Learning-Based Hierarchical Distributed HVAC ... - IEEE Xplore

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Learning-Based Hierarchical Distributed HVAC Scheduling With Operational Constraints Nikitha Radhakrishnan, Member, IEEE, Seshadhri Srinivasan, Senior Member, IEEE, Rong Su, Senior Member, IEEE, and Kameshwar Poolla

Abstract— This investigation proposes an energy management system for large multizone commercial buildings that combines distributed optimization with the adaptive learning. While the distributed optimization provides scalability and models the fresh-air infusion as ventilation constraints, the learning algorithm simultaneously captures the influences of occupancy and user interactions. The approach employs a hierarchical architecture and uses a service-oriented framework to propose a distributed optimization method for commercial buildings. In addition, it also includes operational constraints required for optimizing the building energy consumption not studied in the literature. We show that our hierarchical architecture provides much better scalability and minimal performance loss comparable to the centralized approach. We illustrate that the influences of operational constraints on chiller, duct, damper, and ventilation are important for studying the energy savings. The energy saving potential of the proposed approach is illustrated on a 10-zone building, while its scalability is shown via simulations on a 500-zone building. To study the robustness of the approach meeting cancellations or other events that influence zone thermal dynamics, the resulting energy savings are studied. The results demonstrate the advantages of the proposed algorithm in terms of scalability, energy consumption, and robustness. Index Terms— Commercial building, heating, ventilation, and air-conditioning (HVAC) system, hierarchical distributed optimization, learning-based token scheduling algorithm (LBTSA), model predictive controller (MPC).

Ai Ari Ai , Ai ci cp

N OMENCLATURE Duct cross-sectional area for zone i valve opening (m2 ). Floor area of zone i (m2 ). Minimum and maximum cross-sectional area of duct [m2 ]. Thermal capacitance for zone i [kJ K−1 ]. Specific heat of air [kJ kg−1 K−1 ].

Manuscript received March 13, 2017; accepted June 18, 2017. Manuscript received in final form July 12, 2017. This work was supported in part by the Republic of Singapore’s National Research Foundation through a grant to the Berkeley Education Alliance for Research in Singapore for the Singapore-Berkeley Building Efficiency and Sustainability in the Tropics and in part by a grant through Building & Construction Authority for the Green Building Innovation Cluster under Grant NRF2015ENC-GBICRD001-057. Recommended by Associate Editor A. G. Alleyne. (Corresponding author: Rong Su.) N. Radhakrishnan and R. Su are with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (e-mail: [email protected]; [email protected]). S. Srinivasan is with SinBerBEST, Berkeley Education Alliance for Research in Singapore, Singapore 138602 (e-mail: [email protected]). K. Poolla is with the Mechanical Engineering Department, University of California at Berkeley, Berkeley, CA 94720-1740 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCST.2017.2728004

dr Ev gi Hp i k kf m˙ i m˙ il m˙ ih m˙ OA m˙ SA nz p0 pi Pc Pf Pi Q˙ Q ch Ri Ra

Rp

Tc Ti Til Tih Toa Z pi δ η

Return to total air ratio. System ventilation efficiency. Cooling energy supply to zone i [kJ]. Prediction horizon in time epochs. Zone index. Sample index. Parameter capturing fan efficiency and duct pressure losses. Cool air mass flow rate into zone i [kg s−1 ]. Lower limit on air mass flow rate [kg s−1 ]. Upper limit on air mass flow rate [kg s−1 ]. Mass flow rate of outside air [kg s−1 ]. Mass flow rate of fan supply air [kg s−1 ]. Number of zones. Pressure at supply fan i [Pa]. Pressure at entrance of zone i [Pa]. Chiller power consumption [kJ]. Fan power consumption [kJ]. Population of zone i . Cooling load forecast for zone i [kJ]. Constant for various amounts of cooling loads. Thermal resistance between zone i and the environment [kW K−1 ]. Outdoor air flow rate required per unit area determined by ASHRAE standard 62-2001 [kg s−1 ]. Outdoor air flow rate required per person determined by ASHRAE standard 62-2001 [kg s−1 ]. Temperature of cool air supply [°C]. Temperature of zone i [°C]. Lower thermal comfort bound [°C]. Upper thermal comfort bound [°C]. Temperature of outside air [°C]. Primary outdoor air fraction for zone i . Sampling time [s]. Reciprocal of chiller COP. I. I NTRODUCTION

E

NERGY optimization in large commercial buildings is a significant problem in countries with tropical climate, such as Singapore, wherein the building energy consumption is about 40% [1]. Centralized approaches for energy optimization were studied in the literature (see [2], [3] and references therein). These works use model predictive controllers (MPC) due to their ability to embed information (e.g., weather, occupancy, and so on) [4]. The centralized approaches solve

