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This paper describes a new methodology to evaluate the area interchange control (AIC) in a power flow problem using the Newton-Raphson method. In this methodology, the equations of the AIC are incorporated into the system of equations of the power flow problem. Thus an augmented system of equations, which is linearized and solved, at each iteration, is obtained. The proposed method has been tested and compared with existing methods in the literature using both small and large scale systems. The results presented validate the proposed technique.Index Terms-Area interchange control, augmented system, power flow problem.

This study presents two approaches to handling under-frequency regulation in isolated microgrids. The first one is a governor power flow (PF) model in which the generators steady-state governor equations are modeled into a full Newton PF formulation resulting in an augmented sparse linearised system of equations to be solved at each iteration. As a result, it is possible to evaluate the under frequency problem in the case of microgrid islanding as well as to set the reference bus angle to evaluate the possibility of reconnection to the main grid. The second approach presents an optimal PF (OPF) formulation in which the generators governor equations are considered as additional equality constraints to determine the minimum amount of load shedding to keep the system frequency between specified limits. In both methods, it is also used an equation that provides voltage regulation in a droop-based control. The reactive power generation limits in the OPF approach are bounded by a proposed complementarity constraint-based method adapted for the generators' droop-controlled terminal voltage. The proposed approaches are evaluated and validated through the study of the EHV1 Network, a 61-bus 33/11-kV radial distribution system, and the New England test system. Ω L set of candidate buses to the load shedding p 1 , p 2 , p 3 active parameters of the ZIP model q 1 , q 2 , q 3 reactive parameters of the ZIP model K p f active load frequency dependency factor K q f reactive load frequency dependency factor V a k /V b k voltage auxiliary variables for complementarity constraints V k min /V k max min./max. voltage at bus k

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