Cubic Composite Sensor with Photodiodes for Tracking Solar Orientation

Abstract

A cubic composite solar sensor with photo diode is proposed for tracking the relative solar orientation. The proposed solar sensor composes of five photodiode detectors which are placed on the front, rear, left, right, and horizontal facets in a cubic body, respectively. The solar detectors placed on five facets can detect solar power of different facets. Based on the geometric coordinate transformation principle, the relationship equations of solar light orientation between measured powers with respect to various facets can be conducted. As a result, the solar orientation can be precisely achieved without needing any assistance of electronic compass and extra orientation angle corrector. Eventually, the relative solar light orientation, the elevation angle, and azimuth angle of the solar light can be measured precisely.

1. Introduction

Recently, the renewable energy has drawn great attention due to energy shortage. Many renewable energy researches are focused on solar power system [1–4]. For the solar system, a precise sensor is indispensable to tracking the sunlight orientation. Many studies have been focusing on solar tracking technique. However, there still exist some drawbacks on solar light tracking apparatus. Solar light tracker can, in general, be classified into mechanical and electronic category [5, 6]. Mechanical solar tracker experiences much fault probability and maintenance cost, electronic solar tracker depends highly on electronic compass accompanied by perpetual calendar, and precise perpetual calendar heavily relies on complicated computation through the usage of internet, thus leading to inconvenience in application [7, 8]. Therefore, to develop an electronic solar light tracker, without needing electronic compass and perpetual calendar, is essential to researchers and solar power applications.

An electronic solar light tracker can only be realized through the application of photo detecting devices. There are many photo devices such as photodiode, photo transistor, and resistive CdS components. The CdS components are passive components and usually cannot play the key role in a precise measurement. In this paper, the active photodiodes with wide measuring range and fast response and low dark current are applied as a solar sensor to measure the solar orientation.

The solar light orientation information should consist of the relative elevation angle and azimuth angle between solar source and photo detector. For collecting lights from all possible orientations, this paper employed five photodiodes to compose a cubic structure photo detector in the absence of electronic compass and perpetual calendar to accomplish an electronic solar light orientation tracking system. The composite sensor is composed of five photo diode detectors placed on five different facets: left, right, front, rear, and horizontal facets, to constitute a cubic structure solar light detector. By placing five detectors on five different facets, the sunlight orientation can be derived by geometric coordinate transformation technique.

There exists discrepancy in collecting power amounts for photo detectors on different facets. Moreover, the incident light on the photo diode comprises not only direct solar light but also diffuse light and scattered light [8]. The diffuse and scattered light power is also generally called undisciplined light power, denoted by 𝑃_U. Therefore, the received solar power should be categorized precisely into power of direct incident solar light 𝑃_D and power of undisciplined incident solar light 𝑃_U. Through the geometric transformation analysis and accurate evaluation formula, each collecting solar power on different facets can be divided into direct incident solar power 𝑃_D and undisciplined incident solar power 𝑃_U, to accomplish the calculation of solar light orientation and solar polar powers on all facets.

In this paper, a novel light orientation sensor is proposed to track the solar orientation effectively. No expensive electronic components and no perpetual calendar are required. By appropriate computation based on different solar power quantities collected from five sensors, the sunlight direction can be determined. Also, the solar light orientation and power can easily be attained.

2. Optimal Shunt Resistor Matching and Selection

The ideal photo diode should generate an active current source which is proportional to the incident solar light. The total current through the photodiode is the sum of the dark current and the photo active current, so the dark current must be minimized to maximize the sensitivity of the device. In order to obtain the correct photo voltage, an appropriate shunt resistor 𝑅_𝑃 should be shunted across the output terminals. The application circuit is shown in Figure 1 with external shunt resistor 𝑅_𝑃; the photo voltage is generated at the two ends of the photo diode. The dark current has essential effects on the output voltage. Therefore, a calibration process for the shunt resistor 𝑅_𝑃 is required.

Figure 1 

Photo diode applied circuit for detecting solar power.

