# New Approaches in Dynamic Metrics for Lighting Control Systems: A Critical Review
## 2 Review
### Dynamic Daylighting Metrics for Energy Efficiency
It is a non-binary variable that equals 1 if the horizontal illuminance at a given point (\(\mathrm{E}_{D}\)) is greater than or equal to a predefined illuminance threshold (\(\mathrm{E}_{L}\)) and 0 if the horizontal illuminance at that given point (\(\mathrm{E}_{D}\)) is 0. As long as the value of \(\mathrm{E}_{D}\) stays between \(\mathrm{E}_{L}\) and 0, the \(\mathrm{w}_{fi}\) is assigned a value following the aforementioned example given by [PERSON] et al. [28]\(\mathrm{E}_{L}\) as mentioned is the illuminance threshold, generally set at 300 lux, for the same reasons previously detailed in the DA explanation. Despite its utility in determining energy savings from dimmer controls [45; 46], DAcon has been underutilized in previous studies. However, recent developments have sparked a renewed interest in this metric, particularly with the emergence of Continuous Overcast Daylight Autonomy (Dao.con) [47]. This new metric is derived both from DAcon and from Overcast Daylight Autonomy (DAo). This last metric was renamed by the authors from Minimum Daylight Autonomy [48] to its current, more informative name. Overcast Daylight Autonomy (DAo) provides a bridge between static and dynamic metrics by calculating DA with the parameters of DF, more specifically with a fixed overcast sky. Consequently, its equation resembles that of DA (4):  
\[\mathrm{DAo}=\frac{\sum_{i}(\mathrm{w}_{fi}\cdot\mathfrak{t}_{i})}{\sum_{i} \mathfrak{t}_{i}}\in[0,1];\mathrm{w}_{fi}= \begin{cases}1\text{ if }\mathrm{E}_{D 0}\geq\mathrm{E}_{L}\\ 0\text{ if }\mathrm{E}_{D0}<\mathrm{E}_{L}\end{cases}  \tag{4}\]  
where the value of the horizontal illuminance (\(\mathrm{E}_{\mathrm{Daylight}}\) in the original formula) is replaced by \(\mathrm{E}_{D0}\), the daylight illuminance measured at a given point under overcast-sky conditions. Consequently, the calculation procedure follows the same principles as the DA, but considering only overcast skies. While the DAo metric is useful for calculating the percentage of time annually in which a minimum illuminance threshold is met under overcast-sky conditions, it inherits certain limitations from the Daylight Factor (DF) and Daylight Autonomy (DA). Specifically, like the DF, DAo does not consider fenestration orientation. While DAcon and DAo in isolation have seen limited adoption, DAo.con offers great utility for sensorless lighting smart control systems [47]. By utilizing measured or simulated Daylight Factors and user requirements, the algorithm modifies luminaire's luminous flux without having to rely on internal light sensors. Input device installation and effective control systems in relation to daylight are among the aspects that make daylight-linked controls (DLCs) difficult to implement [49]. The issue is compounded by the stochastic behavior of occupants [50], which can make work plane input devices less effective. DAo.con could therefore help to mitigate the gap between specialized research and common design practice for DLCs. Continuous Overcast Daylight Autonomy (Dao.con) can be expressed as follows (5):  
\[\mathrm{DAo.con}=\frac{\sum_{i}(\mathrm{w}_{fi}\cdot\mathfrak{t}_{i})}{\sum_{i} \mathfrak{t}_{i}}\in[0,1];\mathrm{w}_{fi}= \begin{cases}1\text{ if }\mathrm{E}_{i,o}\geq\mathrm{E}_{t}\\ \mathrm{E}_{i,o}/\mathrm{E}_{t}\text{ if }\mathrm{E}_{i,o}<\mathrm{E}_{t}\end{cases}  \tag{5}\]  
where \(\mathfrak{t}_{i}\) is the occupied time in a year, and \(\mathrm{w}_{fi}\) is the weighting factor dependent on the illuminance threshold, with us assigning values between 1 and 0 while following the same procedure as the DAcon equation. \(\mathrm{E}_{i,o}\) is the daylight illuminance defined at a given point under overcast-sky conditions, and \(\mathrm{E}_{t}\) is the illuminance threshold defined by lighting requirements.