European Wind Energy Conference & Exhibition 2010, Tuesday 20 - Friday 23 April 2010, Warsaw, Poland

References

Introduction

Proposal of an Improved Power Curve Correction Lasse SvenningsenEMD International A/S

An improved power curve air density correction is proposed. The correction accounts for the control of pitch regulated turbines contrary to the IEC61400-12 air density

correction. Calibration has been performed against a suite of density specific power curves provided by various manufacturers. Calculations suggest that at low mean air

densities as 1.0kg/m3, using IEC61400-12 corrected standard 1.225kg/m3 power curves can lead to a +4-5% overestimation of AEP. This error is generally reduced to

<1% by use of the proposed correction.

Abstract

Results

Method/Solution

1) IEC61400-12-1, 2005/12, “Power performance measurements of electricity producing wind turbines”, International Electrotechnical Commission, Geneva, Switzerland.

PO.310

Initial phases of wind turbine projects require accurate estimates of annual energy production (AEP) for judgement of feasibility. Typically, only power curves at standard air

density, 1.225kg/m3, are available for prospect turbine models. With mean air densities of 1.0kg/m3 not uncommon, air density correction of power curves is needed to

prevent serious miss prediction.

The power available in laminar wind is: P=½ρAu3 (eq. 1)

If wind turbine power curves behave as eq. 1 at all wind speeds air density correction is simple and two approaches with mathematically equivalent results are possible:

As the above illustrations indicate procedure 1 and 2 do not produce equivalent results when applied to real life power curves. For this reason approach 1, is used for stall

regulated turbines. Approach 2 is used for pitch controlled turbines and is the IEC61400-12 approach 1.

Real power curves do not have the ρu3 dependence of eq. 1 at all wind speeds, only at the rapidly increasing lower part of the power

curve. At higher wind speeds blades are pitched to level output at the rated power, making approach 1 and 2 invalid in this range.

The problem of the IEC61400-12 approach is illustrated on the left. The black curve illustrates a standard 1.225kg/m3 power curve with

normalized P and u axes. The red curve illustrates the “true” power curve provided by the manufacturer for ρ=1.0kg/m3, and the blue

curve is the resulting IEC corrected standard curve to ρ=1.0kg/m3. The error of the IEC correction is the cyan curve and peaks at app.

0.8∙Prated where it overestimates power by around 10%!

The normalized power curve shown, represents one of the most sold turbines world wide during the past few years.

The proposed and the IEC corrections have been applied

to a number of standard air density power curves, to

compare the error in predicted AEP using corrected power

curves versus density specific power curves from several

large manufacturers. The results are (figure, right):

Proposed method:

AEP errors below ±1% down to 1.0kg/m3

IEC method:

AEP errors up to +4-5%, AEP is overestimated!

1) Scale power at standard air density by site-to-standard

density-ratio (eq. 2). Wind speeds, u, are unaltered.

Psite(u)=Pstd(u)ρsite/ρstd (eq. 2)

2) Scale wind speeds, u, as eq. 3, leaving standard power values

unaltered. Resample power values at original wind speeds.

usite=ustd(ρstd/ρsite )1/3 (eq. 3)

The Problem

The ”missing link” for eq. 1 to properly describe turbine behaviour is the turbine power coefficient CP(u). Typical CP(u) curves peak around 7.5-

8.5m/s, and gradually approaches a decay proportional to u-3 beyond rated power (see figure, top-right). Up to about the peak of CP(u) we

expect the simple ρu3 dependence of eq. 1 to hold approximately. Beyond the peak we expect the dependence to become ρum where m<3.

This observation forms the starting point of an improved power curve correction:

Replace the 1/3 exponent of the IEC approach by 1/m, where m=3 for u<~8m/s and m<3 for u>~8m/s.

A thorough analysis of many density specific power curves validate this simple adjustment to the IEC approach to mimic turbine pitch control.

The analysis suggests a smooth adjustment of the 1/3 exponent in eq. 3, from 1/3 at 7-8m/s, to 1/1.5 at 12-13m/s (figure, right).

The variation of m with u has been further optimized to fit a large pool of data. Optimized values deviate slightly from those given above.

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

u/urated, std.

P/P

rate

d, std

.

Std. 1.225kg/m3

True 1.0kg/m3

IEC 1.0kg/m3

IEC error

0 5 10 15 20 250

0.2

0.4

u [m/s]

CP(u

)

0 5 10 15 20 251

2

3

u [m/S]

Exponent,

m

1 1.1 1.2 1.3-2

0

2

4

[kg/m3]

AE

P E

rror

[%],

A=

9,

k=

2

IEC61400-12 corr.

This method Using the IEC61400-12 method to air density correct std.

power curves can lead to 5% overestimation of AEP.

Errors generally reduce to <1% using the proposed

method.

The method is a simple adjustment to the IEC method

accounting for turbine pitch control at high wind speeds.

The proposed method is implemented in WindPRO 2.7.

Conclusion: