1. 1 © A. Kwasinski, 2015 Cyber Physical Power Systems Fall 2015 Microgrids and Smart Grids

2. 2 © A. Kwasinski, 2015 Distributed Generation: Concept (a first approach) Microgrids are independently controlled (small) electric networks, powered by local units (distributed generation).

3. 3 © A. Kwasinski, 2015 3 What is a microgrid? Microgrids are considered to be locally confined and independently controlled electric power grids in which a distribution architecture integrates loads and distributed energy resources—i.e. local distributed generators and energy storage devices—which allows the microgrid to operate connected or isolated to a main grid Distributed Generation: Concept (newest DOE def.)

4. 4 © A. Kwasinski, 2015 4 Distributed Generation: Advantages With respect to the traditional grid, well designed microgrids are: Higher availability (with diverse power inputs). More efficient More environmentally friendly More flexible Less vulnerable More modular Easier to control Immune to issues occurring elsewhere Capital investment can be scaled over time Microgrids can be integrated into existing systems without having to interrupt the load. Microgrids allow for combined heat and power (CHP) generation. Microgrids

5. 5 © A. Kwasinski, 2015 5 Distributed Generation: Issues Load following Power vs Energy profile in energy storage Stability Cost Architecture / design Optimization Autonomous control Fault detection and mitigation Cost Grid interconnection Microgrids

6. 6 © A. Kwasinski, 2015 Distributed Generation: System Components Generation units = microsources ( aprox. less than 100 kW) PV Modules. Small wind generators Fuel Cells Microturbines Energy Storage (power profile) Batteries Ultracapacitors Flywheels Loads Electronic loads. Plug-in hybrids. The main grid. Power electronics interfaces dc-dc converters inverters Rectifiers

7. 7 © A. Kwasinski, 2015 Application range: From a few kW to MWMicrogrids

8. 8 © A. Kwasinski, 2015 What is not a microgrid? Residential conventional PV systems (grid-tied) are not microgrids but they are distributed generation systems. Why are they not microgrids? Because they cannot operate isolated from the grid. If the grid experience a power outage the load cannot be powered even when the sun is shinning bright on the sky.Microgrids

9. 9 © A. Kwasinski, 2015 Distributed Generation and Smart Grids European concept of smart grids based on electric networks needs [http://www.smartgrids.eu/documents/vision.pdf] : Flexible: fulfilling customers’ needs whilst responding to the changes and challenges ahead; Accessible: granting connection access to all network users, particularly for renewable power sources and high efficiency local generation with zero or low carbon emissions; Reliable: assuring and improving security and quality of supply, consistent with the demands of the digital age with resilience to hazards and uncertainties; Economic: providing best value through innovation, efficient energy management and ‘level playing field’ competition and regulation The US concepts rely more on advanced interactive communications and controls by overlaying a complex cyberinfrastructure over the existing grid. DG is one related concept but not necessarily part of the US Smart Grid concept.

10. 10 © A. Kwasinski, 2015 Smart grids Smart grids definition: Besides being the new buzz word is not a concept but rather many technologies. Smart grid focus: Reliability. Integration of environmentally friendly generation and loads. Concept evolution: “Smart grid 1.0”: Smart meters, limited advanced communications, limited intelligent loads and operation (e.g. demand response). “Smart grid 2.0” or “Energy Internet”: Distributed generation and storage, intelligent loads, advanced controls and monitoring. Future smart grid: integration among infrastructures in smart cities. Examples: Water, natural gas, transportation and electricity, Internet of Things

11. 11 © A. Kwasinski, 2015 A customer-centric view of a power grid includes microgrids as one of smart grids technologies. Smart Grids

12. 12 © A. Kwasinski, 2015 Microgrids Power Generation Technologies

13. 13 © A. Kwasinski, 2015 Microsources Most common microsources: Microturbine (<100 kW/unit) Fuel Cell (<400 kW/unit) Reciprocating Engine – e.g. diesel generator (<100 kVA/unit) PV Module (<250 W/module) Small wind turbine (<10 kW/turbine)

