Dynamic Embedded Optimization and Shooting Methods for Power System Performance Assessment

Power system dynamic performance enhancement can often be formulated as a dynamic embedded optimization problem. The associated cost function quantifies performance and involves dynamically evolving state variables. The dynamic model is embedded within the constraints. Power systems form an important example of hybrid systems, with interactions between continuous dynamics and discrete events playing a fundamental role in behavior. However, it is shown that for a large class of problems, the cost function is smooth even though the underlying dynamic response is non-smooth. Complementing this design-oriented optimization framework, techniques for assessing power system performance and vulnerability can often be expressed as boundary value problems, and solved using shooting methods. It is shown that performance limitations are closely related to grazing phenomena. Techniques are presented for determining parameter values that induce limit cycles and grazing. 179 I.A. Hiskens, J-W. Park and V. Donde, "Dynamic embedded optimization and shooting methods for power system performance assessment", in Applied Mathematics for Deregulated Electric Power Systems: Optimization, Control, and Computational Intelligence, J. Chow, F. Wu and J. Momoh (Editors), Springer, 2004.