Brazilian Journal of Development 18691 ISSN: 2525-8761

Development of a Control Strategy for Tracking Maximum Power Generation

Desenvolvimento de uma estratégia de controlo de painéis solares para rastrear a produção máxima de energia

DOI:10.34117/bjdv7n2-488

Recebimento dos originais: 23/01/2021 Aceitação para publicação: 23/02/2021

Aurélio Gouvêa de Melo Doutorando em Eng. Elétrica Instituição: Universidade Federal de Juiz de Fora Endereço: Galpão Engenharia Elétrica - Via Local - São Pedro, Juiz de Fora - MG E-mail: [email protected]

Milena Faria Pinto D.Sc. Eng. Elétrica Instituição: CEFET-RJ Endereço: R. Gen. Canabarro, 485 - Maracanã, Rio de Janeiro - RJ, 20271-204

Dr. Alessandro R. L. Zachi Instituição: CEFET-RJ Endereço: R. Gen. Canabarro, 485 - Maracanã, Rio de Janeiro - RJ, 20271-204

Dra. Camile A. Moraes D.Sc. Eng. Elétrica Instituição: UFV Endereço: Campus Universitário Viçosa – MG/BR CEP: 36570-900

Cleberson L. A. Melo Graduação Eng. Elétrica Instituição: CEFET-RJ Endereço: R. Gen. Canabarro, 485 - Maracanã, Rio de Janeiro - RJ, 20271-204

Marcos G. L. Moura Graduação Eng. Elétrica Instituição: CEFET-RJ Endereço: R. Gen. Canabarro, 485 - Maracanã, Rio de Janeiro - RJ, 20271-204

ABSTRACT The solar panel is an essential energy conversion component of photovoltaic (PV) systems, an indispensable key for converting clean and sustainable into electricity. Over the last few years, there has been a growing demand for renewable sources due to sustainable development and global warming. Therefore, this work describes the prototype of an electronic supervision and control system for the orientation of a bench solar panel. The developed tracker prototype has as its core an electronic circuit based on a commercial microcontroller model Tennsy 3.0, within which the control algorithm is embedded. In addition to the controller, a supervisory

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Brazilian Journal of Development 18692 ISSN: 2525-8761 software was developed to monitor solar cells’ status in real-time. The supervisory showed the angle of the solar plate and values of luminosity and acquired power. Simulations results were presented to show that the amount of energy generated can reach 37 %.

Keywords: Solar tracker, Microcontroller electronics, Solar energy, PID controller.

RESUMO o painel solar é uma componente essencial de conversão energética dos sistemas fotovoltaicos (pv), uma chave indispensável para a conversão de energia solar limpa e sustentável em electricidade. Nos últimos anos, tem havido uma procura crescente de fontes renováveis, devido ao desenvolvimento sustentável e ao aquecimento global. Portanto, este trabalho descreve o protótipo de um sistema electrónico de supervisão e controlo para a orientação de um painel solar de bancada. O protótipo de rastreador desenvolvido tem como núcleo um circuito electrónico baseado num microcontrolador comercial modelo tennsy 3.0, no qual o algoritmo de controlo está incorporado. Para além do controlador, foi desenvolvido um software de supervisão para monitorizar o estado das células solares em tempo real. A supervisão mostrou o ângulo da placa solar e os valores de luminosidade e potência adquirida. Os resultados das simulações foram apresentados para mostrar que a quantidade de energia gerada pode atingir 37 %.

Palavras-chave: rastreador solar, electrónica de microcontrolador, energia solar, controlador pid.

1 INTRODUCTION The solar panel is the fundamental energy conversion component of photovoltaic (PV) systems Chung et al. (2003). PV systems are essential for converting clean and sustainable solar energy into electricity Liu et al. (2016). Besides, this efficiency range can be further reduced by decreasing irradiance, increasing panel temperature and varying load conditions Bendib et al. (2015). In the last few years, there has been a growing demand for electricity Cui et al. (2019a). Consequently, much work has been done for renewable sources, as presented in Debbichi et al. (2018), which can be related to sustainable development, including concerns about global warming. Recently, many works have been published regarding the plates’ composition and the generation of new materials, as mentioned in Yao et al. (2019); Cui et al. (2019b); Anderson et al. (2019); Genene et al. (2019). Due to the PV’s low relative efficiency and its non-linear characteristics under different operating conditions, it can be beneficial to apply control to track solar radiation maximum point throughout the day. Accordingly, to Chung et al. (2003), Khan et al. (2010), there are three possible methods to maximize the extraction: (i) -tracking; (ii) maximum power

