Sensorless Control of a Polar-Axis Photovoltaic Tracking System

Photovoltaic solar power installations can be broadly classified as static (non-tracking), single-axis tracking, polar axis-tracking and two-axis tracking installations (Agee et al., 2006). In general, tracking photovoltaic systems have higher percentage energy recovery per Kilowatt of installed capacity than static solar power systems (Ed. Kusoke et al., 2003). A key component of existing photovoltaic tracking systems is the solar position sensor and associated conditioning circuitry, which provides the information with which the tracking angle is updated. These sensors add to the overall cost of installed photovoltaics. For example, in South Africa where the average installed cost of photovoltaics is ZAR 29.00/Watt (Greenology, 2010), the percentage sensor(s) cost for installed photovoltaic wattage is shown in Figure 1, based on an average sensor cost of USD110.0. It is evident from Figure 1 that for low power solar photovoltaic applications, the percentage sensor cost motivates the exploitation of alternative tracking strategies that are devoid of sensors. Sensor-less tracking offer a cost effective solution in such low power applications. Sensorless tracking has been reported in literature (Ibrahim et al., 2004; Cheng & Wong, 2009; Power from the Sun, 2010; Chen et al., 2006; Stine & Harrington, 1988) concerning solarthermal systems. These rely on the use of well established astronomical formulae to extract the direction of sunrays as a function of the local clock time, after due compensation for any differences between the local clock time and the solar time. The equation of time (EOT) and the local longitude compensation are factored into the derivation of the final local time equation. EOT is an equation that evaluates the difference between the local clock time and the solar hour. In the discourse presented in the current chapter, the sensor-less tracking of a polar-axis solar tracker is reported. The concepts of differential flatness (Fliess et al.; Fliesss et al.; Levine & Nguyen, 2003; Bitaud, 1990, 1997, 2003) is used for embedding the equations of the direction of sunrays into the feedback loop of the controller. In the rest of the chapter, the physical structure of the polar-axis solar tracker and the derivation of its dynamic equations are described in section two. The concepts of differential flatness and the derivation of the flat output for the polar-axis solar tracker is presented in section three. Controller design is contained in section four. A derivation of the relationship between the local clock time and the direction of sunrays with respect to an observer (or the photovoltaics platform) at a given location, together with the integration of time-based values of the sunrays angle for sensor-less tracking is presented in section five of the