1. © A. Kwasinski, 2014 ECE 2795 Microgrid Concepts and Distributed Generation Technologies Spring 2015 Week #2

2. © A. Kwasinski, 2014 Photovoltaic (PV) modules are made by connecting several PV cells. PV arrays are made by connecting several PV modules. Although the sun will eventually die as a white dwarf star in about 4.5 Billion years, solar power can be considered a renewable source of energy because we can expect that for the next couple of billion years the sun will still radiate power without making the Earth inhabitable. Solar power is radiated through space. Solar power is generated by nuclear fusion. Light propagation can be represented through waves or through particles (dual representation). To represent electricity production in PV cells, the particle (photon) representation is used Photovoltaic modules

3. © A. Kwasinski, 2014 Photons are created at the center or the Sun. It takes an average of 10 million years for the photons to emerge (they collide many times in the Sun interior). Then it takes 8 minutes for a photon to reach the Earth. Fusion reactions: Step 1: ( represents an atom of deuterium = an hydrogen isotope formed by a proton and a neutron, a positron ( p + ) or antielectron is an electron with a positive charge, a neutrino n 0 are very low mass- no charge elementary particles). This reaction requires extreme temperatures and pressures to bring two protons so close (< 10 -15 m) that the repulsion force between them disappears. Step 2: where γ represent a photon. Step 3.1: Step 3.2: where is tritium an hydrogen isotope formed by 2 neutrons and a proton Photons’ Journey into Electricity

4. © A. Kwasinski, 2014 Fusion reactions (continue): Step 4.1: Step 4.2: The overall reaction is: This reaction releases 26 MeV All photons are created equal. So why photons leaving the sun have different energy (as indicated by their different frequency in the dual wave model)? The emitted photons have high energy. This energy is mostly lost in collisions with atoms as the photons leave the sun. This reaction can only occur due to the high pressure generated by the mass contraction at the Sun’ s center. The Sun is mostly composed of hydrogen (73 %) and Helium (25 %). These proportions are changing. Eventually the sun will start the fusion process of heavier elements. Photons’ Journey into Electricity

5. © A. Kwasinski, 2014 Ideal radiation of energy is described by the black body radiation. Black bodies radiate energy at different wavelengths as indicated by The Sun closely behaves like a black body at a temperature T=5800 K (the Sun’s surface temperature) http://en.wikipedia.org/wiki/Image:EffectiveTemperature_300dpi_e.png Total blackbody radiation rate (area under the curve): E=AσT 4 For the Sun it equals 1.37 kW/m 2 Wavelength for the maximum: For the Sun it approximately equals 0.5 μm Photons’ Journey into Electricity

6. © A. Kwasinski, 2014 Finally, the photons reach the Earth. US Solar Insolation Map: NREL Photons’ Journey into Electricity

7. © A. Kwasinski, 2014 The incident power has 3 components depending on the final photons path. Reflected radiation Direct-beam radiation Diffuse radiation Photons’ Journey into Electricity

8. © A. Kwasinski, 2014 Direct-beam radiation: The extraterrestrial solar insolation is given by This is the solar insolation before entering the Earth’s atmosphere. In the equation, SC is the solar constant an equals 1.37 kW/m 2 and n is the day number (January 1 is day #1). The day number takes into consideration that the Earth-Sun distance changes through the year. The solar insolation is attenuated as it passes through the atmosphere. The portion that reaches the earth’s surface. where A and k are constants and m is the air mass ratio that takes into account that the sun’s beam path length through the atmosphere changes with the sun relative position with respect to the earth surface at the location where the analysis is made. Photons’ Journey into Electricity

9. © A. Kwasinski, 2014 Sun’s location terms Photons’ Journey into Electricity

10. © A. Kwasinski, 2014 Magnetic vs. celestial poles: Magnetic poles: Caused by Earth’s magnetic field Can be located with a compass They move along Earth’s surface! Celestial poles: Caused by Earth’s rotation. They are two imaginary stationary points in the sky. Important for PV system applications. Geological Survey of Canada Photons’ Journey into Electricity

11. © A. Kwasinski, 2014 NOON 1 PM 3 PM Jun Dec Sep Sun’s position in the sky throughout the day and during an entire year. Photons’ Journey into Electricity