The values of the output load resistor 𝑅_𝑃. The adopted photo detector in this paper is produced by Hamamatsu Inc. with model code S1087-01. The parameters of the shunt resistor are assorted at 10 Ω, 100 Ω, 220 Ω, 510 Ω, 1 kΩ, and 2 kΩ.

The solar power is defined as 𝑃_solar, the output voltage is defined as 𝑉_out, and 𝑆 is defined as the sensitivity of the detector. In regard to an ideal photo power detector, 𝑆 should be kept with a constant quantity to maintain the linear relationship between sensing power and sensor output voltage as follows. 𝑃_Solar=𝑉_out𝑆. (1)

By shunting appropriate resistor 𝑅_𝑃 in the output terminal, the solar power can be measured as shown in Figure 2, in case that ill condition occurs. The resistor value cannot be used to convert the current into voltage correctly. As shown in Figure 2, during the lower solar power period in the morning or evening periods, the solar power is roughly proportional to the photo current with resistor ranging from 100 Ω to 220 Ω. However, the output power is slightly lower than the standard value during midday with direct sunlight. When the value is above 2 kΩ, the solar power curve lies under the standard curve. When the resistor value is between 510 Ω and 1 kΩ, the output curve is inspected to be better fitting the theoretical solar power.

Figure 2 

Optimal resistor matching and selection.

Since the photo diode has nonlinear equivalent characteristics as shown in Figure 2, an appropriate output resistor is required to be selected. When the sunlight is in either weak condition or strong condition, the solar power curve displays nonlinear phenomenon. When the value falls between 510 Ω~1 kΩ, the curve has the best coincident condition with the standard curve. Considering that the identical solar power would generate identical output voltage, larger resistance will require less output current. Therefore, 1 kΩ resistor is selected to shunt with photo detector to enhance the linearity and precision of the proposed circuit.

In order to obtain the precise voltage conversion, an OPAMP circuit is designed to ensure the precise voltage gain for the five detectors. The calibration circuit of the detector is shown in Figure 3. The 0.01 𝜇F capacitor is connected across shunt resistor 𝑅_𝑃 to eliminate noise.

Figure 3 

Detector calibration circuit.

3. Geometric Coordinate Transformation and Formulation

As designated in Figure 4, photo-detecting device is located at origin of the horizontal plane of 3D coordinate. The polar coordinate representation of position of light source is designated as (𝑟,𝜙,𝛼) which results in the Cartesian coordinate and polar coordinate transformation relationship expressed as follows: 𝑥=𝑟sin𝜙cos𝛼,𝑦=𝑟sin𝜙sin𝛼,𝑧=𝑟cos𝜙, (2) where 𝜙 is the light incident angle, 𝛼 is the azimuth angle, and 𝑟 is the distance between light source and photo diode detector. Then, the elevation angle 𝜙_ℎ can be described as 𝜙_ℎ=90^∘−𝜙. (3) The orientation of sunlight is defined as elevation angle 𝜙_ℎ and azimuth angle 𝛼 that means the orientation of the sunlight can be specified by formulation using the two angles: 𝜙_ℎ and 𝛼.

Figure 4 

Geometric coordinate system.

