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Electrical power systems are transitioning from fuel-based generation to renewable generation and transmission interfaced by power electronics. This transition challenges standard power system modeling, analysis, and control paradigms across timescales from milliseconds to seasons. This tutorial focuses on frequency stability on timescales of milliseconds to seconds. We first review basic results for grid-following (GFL) and grid-forming (GFM) control of voltage source converters (VSCs), typical renewable generation, and high voltage direct current (HVdc) transmission. In this context, it becomes apparent that GFL and GFM control functions are needed to operate emerging power systems. However, combining GFL resources, GFM resources, and legacy generation on the same system results in highly complex dynamics that are a significant obstacle to stability analysis. The remainder of the tutorial provides an overview of recent developments in universal GFM controls that bridge the gap between GFL and GFM control and provide a pathway to a coherent control and analysis framework accounting for power generation, power conversion, and power transmission. 

In this work, we investigate grid-forming control for power systems containing three-phase and single-phase converters connected to unbalanced distribution and transmission networks, investigate self-balancing between single-phase converters, and propose a novel balancing feedback for grid-forming control that explicitly allows to trade-off unbalances in voltage and power. We develop a quasi-steady-state power network model that allows to analyze the interactions between three-phase and single-phase power converters across transmission, distribution, and standard transformer interconnections. We first investigate conditions under which this general network admits a well-posed kron-reduced quasi-steady-state network model. Our main contribution leverages this reduced-order model to develop analytical conditions for stability of the overall network with grid-forming three-phase and single-phase converters connected through standard transformer interconnections. Specifically, we provide conditions on the network topology under which (i) single-phase converters autonomously self-synchronize to a phase-balanced operating point and (ii) single-phase converters phase-balance through synchronization with three-phase converters. Moreover, we establish that the conditions can be relaxed if a phase-balancing feedback control is used. Finally, case studies combining detailed models of transmission systems (i.e., IEEE 9-bus) and distribution systems (i.e., IEEE 13-bus) are used to illustrate the results for (i) a power system containing a mix of transmission and distribution connected converters and, (ii) a power system solely using distribution-connected converters at the grid edge.