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Brazilian Journal of Development 18693 ISSN: 2525-8761 point tracking; or (iii) both. The panel position control ensures that it can produce the maximum power for the available solar radiation. Works like Fathabadi (2016) and Jamroen et al. (2020) presented basic viable methodologies for solar tracking. Despite the results presented, both articles can be optimized by assessing the appropriate time to perform the solar search. This means that tracking only occurs if the power increase is beneficial to the system by evaluating local generation conditions and estimating the increase in generation and the power consumption. Other works such as Kim and Cho (2019) propose efficient methods based on the total measurement of the celestial condition. Although efficient, it has a high financial cost and is not viable on a small scale. Over the years, many researchers have studied control methods to improve the performance of PV systems. Advanced control methods have been developed to achieve better performance, such as in the work of Kiyak and Gol (2016); Zhao et al. (2019). However, conventional control strategies are used in many control problems, especially their dynamics are not completely known or contains uncertainties Sabir and Ali (2016). The widespread of PID is due to its simplicity and easy implementation in almost any microcontroller. This reduces the overall cost, making it more attractive than other advanced systems Aguilar et al. (2019). The main objective of the solar tracking developed in this work is to increase panels efficiency keeping optimal positioning in relation to incident solar radiation. Despite increasing system efficiency, energy costs are created due to the motor’s activation to move the panels. In this way, motors’ activation frequency must be optimized to maximize the energy gain and minimize its consumption. This maximization means that there may be no gain in moving the panel on certain days, such as cloudy days. Thus, a fixed position set-point should be kept, regardless of whether there are slightly brighter regions being detected by the sensor. This work offers a mathematical model and a decision heuristic in order to determine the conditions in which it is feasible to move the panel. Therefore, this work presents a control and optimization system applied to position tracking using a microcontroller. Besides, supervisory software is used to monitor the state of solar cells in real-time. This platform shows the angle of the solar plate and luminosity and power values acquired. This paper is organized as follows. Section 2 presents the model and the mathematical foundations used. Section 3 presents details of the controller and the tracking mechanism. The results and discussions are presented in Section 4. finally conclusions are presented in Section 5.

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2 SOLAR TRACKER SYSTEM MODEL This work focus on the solar panel automatic orientation. It is a mechanism composed of a PV cell mounted on rotating support whose articulation point is corrected to the axis of a DC motor with a reduction box, as illustrated in Figure 1. On the sides of the PV cell that intersects the rotation plane of the mechanism, two Light Dependent Resistors (LDRs) are fixed to sense the incoming light. The LDRs, which are responsible for detecting the sun’s position throughout the day, are mounted on the mechanism’s rotating support sides. This position was selected in order to allow a good position facing the sky. The sensors are positioned with a fixed angle of 65표 relative to the cell plane.

Figure 1: Prototype driving and sensing schematics.

In order to obtain the mathematical model that describes the solar tracker movement, the DC motor dynamic equation and the mechanism geometric relationships are used.

2.1 DC MOTOR The dynamics that DC Motors behavior is well known in the literature Kathushiko (2011). This equation can be organized in function of the motor axis angular position 휃 [푟푎푑]:

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휃̈ = −훼 휃̇ + 훽푉푚 (1) or in function of angular speed 푤 [푟푎푑/푠]:

푤̇ = −훼푤 + 훽푉푚 푤 = 휃̇ (2)

In Equations (1) and (2), the real constants 훼 > 0 and 훽 > 0 are the motor electromechanical parameters and 푉푚 [푉표푙푡푠] is the voltage applied.

2.2 MECHANISM GEOMETRY Figure 2 is a simplified illustration of the tracking mechanism. Due to its geometry, one will observe that the light sensors always move in an imaginary circumference represented by 푅 and defined by the mechanism structure.

Figure 2: Panel geometry and displacement.

The reference point 푂퐴 corresponds to the midpoint of the arc segment that joins the two light sensors on this imaginary circle. When the rotating support tilts from an angle 휃, the midpoint 푂퐴 moves over the circumference along an arc length 푆. Since 휃 is measured in radians, then the relationship between these two displacements can be written as 푆 = 푅 휃.

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When tracking the sun, the midpoint 푂퐴 is aligned with the sun and the mechanism pivot point. In this situation, the angle 휃 reaches its desired value 휃∗. According to the equation 푆 = 푅 휃, the desired angle at the desired arc length is 푆∗. Therefore, when the goal of solar tracking is reached, as variables 휃 and 푆 converge simultaneously to their desired values 휃∗ and 푆∗, respectively. This information will be useful in the following sections.