For a 3D coordinate system, the rear direction is defined as the 𝑋 direction, the right direction is defined as the 𝑌 direction, and the normal vector direction of 𝑋-𝑌 horizontal plane is defined as the 𝑍 direction, as indicated in Figure 4. The solar light incident angle 𝜙 can also be defined as the angle between the sunlight and the normal vector direction of horizontal plane. Thus, the horizontal detector collects direct light power 𝑃_HD which can be expressed as 𝑃_HD=𝑃_Dcos𝜙. (4) The collected direct light power 𝑃_HD of horizontal detector is the multiplication of solar direct radiation power and cosine of incident angle 𝜙. Incident angle 𝜙 is defined as the angle between the normal vector of each facet with its corresponding incident light. Thus, when the horizontal detector rotates an angle 𝜃 along 𝑋, 𝑌, and 𝑍 axis, the associated incident angles of all facets will change accordingly. Figure 5 illustrates the rotational coordinate transformation by rotating along 𝑍-axis with an angle 𝜃_𝑍 or along 𝑋-axis with 𝜃_𝑥 or along 𝑌-axis with 𝜃_𝑦. By doing so, the original coordinate (𝑥, 𝑦, 𝑧) is transformed to a new coordinate (𝑥1, 𝑦1, 𝑧1), and the expression can be written as follows.(1) By rotating 𝜃_𝑧 along 𝑧-axis, 𝑥1, 𝑦1, and 𝑧1 can be obtained as follows =𝑥1𝑦1𝑧1cos𝜃_𝑧−sin𝜃_𝑧0sin𝜃_𝑧cos𝜃_𝑧0𝑥𝑦001𝑧=𝑟sin𝜙cos𝛼cos𝜃_𝑧−sin𝜙sin𝛼sin𝜃_𝑧sin𝜙cos𝛼sin𝜃_𝑧+sin𝜙sin𝛼cos𝜃_𝑧.cos𝜙 (5) In (5), new coordinate 𝑧1 is identical with the original coordinate 𝑧. The angle between incident solar light and normal vector of detector plane of new coordinate still remains 𝜙; the projection on normal vector direction is 𝑟cos𝜙. Therefore, regardless of the rotating angle 𝜃_𝑧, the incident of solar light keeps unchanged, that is, 𝜙.(2) By rotating 𝜃_𝑥 along 𝑥-axis, 𝑥1, 𝑦1, and 𝑧1 can be obtained as =𝑥1𝑦1𝑧11000cos𝜃_𝑥−sin𝜃_𝑥0sin𝜃_𝑥cos𝜃_𝑥𝑥𝑦𝑧=𝑟sin𝜙cos𝛼sin𝜙sin𝛼cos𝜃_𝑥−cos𝜙sin𝜃_𝑥sin𝜙sin𝛼sin𝜃_𝑥+cos𝜙sin𝜃_𝑥. (6) The projection component of solar light on the normal vector of new coordinate plane 𝑧1 deviates a significant quantity from the original projection value 𝑧, so does the incident angle.(3) By rotating 𝜃_𝑦 along 𝑦-axis, 𝑥1, 𝑦1, and 𝑧1 can be obtained as =𝑥1𝑦1𝑧1cos𝜃_𝑦0sin𝜃_𝑦010−sin𝜃_𝑦0cos𝜃_𝑦𝑥𝑦𝑧=𝑟sin𝜙cos𝛼cos𝜃_𝑦+cos𝜙sin𝜃_𝑦sin𝜙sin𝛼−sin𝜙cos𝛼sin𝜃_𝑦+cos𝜙cos𝜃_𝑦. (7) Like that of rotation along 𝑋-axis, the projection of incident light on normal vector of new coordinate plane 𝑧1 deviates noticeably from original one, 𝑧. It implies that incident angle changes with rotation angle 𝜃_𝑦.

Figure 5 

𝜃 rotation along the 𝑋-, 𝑌-, and 𝑍-axis.

After installing five detectors on five different facets, the cubic composite sensor is shown in Figure 6, Aside from the horizontal facet detector, the other four detectors can be looked upon as those coordinates transformed from the horizontal one by rotating either along 𝑋-axis or 𝑌-axis with ±90^∘. The coordinate transformation can be derived in the following section.

Figure 6 

Cubic sensors model in a 3D coordinate system.

