Journal of Energy

Volume 2016, Article ID 5074846, 13 pages

http://dx.doi.org/10.1155/2016/5074846

## A Comfort-Aware Energy Efficient HVAC System Based on the Subspace Identification Method

^{1}Department of Electronics, TEI of Athens, Egaleo, 12210 Athens, Greece^{2}Department of Engineering and Design, Brunel University, Kingston Lane, Middlesex UB8 3PH, UK

Received 12 October 2015; Revised 12 January 2016; Accepted 8 February 2016

Academic Editor: Aleksander Zidansek

Copyright © 2016 O. Tsakiridis et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A proactive heating method is presented aiming at reducing the energy consumption in a HVAC system while maintaining the thermal comfort of the occupants. The proposed technique fuses time predictions for the zones’ temperatures, based on a deterministic subspace identification method, and zones’ occupancy predictions, based on a mobility model, in a decision scheme that is capable of regulating the balance between the total energy consumed and the total discomfort cost. Simulation results for various occupation-mobility models demonstrate the efficiency of the proposed technique.

#### 1. Introduction

As the control and limitation of the energy consumption remain a field with an exceptional technological and economical interest, areas that have been considered as high energy consumers comprise very challenging research issues. According to the US Energy Information Administration from 2013 through 2040 the electricity consumption in the commercial and residential sectors will be increasing by 0.5% and 0.8% per year [1]. It is well established and widely accepted through research studies that the main energy consumers in the commercial and residential buildings are the Heat Ventilation and Air Conditioning (HVAC) systems, as well as the lighting systems.

Buildings contributed a 41% (or 40 quadrillion btu) to the total US energy consumption in 2014. On an average, about 43% of the energy consumption in a commercial and residential building is due to HVAC systems [2]. Therefore, due to the high rate of energy consumption, the necessity of the demand-driven control in the HVAC systems has become inevitable. In modern buildings several sophisticated systems have been applied aiming at providing this type of control in the HVAC systems. The state-of-the-art technology of the HVAC control considers the occupancy of the zones a very important parameter, playing a key role in methods aiming at reducing energy consumption. The detection and prediction of the zones’ occupancy are a very challenging research field and several techniques have been proposed based on historic statistical data as well as on probabilistic models.

Another equally important factor taken into account in advanced HVAC control systems is the thermal comfort of the occupants. The objective of modern HVAC control systems is to reduce energy consumption without compromising the comfort of the occupants. Wireless sensor networks, equipped with temperature, humidity, and occupancy detection sensor nodes, are nowadays the basic platform to build automated HVAC control systems. A number of methods aiming to maintain the thermal comfort while saving energy have been proposed. Some of them are described in Section 2. Towards this direction, a novel technique is proposed in this paper, which aims at balancing the comfort and energy costs in a multizone system. The decisions on heating the zones or not may be taken either centrally or in a distributed manner by wireless sensor nodes scattered in the multizone system. In any case temperature and zone occupancy information must be exchanged between a node, responsible for a zone, and its neighboring nodes. The decision process itself relies on two kinds of predictions: (a) temperature-time predictions for the zones and (b) the zones’ occupancy profile. The emphasis in this paper is on the zones’ temperature predictions and to this end a deterministic subspace identification method is used for modelling the thermal dynamics of each zone. That is, each zone is modelled by a simple state-space model capable of producing accurate predictions based on the surrounding temperatures, the heating power of the zone, and the current state that summarizes the temperature history of the zone. For the zones’ occupancy predictions we consider a semi-Markov model, where occupants (moving as a swarm) stay in a zone for a random period of time and then move to adjacent zones with given probabilities. What is needed by the decision process is the distribution of the first entrance time to unoccupied zones. Aiming at a proactive action, the proposed method periodically computes the risk of activating the heater or not and decides in favor of the action that produces the smaller risk. The computation of the risks relies on the relative weights of the energy and discomfort costs so that the balance between the total energy consumed and the total discomfort cost may be regulated.