2.3 TRACKING ERROR Here, light sensors’ measurements are compared to calculate the panel tracking error about the sun. Each sensor outputs a proportional voltage V1 and V2. In this work, the solar tracking error 푒 will be defined by:

푒 : = 푉1 − 푉2 (3)

It is assuming, for simplicity, that the light sensors obey the positive logic, i.e., the greater the light intensity on the 퐿퐷푅1, the higher its output voltage 푉1 and vice versa. For analysis purposes, consider again the schematic of Figure 2, it is assumed that the ∗ tracker is outside the S ≠ S* and 휃 ≠ 휃 convergence point, with 퐿퐷푅2 focusing the sun directly . Based on the positive logic, the 푉2 voltage will be greater than the 푉1 voltage. According to Equation (3), this will result in a negative error value. Note that, in this same initial situation, the values of 휃∗ and 푆∗ will also be greater than the values of 휃 and 푆, respectively. In this way, it is possible to define a displacement error variable 푒푆, as shown in Equation (4).

∗ 푒푆 : = 푆 − 푆 (4)

This variable will have the same sign as the 푒 error in the Equation (5). In addition, ∗ once tracking is achieved, as discussed in the previous section, we have 푆 = 푆 (푒푆 = 0) and, ideally, the two LDRs start to receive the same light intensity, implying 푉1 = 푉2 and, consequently, 푒 = 0. This means that the errors 푒 and 푒푆 can be related instantly by a function 퐾0:

푒푆 : = 퐾0푒 (5)

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The nature of 퐾0 function depends on how the 푉1 and 푉2 voltages vary during the tracker movement. However, it is possible to state that it is a defined positive function since 푒푠 and 푒 always have the same sign. For simplicity and without losing generality, assume that K0 is a positive constant.

2.4 FULL MODEL ∗ Note that the error 푒푆 is not available because both 푆 and 푆 depend on the angles ∗ 휃 and 휃 , which are not measurable in this project. However, 푒푆 can be estimated indirectly by the error 푒. Indirectly, because 퐾0 is not a known constant. Thus, by deriving the Equation (6) twice in relation to time, after isolating 푒 in the first member, we have that:

1 푒̈ = ( ) 푒̈ 푆 퐾0 1 ∗ (6) 푒̈ = ( ) (푆̈ − 푆̈ ) 퐾0

As the sun movement in the sky is slow when compared to the motor speed, 푆∗, it is possible to consider it as constant, allowing us to derive:

1 1 푒̈ = ( ) 푆̈ = ( ) 푅 휃̈ 퐾0 퐾0 푅 푒̈ = ( ) (−훼푤 + 훽푉푚) 퐾0 (7)

1 퐾 푤 = 휃̇ = 푆̇ = 0 푒̇ 푅 푅

By combining the Equations (8), one can obtain the full model of the solar tracker:

푒̈ = −훼 푒̇ + 훽푉푚 훽푅 (8) 훽 = 퐾0

3 CONTROLLER DESIGN To force the tracking error 푒 towards zero, this work adopts the classical feedback loop, as illustrated in the block diagram of Figure 3.

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Figure 3: Control loop workflow.

ee, the plant is a second-order system with a stable pole and one at the origin. Knowing that 훽 and 훼 are constant, then three types of classic drivers will be used to solve the convergence problem:

P: 퐶(푠) = 퐾푝 퐾 PI: 퐶(푠) = 퐾 + 푖 푝 푠 (9) 퐾 PID: 퐶(푠) = 퐾 푠 + 퐾 + 푖 푑 푝 푠

In this work, authors opted by a PI controller equation (9). This was selected due to its simple implementation and tuning. The tuning method was performed using the classical Ziegler-Nichols method. The method parameters Ziegler-Nichols, response time 푇, delay 퐿, and gain 퐾, where the response curve is acquired from the unit step applied in the system. With the idea to obtain this curve experimentally, tests were performed with fixed light. Using this method, the authors obtained the plot shown in Figure 4.

Figure 4: Experimental test: Unit step response.

From the experimental curve, an average curve was drawn to facilitate the measurement of the parameters 푇 = 166 푚푠, 퐿 = 164 푚푠 and 퐾 = 66. The 퐾푝 and 퐾푖

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Brazilian Journal of Development 18699 ISSN: 2525-8761 earnings of the controller were calculated according to the Ziegler-Nichols presented in the Table 1, resulting in the following control structure of Equation (10).

