How Does Relative Humidity Affect Electricity Demand?

Ying Chen, Tao Hong PhD

6/23/15

at Charlotte

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Outline

• Introduction and motivation • Data • Methodology • Results • Conclusion

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Introduction

Load-temperature scatter plot (Hong, 2010)

Winter Summer

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Motivation

• To find a benchmark model that including both temperature and relative humidity information for load forecasting.

• Requirements of benchmarking process (Hong, 2010): • Simple • Creditable • Widely applicable • Interpretable • Reproducible

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• 2009-2011 hourly load data from North Carolina Electric Membership Corporation

• 2009-2011 hourly weather data from 27 weather stations in North Carolina

Data

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Time series of load (2009-2011) Time series of relative humidity (2009-2011)

Data (cont.)

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Data (cont.)

Load-relative humidity scatter plots for 12 months Load-relative humidity scatter plots for

summer (6, 7, 8, and 9)

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Load-relative humidity scatter plots in summer by hour

Data (cont.)

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Methodology

Choose a benchmark model

Build new models by adding relative humidity terms to the benchmark model

Feed the data to all the models, and compare the Mean Absolute Percentage Errors (MAPEs) of validation data

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• Cross validation is used to calculate the MAPEs.

• The average of MAPEs from the three cases is used for model comparison.

Case number Training data Validation data

Case 1 2009, 2010 2011

Case 2 2009, 2011 2010

Case 3 2010, 2011 2009

Methodology (cont.)

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• Three benchmark models are used.

• Trend: A linear trend variable. • Tt: Current hour temperature. • Tt-k: Temperature of the previous k-th hour. • Ta: Average temperature of the past 24 hours. • Month, Weekday, Hour are class variables (Hong, Pinson, & Fan, 2014).

Main Effects Cross Effects

B1

Trend, Month, Weekday, Hour,

Tt , Tt2, Tt

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Tt*Month, Tt2*Month, Tt3*Month, Tt*Hour, Tt

2*Hour, Tt3*Hour,

Weekday*Hour

B2

B1+

Ta, Ta2, Ta

3

B1+

Ta*Month, Ta2*Month, Ta3*Month, Ta*Hour, Ta

2*Hour, Ta3*Hour

B3

B2+

Tt-1, Tt-12, Tt-1

3

B2+

Tt-1*Month, Tt-12*Month, Tt-1

3*Month,Tt-1*Hour, Tt-12*Hour, Tt-1

3*Hour

Methodology (cont.)

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• RH: Current hour relative humidity. • Summer(S): dummy variable. June, July, August and

September is defined as summer. • RHS: RH*S. • RHS2: RH*RH*S.

• Candidates to be added:

Main Effects: RHS RHS2

Cross effects: Tt*RHS Tt2*RHS Tt*RHS

2 Tt2*RHS2 ...

RHS*Hour RHS2*Hour

Methodology (cont.)

