Power feedback strategy based on eciency trajectory analysis for HCPV sun tracking

Power feedback strategy based on efficiency trajectory analysis for HCPV sun tracking Manuel G. Satu´e1 Escuela T´ecnica Superior de Ingenier´ıa, Universidad de Sevilla, Sevilla, Spain Fernando Casta˜no1 Escuela T´ecnica Superior de Ingenier´ıa, Universidad de Sevilla, Sevilla, Spain Manuel G. Ortega1 Escuela T´ecnica Superior de Ingenier´ıa, Universidad de Sevilla, Sevilla, Spain Francisco R. Rubio1 Escuela T´ecnica Superior de Ingenier´ıa, Universidad de Sevilla, Sevilla, Spain Abstract This paper presents a control strategy for sun trackers which adapts continuously to different sources of error, avoiding the necessity of any kind of calibration by analyzing the produced electric power to sense the position of the Sun. The proposed strategy is able to meet the strict specifications for HCPV sun trackers despite of mechanical uncertainties (misalignments in the structure itself, misalignment of the solar modules with respect to the wing, etc.) and installation uncertainties (misalignments of the platform with respect to geographical north). Experimental results with an industrial-grade solar tracker showing the validity of the proposed control strategy under sunny and moderate cloudy conditions, as well as with different installation precisions by un-calibrating the system on purpose are exposed. Keywords: sun tracker, HCPV, sun tracking strategy, efficiency enhancement Email addresses: [email protected] (Manuel G. Satu´e), [email protected] (Fernando Casta˜no), [email protected] (Manuel G. Ortega), [email protected] (Francisco R. Rubio) Preprint submitted to Renewable Energy April 29, 2020 1. Introduction By using high concentration photovoltaic modules (HCPV), the efficiency of the transformation of light energy into electrical energy can increase twice as much as the provided by regular photovoltaic modules Zubi et al. [21]. HCPV modules can be composed of two king of solar cells: high efficiency silicon and5 multijunction photovoltaic cells. The use of lenses which concentrate the sun rays on to multi-junction solar cells is what allows for increased efficiency P´erezHigueras et al. [13]. HCPV modules concentrate the sun rays on to the solar cells using Fresnel lenses, which are characterized by their half-acceptance angle, α. The half-10 acceptance angle is defined as the maximum angle at which incoming sun rays still fall upon the photovoltaic cells so that and the photoelectric effect occurs. Due to fabrication imperfections, in practice, the half-acceptance angle is defined as the angle for which efficiency drops to 90% of its maximum, as shown if Fig. 1a.15 The half-acceptance angle of HCPV panels is typically around 1 degree Yavrian et al. [20], being this fact a very important restriction for the design of the HCPV sun trackers and its control system. The system must have a very high pointing precision in order to keep the solar modules efficiency around its maximum and thus not waste energy. To achieve the high aiming precision re-20 quirement, HCPV sun trackers use multiple gearboxes and encoders of thousand of pulses per turn, but there are some uncertainties that decrease the pointing accuracy. This uncertainties do not depend on the mechanical design or the different components that constitute the solar tracker, but of its installation, its assembly, etc. The sources of uncertainty that can be found in a sun tracking25 system can be divided into two categories: hardware and software. Regarding the hardware, there are errors related to foundation and mechanical assembly. Misalignment of the sun tracker azimuth zero with respect to geographical north and misalignment of the elevation zero with respect the skyline are caused by a not too precise foundation of the sun tracker. Misalignment of the modules30 2 (a) (b) Figure 1: Concentrator model. 1a) Definition of half-acceptance angle. 1b) Efficiency values on the x−yplane of a virtual cell. with respect to the wing is caused by a not too accurate assembly or by aging of the plant. This last kind of misalignment causes electrical mismatches that distorts the I-V output of the modules array, decreasing the efficiency of the sun tracker Rodrigo et al. [14]. Concerning software, there can be errors related to a bad adjustment of the zero of the encoders, a bad calibration of the system or35 even lack of calibration. Also included in this category are the errors introduced by the Solar Equations, such as the geographical positioning error of the sun tracker, the clock error of the controller unit and the accuracy of the algorithm itself. There are two strategies to track the Sun: open-loop by means of Solar40 Equations and closed-loop, which uses some kind of sensor to locate the Sun. Some examples of open-loop controlled sun trackers are Abdallah