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a complex and large-scale optimization model to optimize energy use, leading to computational challenges and increased hardware cost for buildings with 200+ zones. Distributed approaches overcome the shortcomings of centralized approaches by optimizing the fan energy consumption in the individual zones [5]–[7]. Distributed approaches using dual-decomposition [7], affine quadratic regulator [8], affine disturbance feedback [9], agent-based suboptimal controller [10], decentralized control with loss factor [11], and Dantzig–Wolfe decomposition [12] have been proposed. Though distributed approaches offer good scaling and low complexity, the chiller consumption is not considered in the formulation. Furthermore, the influence of the room size, occupancy, and user interference on the energy optimization has not been studied. The use of occupancy measurement to trigger a set-back temperature in underactuated buildings was studied in [13], where a heuristic algorithm was used to reduce the energy consumption. Stochastic approaches for optimization considering occupancy disturbances have been studied in [15] and [16]. Chiller energy consumption was not considered in these analyses. More recently, a new hierarchical service-based distributed architecture for control and scheduling of heating, ventilation, and air-conditioning (HVAC) operations in multizone commercial buildings called Token-Based Scheduling Strategy (TBSS) was proposed in [1] and [17]. The method provided good scalability and its energy savings were comparable with the centralized approaches. It does not include models for: 1) fresh air infusion considering the room size and occupancy; 2) heating due to occupancy and stray sources; and 3) chiller capacity constraints. Infusing fresh air based on room size and occupancy levels enhances the energy efficiency significantly. Embedding predictive occupancy information within the zone thermal models also improves energy efficiency. Inclusion of chiller capacity constraints within the optimization leads to more realistic control while assuring occupant comfort. This investigation overcomes the shortcomings of TBSS by using ASHRAE standard recommendations (62-2001: ventilation for acceptable indoor air quality) [17] to optimize the amount of fresh air induction. To account for occupancy and stray heating effects in the zones, a learning-based model predictive controller (MPC) is proposed, inspired from [18]. The MPC solves the optimization problem forward-in-time to compute the optimal supply of cooling air, and estimates the occupancy using a moving horizon estimation strategy. The above-mentioned two modifications capture the effects of occupancy and the room size. Constraints modeling the chiller capacity are included within TBSS without affecting its distributed implementation by using the Lagrangian relaxation technique. We show that the energy savings of TBSS are comparable with the existing centralized approach, and that the operational constraints significantly influence the realized energy savings. Our principal contributions are as follows: 1) a learning-based token scheduling algorithm (LBTSA) for commercial buildings, which accounts for occupancy and stray heating;

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2) inclusion of ventilation constraints based on the ASHRAE standard and the chiller capacity constraint; 3) establishing that operating constraints critically affect realized energy savings; 4) exploration of the robustness of our LBTSA by considering the effect of abrupt disturbances, such as meeting cancellations. II. P ROBLEM F ORMULATION A. Energy Optimization in HVAC Systems Consider the zone thermal dynamics of a multizone building ci T˙i = m˙ i c p (Tc − Ti ) + Ri (Toa − Ti ) + Q˙ i .

(1)

Discretizing (1) with a sampling period δ leads to Ti (k + 1) + α1 Ti (k) + α2 m˙ i (k)(Ti (k) − Tc ) = v i (k)

(2)

where α1 = (δ Ri /ci ) − 1, α2 = (δc p /ci ) and v i (k) = (δ/ci )( Q˙ i (k)+ Ri Toa (k)). The bilinear model dynamics can be linearized by introducing a new variable gi = m˙ i (Ti (k) − Tc ), leading to a linear zone thermal dynamics Ti (k + 1) + α1 Ti (k) + α2 gi (k) = v i (k).

(3)

The HVAC system that is used to cool the multizone buildings consists of an air-handling unit (AHU), cooling coils, supply fans, dampers fit with variable air volume (VAV), and a chiller supplying cooled water to the system. The AHU recirculates the return air from each zone plus a fraction of fresh air through the chiller coils using a controlled fan. Whenever, there is an increase/decrease request from the zone, its temperature is changed to command the VAV, leading to pressure change in the ducts. The pressure changes are compensated by adjusting the fan speed, while the temperature is maintained constant by modifying the chiller flow. Consequently, the energy consumed in HVAC system is a sum of chiller and AHU fan power depending on the mass flow rate m i and pressure distribution pi in each zone i ∈ {1, 2 . . . Nz } in the building. Following [1], the optimization problem can be formulated as: Hp  (Pc (k) + P f (k)) min

m˙ i , pi

k=0

s. t. Ti (k + 1) + α1 Ti (k) + α2 gi (k) = v i (k) Til (k) ≤ Ti (k) ≤ Tih (k) nz  gi ≤ gc,cap

(4a) (4b) (4c)

i

m˙ SA − m˙ OA dr = m˙ SA ⎧ nz  ⎪ ⎪ ⎪η1 if gi ≤ Q ch1 ⎪ ⎪ ⎪ ⎪ i=1 ⎪ ⎪ nz ⎨  gi ≤ Q ch2 , % . . . η = η2 if Q ch1 < ⎪ ⎪ i=1 ⎪ ⎪ nz ⎪ ⎪  ⎪ ⎪ ⎪ gi ≤ Q chn . ⎩ηn if Q ch(n−1) < i=1

