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Analysis, Design and Implementation of Grid Connected PV Inverter System David Curdi Dissertation submitted in fulfilment of the requirements for candidature of the degree of Bachelor of Science University of Applied Sciences Darmstadt Supervisors: Prof. Dr. Christian Jakob School of Electronic and Computer Science University of Applied Science Darmstadt, Germany August 2013 ABSTRACT ii Abstract Solar power holds great potential for the future in the realm of renewable energy. The solar energy has room for improvement, due to the low efficiency of the solar panels. It can be implemented everywhere from calculators, buildings, cars, etc. Solar energy is a field that has to be studied and continually researched until the maximum efficiency is reached. This project can help for further developments in photovoltaic system components. This thesis focused on the implementation and design of the components of a photovoltaic system. These components are the MPP tracker, different topologies of DC-DC converters and inverters connected to the grid. More specifically, the implementation of an MPP tracker algorithm, and boost converter was carried out at the end of this thesis. For the algorithm of the maximum power point tracker, the Perturb and Observe algorithm has been used. It is one of the most used algorithms due to its simplicity of its implementation with analogue and digital circuits. After the MPP tracker, the boost converter has been designed in relation to the objective of this project of feeding electricity to the grid. The boost converter will increase the voltage of the solar panel so then it can be transformed from DC to AC, and transformed with different controls synchronized to the grid. DECLARATION iii Declaration I certify that this thesis which I now submit for examination for the award of Bachelor of Sciences, is entirely my own work and has not been taken from the work of others save and to the extent that such work has been cited and acknowledged within the text of my work. This thesis was prepared according to the regulations for Bachelor studies of the University of Applied Science Darmstadt and has not been submitted in whole or in part for an award in any other Institute or University. The work reported on in this thesis conforms to the principles and requirements of the Institutes guidelines for ethics in research. Darmstadt, August 2013 (David Curdi) Candidate ACKNOWLEDGEMENTS iv Acknowledgements I want to sincerely thank all of the people who supported me throughout this bachelor thesis. Especially I thank Dr. Juan Jose Marcuello for giving me the opportunity to come to Darmstadt to finish my studies. Also to Prof. Dr. Christian Jakob for his advice and recommendations on this thesis. To my partner on this thesis Artur, in collaborating with me on the design of the Simulink model. To my family, that without them I couldn’t be studying in Germany my last year of the career. And finally to Maggie, for supporting me on the last days of this thesis. Contents Introduction .................................................................................................................................. 1 1.1 Energy Crisis ......................................................................................................................... 2 1.2 Photovoltaic Energy ............................................................................................................. 4 1.3 Overview of the thesis .......................................................................................................... 5 Theoretical Part ............................................................................................................................. 6 2.1 PV Cells ................................................................................................................................ 7 2.1.1 Cell structure ................................................................................................................. 7 2.1.2 Solar cell modeling ........................................................................................................ 9 2.1.3 Solar cell characteristics ............................................................................................... 11 2.2 MPP tracker ....................................................................................................................... 14 2.2.1 Perturb and Observe ................................................................................................... 14 2.2.2 Incremental Conductance ............................................................................................ 16 2.2.3 Differences between P&O and Incremental conductance ............................................ 17 2.3 DC-DC Converters ............................................................................................................... 18 2.3.1 Boost converter ........................................................................................................... 20 2.3.2 Buck converter ............................................................................................................ 21 2.3.3 Buck-boost converter .................................................................................................. 22 2.4 Inverters............................................................................................................................. 23 2.4.1 Stand alone operation ................................................................................................. 23 2.4.2 Grid tied operation ...................................................................................................... 23 2.4.3 Grid synchronization .................................................................................................... 24 2.4.4 Grid detection ............................................................................................................. 24 2.4.5 Examples of inverters .................................................................................................. 25 Implementation .......................................................................................................................... 27 3.1 PV cell block ....................................................................................................................... 