Page 475 - Decision Making Applications in Modern Power Systems

434 Decision Making Applications in Modern Power Systems

ρ k
2
k 2
k
p k11 5 min :D2p a : 1 U:p a 2p 1P 1u : 2 ð16:35Þ
a
2
a
p a 2
For each EV agent the updated optimization problem is as follows:
ρ k
2
k 2
k
p k11 5 min α n :p n : 1 U:p n 2p 1P 1u : ð16:36Þ
n 2 n 2
p n 2
where α n is a scalar to indicate the weight of battery degradation cost for
each EV agent. In addition, this formulation will also ensure that each EV
will have the minimal power fluctuations. For the aggregator an extra step at
each iteration is taken to update the signal to be sent to EV agents:
k
u k11 5 u 1 P k11 ð16:37Þ
k
k
k
where u is defined as y =ρ, where y is the dual variable for the original
problem at iteration k. Note that each agent only needs to store its own copy
k
of power profile, that is, p , to compute for the new profile p k11 , and the sig-
n n
k
nal from the aggregator agent, u . Thus one side effect of the decentralized
algorithm is the advantage to preserve user privacy by not sharing extra
information. The convergence criteria are defined by the primal feasibility,
k
k
r , and the dual feasibility, s :
n
1 X N EV
k
k
r 5 p 5 U p k n ð16:38Þ
N EV n51
k
k
k
s 52 ρNðp 2 p k21 1 ðp k21 2 p ÞÞ ð16:39Þ
n
n
n
k
:r : # E pri ð16:40Þ
2
k
:s : # E dual ð16:41Þ
2
k
k
k
where s is defined as s ; s ; ... ; s ; and E pri and E dual are the primal and
k

N
2
1
dual convergence criteria, respectively.
Synchronous ADMM for EV load following
1 Initialize N agents with 1 aggregator and N 2 1 EVs;
k
k
2 While :r : $ E pri and :s : $ E dual :
2 2
3 While aggregator receives all EV signals:
4 For each EV agent nAN EV :
5 Solve the local optimization problem and send the profile to the aggregator
agent N
k
k
6 Update p and u within the aggregator agent
k
k
7 If :r : , E pri and :s : , E dual :
2 2
8 Terminate
The detailed algorithm is illustrated in the previous table. We show the
interactive load following performance in Fig. 16.14 by comparing the given
aggregator’s load curve to follow with aggregated EV load curves in