1. Differential Equation Algorithm for Distance Relaying Student: Tatjana Dokic Instructor: Dr. Mladen Kezunovic March 3, 2014 ECEN 679: Computer Relaying

2. Basics Lamped parameter model Time domain approach Uses samples of i and u for calculation Derivative Term Approximation of differential eq. (differential eq. → difference eq.) Integration (integral eq. → difference eq.) Residual Term neglected minimized GOAL

3. Hardware Description PRE- PROCESSOR SAMPLE & HOLD A/D CONVERTER MUX CONTROL CIRCUIT MEMORY PROCESSOR VAVA VBVB VCVC IAIA IBIB ICIC … … …...... ININ Interrupt signal

4. Software Description Wait for interrupt Fault detection Fault classification Calculate R and L Trip Logic Report No fault or recovery Fault Interrupt detected Compare data from current and previous sampling cycle Clarke components

5. Approximate Derivative and

6. Approximate Integral Trapezoidal rule:

7. Benefits Not sensitive to transient DC offset components or transient high frequency components. Three samples are enough, we do not need to record the whole cycle. Shortcomings Depends on the chosen model. Sensitive to noise if residual term is not considered (considering residual term complicates computation). Uses approximation Signal sampling requires synchronization.

8. Literature [1] M. Kezunovic, “Characteristics of Digital Algorithms”, ECEN679 Computer Relaying - lecture notes, Jan 2014. [2] W. Breingan, et. al., “The Laboratory Investigation of a Digital System for the Protection of Transmission Lines,” IEEE PES Winter Meeting, New York, January 30-February 4, 1977. [3] W.J Smolinski, “An Algorithm for Digital Impedance Calculation Using a Single PI Section Transmission Line Model,” IEEE Transactions on Power Apparatus and Systems, Vol. PAS-98, No. 5, pp. 1546-1551, 1979. [4] P. Bornard, J. C. Bastide, “A prototype of Multiprocessor Based Distance Relay,” IEEE Transactions on Power Apparatus and Systems, Vol. PAS-101, No. 2, pp. 491-498, 1982. [5] M. Garcia-Gracia, W. Osal, M. P. Comech, “Line protection based on the differential equation algorithm using mutual coupling,” Electric Power System Research, Vol. 77, pp. 566-573, 2007. [6] M. Akke, J. T. Thorp, “Some Improvements in the Three-Phase Differential Equation Algorithm for Fast Transmission Line Protection,” IEEE Transactions on Power Delivery, Vol. 13, No. 1, pp. 66-72, 1998. [7] A. M. Ranjbar, B. J. Cory, “An Improved Method for the Digital Protection of High Voltage Transmission Lines,” IEEE Transactions on Power Apparatus and Systems, Vol. PAS-94, No. 2, pp. 544-550, 1975. [8] B. Osorno, “Analysis of Microprocessor Based Protective Relay’s (MBPR) Differential Equation Algorithms,” Journal of Computing, Vol. 2. No. 6, pp. 21-25, 2010.

9. Thank you! Questions?