The actually observed weather þ meetingday (W3-IHG-MD)

Control strategies Optimal MPC MMPC Storage priority Optimal MPC MMPC Storage priority Optimal MPC MMPC Storage priority

Total HVAC electricityuse (kWh)

3640 (13%/87%) 3686(14%/86%)

3632 (18%/82%) 3725 (9%/91%) 3811(10%/90%)

3616 (15%/85%) 3473 (9%/91%) 3526(10%/90%)

3379 (15%/85%)

Total cost ($) 163 (100%) 168 (103%) 178 (109%) 152 (100%) 156 (103%) 167 (110%) 142 (100%) 146 (103%) 156 (110%)

S.H. Kim / Building and Environment 67 (2013) 111e128124

W1-IHG-100%. Therefore, the depreciation scenario is designedto focus primarily on highlighting the parameter uncertainty inthe model, system data, and process variables. Specifically forMPC strategies, the depreciation scenario represents the cali-brated model that is still not accurately describing the actualstate,which is likely to cause theunderperformanceof theMPC.For instance, although calibrations have been performed forcritical parameters of the building model of the test building, asynergy of calibration uncertainties can still introduce a sig-nificant bias to the building model in predicting building de-mand and power consumption. Table 1 presents the energysensitive parameters, the selected values of which representpotentially worse energy performance.

iii) Unmeasured disturbance scenario: Disturbance rejection ca-pabilities ofMPCs are evaluated under two operation scenarios

Fig. 14. Chiller load profiles, TES control, and HVAC electricity use profile of the MMPC, MPCof the MMPC per the observed coil load follows in the bottom.

(W2-IHG-MD and W3-IHG-MD) that are not forecasted sce-narios counted during the planning horizon. The internal heatgain scenario IHG-MD stands for a frequently-observed varyingoccupancy (e.g., meeting days) and corresponding lighting,equipment and fan operation profiles as depicted in Fig. 5. Theweather profileW3 denotes the actual weather observed in theindex day in 2008 as depicted in Fig. 11. Time varying (Kalmanfilter) weight of the observed weather W3 with respect to twoweather forecasts W1 andW2 is also presented in Fig. 11.

5.3. Results

In all the forecast scenarios, the adaptive MMPC for TES out-performs the storage priority control while resulting in slightly

and storage priority control in the depreciation scenario. Local model participation ratio

S.H. Kim / Building and Environment 67 (2013) 111e128 125

higher cost than the optimal MPC as shown in Table 2. On-peak andoff-peak use ratios of the MMPC are very closer to those of theoptimal MPC in the forecast scenarios.

In the lower cooling demand scenario W1-IHG-85% (Fig. 12) andthe higher-cooling-demand scenario W2-IHG-115% (Fig. 13), theMMPC charges TES as much as the optimal MPC does while thestorage priority control overcharges in the W1-IHG-85% and un-dercharges in the W2-IHG-115% than the optimal MPC does, whichleads to higher operation cost; in the W2-IHG-115% scenario, inparticular, the main chiller with the storage priority control has toserve the remaining on-peak cooling demand as the red dottedsquare shown in the chiller load profile in Fig. 13.

The MMPC demonstrates its adaptive feature that flexibly con-trols charge and discharge rates according to the observer’ssignature on how much cooling energy will be needed. The localmodel participations of the MMPC (shown in the bottom of Figs. 12and 13) indicate which local models are actively involved at time t,which correspond to the operation range observed at time t.

Fig. 15. Chiller load profiles, TES control, and HVAC electricity use profile of the MMPC, MPCthe meeting day internal heat gain (W3-IHG-MD). Local model participation ratio of the M

In the depreciation scenario shown in Table 3, the adaptiveMMPC still outperforms the storage priority control. As shown inFig. 14, parameter uncertainty involved in this scenario has causedthe coil load to increase more stiffly, thus the operation regime ofthe MMPC keeps moving quickly toward the high coil load regimesas the coil load begins to be observed at 7 am. This adaptive featureenables a marginally sufficient charge of cooling energy while thestorage priority control undercharges (i.e., the main chiller serves asignificant amount of on-peak cooling demand).

The calibrated model used in theMPC has passed the compliancerecommended calibration criteria of theCV-RMSE30% [24]. However,it stillmaycontain significant calibrationuncertainty that causes risksfor the single model-based MPC in meeting the desired control per-formance. Perhaps more stringent calibration criteria would beneeded for the building model being used for the MPC. In reality, aprecise assessment of the actual building state through calibrations isvery dependent on situations in that an effective calibration requireshigh spatial and temporal resolutionmeasured data, such as fine sub-

and storage priority control in the actual observed temperature for the index day andMPC per the observed coil load and ambient temperature follows in the bottom.

