--- title: "Sequence network of loaded generator with Zn" subject: "Power System Analysis II" chapter: 4 key: "semester_5/power_system_analysis_ii:loaded-generator-sequence-network-zn" source: https://www.bctengineer.com/q/semester_5/power_system_analysis_ii/loaded-generator-sequence-network-zn site: BCT Engineering --- # Sequence network of loaded generator with Zn Power System Analysis II · Chapter 4: Unbalanced System Analysis - Asked in: 2079 Bhadra, 2+6 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/loaded-generator-sequence-network-zn - Whole chapter: https://www.bctengineer.com/md/semester_5/power_system_analysis_ii/chapter-4 ## Question What is significance of sequence components? Deduce the sequence network for a loaded synchronous generator grounded through impedance Zn. ## Short answer A loaded synchronous generator grounded through impedance Zn produces only positive-sequence EMF. Sequence networks: V_{a1} = E_a - I_{a1} Z_1, V_{a2} = -I_{a2} Z_2, V_{a0} = -I_{a0}(Z_{g0}+3Z_n). Only zero sequence sees the neutral impedance as 3Z_n because neutral current is 3I_{a0}. ## Answer #### Significance of sequence components Sequence components let an unbalanced three-phase system be analysed as three independent balanced single-phase networks (positive, negative, zero). For balanced equipment the sequence impedances are uncoupled, so unbalanced faults are solved by connecting the sequence networks only at the fault point. #### Sequence networks of a synchronous generator grounded through $Z_n$ A generator produces only **balanced positive sequence EMFs** $E_a$, $E_b = a^2E_a$, $E_c = aE_a$. Let $Z_1$ and $Z_2$ be its positive and negative sequence impedances and $Z_{g0}$ its zero sequence impedance per phase. The neutral is grounded through $Z_n$. ```text Ia --> +-(Ea)--Zg--o a | n +-(Eb)--Zg--o b Va, Vb, Vc measured | to ground +-(Ec)--Zg--o c | Zn In = Ia+Ib+Ic | ground ``` Here $Z_g$ is the winding impedance of each phase. **Positive sequence:** the EMF is purely positive sequence, and positive sequence currents are balanced, so no current flows in $Z_n$: $$ V_{a1} = E_a - I_{a1}Z_1 $$ **Negative sequence:** there is no negative sequence EMF, and the currents are balanced, so no current flows in $Z_n$: $$ V_{a2} = -I_{a2}Z_2 $$ **Zero sequence:** there is no zero sequence EMF. The neutral current is $I_n = 3I_{a0}$, so the drop in $Z_n$ is $3I_{a0}Z_n$: $$ V_{a0} = -I_{a0}Z_{g0} - 3I_{a0}Z_n = -I_{a0}(Z_{g0} + 3Z_n) = -I_{a0}Z_0 $$ In matrix form: $$ \begin{bmatrix} V_{a0}\\V_{a1}\\V_{a2} \end{bmatrix} = \begin{bmatrix} 0\\E_a\\0 \end{bmatrix} - \begin{bmatrix} Z_0&0&0\\0&Z_1&0\\0&0&Z_2 \end{bmatrix}\begin{bmatrix} I_{a0}\\I_{a1}\\I_{a2} \end{bmatrix} $$ ```text Positive Negative Zero F1 o F2 o F0 o | Ia1 ^ | Ia2 ^ | Ia0 ^ Z1 Z2 Zg0 | | | (Ea) | 3Zn | | | N1 o (ref) N2 o (ref) N0 o (ground) ``` **Loaded generator:** when the generator supplies a balanced load before the fault, the load appears in the **positive sequence network** (and in the negative and zero sequence networks with its own sequence impedances). Using Thevenin's theorem at the fault point, $E_a$ is replaced by the prefault voltage $V_f$ at that point, and $Z_1$ by the Thevenin impedance of the generator in parallel with the load. The zero sequence network still contains $3Z_n$. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. A synchronous generator produces EMF of which sequence? A. Positive and negative B. Zero only C. Positive sequence only D. All three Answer: C. Only the positive sequence network contains a source. (Key point: Generator EMF) 2. The zero sequence network of a generator grounded through Zn has impedance: A. Zg0 + Zn B. Zg0 C. 3Zg0 + Zn D. Zg0 + 3Zn Answer: D. Neutral carries 3Ia0, giving drop 3Ia0 Zn. (Key point: Zero network) 3. Why is Zn absent in the positive and negative networks? A. Balanced currents sum to zero in the neutral B. Zn is shorted C. EMF is zero D. Zn is infinite for them Answer: A. Only zero sequence currents flow in the neutral. (Key point: Neutral current in + and -) 4. Positive sequence equation is: A. Va1 = -Ia1 Z1 B. Va1 = Ea - Ia1 Z1 C. Va1 = Ea + Ia1 Z1 D. Va1 = Ea - 3Ia1 Zn Answer: B. Source EMF minus drop in Z1. 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