28 3.2 PV panel block .................................................................................................................... 33 3.3 MPPT block ........................................................................................................................ 34 3.4 Boost converter block ........................................................................................................ 37 Simulation results ....................................................................................................................... 43 4.1 Results of the Solar Cell ...................................................................................................... 44 4.2 Results of the Solar Panel ................................................................................................... 50 4.3 Results of the MPP tracker ................................................................................................. 51 4.4 Results of the Boost Converter ........................................................................................... 55 Conclusion ................................................................................................................................... 60 5.1 Conclusion ......................................................................................................................... 61 Future work ................................................................................................................................. 62 6.1 Future work ....................................................................................................................... 63 References .................................................................................................................................. 64 7.1 References ......................................................................................................................... 65 Annexes ...................................................................................................................................... 66 Table of Figures Figure 1. Cell structure [11] ............................................................................................................ 8 Figure 2. Ideal solar cell. ................................................................................................................ 9 Figure 3. Equivalent solar cell circuit. ........................................................................................... 10 Figure 4. I-V cell characteristic [2]. ............................................................................................... 11 Figure 5. P-V cell characteristic [2]. .............................................................................................. 12 Figure 6. I-V characteristics increasing G [2] ….. ........................................................................... 13 Figure 7. P-V characteristics increasing Tc [2]… ................................................................. ..………..13 Figure 8. Characteristic resistance of a cell ................................................................................... 13 Figure 9. Perturb and Observe algorithm [2] ................................................................................ 15 Figure 10. Incremental conductance algorithm [2] ....................................................................... 16 Figure 11. Perturb and Observe P-V graphic [2] ............................................................................ 17 Figure 12. Incremental conductance P-V graphic [2] ..................................................................... 17 Figure 13. Sawtooth wave and PWM graphic [8]. ......................................................................... 19 Figure 14. Circuit of a boost converter [3] .................................................................................... 20 Figure 15. Circuit of a buck converter [3] ...................................................................................... 21 Figure 16. Circuit of a buck-boost converter [3] ............................................................................ 22 Figure 17. Non-detection zone graphic [2] ................................................................................... 24 Figure 18. H4 inverter topology [9] .............................................................................................. 25 Figure 19. H5 bridge, topology from SMA [9]. .............................................................................. 25 Figure 20. HERIC topology [9]. ...................................................................................................... 26 Figure 21. Simulink model of the solar cell ................................................................................... 31 Figure 22. Simulink model of the solar panel ................................................................................ 33 Figure 23. Simulink model of the MPP block. ................................................................................ 34 Figure 24. MATLAB script of the MPP tracker ............................................................................... 36 Figure 25. Simulink model of the boost converter circuit .............................................................. 38 Figure 26. Circuit of the boost converter when M1 ON and M2 OFF ............................................. 38 Figure 27. Circuit of the boost converter when M1 OFF and M2 ON ............................................. 39 Figure 28. Graphic of the inductor current [3]. ............................................................................. 40 Figure 29. Script of the boost converter ....................................................................................... 42 Figure 30. Parameters of the solar cell ......................................................................................... 45 Figure 31. I-V characteristic of the cell ......................................................................................... 46 Figure 32. P-V characteristic of the cell ........................................................................................ 46 Figure 33. Solar cell scope of the voltage, current and power ....................................................... 