# Self-Powered Solar Tracking Sensor

This article describes the possibility of designing a simple self-powered solar tracking sensor circuit using a Dialog Semiconductor SLG88103 operational amplifier. The complete circuitry is self-powered, since it uses only the power obtained from the photodetectors. There is no need for an additional external power supply. The photodetectors are arranged so that they can sense the direction of solar irradiance. Based upon the signal processing circuitry at the outputs, two highly sensitive voltage signals are generated. These signals correspond to the pitch and roll angles of the sun with respect to the photodiodes. The circuitry has an inherent automatic gain control. Therefore, the output signals are only proportional to these angles and not to the solar irradiation level.

# The Sensor Circuitry

The schematic of the proposed simple self-powered solar tracking sensor circuitry is presented in Figure 1. Processing the signals from the photodetectors requires only two operational amplifiers and several resistors. Additionally, as the photodetectors (photodiodes PDYU1, PDYU2, PDYD1, PDYD2, PDXR1, PDXR2, PDXL1, and PDXL2) work in the photovoltaic mode the generated power is significant enough to power the op-amps. Both the X and Y direction use four photodiodes (PDYU1, PDYU2, PDYD1, and PDYD2) connected in series to power on the operational amplifiers OP1 and OP2. The corresponding voltages, obtained at the photodiodes when in photovoltaic mode, are given by:

𝑉𝑖 = 𝑉𝑇ln ( ℜ𝑃𝑖 / 𝐼S ) (1)

where 𝑉𝑖 is the corresponding i-th (i = YU1, YU2, YD1, YD2, XR1, XR2, XL1, and XL2) photodiode voltage, 𝑉𝑇 is the thermal voltage given by 𝑉𝑇 = 𝑘B𝑇⁄𝑞 where 𝑘B = 1.38×10–23 J/K is the Boltzmann constant, 𝑇 is the absolute temperature, 𝑞 = 1.602×10–19 C is the elementary charge, ℜ is the photodiode responsivity, 𝑃𝑖 is the i-th photodiode captured optical power, and 𝐼S is the photodiode saturation current.

To keep photodiodes in the photovoltaic mode they must be connected to the high impedance nodes, thus requiring high values of the resistance RL. The corresponding photodiode-captured optical power depends upon the shadow position within the enclosure, i.e. it depends on the shadow distribution over the active photodiode surface. This is presented in Figure 1. The activelyilluminated area on the photodiodes’ surface depends upon the pitch and roll angles of the sun with respect to the photodiodes, as presented in Figure 2. This is, naturally, valid only for the photodiodes that are shadowed by the enclosure. For example, if the Sun illuminates the sensor from the first quadrant, shown in Figure 2, only photodiodes PDYU2 and PDXR2 will be in the shadow and their corresponding illuminated area will be:

𝐴XR2 = 𝐴 − 𝐾𝜉 (2.1)

𝐴YU2 = 𝐴 − 𝐾𝜓 (2.2)

where small pitch ξ and roll ψ angles were assumed (ξ, ψ ≪ 1) thus giving, in the first approximation, the linear dependence of the illuminated photodiode area with respect to the corresponding angles, where A is the area of the photodiode active surface, K is the positive proportionality constant that depends on the sensor geometry, and where A ≫ Kξ, Kψ is also valid.

The corresponding photodiode voltages 𝑉𝑖 according to equation (1) are given by:

𝑉XR2 = 𝑉𝑇ln ( ℜ𝐸𝐴XR2 / 𝐼S ) (3.1)

𝑉XR1 = 𝑉XL1 = 𝑉XL2 = 𝑉𝑇ln ( ℜ𝐸𝐴 / 𝐼S ) (3.2)

𝑉YU2 = 𝑉𝑇ln ( ℜ𝐸𝐴YU2 / 𝐼S ) (3.3)

𝑉YU1 = 𝑉YD1 = 𝑉YD2 = 𝑉𝑇ln ( ℜ𝐸𝐴 / 𝐼S ) (3.4)

where E is the solar irradiance. The output voltages VX and VY are given as:

𝑉X = − (𝑅F / 𝑅L) (𝑉XR2 + 𝑉XR1 − 𝑉XL2 − 𝑉XL1) (4.1)

𝑉Y = − (𝑅F / 𝑅L) (𝑉YU2 +𝑉YU1 − 𝑉YD2 − 𝑉YD1) (4.2)

where RF is the feedback resistor resistance. Equations (2), (3), and (4) give:

𝑉X = − (𝑅F / 𝑅L) 𝑉𝑇ln (1− 𝐾𝜉 / 𝐴 ) ≈ (𝑅F / 𝑅L) (𝐾 / 𝐴) 𝑉𝑇𝜉 = 𝑆𝜉 (5.1)

𝑉Y = − (𝑅F / 𝑅L) 𝑉𝑇ln (1 − 𝐾𝜓 / 𝐴 ) ≈ (𝑅F / 𝑅L) (𝐾 / 𝐴) 𝑉𝑇𝜓 = 𝑆𝜓 (5.2)

In the first approximation the output voltage signals VX and VY are directly proportional to the pitch and roll angles with sensor sensitivity S. As the output signals are independent of the solar irradiance the circuitry has an inherent automatic gain control.

