## Abstract

We consider a distribution grid used to charge electric vehicles (EVs) such that voltage drops stay bounded. We model this as a class of resource-sharing networks, known as bandwidth-sharing networks in the communication network literature. We focus on resource-sharing networks that are driven by a class of greedy control rules that can be implemented in a decentralized fashion. For a large number of such control rules, we can characterize the performance of the system by a fluid approximation. This leads to a set of dynamic equations that take into account the stochastic behavior of EVs. We show that the invariant point of these equations is unique and can be computed by solving a specific AC optimal-power-flow problem (ACOPF), which admits an exact convex relaxation. We illustrate our findings with a case study using the SCE 47-bus network and several special cases that allow for explicit computations.

Original language | English |
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Article number | 8709819 |

Pages (from-to) | 1050-1061 |

Number of pages | 12 |

Journal | IEEE Transactions on Control of Network Systems |

Volume | 6 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 2019 |

## Keywords

- AC power flow model
- distribution network
- electric vehicle charging
- fluid approximation
- linearized Distflow
- queueing theory
- stochastic processes