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2 RELATED WORK IN ENERGY
CONTROL
Energy efficiency has been gaining increasing
research interest in the past two decades. As
economic crisis continues, people are keen to design
energy efficient systems and apply them to various
application areas.
Energy efficiency is a traversal problem across
numerous application domains such as sensor
networks (Cui et al., 2004), building management
(Lamoudi et al., 2011), (Samuel, et al., 2011), and
data centre management (Lakshmi, 2012) requiring
sophisticated approaches. Cui (Cui et al., 2004)
showed, for instance, that cooperative multi-input-
multi-output (MIMO) transmission and reception
simultaneously achieve both energy savings and
delay reduction in radio application of sensor
networks.
Buildings account for 40% of worldwide energy
use (US department of energy, 2008). Many EU
projects focus on the energy performance of
buildings, like Adapt4EE (SEC-288150). Model
predictive control (MPC) methods have been applied
to minimize the energy consumption in buildings
(Lamoudi et al., 2011).
3 SCIENTIFIC PROBLEM
FORMULATION
The SEAM4US project is about (1) acquiring
optimized energy consumption minimizing
strategies (2) given a certain context determined by
outside temperature, airflow status, passenger
density, train schedule, etc., (3) while satisfying
various constraints, such as comfort-levels and
operational constraints.
Consequently, SEAM4US defines the control
task as a constrained optimization problem, i.e., find
a distributed, but coordinated, control strategy
i
w
,
which minimize the total energy consumption across
the target metro station.
()
i
i
t
ew dt
(1)
Subject to comfort level constraints:
Temp_L Temp (x, t) Temp_H
L (x, t) _HAirflow Airflow Airflow
Temp_L Temp (x, t) Temp_H
(2)
Hum_L H (x, t) H _Hum um
Co2_L Co2(x, t) Co2_H
Lum_L L (x, t) L _Hum um
and operational constraints:
Ctwtw
ii
||)()1(||
(3)
Where is the frequency of fan or any other
subsystem i, is the energy consumption rate of
fan , lighting or any other subsystems given input
frequency or lighting luminance level, and where
Lxx _
and
Hxx _
refer to the lower bound and
upper bound of the referred context variable,
respectively. For instance,
LTemp _
refers to
minimal requirement of temperature.
Note that passenger density (user modelling) will
influence the Temp, Airflow, humidity, CO2, etc.
Furthermore, all context variables (temperature,
humidity, level of pollutants, airflow rate) are
functions of passenger density (spatial-temporal)
distribution, train effects, and other context variables
such as outside wind, outside temperature, etc.
Therefore, the modelling task is trying to establish
and quantify the relationships between the fan
frequency, lighting luminance level and the
environmental and thermal factors and the passenger
behavioural patterns as part of the contexts such as
temperature, humidity, CO2 concentration, etc.
For constrained optimization the interior point
method (Alizadeh, 1991) is usually used to unify the
inequality constraints into the objective function.
There are two types of interior functions that we can
use, barrier interior function (Gill et al., 1986) and
primal-dual interior function (Alizadeh et al., 1998).
When the constraints are box-like constraints,
meaning that we want to bound the constraints
within a range, barrier interior functions are
typically used. When the constraints are single sided
constraints or change as time goes on, the primal-
dual interior method is often used.
After unifying the constraints into the objective
function, we reach an unconstrained optimization
problem.
If the objective function is twice differentiable,
then Newton’s method is a good candidate to learn
the optimal point. When the objective function is
differentiable, but not twice differentiable, we can
use gradient-based methods (Boyd and
Vandenberghe , 2004), such as steepest gradient
method. When the objective function is not
differentiable, we can use the sub-gradient method
(Boyd and Vandenberghe, 2004) for optimization.
)(
i
we
i
w
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