On the Existence and Linear Approximation of the Power Flow Solution in Power Distribution Networks

By Saverio Bolognani, Sandro Zampieri. IEEE Transactions on Power Systems, 2014

446 citations recorded by the source corpus.

We consider the problem of deriving an explicit approximate solution of the nonlinear power equations that describe a balanced power distribution network. We give sufficient conditions for the existence of a practical solution to the power flow equations, and we propose an approximation that is linear in the active and reactive power demands of the PQ buses. For this approximation, which is valid for generic power line impedances and grid topology, we derive a bound on the approximation error as a function of the grid parameters. We illustrate the quality of the approximation via simulations, we show how it can also model the presence of voltage controlled (PV) buses, and we discuss how it generalizes the DC power flow model to lossy networks.

Subfields: Control and Systems Engineering, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/81031ab2782d70f61ce6dc9d9f51dbdf0d36e41b

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In Control and Systems Engineering

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Citations in the corpus

A Survey of Distributed Optimization and Control Algorithms for Electric Power Systems (2017, methodology): “See [20]–[22] for further details.”
A mixed integer linear programming approach for optimal DER portfolio, sizing, and placement in multi-energy microgrids (2017, methodology): “Also, the norm ‖⋅‖ for a matrix is defined as the maximum of the 2-norm values of its row vectors [37].”