## This content will become publicly available on December 17, 2019

# On the marginal value of electricity storage

## Abstract

We investigate the problem of characterizing the economic value of energy storage capacity to a wind power producer (WPP) that sells its energy in a conventional two-settlement electricity market. The WPP can offer a forward contract to supply power in the day-ahead market, subject to financial penalties for imbalances between the contracted power and the power that is delivered in real-time. We consider the setting in which the WPP has access to a co-located energy storage system, and can thus reshape its wind power production subject to its storage capacity constraints. Modeling wind power as a random process, we show that the problem of determining optimal forward contract offerings—given recourse with storage—is convex. We further establish that the maximum expected profit is concave and non-decreasing in the energy storage capacity, which reveals that the greatest marginal benefit from energy storage is derived from initial investment in small storage capacity. We provide a characterization of the marginal value of small energy storage capacity to the WPP. The formulae we derive shed light on the relationship between the value of storage and certain statistical measures of variability in the underlying wind power process.

- Authors:

- Cornell Univ., Ithaca, NY (United States). School of Electrical and Computer Engineering
- Univ. of California, Irvine, CA (United States). Dept. of Electrical Engineering and Computer Science
- Univ. of California, Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Science

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1571135

- Grant/Contract Number:
- AC02-05CH11231

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Systems & Control Letters

- Additional Journal Information:
- Journal Volume: 123; Journal Issue: C; Journal ID: ISSN 0167-6911

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 25 ENERGY STORAGE; Energy storage; Wind energy; Solar energy; Electricity markets; Stochastic control

### Citation Formats

```
Bitar, Eilyan, Khargonekar, Pramod, and Poolla, Kameshwar. On the marginal value of electricity storage. United States: N. p., 2018.
Web. doi:10.1016/j.sysconle.2018.09.007.
```

```
Bitar, Eilyan, Khargonekar, Pramod, & Poolla, Kameshwar. On the marginal value of electricity storage. United States. doi:10.1016/j.sysconle.2018.09.007.
```

```
Bitar, Eilyan, Khargonekar, Pramod, and Poolla, Kameshwar. Mon .
"On the marginal value of electricity storage". United States. doi:10.1016/j.sysconle.2018.09.007.
```

```
@article{osti_1571135,
```

title = {On the marginal value of electricity storage},

author = {Bitar, Eilyan and Khargonekar, Pramod and Poolla, Kameshwar},

abstractNote = {We investigate the problem of characterizing the economic value of energy storage capacity to a wind power producer (WPP) that sells its energy in a conventional two-settlement electricity market. The WPP can offer a forward contract to supply power in the day-ahead market, subject to financial penalties for imbalances between the contracted power and the power that is delivered in real-time. We consider the setting in which the WPP has access to a co-located energy storage system, and can thus reshape its wind power production subject to its storage capacity constraints. Modeling wind power as a random process, we show that the problem of determining optimal forward contract offerings—given recourse with storage—is convex. We further establish that the maximum expected profit is concave and non-decreasing in the energy storage capacity, which reveals that the greatest marginal benefit from energy storage is derived from initial investment in small storage capacity. We provide a characterization of the marginal value of small energy storage capacity to the WPP. The formulae we derive shed light on the relationship between the value of storage and certain statistical measures of variability in the underlying wind power process.},

doi = {10.1016/j.sysconle.2018.09.007},

journal = {Systems & Control Letters},

number = C,

volume = 123,

place = {United States},

year = {2018},

month = {12}

}