12. © A. Kwasinski, 2014 Photons’ Journey into Electricity The direct-beam insolation I BC depends on the PV module orientation with respect to the sun. If the PV module is fixed, this insolation will change in a deterministic way throughout the day and the year: if the incident angle θ is given by Then, the direct-beam insolation is

13. © A. Kwasinski, 2014 June 21 December 21 March 21 September 21 Equator Tropic of Cancer Latitude 23.45 o Tropic of Capricorn Latitude -23.45 o Austin’s Latitude: 30 o 23.45 o 30 o Edge of PV module (for incidence angle calculation) Earth’s surface (for air mass ratio calculation) Photons’ Journey into Electricity Impact of the sun’s position for the calculation of the direct-beam radiation with respect to the incidence angle and the air mass ratio

14. © A. Kwasinski, 2014 Photons’ Journey into Electricity Assuming that the diffuse radiation does not depends on the sun’s position in a clear sky, then it is modeled using the following equation:\ where C is the sky diffuse factor which can be obtained from ASHRAE. This is another deterministic value. The reflected radiation can be calculated by considering the reflectance ρ of the surface in front of the PV module: This is another deterministic value. The total radiation rate on a PV module is, therefore, given by

15. © A. Kwasinski, 2014 After a long journey, photons are converted into electricity in semiconductors: Whenever a photon with enough energy hits an atom, an electron may jump the energy gap into the conduction band. Once in the conduction band, the electron is free to move in an electric circuit. If the circuit is open or if the load requires less current (charge per time) than the one being produced, the free electrons will eventually decay again. Since it is assumed a continuous slow varying incident solar energy, electrons are freed at a constant rate. Hence, a constant voltage is produced. Photons’ Journey into Electricity

16. © A. Kwasinski, 2014 Photons’ Journey into Electricity Atom’s energy model: Photons energy is quantized. The energy of a photon with a wavelength of λ ( or a frequency of υ ) is where h is Planck’s constant Gap EgEg Conduction band (partially filled) Forbidden band Filled band Electron Energy Gap EgEg Conduction band (Empty at T = 0K) Forbidden band Filled band Electron Energy Metalssemiconductors

17. © A. Kwasinski, 2014 Photons’ Journey into Electricity if the last equation is plotted we obtain that Hence, there is a theoretical limit to a PV cell power output which depends on the semiconductor material being used. For different semiconductors we have that: From the course’s recommended book Lost in heat From the course’s recommended book

18. © A. Kwasinski, 2014 Photons’ Journey into Electricity Efficiency limit can be understood by comparing the following two figures: So for an air mass ratio of 1.5 the efficiencies are (see next slide) From the course’s recommended book http://en.wikipedia.org/wiki/Image:EffectiveTemperature_300dpi_e.png Insufficient energy Excess energy

19. © A. Kwasinski, 2014 For silicon and an air mass of 1.5 the maximum efficiency is about 50% As the band gap energy decreases the efficiency improves somewhat. However, the cost increases significantly. Next class: PV cells electrical characteristics and technologies. Photons’ Journey into Electricity

20. © A. Kwasinski, 2014 PV Cells Technologies Characterization criterion: Thickness: Conventional – thick cells (200 - 500 μm) Thin film (1 – 10 μm). Tend to be less costly than conventional (think) cells but they also tend to be less reliable and efficient. Crystalline configuration: Single crystal Multicrystalline: cell formed by 1mm to 10cm single crystal areas. Polycrystalline: cell formed by 1μm to 1mm single crystal areas. Microcrystalline: cell formed by areas of less than 1μm across. Amorphous: No single crystal areas. p and n region materials: Same material: homojunction (Si) Different material: heterojunction (CdS and CuInSe 2 )

21. © A. Kwasinski, 2014 BP SX170B PolycrystallineBP SX170B Monocrystalline Mitsubishi PV-TD 190MF5 Multicrystalline Uni-Solar Laminate PVL-136 Amorphous Uni-Solar solar shingle Various types of PV Modules PV Cells Technologies