4. Cubic Composite Sensor

The relationship between direct incident solar power 𝑃_D, undisciplined power 𝑃_U, the light incident angle 𝜙, and the azimuth angle 𝛼 can be discussed in this section. Since the five detectors are located on five different facets of a cubic box, the coordinate transformation relationships between five facets will be discussed below.(1) The horizontal (H) detector is located on the facet which 𝜃_𝑥=0^∘ along 𝑧-axis. Therefore, the transformed orientation coordinate of the sunlight and corresponding collecting power can be derived as 𝑥1𝑦1𝑧1=𝑟sin𝜙cos𝛼cos0^∘−sin𝜙sin𝛼sin0^∘sin𝜙cos𝛼sin0^∘+sin𝜙sin𝛼cos0^∘=𝑥𝑦𝑧.cos𝜙=𝑟sin𝜙cos𝛼sin𝜙sin𝛼cos𝜙 (8) The normal vector of horizontal plane 𝑧1 is the same with the original normal vector 𝑧; the incident angle is kept unchanged, that is, 𝜙_H=𝜙, 𝜙_H𝑃=𝜙,_H=𝑃_Dcos𝜙+𝑃_UH=𝑃_Dcos𝜙_H+𝑃_UH. (9)(10) The collected power 𝑃_H on the horizontal detector can be expressed as (10). Wherein, 𝑃_D is the maximum direct incident solar power and 𝑃_UH is the power caused by light diffusion and scattering.(2) The right sensor is located on facet which 𝜃_𝑥=90^∘ along 𝑥-axis. Therefore, the orientation of the sunlight can be derived as 𝑥1𝑦1𝑧1=𝑟sin𝜙cos𝛼sin𝜙sin𝛼cos90^∘−cos𝜙sin90^∘sin𝜙sin𝛼sin90^∘+cos𝜙cos90^∘=𝑥𝑦=𝑟.sin𝜙cos𝛼−cos𝜙sin𝜙sin𝛼−𝑧 (11) As shown in (11), right facet detector is equivalent to rotating horizontal facet by 𝜃_𝑥=90^∘. The normal vector of right plane is directed toward 𝑍-axis which is the positive 𝑌-axis direction of horizontal facet. The light incident angle 𝜙_R is related to original incident angle 𝜙 by (12). Next, the collected power on the right facet detector 𝑃_R is written as 𝜙_R=cos⁻¹,𝑃sin𝜙sin𝛼_R=𝑃_Dsin𝜙sin𝛼+𝑃_UR=𝑃_Dcos𝜙_R+𝑃_UR, (12)(13) where 𝑃_UR is the undisciplined light power collected by right detector.(3) The left sensor is located on facet which 𝜃_𝑥=−90^∘ along 𝑥-axis. Therefore, the orientation of the sunlight can be derived as 𝑥1𝑦1𝑧1=𝑟sin𝜙cos𝛼sin𝜙sin𝛼cos−90^∘−cos𝜙sin−90^∘sin𝜙sin𝛼sin−90^∘+cos𝜙cos−90^∘=𝑥=𝑟𝑧.sin𝜙cos𝛼cos𝜙−sin𝜙sin𝛼−𝑦 (14) As shown in (14), left facet detector is equivalent to rotating horizontal facet by 𝜃_𝑥=−90^∘. The normal vector of left plane is directed toward the negative 𝑌-axis direction of horizontal facet. The light incident angle 𝜙_L is related to original incident angle 𝜙 by (15). More, the collected power on the right facet detector 𝑃_L is written as 𝜙_L=cos⁻¹,𝑃−sin𝜙sin𝛼_L=−𝑃_Dsin𝜙cos𝛼+𝑃_UL=𝑃_Dcos𝜙_L+𝑃_UL, (15)(16) where 𝑃_UL is the undisciplined light power collected by left detector.(4) The front sensor is located on facet which 𝜃_𝑦=90^∘ along 𝑦-axis. Therefore, the orientation of the sunlight can be derived as 𝑥1𝑦1𝑧1=𝑟sin𝜙cos𝛼cos90^∘+cos𝜙sin90^∘sin𝜙sin𝛼−sin𝜙cos𝛼sin90^∘+cos𝜙cos90^∘=𝑧=𝑟𝑦.cos𝜙sin𝜙sin𝛼−sin𝜙cos𝛼−𝑥 (17) As expressed in (16), front facet detector is equivalent to rotating horizontal facet by 𝜃_𝑦=90^∘. The normal vector of front plane is directed toward the negative 𝑋-axis direction of horizontal facet. The light incident angle 𝜙_F is related to original incident angle 𝜙 by (18). Next, the collected power on the front facet detector 𝑃_𝐹 is written as 𝜙_F=cos⁻¹,𝑃−sin𝜙cos𝛼_F=−𝑃_Dsin𝜙cos𝛼+𝑃_UF=𝑃_Dcos𝜙_F+𝑃_UF, (18)(19) where 𝑃_UF is the undisciplined light power collected by front detector.(5) The rear sensor is located on facet which 𝜃_𝑦=−90^∘ along 𝑦-axis. Therefore, the orientation of the sunlight can be derived as 𝑥1𝑦1𝑧1=𝑟sin𝜙cos𝛼cos−90^∘+cos𝜙sin−90^∘sin𝜙sin𝛼−sin𝜙cos𝛼sin−90^∘+cos𝜙cos−90^∘=𝑦𝑥=𝑟.−cos𝜙sin𝜙sin𝛼sin𝜙cos𝛼−𝑧 (20) As shown in (20), rear facet detector is equivalent to rotating horizontal facet by 𝜃_𝑦=−90^∘. The normal vector of rear plane is directed toward the positive 𝑋-axis direction of horizontal facet. The light incident angle 𝜙_Re is related to original incident angle 𝜙 by (21). Next, the collected power on the rear facet detector 𝑃_Re is written as 𝜙_Re=cos⁻¹,𝑃sin𝜙cos𝛼_Re=𝑃_Dsin𝜙cos𝛼+𝑃_URe=𝑃_Dcos𝜙_Re+𝑃_URe, (21)(22) where 𝑃_URe is the undisciplined light power collected by rear detector.

