## 1 Introduction
### Detailed System Performance Observations, Evaluation, and Analysis
The angle-dependent solar illumination flux-cross-section differences between the vertically-mounted and peak-tilted window orientations (eg if placed onto optimally-tilted North-facing roof section) are also significant. These geometric factors correspond to approximately a factor of (1/cos45\({}^{\circ}\)) in peak-power output difference, which allows predicting the orientation-related increases in the energy outputs per window by up to several tens of percent, in future optimally-mounted units. In conventional southern-hemisphere PV installations, the preferred geometric orientation of PV panels corresponds to mounting them on building roof sections facing the North direction (with the horizontal projection of the normal to the solar-cell area aligned with azimuth 0\({}^{\circ}\)) and tilted to the horizontal plane at an angle equaling the local latitude. This optimizes the daily (for most seasons), and also the yearly energy production by ensuring a close-to-normal incidence angle of the solar radiation onto cells at times around midday. Other factors which may affect the precise PV panel orientation preferences include the site-specific shading conditions, and the preferences of system owners in relation to their peak energy production requirements being shifted towards either the morning or evening hours. A common way to approximate the expected daily energy production per orientation-optimized panel is by multiplying the rated nominal (peak) power (measured at standard testing conditions) by the number of peak-equivalent sunshine hours. The latter depend significantly on the geographic location and the day of year, but the data are often available from industry publications reliant on the local weather bureau data. The panel orientation-dependent solar irradiation flux intercepted by the PV panels is also modified according to the cosine function of the angle between the panel normal and the Sun direction. Therefore, if at noon the Sun altitude is at 45\({}^{\circ}\), a vertically-positioned north-facing PV panel will generate about 0.7 of the amount of energy (produced per unit time) by an optimally-tilted, north-oriented roof panel. A yearly-averaged estimate for the daily energy output per 1m\({}^{2}\) of solar window area can therefore be made, based on the observed data, being near 0.1 kWh/m\({}^{2}\), presuming that installation sites are configured favoring the north-facing, azimuth-optimized window orientations. For future dome-type installations, the average daily energy outputs per window can be predicted, by averaging the data from the three main (unshaded) parts of Warwick Grove atrium installation, leading to estimates near 70 Wh/m\({}^{2}\). These estimates can be considered conservative, since only the seasonal increases in the daily sunshine durations were factored in to produce these year-scale averages. In other geographic locations, where stronger yearly insolations are typically measured (eg, Middle East, or the north-west of Australia), higher energy yields will be obtained. Figure 6: Electric output power trends observed with respect to the solar geometry and irradiation-related parameters. (**a**) 3D scatter plot of the output power vs the Sun azimuth and Sun altitude angles; (**b**) 3D scatter plot of the output power vs the time of day and the horizontal-plane solar irradiation intensity; (**c**) 3D scatter plot of the output power shown in correlation with the Sun altitude angle, vs the Sun azimuth direction and the time of day; (**d**) 3D surface plot (and its corresponding 2D contour plot shown in the X-Y plane underneath) illustrating the variations in the electric output power with both the time of day, and the instantaneous weather-dependent (horizontal-plane) solar irradiation intensity. The data were collected over the entire period of study (about 2 months) covering a wide range of weather conditions observed at regular intervals at most times of day.