IEEE Transactions on Power Systems, zyxwvutsr Vol. 9, No. 3. August 1994 zyxwvuts DECISION TREES FOR REAL-TIME zyxwv TRANSIENT STABILITY PREDICTION 1417 Steven Rovnyak zyxwvutsrq * Student Member, IEEE Stein Kretsinger ** non-member James Thorp * Fellow, IEEE Senior Member, IEEE Donald Brown ** * Cornell University Ithaca, New York ** University of Virginia Charlottesville, Virginia Kevwords; Adaptive protection, decision trees, pattern recognition, phasor measurements, real-time, transient stability. ABSTRACT - The ability to rapidly acquire synchronized phasor measurements from around the system opens up new possibilities for power system protection and control. This paper demonstrates how decision trees can be constructed off-line and then utilized on-line for predicting transient stability in real-time. Primary features of the method include building a single tree for all fault locations, using a short window of realistic-precision post-fault phasor measurements for the prediction, and testing robustness to variations in the operating point. Several candidate decision trees are tested zyxwvutsr on 40,800 faults Erom 50 randomly generated operating points on the New England 39 bus test system. 1. INTRODUCTION With the advent of systems capable of making real-time phasor measurements, the real-time assessment of the stability of a transient event in the power system has become an important area of investigation. By synchronizing sampling of microprocessor based systems, phasor calculations can be placed on a common reference [l]. Commercially available systems based on GPS (Global Positioning System) satellite time transmissions can provide synchronization to 1 microsecond accuracy. The phasors obtained from a period or more of samples from all three phases provide a precise estimate of the positive sequence voltage phasor at a bus. The magnitudes and angles of these phasors comprise the state of the power system and are used in state estimation and transient stability analysis. By communicating time-tagged phasor measurements to a central location, the dynamic state of the system can be tracked in real time. Utility experience indicates that communication bandwidths can handle 12 complete sets of phasor measurements per second [2], which corresponds to one set every 5 cycles. Using these phasor measurements for real-time transient stability prediction can advance the fields of protection and control. Out-of-step relaying is an obvious area of application. If an evolving swing could be determined to be stable or unstable, then the appropriate blocking or tripping could be initiated. A control application might involve determining whether the event would be stable under a variety of control 93 SM 530-6 PWRS by the IEEE Power System Engineering Committee of the IEEE Power Engineering Society for presentation at the IEEE/PES 1993 Summer Meeting, Vancouver, B.C. Canada, July 18-22, 1993. Manuscript submitted Jan. zyxwvutsrq 4, 1992; made available for printing May 26, 1993. PRINTED IN USA A paper recommended and approved options. In both cases the determination of stability or instability must be accomplished faster than real time in order for effective action to be taken. In other words it is necessary to predict the outcome before it actually occurs. Many transient stability assessment techniques while simple in off-line application are too complicated for real-time use. Real-time monitoring obviates the need for some of these techniques since the system itself is actually solving the differential equations. What is required is a computationally efficient way of processing the real-time measurements to determine whether an evolving event will ultimately be stable or unstable. Given the possible pay-off, the off-line computation can be extensive if the real-time speed is fast. The availability of powerful workstations and parallel supercomputing make new approaches to the problem possible. Decision trees are a type of classifier that can be constructed off-line from a training set of examples [3,4]. In this paper, decision trees are used to classify a transient swing as either stable or unstable on the basis of real-time phasor measurements. Rather than attempting to solve the power system model in real-time, extensive simulations are performed off-line in order to capture the essential features of system behavior. The tree building process statistically analyzes this data and constructs a decision tree designed to correctly classify new, unseen examples. The resulting decision tree classifier is compact and extremely fast, thus well suited for on-line use. Our decision tree approach falls into the broader category of pattern recognition. In the past 20 years, many forms of pattern recognition have been applied to the power system transient stability problem with varying degrees of success and sophistication [5-111. Decision trees, however, have not been thoroughly investigated for this application. Of notable exception is the work by Wehenkel et al. [12-141 investigating decision trees for predicting the system's susceptibility to a particular fault. In that work, decision trees take as input the static parameters from a pre-fault operating point and then predict whether the critical clearing time of a particular fault falls below a certain threshold. Control strategies are suggested for moving the operating point to a more secure state [12]. Much of the previous work on pattern recognition has traditionally focused on similar questions of dynamic security, i.e. measuring the system's susceptibility to various contingencies as a function of the operating point. The emerging capability to rapidly acquire synchronized phasor measurements enables us to take a different approach. Using a short window of post-fault phasor measurements from a fault that is actually in progress, we seek to predict whether loss of synchronization is going to occur before it actually happens. This information could then be used for example in out-of-step relaying. zyxw Our method incorporates a combination of features which set this work apart: We simulate a non-trivial power system, the New England 39 bus test system, under increased loading conditions in order to exhibit instances of instability caused by ' 0885-8950/94/$04.00 zyxwvut 0 1993 IEEE