S.H. Kim / Building and Environment 67 (2013) 111e128126

metered observations, and lighting and equipment power uses for atleast a year, which are not commonly available for many buildingswhere the Energy Management Systems (EMS) is not installed e orcollecting such data is even prohibited during retro-commissioningdue to the high cost. It is true that an extensive calibration makesthe performance of the MPCs more reliable; however, the adaptiveMPC can be an effective solution for the reality when such extensivecalibration isnot feasible, but onlyminimumcalibrationsare allowed.

In the unmeasured disturbance scenarios W2-IHG-MD andW3-IHG-MD, the adaptive MMPC still outperforms the storage prioritycontrol, as described in Table 3. While the storage priority presentsa static performance in charging and discharging TES regardless ofthe unmeasured disturbance, the adaptiveMMPC has the capabilityto adaptively control charging and discharging rates depending onthe observed coil load, as their distinctive behaviors are compara-tively depicted in the TES control profiles of Fig. 15. In the scenarioW3-IHG-MD that contains the (unmeasured) actually observedweather for the index day, the MMPC starts charging TES early asthe local controllers developed in theweather forecastW2 do, sincethe observed weather is closer to the W2 forecast as depicted inFig. 15. Then it adjusts the charging and discharging rates accordingto the normalized weights for the observed temperature and coilload.

Uncertainty in building material properties and their profiles.

Building material thermalproperties

Base Min. Max. References

ExtWall.U-value (W/m2 K) 0.462 0.462 1.367 The base value standsfor the design condition orcalibrated value. The max.values are assessed eitherassuming the least insulationor based on Ref. [32]

ExtWall.Solar absorptance 0.65 0.65 0.77Roof.U-value (W/m2 K) 0.292 0.292 1.016Roof.Solar absorptance 0.6 0.6 0.72Floor.U-value (W/m2 K) 4.39 4.39 5.68SlabFloor.U-value (W/m2 K) 0.289 0.289 0.99IntWall.U-value (W/m2 K) 2.513 2.513 5.86Glazing.U-value (W/m2 K) 1.76 1.4 5.68Glazing.SHGC 0.65 0.589 0.855

Table A2Uncertainty in interior mass properties and their profiles.

Interior mass properties Base Min. Max. References

Weight f for total interior 9 3 16.02 [33]

6. Discussion and conclusion

This study presents an investigation of the demand-side controlenhancement of TES though comparing the benchmark controlstrategies and newly-suggested adaptive MMPC. Although theproposed adaptive MMPC still lies in prototypical attempts, evalu-ation results, which are carried out in closed-loop simulations foran actual test building that is calibrated with real data and weather,showed that the adaptive MMPC outperforms the storage priorycontrol, which is already known to be practically solid, and alsoensures near-optimal performance in load shifting under variousuncertainty situations, including depreciation scenario and un-measured disturbance scenarios.

Another merit of the multi-model approach for MPC is that, forlegacy MPCs under uncertainty, the computational burden due to aprovision for unmeasured disturbance is centered on optimizationthrough a single model. The adaptive MMPC distributes suchburden to multiple models and optimizations in advance (with lesscomplexity),2 and then the online supervisory controller selects (orinterpolates) the most adequate models and control policies for thecurrent condition. This mechanism is well-suited for parallelcomputing, which the building control domain should consider itsprospective computation platform. Above all, this mechanism of-fers a relaxation to the current MPC practice that updates the statein (quasi) real time (the execution horizon is as short as a singletime step or several time steps). That is, the adaption throughmultiple models is capable of providing near-optimal control so-lutions as the case study demonstrates that the adaptive MMPC stilloutputs a satisfactory performance in handling uncertaintyregardless of the longest execution horizon case (i.e., EH ¼ PH).

2 For instance, the legacy MPC takes 1 h of the execution horizon (EHMPC ¼ 1 h).Thus 24 computation calls are requested for single day control profile. When theadaptive MMPC takes 24 h of the execution horizon (EHMMPC ¼ PH ¼ 24 h; thelongest EH for the example case), only one computation call is requested per day.Instead multiple local control profiles are formulated in parallel at that computationcall. Assuming both control problems are equivalent in computation complexity (forexample, each optimization for the nominal case (PH ¼ 24 h) takes about 30 min),theoretically the real-time computation load of the adaptive MMPC is 1/24 of thelegacy MPC. Compared to the Stochastic MPC [5,8], which is known to be computa-tionally more complex, the real-time computation load reduction would be greater.

BEM is used to construct local models for the adaptive MMPC.Although its simulation speeds are slower than simplified firstprinciple models and data-driven black-box models, BEM enablessemantic model calibrations through which practitioners wouldobtain more model fidelity e the foremost prerequisite that theperformance of MPC depends upon. Currently using BEM for theadaptive MMPC, however, is still limited to the simulation pro-grams that allow explicit state initialization such as TRNSYS.Readers can refer to Refs. [9,11] for further discussions.