The structure of the paper is as follows: In Section 2, prior and related work of the field of the demand-driven HVAC systems that utilize occupancy and prediction methods is presented. In Section 3, the proposed comfort-aware energy efficient mechanism is described, along with the subspace identification method, used for obtaining temperature-time predictions, and a discussion on the distribution of the first entrance time to unoccupied zones. Section 4 contains simulation results and assesses the effectiveness of the proposed algorithm. Finally, Section 5 summarizes the paper and proposes research directions for future work.

#### 2. Prior Work

The necessity of demand-driven HVAC systems, for energy efficient solutions, has orientated the researchers towards occupancy-based activated systems. In multizone spaces the reactive and proactive activation of the heating/cooling of the zones contributes to significant energy savings and improves the thermal comfort for the occupants. Several research works with valuable results of energy savings have utilized the occupancy detection and prediction, in order to control the HVAC system appropriately. For the occupancy detection several types of sensors are used (CO_{2}, motion, etc.), while, for the prediction, combinational systems are usually applied, utilizing mathematical predictive models (e.g., Markov chains) alongside with detected real data.

The authors in [3] proposed an automatic thermostat control system which is based on an occupancy prediction scheme that predicts the destination and arrival time of the occupants in the air-conditioned areas, in order to provide a comfortable environment. For the occupants’ mobility prediction the cell tower information of the mobile telephony system is utilized and the arrival time prediction is based on historical patterns and route classification. For the destination prediction of locations very close to each other (intracell), the time-aided order-Markov predictor is used. The authors in [4] proposed a closed-loop system for optimally controlling HVAC systems in buildings, based on actual occupancy levels named the Power-Efficient Occupancy-Based Energy Management (POEM) System. In order to accurately detect occupants’ transition, they deployed a wireless network comprising two parts: the occupancy estimation system (OPTNet) consisting of 22 camera nodes and a passive infrared (PIR) sensors system (BONet). By fusing the sensing data from the WSN (OPTNet and BONet) with the output of an occupancy transition model in a particle filter, more accurate estimation of the current occupancy in each room is achieved. Then, according to the current occupancy in each room and the predicted one from the transition model, a control schedule of the HVAC system takes over the preheat of the areas to the target temperature. In [5] the authors used real world data gathered from a wireless network of 16 smart cameras called Smart Camera Occupancy Position Estimation System (SCOPES) and in this way, they developed occupancy models. Three types of Markov chain (MC) occupancy models were tested and these are the single MC, the closest distance, and finally the blended (BMC). The authors concluded that BMC is the most efficient and thus they embodied it as the occupancy prediction method in their proposed “OBSERVE” algorithm, which is a temperature control strategy for HVAC systems.

The authors in [6] have developed an integrated system called SENTINEL that is a control system for HVAC systems utilizing occupancy information. For the occupancy detection and localisation, the system utilizes the existing Wi-Fi network and the clients’ smart phones. The occupancy localization mechanism is based on the access point (AP) communication with a client’s smart phone, so that if an occupant’s phone sends packets to an AP then he is located within the range of the AP. By classifying the building areas into two main categories, namely, the personal and the shared spaces, the proposed mechanism activates the HVAC system when an owner of a personal space (e.g., office) has been detected within an area where his/her office is located or when occupants are detected within shared spaces. In [7] an integrated heating and cooling control system of a building is presented aiming to reduce energy consumption. The occupancy behavior prediction as well as the weather forecast, as inputs to a virtual (software based) building model, determines the control of the HVAC system. The occupancy detection technique utilizes Gaussian Mixture Models (GMM) for the categorization of selected features, yielding the highest information gain according to the different number of occupants. This categorization was used for observation to a Hidden Markov Model for the estimation of the number of occupants. A semi-Markov model was developed based on patterns comprised by sensory data of CO_{2}, acoustics, motion, and light changes, to estimate the duration of occupants in the space. The work in [8] proposes a model predictive control (MPC) technique aiming to reduce energy consumption in a HVAC system while maintaining comfortable environment for the occupants. The occupancy predictive model is based on the two-state Markov chain, with the states modelling the occupied and occupied condition of the areas. The authors in [9] propose a feedback control algorithm for a variable air volume (VAV) HVAC system for full actuated (zones consisting of one room) and underactuated (zones consisting of more than one room) zones. The proposed algorithm is called MOBSua (Measured Occupancy-Based Setback for underactuated zones) and it utilizes real-time occupancy data, through a WSN, for optimum energy efficiency and thermal comfort of the occupants. Moreover, the algorithm can be applied on conventional control systems with no need of occupancy information and it is scalable to arbitrary sized buildings.

