# Significant difference between averaged wind speeds and averaged wind power density, for wind generation modelling?

Climate models outputs, particularly the reanalysis datasets, output wind speeds as zonal and meridional averages for the modelled time period (typically 1, 3 or 6 hours). So we get a 2-dimensional vector, the U and V values, each of which is signed. Together, they give us a mean wind speed, and a mean direction.

There are some oddities there, as I understand it. If the wind within one interval were 9 m/s due East for half the time, then 9 m/s due West for the other half, then the UV values would be (0, 0). That's a very contrived case, just to illustrate the netting off for any wind that switches sign on either the U or V directions.

Some reanalysis datasets fix this part of the problem by giving mean wind speeds as well as mean UV components.

But for the estimation of wind electricity generation , what we really need are the mean power densities ($\mathrm{W/m^2}$ in the vertical plane) of wind, at turbine hub height (typically 80m or so). That way, we can multiply the swept area of the blades, by the mean power densities, and combine with a modified version of the turbine power curve, to estimate electricity generation.

Now, the relationship between wind speeds and power densities is cubic. But the average of a cubed value is not the same as the cube of the averaged value. So, taking the cube of average wind speeds is not the same as taking the average of the cube of wind speeds. And then there's the possibility of positive or negative correlations between wind speeds and atmospheric pressure, which would also mess with the averaging.

Is there an analysis of the impact of these distortions on our ability to model & predict wind power generation?

• I can't answer the actual question... off the top of my head, there's clearly no way that one can produce a credible prediction of wind energy resource from mean wind speeds alone... but perhaps a combination of mean wind speeds over long time periods and a wide area, plus more detailed info for a short time and a specific site, plus some judicious assumptions...? – Semidiurnal Simon Sep 3 '14 at 11:02
• Speed is a scalar quantity, and has no direction associated with it. Velocity is speed + direction. The question might be a bit clearer if you rephrase it with that terminology. Do the models you're looking at contain anything other than the mean those wind fields? An hourly mean plus a variance estimate would probably be sufficient for a reasonably decent power density model... – naught101 Sep 8 '14 at 13:06
• These distortions are important; this is one reason why the US DOE supported NREL and others to develop high spatial (2km horizontal) and temporal resolution (5 minute) data sets to investigate grid integration of wind energy. These are based on ERA and other reanalysis. Most consultants use very hi-res flow models for a specific site. Also, a turbine power curve is not really very accurate. Power output depends on the rate and magnitude of the change in wind speed, wind veer with height, change of wind speed with height, turbine maintenance record, dust and dirt on the blades,.... – Andy Clifton Sep 14 '14 at 3:32
• ** So, taking the cube of average wind speeds is not the same as taking the average of the cube of wind speeds. ** You know the mathe yourseĺf, the question that reamins is this affects wind power modelling and related studies does this paper help you: energyexemplar.com/wp-content/uploads/publications/… ? – Sean Sep 23 '15 at 23:34

In ECMWF data, wind direction and wind speed are collected from observation separately. Then based on a well known transformation the wind vectors, u and v are calculated.

You can focus on this part in their documentation:

" **Wind.**There are four wind variables: wind direction(DDD), wind force(FFF),u and v components. For each of these variables the first thing which is done is to get a local copy of it together with its related parameters from an ODB supplied array (GETSETE).Once a variable is made available locally a check is made to ensure that the vertical coordinate is pressure; if instead of pressure a flight level is supplied it is converted into pressure by assuming a standard ICAO atmosphere(Z2PICAO). If the variable in question is either u or v, then DDD and FFF are converted into u and v wind components. Furthermore, for each of the four variables appropriate observation error statistics are assigned (ERRSTAT, FINOERR). Also, if any flags are set at this stage an appropriate word in the local copy is updated (PPVAFL). Finally, an updated local copy of an observed quantity and its related parameters are returned back into the ODB (AIREPBE)."*

Once wind speed and direction are obtained calculations are made to get the two components of wind u and v. e.g. $$u = -FFF sin(DDD \frac{\pi}{180})$$ $$v = -FFF cos(DDD \frac{\pi}{180})$$

In calculating wind power, we need wind speed and not wind direction. If we are given u,v components of wind, we can calculate wind speed as $$U = \sqrt{u^{2} + v^{2}}$$. Then, the power density, $$P = \frac{1}{2}\rho A U^{3}$$ To sum up when we calculate wind power, what we need is the speed and not the direction.