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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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Large-Scale Invariant Sets for Safe Coordination of Thermostatic Loads
Systems often face constraints at multiple levels. For example, in coordinating a collection of thermostatically controlled loads to provide grid services, the controller must ensure temperature constraints for each load (local constraints) and distribution network constraints (global constraints) are satisfied. In this paper, we leverage invariant sets to ensure safe coordination of systems with both local and global constraints. Specifically, we develop a method for constructing a controlled invariant set for a collection of subsystems, modeled as transition systems, to ensure they indefinitely satisfy the constraints, based on cycles in individual transition systems. Then, we develop a control algorithm that keeps the state inside the maximal controlled invariant set.We apply these algorithms to a demand response problem, specifically, the tracking of a power trajectory (e.g., a frequency regulation signal) by a population of homogeneous air conditioners. The algorithm simultaneously maintains local temperature requirements and aggregate power consumption limits, ensuring the control is nondisruptive to consumers and benign to the distribution network.
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- Award ID(s):
- 1837680
- PAR ID:
- 10309789
- Date Published:
- Journal Name:
- American Control Conference (ACC) 2021
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.23919/ACC50511.2021.9483385
