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Optimal Co-Scheduling of HVAC Control and Battery Management for Energy-Efficient Buildings Considering State-of-Health Degradation Tiansong Cui1, Shuang Chen1, Yanzhi Wang2, Qi Zhu3, Shahin Nazarian1 and Qi Zhu Shahin Nazarian Massoud Pedram Massoud Pedram1 University of California, Riverside University of Southern California University of Southern California Riverside, CA, USA Los Angeles, CA, USA Los Angeles, CA, USA 1Department of Electrical Engineering, University of Southern California, USA [email protected] [email protected] [email protected] 2Department of Electrical Engineering & Computer Science, Syracuse University, Syracuse, USA 3Department of Electrical and Computer Engineering, University of California, Riverside, USA 1{tcui, shuangc, shahin, pedram}@usc.edu, [email protected], [email protected] Abstract— The heating, ventilation and air conditioning (HVAC) sys- Although both HVAC control and battery management mechanisms tem accounts for half of the energy consumption of a typical building. are well researched, there has been little work on formulating the inter- Additionally, the need for HVAC changes over hours and days as does actions between the two aspects and addressing them together. In the the electric energy price. Level of comfort of the building residents is, building management system, the demand side scheduling of HVAC however, a primary concern, which tends to overwrite pricing. Dynamic control depends on the availability of battery storage and the price HVAC control under a dynamic energy pricing model while meeting an of grid electricity, while the supply side scheduling of battery stor- acceptable level of residents’ comfort is thus critical to achieving energy age requires the knowledge of HVAC demand [5]. As a result, only efficiency in buildings in a sustainable manner. The presence of a bat- by addressing these two aspects in an integrated framework can we tery energy storage system in a target building would enable peak power achieve the maximal energy efficiency in smart buildings. One chal- shaving through use of a suitable charge and discharge schedule for the lenge with battery management in HVAC control system is that it is battery, while allowing building energy efficiency and user satisfaction be not clear how much battery aging, and therefore also the associated met. This paper addresses the co-scheduling problem of HVAC control warranty, are affected during the charging/discharging process. With- and battery management to achieve energy-efficient buildings, while also out a careful consideration of battery aging, the benefits from battery accounting for the degradation of the battery state-of-health during charg- energy storage can hardly be realized in energy-efficient buildings. ing and discharging operations (which in turn determines the amortized To address the above-mentioned issues, we consider the problem cost of owning and utilizing a battery storage system). A time-of-use dy- of co-scheduling HVAC control and battery management for energy- namic pricing scenario is assumed and various energy loss components are efficient buildings, aiming to minimize the total cost while maintain- considered including power dissipation in the power conversion circuitry ing the temperature within the comfort zone for building occupants. In as well as the rate capacity effect in the battery. A global optimization this problem, we explicitly take into account the degradation of bat- framework targeting the entire billing cycle is presented and an adaptive tery state-of-health (SoH), which is defined as the ratio of full charge co-scheduling algorithm is provided to dynamically update the optimal capacity of an aged battery to its designed (nominal) capacity, dur- HVAC air flow control and the battery charging/discharging decision in ing the charging and discharging process based on an accurate SoH each time slot during the billing cycle to mitigate the prediction error of modeling. We also consider various energy loss components includ- unknown parameters. Experimental results show that the proposed algo- ing power dissipation in the power conversion circuitries as well as rithm achieves up to 15% in the total electric utility cost reduction com- the rate capacity effect in the battery storage system. In addition, a pared with some baseline methods. time-of-use electricity pricing policy is adopted in our model. The ob- jective function to minimize therefore becomes the summation of the building’s electricity bill and the extra cost associated with the aging 1. INTRODUCTION of the battery used in the building energy storage system. The commercial and residential building stock is responsible for The rest of this paper is organized as follows. We describe our sys- 40% of the U.S. primary energy consumption, 40% of the greenhouse tem component models including the building power flow and power gas emissions, and 70% of the electricity use [1]. Among all the conversion, HVAC control system, and battery storage system in Sec- energy