This code provides a visualization of power flow feasibility set, which is defined by the AC power flow equations and operational constraints. The AC power flow equation is a set of nonlinear equations, which creates a nonlinear manifold in high dimension illustrated in Figure (a). The feasibility set projects the manifold onto the power injection space shown in Figure (b).
(The figures are from the reference [2]. Here we provide code for plotting the feasibility set. You can read the references for convex restriction.)
The color and style of the contour represents the type of violated limit.
Solid blue line - Maximum voltage magnitude limit
Dashed blue line - Minimum voltage magnitude limit
Solid Yellow line - Maximum reactive power generation & slack bus active power generation limit
Dashed Yellow line - Minimum reactive power generation & slack bus active power generation limit
Solid Purple line - Line flow magnitude limit
Thick solid blue line - Solvability boundary
The script is based on MATLAB and MATPOWER. Run 'plot_9bus.m' as an example, which can be run without installation.
This research code was developed and used for the following articles.
[1] Convex Restriction of Power Flow Feasibility Set
@article{lee2019convex,
author={Lee, Dongchan and Nguyen, Hung D. and Dvijotham, K. and Turitsyn, Konstantin},
journal={IEEE Transactions on Control of Network Systems},
title={Convex Restriction of Power Flow Feasibility Sets},
year={2019}, volume={6}, number={3}, pages={1235-1245}, month={Sep.}
}
[2] Feasible Path Identification in Optimal Power Flow with Sequential Convex Restriction
@article{lee2019feasible,
title={Feasible Path Identification in Optimal Power Flow with Sequential Convex Restriction},
author={Lee, Dongchan and Turitsyn, Konstantin and Molzahn, Daniel K and Roald, Line A},
journal={arXiv preprint arXiv:1906.09483},
year={2019}
}