Investigating the effect of aggregation on prediction intervals in … · 2017. 12. 15. · Investigating the effect of aggregation on prediction intervals in case of solar power,

Investigating the effect of aggregation on

prediction intervals in case of solar

power, electricity consumption and net

demand forecasting

Dennis van der Meer, Joakim Widén, Joakim Munkhammar Email: [email protected] 2017-10-24

Outline

• Introduction

• Motivation

• Data & Method

• Results

• Conclusion

Introduction

• The smoothing effect is well-studied for deterministic forecasting, but not yet for probabilistic forecasting.

Widén et al., On the properties of aggregate clear-sky index distributions and an improved model for spatially correlated instantaneous solar irradiance, Solar Energy 2017, p. 566-580

Motivation

Fonseca Jr et al., Regional forecasts and smoothing effect of photovoltaic power generation in Japan: An approach with principal component analysis, Renewable Energy 2014, p. 403-413

Data & Method • Public data (PV and electricity consumption) of 300 de-

identified customers in the metropolitan area of Sydney

• Randomly aggregate the de-identified consumers in steps of 30 customers from 1 to 240 (after data cleansing)

• Probabilistic forecasting of PV power, electricity consumption and net demand using Gaussian Processes1 (GPs)

• Net demand = electricity consumption – PV production

1 Rasmussen & Williams, Gaussian Processes for Machine Learning (2006)

Single customer

210 customers

Performance metrics • Prediction interval (PI) coverage probability (PICP) • PI normalized average width (PINAW) • Continuous Ranked Probability Score (CRPS)

• PICP = 1𝑇𝑇∑ 𝜖𝜖𝑡𝑡𝑇𝑇𝑡𝑡=1 , where 𝜖𝜖𝑡𝑡 = �

1 if 𝑦𝑦𝑡𝑡 ∈ 𝐿𝐿𝑡𝑡 ,𝑈𝑈𝑡𝑡0 if 𝑦𝑦𝑡𝑡 ∉ 𝐿𝐿𝑡𝑡 ,𝑈𝑈𝑡𝑡

• PINAW = 1𝑇𝑇𝑇𝑇∑ 𝑈𝑈𝑡𝑡 − 𝐿𝐿𝑡𝑡𝑇𝑇𝑡𝑡=1

• CRPS 𝐹𝐹�𝑡𝑡,𝑦𝑦𝑡𝑡 = 𝔼𝔼𝐹𝐹�𝑡𝑡 𝑌𝑌 − 𝑦𝑦𝑡𝑡Abs. differences

− 12𝔼𝔼𝐹𝐹�𝑡𝑡 𝑌𝑌 − 𝑌𝑌𝑌

Spread

Outline

• Introduction

• Motivation

• Data & Method

• Results

• Conclusion

Aggregating 1 to 240 customers

Aggregating 1 to 30 customers

Electricity consumption forecast

PV power production forecast

Net demand forecast

Conclusions • Disadvantage of this study: de-identified data so no

geographical information

• Most significant improvement occurs for the first 25 customers

• CRPS remain constant while spread decreases absolute differences also decrease

• Forecasting net demand offers computational advantages for similar accuracy

• Future work will focus on removing anomalous behavior by bootstrapping

Thank you

Investigating the effect of aggregation on prediction intervals in case of solar power, electricity consumption and net demand forecastingOutlineIntroductionMotivationData & MethodSingle customer210 customersPerformance metricsOutlineAggregating 1 to 240�customersAggregating 1 to 30�customersElectricity consumption forecastPV power production forecastNet demand forecastConclusionsThank you