• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.189-202
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• 2014

An element r of a commutative semiring R with identity is said to be identity-summand if there exists $1{\neq}a{\in}R$ such that r+a = 1. In this paper, we introduce and investigate the identity-summand graph of R, denoted by ${\Gamma}(R)$. It is the (undirected) graph whose vertices are the non-identity identity-summands of R with two distinct vertices joint by an edge when the sum of the vertices is 1. The basic properties and possible structures of the graph ${\Gamma}(R)$ are studied.

• Journal of Power Electronics
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• v.11 no.3
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• pp.360-368
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• 2011

This paper proposes an active frequency with a positive feedback in the d-q frame anti-islanding method suitable for a robust phase-locked loop (PLL) algorithm using the FFT concept. In general, PLL algorithms for grid-connected PV PCS use d-q transformation and controllers to make zero an imaginary part of the transformed voltage vector. In a real grid system, the grid voltage is not ideal. It may be unbalanced, noisy and have many harmonics. For these reasons, the d-q transformed components do not have a pure DC component. The controller tuning of a PLL algorithm is difficult. The proposed PLL algorithm using the FFT concept can use the strong noise cancelation characteristics of a FFT algorithm without a PI controller. Therefore, the proposed PLL algorithm has no gain-tuning of a PI controller, and it is hardly influenced by voltage drops, phase step changes and harmonics. Islanding prediction is a necessary feature of inverter-based photovoltaic (PV) systems in order to meet the stringent standard requirements for interconnection with an electrical grid. Both passive and active anti-islanding methods exist. Typically, active methods modify a given parameter, which also affects the shape and quality of the grid injected current. In this paper, the active anti-islanding algorithm for a grid-connected PV PCS uses positive feedback control in the d-q frame. The proposed PLL and anti-islanding algorithm are implemented for a 250kW PV PCS. This system has four DC/DC converters each with a 25kW power rating. This is only one-third of the total system power. The experimental results show that the proposed PLL, anti-islanding method and topology demonstrate good performance in a 250kW PV PCS.