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TIME OF DAY CORRELATIONS FOR IMPROVEDWIND SPEED PREDICTIONS ANDREW OLIVER, PhD KRISTOFER ZARLINGVP TECHNOLOGIES WIND DATA ANALYST

7TH MAY 2009

WHY THE NEED?

Diurnal wind speed profile is often very different at lower versus higher levels

Atmospheric stability effects on wind speed at two levels on the same tower

Consequently the relationship between Site and Reference station often varies with Time Of Day

An MCP process that fails to take account of Time Of Day is likely to be deficient for many sites

Many, if not most, long term referencestations (airports, etc) used in M.C.P.analysis (wind speed predictions)measure close to the ground (around 10 m.)

Ratio = 1.20Ratio = 1.61

AN EXAMPLE: DIRECTIONAL RATIOS AND TIME OF DAY RATIOS

Binning by DIRECTION 12 sectors (of 30°) wind speed ratio ranges from 1.35 to 1.92

Binning by TIME 12 sectors (of 2 hours) wind speed ratio ranges from 1.21 to 1.98

Standard Deviation of ratios much greater for TIME than for DIRECTION

Number of counts is few for some DIRECTIONS. TIME sectors have equal counts

Standard Deviation 0.32

Standard Deviation 0.19

Ratio of means analysis for a ‘typical’ Texas site

A STATEMENT AND A QUESTION

STATEMENT

“It seems obvious that better relationships between a site and a reference station can be obtained for SOME SITES by taking a TIME sectoring approach as opposed to a DIRECTION sectoring approach. Particularly where the terrain is less complex and atmospheric stability varies significantly on a diurnal basis.”

QUESTION

“Can it lead to better predictions though?”

A TEST CASE

CORRELATE 1 YEAR OF DATA WITH A NEARBY REFERENCE STATION

First binned the data into the following:

Formed 12 “Least-squares” regressions (Site versus Reference station).

- Note: This was just a test. We do not recommend the use of least-squares for MCP!!!

“Back Predicted” Site wind speed using regressions formed & Reference station data

Determined regression coefficient of “Back Predictions”

- How well did the regressions describe the relationship between Site and Reference?

Direction Bins Sector Size Hour Bins Sector Size Total Bins12 30° 1 24 Hours 126 60° 2 12 Hours 124 90° 3 8 Hours 123 120° 4 6 Hours 122 180° 6 4 Hours 121 360° 12 2 Hours 12

CORRELATIONS IMPROVED WHEN “TIME” WAS INTRODUCED

12 TIME ‘SECTORS’ PRODUCED A BETTER ‘BACK PREDICTION’ THAN 12 DIRECTION SECTORS FOR THIS SITE

‘BACK PREDICTION’ IMPROVED FURTHER WHEN A COMBINATION OF DIRECTION AND TIME WAS USED

A STEP FURTHER

A STEP FURTHER

FURTHER IMPROVEMENT WAS MARGINAL WITH MORE (24), AND VARIABLE WIDTH, TIME AND DIRECTION SECTORS

SO WHAT NEXT?

?

PREDICTION METHODOLOGIES (NON EXHAUSTIVE)

RegressionTypes

Pre-averagingof data before

correlation

Least Squares

Ratio Of Means

Orthogonal Method

York Method

Matrix Method

New Parameter“Time” (a proxy

for stability)

Number of Direction Sectors

1 (no binning)

12

Pre-averagingof data before

Correlation

10 minute (none)

Hourly

Daily

Monthly

40 ways of predicting wind speed in this non-exhaustive list!

Are You Crazy?

