Comparison between power curves for 2 kW and 5 kW turbines

[Bargeman]

Hello,

I have been taking a look at the power curves for Navitron's 2 and 5 kW wind turbines (attached). In the absence of a measured wind speed distribution for a site, the average wind speed seems to be a reasonable proxy. (I am aware that I could model a more accurate Weibull distribution using just the average wind speed, but just at this moment I'm feeling a bit too lazy to put in the effort).

Down here in occasionally breezy Kent, average wind speeds for any suitable sites are going to be between 5 and 7 m/s. When I compare the power curves for the 2 kW and 5 kW turbines, the difference between the two turbines seems minimal. At 5 m/s the power curves on the Navitron website show the 2 kW turbine producing about 350 W and the 5 kW at about 450 W. At 7 m/s the 2 kW produces about 800 W and the 5 kW generates about 1.1 kW.

My cursory conclusion from comparing the power curves on the Navitron web site is that for a low average wind speed site the 5 kW turbine is not significantly more effective than the 2 kW turbine, and that under this kind of wind regime the 2 kW turbine will generate more kWh per £ invested than the 5 kW.

Alternatively it could be that the power curves are suspect ? Or as a further alternative I should apply a Weibull distribution to the average wind speed value before attempting this kind of comparison ? I would appreciate any opinions on whether my tentative conclusion is robust.

regards

[Ivan]

Firstly, average wind speeds do not tell us very much - considering that in low wind sites, most of the time there is very little wind - there is very little power at all. When the wind picks up, the power increases exponentially, so it really depends on whether your site is still most of the time with occasional high winds or still some of the time with more frequent but not so high winds.

The 5kW wind turbine has much larger blades, hub, shaft, bearings etc, so there is considerably more resistance to starting than for the 2kW turbine - this may be the reason that the 2kW turbine appears to perform better at very low wind speeds. As soon as the wind starts to pick up - and this is where most of the real power is derived, the 5kW turbine produces significantly more power.

[Bargeman]

Thanks Ivan,

Finally decided to try to analyse the 2kW and 5kW turbine outputs more rigourously.

Since for most domestic scale wind turbines it is not really economic to undertake a rigorous measurement of the wind regime on a particular site, an alternative method of estimating output based on as realistic a model of wind distribution as possible is needed.

I use a Weibull distribution and assume the shape parameter k = 2 (Rayleigh) and scale parameter can be estimated C = 2 * Average wind speed / pi ^ 0.5 (Bowden). I believe that this produces a reasonably realistic wind speed distribution based solely on an estimated average wind speed, as per attachment. I have generated curves for 5, 5.5, 6 , 6.5 and 7 m/s average wind speeds that particularly concern me.

By applying each of these wind speed distributions to the power curves on the Navitron web site (BTW - could these be made available in a numerical as well as graphical format please Ivan), I have derived annual power outputs for the 2 kW and 5 kW turbines over the range of average wind speeds which particularly concern me. These are given in the attachment.

My, by now slightly more robust, conclusion is that for a site with an average wind speed of 5 m/s the 5kW turbine could be expected to produce about 7.32 MWhs of power per annum, about 58% more than the 4.63 MWh produced by the 2 kW turbine. This output ratio increases to 71% at a higher average wind speed of 6 m/s, where the 5KW turbine produces 11.9 MWh versus 6.96 MWh for the 2 kW model. (Note that these output figures assume 100% uptime and 100% power to electricial efficiency). The output ratio increases to 84% at 7 m/s and 117% at 9 m/s.

From this analysis, given the differential costs for 2kW and 5kW turbines, I would conclude that for a low average wind speed site (5 to 6 m/s) there is not much to be gained by stepping up from a 2kW to a 5kW turbine, particularly since the latter is more than twice as costly as the former.  In fact it would probably be more cost effective (more output at a lower cost) to install 2 x 2 kW turbines rather than a single 5kW machine, assuming balance of system costs are broadly equivalent.

This is somewhat counterintuitive since we all know that with wind power bigger is always better, don't we ?

Ultimately what I'm trying to determine is a soundly based and verifiable assessment of the output that can be expected from these turbines under the kinds of wind regimes experienced in my area. I would appreciate any thoughts, particularly whether the theoretical outputs in my table bear any resemblance to reality.

regards

[charlieblair]

Interesting analysis bargeman.  And definitely a useful goal to be aiming for, but I don;t think you're there yet on the yield estimates.

I only have A level experience in stats and frequency distributions  (I can just about follow the wikipedia article for Weibull), but I can't see how the distribution you've used corresponds to actual wind distributions. Surely the most frequent wind speed at all sites will be zero - with gradually lower frequencies for higher winds.    I doubt whether any site would have an average (mean) wind speed that was also the most frequent (mode).

I guess moving your curve to the left such that the peak is at zero would provide a better basic distribution - but then the shape of the curve would have to be changed so the mean was still 5m/s.

I know the big guys (commercial wind farm developers) convert their wind measurement readings into a simple 'capacity factor' (using a known wind frequency distribution and a known turbine power curve). The capacity factor is a percentage and can be thought of as the percentage of time that a turbine will be generating at rated capacity. Hence calculating the yearly yield (MWh) is simple: 8760 (hours/yr)*rated capacity(MW)*capacity factor(%).     A good commercial site in Scotland has a capacity factor of around 30% so a 5KW turbine (at 100m) could theoretically generate 8760*5*0.3 = 13140KWh, or around 13MWh.   To reach the 26MWh  your spreadsheet suggests for a 7m/s the capacity factor would have to be around 60%!       For my basic calcs on pay back for a 5KW turbine I've been using a capacity factor of 15% (in the absence of measured frequency distribution or a good estimate such as you're aiming for) but that is a guesstimate - I'm hoping a pessimistic one as payback would be over ten years on a yield of 6.5MWh (see thread - 'A proposal - "community" 5KW turbine' for assumptions).

