Thermal Model Parameter Estimation for HVAC Facility using Recursive Least Square Method

In this paper, the parameter estimation of thermal dynamic discrete-time system for heating, ventilating and air conditioning (HVAC) is studied using recursive least square method. Parameters are estimated by using recursive least square method. Thermodynamic model of indoor test bed is formulated by outdoor temperature, HVAC power consumption, and thermal noise and estimated thermal dynamic parameters show improved performance of thermodynamic model for day-ahead indoor temperature compared to original least square parameter estimation approach. In this research, the experiment is implemented to verify the performance of proposed approach in a laboratory environment. Introduction The researches on peak-time load reduction and price volatility have been studied. It is because peak-time load has great impact on energy saving problem. Especially, many researches on home energy management problem have been highly focused on [1-5]. Appliances in household are classified as two categories including interruptible device and delayable device. Delayable devices are shifted from highly used time interval called peak-time to other time interval. To evaluate proper time interval to be moved, cost function is applied considering power consumption and user comfort. Through this process, both reduction of electricity cost and sub optimal comfortability can be obtained. During last decades, many researchers have focused on the problem of heating, ventilation, air conditioning (HVAC) [6-8]. Since HVAC facilities have great part of load on peak-time, the problem of HVAC load reduction is important research issue. Furthermore, since HVAC is used to regulate indoor temperature of household and this information is applied to obtain future horizon data used by various controllers including model predictive controller (MPC), an accurate thermal dynamic model formulation is important. This fact motivated many researchers to formulate various type of thermal dynamic models [9-10]. However, it is noted that although thermal dynamic model predicts future indoor temperature well, temperature pattern changes its own dynamic daily property. To deal with this issue, authors in [11] proposed least square (LS) method to estimate thermodynamic model parameters. LS method showed that it has simple and fast properties but it is very sensitive to outliers, which are thermal noises in case of thermal dynamic model. To solve this problem, we propose recursive least square (RLS) method to obtain thermal dynamic model parameters. Since RLS method is less sensitive to outliers, this can be a good candidate for obtaining thermal model parameters. To the authors best knowledge, there have been yet no results obtained on RLS method to obtain thermal dynamic model parameters and this motivated us to investigate this research. The remainder of this paper is organized as follows. In the next section, the thermodynamic discrete model and recursive least square method are intraduced. Numerical experiments are International Conference on Mechanics, Materials and Structural Engineering (ICMMSE 2016) © 2016. The authors Published by Atlantis Press 221 presented in Experimental Results. Finally conclusion is summarized. Parameter of Thermodynamic Model Thermodynamic Model of Zone Temperature for HVAC. In this section, we introduce discrete-time thermodynamic equation including HVAC unit. The resistive-capacitive (RC) network model is commonly used to estimate zone temperature. This paper estimate zone temperature with modified RC network model which includes thermal load effect [12]. Consider the following form: [ ] [ ] [ ] [ ] ( ) [ ] [ ] ( ) 1 , z z a z AC z T k T k a T k T k bP k c d T k + = + − + + − (1) where, ambient energy flow parameter a , air conditioner energy flow parameter b , thermal load energy flow parameter c and thermal load temperature d , [ ] z T k is zone temperature, [ ] a T k is ambient temperature, and [ ] AC P k is air conditioner power consumption. The zone temperature state-space form of the discrete dynamic thermodynamic model (1) can be formulated as follows: [ ] [ ] [ ] [ ] [ ] [ ] 1 , , x k Ax k Bu k y k Cx k Du k + = + = + (2) where, [ ] [ ] [ ] ( ) [ ] [ ] [1 ], , 1, 0, , and 1 . T z a AC A a c B a b cd C D x k T k u k T k P k = − − = = =