47 Figure 34. Different Irradiances I-V characteristic of the cell ......................................................... 48 Figure 35. Different Temperatures P-V characteristic of the cell ................................................... 49 Figure 36. I-V characteristic of the panel ..................................................................................... 50 Figure 37. P-V characteristic of the panel ..................................................................................... 50 Figure 38. Constant voltage of the signal builder ......................................................................... 51 Figure 39. Variable current of the signal builder ........................................................................... 51 Figure 40. Duty cycle when V constant and I variable ................................................................... 52 Figure 41. Variable voltage of the signal builder .......................................................................... 52 Figure 42. Constant current of the signal builder .......................................................................... 52 Figure 43. Duty cycle when V variable and I constant ................................................................... 53 Figure 44. Graphic of the solar panel voltage and duty cycle ........................................................ 53 Figure 45. Graphic of the boost converter when V and duty cycle are constant values ................. 55 Figure 46. Graphic of the boost converter when PV connected with a resistor ............................. 56 Figure 47. Graphic of the second boost when V and duty cycle are constant values ..................... 57 Figure 48. Voltage of the PV connected to the boost .................................................................... 58 Figure 49. Boost Voltage when the solar panel is connected ........................................................ 58 Figure 50. Boost voltage when MPP and PV connected ............................................................... 59 Figure 51. Duty cycle of Boost-MPP-PV system ............................................................................ 59 1 Introduction CHAPTER 2 – THEORETICAL PART 8 In the next figure the movement of the electrons and holes can be seen that are moving in a single direction. Figure 1. Cell structure [11] A solar cell can also be made of Cadmium Telluride (CdTe) that is made up of thin cells. Enterprises are improving the efficiency of these thin panels as seen a couple months ago when an enterprise achieved 18.7% of efficiency [7]. The problems of this cell are the cadmium toxicity, lower efficiency (around 15% manufacturing), and the lack of abundance of tellurium on Earth (although the source may be found under the sea). Apart from these problems, the cells have a good advantage such as lower costs of manufacturing than silicon and good absorption of sunlight [3]. The Photovoltaic cells can be classified in 3 groups depending on the silicon: - Monocrystalline silicon cell: their performance is 14% - 18%. - Polycrystalline silicon cell: their performance is 12% - 14%. - Amorphous silicon cell: their performance is 8% [6]. CHAPTER 2 – THEORETICAL PART 9 2.1.2 Solar cell modeling 2.1.2.1 Ideal Solar Cell The structure of a solar cell is similar to the one of the diode. When the cell receives the irradiance of the sun, it acts like a current generator whose value increases depending on the quantity of light absorbed [6]. The ideal solar cell can be seen in figure 2. The current of an ideal solar cell can be described with the following equation: Figure 2. Ideal solar cell. The equation that describes the I-V characteristics of most of the solar cells: Where: - Il: photogenerated current - Io: reverse saturation current - q: electron charge - V: output voltage - m: diode ideality factor - k: Boltzmann’s constant - T: Absolute temperature  "  "  " – "  (2.1)           1  (2.2) CHAPTER 2 – THEORETICAL PART 10         (2.3) The modeling of the solar panel in this project will be designed in Simulink using subsystems, so at the end of the design it will be possible to change the temperature of the cell and irradiance of the sun to see the I-V and P-V characteristics of the panel. This panel, not only can change the temperature and irradiance but also the number of cells that the panel has. This will be explained and described in Chapter 3. 2.1.2.2 Solar cell with series and parallel resistance The equivalent circuit of a solar cell will be approximately the same circuit as the ideal cell but now counting the losses that are in the circuit as series resistance and parallel resistance. Figure 3. Equivalent solar cell circuit. The mathematical model that described the behavior of one non ideal solar cell is given by the next expression: Where: - Il: photogenerated current - Io: reverse saturation current - V: output voltage - I: output current               1       (2.4) CHAPTER 2 – THEORETICAL PART 11 - Rs: series resistance. It is the sum of several components of the material themselves and the effects of design and internal manufacturing of the cell, semiconductor resistance and the resistance of the front metal grid [1]. - Vt: this is the thermal voltage. Vt is equal to k (Boltzmann constant;  1.381#10 %&' J/K) by the temperature of the cell in Kelvins divided by q (magnitude of the electrical charge of the electron; (1.602#10 %+, C). The thermal voltage at a temperature of 25ºC is Vt = 25.7 mV [1]. - Rp: parallel resistance. It is mainly due to leakage of current by the side surfaces. This could also be caused by metallic short circuits or diffusion peaks from dislocations or grain boundaries [1]. 