# 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.