(4d)

(4e)

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⎛ pi+1 − pi + f ⎝

nz 

3

⎞2 m˙ q⎠ ≤ 0, i = 0, 1, 2 . . . n z − 1

q=i+1

(4f) 5/2

5/2

Ai Ai [ pi − pz ], m˙ 2i ≥ a a p0 (k) ≤ pcap .

m˙ 2i ≤

[ pi − pz ],

(4g) (4h)

B. Ventilation Requirements The ventilation requirements of a building are represented by the parameter dr in the chiller cost function. In the literature [16], a preset value dr = 1 has been used for unoccupied periods and dr ≤ 1, otherwise. Using ASHRAE standards, we first calculate the amount of fresh air required in each zone according to its expected occupancy and the floor area. The fresh air induction is given by R p Pi + Ra Ari . Z pi = m˙ i n

z Z pi decides E v . The value of E v can be The value of maxi=1 obtained by interpolating the values given in Table 6.3 of the ASHRAE standard 62-2001. The total outdoor air intake flow rate is  nz nz  1  m˙ OA = R p Pi + Ra Ari . (5) Ev

i=1

i=1

The difference between the supply air and the outdoor air requirement gives the mass flow rate of return air. dr is the ratio of return air to supply air and it represents the ventilation requirements of the building m˙ SA − m˙ OA . (6) dr = m˙ SA The occupancy and the size of zones give the total fresh air requirement m˙ OA from (5), and the optimization algorithm gives the cool air supply m˙ SA . These two parameters can be used to calculate the required ventilation at any given time through dr . C. Problem Statement The optimization problem (4) is nonlinear, and solving it for a large building using centralized approaches is computationally cumbersome, leading to scalability issues. Furthermore, in implementation, centralized approaches require transmission of zone-level models and sensor information to the central scheduler (CS) leading to engineering difficulties and increased information exchange. The inclusion of operating constraints (6) and chiller capacity constraints complicates it further. Deviating from existing approaches, this investigation aims to design a distributed approach, wherein numerous zone controllers compute the cooling energy required using zone thermal models and sensor information at the local level. The CS coordinates the supply of cooling energy based on the chiller and duct constraints, thereby reducing the computational complexity and deployment difficulties in the centralized approach. Such a decentralized method provides good scalability to large buildings, low deployment cost, and robustness to thermal disturbances.

Fig. 1.

Token-based scheduling architecture.

III. L EARNING -BASED T OKEN S CHEDULING A LGORITHM A. Architecture and Flow of Information The LBTSA is a hierarchical distributed algorithm that aims at achieving energy savings in HVAC operations without compromising human comfort. The information flow for the LBSTA algorithm is shown in Fig. 1. The idea here is to consider cooling as a service, which is provided by the HVAC system. The zones [using zone modules (ZMs)] are the customers seeking this service (called as tokens), while a CS is the service provider. There are five steps in the algorithm that are explained in the following. 1) Learning: Each zone is controlled using numerous ZMs, which first runs a learning algorithm to correct (if needed) the zone thermal model using an moving horizon estimation approach. 2) Token Requests: The main role of the ZM is to run an MPC using forecast information on weather, occupancy, and cooling demands plus sensor readings (temperature, thermostat, and occupancy sensors) to compute the minimal energy required without breaching userdefined comfort margins. The minimum cooling energy thus computed is conceptually called as cooling energy tokens. 3) COP Constraints: In the third step, the centralized controller checks whether an increase in cooling energy to be supplied using tokens as the lower bound will benefit the coefficient of performance (COP) of the chiller system, thereby increasing the energy efficiency and reducing maintenance cost. The COP constraints are computed inherently in the CS and provided as input to the quadratically constrained quadratic program (QCQP) model based on token requests from ZMs. 4) Mass Flow Rate Constraints: In the fourth step, the tokens are converted into mass flow rates, and the corresponding constraints are calculated. The minimum number of tokens required by each zone is computed based on the mass flow rate constraints in the CS using zone temperature profiles and token requests from ZMs. 5) Token Allocation: In the fifth step, the algorithm modifies the supply mass flow rate allocation to all zones, such that the duct pressure constraints are satisfied. It also ensures that the minimum damper position constraints are not violated. The computations reduce to QCQP.

