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Multistage and decentralized operations of Chapter | 16 419
session from the billed maximum demand period to an off-peak period in a
summer month (summer is May 1 to October 31; winter is November 1 to
April 30). It is noted that the AlcoPark garage is placed on PDP (peak-day
pricing) rate, which provides customers the opportunity to manage their elec-
tric costs by reducing load during high-cost periods or shifting load from
high-cost periods to lower cost periods. There are 9 15 PDP event days per
year. On event days, a surcharge is added between 2:00 and 6:00 p.m., which
is $1.2/kWh for E-19 tariff rate.
16.3.2 Aggregation of electric vehicles
For each individual vehicle n on day d, the following constraints should be
satisfied:
d
d
d
b tðÞUp # p tðÞ # b tðÞUp ð16:1Þ
n n n
d d d
e t 1 1ð Þ 5 e tðÞ 1 p tðÞUη UΔt ð16:2Þ
n n n c
d
e t d;l $ e d ð16:3Þ
n n n;req
d
b tðÞ in Eq. (16.1) is the indicator of whether vehicle n is charging at
n
time t. Note that, the feasible charging range is not continuous so as to
d
model the real-world EV chargers. When b tðÞ is set to 0, both the left and
n
right-hand sides are 0, constraining the charging power to 0, that is, the inac-
tive state. For the active state, the charging power threshold p, that is, mini-
mal charging power, is set to 1.5 kW, which corresponds to the limit of the
chargers used in the demonstration project. Eq. (16.2) indicates the accrual
of energy consumption for each vehicle and the energy consumption value at
d
l
f
the time of charging session finish time t , that is, e t , should be larger
n n n
than the requested amount e d . Note that energy requests for vehicles are
n;req
collected by a driver charger interface.
In order to reduce the number of decision variables in the optimization
problem, modeling approaches from Ref. [20] are adapted to aggregate
numerous individual EVs as one single virtual battery with power and energy
boundaries, hereby improving the computational efficiency. According to
this approach, any trajectory that falls between the power and energy bound-
aries can be achieved by controlling each EV’s charging power. The
approach is summarized as follows:
1=2 X 1=2
e
E d ðtÞ 5 nAN p ðtÞ n;d ðtÞ; tA½0; T ð16:4Þ
t
X
2
1
d
E tðÞ # P τðÞUΔt # E tðÞ; ’tA½0; T ð16:5Þ
d
d
τ50
