Harrison article revisited - Harrison's cube isn't real

On September 13, 2011, we published a reference to John Harrison's analysis of wind farm economics.  In his article, Professor Harrison attempts to dissuade further wind farm investment in Ontario because the financial returns are poor and getting worse. We therefore posed the question, "Why are sophisticated organizations with long histories of renewable energy development in other jurisdictions continuing to invest in Ontario?".

We promised some follow-up analysis and this is the first instalment.  We'll start with Dr. Harrison's technique of correcting historical capacity factors for annual wind speed variation.  We'll demonstrate that his fundamental assumption that wind turbine output varies with the cube of wind velocity isn't true and therefore its use as a normalizing function is flawed.  If you're not interested in the technical details, scroll to the bottom of this post where we conclude that his normalizing factors could be off by 5 to 10%.

The normalizing technique is also used by wind industry professionals to evaluate a wind farm's long term expectation of annual wind speeds.  This is quite an elaborate analytic exercise using data from meteorological towers placed in the wind farm area.  The data is then compared to a number of long term (typically, ten years) wind series maintained by Environment Canada.  Those sites with the highest correlation to the field site are used to normalize the field measurements.

Dr. Harrison has chosen to use Toronto as the reference site for all wind farms in Ontario.  He then combines that data somehow with five other cities to come up with a normalizing factor that he applies to all wind farms in Ontario.  In other words, he assumes that year to year variations at each and every wind farm in Ontario are predominately determined by some averaging of wind over most of the province.  This is similar to saying that the variations in every city's rainfall or temperatures could be accurately predicted by the province's average variations.  If it was rainy in North Bay one year then it must have been rainy in Toronto, as well.  We're not meteorologists, but that doesn't seem intuitively correct.

Secondly, Dr. Harrison assumes that the cube law can be used to predict capacity factors from average wind speed.  He is quite right in stating that the power in the wind goes up by the cube of wind velocity.  However, the power from the turbine does not.  There are many technical reasons why this is so but the performance of a turbine versus wind speed is depicted by a power curve that is specific to each turbine design.  Further, the wind speed variation over the course of a year tends to follow a Weibull distribution that is unique to each wind farm.  He further assumes that  the distribution of wind power in all of Ontario is representative of that seen by each individual turbine and, therefore, that the output of each turbine seldom exceeds 85%.  He is not privy to the operating characteristics of each wind farm (e.g. array losses versus wind direction, availability of turbines, the reset time required when a turbine exceeds rated output, etc.) but most individual turbines frequently operate above 85% of their nameplate capacity.

To put all this into perspective, I approached Tom Lambert, P.Eng.,  owner of Mistaya Engineering, the makers of Windographer.  Windographer has been used by many wind consulting firms for many years with demonstrated accuracy.  He plotted the Windographer model results against a cubic function, forcing the two lines to meet at 5 m/s.  Obviously, the cubic function overstates the amount of energy (a surrogate for capacity factor) dramatically.   Keep in mind that the Windographer model has been verified many times in real situations.

The implications of all this of is that Dr. Harrison's normalizing factor dramatically penalizes all wind farms in 2010-2011.  His normalizing factor could easily be off by 5 to 10%.

Dr. Harrison's well intended analysis is laced with some flawed premises and therefore errs in his concluding message "wind in Ontario doesn't make financial sense".

For our next instalment, we'll look at wind farm availability.