Wireless Sensor and Actuator Networks for Lighting Energy ...

office with K luminaires, for example, and suppose it is discretized into a grid of mn
squares. The generated illuminance models are K m-by-n matrices, l 1 , l 2 ,…,l K ,
associated with each of the K luminaires indicated by the superscript number. Equation
(6.1) is the symbolic representation of the i th illuminance models matrix, l i .
i
i
l 11
… l 1n
l i =
i
i
l m1
l mn
(6.1)
Lighting optimizer
The illuminance of the room at the workplane level (E) is represented as the
linear combination of each model as shown in (6.2), where d i is the light level output of
each luminaire.
i
i
e 11
… e 1n
K
l 11
… l 1n
K
E=
= d
i
l i = d i
(6.2)
e m1
e i=1
i=1 i
i
mn
l m1
l mn
For mathematical manipulation, each matrix is rearranged into a column vector
by concatenating the columns, denoted 1 , 2 ,…,
K
l l l , and (6.2) can be rewritten as a
pure matrix operation expressed in (6.3). The operator L, with the rearranged vectors of
the models as its columns, defines the transformation from a vector of light output level
d into the resulting workplane level illuminance E of the room. E is the vector of
concatenated columns of E due to the rearrangement of the illuminance models.
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