Energy modelling

Before performing an energy calculation, WindFarmer requires a flow model to be run to determine the wind speed and direction probabilities over the site.

WindFarmer then simulates flow cases. It considers each wind direction sector in turn and each wind speed bin individually, often > 5000 flow cases for the frequency domain calculation, using the initiation measurement site as reference. For each wind direction, the program determines the corresponding ambient wind speed for each turbine location.

The wake effect of each turbine on the other turbines is calculated for each flow case. See Wake modelling. The first step in this process is to calculate the wind speed and turbulence intensity incident upon the turbine. If a turbine is in more than one wake, the overall wake effect is taken as the largest wind speed deficit and other (smaller) wake effects are neglected. This methodology is based on the results of the assessment of measured data from many wind farms.

The wind speed incident on each turbine is therefore a combination of the ambient wind speed and the wake effect. This incident wind speed is then used to determine if the turbine is operational (with reference to wind sector management and the turbine type’s operational range) and to define the power output. A power look-up table is created where the power output of each turbine is stored for each reference wind direction and wind speed considered.

The Annual Energy Production output is calculated as the sum product of the reference wind speed and direction frequency distribution table and the bin-averaged power output look-up table. Bin-averaged power results are derived from the point-based power look-up table, using a simple integration method that uses results from the adjacent speed steps:

$$P_{\textrm{binned}}\ (U)\ = \ \lbrack\ P(U - 1)\ + \ 6\ x\ P(U)\ + \ P(U + 1)\ \rbrack\ /\ 8\ $$

The association method

The Association Method is a technique used in WindFarmer to minimise errors caused in the wind flow modelling process which allows for a more accurate energy yield.

Using the Association Method allows the user to:

• Use the measured wind speed and directional frequency distributions from the associated measurement site instead of a Weibull distribution to weight each simulated flow case to predict annual energy production.

• Model the variation of the turbulence intensity over a wind farm using the measured turbulence defined on the associated measurement site.

• Model the influence of the topography on turbine wakes.

When calculating wind resources using a flow model (e.g. WindFarmer’s Simple Flow Model or WAsP), the binned wind speed frequency distribution from the recorded time series data at the mast is often approximated by a Weibull curve, which is represented by just two parameters. This is done to reduce the amount of information to be fed into the wind flow modelling calculation, which is a computationally expensive process. The result of the wind flow modelling process is a wind resource (WRG or RSF) which is in the form of Weibull parameters and direction sector probabilities. The wind resource is calculated for the turbine locations at the turbine hub heights.

The relationship between the mast and the turbine locations is based on speedup values: the mean wind speed at the turbine locations divided by the mean wind speed at the mast. The required mean wind speeds are derived from the Weibull parameters at the turbine and mast locations that have been calculated with the flow model. The speedups are derived for each wind direction.

When the Association Method is used, the energy calculation loops over wind speeds at the mast in steps of 1 m/s and the corresponding wind speed at the turbine is calculated from the speedup, as illustrated in the flow chart below. This wind speed at the turbine is then used in the wake calculation which then results in the power output of the turbines for each wind speed step. The Association Method automatically considers the variation of turbulence intensity over the site and the influence of topography on turbine wakes. When combining the power output with the corresponding probability, the measured frequency distribution at the mast is used instead of the Weibull fit used in the flow model.

This method requires Initiation Masts to hold measurements representative of the conditions for the turbine locations. Multiple measurement sites may be needed in complex terrain to meet this requirement.

Apply direction shift to sector probabilities

By default, WindFarmer assumes that the directional distribution at the point of measurement is representative for the turbine sites when using the association method. However, the direction of the wind flow as predicted by the wind flow model may change when passing over terrain. WindFarmer has an optional use of this shift in direction when using the association method. Directional correction factors are obtained with the same methodology as the non-directional speed-up factors. By using this function, the accuracy of energy results can be improved in areas where the measured direction distribution is no longer an adequate representation of the site conditions. Users are however advised to use this function with care as sparsely occupied direction sectors may lead to unrealistic results.

The direction correction factors are the ratio between the sector probababilities predicted by the flow model at the turbine location over the predicted sector probabilities at the sensor location. The corrected probabilities are then normalized so they add up to 1.

$$Prob_{turbine}(u, \theta) = Prob_{tab}(u,\theta)\frac{Prob_{turbine}(\theta)}{Prob_{sensor}(\theta)}$$

Non-association method

Compared to the association method, there are two major differences in the calculation:

• The wind speed and direction probabilities are directly taken from the Weibull parameters and direction distribution in the WRG/RSF data produced with the flow model.

• The ambient wind speed and turbulence are assumed to be the same at all turbines in the wake model.

The calculation loops over speed and direction at a reference point but all speedups are assumed to be equal to one. This means that the incident ambient wind speed and ambient turbulence conditions are the same at all turbines for all flow individual cases considered in the calculation.

The power output of the turbines is derived considering the wake effects. This is then combined with the turbine-specific wind speed and direction probabilities directly taken from the WRG/RSF data to derive the energy output.

