Investigating Intrinsic Energy Consumption

Seasonality

Adedamola Adepetu, Elnaz Rezaei

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outline

• Introduction• Problem Definition• Data Sets• Our Approach• Challenges

introduction

Seasonality is a repetitive behavior observed in time series

Intrinsic inherent repetitions in load

Days, Weeks, Months, Calendar seasons

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daily season

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Time of day

weekly season

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annual season

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SummerWinter Winter

problem definition

• Does the intrinsic load seasonality correspond to predefined ‘seasons’?

• Why does this seasonality exist (if any)?

• How is this affected by exogenous factors: temperature, prices, hours of day etc.?

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expected results

Establish a procedure for determining actual load seasonality, resulting in:

• Improved electricity pricing structure• More informed load prediction

process• Storage sizing for peak load

reduction

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datasets: ieso• Description: Aggregate load for the whole province

of Ontario

• Time Period: 2002 till date

• Resolution: 1 hour

• Weather data available from Environment Canada

• Electricity prices also available

• This is at the macro level9

datasets: essex• Description: Load profiles for 6800 homes in

Windsor, Ontario

• Time Period: 1.5 years

• Resolution: 1 hour

• Weather data available from Environment Canada

• This is the micro level

• Also contains outages10

datasets: irish• Description: Load profiles for 4560

homes, somewhere in Ireland

• Time Period: 1.5 years

• Average weather data for Ireland?

• Resolution: 30 minutes

• Electricity & gas11

our approach

• Observe (without preconception) seasonality in all datasets

• Determine impact of exogenous features

• Match macro & micro levels, i.e., Ontario & Essex patterns

• Validation

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observing seasonality

• Autocorrelation– Includes Partial Autocorrelation

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observing seasonality

• Fourier series analysis– Spectral analysis

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Time (months)

observing seasonality

• Additive modely = trend + seasonal_component +

error

• Multiplicative modely = trend *seasonal_component + error

Aggregation of home load? Yes & No.

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impact of exogenous features

• Temperature

• Hours of day & night

• Prices (any feedback?)

• Weekends & Holidays (not exogenous per se but still important)

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regression

• Seasonal AutoRegressive Moving Average (SARMA)

• Seasonal ARIMA (verify nonstationarity of data)

• ARMAX? …X for ‘exogenous’

• Use regressive model from macro level as a feature at micro level

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validation

• Bootstrapping“…statistical inference based on building a sampling distribution for a statistic by resampling from the data at hand.” – Fox, 2002

Used to establish confidence intervals

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challenges

• What if we find nothing?

• Longer time periods required for micro-level datasets

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references• Bisgaard, Soren and Kulahci, Murat. John Wiley &Sons, Inc., 2011. ISBN 9781118056943. doi:

10.1002/9781118056943.ch9.

• Espinoza, M., Joye, C., Belmans, R., and DeMoor,B. Short-term load forecasting, prole identication, and customer segmentation: A methodologybased on periodic time series. Power Systems, IEEETransactions on, 20(3):1622 { 1630, aug. 2005. ISSN0885-8950. doi: 10.1109/TPWRS.2005.852123.

• (IESO), Independent Electricity System Operator.Market Data. Accessed on 18 October 2012,at http://www.theimo.com/imoweb/marketdata/marketdata.asp .

• (OEB), Ontario Energy Board. Electricityprices. Accessed on 18 October 2012, at http://www.ontarioenergyboard.ca/OEB/Consumers/Electricity/Electricity+Prices .

• Singh, R. P., Gao, P.X., and Lizotte, D. J. On Hourly Home Peak Load Prediction. In IEEE SmartGridComm 2012, 2012.

• StatSoft. How To Identify Patterns in Time Series Data: Time Series Analysis. Accessed on 18 October 2012, at https://www.statsoft.com/textbook/time-series-analysis/ .

• Fox, J. (2002). Bootstrapping Regression Models. Annals of Statistics 9, 1-14. Available at: http://www.jstor.org/stable/10.2307/2240411.

• http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4463.htm

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