## Abstract

This paper explores solutions to linearized power-flow equations with bus-voltage phasors represented in rectangular coordinates. The key idea is to solve for complex-valued perturbations around a nominal voltage profile from a set of linear equations that are obtained by neglecting quadratic terms in the original nonlinear power-flow equations. We prove that for lossless networks, the voltage profile where the real part of the perturbation is suppressed satisfies active-power balance in the original nonlinear system of equations. This result motivates the development of approximate solutions that improve over conventional DC power-flow approximations, since the model includes ZIP loads. For distribution networks that only contain ZIP loads in addition to a slack bus, we recover a linear relationship between the approximate voltage profile and the constant-current component of the loads and the nodal active-and reactive-power injections.

Original language | English (US) |
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Title of host publication | 2015 53rd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2015 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 211-217 |

Number of pages | 7 |

ISBN (Electronic) | 9781509018239 |

DOIs | |

State | Published - Apr 4 2016 |

Event | 53rd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2015 - Monticello, United States Duration: Sep 29 2015 → Oct 2 2015 |

### Publication series

Name | 2015 53rd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2015 |
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### Other

Other | 53rd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2015 |
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Country/Territory | United States |

City | Monticello |

Period | 9/29/15 → 10/2/15 |

### Bibliographical note

Publisher Copyright:© 2015 IEEE.