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B. Computing Token Requests and Allocation 1) Zone Module—Learning: The ZM performs two operations: learning and token request computation. Learning is used to provide robustness by computing the cooling load Q˙ due to occupancy, user interaction, and other sources. Learning uses moving horizon estimation approach that works backward-in-time to provide disturbance estimates for the next step. Let Tˆi (k) and vˆi (k) be the estimated temperature and disturbance of zone i at time instant k, respectively. From the zone dynamics (4b), we have Tˆi (k) + α1 Ti (k − 1) + α2 gi (k − 1) = vˆi (k − 1)

(7)

where the disturbance is estimated using a moving horizon approach solving the optimization problem for a time horizon N p backward-in-time. At any given time instant t min

a1 ···an

t −1  k=t −N p

(8)

where V = [v(k − 1), . . . , v(k − N p )]T , f = a1 , and P is a positive definite diagonal matrix. The decision variables are the parameters a1 . . . an . The occupancy occi (k) is obtained from occupancy sensors fit for each zone. It can be seen that ˙ the disturbance term is a function of cooling load Q(k) and ˙ stray heating sources. The predictions on Q are obtained from historical data and are corrected using a polynomial regression online. The function f (.) defined earlier is estimated using polynomial regression techniques. 2) Zone Module—Token Requests: In contrast to the token requests proposed in [1], the LBSTA considers the chiller capacity constraints (4c) as well in the formulation and handles it using a Lagrangian relaxation algorithm. Each ZM solves the following optimization problem for a fixed planning horizon H p : J1,i (H p ) = min gi

Hp 

dr (k)gi (k) + λk gi (k)

gi

Hw 

η(k)

k=0

nz 

gi (k)

i=1

s. t. (∀i : 1 ≤ i ≤ n z ) gi (k) ≥ T ok A(k) Chiller Capacity Constraint (4).

(10)

4) Mass Flow Rate Constraints: Consider a fixed planning opt horizon Hw , and let gi (k) be the optimal cooling request that solves the mixed integer linear program in (10). Using (4a), opt we compute the associated optimal temperature profile Ti (k) and the mass flow rate request is computed as opt

opt

m˙ i (k) =



gi (k) opt

c p Ti

(k) − Tc

 , k = 1, . . . , Hw

(11)

T ok Bi (Hw ) =

Hw 

opt

m˙ i (k),

Hw = 1, . . . , W.

k=1

We interpret T ok Bi (Hw ) as the minimum number of tokens needed by zone i on the planning horizon Hw to meet its local temperature constraints. It carries information about the amount of cooling required. 5) Central Scheduler—Token Allocation: The CS allocates the token considering the mass flow profile with respect to the duct pressure distribution. Linearizing the nonconvex constraint in (4g), the token allocation problem solved by the CS is  nz 2 Hw   m˙ i J3 (Hw ) := min m˙ i , pi

s. t.

r 

k=0

i=1

m˙ i (k) ≥ T ok B(r ) (∀r : 0 ≤ r ≤ Hw )

k=0

Constraints (4f), (4g), (4h)



where pcap is the fan pressure rating. The above-mentioned problem is QCQP.

k=1

s. t. Ti (k + 1) + α1 Ti (k) + α2 gi (k) = v i (k) (∀k : 1 ≤ k ≤ H p ) Til (k) ≤ Ti (k) ≤ Tih (k) (∀k : 1 ≤ k ≤ H p ).

J2 (Hw ) := min

and the corresponding minimum total mass flow of cold air on the planning horizon required for zone i is computed as

[Ti (k) − Tˆi (k)]T P [Ti (k) − Tˆi (k)]

s. t. vˆi (k) = f (a1 . . . an , Toa (k), occi (k), V(k))

size Hw and ∀k : 0 ≤ k ≤ Hw , the CS solves a mixed integer linear programming problem in (10) with (4e) as the constraint

IV. L OWER B OUND E STIMATE (9)

The parallel computation of this step is preserved by using the subgradient method to solve the optimization. The multipliers are updated for each iteration n, as   λn+1 = max 0, λnk + sk G(λn ) k  where the gradient G(λn (k)) = i gi (k) − gc,cap , step size n sk = (β/||G(λk )||2 ), and β > 0 is the scaling factor, scalar valued one. 3) Chiller COP Constraints: The inclusion of chiller COP constraints can provide additional savings without significantly affecting the user defined comfort margins. The procedure for converting the piecewise COP constraints to mixed logical linear constraints has been discussed in [1]. For a fixed window

Step 2 of the TBSS generates token requests that represent the optimal chiller power consumption profile subject to thermal comfort constraints and zone dynamics. On the other hand, the centralized strategy computes the mass flow rate profile that optimizes both the chiller and fan energy. In this backdrop, a major concern is whether our token-based solution may lead to a total HVAC energy consumption too far away from the truly optimal one or, in other words, how to measure the quality of our solution in terms of its “distance” from the globally optimal one, since it is practically infeasible to determine the actual globally optimal solution due to the computational complexity. To address this challenge, we will present a specific method to derive a lower bound on the globally optimal HVAC energy consumption. By comparing the difference between the HVAC energy consumption incurred

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by our token-based solution and this lower bound, we can roughly tell whether our solution is sufficiently close to the globally optimal one. The optimization model in (9) has capacity constraints that requires iterative computation of λ(k). We define the optimization model formulated without the capacity constraints as the relaxed token (RT) M1,i given by M1,i := min gi

