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
The main objective of this paper is to review and compare two methodologies to solve the power flow problem considering active power generation droop control. The first methodology is based on a DC power flow model, and the second one is based on a conventional full Newton power flow formulation. The study of two test systems is used to validate the proposed analysis; the first one is the 11-bus system with two distinct areas, and the second one is the 39-bus New England power system. The results presented validate and indicate the effectiveness of the DC power flow approach in order to estimate the steady-state system frequency deviations.
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