22. © A. Kwasinski, 2014 PV Cells Technologies Thick film fabrication techniques: Czochraski’s (CZ): for single-crystal silicon. Costly. Float zone process (FZ): also for single-crystal silicon. Costly Ribbon silicon Cast silicon: for multicrystalline cells. Less costly. Thin film Can be used embedded in semitransparent windows. Techniques: Amorphous Silicon: can achieve higher efficiencies (in the order of 42% thanks to the multijunction (different multiple layers) in which each layer absorb photons with different energy. Gallium Arsenide (GaAs): relatively high theoretical efficiency (29 %) which is not significantly affected by temperature. Less sensitive to radiation. Gallium makes this solution relatively expensive. Gallium Indium Phosphide (GaInP): similar to GaAs. Cadmium Telluride (CdTe): Issue: Cd is a health hazard (it is very toxic). Copper Indium Diselenide (CIS or CuInSe2): relatively good efficiency) Silicon Nitrade (N 4 Si 3 )

23. © A. Kwasinski, 2014 PV Applications More conventional applications (not all necessarily for microgrids)

24. © A. Kwasinski, 2014 PV Applications Less conventional applications (not all necessarily for microgrids)

25. © A. Kwasinski, 2014 The p-n junction diode p-type substrate n-type substrate Bias voltage Ideal diode Real diode IdId V d is the diode voltage I 0 is the reverse saturation current caused by thermally generated carriers At 25 C: I0I0

26. © A. Kwasinski, 2014 PV Cells physics I SC Reverse v-i curve for the diode I SC V OC p-n junction is equivalent to a diode Same curve The bias source (voltage source) is replaced by a current source powered by the photons The current source shifts the reversed diode curve upwards

27. © A. Kwasinski, 2014 PV Cell steady state characteristic From Kirchoff’s current law: The open circuit voltage is Current Power Maximum power point P max  0.7 V oc I sc

28. © A. Kwasinski, 2014 PV Cell steady state characteristic Dependence on temperature and insolation:

29. © A. Kwasinski, 2014 PV Cell steady state characteristic More on the dependence on temperature and insolation:

30. © A. Kwasinski, 2014 For a more realistic representation we can consider the following (equivalent to a diode’s model): 1) Effect current leakage 2) Effect of internal ohmic resistance More complex steady-state models I SC RpRp RSRS VdVd + V - + - where V d = V+IR S This is a transcendental equation

31. © A. Kwasinski, 2014 Both effects can be combined to obtain the more realistic (and complex) steady state model: PV more complex steady-state model I SC RpRp RSRS VdVd V -- where V d = V+IR S This is a transcendental equation ++

32. © A. Kwasinski, 2014 Dynamic effects Capacitive effect As with any diode, there is an associated capacitance. However, this capacitance is relatively small, so the effects on the output can often be neglected. Therefore, PV modules can follow a rapidly changing load very well. One undesirable effect of the capacitance is that it makes PV cells more susceptible to indirect atmospheric discharges.

33. © A. Kwasinski, 2014 Modules combination PV cells are combined to form modules (panels). Modules may be combined to form arrays. More modules (or cells) in series More modules (or cells) in parallel When modules are connected in parallel, the array voltage is that of the module with the lowest voltage. When several modules are connected in series to achieve a higher array voltage, the array’s current equals that of the module delivering the lowest current.

34. © A. Kwasinski, 2014 Shading (n-1)V module - + + - (R p +R s )(n-1)I module A shadowed module degrades the performance of the entire array One module with 50% shadow One module with 100% shadow Two modules with 100% shadow

35. © A. Kwasinski, 2014 Bypass diode Bypass diodes can mitigate the effects of shadows but they don’t solve the issue completely. A better solution will be presented when discussing power electronics interfaces. No shade Shaded with bypass diode Shaded without bypass diode

36. © A. Kwasinski, 2014 Low-power wind generation For microgrids, power output of each generation unit in the order of a few kW. However, there are cases in which wind turbines with a capacity of hundreds of kW have been used for microgrids. Power profile is predominately stochastic. Originally they were used for nautical and rural applications with dc generators. Cost is relatively low. More modern systems use permanent-magnet generators. Air-X 400 400 W Rotor diameter: 1.15 m SW Windpower Whisper 200 1 kW Rotor diameter: 2.7 m LNP 6.4-5000 5 kW Rotor diameter: 6.4 m

