Journal of Power and Energy Engineering, 2015, 3, 282-288
Published Online April 2015 in SciRes. http://www.scirp.org/journal/jpee
How to cite this paper: Choi, H.D., Rhee, S.W., Ahn, C.K. and Lim, M.T. (2015) AC Scheduling Based on Thermodynamics of
Indoor for On-Campus Small Data. Journal of Power and Energy Engineering, 3, 282-288.
AC Scheduling Based on Thermodynamics of
Indoor for On-Campus Small Data
Hyun Duck Choi, Soon Woo Rhee, Choon Ki Ahn, Myo Taeg Lim
School of Electrical Engineering, Korea University, Seoul, Republic of Korea
Email: firstname.lastname@example.org, email@example.com, firstname.lastname@example.org, email@example.com
Received January 2015
This paper proposes a new day-ahead control scheme of an air conditioning (AC) based on ther-
modynamic model of indoor-temperature. The thermodynamic model of ind oor-temperature can
be achieved by modified first-order thermal dynamic equation. For the practical verification of
proposed model, we implemented the home energy management system (HEMS) in the laboratory
and used real experiment data sets. The proposed model can be represented by a state-space
model of indoor-temperature and its parameters are obtained by least square algorithm. Through
the proposed thermodynamic model, indoor-temperature can be predicted closely, and a behavior
pattern of AC can also be achieved. This research involves the experimental verification of the
proposed approach and communication architecture between the aggregator and a system user in
a laboratory environment.
Home Energy Management System (HEMS), Least-Square, Convex Optimization, Demand Response
(DR), Air-Conditioning (AC)
Through the smart grid project offering a two-way communication frame, a home energy management system
(HEMS) is able to manage residential load control based on measurement for the home environment, the user’s
comfort, and electricity bills -. The main issue concerning the design of HEMS is how to provide the intel-
ligent solution for energy consumption that reflects the customer’s specific lifestyle. The suitable HEMS should
have the capabilities to schedule the load demands to minimize the expenditure on electricity bills and user’s
uncomfortable sense simultaneously.
Accurate load forecast for residential appliance is essential for efficient consumption of the electrical energy
 . In order to maintain balance between electricity production and demand on the network, accurate fore-
cast for appliance load is one of the important issues in smart grid. However, residential load forecasting is
usually difficult, due to its random nature of turning on/off. Many researches for residential load forecasting
have been proposed over the years and still remains an important issue.
Air conditioning (AC) unit is the representative appliance which belongs to the category of thermostatically
controlled appliance . Thus, the analysis of thermodynamic model of indoor-temperature with AC is required
H. D. Choi et al.
for efficient load control. The estimation of the indoor-temperature of the next day is essential in order to predict
usage of the AC load in private homes.
Through the thermal dynamic model - of indoor-temperature, it is possible to estimate the indoor-te m-
perature based on the outdoor temperature information of the following day. Based on the user’s characteristic
and estimation of indoor-temperature, the AC scheduling pattern can also be predicted. The indoor-temperature
is also significant information on load shifting or reducing strategy. By providing the indoor temperature infor-
mation of before and after DR response to consumers, the efficient DR reaction can be led.
In this paper, we propose a new day-ahead control scheme of an AC based on a modified thermodynamic
model of indoor-temperature. There are extensive literatures on the thermal dynamic models of large facilities,
however there are limited results in the open literatures on models for residential homes using data of relatively
small size. Thus, we implemented the HEMS with smart AC in the laboratory and used real experiment data sets
for the validation of the proposed method.
2. Day-Ahead Control Scheme for AC Scheduling
2.1. Modified Thermodynamic Model of Indoor-Temperature
As a standard description of thermal dynamics including a residential AC, the discrete-time dynamic equation of
indoor-temperature  can be represented as follows:
[ ][ ][ ][ ]
[ ][ ]
1TkTkTk TkP kcwk
is the indoor-temperature at time
is the outdoor-temperature at time
is power consumed by AC; and
is white Gaussian noise. First, we have performed validation of the
model using real data collected from our laboratory. The collected data includes indoor-temperature, outdoor-
temperature, and AC power usage. However, the above model did not fit well because the effectiveness of in-
ternal thermal noise is simply modeled by constant scalar c. In this paper, in order to give more detailed descrip-
tion for the effectiveness of internal thermal noise, we propose a modified thermal dynamic model for indoor-
temperature as following form:
[ ][ ][ ]
[ ][ ]
1TkTkTk TkP kTk
are defined above and
are the model parameters to
be estimated. In this equation, the effectiveness of internal thermal noise is represented by the term of
denotes the temperature of internal thermal noise and it needs to be estimated. The difference
between the temperature of internal thermal noise
affects the next indoor temperature in the
proposed model. Based on the dynamic model in (2), the state-space form of indoor-temperature can be repre-
1x kAx kBu k
whe r e
[ ][ ][ ][ ]
As a model fitting method, we use a least-square (LS) algorithm.
[ ][ ]
where N is the number of observations used in the parameter estimation. In this study, we considered the case
H. D. Choi et al.
when N corresponds to 30 days of measurements. The model extracted from the data needs to be validated using
real experiment data sets. With the estimated parameters
obtained from data set, we test
the accuracy of the model using a different data set. Based on the state-space model, the prediction of indoor-
temperature can be obtained
[ ][ ]
ˆ1x kAx kBuk+= +
The mean squared Prediction Error (PE) is given by
The validation of indoor-temperature prediction is given in Section 3.
