Abstract
This paper provides an overview of various methods for finding limit states in power systems based on the condition of static aperiodic stability. The focus is on methods such as sequential load increase, the method of analytical limit state equations, and the optimization search for the limit state. Both domestic and international sources on this topic were reviewed. The method of finding the limit state through sequential load increase, currently used in operational dispatch control, is examined in detail. This method is established in the "Guidelines for Power System Stability" and key regulatory technical documents of the system operator. Additionally, the foreign equivalent, Continuation Power Flow, which is generally considered analogous to sequential load increase despite significant algorithmic differences, is described. There are alternatives to the sequential load increase method that allow for finding limit states. One research direction in this area is the analytical method, which formulates limit state equations. These are nonlinear equations whose solution represents the nearest limit state. Another research direction is the optimization approach to finding the limit state. Studies vary in terms of which specific state needs to be found from all possible limit states affecting the objective function. Moreover, various mathematical optimization methods are explored for their computational stability and convergence to the required solution depending on the initial approximation point. The proof of the identity between the analytical form of the limit state equations and the optimization procedure for finding the nearest limit state is also considered.
Keywords
voltage stability limit, electrical power system, continuation power flow, optimization procedure, limit equations, controlled section
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