Estimating uncertainties in multiple wind farm Annual Energy Production (AEP)

Transcription

1 Estimating uncertainties in multiple wind farm Annual Energy Production (AEP) Peter Taylor 1,2, Jim Salmon 2 1 York University, 2 Zephyr North Canada Contact: pat@yorku.ca 3C7.2 ID:5423

2 One of the first tasks in the evaluation of a potential wind farm site is to estimate and then measure the wind, ideally at hub height and for at least one full year but typically for two or more years. Estimating annual energy production (AEP) then requires modeling any effects of terrain and roughness variations causing wind variations across the site and also effects of the wakes of turbines. Other factors such as noise may also impact the design but a basic task is to maximize the AEP under constraints affecting the design. MCP adjustments are made associated with whether the limited, one or more year wind data are representative of long term, climatological values. The resulting AEP estimate is an average, or P50, value.

3 The P50 AEP estimate will include adjustments for various losses but there are also uncertainties. Uncertainties - How much uncertainty is involved, and what are the causes? a) AEP estimate errors - wind measurement, and flow and wake modelling. Hardware uncertainties (e.g. power curves). b) Operational uncertainties (turbine failures, maintenance, grid connection availability etc.) c) Meteorological factors, icing and year to year variability. Wind farm finance agencies are often concerned about the uncertainty in the prediction of the secure (P90) multi-year return on their investments.

4 Single Wind Farm We denote the long term AEP (P50) by P50. Perturbations from P50 in any given year are denoted by p' with a long term mean of zero. If the p' are normally distributed and if we denote the root mean square of p' over many years as σ, then the 1-year P90 is P(90-1 year) = P σ (1-year) The same relationship would hold for multi-year P90 (Y-year) values with a reduced multi-year standard deviation (assuming each year is independent) as, σ (Y-year) = σ (1-year)/ Y But not all uncertainties will vary from year to year - e.g possible errors in the resource assessment, so...

5 Ideally the σ values would be equivalent to the uncertainties in a Net Production estimate but while a part of the uncertainty assessed prior to wind farm operation will vary from year-to-year and have zero long term mean, a part will represent uncertainties associated with, for example the pre-construction assessment of the wind resource or of wake losses, or the expected turbine performance. As estimates, these uncertainties should have zero mean, but are essentially fixed and will not vary from one year to the next. Uncertainties with zero long-term mean include year-to-year variations in wind speeds, which can be estimated, plus other factors such as equipment failure, power grid outages and icing losses which will be termed mechanical that are sometimes harder to assess.

6 Denoting one-year uncertainties as u = f + m where the f are fixed uncertainties and m are uncertainties with zero long term mean, the multi-year uncertainties are assumed to be given as u(y-year) = (f 2 + m 2 (1-year)/Y) As an example, consider a case with one year wind and random mechanical variability giving a relative production uncertainty (m/p50) of 10% and the relative fixed uncertainties (f/p50), associated with original measurement errors, modelling errors, turbine variability, etc., of 10%. Combined, these give a 1-year relative AEP uncertainty (square root of sum of squares) of 14.14% and a 10-year AEP uncertainty of 10.50%. The fixed uncertainty remains until the farm is built, operating and these factors become known.

7 Multiple Wind Farms In the case with N wind farms, let P = P 1 + P P N where P i is the AEP for an individual wind farm. The long term variance of the total perturbation is, where <... > indicates a long term average. In the simple case where all <p' i2 > are equal to σ 2, the overall standard deviation could vary from N σ, if there is 100% correlation between annual production at all wind farm to N 1/2 σif there is no correlation. A considerable benefit in terms of P90, noting that P(90-1 year) = P σ (1-year)

8 If multiple wind farms are involved, correlation between AEP at different locations will be a factor. A methodology is developed to combine the uncertainties associated with each farm to provide a single uncertainty and multi-year P90 values for an investment in a multi-farm project. It is assumed that most factors are uncorrelated between farms but there may be correlation between annual wind regimes and the wind resource at different sites in any given year. How do we establish these correlations, or lack of correlation? We work with annual values, since that eliminates seasonal variability.

9 In the planning stage there are usually only one or two years of data from each wind farm site, and they may not be for the same years. We can look at correlations between EC stations near to each of the farms but these are somewhat different data (10m height and more strongly affected by diurnal variations). In this study we use ten year VORTEX reanalysis wind data for heights of order 100m for a number of locations across Canada. We note that these show less year-to-year variability (about 3%) than has often been assumed in other uncertainty studies (6%).

10

11 Ten Year VORTEX data from ten Canadian sites, ordered West to East, 100m height

12 Vortex data + generic power curve. AEP for 10 sites across Canada

13 Cross-correlations, AEP: High are bad, low are good, negative very good. Acknowledgement: Several Zephyr North clients have kindly allowed us to use their Vortex data for this study.

14 Conclusions 1) P90 AEP estimates can be affected by different types of uncertainty, some are "fixed" and some should have zero long term means. 2) There may be less year to year variation in annual average hub height winds and AEP than has often been assumed in the past. 3) Hub height wind speed variability can be estimated from computations based on reanalysis data such as those available from Vortex. 4) If multi-year P90 values are critical for a multifarm development there are advantages in geographic diversification.