and Nijmeh [1] and Fathabadi [8]. Regarding closed-loop controlled sun trackers, Roth et al. [15] designed and constructed an electromechanical system to track the position of the Sun using a four-quadrant photo detector to sense the position of the Sun.45 Yao et al. [19] presented a dual-axis solar tracker with two operation modes, one for PV systems and another for HCPV systems, was built. The HCPV mode used a combination of open-loop and closed-loop controls. The closed-loop is meant for fine pointing, while the open-loop is used in cloudy conditions. The 3 sensor used is a four-quadrant photocell circuit. In Oh et al. [12] high precision50 solar tracking was achieved also by a combination of open-loop and closed-loop controls. It operates in open-loop by means of Solar Equations until the tracking error exceeds a threshold, and in that time instant it switches to closed-loop control. The feedback sensor consists of a camera that senses the position of the Sun by looking directly to it. Fathabadi [7] built and compared two sun trackers,55 one open-loop and one closed-loop. In order to close the loop an irradiance sensor equipped with a radiance limiting tube is mounted in a secondary dualaxis machanical system. Garrido and Daz [9] propose a cascade closed-loop control, where the inner loop employs non-linear proportional - proportional integral (NP-PI) controller and the outer loop used a proportional integral (PI)60 controller, in order to improve the tracking accuracy and reduce the actuator wear. Abdollahpour et al. [2] also used a camera to locate the Sun, but in this case the shadow projected over a plate by a shadow-casting object is analyzed to infer the position of the Sun. An interesting work by Carballo et al. [4] uses computer vision and deep learning for solar tracking. This approach can provide65 additional information for the sun tracking system control like cloud movements prediction, atmospheric attenuation or measures of concentrated solar radiation, which can improve the control strategies of the system and therefore the system efficiency. The control system was tested with a heliostat in CESA central tower system, located in Plataforma Solar de Almer´ıa, but the authors claims that the70 same approach can be used for other kind of sun trackers, as HCPV sun trackers. As open-loop control strategies rely exclusively on Solar Equations to determine the position of the Sun, this strategies are greatly affected by installation errors, errors introduced by the possible lack of accuracy of the Solar Equations and errors due to the apparent position of the Sun for certain conditions of75 the atmosphere caused by refraction. Closed-loop control strategies use electrooptical sensors as SolarMems [18], pyrheliometers, or other sensors that can provide the position of the Sun with respect to the reference frame of the sensor itself. Closed-loop control strategies are not affected by installation errors but by a bad assembly of the sensor on to the wing of the sun tracker, which can80 4 produce a misalignment between the reference frames of the wing (or solar modules) and the optical sensor. Generally, closed-loop strategies are best suited for HCPV sun tracking because they deliver smaller tracking errors, but the great disadvantage is that they do not perform well on cloudy days, as their input is a measure of the position of the Sun. In order to mitigate the sources of uncer-85 tainty related to the installation the common actions are to perform a precise installation of the sun tracker by specialized personnel, which is time consuming and costly, or to perform a system calibration after installation Satu´e et al. [17], which is a complex task. This paper presents the design, implementation and experimental testing of a90 control algorithm for HCPV sun trackers which allows the auto-correction of the different error sources that affect the tracking system by analyzing the electrical power produced to provide a sun position measurement to close the control loop. To use explicitly the electric power produced as a sensor is important because the effect of the refraction of solar radiation in the atmosphere can95 modify the apparent position of the Sun for certain conditions of the atmosphere Jenkins [11]. On the other hand, using the variable to be maximized as an indirect measure of the position of the Sun is an advantage over other solar sensors, which may be misaligned with respect to the solar modules. Therefore, the need to perform an accurate and expensive installation of the equipment100 or the need to perform a initial or periodic calibrations in order to estimate the transform relations between different reference frames of the sun tracker is eliminated. The proposed control strategy is valid as far as the sun tracker is able to perform movements in the azimuth and elevation