2.1.3 Solar cell characteristics The characteristics of a solar cell can be seen in a nonlinear curve. The parameters that determine the performance of a solar cell are reflected in the I-V and P-V curves, where “Isc”, ”Voc”, “Im”, “Vm”, “Pm” and “MPP” can be detected. If the solar cell is acting in ideal conditions, that means the irradiance is the maximum (1000 W/m2), the cell temperature is the same as the ambient temperature (25 ºC), and the diode ideal factor is 1, the cell will start in Isc and finish in Voc. If that is not the case it will start lower than Isc and finish before Voc. The characteristics of a solar cell can be seen in the next figures. Figure 4. I-V cell characteristic [2]. CHAPTER 2 – THEORETICAL PART 12 Figure 5. P-V cell characteristic [2]. The short circuit current “Isc” is the current that is obtained from the cell when the voltage at its terminals is 0V. This is the maximum current that can be obtained from this solar cell. The open circuit voltage “Voc” is the voltage obtained when the cell current is 0A. This is the maximum voltage that can be extracted from this solar cell. The maximum power point “MPP” is defined by the product of the maximum current “Im” and the maximum voltage “Vm” [2]. - . "  " . ∗ 0. (2 .5) CHAPTER 2 – THEORETICAL PART 13 The characteristics of the cell can be changed, depending on the irradiance, the temperature and age of the cell. Decreasing the irradiance decreases the current as shown in Figure 6, and increasing the temperature decreases the voltage also shown in Figure 7. Figure 6. I-V characteristics increasing G [2] Figure 7. P-V characteristics increasing Tc [2] To know where the MPP is on the cell, a load has to be applied on it. After some time, the right R may be found. When the straight line of the resistor crosses the MPP (where the knee of the curve is) that is called the “characteristic resistance of the cell”. Figure 8. Characteristic resistance of a cell 04812 16 20 24 28 0 0.5 1 1.5 2 2.5 3 Panel Voltage Panel Current Increasing Luminance 0 4 8 12 16 20 24 28 0 8 16 24 32 40 56 Panel Voltage Power 48 CHAPTER 2 – THEORETICAL PART 14 2.2 MPP tracker The main function of a MPP tracker is to adjust the output voltage of the solar panel so that it can extract the maximum power. The MPP tracker is designed to track the maximum power point from a solar panel which external conditions are unknown for the MPP [1]. The characteristics of the solar panel are changing every moment. Different irradiance and temperature will give a different MPP. So the MPPT will have to search where the solar panel is working and in which direction it has to move so it reaches the maximum power point. This will be done with an algorithm that will know which changes are necessaries [1]. A MPP tracker algorithm is a finite operation of steps that requires optimizing and controlling de maximum power point of the solar panel. A MPP tracker reads the input voltage and the input current. Additionally, within its internal circuit, there are some changes that modify the input impedance and that make a change in the voltage and current at the input of the MPP. Also a MPP tracker has to be careful with the speed adaptation due to the solar panel changing conditions [1]. There are many types of MPPT today, but the most used are Perturb and Observe, and Incremental Conductance. In this project both of them will be explained and Perturb and Observe is the one used in this project because it is the most used in industry and easier to implement. 2.2.1 Perturb and Observe The efficiency of a solar panel can be improved by using a hill-climbing MPP tracker such as Perturb and Observe. This is an algorithm that does not need to know the previous characteristics of the solar panel or the cell temperature and irradiance. It is an easy method to implement with analogue and digital circuits [2]. The algorithm perturbs the point where the solar panel is working by increasing or decreasing the duty cycle by a small amount and then measures the output of the solar CHAPTER 2 – THEORETICAL PART 15 panel before and after the perturbation. If the power increases, the algorithm perturbs in the same direction otherwise it will perturb in the opposite direction [3]. The Perturb and Observe algorithm will increase the output voltage if the difference between the input voltage and the output voltage is positive and the power difference is also positive, or if both voltage difference and power difference are negative. Otherwise it will reduce the voltage. This can be seen in the following figure. In figure 9, the Perturb and observe algorithm is explained in a graphic way, so it is easier to understand and follow the path to know how to find the maximum power point. Figure 9. Perturb and Observe algorithm [2] Sample Inputs V=Vpv, I=Ipv Calculate Power P(n) = V * I Increment VmppOut Decrement VmppOut Decrement VmppOut Increment VmppOut P(n) > P(n-1) V > V(n-1) V > V(n-1) Return V(n-1) = V P(n-1) = P(n) Yes No Yes YesNoNo CHAPTER 2 – THEORETICAL PART 16 2.2.2 Incremental Conductance The Incremental Conductance algorithm has a more complex method than the Perturb and Observe algorithm. This method measures incremental changes (dI/dV) to predict the result of voltage changes. This one more rapidly detects the change that the solar panel has, compared to the Perturb and Observe algorithm. In the incremental conductance method, the array terminal voltage is always adjusting according to the MPP voltage. It is based on the incremental and instantaneous conductance of the solar panel. When 12 1 is equal to 0 then it’s in the MPP. The MPP increases when it goes to the left and decreases to the right of the MPP. This can be seen in figure 10 [2]. Figure 10. Incremental conductance algorithm [2] Sample Inputs V=Vpv, I=Ipv dI = I-I(n-1) dV = V-V(n-1) Increment VmppOut Decrement VmppOut Decrement VmppOut Increment VmppOut dV=0? dI/dV = -I/V dI=0? dI>0?dI/dV > -I/V? Return I(n-1) = I, V(n-1) = V Yes No Yes Yes No No Yes No Yes No 12 1  1 3  ∗  4 1   5 0 1 1  6  5 0 7  7  (2.6) CHAPTER 2 – THEORETICAL PART 17 2.2.3 Differences between P&O and Incremental conductance For perturb and observe method: The voltage of reference is all the time perturbed, and changes the power that is observed. The perturbations will make this algorithm know which direction it has to go whether it increases or decreases. The voltage is oscillating near the maximum power point. This can be seen in figure 11[2]. Figure 11. Perturb and Observe P-V graphic [2] For incremental conductance: It is working with slopes. If the slope is zero then is at the MPP, positive will be at the left side of the MPP and negative to the right side. The incremental conductance method, once it reaches the MPP, it will maintain there until there is a change in AI. That means an atmospheric change and that leads to another maximum power point. This can be seen in the following figure 12 [2]. Figure 12. Incremental conductance P-V graphic [2] CHAPTER 2 – THEORETICAL PART 24 2.4.3 Grid synchronization To synchronize the inverter to the grid, the inverter has to verify some conditions because some changes can occur on the grid such as the connection and disconnection of loads, harmonics injected by some equipment, faults,….. The quality of the grid can affect the voltage and current of the equipment connected to the grid. Thus, the grid parameters including phase and magnitude must be measured at all times to ensure that a correct connection can be made [2]. 