Distributed energy resources flexibility as volumetric options on electricity

Helyette Geman; Yuanye Ma

doi:10.3934/fmf.2023018

Article Contents

2023, Volume 2, Issue 4: 478-496. Doi: 10.3934/fmf.2023018 open access

This issue Previous Article Risk measures under model uncertainty: A Bayesian viewpoint Next Article Backtestability and the ridge backtest

Distributed energy resources flexibility as volumetric options on electricity

Helyette Geman^1,2, and
Yuanye Ma^1, ,

1.
Department of Applied Mathematics and Statistics, Johns Hopkins University, United States
2.
Ralph O'Connors Sustainable Energy Insitute, Johns Hopkins University, United States

^*Corresponding author: Yuanye Ma
^*Corresponding author: Yuanye Ma

Received: August 2023

Revised: August 2023

Early access: September 2023

Published: December 2023

The authors are supported by [U.S. Department of Energy Advanced Research Projects Agency–Energy Award No. DE-AR001274 and Work Authorization No. 19/CJ000/07/08]

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Abstract

The goal of the paper is twofold: a) following the identification of the merits of Distributed Energy Resources (DERs) by FERC 2222 for the flexibility they bring to the grid, we recognize water heaters and thermostats as mini-batteries and introduce volumetric/swing options that the Aggregator can sell by shifting consumers' consumption while rewarding them; b) We propose to address the pricing complexity of these volumetric options - which are in our setting very general in terms of number of exercises and quantities constraints - by a novel approach that combines Monte Carlo simulations and Recurrent Neural Networks (RNN).

Keywords:

Mathematics Subject Classification: 68T07, 68T09, 60H15, 90C39.

Citation:

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Figure 1. Histogram of control durations in the PE dataset

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Figure 2. Examples of average consumption in the PE dataset

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Figure 3. Ground truth versus fitted value of the electricity price $ S_t $

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Figure 4. Five simualted electricity price paths for 10/01/2021 from 12AM to 5PM

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Table 1. Summary of control types in the Packetized Energy dataset

Number of Days with Control	Control Time Range	Control Duration
119	1:30pm to 6:15pm	3 to 4.75 hours
118	5pm to 9:15pm	2 to 4 hours
106	5pm to 8:15pm	0.25 to 1 hour

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Table 2. Summary of Delta obtained from the RNN

	8AM	9AM	10AM	11AM	12PM	1PM	2PM	3PM	4PM	5PM
$ \Delta_t $	5.10	1.12	0.77	0.82	0.32	1.81	15.87	1640.6	1057.7	1378.0

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Table 3. Linearity scaling of the volumetric option in the EcoBee dataset

Scale $ c $	100	10	4	2	1	0.5	0.25	0.1	0.01
Revenue
Scaled
by $ c^{\prime} $	100	9.99	3.99	1.99	1	0.501	0.244	0.0992	0.0100
$ c/c^{\prime} $	1	0.999	0.9975	0.995	1	1.002	0.976	0.992	1

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Table 4. Linearity scaling of the volumetric option in the PE dataset

Scale $ c $	100	10	4	2	1	0.5	0.25	0.1	0.01
Revenue
Scaled
by $ c^{\prime} $	99.7	9.98	4.04	2.01	1	0.505	0.251	0.0993	0.00999
$ c/c^{\prime} $	0.997	0.998	1.01	1.005	1	1.01	1.004	0.993	0.999

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