Environmental Engineering Reference
In-Depth Information
In order to complement the nodal PHEV equations presented in the previous
subsection, it is necessary to define the variables that keep track on the SOC of the
storage resources. For this, it is imperative to introduce a time variable. Likewise, it
is required to define the limits on how much energy the batteries are able to charge
and discharge in terms of total capacity and per unit of time.
We begin by addressing the storage balance equation that must be fulfilled every
day. Thus, there must be a term that takes into account all the energy charged and dis-
charged from the batteries. Similar to (4.31) there must be a nodal equation exclusive
to PHEV units which determines the sum of the energy charged (G2V), discharged
to the grid (V2G) and used for transportation (V2R). This expression is defined as
the nodal electric vehicle storage balance and for node
k
, battery equations it can be
stated as:
η
G
2
V
·
nβ
V
2
G
store
k
,
β
η
V
2
G
V
2
R
store
k
,
β
η
V
2
R
EV
store
Bk
G
2
V
store
k
,
β
=
−
−
=
0
(4.49)
β
=
1
⎧
⎨
β
is the time interval being analysed
nβ
is the number of time intervals into which the full period is divided
G
2
V
store
k
,
β
where
is the energy charged into the battery (Wh
el
)
⎩
V
2
G
store
k
,
β
is the energy discharged from the battery for V2G services (Wh
el
)
V
2
R
store
k
,
β
is the energy discharged from the battery for V2R services (Wh
el
)
1 it is necessary
to have the previous storage value at time
β
; this can be formulated as:
To define the SOC for the storage system in node
k
at time
β
+
EVSOC
store
k
,
β
+
EVSOC
store
k
,
β
EVSOC
store
k
,
β
=
+
(4.50)
1
k
,
β
must be equal or greater than 0
for all time intervals because storage levels cannot have a negative value. However,
this constraint does not apply to the term which calculates the change in the SOC for
a specific time interval
β
, and is determined by:
Needless to mention, the value for
EVSOC
store
EVSOC
store
k
,
β
G
2
V
store
k
,
β
V
2
G
store
k
,
β
V
2
R
store
k
,
β
=
−
−
(4.51)
Once the battery SOC equations are defined, it is necessary to calculate the
energy injections that influence the energy levels of the batteries:
G
2
V
store
k
,
β
,
V
2
G
store
k
,
β
and
V
2
R
store
k
,
β
. These energy transfer values, that alter the state of charge of the batteries,
are analogous to terms
P
phev
Dk
,
P
phev
Gk
and
M
phev
Gk
from Figure 4.21.
Taking the battery units at node
k
for time interval
β
, these terms of energy
injections can be expressed as:
hr
total
nβ
P
phev
Dk
,
β
G
2
V
store
k
,
β
W
store
G
2
Vk
,
β
=
·
·
(4.52)
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