Abstract
Most of renewable energy technologies and energy storage devices are operated in dc. Indeed, solar photovoltaic generation and batteries require a dc/ac converter in order to be integrated into a conventional ac distribution grid. Dc distribution emerges a suitable alternative that reduces the losses and increases reliability in modern smartgrids. Classical methodologies such as the optimal power flow require to be adapted to this new scenario. However, just as in the case of ac grids, the power flow in dc distribution grids is non-linear non-convex. Therefore, convex approximations are required in order to guarantee convergence and global optimality. Several approximations can be proposed including second order cone optimization, semidefinite programming and linealization. These approximations are analyzed theoretically and numerically in this chapter.
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Notes
- 1.
There are more general definitions of affine spaces, however, this simple definition is enough for our purposes.
- 2.
we maintain the absolute value representation for the sake of simplicity. Notice also that any software for disciplined convex programming, such as cvx and cvxpy, allows to include effortless norm constraints.
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Acknowledgements
This work is a partial result of the project 111077657914, funded by the Colombian Administrative Department of Science, Technology, and Innovation (COLCIENCIAS), contract number 031-2018.
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Garcés, A. (2020). Convex Optimization for the Optimal Power Flow on DC Distribution Systems. In: Resener, M., Rebennack, S., Pardalos, P., Haffner, S. (eds) Handbook of Optimization in Electric Power Distribution Systems. Energy Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-36115-0_4
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