1 Stochastic Assessment of Voltage Dips (Sags): The Method of Fault Positions versus a Monte Carlo Simulation Approach G. Olguin, Member, IEEE, D. Karlsson, Senior Member, IEEE, R. Leborgne, Member, IEEE Abstract-- Two methods for stochastic assessment of voltage dips (sags) are compared. The method of fault positions and a Monte Carlo simulation approach are utilized to stochastically describe the expected dip performance at some sites of a large transmission system. Fault scenarios are created and pseudo measurements are obtained in order to compare stochastic assessment with simulated measurements. It is shown that the method of fault positions cannot be used to predict the performance of a particular year, unless correcting factors are used to adjust the assessment. A Monte Carlo simulation approach is suggested to better describe the expected dip performance. Whereas the method of fault positions gives long- term mean values, the Monte Carlo approach provides the complete frequency distribution function of selected sag indices (SARFI-X). Index Terms — Method of fault positions, Monte Carlo simulation, power quality, stochastic assessment, voltage dips, voltage sags I. INTRODUCTION OLTAGE SAGS (or dips) are short duration reductions in rms voltage, basically two-dimensional events comprising magnitude (residual voltage) and duration (time for which the rms voltage stays below a given threshold). Voltage sags, as other power quality disturbances, must be treated as an electromagnetic compatibility problem between the sensitive load and the power supply [1],[2]. In order to ensure compatibility both, the sensitivity of the load to voltage dips (ride-through) and the expected electrical environment must conveniently be described. The information about the sensitivity of individual equipment to voltage dips can be obtained either from the equipment manufacturer or through comprehensive laboratory tests and it is usually presented by means of voltage tolerance curves, like the CBEMA or its updated version ITIC curve This work was supported by the Swedish Energy Agency, Elforsk and ABB under the Elektra program. G. Olguin and R. Leborgne are with the Department of Energy and Environment, Division of Electric Power Engineering, Chalmers University of Technology. Gothenburg, Sweden (e-mails: gabriel.olguin@ieee.org roberto.leborgne@elteknik.chalmers.se). D. Karlsson is with Gothia Power A. B., Gothenburg, Sweden (e-mail: daniel.karlsson@gothiapower.com). [3],[4]. These curves are based on the two-dimensional description of the event: magnitude or residual voltage and duration. To perform the compatibility study, the sensitivity of the equipment must be compared with a suitable description of the dip performance of the network at the point of connection. Monitoring of power supply can be used to characterize the performance of a particular site or of a system as a whole, however it is expensive and it requires long monitoring periods [1], [4]. The dip characterization of the power supply at a single site is basically done by counting events within a given magnitude-duration window [5], [6]. If only magnitude is of concern, then a general representation of the site performance is done by means of cumulative frequency histograms, in which the number of events with a residual voltage less than a given value is shown. At the system level, characterization of dip performance requires the use of indices. The performance of a number of sites is statistically processed to describe the system performance [6]. An alternative to monitoring of power supply is a stochastic assessment of voltage dips. Stochastic assessment of voltage dips is a simulation method that combines deterministic results with stochastic data to produce a probabilistic assessment of voltage dips at a given bus in the system. The method of fault positions is used here. It combines the residual voltages at an observation bus with the likelihood of their cause (long-term average fault rate) to provide the probabilistic assessment of voltage dips [7]. The method is an effective tool for assessing the long-term dip performance, but as any probabilistic method cannot predict the performance during a particular year, because long-term average values are used to model stochastic variables. This paper discusses the method of fault positions with regard to the suitability to predict the sag performance of a particular year, and compares it with a Monte Carlo approach. It shows that the stochastic assessment may differ from the measured performance. A Monte Carlo approach is proposed to better describe the expected performance of the network. Whereas the method of fault positions gives only long-term mean values the Monte Carlo approach gives the complete distribution function allowing further analysis [8]. Both approaches are applied to an existing 87-bus system. V