Figure 6 defines incident quadrant of the solar light. The assessing criteria of incident quadrant are based on the collecting light power of five facets 𝑃_H, 𝑃_R,  𝑃_L, 𝑃_F, and 𝑃_Re, respectively. By comparing the quantities of the collecting light power, the criteria are described as follows.(1)When the 𝑃_R>𝑃_L and 𝑃_F>𝑃_Re, the sunlight comes from the first quadrant. (2)When the 𝑃_L>𝑃_R and 𝑃_F>𝑃_Re, the sunlight comes from the second quadrant.(3)When the 𝑃_L>𝑃_R and 𝑃_Re>𝑃_F, the sunlight comes from the third quadrant. (4)When the 𝑃_R>𝑃_L and 𝑃_Re>𝑃_F, the sunlight comes from the fourth quadrant.Once the solar light incident quadrant is determined, the solar power orientation and power information can be obtained by substituting (8) in to (22). When the sunlight is incident to the fourth quadrant, the relationships of 𝜙_F, 𝜙_R, 𝛼, and 𝑃_D can be conducted from (12) to (15) to arrive at (23) as follows: 𝑃_Dcos𝜙_Re=𝑃_D𝑃sin𝜙cos𝛼,_Dcos𝜙_R=𝑃_Dsin𝜙sin𝛼. (23) Since the incident light falls on the fourth quadrant, the direct light cannot reach front and left facets. The collecting solar power can merely come from the undisciplined light power. Consequently, the undisciplined light power of (23) can be roughly substituted by collected power quantity of adjacent facets. In other words, the direct solar light falling on the fourth quadrant comes from right and rear directions; the undisciplined light power on the rear facet 𝑃_URe is approximated by left facet light power 𝑃_L; the undisciplined light power on the right facet 𝑃_UR is approximated by front facet light power 𝑃_F.

From (23), the 𝛼 angle can be derived as follows 𝑃_RD𝑃_ReD=𝑃_Dsin𝜙sin𝛼𝑃_D=sin𝜙cos𝛼sin𝛼cos𝛼=tan𝛼⟹𝛼=tan⁻¹𝑃_RD𝑃_ReD. (24) From (10) and (22), the 𝜙 angle can be derived as follows 𝑃_ReD𝑃_HD=sin𝜙cos𝛼cos𝜙=tan𝜙cos𝛼⟹𝜙=tan⁻¹𝑃_ReD𝑃_HD.cos𝛼 (25) After the 𝜙 angle is decided, the 𝑃_D can be derived as 𝑃_D=𝑃_HD.cos𝜙 (26) The incident quadrant of incident light is changing with time. Similar derivation can be used to obtain the solar light orientation and power information.