2.4.4 Grid detection To know and detect the grid status, this can be made by monitoring the voltage and the frequency of the grid. If there is a fault on the grid, the voltage and the frequency will drift. Nevertheless, there is a non-detection zone where the voltage and frequency cannot be detected by the inverter. With this problem, the inverter cannot detect if the grid is there or not [2]. There are different zones that the inverter can detect. When the AQ is positive, there is an over frequency, but if it is negative there is an under frequency. Additionally if the AP is positive there is an over voltage. Otherwise there will be an under voltage. This can be seen in figure 17: Figure 17. Non-detection zone graphic [2] CHAPTER 2 – THEORETICAL PART 25 2.4.5 Examples of inverters - The first example will be the H4 topology. This one is the simple one, and it was explained in this chapter. Figure 18. H4 inverter topology [9] - The second example will be the H5 topology. This topology improves the efficiency of the inverter. This one has four switchers S1, S2, S3, S4 and the DC-bypass switcher. The peak of efficiency is around 98%. The H5 topology is based on the concept of disconnecting the Solar panel from the grid during freewheeling periods. This topology is patent by SMA [9]. Figure 19. H5 bridge, topology from SMA [9]. CHAPTER 2 – THEORETICAL PART 26 - The third example is the H6 topology, or HERIC. HERIC means Highly Efficient and Reliable Inverter Concept. With this structure it can avoid potential fluctuations on the DC terminals of the solar panel by disconnecting from the grid. As the name says, it is very efficient around the 98-99% [9]. Figure 20. HERIC topology [9]. 27 Implementation CHAPTER 3 - IMPLEMENTATION 28 In this chapter, the Simulink model will be described and explained. First, there will be a description of the process of making the solar cell and implementing a factor into the equations so that the number of series cells can be changed in the main solar cell block. The formulas that have been used in the PV cell block will also be explained. Then, the algorithm used in this project for the MPPT will be described. The MPP algorithm was written with a script in MATLAB. And the third point will be the boost converter block, explaining the calculus behind the circuit. 3.1 PV cell block The solar cell has been designed to depend on two variables: irradiance and cell temperature. It has been made with Simulink. A lot of subsystems are present inside the solar cell block. It contains different blocks describing the solar cell equation. The problem that the equation 2.4 has is that it does not depend directly on the irradiance or cell temperature. The photogenerated current (IL) and the reverse saturation current (Io) are not components that can be measured directly. That is the reason why some changes have to be made. To be able to use the solar cell equation some approximations are necessary: - First of all, the parallel resistance can be neglected in the equation due to the parallel resistance being higher than the operation of the voltage of the cell plus series resistance for current of the cell. In this Simulink model this equation has been used because it will get more accuracy at the end of the circuit and it will have a more realistic behavior [1]. If " " " IJ ≫ " 3 0 5  ∗ IL ) then    ∗ M  = 6 0 (3.1) CHAPTER 3 - IMPLEMENTATION 29 - Secondly, the photogenerated current (IL) and the short circuit current (Isc), can be considered equal. The photogenerated current is equal to the short circuit current multiplied by the irradiance and divided by 1000 (that is the earth’s surface irradiance and also the optimal for solar cell). And when the voltage in the output on the solar cell is 0, it’s working on the short circuit region; 6LN [1]; Supposing that the solar cells are: - The third point is when the solar cell is in open circuit the current is equal to 0. The resulting equation is [1]: Assuming that the short circuit current is much bigger than the reverse saturation current: And changing this expression in the equation 3.4 and assuming 3 OP  4" is greater than 1, the solar cell equations change to [1]: The Simulink model is based on the mathematical model of the equation 2.4. This can be written as: The value Isc(g,Tc) is equivalent to iL that corresponds to the short circuit current and G,Tc are the irradiance and cell temperature. To be able to calculate Isc(g,Tc) and Voc(g,Tc), they have to be extrapolated with the next equations so that they become standard test conditions (STC). The STC are conditions where the solar cells are certified and pass through measurement so they can be sold [1]. 0N " > "  ∗ IL (3.2) 0N = 0 0= ∗ G ( R : + 1 ) = 6 0= ∗ G ( R : ) (3.3)  = Isc ∗  ( % OP  ) (3.4) JV = LNW − LNW ∗  ( XY Z OP[  [ ∗ [  ) (3.5)  =  −  = LN ( W , ]N ) − LN ( W , ]N ) ∗  ( XY Z OP ( [ , P )   ∗  ^ ∗  ∗  _ ) (3.6) CHAPTER 3 - IMPLEMENTATION 30 Where: - Isc(g,Tc): Short circuit current depending on the irradiance and cell temperature. It’s the STC short circuit current. - Isc: It’s the short circuit current of the solar panel - G: Irradiance of the sun. It is measured in W/m2. The maximum irradiance is 1000 W/m2. - `N: Coefficient of the current variation with the cell temperature. The value of this coefficient can be 1 mA/ºC if there is no measurement. - Tc: It’s the cell temperature. Measured in (ºC). - Tamb: Ambience temperature. It will be taken normally as 25 ºC for measurements. - Voc(g,Tc): Open circuit voltage depending on the irradiance and cell temperature. It’s the STC open circuit voltage. - Voc: It’s the open circuit voltage of the solar panel. - aN: Coefficient of the voltage variation with the cell temperature whose value is -2.3mV/ºC Now that the Isc(g,Tc) and Voc(g,Tc) have been extrapolated to standard test conditions, another component of the equation 3.6 can be calculated. That is the series resistance. The value of the series resistance can