--- title: "Zero sequence Thevenin impedance at bus 2" subject: "Power System Analysis II" chapter: 4 key: "semester_5/power_system_analysis_ii:zero-sequence-thevenin-bus2" source: https://www.bctengineer.com/q/semester_5/power_system_analysis_ii/zero-sequence-thevenin-bus2 site: BCT Engineering --- # Zero sequence Thevenin impedance at bus 2 Power System Analysis II · Chapter 4: Unbalanced System Analysis - Asked in: 2070 Asar, 4 marks - Video: [POSITIVE, NEGATIVE, ZERO SEQUENCE REACTANCE DIAGRAM / KTU/ POWER SYSTEM ANALYSIS](https://www.youtube.com/watch?v=zWNFHgJ7b5s) — praveen raj - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/power_system_analysis_ii/zero-sequence-thevenin-bus2 - Whole chapter: https://www.bctengineer.com/md/semester_5/power_system_analysis_ii/chapter-4 ## Question For the power system shown in figure below, draw the zero sequence network hence determine the Thevenin's equivalent zero sequence impedance as view from bus-2. [Figure: generator G 100 MVA, 13.8 kV, X0 = 0.05 pu (Y grounded) - T1 100 MVA, 13.8/138 kV, Δ/Y grounded, x = 0.10 pu - line X0 = 60 Ω - T2 100 MVA, 138/13.8 kV, Y grounded/Δ, x = 0.1 pu - bus 2 - motor M 100 MVA, 13.8 kV, X0 = 0.1 pu, neutral grounded through Xn = 0.05 pu] ## Short answer The delta windings block zero sequence from the generator and transformer, so only the motor branch appears. Adding the motor reactance and three times the neutral reactance gives j(0.1 + 3×0.05) = j0.25 pu. Thevenin zero sequence impedance at bus 2 is j0.25 pu on 100 MVA base. ## Answer The zero sequence network is drawn from the winding connections: a delta winding blocks zero sequence current from its line side, and a neutral reactance appears as $3X_n$. Bus 2 lies between T2 (delta on the 13.8 kV side) and the motor. #### Per unit values (100 MVA, 138 kV line base) - Generator: $X_0 = 0.05$ pu (Y grounded) - T1 (Δ / Y-grounded): $0.10$ pu - Line: $Z_b = 138^2/100 = 190.44\ \Omega$, $X_0 = 60/190.44 = 0.315$ pu - T2 (Y-grounded / Δ): $0.10$ pu - Motor: $X_0 = 0.1$ pu, neutral $3X_n = 3 \times 0.05 = 0.15$ pu #### Zero sequence connections - **T1 (Δ on generator side, Yg on line side):** the line side is connected to the reference through 0.10; the generator side is open. So the generator is isolated from the rest. - **T2 (Yg on line side, Δ on bus-2 side):** the line side is connected to the reference through 0.10; bus 2 side is open. - **Motor:** star grounded through $X_n$, so its branch is $0.1 + 0.15 = 0.25$ pu to reference. ```text G T1 Line T2 bus 2 M o o o----j0.315----o o o-------+ | | | | | | j0.05 open j0.10 j0.10 open j0.10 | | | | | | | j0.15 (3Xn) | | | | ==+=======+==== reference (ground) ===========+== ``` #### Thevenin zero sequence impedance at bus 2 Looking into bus 2, the path through T2 is open (delta on the bus-2 side), so only the motor branch is seen: $$ Z_{0,th} = j(X_{0M} + 3X_n) = j(0.10 + 0.15) = j0.25\ \text{pu} $$ **Answer: $Z_{0,th}$ at bus 2 = j0.25 pu** (100 MVA base). The generator, T1, line and T2 do not contribute because of the delta windings. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. T2 has its delta winding on the bus-2 side. How does it affect zero sequence looking in from bus 2? A. It passes zero sequence current to the line B. It adds a series reactance C. It isolates the line side, so bus 2 does not see the line, T1 or the generator D. It doubles the impedance Answer: C. The delta winding gives no path from bus 2 side to the line, so only the motor branch matters. (Key point: Delta winding blocks zero sequence) 2. The motor has X0 = 0.1 pu and neutral reactance Xn = 0.05 pu. Its zero sequence branch is: A. 0.10 + 0.05 = 0.15 B. 0.10 + 0.15 = 0.25 pu C. 0.05 D. 0.10 x 0.05 Answer: B. Xn appears as 3Xn = 0.15, so the branch is 0.10 + 0.15 = 0.25 pu. (Key point: Motor branch) 3. What is the zero sequence Thevenin impedance at bus 2? A. j0.25 pu B. j0.60 pu C. j0.315 pu D. j0.10 pu Answer: A. Only the motor branch is seen, so Z0,th = j0.25 pu. (Key point: Thevenin result) ## Related in Power System Analysis II - [Equivalent Z0, Z1, Z2 at bus 3](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Asequence-thevenin-z0-z1-z2-bus3) — Power System Analysis II, chapter 5 - [LLG fault sequence currents at bus 3](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Allg-fault-bus3-sequence-currents) — Power System Analysis II, chapter 5 - [DLG fault at bus 2, fault MVA](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Adlg-fault-bus2-sequence-networks) — Power System Analysis II, chapter 5 - [SLG fault at bus 3, currents and voltages](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Aslg-fault-bus3-three-generators) — Power System Analysis II, chapter 5 - [L-L fault current in kA at bus 3](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3All-fault-bus3-ka) — Power System Analysis II, chapter 5 - [Fault through impedance at bus 2](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Afault-impedance-bus2-actual-currents) — Power System Analysis II, chapter 3 ## Related in other subjects - [Impedance diagram, 100 MVA 132 kV base, with load](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aimpedance-diagram-100mva-132kv-load) — Power System Analysis I, chapter 3 - [Impedance diagram: 25 MVA generator, two motors](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aimpedance-diagram-25mva-two-motors) — Power System Analysis I, chapter 3 - [Reactance diagram: 50 MVA, 13.8 kV base, three generators](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Areactance-diagram-50mva-13-8kv) — Power System Analysis I, chapter 3 - [Reactance diagram: 300 MVA, 20 kV generator, two motors](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Areactance-diagram-300mva-20kv) — Power System Analysis I, chapter 3