coordinates in an independent manner. Although there are different possibilities for the kinematic105 configuration of a sun tracker, almost all commercial sun trackers have this twoaxis kinematic configuration Crist´obal L´opez et al. [6]. The idea is to use the photovoltaic modules as a sensor to estimate the position of the Sun, and the Solar Equations to predict the future position of the sun with the purpose of maintaining the pointing vector of the sun tracker ahead of the position of the110 Sun. By using the produced electric power as a measure of the position of the 5 Sun, the control strategy is explicitly trying to maximize the collected energy. In addition, the algorithm allows to reduce the number of movements that the sun tracker performs throughout the day. This is achieved by maximizing the path of the solar beam projection on the plane of the solar cell, so that all the115 space within the limits of the maximum efficiency zone is used (see Fig. 1a). To do this, it is necessary to predict the position of the Sun in the future and to use a simple model of the lens of the solar collector together in conjunction with the kinematic model of the solar tracker. Until the Sun projects outside the region of maximum efficiency, there will not be a new pointing movement.120 The tracking of the position of the Sun is carried out by means of a closedloop control strategy in which the Solar Equations are a feed-forward which provide approximate coordinates for the pointing of the wing of the sun tracker, while a controller applies a correction on these coordinates by feed-backing the instantaneous DC power produced to estimate the real position of the Sun.125 This work is inspired by the algorithm proposed in Rubio et al. [16]. The main difference of the algorithm presented in this paper with respect Rubio et al. [16] is that the produced power trajectories are analyzed and certain estimation rules are applied in order to estimate the position of the sun instead of just searching for a maximum in the produced power, which is prone to130 errors due to noisy signals and other effects. On the other hand, the sun tracker used in Rubio et al. [16] did not have HCPV solar modules, so the authors emulated its behavior by using conventional modules with tubes perpendicular to the modules cells. Furthermore, a constant not optimal electric load was used instead of a power inverter. Moreover, the used solar tracker was a low-cost135 domestic tracker. In this work, test results performed with a high concentration solar tracker of larger dimensions and nominal output electric power, such as those found in solar plants, are provided. The main innovation provided by this work is to make possible the start-up of a industrial-grade HCPV solar tracker without the need for a fine adjustment140 through calibrations, and to keep it continuously correcting, by analyzing the electrical power produced to provide a sun position measurement to close the 6 control loop. The remainder of the paper is structured as follows: the sun tracker characteristics are described in Section 2. Section 3 explains the proposed control145 strategy to track the Sun. The devices used to build the control system and their relationships are described in Section 4. Experimental results, including a comparison with an open-loop strategy, are shown in Section 5. The main conclusions of this work are drawn in Section 6. 2. Sun tracker specs150 The sun tracker used in this work, depicted in Fig. 2, is located on the roof of the Department of Systems and Automatic Control Engineering Laboratories at the University of Seville, Spain. For the description of the installation that constitutes the solar tracker, it can be divided into the following parts: mechanical structure (fixed and mobile),155 generation and transformation devices, orientation movement control equipment and specific instrumentation equipment. The mechanical structure of the sun tracker has two degrees of freedom to follow the movement of the Sun in Azimuth and in elevation independently. It consists of a fixed pole on which the azimuthal rotation mechanism (worm drive)160 is supported, which in turn supports the elevation mechanism (high accuracy linear actuator) and the wing. The HCPV modules are mounted on the wing. To actuate on the spatial orientation of the wing there are two three-phase asynchronous motors (with a rated power of 550 W for the orientation motor and 750 W for the elevation motor) commanded by two variable frequency drives165 which are managed by a programmable logic controller (PLC). The orientation motor has two gearboxes attached in order to increase accuracy. The sun tracker orientation coordinate, θori, is measured by an encoder with a resolution of 214 pulses per revolution. The measure of the elevation coordinate, θele, is provided by an inclinometer with an accuracy of ±0.1 degrees. With this configuration,170 the sun tracker has an accuracy below 0.1 degrees in orientation movements and 7 Figure 2: Sun Tracker used for the tests. Located on the roof of the Department of Systems and Automatic Control Engineering Laboratories at the University of Seville, Spain. θori and θele are sun tracker orientation and elevation coordinates, respectively. The reference system for the Solar Equations (red) and the reference system of the platform of the sun tracker (yellow) are not aligned. equal to 0.1 degrees for elevation movements. The generator equipment is constituted by the HCPV modules and the transformation equipment is a power inverter. The installation has 24 solar modules with a total catchment area, Sc, of 9.3 m2. The electrical characteristics of the175 modules are shown in Table 1. The modules are connected in series, so that the voltage that can be reached in terminals will be approximately 443 V open circuit. The power inverter is a SMC Sunny Boy with a nominal power of 2500 W. Its input DC characteristics are a voltage between 260 and 500 volts and maximum amperage of 10 A. The output AC characteristics are 230 V (50 Hz)180 and 11 A. As main control equipment, an Schneider MC80 programmable logic controller has been used in conjunction with a PC. The control algorithm determines the time instant at which the motors must rotate and generates the 8 Short-circuit current Isc 6.35 A Open-circuit voltage Voc 18.45 V Power DCpower 95 W Max. power current Imp 5.73 A Max. power voltage Vmp 16.62 V 83.6 W 3 %, 900 W/m2, Tc= 60 ◦C Table 1: Electrical characteristics of ISOFOTON GEN-2 solar module. corresponding references for the variable frequency drives.185 Regarding the specific instrumentation, a power meter to measure the instantaneous power generated by the installation on the direct current side and an optical sensor that provides the direct normal solar irradiance (dni) as well as the sun vector referred to the sensor reference system are installed. Figure 3: Power surface obtained scanning an area around the sun vector projection on the plane of a virtual cell. Sampled data is represented as magenta dots. In order to measure the value of the semi-acceptance angle of the HCPV190 modules, an experiment was carried out. It consisted in closing the DC circuit with an electrical dissipation resistance (leaving the power inverter out of the circuit) and performing orientation and elevation movements while sampling the 9 Figure 7: Types of efficiency trajectories. The types are described below:325 •Type T1: Off-center trajectory. This type of trajectory arises when the controller is in a start-up phase or after a cloudy period. The value of the sun tracker coordinate where the sun is located, ˆ θ, is chosen where the maximum efficiency is located. •Type T2: Centered trajectory 1. This type of path is the expected when330 the controller is not in a start-up phase, but in normal operation. It is characterized by the following facts: initial and final points are below the threshold, T, and the point with maximum efficiency, is not A nor B. The points A and B are obtained by iterating from the beginning and ending points of the trajectory and checking when they exceed the threshold.335 The value of ˆ θis the mid-point between points A and B. The coordinate with maximum efficiency is not chosen because, although the trajectories are filtered, noise and perturbations can still deform the shape of the trajectories. •Type T3: Centered trajectory 2. This type of path is the expected when340 the controller is not in a start-up phase, but in normal operation. Its characteristics are: initial and final points are over the threshold, T, and 16 the point with maximum efficiency, is not A nor B (and is greater than the efficiency of A and B). The value of ˆ θis also chosen as the mid-point between points A and B.345 •Type T4: Half-centered trajectory. This kind of trajectory will be obtained in a start-up phase of the controller at the beginning of the day. One of the extreme points is below the threshold and the other is over it. The point A is obtained by iterating from the point below the threshold and checking when it exceed the threshold. The value of ˆ θis also chosen350 as the mid-point between points A and B. There are situations during normal operation of the sun tracker in which the trajectories may not provide information. These cases are usually directly related with the start-up phase of the power inverter. It may take about two minutes for the power inverter to start the power injection once it begins to355 receive enough solar radiation, which means that at the beginning of the morning and during prolonged periods with clouds, the efficiency falls below a minimum threshold to work with. These low efficiency situations also must be taken