Hp 

gi (k)

k=1

s. t. Til (k) ≤ Ti (k) ≤ Tih (k) (∀k : 1 ≤ k ≤ H p ). We have the following main theorem. Theorem 1: Let P1 and P2 denote the power consumption for mass flow rate profiles {m˙ 1,i (k)|1 ≤ k ≤ H P } and {m˙ 2,i (k)|1 ≤ k ≤ H p  } for zone i ,respectively. Then,  if P1 ≤ P2 , we have that k m˙ 1,i (k) ≤ k m˙ 2,i (k). Proof: For each i ∈ {1, 2}, consider ⎛ Hp  m˙ i (k) Pi := c p ⎝(1−dr )(Toa −Tc ) k=1

+ dr

Hp 

⎞

m˙ i (k)(Ti (k)−Tc )⎠.

Let γ = c p ((1 − dr )Toa − Tc ). Then, substituting from thermal dynamics (4a) and with a little rearranging Hp 

Hp c p dr  m˙ i (k) + [Ti (k + 1) − Ti (k) + v(k)] =γ α k=1 k=1 ⎤ ⎡ Hp Hp   c p dr ⎣Ti (H p ) − Ti (1) + m˙ i (k) + v(k)⎦ =γ α k=1

where Ti (1) is the initial temperature and v(k) is the disturbance due to unpredictable changes in weather and occupancy, which are assumed known in advance. If P1 ≤ P2 , substituting for corresponding mass flow rate profiles ⎡ ⎤ Hp Hp   c p dr ⎣Ti (H p ) − Ti (1) + γ m˙ 1,i (k) + v(k)⎦ α k=1 k=1 ⎡ ⎤ Hp Hp   c p dr ⎣Ti (H p ) − Ti (1) + ≤γ m˙ 2,i (k) + v(k)⎦ α k=1 Hp

⇒γ

 k=1

≤γ

Hp  k=1

k=1

m˙ 1,i (k)+

c p dr Ti (H p ) ≤ γ α

Hp 

m˙ 2,i (k)+

k=1

c p dr Ti (H p ) α

c p dr Ti (H p ) m˙ 2,i (k) + α

where α < 1 and c p , dr , α, and γ are constants. Therefore, given the same final temperature Ti (H p ) Hp  k=1

m˙ 1,i (k) ≤

Hp 

m˙ 2,i (k)

k=1

which concludes the proof of the theorem.

Corollary 1: Let mˆ˙ i (k) and m˙ C P,i (k) denote the solutions of the RT and the centralized optimization problem (CP) stated in (18), respectively. Then, we have Hp 

mˆ˙ i (k) ≤

k=1



Hp 

m˙ C P,i (k).

(12)

k=1

 Proof: Since m˙ C P,i (k) is the solution of the CP, we know that it must also be a solution to the RT, as all constraints in the RT must be satisfied by m˙ C P,i (k). Since mˆ˙ i (k) is the optimal solution of the RT, we know that the energy consumption P1 incurred by m˙ C P,i (k) in the RT must be higher than the energy consumption P2 incurred by mˆ˙ i (k). Thus, by Theorem 1, we know that the corollary is true.  Let gˆ i (k)∗ denote the optimal cooling energy required for each zone during any time period k working with the RT. The corresponding optimal mass flow rate profile is mˆ i (k)∗ . We insert the following constraint in the CP: for all i : 1 ≤ i ≤ n z : Hp 

m˙ i (k) ≥

k=1

k=1

k=1

5

Hp 

mˆ˙ i (k) (k : 1 ≤ k ≤ H p )

k=1

and denote the revised CP as RCP. By Corollary 1, we know that the optimal energy consumption of the RCP and the optimal energy consumption of the CP are the same, i.e., the newly added constraints, which are essentially derived from solving Stage A of the LBTSA, do not place any active restriction on the optimal solution of the CP. With this important observation, we slightly modify Stage B of the LBTBSA by replacing the constraint r  m˙ i (k) ≥ T ok B(r )) (∀r : 0 ≤ r ≤ Hw ) k=0

with a new constraint Hp  k=1

m˙ i (k) ≥ T ok B(H p ) =

Hp 

mˆ˙ i (k)

k=1

and denote this revised TBSS as RLBTSA. We now state our main lower bound result. Theorem 2: Let P1 and P2 be the optimal energy consumptions of the RLBTSA and the CP, respectively.  Then, P1 ≤ P2 . Proof: By the above-mentioned argument, we know that the optimal energy consumption of the RCP is P2 . On the other hand, we know both Stage A and Stage B of the RLBTSA are subproblems of the RCP, and it is clear that P1 ≤ P2 .  Theorem 2 finally establishes a lower bound estimate of the energy consumption of the original CP. Such a lower bound is obtained by running the RLBTSA on the CP. Considering that Stage B of the RLBTSA is a nonconvex QCQP problem, by removing those complex pressure constraints, we can convert the problem into a convex QP problem, which can be solved efficiently. Similarly, we could also remove constraints in Stage A. It is not difficult to see that the resulting optimal energy consumption is also a lower bound of the optimal energy consumption of the CP. Nevertheless, the more the