be calculated using the Green’s approximation [1]. The Green’s approximation determines Rs from the maximum power conditions. It is a good and accurate method [1]. First, open circuit voltage has to be normalized for the ideal form factor with the following equation: VN  0N 0= ∗ . & c (3.9) LN ( W , ]N ) = Isc ∗ d +eee + `N ∗ ( ]N − ]f.g ) (3.7) 0N ( W , ]N ) = 0N + aN ∗ ( ]N − ]f.g ) + 0= ∗ . & ∗ ( G d +eee ) (3.8) CHAPTER 3 - IMPLEMENTATION 31 This equation works for the ideal form factor “FFo” if voc > 15V. The equation for the ideal form factor is: And the real form factor: Where: - Im: It’s the current when the solar cell is working in the MPP. - Vm: It’s the voltage when the solar cell is working in the MPP. These measurements are in standard test conditions measured in a lab. These values are provided by the manufacturer [1]. After these equations, Rs can be calculated with the next expression: The Simulink model of the solar cell formed with the described equations above is the following one: Figure 21. Simulink model of the solar cell hh  i:R % j; 3 i : R  e . k& 4 i:R  + (3.10) hh  l ∗ l R ∗ :R (3.11) IL  :R ∗ 3 + % mm mmO 4 R (3.12) CHAPTER 3 - IMPLEMENTATION 32 The whole model is made with Simulink. Each element of the equation is with subsystems. The problem that the solar cell has is that the voltage and the current are inside the equation that will lead to the creation of a loop on the system. A current generator is used so the loop is partially fixed. The loop that the solar cell has can be solved with the Newton - Raphson Method. The Newton-Raphson method is an iterative method that allows an approximate solution for an equation like f(x) = 0. The method starts with an initial estimation of the solution with a value x0. Then it builds a sequence of approximations repeating the method. The more it is repeated, the more accurate the solution is. Because of the current generator, the solar cell model finishes with two terminals. These terminals are the positive and negative. In Simulink a model can’t be simulated if the circuit is open. For this solar cell, a variable resistor has to be placed so the I-V and P-V characteristics can be seen. The graphics and results of the solar cell will be explained in chapter 4. CHAPTER 3 - IMPLEMENTATION 33 3.2 PV panel block To be able to build a solar panel in Simulink, a lot of solar cells in parallel and series have to be put together so the current and voltage increase. Cells in series will increase the voltage and cells in parallel will increase the current. After knowing which elements of the equation 3.6 are going to change and depending on how many cells the panel has in series or parallels, it will be easier to implement a factor so the Simulink model can work as a solar panel. The changes that have to be carried out are: - One factor that will increase the solar panel series cells. That means this factor has to change the voltage and the series resistance. On this Simulink model the factor is called Ns (number of series cells). This factor was implemented in the different elements of the equation 3.6. Voc(g,Tc) has the Ns factor due to it needing to change the voltage. The Rs equation also has the Ns factor because the losses of the series resistance will change depending on how many series cells are. Also in the equation 3.6 it will be multiplying Vt. - The second factor that will increase the solar panel parallel cells. This factor has to change the current. In this Simulink model this factor has not been added because in parallel only two solar panels have been used. So by only putting the PV cell blocks in parallel, the current increases. The next figure represents a solar panel. Two arrays block are in parallel and inside of each block is the same number of series cells. Figure 22. Simulink model of the solar panel CHAPTER 3 - IMPLEMENTATION 40 This equation is easier to understand with figure 28. Figure 28. Graphic of the inductor current [3]. Now, the inductor-volt second balance has to be applied. The inductor relation over a period is [4]: But over a cycle in steady state period the average inductor voltage is zero V3=4 ris 0∶ The result of applying the inductor-volt second balance is the equation 3.25. If the circuit is been calculated or analyzed ideally, then the resistor Ron is not on the MOSFET. So the equation will result [4]: Ideal MOSFETS 00JV 18 c (3.26) After solving the equations, now it is possible to determine the inductor current ripple that changes from the minimum current to maximum current for 0v=v8]L. V 3 = 4  w ∗ 1Ej 3 D 4 1 D (3.21) " 3 0JV  F ∗ 3 I 5 IG 4 4 ∗ 8]L 5 3 0JV  0  F ∗ 3 I 5 IG 4 4 ∗ 3 1  8 4 ∗ ]L  0 (3 .22) 0JV0508F3I5IG40 (3.23) 0JV 031845  3+%A4 3I5IG4 (3.24) 0  i 3 + % A 4  xOy  3 z Z { 4 (3.25) CHAPTER 3 - IMPLEMENTATION 41 This can be calculated seeing the line-segment in the previous figure 28. After reaching this point, with this equation and implementing this to "F.FG|0, the minimum inductance is possible to calculate [4]. The equation 3.32, determines the minimum value of inductance so the converter operates in continuous conduction mode. After explaining the circuit of the boost converter, it is easier to understand the second boost created with a MATLAB script. Figure 29 is the script implemented in MATLAB. 2 ∆ F  3 L J  " p " = q  " FG<N=~ " N<~~G= 4 ∗ 8]L (3.27) ∆F  + & ∗30JV  3+%A4 3I5IG44∗8]L (3.28) ∆ F  A & H ∗ 3 0JV  3j:;4  3 + % A 4 4 (3.29)  .FG | 0 ;   ∆ F | 0 (3.30)  3+%A4 | A &H ∗30JV 3j:;4 3+%A4 4 (3.31) w.FG | A & H ∗ 3 0JV 3 1  8 4 I  0 3 I 5 IG 4 4 (3.32) CHAPTER 3 - IMPLEMENTATION 42 Figure 29. Script of the boost converter As it can be seen, the equations used in this boost are the same ones that were in the other boost. In this boost, it is necessary to implement the d created by the MPPtracker by converting the signal with a PWM. To be able to implement this model, it is necessary to program all the values of the inductor, capacitor and the resistances of it. Then the equations are written in MATLAB language. These equations are: - The equation of the output boost voltage can be written with the branch of the capacitor or the equation obtained with the inductor-volt second balance 4.25. - Then, equaling the current from the solar panel and the inductor of the boost. - The other equation is the current passing through the capacitor. The equation is equal to 4.16 but only changing the 0I c with iout. - The last equation is the inductor voltage. This equation is obtained by the assumption of the first MOSFET is on and the second MOSFET off. After explaining how the different parts of the project were implemented in Simulink, the results of the graphics of them have to be explained. 