Abstract—In this presentation, we discuss a symbolic tool, implemented in Mathematica©, that converts a hybrid automaton model of a power system into either a mixed logical dynamic system’ (MLD) or a ‘dynamic mixed integer program’ (DMIP). The tool, converts any logical specification into mixed-integer formulas (IP formulas). For example the transition specification for the automaton is converted into a set of inequalities involving Boolean variables. The IP formulas can be used in decision computations using mixed integer programs or mixed integer dynamic programming. An example will be given involving controller design for a power conditioning system. Index Terms—Power System Security Assessment, Static Contingency Analysis, Symbolic Computation I. INTRODUCTION The prevention of widespread power system failure remains a serious concern today. The basic physics and mathematics of power system collapse are now well known. Earlier efforts laid the groundwork for a number of investigators in the mid and late 1980’s at which time a precise understanding of voltage collapse as a bifurcation of the underlying differential-algebraic equations was established, e.g. [1-4]. All of these efforts are central to understanding how power systems break down during disruption. However, the picture is not complete because the system collapse usually involves a period of discrete events associated with the action of various protection systems intended to prevent, or at least limit the scope, of any failure. It is an unfortunate fact that these systems frequently fail to achieve that goal – and worse, they sometimes amplify the effect of a small disturbance into a major outage. The Northeast blackout of August 2003 is a recent example. The underlying issue is how do we model, analyze and synthesize systems consisting of both complex nonlinear This work was supported in part by the Office of Naval Research under contract #N00014-04-M-0285. H. Kwatny, E. Mensah and D. Niebur are with the Center for Electric Power Engineering, Drexel University, Philadelphia, PA 19104, USA (e-mail: kwatny@coe.drexel.edu, edoe.fernand.mensah@drexel.edu, niebur@drexel.edu). C. Teolis is with Techno-Sciences, Inc., Lanham, MD 20706. (e-mail: carole@technosci.com) continuous dynamics and discrete event dynamics. A power system’s continuous dynamics might include a classical differential algebraic equation (DAE) model of the network with generators and loads and also continuous controllers like governors and automatic voltage regulators. Discrete event dynamics can be defined by a finite state machine that models various discrete controllers like tap-changing transformers, capacitor banks, load shedding devices and protection systems. Thus, the system can be modeled as a hybrid automaton. While the hybrid automaton model is a convenient theoretical tool, other forms of models are far more convenient for control system design and some other computational purposes. Such models include the ‘mixed logical dynamic system’ (MLD) [5, 6] or a modified version that we call the ‘dynamic mixed integer program’ (DMIP). In this presentation, we discuss a symbolic tool that converts a hybrid automaton model of a power system into one of these forms. The tool, implemented in Mathematica © , converts any logical specification into mixed-integer formulas (IP formulas). For example the transition specification for the automaton is converted into a set of inequalities involving Boolean variables. Our work extends earlier work in this area reported in [7]. Many decision problems are most naturally formulated in terms of logical specifications, but are more easily solve by mathematical programming. Consequently, the idea of reducing logical specifications into IP formulas has along history, see for example [8]. The IP formulas can be used in decision computations using mixed integer programs or mixed integer dynamic programming. Our approach derives a feedback policy based on finite, receding horizon dynamic programming. Other methods that have been proposed for hybrid systems, specifically, model predictive control, perform the computations on-line. Given the current state, they compute the optimal trajectory over a specified future time period. The computation is repeated every t ∆ sec. However, the feedback policy is computed once off-line and implemented in a form such as table look-up. To do this efficiently, we need to exploit the special structure of the power system decision problem. Symbolic Construction of Dynamic Mixed Integer Programs for Power System Management Harry G. Kwatny, Fellow, IEEE, Edoe F. Mensah, Dagmar Niebur, Member, IEEE, Carole Teolis 369 142440178X/06/$20.00 ©2006 IEEE PSCE 2006