Anyway. Keep at it refining the frequency distribution for wind Bargeman. Does anyone have an actual measured distribution?

Charlie

[Bargeman]

Thanks for that Charlie,

Whilst there will be a greater proportion of low wind speeds encountered in any wind speed distribution, in fact zero wind speed is not the most frequent wind speed encountered at virtually any site in the UK. The Weibull distribution is the standard probability distribution function used for modelling wind speed distributions in the wind industry, i.e. it is used by commercial wind farm developers for exactly this purpose in the absence of a full set of measurement data, but where average wind speed and ideally standard deviation of wind speeds are available. This is usually at the site prospecting stage before deciding to set up an anemometer.
The k = 2 value (aka Raleigh distribution) which defines the shape of the distribution is generally acknowledged to be a reasonable approximation for most UK wind conditions (at least that is what we were taught on my Masters course).

The Weibull distribution does not produce a mode that is equal to the mean (apologies that the misalignment in the x-axis labelling on the graph might suggest this). The mode in the particular chart I attached is 4 m/s whereas the average is 5m/s. Note that I have only used integer wind speeds to generate probability values and that in practice the mode will be non integer.

As you say, capacity factor can be used to provide a simple representation of turbine performance. Generally this is a 'post facto' measurement, i.e. it is applied to provide a standardised way of comparing the actual performance of turbines once in situ. It is a 'rule of thumb' value which tells you nothing about how a turbine can be expected to perform on a particular site; it is perfectly possible to achieve a capacity factor of zero by badly siting a turbine. A capacity factor is the product of wind speed distribution analysis (and many other analyses), not a substitute for it. However as you say, it does provide a good sanity check.

Erratum - the values labelled as 7 m/s average wind speeds in the table were actually values for 9 m/s. A new table with the actual 7m/s values, 9.11 MWh for 2kW and 16.76 for 5kW, is attached. Mea culpa.

Thus far the analysis is principally aimed at providing a comparison between the 2 and 5 kW versions using a similiar wind speed distribution. As stated, it reflects just the power output from the turbine and makes no allowance for losses converting to electrical output or operational downtime. Clearly both of these will reduce the annual output and hence the capacity factor.

To be continued.

regards

[Ted]

Interesting stuff.

Is there a corresponding relationship between the swept areas of the two turbines? 

In theory the two power curves should just be a reflection of this.

[Ivan]

The only way to be certain is to put two alongside each other in identical wind conditions (difficult to achieve!). Not sure about achieving that, but Navitron will be installing various wind turbines from 200W up to 20kW at the site in Oakham in the new year. We should be able to see some comparison between the different wind turbines, from this.

Incidentally, it is always cheaper, and usually more cost effective on a £/w basis to install two smaller turbines rather than one big turbine - this is because when the turbine size increases, it will need require everything to be beefed up - to quite a large extent. Also, planners often prefer two smaller turbines to one large turbine, so it makes planning applications easier if you are considering large turbines.

Ivan

[Bargeman]

Hello Ted,

Based on the power formula P = 0.5 x air density x swept area x wind speed ^ 3, then, all else being equal, the total power available would clearly vary in proportion to swept area for a given wind speed, as you say.

However this is not the same as power extracted from the wind. Different turbines will translate this available power into actual power with varying efficiencies, which ought to be reflected in their respective power curves. Turbines will perform with varying efficiencies at different wind speeds, i.e. some will be more efficient at low wind speeds than others. In the Navitron case, based solely on their power curves, the 2 kW turbines seem to perform better at the low wind speeds than the 5 kW. As Ivan says, it will be interesting to see how this works out in practice.

Ted - from a previous post I understand you are the proud possessor of a Proven 6kW turbine. I wonder if you would be prepared to let me have some performance data for the turbine, via a PM perhaps ? It would be interesting to compare the actual performance of the Proven turbine to its power curve.

One further thing I'm not clear about, which hopefully Ivan or his team my be able to answer - do the Navitron power curves indicate the power 1) at the turbine alternator, 2) at the point of delivery to the charge controller (AC) or 3) at the point of delivery from the charge controller (DC) ? I'm fairly sure that it will be (1) and that an allowance has to be made for electrical losses in the cables and charge control and rectification. I can estimate cable and inverter losses; is there any information which would help me estimate losses for the charge controller ?

regards

[Ted]

The only data I have for my Proven is a daily figure for kWh generated back to March 06 which I am happy to share. I don't have any accompanying wind speed data though.

[Bargeman]

Hello Ted,

Thanks for the offer Ted. Your data would help me test my methodology for assessing prospective turbine performance in the absence of any specific wind speed measurements for a site.

I have the power curve for the Proven 6 kW. If you let me have your post code I will use it to lookup the NOABL value for average wind speed in your area, then use that to generate a wind speed distribution. Then I can merge the power curve and wind speed distribution data to generate expected output. Then compare the results to the power you've actually generated since March.

So I would be mighty obliged if you can PM me the data and your post code. If you're in agreement, I'll post the results on the forum.

regards