Uniqueness of the power flow solutions in low voltage direct current grids

- Existence and uniqueness of the solution of the power flow in LVDC grids.
- This is independent of the numerical method.
- It is independent of size and topology of the LVDC grid.
- The analysis is extended to high load conditions.
- A computational simulation corroborates the theoretical analysis.

Low voltage direct current (LVDC) is a promising technology for future power distribution grids and smart grids applications. Power flow in these grids is a non-linear problem just as its counterpart AC. This paper demonstrates that, unlike in AC grids, convergence and uniqueness of the solution can be guaranteed in this type of grid under well defined practical considerations. The result is neither a linearization nor an approximation, but an analysis of the set of non-linear algebraic equations, which is valid for any LVDC grid regardless its size, topology or load condition. Computer simulation corroborates the theoretical analysis.

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