consumed in buildings, 50% of it is directly related to space tion 2. In Section 3, we provide the formulation and solution of the heating, cooling, and ventilation [1]. Therefore, reducing building optimal co-scheduling problem of HVAC control and battery man- energy consumption by designing smart control mechanism to oper- agement under the time-of-use electricity pricing policy. Section 4 ate the heating, ventilation and air conditioning (HVAC) system in a presents experimental results, and Section 5 concludes the paper. more efficient way is critically important to address the nation’s en- ergy and environmental concerns. In the literature, various HVAC 2. SYSTEM COMPONENT MODELS control mechanisms are proposed to reduce energy cost through stor- age of thermal energy [2], co-design of HVAC control and embedded In this paper, we consider an energy-efficient smart building with platform [3], minimization of total and peak energy consumption us- both HVAC control and battery storage systems. Considering that the ing MPC [4], and so on. photovoltaic (PV) system, which converts solar radiation into elec- Another promising methodology of improving energy efficiency is tricity, is increasingly becoming a key power source and is believed the adoption of hybrid energy supply in energy-efficient smart build- to play an important role in the process of transferring to the future ings, where multiple energy sources are scheduled together to reduce low-carbon power system [12, 13], we consider the building is also the peak demand and leverage renewable energy sources such as so- equipped with a PV power generation system as well. Our objec- lar radiation [5]. Previous papers have proposed different approaches tive is to minimize the combined cost of electricity bill and battery for efficiently scheduling multiple energy sources [6, 7]. Battery stor- SoH degradation of the building by co-scheduling the air flow of the age is the one of the most popular hybrid energy sources in energy- HVAC control system and the charging/discharging process of the bat- efficient buildings, because the chemical energy stored inside electro- tery storage system. chemical batteries can be converted into electrical energy and deliv- ered to electrical systems whenever and wherever energy is needed 2.1 Model of Building Power Flow and Power [8]. Through proper charging and discharging schedule, the storage Conversion ability of batteries is exploited for frequency regulation, load balanc- The block diagram of the power flow in a typical energy-efficient ing, and peak demand shaving [9, 10, 11]. smart building is shown in Figure 1. The PV system, providing a power supply of Ppv, and the battery storage system, in which the the equation: charging power is denoted by P , are connected to the building DC bat T (t + ∆ )= A · T (t) + B · u(t) + E · D(t); power bus through unidirectional and bidirectional DC-DC convert- ctrl t n ctrl n n (2) ers, respectively. Notice that Pbat can be positive, negative or zero. A where An, Bn and En are HVAC specific parameters which are func- positive value of Pbat means the battery is being charged, a negative tions of ∆t, Tctrl(t) is a state vector comprised of five elements, and value indicates discharging from the battery storage, and zero repre- D(t) is the disturbance from external sources (e.g. solar radiance, sents no charging or discharging operation. The DC power bus is fur- wind, etc.) at time t. The five elements in Tctrl(t) correspond to ther connected to the residential AC power bus via bidirectional AC- the temperature of the four surrounding walls of a room and the tem- DC interfaces (e.g., inverters, rectifiers, and transformer circuitries). perature of the room itself. To maintain the building temperature at a The power consumption from HVAC control system (Phvac) is the comfortable zone, at any time t, Tctrl(t) needs to satisfy the following part that we need to manage in this paper. The building AC load on constraint: the AC bus (Pload) corresponds to other building tasks such as light- ing, fire and security. The AC power bus is further connected to the TlowBound(t) ≤ Cn · Tctrl(t) ≤ TupBound(t); (3) state-level or national smart grid and the power from the grid Pgrid is where Cn = [0 0 0 0 1] is used to find the temperature of the room, related to the building’s electricity bill. We consider realistic power and TlowBound(t) and TupBound(t) are the lower bound and upper conversion circuits (i.e., the power conversion efficiency is less than bound of the comfort zone in terms of air termperature at a certain 100%) in this work, and use η1, η2 and η3 to denote the power ef- time. The air flow also needs to follow the constraint: ficiency of the converters between the PV system and the DC power bus, the converters between the battery storage and the DC power bus, UlowBound ≤ u(t) ≤ UupBound; (4) and the AC-DC interface connecting the DC power bus and the AC meaning that the maximal achievable value of u(t) is UupBound, while power bus, respectively.

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