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This work presents a study of critical areas by using sensitivities and participation factors in different operating points in power systems. Among these operating points are the base case (current operating point), the maximum loading point (MLP) for a direction of load increase with constant power factor, the MLP for a direction of load increase with other power factors and finally the MLP for the worst direction of load increase where the minimum margin is found. The identification of the critical areas is vital in power systems operation and monitoring, it allows the operators taking the more appropriate control actions for guaranteeing a secure system operation, avoiding emergency situations and/or voltage collapse. These control actions are related with active or reactive power re-scheduling, reactive power compensation and load shedding in dangerous situations. The sensitivity analysis is based on the diagonal elements of the Jacobian matrix, which can be used for assessing these critical areas, it measures the activity of the static variables of the system and it is computed with less computational effort when compared with participation factors. It is important to emphasize that the scope of this work tends to demonstrate that by using sensitivity analysis, a dependable shape of the critical areas can be also obtained. Eigenvalues, eigenvectors and other matrices are not necessary for assessing the related critical areas, thus it results in a useful technique for real time applications such as online control and monitoring. IEEE and realistic systems are tested and they are compared with modal analysis in each operating point. In all cases for the active shape it is possible to assess the most critical areas from the current operating point; the shape is dependable in all the cases even in the worst direction of load increase. This behavior presents a variation for the reactive shape, in some cases it is not dependable, therefore, for reactive compensation the reactive shapes should be assessed in each operating point. Finally, contingency emergency situations are shown and assessed both by using sensitivities and participation factors in order to apply the best remedial action for improving the margin, warranting the secure operation. |
