In today’s climate of growing energy needs and increasing environmental concerns, alternatives to the use of non-renewable and polluting fossil fuels have to be investigated. One such alternative is solar energy. This study is based on the implementation of a mathematical computation – the PSA (Plataforma Solar de Almeria) computation developed at PSA (the European Test Centre for solar energy applications) – embedded in a control algorithm to locate the position of the sun. Tests were conducted on a solar parabolic trough (SPT) constructed at the Solar Thermal Applications Research Laboratory of the Mangosuthu University of Technology (Durban, South Africa) for optimal position control using the PSA value. The designed control algorithm embedded in an industrial Siemens S7-314 C-2PtP programmable logic controller compared the PSA computation to a measured position of the SPT to optimally rotate the SPT to a desired position with the constant movement of the sun. The two main angles of the sun relative to the position of the SPT on earth, the zenith angle and the azimuth angle, both calculated in the PSA from the vertical and horizontal planes, respectively, were applied to the control algorithm to generate an appropriate final tracking angle within a 0.007 radian (0° 24′ 3.6″) tolerance, in accordance to the construction specifications and solar collector testing standards of the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE, 1991). These values, together with the longitude and latitude applicable to the geographical location of the SPT, were processed in the control software to rotate the SPT to an optimal position with respect to the position of the sun in its daily path, for solar-to-thermal conversion.

A solar parabolic trough (SPT) is a linear solar collector with, as its name implies, a parabolic cross section. Its reflective surface concentrates sunlight onto a receiver tube located along the trough’s single horizontal focal line, therefore tracking the sun along only one axis, either north–south or east–west.^1,2,3 A north–south orientation provides slightly more energy per year than an east–west orientation, but its winter output is low in mid-latitudes whereas an east–west orientation provides a more constant output throughout the year.⁴ The SPT at STARlab was constructed and installed in a north–south position to track the sun in an east–west direction, referred to as a one-axis SPT. A two-axis SPT has the disadvantage of losing thermal energy and is not cost effective. Each parabolic trough collector and its associated receiver tube, tracking device and controls form a modular collector assembly that can be connected in various series or parallel-flow circuits to achieve a range of performance characteristics. Solar tracking is particularly important in systems that operate under concentrated sunlight.^1,5,6

Energy losses arise from inefficient solar tracking and position control of the collector. Various factors may reduce the system output efficiency. The performance of a solar–thermal plant reflects the efficiency and reliability of its four principal systems, i.e. collector, receiver, transport–storage and conversion.⁷ The remaining sunlight is defined as the usable or available solar energy because some solar input is lost when the plant cannot operate. A certain amount of energy is lost at each processing stage, e.g. sunlight is lost in the collector system as a result of sun-angle effects and optical losses, thermal energy is lost in the receiver and heat-transport system, and a significant loss occurs in the conversion process. The efficiency of the collector system depends on the reflectivity of its mirrors and the optical effectiveness of its geometry. Losses in the system result from sun-angle effects (also called cosine losses), soiling of the mirrors, shadowing, optical losses at the receiver and blocking of sunlight from the reflective surface by other components, as well as spillage of reflected sunlight outside the receiver boundaries.^8,9,10 Compensation in the calculated acute angle was required to generate a final angle to correctly position the trough in one of the four mathematical quadrants of the coordinate plane according to the tangent trigonometric ratio.¹¹

Experimental set-up

Figure 1: The experimental set-up of the solar parabolic trough: (a) the nondrive end, (b) the drive end and (c) the operations station, programming and control units in the control room.

Establishing control aspects for optimal solar-to-thermal conversion

Figure 2: Rotational movement of the solar parabolic trough relative to the daily movement of the sun, as seen from the drive end of the trough.

Developing the control algorithm to generate a calculated final angle of the SPT

The pulsed signal was applied to a quadruple counter in the software, converting the 1250-pulse signal to a 5000-pulse signal (2500 pulses on either side of the vertical) for higher bit-resolution in the digital controller, improving data processing to contribute to control optimisation. The trough at sunrise was represented by +2500 pulses (+90º), the trough at the vertical position was represented by 0 pulses (0º) and the trough at sunset was represented by -2500 pulses (-90º) (Figure 2). However, the control software was configured to the limits of +2600 pulses and -2600 pulses for technical considerations to prevent the SPT exceeding the maximum safety limits. The additional 100 pulses were assigned to prevent software conflict for uninterrupted operation if the SPT exceeded either the -90º or +90º positions.¹⁵

The incremental encoder generated three pulses, namely pulses A, B and C. Pulse A was active when there was rotational movement of the SPT (Figure 3); the specification of the pulse was determined by the speed at which the SPT rotated. Pulse B determined the direction of rotation of the SPT. If pulse B was in phase with pulse A, the SPT was rotating forward. Reverse rotation was detected by pulses A and B being out of phase with each other. Marker pulse C set the reference point to detect the 0° position of the trough. Pulse C commenced at logic 1 at the start of SPT movement (from sunrise) and remained at logic 1 until the vertical position of the SPT when it reached a transition state to logic 0. The same applied from the vertical to sunset positions. In the event of a power failure, marker pulse C made provision for the SPT to rotate to the zenith position and return to its operating position after power restoration, preventing software conflict.¹⁵

Figure 3: Block diagram of the control algorithm.

