## Abstract

Smart grids should efficiently integrate stochastic renewable resources while effecting voltage regulation. Energy management is challenging since it is a multistage problem where decisions are not all made at the same timescale and must account for the variability during real-time operation. The joint dispatch of slow- and fast-timescale controls in a smart distribution grid is considered here. The substation voltage, the energy exchanged with a main grid, and the generation schedules for small diesel generators have to be decided on a slow timescale; whereas optimal photovoltaic inverter setpoints are found on a more frequent basis. While inverter and looser voltage regulation limits are imposed at all times, tighter bus voltage constraints are enforced on the average or in probability, thus enabling more efficient renewable integration. Upon reformulating the two-stage grid dispatch as a stochastic convex-concave problem, two distribution-free schemes are put forth. An average dispatch algorithm converges provably to the optimal two-stage decisions via a sequence of convex quadratic programs. Its non-convex probabilistic alternative entails solving two slightly different convex problems and is numerically shown to converge. Numerical tests on real-world distribution feeders verify that both schemes yield lower costs over competing alternatives.

Original language | English (US) |
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Article number | 7820228 |

Pages (from-to) | 4282-4292 |

Number of pages | 11 |

Journal | IEEE Transactions on Smart Grid |

Volume | 9 |

Issue number | 5 |

DOIs | |

State | Published - Sep 2018 |

### Bibliographical note

Funding Information:Manuscript received August 3, 2016; revised December 2, 2016; accepted January 10, 2017. Date of publication January 17, 2017; date of current version August 21, 2018. This work was supported in part by the Spanish Ministry of Education under FPU Grant AP2010-1050, in part by the CAM under Grant S2013/ICE-2933, in part by the MINECO under Grant TEC2013-41604-R, and in part by the NSF under Grant 1423316, Grant 1442686, Grant 1508993, and Grant 1509040. Paper no. TSG-01019-2016.

Publisher Copyright:

© 2017 IEEE.

## Keywords

- Multistage economic dispatch
- convex-concave problem
- stochastic approximation
- voltage regulation