14. 14 © A. Kwasinski, 2015 Real microsources Wind turbines + PV modules Microturbines PAFC MCFC

15. 15 © A. Kwasinski, 2015 Characteristics: For a voltage (current) source, the internal impedance is zero (infinity): No internal losses. Instantaneous dynamic response. For an ideal voltage source, current has no effect on the voltage output: The output voltage value and waveform are always the same regardless of the load. For current sources replace current by voltage in the last statement. An ideal capacitor with an infinite capacitance behaves as a dc voltage source. An ideal inductor with an infinite inductance behaves as a dc current source. Ideal sources

16. 16 © A. Kwasinski, 2015 Fuel Cells Basics Fuel cells convert chemical energy directly into electrical energy. Difference with batteries: fuel cells require a fuel to flow in order to produce electricity. Heat is produced from chemical reaction and not from combustion. Types of fuel cells: Proton exchange membrane (PEMFC) Direct Methanol fuel cell (DMFC) Alkaline fuel cell (AFC) Phosphoric acid fuel cell (PAFC) (*) Molten-carbonate fuel cell (MCFC) (*) Solid-oxide fuel cell (SOFC) (*) (*) Best suited for microgrids.

17. 17 © A. Kwasinski, 2015 Fuel cells operation Example: PEMFC The hydrogen atom’s electron and proton are separated at the anode. Only the protons can go through the membrane (thus, the name proton exchange membrane fuel cell). Hydrogen Oxygen Water Heat Membrane (Nafion) Catalyst (Pt) Anode (-) Catalyst (Pt) Cathode (+) dc current

18. 18 © A. Kwasinski, 2015 The Tafel equation yields the cell’s output voltage E c considering additional loosing mechanisms: The first term is the reversible cell voltage (1.23V in PEMFCs) The last term represents the ohmic losses, where i is the cell’s current density, and r is the area specific ohmic resistance. The second term represent the losses associated with the chemical kinetic performance of the anode reaction (activation losses). This term is obtained from the Butler-Volmer equation and its derivation is out of the scope of this course. In the second term, i 0 is the exchange current density for oxygen reaction and b is the Tafel slope: PEMFC output: Tafel equation

19. 19 © A. Kwasinski, 2015 In the last equation R is the universal gas constant (8.314 Jmol -1 K -1 ), F is the Faraday constant, T is the temperature in Kelvins, n is the number of electrons per mole (2 for PEMFC), and β is the transfer coefficient (usually around 0.5). Hence, b is usually between 40 mV and 80 mV. The Tafel equation assumes that the reversible voltage at the cathode is 0 V, which is only true when using pure hydrogen and no additional limitations, such as poisoning, occur. The Tafel equation do not include additional loosing mechanisms that are more evident when the current density increases. These additional mechanisms are: Fuel crossover: fuel passing through the electrolyte without reacting Mass transport: hydrogen and oxygen molecules have troubles reaching the electrodes. Tafel equation also assumes that the reaction occurs at a continuous rate. PEMFC output: Tafel equation

20. 20 © A. Kwasinski, 2015 PEMFC electrical characteristics Maximum power operating point E r = 1.23 V Activation loss region Ohmic loss region (linear voltage to current relationship) Mass transport loss region E r =1.23V b=60mV, i 0 =10 -6.7 Acm -2 r=0.2Ωcm 2 Actual PEMFCs efficiency vary between 35% and 60%

21. 21 © A. Kwasinski, 2015 A very good dynamic model of a PEMFC is discussed in: Wang, Nehrir, and Shaw, “Dynamic Models and Model Validation for PEM Fuel Cells Using Electrical Circuits.” IEEE Transactions on Energy Conversion, vol 20, no. 2, June 2005. Some highlight for this model: R ohm : represents ohmic losses R act : represents the activation losses (related with 2 nd term in Tafel equation) R conc : losses related with mass transport. C: capacitance related with the fact that there are opposing charges buildup between the cathode and the membrane. PEMFC electrical characteristics Basic circuit

