University of Groningen
DC power flow feasibility for constant-power loads Jeeninga, Mark
DOI:
10.33612/diss.168071798
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Publication date: 2021
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Jeeninga, M. (2021). DC power flow feasibility for constant-power loads. University of Groningen. https://doi.org/10.33612/diss.168071798
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1. For a DC power grid with constant-power loads, there exists a one-to-one correspondence between the feasible vectors of power
demands and the long-term voltage semi-stable operating points. (Chapter 4)
2. The operating points associated to a feasible power demand which are either long-term voltage semi-stable, a high-voltage solution, or dissipation-minimizing, are one and the same.
(Chapter 4)
3. There exists a necessary and sufficient LMI condition for DC power flow feasibility. (Chapter 4)
4. In case of nonnegative constant-power demands, there exists a necessary and sufficient scalar-valued condition for DC power flow feasibility. (Chapter 5)
5. A plug-and-play certificate can be formulated to ensure the DC power flow feasibility upon the interconnection of multiple DC microgrids. (Chapter 7)
6. Braess' paradox may occur in most practical DC power grids with constant-power loads and multiple sources, and can be circumvented by ensuring strong feasibility.
(Chapter 8)
7. The power of thorough research is a product of knowing the current state of the art, and seeing the potential for improvement. 8. Without loss of generality mathematics cannot exist.
9. To cheer up any person working in systems and control, simply provide them with a $u(t)$ such that $x(t) > 0$ for all $t>0$.
