Power Generation from Renewable Energy Sources Fall 2013 Instructor: Xiaodong Chu ： Office Tel.:

Flashbacks of Last Lecture From simple estimates of overall system efficiency associated with wind probability statistics to techniques applied to individual wind turbines based on their own specific performance characteristics To understand how rotor blades extract energy from the wind, we start from some parameters associated with aerodynamics of wind turbines – Lift and drag forces – Angle of attack – Pitch angle

Flashbacks of Last Lecture The most important technical information for a specific wind turbine is the power curve, showing the relationship between wind speed and generator electrical output

Flashbacks of Last Lecture There are trade-offs between rotor diameter and generator size as ways to increase the energy delivered by a wind turbine – Increasing the rotor diameter, while keeping the same generator, shifts the power curve upward so that rated power is reached at a lower wind speed – Keeping the same rotor but increasing the generator size allows the power curve to continue upward to the new rated power

Wind Power Systems – Specific Wind Turbine Performance Calculations Specific wind turbine performance calculations – Using real power curves with Weibull or Rayleigh statistics – Using capacity factor to estimate energy produced

Wind Power Systems – Specific Wind Turbine Performance Calculations The resemblance between the real and idealized power curves – The rounding of the curve around the rated wind speed makes it difficult to pin-point the exact V R How to use the real power curve?

Wind Power Systems – Specific Wind Turbine Performance Calculations Calculation of wind energy production – Power curve available -> power any given wind speed × each wind speed -> the total kWh delivered – If site wind data available for each wind speed, just use it – If site wind data incomplete -> assume Weilbull statistics with appropriate k and c – If only the average wind speed known -> use Rayleigh statistics (k=2; )

Wind Power Systems – Specific Wind Turbine Performance Calculations The probability that the wind is less than some specified wind speed V is given by which is called the cumulative distribution function Recall the Weibull p.d.f function and the cumulative distribution function for Weibull statistics

Wind Power Systems – Specific Wind Turbine Performance Calculations For Rayleigh statistics

Wind Power Systems – Specific Wind Turbine Performance Calculations The probability that the wind is greater than a certain value For Weibull statistics For Rayleigh statistics

Wind Power Systems – Specific Wind Turbine Performance Calculations

Modify the continuous p.d.f. to estimate hours at discrete wind speeds – With hours at any given speed and turbine power at that speed, we can easily do a summation to find energy produced – If we combine the power at any wind speed with the hours the wind blows at that speed, we can sum up total kWh of energy produced – What is the probability that the wind blows at some specified speed v? – What is the probability that the wind blows between v − Δv/2 and v + Δv/2? – We can use the p.d.f. evaluated at integer values of wind speed to represent the probability that the wind blows at that speed Example 6.14 and Example 6.15

Wind Power Systems – Specific Wind Turbine Performance Calculations

One of the most important characteristics of any electrical power system is its rated power; that is, how many kW it can produce on a continuous, full-power basis The capacity factor CF is a convenient, dimensionless quantity between 0 and 1 that connects rated power to energy delivered Estimate CF and use it to estimate energy delivered

Wind Power Systems – Specific Wind Turbine Performance Calculations

In its linear region, CF can be estimated by an linear equation which can be fitted with the two parameters m and b obtained

Wind Power Systems – Specific Wind Turbine Performance Calculations it is found that the following relationship derived from a particular turbine is applicable to general wind turbines with reasonable accuracy: Rayleigh winds

Wind Power Systems – Specific Wind Turbine Performance Calculations Using the above equation for CF, a very simple method for estimating the energy delivered is realized as follows: All we need are rotor diameter, rated power in Rayleigh winds with average wind speed Example 6.17 on page 370

Wind Power Systems – Wind Turbine Economics Wind turbine economics have been changing rapidly as machines have gotten larger and more efficient and are located in sites with better wind While the rated power of new machines has increased year by year, the corresponding capital cost per kW dropped The impact of economies of scale is evident – The labor required to build a larger machine is not that much higher than for a smaller one – The cost of electronics are only moderately different – The cost of a rotor is roughly proportional to diameter while power delivered is proportional to diameter squared – Taller towers increase energy faster than costs increase

Wind Power Systems – Wind Turbine Economics

Operations and maintenance costs (O&M) include regular maintenance, repairs, stocking spare parts, land lease fees, insurance, and administration Some of these are annual costs that don’t particularly depend on the hours of operation of the wind turbines, such as insurance and administration, while others, those that involve wear and tear on parts, are directly related to annual energy produced In general, O&M costs depend not only on how much the machine is used in a given year, but also on the age of the turbine – Toward the end of the design life, more components will be subject to failure and maintenance will increase

Wind Power Systems – Wind Turbine Economics To find a levelized cost estimate for energy delivered by a wind turbine, we need to divide annual costs by annual energy delivered To find annual costs, we must spread the capital cost out over the projected life time using an appropriate factor and then add in an estimate of annual O&M To the extent that a wind project is financed by debt, we can annualize the capital costs using an appropriate capital recovery factor (CRF) that depends on the interest rate and loan term

Wind Power Systems – Wind Turbine Economics The annual payments on such a loan where A represents annual payments ($/yr), P is the principal borrowed ($), i is the interest rate, n is the loan term (yrs)

Wind Power Systems – Environmental Impacts of Wind Turbines Wind systems have negative as well as positive impacts on the environment – The negative ones relate to bird kills, noise, construction disturbances, aesthetic impacts, and pollution associated with manufacturing and installing the turbine – The positive impacts result from wind displacing other, more polluting energy systems

Wind Power Systems – Environmental Impacts of Wind Turbines Birds do collide with wind turbines – Early wind farms had small turbines with fast-spinning blades and bird kills were more common but modern large turbines spin so slowly that birds now more easily avoid them – A number of European studies have concluded that birds almost always modify their flight paths well in advance of encountering a turbine, and very few deaths are reported

Wind Power Systems – Environmental Impacts of Wind Turbines People’s perceptions of the aesthetics of wind farms are important in siting the machines A few simple considerations have emerged, which can make them much more acceptable – Arranging same-size turbines in simple, uniform rows and columns seems to help, as does painting them a light gray color to blend with the sky – Larger turbines rotate more slowly, which makes them somewhat less distracting

Wind Power Systems – Environmental Impacts of Wind Turbines

Noise from a wind turbine or a wind farm is another potentially objectionable phenomenon, and modern turbines have been designed specifically to control that noise – It is difficult to actually measure the sound level caused by turbines in the field because the ambient noise caused by the wind itself masks their noise – At a distance of only a few rotor diameters away from a turbine, the sound level is comparable to a person whispering

Wind Power Systems – Environmental Impacts of Wind Turbines

The air quality advantages of wind are pretty obvious – Other than the very modest imbedded energy, wind systems emit none of the SO x, NO x, CO, VOCs (Volatile Organic Compounds ), or particulate matter associated with fuel-fired energy systems Since there are virtually no greenhouse gas emissions, wind economics will get a boost if and when carbon emitting sources begin to be taxed