22. 22 © A. Kwasinski, 2015 PEMFC electrical characteristics Model for the internal fuel cell voltage E where, Comments: The voltage drop related with fuel and oxidant delay is represented by E d,cell. The fuel cell output voltage depends on hydrogen’s and oxygen’s pressure The fuel cell output voltage also depends on the temperature. The time constants for these chemical, mechanical, and thermodynamic effects are much larger than electrical time constants. Equal to E r

23. 23 © A. Kwasinski, 2015 PEMFC electrical characteristics E d,cell can be calculated from the following dynamic equation: where τ e is the overall flow delay. In steady state, both derivatives are zero, so E d,cell = 0. But when the load changes, di(t)/dt is not zero, so E d,cell will be a non-trivial function of time that will affect the fuel cell internal output voltage. When considering fuel cells dynamic behavior, they all tend to have a slow response caused by the capacitance effect in slide 21, the flow delays, the mechanical characteristics of the pumps, and the thermodynamic characteristics. Influence of temperature dynamics on fuel cell output is an important cause for fuel cells slow response.

24. 24 © A. Kwasinski, 2015 PEMFC Technology and issues Expected life of PEMFC is very short (5,000 to 10,000 hours) and not suitable for DG. The most commonly used catalyst (Pt) is very expensive. The most commonly used membrane (Nafion – a sulfonated tetrafluorethylene copolymer is also very expensive). PEMFCs are very expensive. CO poisoning diminishes the efficiency. Carbon monoxide (CO) tends to bind to Pt. Thus, if CO is mixed with hydrogen, then the CO will take out catalyst space for the hydrogen. Hydrogen generation and storage is a significant problem. Additional issues to be discussed when comparing other technologies: dynamic response and heat production.

25. 25 © A. Kwasinski, 2015 The main advantage is that they use a liquid fuel. Reactions: Anode Cathode Voltages: 0.046 V at anode, 1.23 V at cathode, 1.18 V overall. Methanol has high energy density so DMFC are good for small portable applications. Issues: Cost Excessive fuel crossover (methanol crossing the membrane) Low efficiency caused by methanol crossover CO poisoning Low temperature production Considerable slow dynamic response Direct Methanol Fuel Cells (DMFC)

26. 26 © A. Kwasinski, 2015 One of their main advantages is their long life in the order of 40,000 hours. The phosphoric acid serves as the electrolyte. The reactions are the same than in a PEMFC. Hence, the reversible voltage is 1.23 V The most commercially successful FC: 200 kW units manufactured by UTC They produce a reasonable amount of heat They support CO poisoning better than PEMFC They have a relatively slow dynamic response Relative high cost is an important issue Phosphoric Acid Fuel Cells (PAFCs)

27. 27 © A. Kwasinski, 2015 The main advantage is that their cost is relatively low (when considering the fuel cell stack only without “accessories”. Reactions: Anode Cathode Developed for the Apollo program. Very sensitive to CO 2 poisoning. So these FCs can use impure hydrogen but they require purifying air to utilize the oxygen. Issues: Cost (with purifier) Short life (8000 hours) Relatively low heat production Alkaline Fuel Cells (AFCs)

28. 28 © A. Kwasinski, 2015 One of the main advantages is the variety of fuels and catalyst than can be used. Reactions: Anode Cathode They operate at high temperature. On the plus side, this high temperature implies a high quality heat production. On the minus side, the high temperature creates reliability issues. They are not sensitive to CO poisoning. They have a relatively low cost. Issues: Extremely slow startup Very slow dynamic response Molten Carbonate Fuel Cells (MCFCs)

29. 29 © A. Kwasinski, 2015 Solid Oxide Fuel Cells (SOFCs) One of the main advantages is the variety of fuels and catalyst than can be used. Reactions: Anode Cathode They operate at high temperature with the same plus and minus than in MCFCs. They are not sensitive to CO poisoning. They have a relatively low cost. They have a relatively high efficiency. They have a fast startup The electrolyte has a relatively high resistance.