# Realization with SLG88103 Operational Amplifiers

The realization of a simple self-powered solar tracking sensor circuitry will be based on the extremely low-power characteristics of the SLG88103 operational amplifiers [SLG88103/4 Rail to Rail I/O 375 nA/Amp Dual/Quad CMOS Op Amps with Power Down, Datasheet, Dialog Semiconductor]. To test the proposed circuitry a simulation in LTspice has been performed. The simulated circuitry, only for a single axis, has been presented in Figure 3. The system circuitry consists of two such sub circuitries, each aimed for sensing a single axis position of the sun. As the photodetectors, four BPW34 photodiodes from OSRAM Opto Semiconductors have been used in the simulation due to their relatively large sensing area of 7.45 mm2 (2.73 mm × 2.73 mm). The spice model of the photodiodes is provided by Opto Semiconductors as well [BPW 34 B Silicon PIN Photodiode with Enhanced Blue Sensitivity; in SMT Version 1.6, Datasheet, OSRAM Opto Semiconductors].

The solar irradiance has been modeled by two voltage sources VPD1 and VPD2, where the voltage in millivolts (mV) corresponds to the solar irradiance in mW/ cm2. The solar irradiance was swept within the range of 1 mW/ cm2 (1 mV) and 100 mW/cm2, (100 mV), wherein 100 mW/cm2 also represents the maximal possible value of the solar irradiance. As mentioned above, if the angle between the sensor surface and the Sun is not perpendicular, i.e. the pitch and roll angles are not equal to zero, due to intentional partial-shading of the photodiodes, there will be an unequal distribution of the irradiance at the photodiode surface. The unequal distribution of the solar radiation over the photodiode surfaces has been modeled with the different values of the solar irradiance, i.e. with the different values of the voltage sources VPD1 and VPD2. The corresponding simulation results are presented in Figure 4.

The conclusion, which can be drawn from the simulation results, is that the circuitry is highly sensitive to the change in the solar illumination direction, which correlates to the change of the corresponding voltages of the voltage sources VPD1 and VPD2. The important characteristic of the proposed design is that the sensor sensitivity doesn’t depend on the overall illumination of the sun, provided the rail-to-rail voltage of the op-amp is greater than 1.71 V. This can be concluded from the same slopes of the sensor response in the logarithmic scale. Therefore, the sensor has inherent gain control, which is a very important feature of this sensor circuitry, especially if it has been used in the control loop where the overall system stability is of the paramount importance. The same sensor sensitivity for a broad range of the solar irradiances leads to the very simple design of the control loop.

The photodiode shunt resistance RSH is given as:

𝑅SH = 𝑉𝑇 / ℜ𝐴𝐸 (6)

which, in the case of the BPW34 photodiode, with ℜ = 0.5 A/W, A = 7.45 mm2 and the minimum solar irradiance of E = 1 mW/ cm2, gives the maximum value of the photodiode shunt resistance of RSH ≈ 670 Ω. To operate in the photovoltaic mode the shunt resistance of the photodiode must be much smaller than the load resistance of the photodiode, i.e. must be fulfilled RSH ≪ RL. By choosing RL = 1 MΩ this condition is certainly fulfilled. The value for the feedback resistance RF can be arbitrarily chosen to obtain the desired sensitivity. In this application the value of RF = 30 MΩ was chosen.

According to the simulated results in Figure 4, the maximum output voltage is in the range of VX,YMAX ≈ 1 V. Therefore, the current that flows through the feedback resistor and thus through the load resistors is smaller than IFMAX = VX,YMAX/RF ≈ 33 nA, which is much smaller than the operational amplifier quiescent current of IQ = 375 nA. The operational amplifier quiescent current must fulfill the condition IQ ≪ ℜAE to enable the simultaneous work of the photodiode in the photovoltaic mode and proper biasing the operational amplifiers. Since ℜAE ≈ 37 μA for the minimum solar irradiance of E = 1 mW/ cm2 this condition is also fulfilled.

# Example Implementation

Using an evaluation board for the SLG88103 operational amplifiers and photodiodes the test circuitry was created. The photo of the proto-board realized circuitry, together with the photodiode-based sensor, is shown in Figure 5. The cylinder, i.e. the shadower, is fixed onto the sensor board in order to form the shadow when illuminated by the Sun. The cylinder dimensions can be chosen with regard to the sensor sensitivity and the required measurement range. The sensor that was used in this project has a shadower of the cylindrical shape with the inner diameter of the cylinder of 38 mm and the height of the cylinder of 35 mm.

In order to determine the overall sensor circuitry transfer function, the sensor was mounted on a platform, whose tilt angles can be varied. The sensor was directed toward the Sun and by controlling the tilt angles, i.e. the pitch and roll angles of the platform, both voltages VX and VY were adjusted to be as close as possible to zero. Then, by changing the corresponding tilt angles of the platform, the pitch and roll angles of the sensor were changed with respect to the Sun in the range from — 5° to + 5° while simultaneously measuring the output voltages. The transfer function of the sensor circuitry is presented in Figure 6. Based on the measured data set it was estimated that the sensor sensitivity is approximately S ≈ 56 mV/°.

# Conclusion

Solar tracking sensor has a very important role in many solar power systems (photovoltaic systems) to increase the overall system efficiency. In order to direct the solar panels toward the Sun a control loop, using the signals obtained from the solar tracking sensor, rotates the panels toward the Sun. Therefore, a simple, reliable (without additional power supply), and cost-effective sensor, as presented in this application, will improve the characteristics of the solar power system.

The presented self-powered solar tracking sensor circuitry can be tested with different combinations of photodetectors and shadowing geometries to achieve characteristics that can better fit into the end user requirements.