# New Approaches in Dynamic Metrics for Lighting Control Systems: A Critical Review
## 2 Review
### Dynamic Daylighting Metrics for Energy Efficiency  
Created in 1989 by the Association Suisse des Electriciens [41] and refined by [PERSON] et al. [28,42] in 2001, Daylight Autonomy (DA) measures the proportion of occupied time each year in which daylight meets a specified illuminance level. Inversely, increased DA leads to a decrease in electric lighting usage. It can be expressed as follows (2):  
\[\text{DA}=\frac{\sum_{\text{i}}(\text{w}_{\text{f}}\cdot\text{t}_{\text{i}})}{ \sum_{\text{i}}\text{t}_{\text{i}}}\in[0,1];\text{w}_{\text{f}}= \begin{cases}1 \text{ if }\text{E}_{\text{Daylight}}\geq\text{E}_{\text{lim}}\\ 0\text{ if }\text{E}_{\text{Daylight}}<\text{E}_{\text{lim}}\end{cases}  \tag{2}\]  
where t\({}_{\text{i}}\) refers to the occupied time throughout the year in hours, and w\({}_{\text{f}}\) functions as a weighting factor. It is a binary variable that equals 1 if the horizontal illuminance at a given point (E\({}_{\text{Daylight}}\)) is greater than or equal to a predefined threshold, and 0 otherwise. E\({}_{\text{lim}}\) refers to the illuminance threshold chosen in accordance with the task. It is generally agreed that a minimum illuminance of 300 k is required for most tasks, with 500 lx recommended to minimize eye strain [43,44]. The Daylight Autonomy (DA) index offers enhanced precision in determining the annual illuminance of an interior space by accounting for factors relevant to the study of illumination, including diverse sky types and location-specific climatic data. Furthermore, it has served as a foundational metric for other energy efficiency indicators developed over the years. However, DA presents several limitations that constrain its comprehensive applicability in real-world contexts:  
* It does not account for the presence or behavior of electric lighting control systems. * It overlooks seasonal and temporal variability, such as the lack of occupancy during summer breaks in educational buildings. * It involves a relatively complex process for analyzing and comparing performance across a grid of calculation points, each with its own DA value. This spatial dispersion of results can make it difficult to draw immediate conclusions about the overall daylighting performance of a space, often requiring additional post-processing, visualization, or aggregation techniques to support design decisions. * It fails to capture the risk of overexposure or glare, which can negatively impact visual comfort. * It ignores the spectral distribution of daylight, which varies throughout the day and plays a crucial role in circadian stimulation, thereby affecting health and well-being. To address these limitations, several enhanced metrics have been proposed. One of the earliest was Continuous Daylight Autonomy (cDA, DAC, or more commonly DAcon), introduced by [PERSON] [28]. This calculates the time fraction throughout the year when a minimum illuminance threshold is met by daylight. This metric refines the binary nature of DA by assigning partial credit linearly for illuminance levels below the threshold, and full credit for those that exceed it. In this way, DAcon offers a more nuanced representation of annual daylight availability. An example given by [PERSON] et al. in his article [28] explains how, if a work plane requires 600 lx and the provided daylight level is 500 lx, a partial credit of 500/600 (0.8) is attributed. DAcon can be expressed as follows (3):  
\[\text{DAcon}=\frac{\sum_{\text{i}}(\text{w}_{\text{fi}}\cdot\text{t}_{\text{i}} )}{\sum_{\text{i}}\text{t}_{\text{i}}}\in[0,1];\text{w}_{\text{fi}}=\begin{cases} 1\text{ if }\text{E}_{\text{D}}\geq\text{E}_{\text{L}}\\ \text{E}_{\text{D}}/\text{E}_{\text{L}}\text{ if }\text{E}_{\text{D}}<\text{E}_{\text{L}}  
where \(\mathfrak{t}_{i}\) is the occupied time in a year, and \(\mathrm{w}_{fi}\) is the weighting factor dependent on the illuminance threshold.