Journal of Control, Automation and Electrical Systems https://doi.org/10.1007/s40313-019-00507-5 Loading Margin Sensitivity in Relation to the Wind Farm Generation Power Factor for Voltage Preventive Control Victor R. Neumann Silva 1 · Roman Kuiava 2 Received: 8 April 2019 / Revised: 24 June 2019 / Accepted: 3 August 2019 © Brazilian Society for Automatics–SBA 2019 Abstract Due to the growing importance of wind farms in the electric power generation matrix in many countries, for example, in Brazil, this paper proposes voltage preventive control actions as an activity to support the programming of the operation of the electric system, based on the ranking of wind power units that most significantly impact the system’s loading margin through the control of its power factor. A sensitivity index is proposed to obtain this ranking, whose mathematical formulation is based on a linear approximation of the power balance equations in the vicinity of the maximum loading point. The system used to test this proposal is a 56-bus system prepared with current real data from the Northeast subsystem of the National Interconnected System of Brazil that includes 22 wind farms with 234 wind turbines, which comprise a total of 600 MW of installed capacity. The results obtained for the 56-bus test system show the applicability of the proposed voltage preventive control actions by indicating the wind farms that can contribute most significantly to the increase in the system’s loading margin from an adequate adjustment of the power factor of these units. Keywords Voltage preventive control · Wind farms · Sensitivity analysis · Loading margin · Modified power factor · Saddle-node bifurcation 1 Introduction Points of interconnection (POIs) can represent reactive power reservoirs when the renewable generation coupled to the sys- tem, mainly at the sub-transmission level, comes from wind or solar photovoltaic, and may lead to diverse consequences on system stability, as highlighted in Baghsorkhi (2015). In contrast, Tamimi et al. (2011) mentions that the behavior of photovoltaic generation in the electric grid is determined by the way the active and reactive output powers are con- trolled by the inverters, allowing the control of the voltage magnitude in the POI. Other studies point out that if the cou- pled distributed generation is from plants with synchronous B Victor R. Neumann Silva vneumann@ufpr.br Roman Kuiava kuiava@eletrica.ufpr.br 1 Department of Engineering and Exact Sciences, Federal University of Parana, R. Pioneiro, 2153, Palotina, PR ZIP 85950-000, Brazil 2 Department of Electrical Engineering, Federal University of Parana, P.O. Box 19011, Centro Politecnico, Curitiba, PR ZIP 81531-980, Brazil generators, which may be from small hydroelectric power plants or thermoelectric generators, the control variables of these generators (Greene et al. 1997), such as power factor (PF) adjustment (Hatziargyriou et al. 2017), could be used as resources that contribute to the stability of the electrical system, or at least in the vicinity of the POI. Nowadays, due to the growing importance of wind farms in the electric power generation matrix in many countries, and especially in Brazil, it is fundamental to deepen the stud- ies about their behavior during possible disturbances in the grid and, as one of the objectives of this paper, how the cou- pling of wind farms to the electrical system can contribute to mitigate voltage stability problems. Several studies have pro- posed the use of reactive power generation capacity of wind farms to improve the transient stability of the power system (PES) for the improvement in fault ride-through (FRT) to reduce losses of the system and to attenuate the voltage fluc- tuations (Abdelrahem and Kennel 2016; Meegahapola et al. 2010, 2013; Konopinski et al. 2009). In this context, the main contribution of this paper, compared with these studies, is a proposal of a voltage preventive control using the resources of reactive power generation of the wind farms. This volt- age preventive control is based on the wind power units that 123