2.2. Optimization Framework for HEMS Based on the Modified Thermodynamic Model
The residential consumer’s interest is two-fold. One is to minimize residential consumer payment and the other
is the user’s comfort. It is clear that these two objectives can be conflicting in many scenarios. One of the im-
portant issues for optimization problem in HEMS is how to select a cost index for user’s comfort. If one can
predict user’s power consumption pattern for next day, cost selection problem becomes easy. Taking this into
consideration, we can get the cost function to be minimized as follows:
[ ][ ]
JC kPkT kT k
is the prediction of indoor-temperature considering the usual power usage pattern;
is power consumed by AC;
are adjusting weight parameters. The first
and second terms of the objective function in (8) denote the total electricity payment amount and the total cost of
uncomfortableness, respectively. As shown in (8), user’s discomfort index becomes simply the distance from the
normal pattern which can be obtained by estimation of indoor-temperature and user’s AC operating guide.
Based on the cost function in (8), we can formulate the optimal AC scheduling problem as the following con-
strained optimization framework:
[ ][ ]
stxkAx kBu k
is normal AC load based on the prediction indoor-temperature and user’s pattern;
is load reduc-
tion ratio. As shown in (9), the thermodynamic of indoor-temperature and
can be integrated as constraint.
The optimization variables are the energy consumption scheduling vectors for AC. Given the feasible AC sche-
duling sets and the model in (3), the goal is to find the best AC scheduling vectors to make the cost minimize.
3. Experimental Results
3.1. Experiment Setup Environment for Measurement Data
For the practical verification of proposed method, we implemented the HEMS with smart AC in the laboratory
and used real experiment data sets. Figure 1 shows the HEMS setup operated by laptop and micro controller
unit (MCU) in our laboratory environment. The experiment was carried out in the research laboratory in the
Department of Electrical Engineering at Korea University. This 35 m2 house is designed to represent real living
space for three people. In our experiment, a smart AC which is possible to communicate with MCU for DR was
used. The MCU consists of SEP 2.0 communication unit, control unit for AC usage, and AC power measuring
unit. The HEMS consists of a laptop with Internet connectivity that runs the HEMS program and can be com-
municated with the smart AC through Korean DR protocols (Open ADR 2.0/SEP 2.0) standard. Detailed speci-
fications of equipment for HEMS in laboratory are shown in Table 1. The loading profile of the smart AC is
H. D. Choi et al.
Figure 1 . Layout of HEMS and setup environment.
Table 1. Device configuration.
Model Processor Memory OS
Lenovo ThinkPad E540
4 GB Windows 7 32 bit
Model Fun ction Communication Perform ance
ATmega2560 communication with Server and AC
operating AC with DR level interface: RS232C
communication level: TTL
CPU: 8-bit AVR
Flash: 256 KB
Max operating Frequency : 16MHz
Model Fun ction Voltage Current
Carrier CPM-A157TGB0 Air Conditioner Dehumidi fier 220 V 8.1 A
obtained by MCU measurement data, which has been measured for 30 days in the area where the house is lo-
cated. In the same manner, MCU has ability to turn on/off AC using its own outputs. Indoor-temperature and
humidity were obtained through the thermostat and outdoor-temperature brought in meteorology. Using these
collected data, we validate the effectiveness of the proposed prediction approach based on the modified thermo-
dynamic model in Section 3.
3.2. Result Validation
In this section, we present the experiment results and assess the performance of the proposed prediction of in-
door-temperature for AC scheduling. Model parameters of thermodynamic model calculated by least square al-
H. D. Choi et al.
gorithm are listed in Table 2. The collected data includes AC load consumption, humidity, indoor-temperature
and outdoor-temperature within a month period from July 1, 2014 to July 31, 2014. We mainly focus on a three
days period due to limited space. After the prediction of next day indoor-temperature, HEMS presents the AC
scheduling based on user’s pattern in Table 3. To make the simulation more close to the realistic and show the
impact of accuracy of the parameter fitting, real measurement data of indoor-temperature and model based esti-
mation of indoor-temperature are plotted for a comparison. The real measurement data of outdoor-temperature,
real measurement data of indoor-temperature using AC, predictive indoor-temperature using AC based on con-
sume r’s AC usage pattern are shown in Figure 2. Figure 3 shows the PE of indoor-temperature. As shown in
Figure 2 and Figure 3, the model-based estimation of indoor-temperature is similar to the measurement data.
Forecast of indoor-temperature and AC usage for the next day can be integrated into convex optimization
framework for optimal AC scheduling.
Table 2. P aramters.
0.1176 –2.0121 2 7.1269 0.5081 0 .3
Table 3. AC operating rule based on predictive indoor temperature and humidity.
minimum continuous operation hours 20 minutes
maximum continuous operation hours 4 hours
maximum operating time per day 8 hours
The predictive temperature > 27 & humidity < 70% turn on
The predictive temperature > 26 & humidity > 70% turn on
Figure 2. C o lle cted data and estimation of indoor-temperature.
H. D. Choi et al.
Prediction error (˚C)
Figure 3 . Predi ction error (PE) for indoor-temperature.
In this paper, we implemented HEMS for day-ahead AC scheduling based on thermodynamic model in a labor-
atory environment. The AC load forecasting is usually difficult, due to its random nature of turning on/off. The
proposed HEMS estimated indoor-temperature based on the modified thermodynamic model and used this in-
formation to forecast behavior pattern of AC rather than estimating the AC prediction pattern directly. The case
study of the smart AC provides a closed system which is suitable for demonstration purpose in a laboratory en-
vironment. The proposed prediction approach based on the modified thermodynamic model can describe ther-
mal characteristic of indoor-temperature and can be integrated into the optimization framework for optimal AC
scheduling. The ideas described in this paper can be extended to address other thermostatically controlled ap-
This work was supported by R&D Program of MOTIE/KEIT, Korea. The authors would like to thank the Min-
istry of Trade, Industry and Energy, Korea. (No: 10041779, Development of Energy Demand Response System
for Smart Home).
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