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Results: B1

B1 RHS RHS2

Tt*RHS Tt

2*RHS Tt*RHS

2 Tt

2*RHS2 RHS*Hour RHS2*Hour MAPE

B1M1 x 5.21%

B1M2 x x 5.20%

B1M3 x x x 5.08%

B1M4 x x x x 5.03%

B1M5 x x x x x 4.91%

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B2 RHS RHS2

Tt*RHS Tt

2*RHS Tt*RHS

2 Tt

2*RHS2 Ta*RHS Ta

2*RHS Ta*RHS

2 Ta

2*RHS2 RHS*Hour RHS2*Hour MAPE

B2M1 x 4.10%

B2M2 x x 4.10%

B2M3 x x x 4.03%

B2M4 x x x x 3.98%

B2M5 x x x x x 3.96%

B2M6 x x x x x x 3.96%

B2M7 x x x x x x x 3.84%

Results: B2

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B2 RHS RHS2

Tt*RHS Tt

2*RHS Tt*RHS

2 Tt

2*RHS2 Ta*RHS Ta

2*RHS Ta*RHS

2 Ta

2*RHS2 RHS*Hour RHS2*Hour MAPE

B2M1 x 4.10%

B2M2 x x 4.10%

B2M3 x x x 4.03%

B2M4 x x x x 3.98%

B2M5 x x x x x 3.96%

B2M6 x x x x x x 3.96%

B2M7 x x x x x x x 3.84%

B2M8 x x x x x x 3.84%

Results: B2

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B2 RHS RHS2

Tt*RHS Tt

2*RHS Tt*RHS

2 Tt

2*RHS2 Ta*RHS Ta

2*RHS Ta*RHS

2 Ta

2*RHS2 RHS*Hour RHS2*Hour MAPE

B2M1 x 4.10%

B2M2 x x 4.10%

B2M3 x x x 4.03%

B2M4 x x x x 3.98%

B2M5 x x x x x 3.96%

B2M6 x x x x x x 3.96%

B2M7 x x x x x x x 3.84%

B2M8 x x x x x x 3.84%

B2M9 x x x x x 3.85%

Results: B2

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B3 RHS RHS2

Tt*RHS Tt

2*RHS Tt*RHS

2 Tt

2*RHS2 Ta*RHS Ta

2*RHS Ta*RHS

2 Ta

2*RHS2 Tt-1*RHS Tt-1

2*RHS Tt-1*RHS

2 Tt-1

2*RHS2 RHS*Hour RHS2*Hour MAPE

B3M1 x 3.87%

B3M2 x x 3.87%

B3M3 x x x 3.82%

B3M4 x x x x 3.76%

B3M5 x x x x x 3.74%

B3M6 x x x x x x 3.74%

B3M7 x x x x x x x 3.74%

B3M8 x x x x x x x x 3.74%

B3M9 x x x x x x x x x 3.68%

Results: B3

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B3 RHS RHS2

Tt*RHS Tt

2*RHS Tt*RHS

2 Tt

2*RHS2 Ta*RHS Ta

2*RHS Ta*RHS

2 Ta

2*RHS2 Tt-1*RHS Tt-1

2*RHS Tt-1*RHS

2 Tt-1

2*RHS2 RHS*Hour RHS2*Hour MAPE

B3M1 x 3.87%

B3M2 x x 3.87%

B3M3 x x x 3.82%

B3M4 x x x x 3.76%

B3M5 x x x x x 3.74%

B3M6 x x x x x x 3.74%

B3M7 x x x x x x x 3.74%

B3M8 x x x x x x x x 3.74%

B3M9 x x x x x x x x x 3.68%

B3M10 x x x x x x 3.68%

Results: B3

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B3 RHS RHS2

Tt*RHS Tt

2*RHS Tt*RHS

2 Tt

2*RHS2 Ta*RHS Ta

2*RHS Ta*RHS

2 Ta

2*RHS2 Tt-1*RHS Tt-1

2*RHS Tt-1*RHS

2 Tt-1

2*RHS2 RHS*Hour RHS2*Hour MAPE

B3M1 x 3.87%

B3M2 x x 3.87%

B3M3 x x x 3.82%

B3M4 x x x x 3.76%

B3M5 x x x x x 3.74%

B3M6 x x x x x x 3.74%

B3M7 x x x x x x x 3.74%

B3M8 x x x x x x x x 3.74%

B3M9 x x x x x x x x x 3.68%

B3M10 x x x x x x 3.68%

B3M11 x x x x x 3.70%

Results: B3

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Results: summary

• The proposed benchmark model including both temperature and relative humidity effects are:

+ RHS RHS2

Tt*RHS Tt

2*RHS Tt*RHS

2 Tt

2*RHS2

RHS*Hour RHS2*Hour

Effects to temperature benchmark models

3%

4%

5%

6%

B1 B2 B3

5.21%

4.10% 3.87%

4.91%

3.85% 3.70% MA

PE

Benchmark model Plus RH

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Conclusion • Scatter plot shows there is relationship between load and relative

humidity, especially during summer months (6-9), and the influence of relative humidity has hourly difference.

• Adding relative humidity terms to three different benchmark models shows that they can reduce the models’ MAPEs around 0.2-0.3%.

• The proposed benchmark model including both temperature and relative humidity effects are:

+ RHS RHS2

Tt*RHS Tt

2*RHS Tt*RHS

2 Tt

2*RHS2

RHS*Hour RHS2*Hour

effects to temperature benchmark models

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Q&A

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Reference

• Hong, T. (2010). Short term electric load forecasting (Doctoral dissertation). Retrieved from ProQuest Dissertations and Theses. (Accession Order No. AAT 3442639).

• Hong, T., Pinson, P., & Fan, S. (2014). Global Energy Forecasting Competition 2012. International Journal of Forecasting, 30(2), 357-363.

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