Optimal Distribution of Grid-Following and Grid-Forming Converters for Charging Control of Electric Vehicles

We address the problem of determining the optimal combination of grid-following (GFL) versus grid-forming (GFM) modes of control in electric vehicle charging stations (EVCSs) to maintain an acceptable balance between small-signal stability and voltage stability of electric distribution grids. We recall the state-space dynamic models of EVCSs operating in GFL and GFM modes and demonstrate how high charging rates of electric vehicles (EVs) in the GFL mode can impact small-signal performance. We then optimize the GFL-to-GFM ratio while also determining the optimal EV charging setpoints and a state-feedback controller to minimize the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub>-norm of the grid transfer function (TF). To make the proposed optimization computationally favorable, we use participation factor analysis to identify the most dominant EVCSs in the GFM mode so that they can be prioritized for optimization. We validate our results using a modified model of the IEEE 33-bus power distribution test system with ten EVCSs.