## Abstract

The distribution side of the traditional power grid is changing as the users (known as prosumers) can inject power to the grid. However, uncontrollable injection of power can destabilize the grid. Thus, the stability of the grid must be maintained. Since the prosumers are self-interested entities, they will take their actions to maximize their own pay-offs. We formulate the problem as a non-cooperative game theoretic problem where the magnitude of the voltage must be within an acceptable limit at each node of the power network. Since the power-flow equations must be satisfied at each node, it becomes a coupled constrained game where the constraints are the same across the prosumers. We propose a distributed penalty based algorithm which converges to an equilibrium. In this mechanism, the prosumers are quoted a price based on the active and reactive power drawn or injected to the power grid. The algorithm is easy to implement and it converges to an efficient solution which maximizes the sum of the utilities of the prosumers while maintaining the grid’s stability.

Original language | English (US) |
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Article number | 452 |

Journal | Energies |

Volume | 13 |

Issue number | 2 |

DOIs | |

State | Published - 2020 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Renewable Energy, Sustainability and the Environment
- Fuel Technology
- Energy Engineering and Power Technology
- Energy (miscellaneous)
- Control and Optimization
- Electrical and Electronic Engineering

## Keywords

- Convex optimization
- Coupled constrained game
- Nash equilibrium
- Power flow model
- Primal-dual algorithm