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Published December 2010 | Published
Book Section - Chapter Open

A simple optimal power flow model with energy storage


The integration of renewable energy generation, such as wind power, into the electric grid is difficult because of the source intermittency and the large distance between generation sites and users. This difficulty can be overcome through a transmission network with large-scale storage that not only transports power, but also mitigates against fluctuations in generation and supply. We formulate an optimal power flow problem with storage as a finite-horizon optimal control problem. We prove, for the special case with a single generator and a single load, that the optimal generation schedule will cross the time-varying demand profile at most once, from above. This means that the optimal policy will generate more than demand initially in order to charge up the battery, and then generate less than the demand and use the battery to supplement generation in final stages. This is a consequence of the fact that the marginal storage cost-to-go decreases in time.

Additional Information

© 2010 IEEE. This work is partially supported by Southern California Edison (SCE), the Boeing Corporation, and the National Science Foundation. The authors wish to thank Christopher Clark, Jeff Gooding, and Percy Haralson of SCE for helpful discussions.

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