Compensation in the final angle to correct the SPT position

The eight plotted points were derived for peak winter and summer regions (Figure 4b and Table 1). The generated value was not necessarily correct as it may have existed in any of the four quadrants of the Cartesian plane. All points represent the direct relationship between the generated answer before and after tangent compensation, indicating that points 1 and 5 commenced at the same value in each seasonal change but deviated with time. In winter, the angular value increased throughout the day, without compensation, and in summer it decreased.⁴ As the SPT rotated about its axis from the horizontal, 0-degree axis in the east position to the horizontal, 180-degree axis in the west position, the captured data with compensation represents a closer resemblance of this rotational movement. As a result of the variation in the sun’s path with seasonal changes, as indicated in the rotational profile, a one-axis system requires further compensation. Seasonal effects on our one-axis, east–west system, resulted in an incorrect position of the SPT, especially in winter (Figure 5). In summer, there was a constant beam radiation from sunrise to sunset which allowed for constant solar-to-thermal conversion throughout the day (Figure 5a). In winter the beam radiation decreased towards midday, from sunrise to sunset, which decreased the solar-to-thermal conversion (Figure 5b). This resulted in partial reflected radiation from the collector onto the receiver, which reduced the solar-to-thermal conversion process. The reflected radiated beam had to be focused along the maximum longitudinal axis of the receiver, closest to the central point of the SPT, to decrease energy losses. As the SPT was fixed in the north–south position to track the sun in the east–west direction, an alternative method to compensate for this bias in winter had to be incorporated by introducing an offset. ^16,17 The geographical location of the SPT and seasonal changes resulted in an inverted angular position, which required an offset to optimise position control according to the Step7 PLC software.¹³

Figure 4: Determination of the final angle of the solar parabolic trough in the control software by (a) locating the correct quadrant for final angle calculation and (b) comparing the final angle before and after tangent compensation.

Figure 5: Effects of reflected radiation from the collector to the receiver as a result of seasonal changes in (a) summer and (b) winter.

The calculated and measured values from the PSA computation and incremental encoder, respectively, are expressed as pulse counts in this section because the PLC software processes them in this format to generate a corrective output signal when there is a difference between the two input values at the summing point of the controller (Figure 3). The +2500 pulses, east position to the -2500 pulses, west position are represented on the z-axis (Figure 6). The tracking time in South African Standard Time (SAST) as captured in the PLC is represented on the x-axis. The three comparative variables – error signal, sun position and trough position – are represented on the y-axis. The error signal (an indication of the controller response) is the difference between the sun position (the computed value from the PSA calculation) and the trough position (measured from the encoder). As the computed PSA value varied with the sun’s daily movement, the control algorithm measured the pulse count difference between the signals from the PSA computation and the incremental encoder (Figure 3). The measurable tolerance to meet the 0.007 radian limit was a three-pulse count to maintain the calculated 2.78 pulse according to the encoder specifications. The captured data ranged from +2000 pulses to -1000 pulses. Because the SPT commenced at the sunrise horizontal plane at +2000 pulses, east elevation and continued to rotate to the sunset horizontal plane at -1000 pulses, west elevation for the test condition, the actual vertical position at 11:50 was a 0-pulse signal. The trough was positioned in the east quadrant until 11:50, indicating all positive values, i.e. the sunrise side. In this quadrant the encoder signal of +2500 pulses to 0 pulses was representative of a movement from sunrise to the vertical position. After 11:50 the trough was positioned in the west quadrant, indicating all negative values, i.e. the sunset side. The pulsed signals were processed as negative values. In this quadrant the encoder signal of 0 pulses to -2500 pulses was representative of a movement from the vertical position to the sunset position (Figure 2 and Figure 6).^2,3,5

Figure 6: Implementation analysis to test the accuracy of the computed Plataforma Solar de Almeria (PSA) value and solar parabolic trough position with respect to the controller response.

Both the trough position and sun position values varied by a constant amount, thereby allowing the trough to be focused in the path of the radiation of the sun for maximum reflection from the collector onto the receiver, for maximum absorption of solar energy to be converted to thermal energy. This phenomenon can be observed by the error signal being an almost straight line (indicating zero), along the x-axis, and the sun and trough positions decreasing from 2000 pulses to -1000 pulses, along the z-axis. The error signal was precisely a maximum value of 3 pulses for optimal position of the parabolic trough, as processed in the software program, in keeping with the required tolerance of 0.007 radians (0° 24′ 3.6″).^6,8,10

We thank the Mangosuthu University of Technology, Eskom and the National Research Foundation (South Africa) for financial support; USAID, Siemens Automation & Drives and the Nelson Mandela Metropolitan University for equipment; and JVR Consulting Engineers for technical support.

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