
analyzed. The calculation formula of Pearson’s correlation
coefficient can be written as [33]:
r ¼
P
N
i¼1
ðx
i
xÞðy
i
yÞ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
P
N
i¼1
(x
i
x)
2
P
N
i¼1
(y
i
y)
2
s
ð1Þ
where x
i
is the meteorological parameter value for each
sampling hour;
x is the average value of all the x
i
; y
i
is the
public building’s CAC load for each sampling hour (kW);
y
is the average value of all the y
i
(kW); N is the total number
of the sampling hours, which is taken as 24.
According to the Pearson’s similarity theory, x has the
strong correlation with y when |r| is greater than 0.7; x has
the general correlation with y when |r| is from 0.4 to 0.7;
x has the weak correlation with y when |r| is smaller than
0.4. Taking the public buildings’ CAC load in a region of
the city of Nanjing as an example, the Pearson’s correlation
coefficients between public building’s CAC load and dif-
ferent meteorological parameters for every hour from June
15
th
to September 15
th
of 2013 are calculated as follows:
(a) For the meteorological parameter of temperature,
r equals 0.758; (b) For the meteorological parameter of
humidity, r equals -0.704; (c) For the meteorological
parameter of atmospheric pressure, r equals -0.344;
(d) For the meteorological parameter of wind velocity,
r equals 0.189; (e) For the meteorological parameter of
rainfall, r equals -0.207. It can be seen that, the meteo-
rological parameter of temperature and humidity have the
strong correlation with the public building’s CAC load.
Therefore, these two meteorological parameters are selec-
ted to participate in the short term load forecasting for
public building’s CAC baseline load.
Furthermore, considering the accumulation effect of
both temperature and humidity to the forecast of public
building’s CAC load, the meteorological index of Weigh-
ted Temperature and Humidity Index (WTHI) is taken for
participating in the load forecasting. This meteorological
index is adopted by the PJM’s electricity market in the
United States and its definition can be expressed as [34]:
K
WTHI
¼ 10 K
THI
þ K
THI;1
þ K
THI;2
=14 ð2Þ
K
THI
¼ T
F
þ (0.55 0.55H
L
) (T
F
58) ð3Þ
where K
WTHI
is the Weighted Temperature and Humidity
Index of the sampling day; K
THI
, K
THI,-1
and K
THI,-2
are
respectively the temperature and humidity index (THI) of
the sampling day, the day before the sampling day and
2 days before the sampling day; T
F
is the average
Fahrenheit temperature of the sampling day; H
L
is the
humidity of the sampling day (%). The absolute values of
error between the K
WTHI
of the forecasted day and the
K
WTHI
of the days within two months before the forecasted
day are respectively calculated. Twenty days with the
minimum absolute values of error are selected as the typ-
ically similar day.
Finally, the back propagation neural network (BPNN) is
adopted. For this BPNN, the input variables are K
THI
and
K
WTHI
and the output variables are 96 public building’s
CAC load values for each regulation period of a day (A day
is divided into 96 regulation periods whose duration is
15 min in this paper. In addition, assume that the values of
all the power variables and cooling capacity variables
discussed in this paper remain constant in each regulation
period). By using the values of the input and output vari-
ables of the 20 typically similar days, the connection
weights between the hidden layer and the output layers for
the BPNN are determined. Then, based on these connection
weights, the 96 public building’s CAC load values for the
forecasted day are acquired by inputting the values of its
K
THI
and K
WTHI
.
To verify the forecast precision, the load forecasting
method is firstly adopted to obtain the baseline load values
of one public building’s CAC system in Nanjing on July
30
th
, 2013. After comparing the 96 forecasted load values
with the actual load values, the average error ratio which
equals 3.52% is small enough for the DAPND in the fol-
lowing sections. Thus, in this paper, the short term load
forecasting method above is applied to acquire the baseline
load of each studied public building’s CAC system in peak
load shaving period (PLSP).
3 Modeling of public building’s CAC load
Usually, a set of CAC system is employed as the
cooling system of public building, which mainly includes
one or more chiller units, the corresponding number of
chilled water pumps, cooling water pumps and cooling
towers and the terminal equipment of fan coil units, fresh
air units and climatic conditioning cabinets. The required
cooling capacity of the building is all supplied by the
chiller units. According to the law of conservation of
energy, the sum of instantaneous gain of heat q
cl
,freshair
load q
nw
and heat storage capacity of interior wall q
x
is
equal to cooling capacity of CAC system q
ch
q
cl
is equal
to the sum of hourly cooling load forming by the transient
heat transfer from the exterior wall and roof q
er
,hourly
cooling load forming by the transient heat transfer from
the external window q
ew
, hourly cooling load forming by
the radiant heat of the sun from the external window q
rh
,
hourly cooling load forming by the heat dissipation of
indoor electro thermal equipment q
e
, hourly cooling load
Strategy of constructing virtual peaking unit by public buildings’ central air conditioning… 189
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