is read every 5 minutes. In order to have a more accu-
rate automaton, we can discretize time in more steps.
Those works will be shown in a further paper.
Depending on the dirtiness of the dishes, the dish-
washer cycle will require heating the water a different
number of times and for different times as shown in
Figure 1. However the states ”cleaning” and ”rins-
ing” (with a consumption respectively at 2100W and
40W) remain the same. Thus, the automaton makes it
possible to model all the cycles with only three states
representing its consumption: StandBy, 2100 and 40
(Figure 2).
It allows a large number of arrangements. Indeed,
according to the conditions (C
i
V ) the automatons will
create a stack of alphabets elements (L
i
) describing
the succession of the stages of the cycle. The automa-
ton will unstack from one element to another until the
end of the cycle.
For example, to model the test1 consumption the
automaton take the following stack:
L
1
= 40, 2100, 2100, 40, 40, 2100, 40, 40, 40, 40,
40, 40, 40, 40, 2100, 2100, 2100, 40, 40, 40
And to model the test2 consumption the automa-
ton take the following stack:
L
2
= 2100, 2100, 40, 40, 2100, 40, 40, 2100, 40, 40,
40, 40, 40, 40, 40, 2100, 2100, 2100, 2100, 40
The presented automaton has a problem in the
case where the average consumption during 5min is
in fact neither 2100W nor 40W . It is then necessary to
either round to the nearest state as done for the 35min-
40min section of the red curve, or to create an au-
tomaton with more states in order to be more accurate
to the real curves, and to take a better discretization
of time (each 2min for example). Another automaton
for the dishwasher is shown in Figure 3).
The following stack represents consumption of
test2:
L
2bis
= 2100, 2100, 40, 40, 2100, 40, 40, 600, 40, 40,
40, 40, 40, 40, 40, 2100, 2100, 2100, 2100, 40
The model can be refined to the point of repre-
senting any consumption’s curve. It is then possible,
according to the discretization of the time, to estimate
the various actions of the automaton. In our example,
the input stack is fixed, so there is only one possibility
of consumption.
For another automaton, we obtain a prefix tree of
the form presented in Figure 4. It is important to note
that from a prefix tree, it is also possible to build the
associated finite state automaton as shown in Figure
5, so building an automaton for a device can be done
by machine learning.
4 MULTI-AGENT MODEL
A system which consists of large populations of con-
nected agents, or collections of interacting elements,
is said to be complex if there exists an emergent
global dynamic. This behavior results from the ac-
tions of its parts rather than being imposed by a cen-
tral controller. That is a self-organizing collective be-
havior that is difficult to anticipate from the knowl-
edge of local behavior (Boccara, 2004). The complex
system approach is described in the following articles
(Ahat et al., 2013) and (Amor et al., 2014).
Computer modeling and simulation have proven
to be a useful tool, if not essential, to help decision
making in studying and designing complex artificial
systems (Molderink et al., 2009). Any change in
a Smart Grid involves millions or billions of Euros.
Thus, any change needs a deep study and some sim-
ulations to integrate or to understand all the conse-
quences and any kind of new behaviors, disruptions
in the new grid.
A Smart Grid presents a shared resource among
multiple actors, with divergent interests. A multi-
agent system (MAS) modeling presents the global dy-
namic of the system from individual components and
explores emergent properties associated with this dy-
namic. However, it should be noted that MAS have
a major drawback: one model run does not allow to
conclude about the relationship between model and
results (Weiss, 1999). We will present in the next sec-
tion some results, but previously let us expose our first
model.
Our model focuses on microgrid. A microgrid is a
broader view of local consumers, it is a tree structure
representing an eco-district bounded by the upstream
substation. Its goal is to distribute energy from a sub-
station to consumers. It orders an amount of energy
from the T&D network to local consumers.
A local consumer supports the consumption of en-
ergy, which is the distribution of energy among de-
vices under its responsibility. In other words, a local
consumer is defined by the area under the control of
a smart meter or other automation/management con-
troller. Those devices may also produce energy or
storage energy.
The goals of any microgrid are to limit using ex-
ternal sources of energy, to avoid brutal changes in its
consumption curve. The consumption of each device
from each house has to be adapted accordingly to the
microgrid’s behavior. For the first simulation, we take
four houses for one microgrid.
In each of the houses there are a number of de-
vices: some have batteries others do not, some are
cyclic other are not etc. These devices will turn them-
Multi-agent Model for Domotics and Smart Houses
225