43 Simulation results CHAPTER 4 – SIMULATION RESULTS 44 In this chapter, the results of the simulation in Simulink will be explained. First, there will be an explanation why the solar cell has different results depending on the irradiance and the temperature. Then, the understanding of the results of a complete solar panel will be described. After that, there will be an explanation of the duty cycle generated by the MPP tracker with and without a solar cell. And the last point will be the description of the different circuits of the boost converter. The different circuits are: the boost without a solar panel or MPP tracker, then the boost with a constant duty cycle implementing the solar cell. The third one will be with the MPP tracker. And after these three circuits, a resistance is implemented in the solar cell so a constant voltage is created and the graphic will be explained. 4.1 Results of the Solar Cell First of all, to be able to get the result, it is necessary to choose the solar panel that is going to be used. In this project the panel Shell Power Max Ultra 175-PC has been used. More information about the solar panel will be put in the annexes at the end of the project. The parameters of the panel that are going to be programed in Simulink are: Short-circuit current (Isc), open-circuit voltage (Voc), MPP current (Im), MPP voltage (Vm), parallel resistance (Rp), Nº series cell (Ns), temperature ambient (Tamb), standard test conditions irradiance (G0) and ideality diode factor (m). The solar cell is implemented so it is possible to change the parameters of it by just a step. By clicking twice on the solar cell, Simulink will open a new window with the programed information. There, it will be possible to change the parameters. In the next figure the parameters are shown from a picture of the solar cell. Those values are for one cell. Due to the panel having 72 series cells, the voltages have to be divided by 72 and the value is for one cell. Only the voltage has to be divided, not the current. CHAPTER 4 – SIMULATION RESULTS 45 Figure 30. Parameters of the solar cell With these parameters, it will be possible to simulate them on the PV cell. By putting a constant irradiance (G) and a constant temperature (T), the solar cell will give the I-V and P-V characteristics of the cell. CHAPTER 4 – SIMULATION RESULTS 46 These graphics can be seen in figure 31 and figure 32. Figure 31. I-V characteristic of the cell Figure 32. P-V characteristic of the cell CHAPTER 4 – SIMULATION RESULTS 47 The G and Tc chosen were for an ideal behavior for the solar cell. So it is possible to see on the graphic the values of Isc and Voc of this cell. Those values are Isc = 5.43 A, Voc = 0.6194 V. With the block scope it is possible to calculate I maximum and V maximum, by searching for the maximum power point in the graphic of the cell. The results of the scope are: Figure 33. Solar cell scope of the voltage, current and power Where the maximum power point is, it doesn’t mean that the current and voltage are maximum too, but those are the MPP values for that irradiance and temperature. CHAPTER 4 – SIMULATION RESULTS 48 After seen how the cell acts with the ideal parameters, it is possible to see how it acts with different irradiances and temperatures as shown in the next figures. The cell is going to be first with different irradiances and a constant temperature that will be 25 ºC. The irradiances are 400, 600, 800, 1000 W/m2. And then the cell is going to be studied with different temperatures and a constant irradiance that will be 1000 W/m2. The temperatures are 25,40,60,70 ºC. In the figure 34, it is possible to see that the lower the irradiance, the lower is the characteristic of the cell. And with a higher irradiance, the graphic gets higher. Figure 34. Different Irradiances I-V characteristic of the cell And in the figure 35, it is changing with the temperature. The higher the temperature is, the characteristics of the cell are lower. The best moments are when the cell is acting with a 25 ºC temperature. CHAPTER 4 – SIMULATION RESULTS 49 Figure 35. Different Temperatures P-V characteristic of the cell So, as seen in the theoretical part when the irradiance is decreasing, the current also decreases. And, when the temperature increases, the voltage decreases. This conclusion can be seen in the graphics and also in the equations. In the equation 3.7, if the temperature is constant and the irradiance is lower than 1000, then the Isc gets lower, as it can be seen ( LN3W,]N4LN∗ d +eee 5⋯ ). In the equation 3.8, if the irradiance is constant and the temperature is getting higher, the difference between Tc-Tamb is multiplied by the constant aN that is negative, then the Voc (g,Tc) decreases. After studying the function of the cell, the next point will be to study the panel. CHAPTER 4 – SIMULATION RESULTS 56 With this block, the loop is not going to appear and it is possible to simulate the circuit. The results that the boost shows don’t make sense. The voltage of the solar panel is not the one it should be so at the end, the boost doesn’t work as it should be. This circuit can only be simulated with this panel by connecting a resistor to the panel. The panel with the resistor will generate a constant voltage and current and with the controlled voltage source block in Simulink, the voltage is converted to a signal that can be connected with this boost. The results that this circuit gives are normal and expected. The boost is increasing the voltage and then it will remain constant at a certain value that will be controlled by the duty cycle. The simulation is carried out with a 1.5 Ohm resistor connected to the solar panel. The voltage that the panel will give is 16.29 V and a constant duty cycle is connected to the boost with the value of 0.5. These values can be seen in the following graphics. Figure 46. Graphic of the boost converter when PV connected with a resistor So it is possible to see that the voltage has increased from 16.29 V to the values in between 31.5 and 33.5 V. CHAPTER 4 – SIMULATION RESULTS 57 The