1. A Set Membership Framework for Dynamic Security Assessment
PSERC Summer Workshop
Lake Tahoe, CA
August 4-7, 2008
Alejandro D. Dominguez-Garcia
Department of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign

2. PJM Motivational Example
PJM Real-Time Stability Assessment and Control for DSA:
the tool explicitly considers models of PJM and the neighboring MISO;
the rest of the system is modeled as an equivalent;
the assessment cycle is 15 minutes and only takes into account the state of the system at the beginning of the period
PJM
MISO
External

3. Parametric Uncertainty
During the 15 minutes window:
A major change in the EXTERNAL system could modify the parameters of the equivalent
The new state of the EXTERNAL system (represented by its equivalent) might have a major impact on the PJM system operation
This will go undetected until the next assessment cycle
Possible changes in the EXTERNAL system can be accounted for by explicitly including parametric uncertainty in the equivalent of the EXTERNAL system

4. Approach
Probabilistic approach to uncertainty modeling is not appropriate:
Difficulty in developing probability distributions
Operators have “fire fighters” mentality
Guaranteed (Set-Membership) approach to uncertainty modeling seems appropriate:
Bounds on the operating conditions of the EXTERNAL system are easier to establish than complete probability distributions
Unlike probabilistic models, in which one can talk about “most probable" trajectories, in set-membership models, it is always known for certain that the system trajectories will lie within some set (called reachable set)