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TABLE II T HERMOSTAT S ETTINGS FOR T EN Z ONES

Fig. 2. Percentage difference between original and relaxed strategy versus number of zones. TABLE I T HERMAL PARAMETERS

constraints that we remove, the lesser the lower bound will be, which means the less informative of such a lower bound. Thus, the usefulness of a lower bound and the corresponding computational complexity compete with each other, which is a well-known fact. To illustrate the use of the lower bound estimate, the RBLSTA is solved without involving the constraints on the chiller coefficient of performance, the duct pressures, and the damper positions. Fig. 2 shows the percentage difference between the optimal energy consumptions of the LBTSA and the RLBTSA. For cases with more than 250 zones, the difference is more than 16%. On the other hand, if we retain all those complex constraints, the gap between the optimal energy consumptions incurred by the LBTSA and the RLBTSA becomes significantly small (0.01% difference).

Fig. 3. Zone temperature, zone cool air mass flow rate, power consumption, and return-total-air ratio with token-based scheduling. TABLE III C OMPUTATION T IMES FOR D IFFERENT B UILDING S IZES

V. R ESULTS We now present simulation results of applying LBSTA for a ten-zone buildings and compare its performance with 1) the centralized approach proposed in [19] and 2) the token-scheduling approach in [1]. The building parameters and comfort band from the user for different hours of the day are given in Tables I and II, respectively. The experimental results to study the performance of the ZMs, computation time, scalability, learning, and closed loop operation of the LBSTA are verified using prototypes of ZMs collecting information using sensors. The zone temperatures, cool air supply mass flow rates, and power consumption profiles are shown in Fig. 3. We observe that the LBTSA regulates zone temperature near the upper comfort band setting in order to reduce energy consumption.

A. LBTSA Versus Centralized Approach Comparison of computation time per iteration of the LBTSA and centralized strategy for different numbers of zones is shown in Table III. The computation time for one iteration of the LBSTA for a building with 500 zones is 5.23 s, whereas the centralized scheme does not scale beyond 50 zones. It should be noted here that the centralized approach does

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TABLE IV E NERGY C ONSUMPTION C OMPARISON

Fig. 4.

Fig. 5.

Fig. 6.

Temperature profile at the time of set-point change and end of day.

Fig. 7. of day.

Temperature profile at the time of meeting cancellation and end

Energy consumption: centralized versus LBTSA.

Energy consumption: TBSS versus LBTSA.

not consider the chiller capacity and ventilation constraints. As for the energy consumption, the LBTSA energy savings are comparable with that of the centralized approach, as shown in Fig. 4 and Table IV. This result demonstrates that the LBTSA leads to significant computation advantages without compromising the energy savings and is a more suitable for commercial buildings. B. LBTSA Versus TBSS A comparison of computation time and energy consumption with LBSTA versus token scheduling algorithm reveals that the energy savings is improved by 5.7% and computation time increases from 0.12 to 0.29 s. This is mainly due to the inclusion of learning and additional constraints. The power consumption with LBSTA and TBSS algorithm is shown in Fig. 5. The result shows that the LBSTA provides better energy savings than TBSS without a significant increase in computation time. C. Performance of LBTSA for Sudden Change in Temperature Demands To study the robustness of the energy savings provided by LBSTA, a typical scenario wherein zone 3 temperature setting is suddenly changed from 30 °C to 25 °C at 10 A . M . is studied

in Fig. 6. The algorithm tries to incorporate this new demand and pushes in as much air as it would be necessary to attain this new set point at the earliest. When the temperature profile is observed at the end of the day, it is seen that there was a delay of only one time step (10 min) to decrease the temperature of the zone. The hierarchical architecture makes it easier to handle sudden changes in set points. D. Performance of LBTSA for Sudden Cancellation of Meeting A sudden cancellation or shifting of the meetings provides good insights into the agility of the LBSTA to respond to changes in demand. In this brief, a meeting scheduled in zone 6 at 11:00 A . M . for 1 h is canceled at the last minute. The system being provided a meeting schedule initially precools the building to 22 °C, as shown in Fig. 7 (left). On receiving the meeting cancellation information, the LBSTA tries to save energy by pushing the temperature back to the upper comfort margin, 24 °C. The final temperature profile shown in Fig. 7 shows that the precooling that starts predicting an increase demand stops immediately with the cancellation information is conveyed to the HVAC system, illustrating the agility of the LBSTA to sudden changes in demand. The results demonstrate that the LBSTA provides good scalability, robustness, and agility compared with existing approaches in the literature. In addition, the energy savings are better than the TBSS and centralized approaches. E. Experiments Zone Module To experiment with the LBSTA, the ZMs were implemented on the Raspberry PI interfacing with CO2 and temperature sensors. The DFRobot make CO2 sensor with an MG-811 module was used to measure the occupancy, while

