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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
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Outline
• Introduction
• Motivation
• Data & Method
• Results
• Conclusion
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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
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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
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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)
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Single customer
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210 customers
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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
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Outline
• Introduction
• Motivation
• Data & Method
• Results
• Conclusion
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Aggregating 1 to 240 customers
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Aggregating 1 to 30 customers
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Electricity consumption forecast
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PV power production forecast
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Net demand forecast
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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
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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