Patchworking the Log-critical locus of planar curves

We establish a patchworking theorem \`a la Viro for the Log-critical locus of algebraic curves in $(\mathbb{C}^*)^2$. As an application, we prove the existence of projective curves of arbitrary degree with smooth connected Log-critical locus. To prove our patchworking theorem, we study the behaviour of Log-inflection points along families of curves defined by Viro polynomials. In particular, we prove a generalisation of a theorem of Mikhalkin and the second author on the tropical limit of Log-inflection points.Comment: 30 pages, 11 figures. Version 2: minor changes, new Remark 3.1, new Figure 6. Comments are welcom

Real phase structures on matroid fans and matroid orientations

We introduce the notion of real phase structure on rational polyhedral fans in Euclidean space. Such a structure consists of an assignment of affine spaces over $\mathbb{Z}/2\mathbb{Z}$ to each top dimensional face of the fan subject to two conditions. Given an oriented matroid we can construct a real phase structure on the fan of the underlying matroid. Conversely, we show that from a real phase structure on a matroid fan we can produce an orientation of the underlying matroid. Thus real phase structures are cryptomorphic to matroid orientations. The topes of the orientated matroid are recovered immediately from the real phase structure. We also provide a direct way to recover the signed circuits of the oriented matroid from the real phase structure.Comment: 24 pages, 5 figures. Comments are welcome

Ultracapacitor storage enabled global MPPT for photovoltaic central inverters

In most large scale grid-tied photovoltaic (PV) plants, central inverter configurations are used, mainly due to higher efficiency and lower cost per kW. However, compared to other configurations its Maximum Power Point Tracking (MPPT) efficiency is the lowest since it is the less distributed configuration. Under non-uniform conditions, as partial shading, several local maxima may arise in the PV curve, hence requiring additional actions to maximize the output power of the PV plant. Moreover the growth of renewable sources in electric markets has tightened grid codes; requiring for PV systems to limit power fluctuations to a certain maximum. This paper presents an alternative to perform Global MPPT (GMPPT) while complying with new grid code limitations for electric markets with high penetration of renewables. The proposed alternative consists on adding an Energy Storage System (ESS) at inverter level. The proposed system consists in an ultracapacitor (UC) bank connected to the DC-link of the central inverter through interleaved DC-DC power converters. The proposed configuration is validated through simulations and tested through extreme conditions. The performance of the system is analyzed and compared to other existing solutions