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Power-flow modeling of a unified power-flow controller (UPFC) increases the complexities of the computer program codes for a Newton-Raphson load-flow (NRLF) analysis. This is due to the fact that modifications of the existing codes are needed for computing power injections, and the elements of the Jacobian matrix to take into account the contributions of the series and shunt voltage sources of the UPFC. Additionally, new codes for computing the UPFC real-power injection terms as well as the associated Jacobian matrix need to be developed. To reduce this complexity of programming codes, in this paper, an indirect yet exact UPFC model is proposed. In the proposed model, an existing power system installed with UPFC is transformed into an augmented equivalent network without any UPFC. Due to the absence of any UPFC, the augmented network can easily be solved by reusing the existing NRLF computer codes to obtain the solution of the original network containing UPFC(s). As a result, substantial reduction in the complexities of the computer program codes takes place. Additionally, the proposed model can also account for various practical device limit constraints of the UPFC.Index Terms-Flexible ac transmission systems (FACTS), Newton power flow, unified power-flow controller (UPFC).

Abstract. Cannibalism, which is the act of killing and at least partial consumption of conspecifics, is ubiquitous in nature. Mathematical models have considered cannibalism in the predator primarily, and show that predator cannibalism in two species ODE models provides a strong stabilizing effect. There is strong ecological evidence that cannibalism exists among prey as well, yet this phenomenon has been much less investigated. In the current manuscript, we investigate both the ODE and spatially explicit forms of a Holling-Tanner model, with ratio dependent functional response. We show that cannibalism in the predator provides a stabilizing influence as expected. However, when cannibalism in the prey is considered, we show that it cannot stabilise the unstable interior equilibrium in the ODE case, but can destabilise the stable interior equilibrium. In the spatially explicit case, we show that in certain parameter regime, prey cannibalism can lead to pattern forming Turing dynamics, which is an impossibility without it. Lastly we consider a stochastic prey cannibalism rate, and find that it can alter both spatial patterns, as well as limit cycle dynamics.

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Language competition models help understand language shift dynamics, and have effectively captured how English has outcompeted various local languages, such as Scottish Gaelic in Scotland, and Mandarin in Singapore. India, with a 125 million English speakers boasts the second largest number of English speakers in the world, after the United States. The 1961-2001 Indian censuses report a sharp increase in Hindi/English Bilinguals, suggesting that English is on the rise in India. To the contrary, we claim supported by field evidence, that these statistics are inaccurate, ignoring an emerging class who do not have full bilingual competence and switch between Hindi and English, communicating via a code popularly known as "Hinglish". Since current language competition models occlude hybrid practices and detailed local ecological factors, they are inappropriate to capture the current language dynamics in India. Expanding predator-prey and sociolinguistic theories, we draw on local Indian ecological factors to develop a novel three-species model of interaction between Monolingual Hindi speakers, Hindi/English Bilinguals and Hinglish speakers, and explore the long time dynamics it predicts. The model also exhibits Turing instability, which is the first pattern formation result in language dynamics. These results challenge traditional assumptions of English encroachment in India. More broadly, the three-species model introduced here is a first step towards modeling the dynamics of hybrid language scenarios in other settings across the world.