On Balancing Phase Angles with Droop Control

Citation Author(s):
Siddharth
Raju
University of Minnesota
Brian
Johnson
University of Texas
Alejandro
Domınguez-Garcia
University of Illinois
Sairaj
Dhople
University of Minnesota
Submitted by:
Siddharth Raju
Last updated:
Tue, 12/10/2024 - 22:12
DOI:
10.21227/y1pc-5a61
License:
Creative Commons Attribution
83 Views
Categories:
Power and Energy
Electric Utility
Keywords:
Delta interconnection, droop control, phase balance, wye interconnection.
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Abstract 

We establish topological and parametric conditions under which phase angles across three identical impedances can be balanced with small-signal stability guarantees when served from three single-phase sources executing active-power frequency droop control. All standard topologies involving Delta and Wye interconnections of sources and loads are examined. The equilibria of phase-angle dynamics are shown to include the desired phase-balanced state, but in addition, they also exhibit an undesirable phase-synchronized state and bi-cluster synchronous state (in which two of the phase angles coincide). The aforementioned analytical conditions for asymptotic stability of phase-balanced equilibria are uncovered by examining the spectral properties of the Jacobian of the linearized dynamics. Simulation results validate the analytical findings.

Instructions: 

Content:

1. UnifiedClosedForm.pdf: This contains the step-by-step derivation for every expression in the paper.

2. Notebook.mlx (verified to be working on Matlab 2023a): Matlab live script file to:

    • Verify all the closed-form expressions obtained for the different topologies,
    • Verify the equilibrium points,
    • Verify/determine the stability constraints,
    • Generate the vector plot for the phase-angle dynamics.

    3. TimeDomainSimulation folder (verified to be working on Matlab 2023a): Simulink model for the time-domain simulation for (Δ/Y) and (Y/Y) cases. 

     

    Instruction to run the live script:

    1. Requires MATLAB (tested on 2023a).
    2. This document is self-explanatory. Initialize all the parameters in the script, including selecting the desired topology.
    3. Run the script. The results will show up against each section on the right.

    Instruction to run the time-domain simulation :

    1. Requires MATLAB Simulink (tested on 2023a).
    2. Run the "init.m" file to initialize all the parameters.
    3. Run either the "delta_y.slx" for the (Δ/Y) case or the "y_y.slx" for the (Y/Y) case.

    Dataset Files

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