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the CC2650TK was used to measure the temperature that transmitted the measurement via a wireless network. The measurements were interfaced with the Raspberry PI processor ported with Python routines to execute the token requests and learning. The CS implemented in a PC was interfaced with the ZMs that used the Scipy method linprog to solve the MPC problem. The experiments were performed to verify the distributed computation and the computation times required. The average computation time for generating one token request on the Raspberry PI 3 board is 9.5 ms over 500 iterations, while the minimum and maximum times recorded are 9.1 and 9.9 ms, respectively. Similarly, for the model adaptation, the average execution time over 500 iterations is 10.1 ms with the minimum computation time of 9.3 ms and the maximum of 10.4 ms. Furthermore, the communication time between ZM working as a server and the CS as the client had an average value of 5.2 ms. The computation time shows the scalability of the proposed LBSTA on dedicated embedded boards and realization of the algorithm. VI. C ONCLUSION This brief presented a learning-based distributed hierarchical TBSS (LBTSA) for building HVAC systems. The proposed method built the following features over existing TBSS: learning the model from sensor measurements to include the effect of stray heating and occupancy, and the inclusion of fresh air infusion rate following ASHRAE standard and COP constraints. This brief further demonstrated that the decentralized computation of token algorithm does not neglect the global optimum and the operating constraints are important for computing energy savings. The performance of the proposed method was compared with the centralized optimization and TBSS approach. Our results showed that the proposed approach provided better scalability than centralized optimization and enhanced the energy saving of TBSS by 5.6%. The simulations were compounded by experiments on embedded hardware. Our results demonstrated the scalability and computational efficiency of the proposed approach. Inclusion of energy prices for performing demand response is the future course of this investigation.

[4] A. Schirrer, M. Brandstetter, I. Leobner, S. Hauer, and M. Kozek, “Nonlinear model predictive control for a heating and cooling system of a low-energy office building,” Energy Buildings, vol. 125, pp. 86–98, Sep. 2016. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0378778816302845 [5] S. Koehler and F. Borrelli, “Building temperature distributed control via explicit mpc and trim and respond methods,” in Proc. IEEE Eur. Control Conf. (ECC), Sep. 2013, pp. 4334–4339. [6] B. Sun, P. B. Luh, Q. S. Jia, and B. Yan, “Event-based optimization within the Lagrangian relaxation framework for energy savings in HVAC systems,” IEEE Trans. Autom. Sci. Eng., vol. 12, no. 4, pp. 1396–1406, Oct. 2015. [7] Y. Ma, G. Anderson, and F. Borrelli, “A distributed predictive control approach to building temperature regulation,” in Proc. Amer. Control Conf., 2011, pp. 2089–2094. [8] V. Putta, G. Zhu, D. Kim, J. Hu, and J. Braun, “Comparative evaluation of model predictive control strategies for a building HVAC system,” in Proc. IEEE Amer. Control Conf. (ACC), Apr. 2013, pp. 3455–3460. [9] F. Oldewurtel, C. N. Jones, A. Parisio, and M. Morari, “Stochastic model predictive control for building climate control,” IEEE Trans. Control Syst. Technol., vol. 22, no. 3, pp. 1198–1205, May 2014. [10] H. Scherer, M. Pasamontes, J. Guzmän, J. Álvarez, E. Camponogara, and J. Normey-Rico, “Efficient building energy management using distributed model predictive control,” J. Process Control, vol. 24, no. 6, pp. 740–749, 2014. [11] V. Chandan and A. G. Alleyne, “Decentralized architectures for thermal control of buildings,” in Proc. IEEE Amer. Control Conf. (ACC), Sep. 2012, pp. 3657–3662. [12] P.-D. Morosan, R. Bourdais, D. Dumur, and J. Buisson, “Distributed MPC for multi-zone temperature regulation with coupled constraints,” IFAC Proc. Vol., vol. 44, no. 1, pp. 1552–1557, 2011. [13] J. Brooks, S. Kumar, S. Goyal, R. Subramany, and P. Barooah, “Energyefficient control of under-actuated HVAC zones in commercial buildings,” Energy Buildings, vol. 93, pp. 160–168, Apr. 2015. [14] A. Parisio, D. Varagnolo, M. Molinari, G. Pattarello, L. Fabietti, and K. H. Johansson, “Implementation of a scenario-based MPC for HVAC systems: An experimental case study,” IFAC Proc. Vol., vol. 47, no. 3, pp. 599–605, 2014. [15] A. Parisio, L. Fabietti, M. Molinari, D. Varagnolo, and K. H. Johansson, “Control of HVAC systems via scenario-based explicit MPC,” in Proc. IEEE 53rd Annu. Conf. Decision Control (CDC), Jun. 2014, pp. 5201–5207. [16] N. Radhakrishnan, Y. Su, R. Su, and K. Poolla, “Token based scheduling of HVAC services in commercial buildings,” in Proc. Amer. Control Conf. (ACC), 2015, pp. 262–269. [17] A.-C. E. I. American Society for Heating. (2002). Refrigirating. ASHRAE 62-2001: Ventillation and Acceptable Air Quality. [Online]. Available: http://www.ashrae.org [18] A. Aswani, H. Gonzalez, S. S. Sastry, and C. Tomlin, “Provably safe and robust learning-based model predictive control,” Automatica, vol. 49, no. 5, pp. 1216–1226, 2013. [19] A. Kelman and F. Borrelli, “Bilinear model predictive control of a HVAC system using sequential quadratic programming,” in Proc. IFAC World Congr., 2011, pp. 9869–9874.

