--- title: "Line model classification and short-line ABCD" subject: "Power System Analysis I" chapter: 5 key: "semester_4/power_system_analysis_i:classify-models-short-line-abcd" source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/classify-models-short-line-abcd site: BCT Engineering --- # Line model classification and short-line ABCD Power System Analysis I · Chapter 5: Transmission Line Modeling - Asked in: 2082 Kartik (new course), 2+4 marks - Video: [ABCD parameters of short transmission line by Prof. Irfan Mujawar](https://www.youtube.com/watch?v=cKmgHdoqVW8) — Dr. Irfan Mujawar - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/classify-models-short-line-abcd - Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-5 ## Question Classify transmission line models. Find the A, B, C, D parameters of a short transmission line and also draw its phasor diagram with lagging and leading power factor of the load. ## Short answer Models: short line (≤80 km, series impedance only), medium line (80–250 km, nominal-π or T), long line (>250 km, distributed parameters). Short-line ABCD: A=1, B=Z=R+jX, C=0, D=1. For lagging load, V_S leads V_R and is larger. For leading load, V_S can be less than V_R giving negative regulation. ## Answer #### Classification of transmission line models Based on length (for 50 Hz lines): | Type | Length | Model | Capacitance | |---|---|---|---| | Short line | up to about 80 km | Series $R + jX$ only | Neglected | | Medium line | 80–250 km | Nominal-Π or nominal-T | Lumped | | Long line | above 250 km | Distributed (exact) / equivalent Π or T | Distributed | #### ABCD parameters of a short line The shunt capacitance is neglected, so the same current flows through the whole line. ```text IS = IR R jX IR o---->----[ R ]----[ jX ]---->----o VS VR o---------------------------------o ``` $$ \begin{aligned} I_S &= I_R \\ V_S &= V_R + I_R(R + jX) = V_R + Z I_R \end{aligned} $$ Comparing with $V_S = AV_R + BI_R$ and $I_S = CV_R + DI_R$: $$ A = 1, \quad B = Z = R + jX\ \Omega, \quad C = 0, \quad D = 1 $$ Check: $AD - BC = 1 - 0 = 1$. #### Phasor diagrams Take $V_R$ as reference. The drop $I_R R$ is parallel to $I_R$ and $I_R X$ leads $I_R$ by 90°. $\delta$ is the angle between $V_S$ and $V_R$. **Lagging p.f. load** ($I_R$ lags $V_R$ by $\phi_R$): ```text + tip of VS VS . | . | IR.X (90 deg . | ahead of IR) . d | O------------------------> VR \ phiR \ IR.R (along IR) \ + v IR ``` Here $V_S > V_R$ and $V_S \approx V_R + I_R R\cos\phi_R + I_R X\sin\phi_R$, so regulation is positive and large. **Leading p.f. load** ($I_R$ leads $V_R$ by $\phi_R$): ```text ^ IR / IR.X + tip of VS / (90 deg \ / ahead of IR) \ / VS . + IR.R / phiR . / (along IR) / . d / O------------------------> VR ``` Here $V_S \approx V_R + I_R R\cos\phi_R - I_R X\sin\phi_R$; the $I_R X$ drop tilts backwards, so $V_S$ can be less than $V_R$ (negative regulation). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which classification of 50 Hz lines by length is correct? A. Short up to 80 km, medium 80-250 km, long above 250 km B. Short up to 250 km, medium 250-400 km, long above 400 km C. Short up to 20 km, medium 20-100 km, long above 100 km D. Short up to 150 km, medium 150-500 km, long above 500 km Answer: A. The usual limits are 80 km and 250 km, with nominal-Π or T for medium lines and distributed parameters for long lines. (Key point: Classification by length) 2. The ABCD constants of a short transmission line are: A. A = 1, B = Z, C = 0, D = 1 B. A = Z, B = 1, C = 0, D = Z C. A = 1, B = 0, C = Y, D = 1 D. A = 0, B = Z, C = 1, D = 0 Answer: A. Since IS = IR and VS = VR + Z IR, A = D = 1, B = Z and C = 0. (Key point: ABCD of short line) 3. For the short line, AD - BC equals: A. Z B. 0 C. 1 D. Z^2 Answer: C. AD - BC = 1 x 1 - Z x 0 = 1, showing the network is reciprocal. (Key point: Check relation AD - BC) 4. With a leading power factor load on a short line, the sending-end voltage compared with the lagging case: A. Is always larger than VR B. Is smaller; IR X term tilts backwards and VS can be less than VR (negative regulation) C. Is exactly equal to VR D. Leads VR by 90 degrees Answer: B. VS ≈ VR + IR R cosφ - IR X sinφ for leading load, so VS can fall below VR. 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