Table 1: Ziegler-Nichols. Kp Ki Kd P T/L 0 0 PI 0.9 T/L 0.3/L 0 PID 1.2 T/L 0.5/L 0.5L

5,4667 퐶(푠) = 0,9659 + (10) 푠

4 RESULTS AND DISCUSSIONS 4.1 PROTOTYPE ASSEMBLY Figure 5 shows the tracker prototype. The embedded electronics core is the 3.0 Teensy microcontroller card, which is based on the 32-bit ARM Cortex-M4 chip. In Figure 6,there is an image of the Teensy 3.0 plate showing the connections with the LDR sensors and the DC motor. This configuration was set up to test the tracker concept and adjust the control direction signal. The PI Eq. (9) controller equation was coded in C language. The voltage signal 푉푚 for the motor is also generated by the board using PWM modulation. To save energy from the power supply when convergence is reached, a function has been programmed in the firmware to shut down the engine for certain time

Figure 5: Developed tracker prototype

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Figure 6: Simplified schematic circuit for sensor connection and prototype servomechanism .

4.2 SUPERVISORY This work presents a supervisory system developed to access the system data. Figure 7 illustrates the developed HMI interface. Note that only two graphs are shown, where the first one shows the position of the servomechanism, that is, where it is pointing to, and the second graph shows the PID, input, output, and setpoint parameters.

Figure 7: HMI interface.

The graph with the controller’s parameters helps the user visualize what actually occurs in the system. Communication with the microcontroller is performed through the Modbus protocol, where the choice of using this protocol is due to its simplicity and easy implementation.

4.3 SOLAR TRACKING MONITORING It is possible to determine the amount of energy incident on any plane on the earth’s surface by knowing its declination 훿 given by Equation (11), where 푁 is the day of the year, latitude 휙, altitude 훼 and azimuth 훽. From the information derived from irradiation tables, it is possible to determine the amount of energy incident on a plane. Therefore, we can estimate the increase or decrease in the amount of incident energy

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Brazilian Journal of Development 18701 ISSN: 2525-8761 without considering local atmospheric and environmental conditions, as in equations (12). Figure 8 represents this.

Figure 8: Solar movement in relationship to PV panel.

훿 = 23.45 ⋅ 푠𝑖푛(360/365 ⋅ (284 + 푁)) 푐표푠(휃) = 푐표푠(훽) ⋅ 푐표푠(훾) ⋅ 푐표푠(훴) + 푠𝑖푛(훽) ⋅ 푐표푠(훴) (11)

퐼푎푛푔 = 푎푐표푠(푠𝑖푛(휙) ⋅ 푠𝑖푛(푑) ⋅ 푐표푠(훽) − 푐표푠(휙) ⋅ 푠𝑖푛(푑) ⋅ 푠𝑖푛(훽) ⋅ 푐표푠(푍) + 푐표푠(휙) ⋅ 푐표푠(푑) ⋅ 푐표푠(ℎ) ⋅ 푐표푠(훽) + (12) 푠𝑖푛(휙) ⋅ 푐표푠(푑) ⋅ 푐표푠(ℎ) ⋅ 푠𝑖푛(훽) ⋅ 푐표푠(푍) + 푐표푠(푑) ⋅ 푠𝑖푛(ℎ) ⋅ 푠𝑖푛(훽) ⋅ 푠𝑖푛(푍)) ⋅ 180/휋

Figure 9 shows the generation of a solar plate in a fixed position with an inclination of -22 degrees throughout the year. The latitude of the city of Rio de Janeiro - RJ / Brazil was considered to generate the figure. Note that throughout the year, with the solar declination variation, there is a variation in the plate’s efficiency.

Figure 9: Generation for a fixed panel throughout the year.

By averaging the daily values of Figure 9, it is possible to determine the amount

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Brazilian Journal of Development 18702 ISSN: 2525-8761 of average energy generated per year for the plate at a fixed slope. This can be seen by the blue curve in Figure ref fig: track. The same set of equations allows the simulation of the movement of the plate, both azimuth and altitude. The result is shown in Figure 10 by the orange curve by performing the simulation of solar altitude tracking. The curve shows a gain of approximately 37% for tracking solar altitude. Note that this is a maximum theoretical value if the tracking is performed online. Note that the actual values may vary with the tracking frequency.

Figure 10: Power generation (p.u.): Tracking vs fixed panel.

It is possible to observe that the model allows the generation estimate at the current angle and the new angle for a solar plate. Starting from this amount of incident energy and the model I-V of the solar panel, it is possible to determine the real gain or loss of power due to the variation of the solar panel position, as presented in Equation (13). Still, it is necessary to consider that other factors may influence the typical I-V curve. As an example, we can mention temperature, amount of dirt, among others. However, this work considers that good maintenance practices and good design can mitigate these effects, and in this way, they can be neglected.

