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where
h
j
(
k
) represents the non-EV power consumption for the
j
th house on
the distribution network at time
k
,
c
i
(
k
) is the charge rate of the
i
th active
EV charge point,
N
is the number of houses on the distribution network and
N
(
k
) is the number of active charge points. The instantaneous available power
is computed as
P
(
k
)=
P
rated
−
λ
−
Δ
(
k
)
.
(3)
Here
P
rated
(kVA) is the maximum capacity that can be drawn from the sub-
station and is the lesser of the available generation capacity or the substation
rating.
λ
(kVA) is a constant 'safety margin' for secure operation.
Δ
(
k
)(kVA)
is a time varying factor introduced to create an artificial reduction in available
power at times of high electricity prices and is computed as
Δ
(
k
)=(
E
(
k
)
−
E
min
)
.ξ.
(4)
In (4)
ξ
is a constant tuning parameter,
E
(
k
) (cent/kWh) is the Time-of-
Use(TOU) price [11] at time
k
and
E
min
is the minimum TOU price during
the day.
In the AIMD EV charging study in [5] EV charging was considered indepen-
dently of other household power consumption with
P
(
k
) computed according
to (1). This results in a significant communication overhead as the central sub-
station cannot distinguish EV charge point power usage from other residential
power consumption, hence this information must be communicated continuously
to the central monitoring station by the active EV charge points. In our formula-
tion
P
(
k
)and
P
(
k
) are defined in terms of overall residential power consumption
levels, hence
P
(
k
) can be directly sensed at the central substation.
3 Simulation Platform
To evaluate the performance of the proposed AIMD charging strategy a test
distribution network incorporating EVs is simulated based on a typical LV res-
idential feeder layout. A simplified schematic diagram for the test network is
given in Fig. 1. In our simulations, the voltage is set at 1.05pu at the source
end of the external grid. A 2MVA distribution substation is connected to the
external grid to bring the voltage level to 10kV. This substation feeds three dis-
tribution transformers serving residential areas. Each distribution transformer
is connected by an unbalanced 336 MCM ACSR transmission line of different
length (modeled as Pi-Equivalent circuits). Both household loads and EV charg-
ing loads are connected at the secondary side of each distribution transformer. As
illustrated in Fig.1, the household loads with EV charging points are separated
into three phases, and the number of houses connected to each phase is indicated
in parenthesis. Non-EV charging loads are lumped together using balanced three
phase modeling. The distance between each house connected to a given phase
is randomly chosen between 10-50m. To simulate EV charging with this net-
work a custom OpenDSS-Matlab platform was employed. OpenDSS [9], an open
source electric power Distribution System Simulator, was used to simulate the
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