ACKNOWLEDGMENT Berkeley Education Alliance for Research in Singapore has been established by the University of California at Berkeley, as a center for intellectual excellence in research and education in Singapore. R EFERENCES [1] N. Radhakrishnan, Y. Su, R. Su, and K. Poolla, “Token based scheduling for energy management in building HVAC systems,” Appl. Energy, vol. 173, pp. 67–79, Jul. 2016. [2] Y. Ma, J. Matuško, and F. Borrelli, “Stochastic model predictive control for building HVAC systems: Complexity and conservatism,” IEEE Trans. Control Syst. Technol., vol. 23, no. 1, pp. 101–116, Jan. 2015. [3] Y. Ma, A. Kelman, A. D. Daly, and F. Borrelli, “Predictive control for energy efficient buildings with thermal storage: Modeling, stimulation, and experiments,” IEEE Control Syst., vol. 32, no. 1, pp. 44–64, Jan. 2012.

Nikitha Radhakrishnan (S’13–M’17) received the B.E. degree in electrical and electronics engineering from Anna University, Chennai, India, in 2012, and the Ph.D. degree in electrical and electronics engineering from Nanyang Technological University, Singapore, in 2017. She was a Graduate Student Researcher with Berkeley Education Alliance for Research in Singapore, Singapore. She is currently a Scientist with the Electricity Infrastructure and Buildings Division, Pacific Northwest National Laboratory, Richland, WA, USA. Her current research interests include building-energy systems optimization and buildings-grid integration.

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. RADHAKRISHNAN et al.: LEARNING-BASED HIERARCHICAL DISTRIBUTED HVAC SCHEDULING

Seshadhri Srinivasan (SM’16) received the Ph.D. degree from the National Institute of Technology, Tiruchirappalli, India. He was with ABB GISL, Tamil Nadu, India, as an Associate Scientist and with the Center for Excellence in Nonlinear Systems, Tallinn, Estonia, as a Scientist. He also had research stints with the University of Sannio, Benevento, Italy, and the Technical University of Munich, Munich, Germany, and is currently with Berkeley Education Alliance for Research in Singapore, Singapore. Dr. Srinivasan has been a member of the IEEE CSS Standing Committee on Standards since 2016. Rong Su (M’11–SM’14) received the B.E. degree in automatic control from the University of Science and Technology of China, Hefei, China, in 1997, and the M.A.Sc. and Ph.D. degrees in electrical engineering from the University of Toronto, Toronto, ON, Canada, in 2000 and 2004, respectively. Since then he has been affiliated with the University of Waterloo, Waterloo, ON, Canada, and the Technical University of Eindhoven, Eindhoven, The Netherlands, and joined Nanyang Technological University, Singapore, in 2010. He has authored or co-authored over 130 publications in journals, book chapters, and conference proceedings, and two patents in his research areas. His current research interests include discrete event systems, supervisory control, model-based fault diagnosis, multi-agent systems, optimization and scheduling with applications in green buildings, flexible manufacturing, and power management and intelligent transportation systems. Dr. Su is an Associate Editor of the Journal of Discrete Event Dynamic Systems: Theory and Applications, the Journal of Control and Decision, and the Transactions of the Institute of Measurement and Control, and the Chair of the IEEE Control Systems Society Technical Committee on Smart Cities.

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Kameshwar Poolla was the Founding Director of the IMPACT Center for Integrated Circuit Manufacturing. He is currently the Cadence Distinguished Professor of electrical engineering and computer science and mechanical engineering with the University of California at Berkeley, Berkeley, CA, USA. His current research interests include many aspects of future energy systems, including economics, security, and commercialization. Dr. Poolla co-founded OnWafer Technologies, which was acquired by KLA-Tencor in 2007. He was a recipient of the 1988 NSF Presidential Young Investigator Award, the 1993 Hugo Schuck Best Paper Prize, the 1994 Donald P. Eckman Award, the 1998 Distinguished Teaching Award of the University of California, the 2005 and 2007 IEEE T RANSACTIONS ON S EMICONDUCTOR M ANUFACTURING Best Paper Prizes, and the 2009 IEEE CSS Transition to Practice Award.