Dynamic wind farm power simulation
Dougal McQueen, Alan Wood, Allan Miller
University of Canterbury, New Zealand
[email protected]
To manage increased wind power in electricity networks accurate time-series models of generation are required.
Congruent sets of wind speed time-series can be obtained from weather model hindcasts. Transformation from wind
speed to power requires capturing the static and dynamic characteristics.
The static character (topography) is captured using a Gaussian distribution of speed ups. The dynamic character
(spatial and inertial integration) can be modelled using the Sandia method (applying Fourier expansion).
However, the volatility of wind is proportional to the wind speed. The Sandia method assumes homo-skedasticity
thus a method using Wavelet Multi-Resolution analysis is developed.
Test case: Mt Stuart Wind Farm, New Zealand
• Owner: Southern Generation Limited Partnership,
• Operator: Pioneer Generation Limited,
• 9 Gamesa G52 turbines,
• Rolling ridge perpendicular to prevailing wind,
• Nacelle anemometers used to define
• spatial correlations,
• static variation via generalised MCP,
• Meteorological mast used to define low
frequency wind speed time-series.
Sandia method
1. Generate white noise series for each
turbine,
2. Obtain spectra using Fourier transform,
3. Colour noise to Kolmogorov spectrum,
4. Embed correlation using Cholesky
decomposition
of
Davenport’s
coherence (for each frequency),
5. Replace low frequencies (below concomittance < 96 minutes) with scaled
wind speed time series derived from
met mast,
6. Inverse Fourier transform to obtain wind
speed time series for each turbine,
7. Apply wind turbine power curve,
8. Aggregate to find wind farm power time
series.
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Sandia
Fourier transform = sinusoid basis
Assumes variability of wind speed
not related to magnitude of wind
speed (homo-skedasticity)
Over estimates variability at low
wind speeds,
Under estimates high wind speed
variability
Performs very well for test case.
Wavelet Multi-Resolution
1.
For each turbine and scale generate white
noise (Kolmogorov magnitudes) to simulate
wavelet series,
2. For each scale determine correlations (loglinear distance relationship) and
find
weighting
matrices
using
Cholesky
decomposition,
3. Process wavelet series through autoregressive
iteration
with
innovations
multiplied by weighting matrices,
4. Johnson transform, to modify Gaussian series
to match empirical,
5. Taylor transform to model hetero-skedasticity,
6. Appropriate wavelet series into dyadic
structure,
7. Appropriate residual time-series with scaled
wind speed times series (derived from met
mast) into dyadic structure,
8. Inverse wavelet transform to obtain wind
speed time series for each turbine,
9. Apply wind turbine power curve.
10. Aggregate to find wind farm power time
series.
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Wavelet
Beylkin Wavelet (basis) selected to
minimise cross correlation,
Over estimates variability at
medium wind speeds,
Over estimates variability at high
wind speed (high wind hysteresis
control loop not replicated),
Physically more accurate (second
order importance c.f. power curve).