LECTURE 22 WIND POWER SYSTEMS ECE 71 Sustainable Energy Systems 1
AVG POWER IN WIND WITH RAYLEIGH STATISTICS The average value of the cube of wind speed can be calculated with Raleigh probability density function formula 0 ) ( 2 0 ) ( 6 ) 2 ( 4 ) ( 4 2 ) ( ) ( 2 v v v c dv e c v v dv v f v v avg c v avg π π π π = = = = = 2
AVG POWER IN WIND WITH RAYLEIGH STATISTICS Now the average power in wind from Rayleigh statistics is P P P avg = = = 1 2 1 ρ 2 6 ( π ρ A ( v 1 2 The average power in wind is power found at the average windspeed multiplied by 6/π 6 A ( v) π ρ A v ) ) avg
WIND POWER CLASSIFICATION & U.S. POTENTIAL Standard wind power classification is shown below 4
WIND POWER CLASSIFICATION & U.S. POTENTIAL 5
WIND POWER CLASSIFICATION & U.S. POTENTIAL 6
WIND POWER CLASSIFICATION & U.S. POTENTIAL 2011 U.S. Demand =.9 PWh/yr 7
WIND POWER CLASSIFICATION & U.S. POTENTIAL Assuming overall turbine efficiency of 25% and array and system losses of 25%, the exploitable wind resource in U.S. is With no land use restriction = 16.7 PWh/yr With the most severe land use restriction = 4.6 PWh/yr In 2011, the total electricity generated in U.S. was.9 PWh Where peta is P =10 15 8
WIND FARMS Wind Farm Collector System
WIND FARMS 10
Feature GE 1.5-77 GE 2.5-100 GE 4.1-11< Rated capacity (MW) 1.5-77 2.5-100 4.1-11 Cut-in wind speed.5 m/s (11.5 ft/s).5 m/s (11.5 ft/s).0 m/s (9.8 ft/s) Cut-out wind speed 20 m/s (65.6 ft/s) 25 m/s (82.0 ft/s) 25 m/s (82.0 ft/s) Rated wind speed 11.5 m/s (7.7 ft/s) 12.5 m/s (41.0 ft/s) 14 m/s (45.9 ft/s) Operational temperature Frequency (Hz) 50 60 Voltage 690-0 40 C (-22 104 F) Rotor diameter 82.5 m (271 ft) 100 m (28 ft) 110 m (61 ft) Rotor swept-area 5,46 m 2 (57,544 sq ft) 7,854 m 2 (84,540 sq ft) 9,567 m 2 (102,978 sq ft) Hub heights 80 m (262 ft) 75 100 m (246 28 ft) Site dependant In the GE 1.5-megawatt model, the nacelle alone weighs more than 56 tons, the blade assembly weighs more than 6 tons, and the tower itself weighs about 71 tons a total weight of 164 tons. 11
INDIANA WIND MAPS 12
INDIANA WIND MAPS 1
INDIANA WIND MAPS 14
USING CAPACITY FACTOR TO ESTIMATE ENERGY PRODUCED An important characteristic of any power equipment is its rated power It indicates how many kw it can produce on a continuous, full-power basis If the wind power generator were to deliver rated power for a full year, then the energy delivered would be the product of: rated power 8760 h/yr 15
USING CAPACITY FACTOR TO ESTIMATE ENERGY PRODUCED Since power equipment, especially wind turbines, don t run at full power all year, they produce something less than that maximum amount The capacity factor is a convenient, dimensionless quantity between 0 and 1 that connects rated power to energy delivered 16
USING CAPACITY FACTOR TO ESTIMATE ENERGY PRODUCED If CF is the capacity factor, and P R is the rated power Annual Energy ( kwh / yr) = P R ( kw ) 8760 ( h / yr) CF Then, CF = Actual energy delivered P 8760 R Or, CF = Actual energy delivered P R / 8760 h / yr = Average power Rated power 17
USING CAPACITY FACTOR TO ESTIMATE ENERGY PRODUCED The real purpose of introducing the capacity factor is to use it to estimate the delivered energy If we use the procedure demonstrated in Example 7.9 to find the capacity factor for a Vestas WTG by varying the average wind speed, then we will obtain an S-shaped figure 18
USING CAPACITY FACTOR TO ESTIMATE ENERGY PRODUCED This S-shaped curve can be linearized Figure 6.9 19
USING CAPACITY FACTOR TO ESTIMATE ENERGY PRODUCED Then the capacity factor is CF = m V + b This linear fit for the Vestas WTG is CF = 0.087 V 0.25 20
USING CAPACITY FACTOR TO ESTIMATE ENERGY PRODUCED For this machine the ratio of rated power to the square of diameter is P R /D 2 = 075 kw/(112 m) 2 = 0.25 This is an interesting coincidence that for this particular wind turbine the y-axis intercept b is equal to the ratio of rated power to the square of diameter 21
USING CAPACITY FACTOR TO ESTIMATE ENERGY PRODUCED Therefore, for this machine we can write the capacity factor as CF = 0.087 V P R /D 2 (1) Although this estimate was derived for a single turbine, it works quite well for other machines The following figure shows the comparison of equation (1) with the correct capacity factors computed using the spreadsheet approach 22
USING CAPACITY FACTOR TO ESTIMATE ENERGY PRODUCED 2
USING CAPACITY FACTOR TO ESTIMATE ENERGY PRODUCED Then with Rayleigh statistics we can estimate Annual energy (kwh/yr) = 8760 x P R (kw) x [0.087 V(m/s) P R (kw)/d 2 (m) 2 ] (2) The spreadsheet approach of Example 7.9 has a solid theoretical basis, and it is the preferred method for determining the annual energy generated But, equation (2) is a handy equation when little data are available 24
USING CAPACITY FACTOR TO ESTIMATE ENERGY PRODUCED CF is not a good indicator of the overall economics for the wind plant A high CF means that a significant fraction of the wind s energy is not being captured Blades are purposely shedding wind to protect generator It would be better to have a larger generator to capture higher-speed winds (generator costs more) More energy is delivered CF goes down, since the generator rating is larger Therefore, CF is not a good economics indicator 25