30. 30 © A. Kwasinski, 2015 Microturbines Microturbines are essentially low-power versions of traditional gas turbines used in large power plants. Typical power outputs of microturbines range from a few tens of kW to a few hundred of kW. Natural gas is the most common fuel, but other hydrocarbons, such as kerosene, or bio-fuels can be used, too. Natural Gas Air Generator Compressor Recuperator Combustion Chamber Turbine Exhaust

31. 31 © A. Kwasinski, 2015 Microturbines Capstone 30 kW and 60 kW units Ingersoll 70 kW Induction microturbine 250 kW synchronous microturbine Wilson TurboPower 300 kW Mariah Energy 30 kW and 60 kW units

32. 32 © A. Kwasinski, 2015 Microturbines Moderate cost and efficiency High-frequency output is rectified (and inverted again in ac microgrids). Generator output frequency is in the order of a few kHz (e.g. 1600 Hz for Capstone’s 30 kW microturbine). Power shaft rotates at high speeds, usually on the order of 50 000 to 120 000 rpm Very reliable technology (Essentially microturbines are aircraft’s APU’s). Critical parts: bearings and generator. Generator technologies: Synchronous and permanent magnet Moderately fast dynamic response

33. 33 © A. Kwasinski, 2015 http://www.energy.ca.gov/distgen/equipment/microturbines/microturbines.html Microturbines Oak Ridge National Laboratory; ORNL/TM-2003/74

34. 34 © A. Kwasinski, 2015 Gas turbines operation follow a Brayton cycle Brayton Cycle 1 23 4

35. 35 © A. Kwasinski, 2015 Brayton Cycle From the previous slide: Also, from the previous slide Thus,

36. 36 © A. Kwasinski, 2015 It can be shown that Then, the simplified expression for the efficiency is Usually, the efficiency is expressed in terms of the temperature ratio (TR) or the pressure ratio (PR) where and Brayton Cycle

37. 37 © A. Kwasinski, 2015 Microturbine characteristics The efficiency is improved if T 2 is increased. The recuperator is used for that purpose. Other ways of preheating the air before the combustion stage could be to use heat from a fuel cell. The efficiency decreases as the input temperature increases: Capstone C30 datasheet Ingersoll 70L datasheet

38. 38 © A. Kwasinski, 2015 Reciprocating engines This is likely the most common DG technology. Some types of reciprocating engines are the internal combustion engines and the Stirling engines. Types of internal combustion engines: Spark ignition (fuel: natural gas) Compression ignition (fuel: diesel) The engines are used to drive synchronous or permanent magnet generators. http://www.energy.ca.gov/distgen/equipment/reciprocating_engines/reciprocating_engines.html

39. 39 © A. Kwasinski, 2015 Spark Ignition engines Natural gas is the most commonly used fuel. Thermodynamically they follow an Otto cycle with 4 strokes: 1. intake (induction) stroke 2. compression stroke 3. power stroke: combustion/expansion 4. exhaust stroke Efficiency: r is the compression ratio V 1 /V 2 http://en.wikipedia.org/wiki/Imag e:4-Stroke-Engine.gif#file

40. 40 © A. Kwasinski, 2015 Diesel is the most commonly used fuel. Thermodynamically they follow a Diesel cycle 1. intake (induction) stroke 2. compression stroke 3. power stroke 4. expansion stroke Efficiency: r is the compression ratio V 1 /V 2 and α is the ratio V 3 /V 2 Compression Ignition engines http://library.thinkquest.org/C006 011/english/sites/diesel.php3?v=2 More animated engines: http://library.thinkquest.org/C006 011/english/sites/animations.php3 ?v=2

41. 41 © A. Kwasinski, 2015 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

