Page 465 - Decision Making Applications in Modern Power Systems

424 Decision Making Applications in Modern Power Systems

market. For EVs with V2G capabilities, “sell” operations can be achieved by
discharging the vehicle batteries, while for V1G, “selling” of power would
be achieved by reducing the aggregate power consumption relative to a
power consumption baseline. The model is presented as follows:
X X d d
R PDR 5 R t ðÞUπ ðÞUΔt ð16:23Þ
t
dAD tAT sell pdr

d
d
M s U 1 2 b PDR t ðÞ # P tðÞ 2 B tðÞ 1 R d t ðÞ # M b U 1 2 b PDR ðtÞ ð16:24Þ
agg sell agg
d
b sell t ðÞUR PDR # P tðÞ # b sell t ðÞUP d ð16:25Þ
agg sell n agg
The revenue from the PDR market is a product of the virtual sell power,
that is, R d sell t ðÞ, multiplied by the corresponding PDR market prices, that is,
d
d
π ðÞ in Eq. (16.26). The baseline power consumption B tðÞ is typically the
t
pdr n
averaged value of a number of previous days; thus here we model it as a
known profile before optimization. In reality, PDR market participation has a
requirement of a minimal threshold for virtual sell power, that is, Rsell PDR in
Eq. (16.28).In Eq. (16.27), b PDR t ðÞ is the binary indicator of whether the fleets
agg
are participating in the PDR market. When b PDR t ðÞ 5 1, that is, participating,
agg
Eq. (16.27) is reduced to
d
d
P tðÞ 5 B tðÞ 2 R d t ðÞ ð16:26Þ
sell
d
where the actual power consumption value P tðÞ equals the baseline power
n
d
B tðÞ minus the virtual sell power R d t ðÞ. When b PDR t ðÞ 5 0, indicating no
sell agg
participation, Eq. (16.20) evolves to
d
d
M s # P tðÞ 2 B tðÞ 1 R d ð16:27Þ
sell t ðÞ # M b
where M s is a sufficiently small number and M b is a sufficiently big number.
Eq. (16.30) remains true for all cases, making it a redundant constraint in the
optimization problem, which can be effectively handled by current solvers
with mixed-integer capabilities. In addition, to model the consecutive
engagement constraint, some numerical approaches are applied as shown in
Eqs. (16.31) and (16.32):
b c t 0 ðÞ 5 b PDR t 0 ðÞ ð16:28Þ
agg
b c tðÞ # 1 2 b PDR ð t 2 ΔtÞ ð16:29Þ
agg
b c tðÞ # b PDR t ðÞ ð16:30Þ
agg
b c tðÞ $ b PDR t ðÞ 2 b PDR ð t 2 ΔtÞ; ’tAT ð16:31Þ
agg agg
min t1N
ð
X c 21;TÞ
b PDR t ðÞ 2 N c $2 N b U 1 2 sc tðÞÞ; ’tAT ð16:32Þ
ð
agg
τ5t