luke whincop supervisor: nikos kourentzes 5th september … · luke whincop supervisor: nikos...

Modelling solar irradiance for energy generation

Luke WhincopSupervisor: Nikos Kourentzes

5th September 2014


Luke Whincop

Background

Renewable energies like solar power have invaluableimportance for shaping the future of energy security.

Research into solar irradiance can give more efficiency inutilising solar power.

Finding the best way to model it can give us this efficiency, asrenewable energies are not as stable as other sources likenuclear power.

Observing time series will enable us to do this.


Luke Whincop

What is seasonality?

Definition

Seasonality is the predictable pattern in a series influenced byseasonal periods (e.g months of the year).

Usefulness in our problem

We focus splitting the model of SI into different seasonalcomponents, such as particular hours, days or months.

We must deem which seasonal period will produce the bestforecasts.


Luke Whincop

Seasonality Equations

Seasonality Equations and Notation

We can have different seasonality equations:

yt = α +s−1∑k=1

γiDit + ut , t = 1, 2, ... (1)

φ(Ls)yt = θ(Ls)ut , t = 1, 2, ... (2)

These represent deterministic and stochastic seasonality equationsrespectively, where yt is the time series data, Dit is a dummyvariable, ut is white noise, and φ(Ls) and θ(Ls) are AR(Auto-Regressive) and MA (Moving Average) polynomials.


Luke Whincop

SI data from SpainTime Series decomposition of Solar Irradiance over three years

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Figure: Time Series decomposition of SI data in Spain.


Luke Whincop

Time Series decompositionSolar Irradiance at 1:00pm over three years

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Figure: Time Series decomposition of all the 1pms.


Luke Whincop

Limitations in our problem

Seasonality Limitations

However, SI can vary significantly and has multiple seasonalities, soit does not follow conventional seasonality definitions. In fact:

We cannot use (1) or (2) for a direct model. Seasons aredeterministic but don’t fit (1).

Neither additive or multiplicative seasonalities give us a full SImodel either.

Trigonometric seasonalities however could be better at givingus an idea for a full model.

Thus, we consider a different approach in modelling SI seasonality;understanding the causes of its variations can evoke a full pictureof the situation.


Luke Whincop

Causes of SI Variability

Solanki and Unrah (2013) identified several causes of variations inSI:

An 11-year solar cycle with aperiodic fluctuations, and alsoevidence of a 22-year Hale cycle.

P-mode oscillations, granulation and magnetic fields onminutes-hours and hours-day scales respectively.

Variations in spectral solar irradiance, although in what wewish to model, we need not include this.


Luke Whincop

Causes of SI Variability

We can also detect causes of variations from the Earth itselfincluding:

Atmospheric changes like cloud cover and pollution.

Orbital changes, as well as variations in planetary motion.

Other factors such as reflections from car lights, moonlightand ice, depending on the location.

We can now proceed with creating the model.


Luke Whincop

Modelling SI: Spanish Data

We have been able to use data from Spanish power plants and useit to simulate models.

Simulation

The simulation consists of the following:

Extract the data, sample from seasonal periods, such as aparticular hour of the day in this case, and put them in a plot;

Find an appropriate function to fit the plot;

Find the RMSE (Root Mean Square Error) of the data.


Luke Whincop


0 200 400 600

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SI at 1:00pm over two years

Time (days)

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Figure: A pointwise 2 year time plot of SI data at 1pm in Spain.


Luke Whincop


Results of Simulation

We produced a curve that was trigonometric in appearance,using the loess function to create the model.

This indicates possible trigonometric seasonalities.

We then decompose the data in order to forecast it and thenbenchmark the forecasting methods.


Luke Whincop

Time Series decompositionSolar Irradiance at 1:00pm over three years

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Figure: Time Series decomposition of all the 1pms.


Luke Whincop

Forecast Analysis and results

Analysis

We can observe seasonal patterns, the second component,that once again look trigonometric.

We then conduct an out-of-sample test of 2 years of data tofind short, mid and long term forecasts.

We proceed to create models using various typical forecastingmethods such as ARIMA and Exponential Smoothing (ETS)

We also use TBATS, a function in R based on the ETS statespace model with other factors like data stabilization, errorinclusion and trend and seasonal components; it in particularlooks at Trigonometric Seasonality.


Luke Whincop


SI forecast one month into the future

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2010.5 2010.6 2010.7 2010.8 2010.9 2011.0 2011.1

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Figure: Forecast one month ahead using tbats


Luke Whincop


SI forecast one year into the future

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Figure: Forecast one year ahead using tbats.


Luke Whincop


Results

The TBATS forecast, a variation of an ETS state-spacemodel, produces an excellent seasonal prediction, withmarginal error between predicted and actual third year data inthe long run.

Short and mid-term forecasts, such as one month, are in linewith the actual data.

This will be helpful for optimizing the operations within thesolar power plant.


Luke Whincop

Empirical Evaluation

ETS ARIMA MAPA TBATS9754.93 7340.47 8468.01 7366.24

Table: Table showing the error of each forecasting methods

The table shows the values obtained, from each forecastingmethod, that are calculated by taking row means of eachforecast value against the actual out-of-sample data pointvalues.

In our case, we believe that ARIMA has the lowest error andthus does the best forecast; TBATS is also very good.


Luke Whincop

Empirical Evaluation

Evaluation

ETS cannot do the optimal forecast as it is limited byimplementation.

It is also useful to check which methods account forseasonality; ETS and MAPA for example don’t do so butTBATS and ARIMA do.

Although some forecasting methods are less efficient in thiscase, they should not be discounted entirely, as they could beuseful in a different error approximation or for differentforecasting periods, such as one month of a year.


Luke Whincop

Conclusions

Taking smaller seasonal periods seems to be an easy, accurateapproach.

Trigonometric seasonal patterns with accurate forecasts havebeen observed.

The current approach could be improved by:

Model over different hours; there might be more volatility atsunsets for example.

Modelling over further seasonality periods, such as a month ofthe whole data set and compare it to the individual hours.

Benchmark the forecasts over these different seasonal periods.

Would solar plants work in the same way in other places likethe UK?


Luke Whincop

References

Thank you, any questions?

References

Solanki, S. K. ; Unruh, Y. C. (2013). Solar irradiance variability.

Hyndman, R.J. ; Athanasopoulos.G (2013). Forecasting: Principles andpractice

De Livera, A.M. ; Hyndman, R.J. ; Snyder, R. D (2011) Forecasting timeseries with complex seasonal patterns using exponential smoothing

Concerning the TBATS function in R.

Caporale, G.M. ; Cunado, J; Alana, L.A.G (2007) Deterministic vsstochastic seasonal fractional integration and structural breaks


Luke Whincop

luke whincop supervisor: nikos kourentzes 5th september … · luke whincop supervisor: nikos...

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