42. 42 © A. Kwasinski, 2015 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. The most common Hydrogen fusion 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 and will die as a white dwarf. Photons’ Journey into Electricity

43. 43 © A. Kwasinski, 2015 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

44. 44 © A. Kwasinski, 2015 Photons reach Earth in an uneven distribution. US Solar Insolation Map: NREL Photons’ Journey into Electricity

45. 45 © A. Kwasinski, 2015 The incident power has 3 components depending on the final photons path. Reflected radiation Direct-beam radiation Diffuse radiation Photons’ Journey into Electricity

46. 46 © A. Kwasinski, 2015 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

47. 47 © A. Kwasinski, 2015 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

48. 48 © A. Kwasinski, 2015 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

49. 49 © A. Kwasinski, 2015 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

50. 50 © A. Kwasinski, 2015 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

51. 51 © A. Kwasinski, 2015 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: Lost in heat From Master’s book on alternative energy

52. 52 © A. Kwasinski, 2015 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) http://en.wikipedia.org/wiki/Image:EffectiveTemperature_300dpi_e.png Insufficient energy Excess energy From Master’s book on alternative energy

53. 53 © A. Kwasinski, 2015 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. Photons’ Journey into Electricity

54. 54 © A. Kwasinski, 2015 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 )

55. 55 © A. Kwasinski, 2015 BP SX170B PolycrystallineBP SX170B Monocrystalline Mitsubishi PV-TD 190MF5 Multicrystalline Uni-Solar Laminate PVL-136 Amorphous Uni-Solar solar shingle PV Modules at ENS PV Cells Technologies

56. 56 © A. Kwasinski, 2015 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 )

57. 57 © A. Kwasinski, 2015 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

58. 58 © A. Kwasinski, 2015 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

59. 59 © A. Kwasinski, 2015 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

60. 60 © A. Kwasinski, 2015 PV Cell steady state characteristic Dependence on temperature and insolation:

61. 61 © A. Kwasinski, 2015 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 ++ Ideal More realistic

62. 62 © A. Kwasinski, 2015 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.

63. 63 © A. Kwasinski, 2015 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.

64. 64 © A. Kwasinski, 2015 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

65. 65 © A. Kwasinski, 2015 Low-power wind generation Power output of each generation unit in the order of a few kW. 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

66. 66 © A. Kwasinski, 2015 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

67. 67 © A. Kwasinski, 2015 Average wind power in the US http://rredc.nrel.gov/wind/pubs/atlas/maps.html

68. 68 © A. Kwasinski, 2015 Average wind power in Europe http://www.geni.org/globalenergy/library/renewable-energy- resources/europe/Wind/Wind%20Map%20of%20Western%20Europe_files/euromap.gif

69. 69 © A. Kwasinski, 2015 Generators: Synchronous machine Output: ac. Electric frequency depends on the rotor angular speed. Requires a dc input. Ideally P mec,in = P elect,out

70. 70 © A. Kwasinski, 2015 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

71. 71 © A. Kwasinski, 2015 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

72. 72 © A. Kwasinski, 2015 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.

73. 73 © A. Kwasinski, 2015 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,

74. 74 © A. Kwasinski, 2015 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

75. 75 © A. Kwasinski, 2015 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

76. 76 © A. Kwasinski, 2015 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

77. 77 © A. Kwasinski, 2015 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

78. 78 © A. Kwasinski, 2015 Conversion efficiency

79. 79 © A. Kwasinski, 2015 Variable rotor speeds The maximum power point changes as the rotor speed changes. From Master’s book on alternative energy

80. 80 © A. Kwasinski, 2015 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.

81. 81 © A. Kwasinski, 2015 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

82. 82 © A. Kwasinski, 2015 Emissions comparison http://www.raponline.org/ProjDocs/DREmsRul/Collfile/DGEmissionsMay2001.pdf

83. 83 © A. Kwasinski, 2015 DG technologies comparison Resource Dynamics Corporation, “Assessment of Distributed Generation Technology Applications”, Feb. 2001