1(no binning)

12

Some combination of m Direction sectors and n Time sectors

4 ways were compared in this study

GATHERING THE DATA & PREDICTING

Selected 19 sites where RES Americas had collected at least 2 years of data

Good data availability (All >95%)

Geographically dispersed

Meteorologically varied

Use one year to predict another year. Two Ways:

Sliced: 2nd Year Predicts 1st Year & Vice Versa

Akin to what happens in the “real world”

Diced: Every even day Predicts every Odd Day & Vice Versa

Removes annual trending biases (if any)

Site

Reference Station

Year 2Year 1

Time

Regression

Odd Day

Even Day

GATHERING THE DATA & PREDICTING, continued

A 6 month subset was also used to establish the relationship between Site & Reference

Tested ability of prediction method to account for seasonality

The total number of predictions carried out was:

19 Sites *

4 Regression methods *

2 Ways (Sliced & Diced) *

2 Years (Use 1st Year to predict 2nd Year & Vice Versa) *

2 Concurrent data lengths (1 Year and 6 months of data)

608 Total

For the Direction / Time Combination method the following sectoring was used:

6 Direction Sectors (1st centered on North) and 2 Time Sectors (6:00am to 6:00pm)

No “finesse” about how the hours, or directions were selected

RESULTS

In all cases, the r value (weighted by sector counts) was greatest for the “12 Time” sector regressions

YEAR “SLICED”

RESULTS cont.

Mean Absolute Error

“6 Direction & 2 Time” gave the lowest Mean Absolute Error in each case tested:

No significant differences in distributions of errors were observed

Direction is obviously still important. Mixed results compared with Time only

Not a huge improvement, but “6 Direction / 2 Time” was chosen arbitrarily

Simply keeping 12 directions and dividing the data into ‘day’ and ‘night’ could yield improved results without leaving too few data points for regression (50% reduced)

Single 12 dir 12 time 6 dir 2 timeYear Diced 0.84% 0.59% 0.67% 0.56%Year Sliced 1.33% 1.37% 1.34% 1.28%6 months Diced 1.03% 1.06% 1.07% 0.97%6 months Sliced 3.42% 3.27% 3.34% 3.18%

MethodMean Absolute Error (%)

RESULTS cont.

Head to head: Direction versus Combination method (which is best?)

If we cannot a priori figure out which method to use then using 6 Direction and 2 Time sectors produces a better result than 12 Direction sectors in the majority of cases!!!

An important result

12 dir 6 dir 2 timeYear Diced 42.1% 57.9%Year Sliced 34.2% 65.8%6 months Diced 44.7% 55.3%6 months Sliced 47.4% 52.6%

MethodSectoring Type

CONCLUSIONS

Time of Day has been introduced as a binning parameter in MCP as a proxy for atmospheric stability

Time of Day is an important factor to consider in MCP

Regression coefficients were improved in 100% of ‘Year Sliced’ test cases (12 Time Sectors versus 12 Direction Sectors). 95% for ‘6 Months Sliced’

Choosing 6 Direction sectors and 2 Time sectors instead of the traditional 12 Direction approach produced a better prediction in the majority of cases

This choice was fairly arbitrary. It is postulated that varying Time and Direction sector widths on a case by case basis will yield improved results

It is further postulated that keeping the traditional 12 Direction Sectors, but adding 2 Time Sectors (for a total of 24 sectors) will also improve predictions while still retaining enough data points in each sector (50% reduced)

FUTURE WORK

Understand how to optimize the binning of data into m Direction and n Time sectors

Ideal problem for Neural Networks?

Understand Energy Bias errors (how well is the wind speed distribution is predicted)

But the wider question and the “Holy Grail” for MCP is still:

Which regression method should I use for a given site in order to minimize my error?

And the most important consideration (often overlooked) is that one has to have a decent long term reference station in the first place!

THANK YOU

ANDREW OLIVER, PhD KRISTOFER ZARLING VP TECHNOLOGIES WIND DATA ANALYST

RES AMERICAS, INC.11101 West 120th Avenue, Suite 400

BROOMFIELD, CO 80021(303) 439 4200

With thanks to Mike Anderson, Jerry Bass, Rajan Arora, Alex Kapetanovic & Karen-Anne Hutton