OSA WATER WORKS

WIND POWER DESIGN ANALYSIS

The mathematical function that defines wind power potential is given as Equation (1)

                                                                                                                                                                                                                                                  (1)

where P = Power in watts, α is an efficiency coefficient, ρ  is the density of the air in kilograms per cubic meter, r = radius of the area swept by wind turbine in meters, and v = velocity of the air in meters per second.  Betz's law states that the maximum theoretical value for α is 0.59, though turbine manufacturers report the value which below the Betz Law limits varies as a function of turbine configuration. 

Air at sea level has a density of 1.225 kilograms per cubic meter.  Therefore a 15 mph breeze (6.67 m/s) and a rotor diameter of 4 meters (radius of 2 meters) would have a frictionless potential power generation of 727 watts.  Applying Betz's law means that the practical limit for such a configuration is actually somewhat less than 428 watts.  If this wind speed were sustained across 24 hours per day on average, that would amount to a total of 10 kw-hours of daily power production, which is about the amount of power used in a small household with modest power needs.  In this hypothetical example, there are some things that can be adjusted and some that cannot be.  Wind constancy is largely beyond control, but wind speed can be increased by placing the turbine higher above ground.  Also, it is possible to increase the swept area by increasing the turbine's rotor length.  In the preceding example, doubling the length of the rotor arms, for instance, changes the power generation four fold.  Even more dramatic, each doubling of wind velocity boosts power by eight times.  This reveals that even small adjustments to optimize wind speed and swept area can result in dramatic performance enhancements.

The optimal approach to design is to converge toward the result from both ends of the analysis.  In the above example, we have shown the power that can be produced from a given wind-speed.  Now, let us examine power requirements.  I recommend filling out a spreadsheet of household appliances and the period of time each is to be used.  I have published an example here and here to assist in the design of alternative energy applications like hydroelectric, solar, and wind power.  I have summarized a modestly anointed household in the summary pasted below.  This household presumes that water heating, cooking, and clothes drying are done with gas and hybrid appliances since they are large electrical users.

Item	Qty	Watts	Hours	Smlty	Demand	SAME TIME
					0
DC Refrigerator	1	120	10	1	1200	120
dish washer	1	1350	3	1	4050
Microwave	1	1000	0.5	1	500
Blender	1	300	0.25	1	75
Coffee Maker	1	900	0.5	1	450	900
Toaster	1	1000	0.25	1	250
Slow Cooker	1	750	1	1	750
Rice Maker	1	750	0.5	1	375
Computer	1	250	4	1	1000	250
Monitor	1	150	4	1	600	150
Television	1	100	4	1	400	100
Internet modem	1	60	4	1	240	60
satellite tv or cable box	1	40	4	1	160	40
stereo system	1	100	2	1	200
Light bulbs wattage 2	8	75	4	0.5	1200	300
Ceiling Fan	8	65	15	0.5	3900	260
Washing machine	1	500	1	1	500	500
Hybrid dryer	1	400	1	1	400
					16250	2680

The total daily power demand under this usage pattern is 16.3 kw-hours (total shown in red in the above table).  In our example above, a 4-meter turbine in a 15 mph breeze sustained for 14 hours can generate only 10 kw-hours, or about two thirds of the total daily demand.  If we boost the turbine rotor length from 4 to 6 meters in diameter, the wind potential of 23.2 kw-hours easily satisfies the home's anticipated power demands.  Clearly, optimal wind-power system design requires as much information as possible about the variation in wind speeds at all hours of the day in order to reasonably project the amount of energy that can be produced.  Since both wind speed and swept area are variables that can be favorably boosted through added capital investment, the convergent analysis is the best approach to settling on the system that best fits:  1)  power demands;  2)  local wind patterns;  and 3)  capital budget. 

In our example, presuming we are confident about the average wind speeds for the area, a six meter diameter rotor size is reasonable.  The remainder of the self-standing system design is not so simple, comprising an inverter, charge controller, battery bank, and secondary power source.  In the far right hand column of the table above I have left a series of appliances that may be on simultaneously.  The total amount of simultaneous power demand is the design criterion for inverter sizing.  In this case, an instantaneous power requirement of 2680 watts (shown in blue in the table above) would logically presume the deployment of a 3000-watt inverter.  Additional design decisions revolve around the input voltage, which can be either 12-, 24- or 48-volt.  In most cases, 24-volt systems offer the best balance between functionality and economy.  Twelve-volt systems are less expensive but offer less amperage and less overall versatility.  Forty-eight volt systems, on the other hand are top-end, requiring twice as many batteries and greater expense but having a number of advantages over 24-volt systems.

Having settled on a 24-volt system in our hypothetical case, the remaining design variable is the amount of reserve energy storage to be allocated in batteries.  While rigorous designs might call for three days of battery backup power, that amounts to 34.9 kilowatt-hours of backup, which for a 24-volt system amounts to a capacity of 2020 amp-hours once 80% battery draw-down and 90% inverter efficiency safety factors are included in the calculations.  For 520 amp-hour L-16 6-Volt batteries, this would presume a parallel array of four such batteries to achieve the amp-hour battery backup and a series of four batteries along each leg to achieve the voltage.  This adds up to 20 batteries, which at $500 average cost in Costa Rica is a $10,000 investment, considerably more than most homeowners are willing to consider.

Most people, rather than spend so much on batteries, are more inclined to purchase four batteries to achieve the voltage and use a fossil fuel generator or solar panels for supplemental power generation when winds fall, rather than capitalizing substantial battery backup capacity.  Even with three days of battery backup, it is likely that across the life of a project installation that the winds will periodically fall beneath design plans and periodically require supplemental power.

Wind power solutions make ideal grid tie-ins.  For a grid-tie wind turbine application, homeowners do not require inverters, batteries, charge controllers, nor must they be concerned about periods of low wind speed.  In grid-tie systems, homes provide power to the grid when producing more than the house is consuming.  And when winds are still, the house pulls power from the grid to meet its needs.  The whole balance of power is automated, so that no disruptions or attention is required, and the power meter measures the balance of energy flow.  For homes that produce more power on average than they consume, the extra power is fed into the national power grid and available for other users, and the homeowner receives a monthly check in compensation.  And for those users that use more power than they are able to generate, they nevertheless achieve savings on their power bill and are able to capitalize installation costs much more easily than if they were forced to include inverter, battery bank, and backup power generation in the original capital outlay.

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