Wolf-Gerrit Früh Christina Skittides With support from SgurrEnergy Preliminary assessment of wind climate fluctuations and use of Dynamical Systems Theory for resource assessment

Questions How sensitive is the electricity production of a wind farm to the local wind statistics How will climate change affect the electricity production from wind farms? How large are inter-annual variations in the electricity production due to weather fluctuations? How much can a large spatial distribution of wind farms smooth electricity output Can we use dynamic information for an improved wind resource assessment and prediction at potential development sites? 2

Data used Land surface wind data from the MIDAS data record provided by the British Atmospheric Data Centre, maintained by NERC – Hourly winds from weather stations all over the UK – In particular from two stations in Edinburgh, Gogarbank and Blackford Hill – Data format Wind speed in knots at 10 m above sea level Wind direction in degrees Wind data converted to m/s at a typical turbine hub 3

Assumptions Standard wind shear profile Best-fit Weibull distribution Typical turbine performance curve Ideal turbine response All generation exported for use 4

From wind distribution to electricity Number of hours during which the wind was u: Φ(u) * T The output from a turbine during that time: P(u) The electricity generated during those hours: E(u)= P(u) * Φ(u) * T Total output: E total = Σ E(u) 5

Weibull and Rayleigh distributions Cumulative Weibull – k: shape factor Weibull – c: scale factor 6

Capacity factor vs c with k = 2 7

Sensitivity analysis Example: 100 MW farm with expected Capacity factor 30%: Income £26.2 m Actual Capacity factor 27%: Income £23.6 m Deficit: £ 2.4 m

Does the wind always blow somewhere? 9 Fraction of sites producing at full capacity Fraction of sites producing at part capacity Fraction of sites not producing

National capacity factor for first 1000 days in

Has the wind changed? 11 C cap = 0.14 ± 0.06 Edinburgh Gogarbank

Has the wind changed? 12 C cap = 0.28 ± 0.08 Edinburgh Blackford Hill

Assessing resource from a short measurement campaign Short time to measure potential site – Does not give good statistics Are the measurements correlated to a site nearby with existing longer record?  Use ‘MCP’ – Measure a short record – Correlate with longer record – Predict resource at location with shorter record  Christina 13

Statistical Modelling of Wind Energy Resource Christina Skittides Supervisor: Dr. Wolf G. Früh 17 th March

MCP Methods MCP goal: characterize wind speed distribution and estimate the annual energy capture of a wind farm MCP methods: model relationship between wind speed and direction at two sites  Measurement period: a year or more  Input: wind speed and wind direction  Output: mapping from one site to other  Use: apply mapping to more data from reference site 15

MCP Methods MCP invariants:  wind speed, direction  distance, eg. time of flight delays  effects of terrain on the flow, eg. local obstructions  large/small–scale weather, eg. atmospheric stability 16 Reference DerrickWoods & Watson “Variance Ratio” Method Characterisation typical MCP method refinement of typical method alternative Approachwind speed linear regression fit same wind speed, binned wind direction relate variances from reference and target site

Dynamical Systems Theory Dynamical systems involve differential equations that depend on position and momentum Phase space: describes the system’s variables Attractor: defines the solution of the system Orbit: the path the system follows during its evolution Method needed to define equivalent variables to the phase space ones Time-delay 17

Time-Delay/PCA Theory Time-Delay: practical implementation of dynamical systems Results sensitive to choice of delays PCA PCA: non-parametric method to optimize phase space reconstruction identifies number of needed time- delays gives picture of their shape reduces dimensions so as to extract useful information 18

PCA theory Useful PCA outputs: Singular Vectors: represent the dimensions of the phase space, describe optimum way of reconstructing it Singular Values: measure total contribution of each dimension to total variance Principal Components (PC): describe the system’s time series, separate important variables from noise 19

Pendulum Example Dynamical system with two inputs x,y  Case A (without noise): x= 3sin(t/0.7) y= x+0.4sin(t/π)  Case B (with noise): x= 3sin(t/0.7) y= x+0.4sin(t/π) + 0.6ε 20

Pendulum Example  Case A 21

Noisy Pendulum Example  Case B 22

Conclusions PCA is robust and useful for time series of multiple inputs Noisy or “clean”data: no significant differences Choice of time-delay length and gap of entries in the matrix not important 23

Gogarbank Data 10 year ( ) data taken from Gogarbank station, Edinburgh Input variables: wind speed, direction, pressure, temperature Apply PCA to different models:  all variables  wind speed, direction and pressure  only wind speed and direction 24 hourlyevery 3 hoursdaily weekly×× 2 weeks×× monthly×× seasonal×

Gogarbank Data Only wind speed and direction, hourly measurements per week 25

Conclusions Gogarbank station wind: dynamic behaviour found in structure of PCs and singular vectors Adding pressure no significant difference Temperature changes results significantly since PCs concentrate on seasonal cycle Cyclic behaviour over the year, more windy around January and from September- December Using 1 week or 2 weeks identifies weather (typical predictability of weather ~ 14 days) 26

Following Steps Apply PCA to simultaneous data from two weather stations (Gogarbank & Blackford Hill, Edinburgh)  Application to a one-year segment  Using Gogarbank for other years to predict Blackford Hill  Comparison with actual measurements from Blackford Hill 27