37. © A. Kwasinski, 2014 Low-power wind generation Bergey Excel 7.5 kW Rotor diameter: 6.4 m Solerner 3 kW YM-CZ3kW 3 kW SW Windpower Whisper 500 3 kW Rotor diameter: 4.5 m Wind generators In Tokyo

38. © A. Kwasinski, 2014 Average wind power in the US http://rredc.nrel.gov/wind/pubs/atlas/maps.html

39. © A. Kwasinski, 2014 Average wind power in Europe http://www.geni.org/globalenergy/library/renewable-energy- resources/europe/Wind/Wind%20Map%20of%20Western%20Europe_files/euromap.gif

40. © A. Kwasinski, 2014 Generators: Synchronous machine Output: ac. Electric frequency depends on the rotor angular speed. Requires a dc input. Ideally P mec,in = P elect,out

41. © A. Kwasinski, 2014 Generators: Dynamos (Brushed dc generator) Output: ac + dc. AC component electric frequency depends on the rotor angular speed. Important maintenance and reliability issues caused by the brushes Ideally P mec,in = P elect,out

42. © A. Kwasinski, 2014 Brushless/Permanent magnet generators Output: ac. Electric frequency depends on the rotor angular speed. No issues with brushes Ideally P mec,in = P elect,out

43. © A. Kwasinski, 2014 Wind generators model The output in all types of generators have an ac component. The frequency of the ac component depends on the angular speed of the wind turbine, which does not necessarily matches the required speed to obtain an output electric frequency equal to that of the grid. For this reason, the output of the generator is always rectified. The rectification stage can also be used to regulate the output voltage. If ac power at a given frequency is needed, an inverter must be also added. There are 2 dynamic effects in the model: the generator dynamics and the wind dynamics.

44. © A. Kwasinski, 2014 Wind power Consider a mass m of air moving at a speed v. The kinetic energy is Then power is The last expression assumes an static wind behavior (i.e. v is constant) The mass flow rate dm/dt is Thus,

45. © A. Kwasinski, 2014 Typical Power-speed characteristics SW Windpower Whisper 200 1 kW Rotor diameter: 2.7 m SW Windpower Whisper 500 3 kW Rotor diameter: 4.5 m

46. © A. Kwasinski, 2014 Conversion efficiency In the previous slide, power does not varies with the cube of the wind speed. Why? Because not all the wind power is transmitted through the blades into the generator. Consider the next figure: vbvb vuvu vdvd Downwind Upwind Rotor area A

47. © A. Kwasinski, 2014 Conversion efficiency The wind energy “absorbed” by the wind turbine rotor equals the kinetic energy lost by the wind as it pass through the blades. Hence, the energy transmitted by the wind to the rotor blades is the difference between the upwind and the downwind kinetic energies: In the last equation it is assumed that there is no turbulence and the air passes through the rotor as a steady rate. If it is assumed that v b is the average between v u and v d, then the mass flow rate is If we define the ratio

48. © A. Kwasinski, 2014 Conversion efficiency Then The rotor efficiency is maximum when λ is 1/3. For this value, C p is 0.593. Still, we still need to know how much of the “absorbed” power by the blades is transmitted to the generator. This conversion stage is characterized based on the tip-speed ration (TSR): Power in the wind Fraction extracted Rotor efficiency C p

49. © A. Kwasinski, 2014 Conversion efficiency From the course’s recommended book

50. © A. Kwasinski, 2014 Variable rotor speeds The maximum power point changes as the rotor speed changes. From the course’s recommended book

51. © A. Kwasinski, 2014 Wind stochastic nature Wind speed probability (then generated power, too) is an stochastic function. Wind speed probability can be represented using a Rayleigh distribution, which is a special case of a Weibull distribution. The Rayleigh distribution appears when a 2-dimentional vector has characteristics that: are normally distributed are uncorrelated have equal variance. A typical probability density distribution for wind speed is shown next. Rayleigh distributions approximates these curves.

52. © A. Kwasinski, 2014 Wind stochastic nature The Rayleigh probability density function is given by where c is a parameter. The average value of the random variable (wind speed v ) is The average power is If Then