Applying Transformer Limits in Power Flow Studies Using Unconstrained Optimizations

The letter proposes a new method which analyses the states of transformers in power flow studies, by directly considering the limits of both the transformer state (e.g., minimum and maximum tap) and the control (e.g., minimum and maximum voltage). The method uses an empirically developed cost function, which rapidly increases where the transformer limits are exceeded, and decreases where they are not. Unconstrained optimization techniques are used to minimize the cost function. Since the structural limits (e.g., maximum or minimum tap) are stricter than the control limits (e.g., minimum and maximum voltage), the cost function is designed so that its increase rate for exceeding control limits is lower if structural limits are exceeded. The method is developed for phase-shifting, tap-changing, and quadrature-boosting transformers, and is tested on the IEEE 300 bus system with six devices operating simultaneously.