퐸표푏푠푒푟푣푒푑 푃1 푃2 𝑔푎𝑖푛 = ⋅ (푐표푠(퐼푎푛푔) − 푐표푠(퐼푎푛푔)) (13) 퐸푒푥푝푒푐푡푒푑

푃1 In the Equation (13), the variable 퐼푎푛푔 represents the incidence angle in the 푃2 position 1, and the variable 퐼푎푛푔 the angle of incidence in position 2. This equation

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Brazilian Journal of Development 18703 ISSN: 2525-8761 determines the gain in p.u. to move the panel to a new position. Despite this gain, it is necessary to consider the energy cost of moving it.

The energy cost for moving a panel 푝푚표푣 is extremely dependent on the technology used for moving, the panel’s weight, among other factors. Therefore, the case study applied in this work considers as a fixed value in 푊/푑푒𝑔푟푒푒푠, equivalent to 2 % of the panel generation, representing a specific cost in the function of the necessary movement angle. The resulting amount of energy is then given by Equation (14) and determines if the movement is viable if the variable is positive. In this way, the position setpoint is only changed in this case, improving the system’s overall efficiency.

퐸푡 = 퐸표푏푠푒푟푣푒푑 ⋅ 𝑔푎𝑖푛 − 푝푚표푣 ⋅ 휎 (14)

where 퐸푡 is the resulting energy, 퐸표푏푠푒푟푣푒푑 is the energy absorbed by the panel,

푝푚표푣 represents the energy cost for moving a panel, 𝑔푎𝑖푛 is the gain in p.u. of moving the panel to a new position, and 휎 is the angle required to reach the new position. By using the data obtained, it is possible to define an interesting resource for the tracker, that is, so that the system is prepared for tracking after sunset, it must return to the starting position. figure 11 shows for the year 2020 the sunrise and sunset times using the altitude, latitude, and longitude of the CEFET-RJ Maracanã campus, as a reference.

Figure 11: Sunrise and sunset thorough 2020 for 30m of height and CEFET-RJ latitude.

Solar tracking is very efficient during times when there is full sun. Because of this, the maximum and minimum azimuth tracking angles must be adjusted for greater

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Brazilian Journal of Development 18704 ISSN: 2525-8761 efficiency. Figure 12 shows the values of azimuth and solar zenith for all days of 2020. It is observed in the curve that the maximum value is ±120 degrees. Another important observation is that there is an almost straight line at the beginning and end of the graph. This indicates that the angle varies more than the rest of the day.

Figure 12: Zenith and azimuth angles throughout the year 2020.

We can also analyze the tracking error compared to a fixed plate, as shown in Figure 13. For this, the sun’s incidence angle was estimated for each day and time of the year 2020 using the same location as the previous figures. The vertical lines at each hour represent variations in the incidence angle for a given time during the year.

Figure 13: Tracking error compared to a panel with north orientation and tilt equivalent to local latitude.

By using data from automatic stations at the Instituto Nacional de Meteorologia

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(INMET), located in Rio de Janeiro - Vila Militar, OMM Code:86879 inmet (2020), it is possible to establish an estimate of daily solar radiation in the City of Rio de Janeiro in the year 2020. This result is shown in Figure 14. Note that the 24-hour moving average presented indicates that most days are of high insolation, which is corroborated by the local solarimetric atlas Costa et al. (2018) and Farias et al. (2020).

Figure 14: Real data from Rio de janeiro metereological station at Vila Militar gathered from INMET database.

5 CONCLUSIONS AND FUTURE WORKS This research work presented a combination of optimization with control applied in a low-cost solar tracking system using a microcontroller to improve performance. In addition, it is proposed a mathematical model and a decision heuristic to determine which feasible conditions for moving the panel. This allows the system to optimize energy usage by reducing unecessary movements. Simulations demonstrated an theoretical efficiency increase of 37 % for declination in the city of Rio de Janeiro. Solarimetric data from the city also indicate that the high levels of local solar radiation. This further contributes to the proposed methodology feasibility. For future work, the authors intend to apply different control techniques to determine which are the most efficient for the proposed system. In addition, it is intended to add a second axis to the system so that it can capture more solar energy peak points throughout the day.

ACKNOWLEDGMENTS The authors would like to thank the support of the following federal agencies CEFET-RJ, UFJF, CAPES, CNPq, and FAPERJ.

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Brazilian Journal of Development, Curitiba, v.7, n.2, p. 18691-18707 feb. 2021