As the adaptive MMPC presumes a reasonable boundary of un-certainty, the quality of model input data and operation scenarioforecast is a key factor for achieving the desired demand-side controlperformance. Additionally increasing the predictability of theobserver such as using Extended Kalman, Ensemble Kalman, orFuzzy Kalman filters [17] would be a readily available enhancement.Sharper calibration criteria for models specifically used for MPC andanalytical proof for its robustness and stability are a theoreticalextent that warrants further study. A capability of online parametertuningmay be a practical extent that couldmake the adaptiveMMPCa more viable solution, for which Lee and Lee proposes a feasiblemethod [20]. An extraction of near-optimal rule sets that are readilyimplementable to the digital control system [42] can be a furtherpractical use case of the adaptive MMPC. In summary, with thesefuture works, the adaptive MMPC can be a promising control tech-nique for TES meeting the required demand-side performance.

Acknowledgment

The author acknowledges the support of professor GodfriedAugenbroe of Georgia Institute of Technology, the U.S. SiemensCorporate Research and Dr. Chellury Ram Sastry of the Pacific North-westNationalLaboratoryunder theHighPerformanceBuildingProject.

Appendix. Uncertainty sources in model and configurationparameters used in developing the adaptive MMPC are asfollows:

Table A1

thermal massnoteA1

Capacitance (f � Vol) 12 � Vol 4.8 � Vol 20.4 � VolSouthZone. capacitance (kJ/K) 9799 3920 16,678 Calculated

based onthe volumeof each zone.

EastZone. capacitance (kJ/K) 9799 3920 16,678NorthZone. capacitance (kJ/K) 9799 3920 16,678WestZone. capacitance (kJ/K) 9799 3920 16,678CoreZone. capacitance (kJ/K) 98,893 39,557 168,317

Note A1: Total interior thermal mass ¼ (1 þ f) � Air_Mass; Air_Mass denotes thetotal thermal capacity of the indoor air (¼rairVroomCp,air); f denotes the ratio of thetotal internal thermal capacities from furniture and interior partitions and thethermal capacity of indoor air [33]. The base value has also been calibrated throughcomparisons between TRNSYS and EnergyPlus models for the same configuration.

Table A3Uncertainty in external environment and their profiles.

External environment properties Base Min. Max. References

External convective heat transfercoefficient hfnoteA2 (winward)

hf 0.82 hf 1.18 hf [33,34,35,36]

External convective heat transfercoefficient hfnoteA2 (leeward)

hf 0.8 hf 1.2 hf

Ground albedo 0.17 0.15 0.3 [32]

Note A2: Using Palyvo’s linear model hf ¼ 7.4 þ 4.0 Vb; Vb denotes the free streamwind speed (w10 m above roof) in m/s.

Table A4Uncertainty in thermal zone properties and their profiles.

Thermal zone properties Base Min. Max. References

Internal convective heat transfercoefficient (ceiling) (kJ/h-m2 K)

1.8 1.08 2.88 [34,36]

Internal convective heat transfercoefficient (floor) (kJ/h-m2 K)

10.8 10.8 18 [34,36]

Internal convective heat transfercoefficient (interior wall) (kJ/h-m2 K)

9 5.72 14.7 [33,34,35,36]

Infiltration (ACH) noteA3 0.3 0.3 0.6 The base andmax value arebased on [38].

Note A3: Calculated using the DOE-2 Methodology [37] assuming only perimeterzones have infiltrations during ventilation-off.

Table A5Uncertainty in power efficiency and degradation of primary HVAC&R systems andtheir profiles

Power efficiency anddegradation of primaryHVAC&R systems

Base Min. Max. References

Outside air rate (ACH) 1.24 1.24 1.5 The base value is basedon the ASHRAE 62. Themax value stands for20% more due todegradation.

Chiller degradationcoefficient noteA4

0 0 2.6 [33]

Chilled water supplytemperature (�C)

6.67 6.67 9.3 [39]

Chilled water looptemperaturedifferential (�C)

5.5 5.5 6 [39]

Condenser water looptemperaturedifferential (�C)

5.5 5.5 6.6 [39]

FCU cooling supply airtemperature (�C)

12.7 11.4 14 Based onmanufacturer

FCU total fan efficiency 0.33 0.27 0.33 Based onmanufacturer

Pump efficiency 0.77 0.6 0.77 [40]Pipe heat loss coefficient

(kJ/h-m2 K)15.8 15.8 16.6 [32]

TES heat loss coefficient(kJ/h m2 K)

1.19 0.155 1.58 [41]

TES additional thermalconductivity(kJ/h m2 K)

0.9 0.83 0.97 [41]

Note A4: COPcyclic ¼ COPsteady�state � PLF; PLF¼ 1 � Cd � (1 � PLR); COP denotes thecoefficient of performance; PLF denotes the part load factor; Cd denotes thedegradation coefficient; and PLR denotes the partial load ratio.

S.H. Kim / Building and Environment 67 (2013) 111e128 127

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