Z E M C H 2 0 1 2 I n t e r n a t i o n a l C o n f e r e n c e
172
Figure 4c reflects the week usage of gas. Five highest usage weeks include week 18,
26, 24, 22 and 27, which fall in the winter season. It demonstrates that the gas
consumption is highly related to the weather conditions. But there are no significant
fluctuations for electricity and water during this period, which means less correlation
between gas and electricity or water usage.
a) Electricity
b) Water
c) Gas
Figure 4. Energy usage patterns in weeks
The correlation among electricity, water and gas consumptions in hours
We have also conducted correlation analysis among electricity, water and gas
consumptions. We constructed the observations of 301 days (hourly data) as Matrix A in
equation 1. Where Column 1 represents the electricity consumption; Column 2
represents the water consumption and Column 3 represents the gas consumption. Each
row represents the hourly observation (with 24x301=7,224 rows in total). We calculated
the correlation R in equation (3) based on the covariance matrix Cov(A) in equation 2.
A
=
A
11
A
21
A
13
.
.
.
A
n
1
A
n
2
z
n
3
(1)
Cov
(
A
)
=
cov(
A
im
,
A
jm
)
m
=
1, 2, 3
=
E
(
A
im
−
µ
im
)(
A
jm
−
µ
jm
)
[
]
(2)
where
µ
im
=
E
(
A
im
)
is the expected value of the i
th
entry in the Matrix A.
R
(
im
,
jm
)
m
=
1, 2, 3
=
C
(
im
,
jm
)
C
(
im
,
im
)
C
(
jm
,
jm
)
(3)
Figure 5a and 5b show the correlation among electricity, water and gas consumptions
during working days and non-working days. Figure 5a shows the consumption of working
0
5
10 15 20 25 30 35 40 45
0
0.2
0.4
0.6
0.8
1
1.2
1.4
weeks
relative value
electricity
0
5
10 15 20 25 30 35 40 45
0
0.2
0.4
0.6
0.8
1
1.2
1.4
weeks
relative value
water
0
5
10 15 20 25 30 35 40 45
0
0.5
1
1.5
2
2.5
weeks
relative value
gas