Annual Energy Production predictions: Gross, Full and Net yield

WindFarmer reports multiple yield types, considering different models as detailed below:

	Calculated from	Description
Gross	Energy and Wake	The Gross yield is a theoretical energy output of the turbines in free stream conditions in the absence of any wake effects (see note1 about large wind farm effect) or other losses. Factors modelled include air density correction of the turbine power curves according to IEC 61400-12-1 and wind flow modelling to predict the wind turbine location wind climates.
Full	Energy and Wake	The Full yield is the energy yield predicted by the WindFarmer wake and energy model. Depending on your calculation settings, in addition to the modelling within the gross yield prediction, it includes modelling of wakes, wind sector management and high wind speed hysteresis. The Full yield does not include the Blockage Correction (WFA 1.2)
P50 Gross	Monte Carlo Net Energy	The Gross yield after accounting for uncertainty in the wind speed inputs to the wake and energy calculation. Note that because of the asymmetric nature of the wind-speed to energy sensitivity curve the P50 Gross is not equal to the Gross. The P50 Gross is the Gross yield value at which 50% of possible future wind farm energy outcomes are above the value, and 50% are below the value.
(P50) Net	Monte Carlo Net Energy	Net yield is reserved for the outputs of the Monte Carlo Net Energy calculation which accounts for all losses and uncertainties. Different “P” exceedance values can be drawn to understand the uncertainty. The P90 is the energy production at which 90% of possible wind farm energy production outcomes exceed the value.

1. WindFarmer 5.3 included the large wind farm correction and wind sector management in the gross yield. In WindFarmer: Analyst we have the option to run the “Efficiencies” calculation in the energy calculation settings. When this is checked WindFarmer: Analyst will run multiple energy calculation variants with different settings in order to estimate the calculated efficiencies (high wind speed hysteresis, internal wake effect, external wake effect, wind sector management). When the efficiencies calculation is run you get the more useful gross yield with no large wind farm correction or wind sector management.

Time series power

The time series calculation performs a wake and power calculation for a given flow case or a list of flow cases. The ambient conditions input by the user are considered at a reference location, these are then transposed to the turbine location using the speed-ups calculated by the flow model. A flow case is defined by mean wind speed, wind speed standard deviation and wind direction. The air density is required as additional input to run the simulation.

The following models are considered

• Eddy Viscosity wake model (without option for closely spaced turbines)

• Large Wind Farm model

• Turbine sector management rules

• Correction of turbine power curve to local air density at the individual turbine locations

• Speed-ups between measurement sites can also be considered when turbines are initiated from different measurement sites.

Model outputs are the incident wind speed at the individual turbines and the corresponding power output.

Power curve correction to local air density

WindFarmer uses the power at the hub height air density (local air density) to calculate the energy produced by each turbine. Since a power curve at each turbine's hub height air density is not usually available, the necessary values are calculated from the power curves supplied to WindFarmer.

The WindFarmer energy calculation uses a two step approach to obtain the local air density power curve. WindFarmer uses the reference air density input as a representative air density for the whole site.

The first step is to correct from the power curve air density of the turbine type to the site reference air density using the IEC 61400-12 method, described in the next section, to correct the wind speeds and then linearly interpolate the power at the originally defined wind speeds.

In the second step the reference air density power is corrected to the local hub height air density using a density sensitivity ratio to account for the differences between the reference height and the turbine's hub height.

This is the default method used in WindFarmer Analyst.

The WindFarmer: Analyst energy calculation, from version 1.3, also allows users to input multiple power curves at different air densities for a single turbine type. The energy calculation selects the closest power curve to the local air density for each time step and for each turbine prior to applying corrections.

IEC correction

For pitch regulated turbines, the IEC 61400-12 correction is applied to the wind speeds of the power curve to obtain the local air density wind speeds. These are then linearly interpolated to obtain the corrected power output at the turbine incident wind speeds.

$$u_{local} = u_{src}\left(\frac{\rho_{src}}{\rho_{local}}\right)^{\frac{1}{3}}$$

Where u_local is the local air density wind speed and u_src is the turbine type power curve wind speed.

For stall regulated turbines, the correction is directly applied to the power values.

$$P_{local} = P_{src}\frac{\rho_{local}}{\rho_{src}}$$

Where P_local is the local air density power and P_src is the turbine type power curve value.

Air density correction for modulated high wind speed shutdown polices

Some wind turbines have a high wind speed shutdown policy with a "storm control" or "high wind ride through" feature. For these turbines the turbine de-rates at high wind speeds near cut-out to enable a smoother transition to a non-operational state.

For these wind turbines WindFarmer assumes the controller is driven by wind speed signals not impacted by air density, such as those from the nacelle anemometer. Therefore, no air density correction is applied to pitch-controlled turbines operating above the wind speed at which rated power is reached.

Tip

To reduce uncertainties, we recommend using power curves closer to the site air density and using the multi-air density turbine type feature so that the best performance data is selected automatically by the energy calculation for each turbine.