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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.
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A Three-phase Power Flow Model and Balanced Network Analysis
First we present an approach to formulate unbalanced three-phase power flow problems for general networks that explicitly separates device models and network models. A device model consists of (i) an internal model and (ii) a conversion rule. The conversion rule relates the internal variables (voltage, current, and power) of a device to its terminal variables through a conversion matrix Γ and these terminal variables are related by network equations. Second we apply this approach to balanced three-phase networks to formalize per-phase analysis and prove its validity for general networks using the spectral property of the conversion matrix Γ.
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- Award ID(s):
- 1932611
- PAR ID:
- 10402368
- Date Published:
- Journal Name:
- 11th Bulk Power Systems Dynamics and Control Symposium (IREP 2022)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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