5. Experimental Results

In order to verify the formulation, an experimental measurement was performed on June 02, 2013. Table 1 lists the collecting solar power of all facet detectors on the hour.

Table 1 

Solar power with respect to five detectors (unit: (W/m²)).

In Table 1, to take data at 12:00 A.M. as an example, the cubic sensor receives the incident light from the fourth quadrant, the detectors on the right, rear, and horizontal facets can absorb power of direct incident solar light 𝑃_D. However, the left and front facets can only absorb power of undisciplined incident solar light 𝑃_U. Therefore, the collecting solar power on the left detector 𝑃_L is near the undisciplined power 𝑃_UL. Also, the collecting solar power on the front detector 𝑃_F can be approximated by the undisciplined power 𝑃_UF. The collected undisciplined power on the horizontal detector equals around the average of these two quantities. Besides, any detector, with direct incident solar power, possesses collected undisciplined solar power which is similar with the power collecting environment of adjacent facet detector. Thus, the collected undisciplined solar power can be substituted by collecting solar power on adjacent facet detector. It means that 𝑃_URe equals 𝑃_L and 𝑃_UR equals 𝑃_UF. Table 2 lists the undisciplined powers of each facet on the hour. Table 3 lists the direct incident solar power of each detector which is obtained by deducting undisciplined power from measured power. Therefore, the listed quantities in Table 1 are equal to the summation of those corresponding entities in Tables 2 and 3.

Table 2 

Undisciplined incident solar light power with respect to five detectors (unit: (W/m²)).

Table 3 

Direct incident solar light power with respect to five detectors (unit: (W/m²)).

Based on the direct incident solar light power on five facets listed in Table 3, the orientation angles at different times can be evaluated. Taking the measured power at 12:00 A.M. on the selected day as an example, the azimuth angle and elevation angle are calculated and obtained as follows.

According to (24), it arrives at 𝛼: 𝛼=tan⁻¹𝑃_RD𝑃_ReD=tan⁻¹148.98.9=86.58^∘. (27) Using (25), incident angle 𝜙 can be obtained as 𝜙=tan⁻¹𝑃_RD𝑃_HDsin𝛼=12.1^∘. (28) Elevation angle is the complimentary angle of incident angle; thus, 𝜙_ℎ=90−𝜙=77.9^∘. (29) The theoretical azimuth angle and the computed azimuth angle are shown in Table 4, and the theoretical elevation angle and the computed elevation angle are shown in Table 5, respectively. Theoretical azimuth angles and elevation angles are obtained from perpetual calendar.

Table 4 

Azimuth angles comparison between theoretical and computed values.

Table 5 

Elevation angles comparison between theoretical and computed values.

In this paper, the light diffusion factor is neglected and not taken into the formulation. Only simple constant offset value is used to present the diffusion power. In Tables 4 and 5, the elevation angles and azimuth angles are quoted and calculated. In Table 4, by comparing the theoretical azimuth angles and computed azimuth angles, the errors are kept below 3.55°. In Table 5, by comparing the theoretical elevation angles and the computed elevation angles, the errors are also kept below 3.81° which is within acceptable range.

6. Conclusion

This paper has successfully proposed a cubic composite sensor with five sensors placing on five different facets. By coordinate transformation and detailed formulation, the azimuth angles and elevation angles for different sunlight orientations can be derived. Accordingly the sunlight orientation can be determined. No electronic compass and CdS resistors are required in the mechanism. Results show that the proposed method has precise solar tracking performance. This proves the validity of the proposed formulation to estimate the sunlight orientation and solar power. Besides, the solar light power can also be measured and provide valuable information for the solar tracking system.

Conflict of Interests

The author declares that there is no conflict of interests regarding the publication of this paper.

Acknowledgment

The author would like to acknowledge the financial support of the National Science Council of Taiwan, through grant number 102-2622-E-150-005-CC3.