Advanced Building Simulation

174 Mahdavi
irradiance sensors that were installed on the daylight monitoring station on the roof
of the IW. As an initial feasibility test of the proposed simulation-based control
approach, we considered the problem of determining the “optimal” louver position.
Step 1. In this simple case, the control state space has just one dimension, that is,
the position of the louver. We further reduced the size of this space, by allowing only
four discrete louver positions, namely 0� (vertical), 30�, 60�, and 90� (horizontal).
Step 2. Given the small size of the control state space in this case, we considered
all four possible louver positions as potential candidates to be compared.
Step 3. LUMINA (Pal and Mahdavi 1999), the lighting simulation application in
SEMPER (Mahdavi 1999), was used for the prediction of light levels in the test space.
LUMINA utilizes the three-component procedure (i.e. the direct, the externally
reflected, and the internally reflected component), to obtain the resultant illuminance
distribution in buildings. The direct component is computed by numerical integration
of the contributions from all of those discretized patches of the sky dome that are
“visible” as viewed from reference receiver points in the space. Either computed or
measured irradiance values (both global horizontal and diffuse horizontal irradiance)
can be used to generate the sky luminance distribution according to the Perez model
(Perez et al. 1993). External obstruction (i.e. light redirection louvers) are treated by
the projection of their outline from each reference point on to the sky dome and the
replacement of the relative luminance values of the occupied sky patches with those
of the obstruction. A radiosity-based approach is adopted for computing the internally
reflected component. The results generated by LUMINA have shown to compare
favorably with measurements in several rooms (Pal and Mahdavi 1999). In the
present case, measured irradiance values were used at every time-step to generate the
sky model in LUMINA for the subsequent time-step. However, trend-forecasting
algorithms could be used to predict outdoor conditions for future time-steps.
For each time-step the simulation results (mean illuminance and uniformity levels on
a horizontal plane approximately 1 m above the floor) were ordered in a table, which
was used to rank and select the most desirable control scenario based on the applicable
objective functions. Two illustrative objective functions were considered.
The first function aims at minimizing the deviation of the average (daylight-based)
illuminance level E m in the test space from a user-defined target illuminance level E t
(say 500 lx):
Minimize (|E t – E m|) (7.1)
The second objective function aims at maximizing the uniformity of the illuminance
distribution in the test space as per the following definition (Mahdavi and Pal 1999):
Maximize U, where U � E m · (E m � E sd) �1 (7.2)
Here E m and E sd are the mean and standard deviation of the illuminance levels measured
at various locations in the test space.
At time interval t i, the simulation tool predicted for four candidate louver positions
the expected interior illuminance levels for the time interval t i�1 (test space geometry