Page 477 - Decision Making Applications in Modern Power Systems
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synchronous algorithm, whereas the aggregator will only need minimal num-
ber, that is, N min , of signals received from the EV agents to start the optimi-
zation and will keep records of the time lag of each EV agent, that is, L n .In
each iteration of the updated algorithm the aggregator needs to ensure that
(1) the number of distinct signals from EV agents is larger than the minimal
required number, that is, N rec $ N min , and (2) the maximum time lag among
all the EV agents is less than the maximum lag allowed, that is,
max L 1 ; L 2 ; ... ; L N21 Þ # L max . The details in the asynchronous ADMM
½ ð
algorithm are as follows:
Asynchronous ADMM for EV load following
1 Initialize N agents with 1 aggregator and N 2 1 EVs, and N 2 1 copies of power
profiles, i.e., ½^ p ; ^ p ; .. . ; ^ p N21 within aggregator;
2
1
k
k
2 While :r : $ E pri and :s : $ E dual :
2 2
3 While max L 1 ; L 2 ; .. . ; L N21 Þ # L max and N rec $ N min
½ ð
4 For each EV agent n received:
5 Set agent lag L n to 1
6
Update the profile copy within the aggregator by ^ p 5 p n
n
7 For each EV agent in the fleet but not received:
8 Increase the agent lag by 1, i.e., L n 5 L n 1 1 P N EV p k
k
k
9 Update p within the aggregator agent by p 5 n51 n
N EV
k
k
10 If :r : , E pri and :s : , E dual :
2 2
11 Terminate
FIGURE 16.15 Primal residuals of sync-ADMM and async-ADMM.
The key difference between the asynchronous ADMM and the synchronous
counterpart is that the average power update step in the asynchronous version,
that is, line 9 in the previous table, does not need full information from all the
EV agents in the same iteration. In other words, it allows the signals from some
EV agents to be out of date and only uses the partial information to drive the
system to the global optimality. However, the aggregator has to ensure the