into account by the classifier. The resulting measured sun coordinates will not always be a good estimation360 because of the lack of information in the trajectories, but at least must point in the right direction. If this requirement is met, the control strategy will correct the discrepancies between Solar Equations and measurements over time, and the trajectories will have better information which will allow calculating better estimates.365 4. Control system The control system is divided in two layers. The low level layer deals with the control of the position of the two three-phase motors according to a given reference. This control is based on feedback of the motor shaft position by reading the pulses provided by the encoder and the angle provided by the inclinometer.370 17 The high level layer deals with the calculation of the set-points for the low level layer, that is, the values that must be taken by the articular coordinates of the positioner to track the sun during the day. This is accomplished by feeding back the electric power produced by the solar tracker using the strategy described in Section 3. Figure 8 shows a scheme of the sun tracker control system with all375 the devices and their relationships. The measures of electric power are provided by a custom DC power meter that generates a low voltage signal proportional to the electric power. It is connected to an analog input of the PLC. There is also an optical sensor mounted on the wing of the sun tracker that provides measures of solar irradiance (DNI).380 It communicates with the PLC over a Modbus RTU bus. This last measurement is necessary to compute the efficiency, although the tracking strategy would also work directly with the power readings. As can be seen in Fig. 8, the PLC is shared by the two control layers. The PLC takes care of all the tasks regarding sensors reading and values conversion385 to engineering units as well as low level control. The PLC cycle time is less than 10 ms, and the highest sensor period reading is 125 ms (optical sensor). The high level layer comprises the PLC and a PC, which is in charge of perform time and memory consuming tasks. These tasks that are too demanding to be ran in the PLC are trajectories storage, non-causal FIR filtering, analysis, and390 prediction using Solar Equations, etc. The PC executes an application that performs functions of monitoring measurements and other variables, supervision and data logging on disk. Some parameters of the program that the PLC executes can be changed using this application. These configuration parameters are related to motion (motor speeds,395 resting position, sun tracker coordinates motion limits, etc.), and to the system (PLC clock setting, resting schedule, set encoder zero, etc.). It also allows to operate the sun tracker in jog mode and to switch between several control strategies (closedloop with power feedback, openloop with Solar Equations, etc.). The information exchange between PC and PLC is done over a Modbus400 TCP field-bus with a period of 250 ms. 18 Figure 8: Scheme of the sun tracker control system. 5. Experimental results Some considerations have to be taken into account for the presented tests. The zero of the orientation encoder of the sun tracker was adjusted in a coarse manner using visual references. No precise calibration was performed in order405 to test the validity of the proposed control algorithm. In all the experiments the value of βis equal to 0.5 degrees. In order to avoid collisions of the wing with the devices attached to the pole of the sun tracker, the controller has a software limit in the elevation coordinate, θele, equal to 20 degrees. Therefore, until the Sun elevation reaches 20 degrees the sun tracker is stuck at this elevation and410 can not perform elevation movements. The main source of assembly uncertainty in the sun tracker is caused by a not too precise mounting of the solar modules onto the wing. Their catching surfaces do not lie in a common plane, but there are deviations up to half a degree in different orientations. This causes electrical mismatches which decrease the final efficiency of the sun tracker, and also415 can cause efficiency variations depending on where the concentrated sun beam projects onto the virtual cell (as it will be a different point on each module). 