#### 3. Comfort-Aware Energy Efficient Mechanism

We consider a multizone HVAC system consisting of zones , . Each zone is equipped with a wireless sensor node capable of conveying the zone’s temperature and occupancy information to its neighbors or to a central processing unit. The occupancy information may be very simple, that is, binary information indicating the presence or absence of individuals in the zone, or more advanced like the number of occupants in the zone. The objective is to minimize the total energy and discomfort cost defined asNote that only the heating problem is addressed in this paper. Thus, the case of spending energy for cooling the zones and keeping the temperature within a certain comfort zone is not treated for simplicity. In (1) denotes the indicator function which takes the value 1 or 0 depending on whether condition is true or false. is the power of a heater that covers zone and is the state of the heater; that is, the heater is on or off. Thus, the first term of (1) is the total energy consumed by the multizone system. For the discomfort cost we define the cost per unit time and the target comfort threshold . As long as the zone’s temperature is higher than the occupants do not feel discomfort. The parameter may depend on the zone, the number of the occupants (e.g., the total system’s discomfort cost is proportional to the number of people experiencing discomfort), and the difference of the zone’s temperature and the comfort threshold . It is worth noting that there is a tradeoff between energy savings and discomfort cost. We may preheat all zones to the comfort level thus rendering the discomfort cost equal to zero. This policy is inefficient due to the large amount of energy consumed. In the other extreme we could act reactively by heating a zone only upon detecting occupants in it. In this case the energy cost would be as small as possible but the discomfort cost could increase dramatically. In the sequel we will describe a method that acts proactively by taking periodically decisions on whether to heat a zone or not. If the entrance to a zone is delayed then we postpone heating until the next decision epoch. If, on the contrary, it is anticipated that a zone will be occupied before the zone’s temperature reaches the comfort level, then we preheat the zone.

The decision of whether or not the heater of an unoccupied zone should be turned on depends on (a) the current state of the zone, (b) the relative value of the energy cost () and discomfort cost () per unit time, (c) the temperatures of the surrounding zones, and (d) an estimate of the time that the zone will become occupied. This decision may be taken either centrally from the central processing unit that gathers information by all zones or in a distributed manner by each zone’s node after collecting the relative information. There is also the possibility of dividing the decision process functionality between the central unit and the wireless sensor network nodes. For example, the prediction of the first entrance times to unoccupied zones may be taken by the central unit that is aware of the location of people in the multizone system, and then the predicted values may be communicated back to the zones’ nodes for the final decision. The specific implementation of the decision process is irrelevant to this paper and it will not be further analyzed.

We assume that time is discretized , is the sampling period, and that each node takes its decisions periodically every sampling periods. Note that there is no need for the nodes to be synchronized to each other. Let denote the random variable that models the remaining time from the current time instant until entrance to the unoccupied zone . It is obvious that the random variables , for the various unoccupied zones , do not follow the same distribution. We further assume that the node is capable of making predictions for the time it takes to exceed the comfort threshold . To this end, let denote the time period that is required to exceed if the heater is turned on immediately. Similarly, we define as the predicted time to reach the comfort threshold if the heater remains off for a period and then, at the next decision epoch, it is turned on. The relation of the aforementioned parameters is shown in Figure 1.