second boost converter, the one implemented with a MATLAB script, has to be studied too as the first one. By connecting constant values to the boost, it will be possible to see the behavior of the boost converter. To this boost converter a voltage of 15 V and duty cycle of 0.5 have been connected to carry out this simulation. The voltage that it should have is 30 V. The next figure will show the behavior of the second boost converter connected with constant values of voltage and duty cycle. Figure 47. Graphic of the second boost when V and duty cycle are constant values As it can be seen in figure 47, the voltage that this boost converter gives is 30 V as expected. After studying the boost converter with constant values, the solar panel will be connected. By connecting the solar panel it will be possible to test out the behavior of this boost versus a photovoltaic system. The solar panel will show the voltage of it. First, the voltage will increase and until a certain point, it will remain constant. The duty cycle will be constant with a value of 0.5. With these values, the boost will have to increase the voltage of the solar panel all the way until it becomes constant and it will be possible to see the final boost result. CHAPTER 4 – SIMULATION RESULTS 58 The next figures will show the graphics of the boost converter connected with the solar panel. Figure 48. Voltage of the PV connected to the boost Figure 49. Boost Voltage when the solar panel is connected CHAPTER 4 – SIMULATION RESULTS 59 As the figure shows, the boost converter was increasing the voltage of the solar panel all the time until the voltage remains constant in the solar panel, in that moment the boost converter stops increasing and remain constant too. The last step is to connect all the three parts of the project, the solar panel, the MPP tracker, and the boost converter. In this step, only the irradiance and the temperature will remain constant. The voltage and current will be connected to the MPP to generate the duty cycle to obtain the maximum efficiency of the panel. This duty cycle and the solar panel voltage will be connected to the boost that will have to increase the voltage depending of the duty cycle. These are the results that the system gives. Figure 50. Boost voltage when Figure 51. Duty cycle of Boost-MPP-PV MPP and PV connected system The results obtained in this system are not good. The MPP doesn’t move, but rather it stays in 0.5, so the duty cycle that is giving to the boost converter is just a normal value but not the optimal one. 60 Conclusion CHAPTER 5 - CONCLUSION 61 5.1 Conclusion Through the study and development of this photovoltaic system, I gained a good knowledge of the solar energy and its components. Not only was knowledge gained about solar energy, but also in programming skills through the use of MATLAB/SIMULINK. At first, it’s a complex program due to the programming skills required, but then it is a really useful and powerful tool for engineers to simulate all kinds of systems. The difficult phases of the project have made me work harder to ultimately get a SIMULINK working model. There were difficult parts of the process that were not easy to solve. For example, there was a problem with the solar cell loop that was generated by the solar cell characteristics. With this problem that the cell has, there was not much practical information about how to solve it. The solar energy is relatively new and there is just general information about it. It is a really good energy with a lot of areas where it can be improved. This could be the energy of the future and can be installed everywhere. For that, many studies have to be carried out to improve this energy that will be needed in the future. 62 Future work CHAPTER 6 – FUTURE WORK 63 6.1 Future work Due to the time constraints, a few parts of the project couldn’t be finished. The model needs small parts to be improved. The solar panel can be modified to improve its behavior. After spending a lot of time doing and designing the solar cell, at the end the cell only depends on the irradiance, cell temperature, and the characteristics of the cell. There are not many projects where that can be seen. The only improvement in this part would be to add a block to remove the loop. The loop can be solved too by modeling a cell with MATLAB code so the NewtonRaphson method can be implemented easier. Focusing on the boost converter, another control can be implemented so the voltage at the output of the boost can be fixed like the photovoltaic systems have. The next part of the project was to feed the current converter on the inverter to the grid. To carry this out, a block in Simulink can be implemented to act like an inverter. That block is called Universal Bridge. With this block, a buck-boost converter can be made. Apart from the inverter, the synchronization control to be able to feed the system to the grid had to be designed 64 References CHAPTER 7 - REFERENCES 65 7.1 References [1] D. R. Orduz Marzal, “Contribución a los sistemas de control de potencia micro-distribuida en edificios photovoltaicos”. Madrid, Jul. 2009. [2] Texas Instruments, “Introduction to PhotoVoltaic (PV) Systems”. Solar Workshop. [3] V. Quaschning, “Understanding Renewable Energy Systems”. London, 2005. [4] S. Christian, “Fundamental of Boost Converter”. 2012. Retrieved from Eprimes blog. http://eprimes.wordpress.com/2012/06/30/fundamental-of-boost-converter/ . [5] J. Francisco Jiménez Ortiz, “Estudio y simulación de sistemas de conversión Fotovoltaica eléctrica mediante Matlab – Simulink”. Barcelona, Jan. 2009. [6] A. Castaño Vicente-Gella, “Estudio y simulación de sistemas de generación Fotovoltaica utilizando MATLAB/SIMULINK”. Valencia, Jun. 2010. [7] “First solar sets new world record for CdTe solar cell efficiency”. First Solar, Inc. 2013. Retrieved from First Solar website: http://investor.firstsolar.com/releasedetail.cfm?ReleaseID=743398. [8] D. Maksimovic, “Modeling and Control of Power electronic systems”. PPT. [9] J. Wang, B. Ji, J. Zhao, J. Yu, “From H4, H5, to H6 – Standardization of Full-Bridge Simple Phase Photovoltaic Inverter Topologies without Ground Leakage Current Issue”. Nanjing, 2012. [10] NXP, “Buck converter for SSL applications”. 2011. [11] How Stuff Works, “How Solar Cells Work”. 2006. Retrieved from Howstuffworks website: http://home.howstuffworks.com/solar-light2.htm .