5.1. SUNNY DAY The test was carried out on 2/10/2020 from 8 h to 16 h (solar time). The efficiency trajectories sampled during the orientation and elevation movements420 19 are shown in Figs. 9 and 10 respectively. The text over the trajectories represents the corresponding trajectory number (starting at one) associated to a sun tracker movement, and the time instant at it was performed (solar time). Each movement is represented with a different color for the sake of clarity. It can be seen how the first orientation movements in the morning have null effi-425 ciency trajectories due to collision avoiding, and also that there are no elevation movements. In the detail view of Figs. 9 and 10, the vertical dashed lines represent the estimated sun position during each scan movement in sun tracker orientation coordinate and elevation coordinate, respectively. -40 -20 0 20 40 60 Sun tracker orientation (º) 0 0.05 0.1 0.15 0.2 0.25 Performance Orientation movements 16 21, 09:55:59 h 26 31, 10:43:50 h 36 41, 11:28:04 h 46 51, 12:09:57 h 56 61, 12:55:05 h 66 71, 13:36:35 h 76 81, 14:19:58 h 86 91, 15:06:39 h 96 -20 -15 -10 -5 0.16 0.17 0.18 66 Figure 9: Efficiency trajectories associated to orientation movements. Each movement is represented with a different color for the sake of clarity. In the detail view the vertical dashed lines represent the estimated sun position in sun tracker elevation coordinate. Figure 11 shows the sampled efficiency trajectories while the sun tracker is430 motionless in the time interval between pointing movements. It can be seen how the trajectories in the time interval from 9 h to 10 h, once the power inverter starts the power injection, are very unbalanced (not symmetrical) and start to become centered after some movements, acquiring the expected shape. The computed Azimuth and elevation offsets which are used to correct the435 Solar Equations are depicted in Fig. 12. The initial values for these offsets are the last values stored the previous day. Figure 13 shows the electric power 20 produced in the DC side of the power inverter along with the orientation and elevation trajectories the sun tracker follows, in sun tracker coordinates. The periodic power drops are caused by the maximum power point tracking (MPPT)440 algorithm of the power inverter. 20 22 24 26 28 30 32 34 36 38 Sun tracker elevation (º) 0 0.05 0.1 0.15 0.2 0.25 Performance Elevation movements 18 23, 10:06h 90, 14:57h 28 85 33, 10:53h 38 75 43, 11:36h 48 53, 12:18h 65 70, 13:28h 80, 14:11h 95 100, 15:47h 21 22 23 24 25 26 0.15 0.16 0.17 0.18 18 95 100 Figure 10: Efficiency trajectories associated to elevation movements. Each movement is represented with a different color for the sake of clarity. In the detail view the vertical dashed lines represent the estimated sun position in sun tracker elevation coordinate. Figure 11: Efficiency in the time interval between pointing movements. 21 8 9 10 11 12 13 14 15 16 17 solar hour -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 degrees Offsets AZIMUTH OFFSET ELEVATION OFFSET Figure 12: Calculated azimuth and elevation offsets used to correct the Solar Equations. 22 9 10 11 12 13 14 15 16 solar hour 0 500 1000 1500 W, W/m2 POWER IRRADIANCE 9 10 11 12 13 14 15 16 solar hour -50 0 50 degrees ORI REF ORI 9 10 11 12 13 14 15 16 solar hour 15 20 25 30 35 40 degrees ELE REF ELE 11.9 12 13.4 13.6 13.8 10.6 10.7 30.8 31 12 12.2 12.4 1100 1200 1300 Figure 13: Produced DC power and sun tracker trajectories in its own coordinate system for a sunny day. The detail views show the accuracy of the aiming system to reach the references. 5.2. Cloudy day Figures 14 and 15 show the sun tracking results of an experiment carried out on 09/17/2019, a day with a relatively long cloudy period. It can be observed in Fig. 14 that between 11 h and 11:45 h the irradiance becomes zero due to the445 passing of a cloud, while Fig. 15 shows how during this cloudy time period the PI controllers are not actualized (when irradiance is zero, the efficiency is also set to zero and the trajectories are classified as low efficiency). Therefore, the 23 last computed azimuth and elevation offsets are kept and continues correcting the Solar Equations during the passing of the cloud. This means that the sun450 tracker keeps moving as usual during the cloudy period, but its tracking accuracy will be reducing with the time. When the cloudy time period ends, the next sampled trajectories are valid again (they are not classified as low efficiency) and the controller continues computing new offsets. 9 10 11 12 13 14 15 16 solar hour 0 200 400 600 800 1000 1200 W, W/m2 POWER IRRADIANCE 9 10 11 12 13 14 15 16 solar hour -100 -50 0 50 100 degrees ORI REF ORI 9 10 11 12 13 14 15 16 solar hour 20 30 40 50 60 degrees ELE REF ELE Figure 14: Produced DC power and sun tracker trajectories in its own coordinate system for a cloudy day. 24 9 10 11 12 13 14 15 16 solar hour -1 -0.8 -0.6 -0.4 -0.2 degrees Offsets AZIMUTH OFFSET ELEVATION OFFSET Figure 15: Calculated azimuth and elevation offsets for a cloudy day. 5.3. Behaviour with a higher degree of uncalibration455 With the objective of testing the proposed control strategy under more unfavorable conditions, a small change is introduced in the rotation matrix that relates the Solar Equations frame with the sun tracker platform frame. 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