Cycle Detection and Removal in Electricity Markets

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Cycle Detection and Removal in Electricity Markets

• Lunch at Lab Presentation
• Matt Lyle
• Department of mathematicsstatistics
• University of Calgary, Alberta

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Outline

• Characteristics of electricity spot prices
• Electricity price function
• The Seasonal Function
• The FFT
• The sweeping method
• Noise characteristics
• Some ending remarks

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Electricity spot price characteristics

• Very high volatility
• Numerous price spikes
• High rate of mean reversion
• Seasonal (cyclical) behaviour
• Cannot be economically be stored

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Hrly prices for AB and PJM markets
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Electricity Price Function

• Suppose that the spot price is as follows
• Where
• is the deterministic component
• is the Stochastic component
• is the spot price

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Electricity Price Function

• We would like to be able to model
  directly, but it is complicated
• Instead we try to model its components separately
  and then combine them afterwards

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Seasonal Function

• Since in this presentation we are concerned with
  the deterministic component of the price, we
  begin by assuming
• Where can be estimated using a linear
  fit on the data set
• And is the seasonal or cyclical term that
  needs to be determined

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Seasonal Function

• Going back to we have

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The Fast Fourier Transform

• The continuous time Fourier Transform is defined
  as
• Discretizing
• We get the discrete Fourier Transform

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The Fast Fourier Transform

• With now de-trended we can now perform the
  FFT on the data

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The sweeping method

• With the cyclical components identified we now
  need to separate them from the noise
• We can do this by first noting the location of
  the spikes in the frequency domain. We use the
  first eight most dominant spikes.
• And then remove those spikes from the set

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The Sweeping Method

• After removing the eight spikes from the set we
  can see that spikes still remain

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The Sweeping Method

• We again identify the eight most dominant spikes
  and remove them

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The Sweeping Method
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The Sweeping Method
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The Sweeping Method

• After the third sweep we stop. But more or
  less sweeps can be applied for different data
  sets

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The Sweeping Method
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The Sweeping Method
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The Sweeping Method

• We know have our cyclical and stochastic
  components separated
• By taking the inverse FFT or IFFT we can restore
  the seasonal and stochastic components to the
  time domain
• And we now have the stochastic component by itself

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Noise Characteristics

• The time domain of the noise

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Noise Characteristics

• Density of the Alberta spot prices

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Noise Characteristics

• Density of PJM spot prices

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Ending Remarks

• Some advantages with this method
• 1) Robust
• 2) Allows for a visual interpretation of the
  cycles
• 3) FFT algorithm is common in many
  computational packages
• 4) Calibration time is reduced

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Ending Remarks

• Some disadvantages with this method
• 1) Hard to identify low frequency components
• 2) More work at the front end of model
  construction
• 3) Deciding how many sweeps to do is hard to
  identify

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Thank you

• mrlyle_at_math.ucalgary.ca