Uncertainty analysis

In Vind AI, energy yield analyses report the mean net energy by default, without accounting for uncertainties. This value is also used in the financial analysis to calculate the Levelized Cost of Energy (LCoE). However, Vind AI can also incorporate uncertainties in input parameters to assess how they propagate through to the distribution of net energy results, and ultimately affect the LCoE. The following section describes the methodology and assumptions behind the uncertainty analysis.

The uncertainties taken into account in the analysis are divided into four main categories:

All of these, except for the interannual variability, are specified by the user in the analysis configuration. Default values have been set based on numbers from Lee and Fields [1]. A detailed description of the modelling of these is provided below.

The uncertainty due to interannual variations is calculated automatically based on the long term wind time series used in the yield analysis, where a 1-year averaging is considered. As a long term time series typically covers only 20-60 years, fitting a distribution to the data to estimate the interannual variability could lead to large inaccuracies. To robustly estimate the variability, the implementation in Vind AI therefore follows the method described by Hrafnkelsson et al. [2]. Here, the year is divided into N blocks, each consisting of d = (365/N) days. A Monte Carlo simulation is then performed to sample a large number of new artificial years by selecting each of the N blocks by random from the different years available in the long term data. Based on internal studies, d is taken as 5 in this implementation, as the autocorrelation in the wind speed is found to be negligible at this point. This way, the seasonality and autocorrelation in the data is preserved.

This method still requires a certain length of wind data to give robust estimates on the uncertainty. Therefore, if the wind time series used in the yield analysis covers a shorter time span than 10 years, the uncertainty analysis will not run.

An arbitrary number of wind speed uncertainties can added by the user in the analysis configuration, and they are assumed to be independent from each other. Each uncertainty is assumed to be normally distributed, and is translated into an AEP uncertainty. This translation is based on the yield analysis already performed, where a response surface of the park power production is created as a function of wind speed and wind direction. To find the sensitivity in net energy for a given change in wind speed, an interpolation is performed in this response surface for each time step, and summed up to find the total change in AEP. The uncertainties are then applied as the other energy uncertainties described below.

An arbitrary number of energy uncertainties can added by the user in the analysis configuration, and they are assumed to be independent from each other. Each uncertainty is assumed to be normally distributed, and is added on the net energy.

The availability uncertainty can be added by the user in the analysis configuration. The availability is assumed to be beta distributed [3], where the mean value is taken as the availability loss value which is set by the user in the Fixed losses tab in the analysis configuration. The availability uncertainty is added on the net energy.

All individual uncertainties added to the input are considered independent, and their contributions are therefore multiplied. A Monte Carlo simulation is then performed until the P90 value for the net energy has converged to 0.1%.

Several percentiles, such as P90 and P50, are reported based on the empirical cumulative density function (CDF) resulting from the Monte Carlo simulation. In addition, the net energy distribution is shown as a histogram in the dashboard. The user can also select which percentile to use for the AEP in the LCoE calculations, through an input in the financial configuration.

[1] Lee and Fields, 2021, "An overview of wind-energy-production prediction bias, losses, and uncertainties". Wind Energ. Sci., 6, 311–365.

[2] Hrafnkelsson, Oddsson and Unnthorsson, 2016, "A Method for Estimating Annual Energy Production Using Monte Carlo Wind Speed Simulation". Energies 2016, 9(4), 286.

[3] Horn and Leira, 2019, "Fatigue reliability assessment of offshore wind turbines with stochastic availability". Reliability Engineering and System Safety 191 (2019) 106550.