- Parent Category: Coordination
- Category: 15-Bus Systems
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# 15-Bus System (System I)

** I. Introduction:**

\(\bullet\) This system has \(3\phi\) close-in faults on all the lines, as shown in the below figure.

\(\bullet\) The test case is presented as an example of highly distributed generation (DG) penetrated distribution networks.

\(\bullet\) This system consists of 15 buses and 21 branches, and hence it has 42 directional overcurrent relays (DOCRs) and 82 primary/backup (P/B) relay pairs with 84 variables "*if only one time-current characteristic curve (TCCC) is used for all DOCRs*".

\(\bullet\) The total constraints are 250, and addressed as: 82 inequality constraints for P/B selectivity criteria, 42 inequality constraints for minimum allowable operating time, 42 inequality constraints for maximum allowable operating time, 42 side constraints for the time-multiplier setting (\(TMS)\) and 42 side constraints for the plug-setting (\(PS\)); where \(TMS\) is greater than 0.1, and \(PS\) is considered discrete in uniform steps of 0.5 A.

\(\bullet\) All the generators have the same ratings of 15 MVA, 20 kV and a synchronous reactance of \(x=15\%\). Also, all the lines have the same impedance of \(Z=0.19+j0.46 \ \Omega/km\). Bus 8 is connected to an external grid that is modeled by 200 MVA short-circuit capacity. The fault analysis is done based on IEC standard.

\(\bullet\) The listed relays' CT ratios (\(CTRs\)), P/B relay pairs, currents for the close-in \(3\phi\) faults, and the other information regarding this test system are available below (*click on them for bigger size*):

\(\bullet\) We have found some typo-errors on the short-circuit currents given in [1]. These typo-errors have been addressed carefully and shown in Table 2. I want to thank Alexandre Akira Kida for the discussion about these corrections, and I think it is important to highlight them here too:

\(\bullet\) Based on the given data in [1], the relay \(R_{13}\) sees \(1503A\) when it is a backup for \(R_{12}\), and it sees \(1053A\) when it is a backup for \(R_{23}\). Because all the near-end/close-in faults are simulated by a bolted \(3\phi\) short-circuit on the bus \(x\), so the backup relay should see same \(I_f\) for all the primary relays that is associated with. Therefore, the question is: *which one should I select; \(1503A\) or \(1053A\)?* We have tried contacting the author of [1] regarding this issue. From our analysis, we found that the results given in [1] will give some violations when 1053A is selected. Based on that, 1503A is selected instead.

\(\bullet\) Similar thing happens with the relay \(R_{21}\) when it acts as a backup relay for the primary relays \(R_{24}\) and \(R_{33}\). With similar impedance for all the lines, it is hard to select \(175A\) as the correct answer, especially if we see all the other faults happen with high \(I_f\). Thus, we have selected \(1326A\) as the correct value for the relay \(R_{21}\) when it acts as a backup relay.

** II. Single-Line Diagram:**

\(\bullet\) This single-line diagram was drawn by Ali R. Alroomi in Mar. 2014 and all the necessary data were coded in MATLAB m-files.

** III. Files:**

\(\bullet\) System DATA (MATLAB, m-file Format) [Download]

\(\bullet\) Results Tester (MATLAB, m-file Format) [Download]

** IV. References (Some selected papers that use this system):**

[1] T. Amraee, "Coordination of Directional Overcurrent Relays Using Seeker Algorithm," * IEEE Transactions on Power Delivery*, vol. 27, no. 3, pp. 1415–1422, Jul. 2012.

[2] M. Alipour, S. Teimourzadeh, and H. Seyedi, "Improved Group Search Optimization Algorithm for Coordination of Directional Overcurrent Relays," *Swarm and Evolutionary Computation*, vol. 23, pp. 40–49, Aug. 2015.

[3] M. N. Alam, B. Das, and V. Pant, "A Comparative Study of Metaheuristic Optimization Approaches for Directional Overcurrent Relays Coordination," *Electric Power Systems Research*, vol. 128, pp. 39–52, Nov. 2015.