GATE Electrical Engineering Power Systems Syllabus

Power Systems syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Power Systems in GATE Electrical Engineering, not a summary of it.

1. 1

   Basic concepts of electrical power generation

   2 topics

   • AC Transmission Concepts
   • DC Transmission Concepts
2. 2

   Models and performance of transmission lines and cables

   overview

   Examined as a single unit within Power Systems — no further topic split in the official outline.

3. 3

   Economic Load Dispatch

   2 topics

   • With considering transmission losses
   • Without considering transmission losses
4. 4

   Series and shunt compensation

   overview

   Examined as a single unit within Power Systems — no further topic split in the official outline.

5. 5

   Electric field distribution and insulators

   overview

   Examined as a single unit within Power Systems — no further topic split in the official outline.

6. 6

   Distribution systems

   overview

   Examined as a single unit within Power Systems — no further topic split in the official outline.

7. 7

   Per‐unit quantities

   overview

   Examined as a single unit within Power Systems — no further topic split in the official outline.

8. 8

   Bus admittance matrix

   overview

   Examined as a single unit within Power Systems — no further topic split in the official outline.

9. 9

   Gauss- Seidel and Newton-Raphson load flow methods

   overview

   Examined as a single unit within Power Systems — no further topic split in the official outline.

10. 10

    Voltage and Frequency control

    overview

    Examined as a single unit within Power Systems — no further topic split in the official outline.

11. 11

    Power factor correction

    overview

    Examined as a single unit within Power Systems — no further topic split in the official outline.

12. 12

    Symmetrical components

    overview

    Examined as a single unit within Power Systems — no further topic split in the official outline.

13. 13

    Symmetrical and unsymmetrical fault analysis

    overview

    Examined as a single unit within Power Systems — no further topic split in the official outline.

14. 14

    Principles of over‐current, differential, directional and distance protection

    overview

    Examined as a single unit within Power Systems — no further topic split in the official outline.

15. 15

    Circuit breakers

    overview

    Examined as a single unit within Power Systems — no further topic split in the official outline.

16. 16

    System stability concepts

    overview

    Examined as a single unit within Power Systems — no further topic split in the official outline.

17. 17

    Equal area criterion

    overview

    Examined as a single unit within Power Systems — no further topic split in the official outline.

Power Systems flashcards for GATE Electrical Engineering

25 of 49 cards from the Power Systems deck — real questions with worked answers.

1. In AC transmission, what is meant by the surge impedance loading (SIL) of a line?

   SIL is the power delivered to a purely resistive load equal to the surge impedance $Z_c=\sqrt{L/C}$. It is given by $SIL=\dfrac{V_L^{2}}{Z_c}$ (with $V_L$ the line-to-line voltage). At SIL the line's reactive power generated by $C$ exactly balances that absorbed by $L$, so the voltage profile is flat.

2. Define the surge (characteristic) impedance of a lossless transmission line and give its formula.

   The surge impedance is the ratio of voltage to current of a travelling wave on a lossless line: $$Z_c=\sqrt{\frac{L}{C}}$$ where $L$ and $C$ are the per-unit-length inductance and capacitance. It is purely resistive (typically $\approx 400\,\Omega$ for overhead lines).

3. State the per-phase ABCD relationship for a transmission line and the constraint linking the constants.

   $$\begin{pmatrix}V_S\\I_S\end{pmatrix}=\begin{pmatrix}A&B\\C&D\end{pmatrix}\begin{pmatrix}V_R\\I_R\end{pmatrix}$$ For a reciprocal, symmetric line $A=D$ and the constraint is $AD-BC=1$. $A,D$ are dimensionless, $B$ has units of $\Omega$, and $C$ has units of $\text{S}$ (siemens).

4. Write the ABCD constants of a medium-length transmission line using the nominal-$\pi$ model.

   $$A=D=1+\frac{ZY}{2},\quad B=Z,\quad C=Y\left(1+\frac{ZY}{4}\right)$$ where $Z$ is the total series impedance and $Y$ is the total shunt admittance of the line.

5. For a long transmission line, what are the exact ABCD constants in terms of the propagation constant $\gamma$ and surge impedance $Z_c$?

   $$A=D=\cosh(\gamma l),\quad B=Z_c\sinh(\gamma l),\quad C=\frac{1}{Z_c}\sinh(\gamma l)$$ where $\gamma=\sqrt{zy}$ (per-unit-length), $Z_c=\sqrt{z/y}$, and $l$ is the line length.

6. Define the propagation constant of a transmission line and name its two components.

   The propagation constant is $\gamma=\sqrt{zy}=\alpha+j\beta$, where $\alpha$ is the attenuation constant (Np/m, governs amplitude decay) and $\beta$ is the phase constant (rad/m, governs phase shift) of the travelling wave.

7. What is voltage regulation of a transmission line and how is it computed from the receiving-end voltages?

   Voltage regulation is the rise in receiving-end voltage when full load is removed (sending-end voltage held constant): $$\%\,VR=\frac{|V_{R,NL}|-|V_{R,FL}|}{|V_{R,FL}|}\times100$$ Using ABCD constants, $|V_{R,NL}|=\dfrac{|V_S|}{|A|}$.

8. In an AC line, what is the Ferranti effect and when does it occur?

   The Ferranti effect is the phenomenon where the receiving-end (no-load) voltage is greater than the sending-end voltage. It occurs on long or lightly loaded lines due to the capacitive charging current flowing through the line inductance, raising the receiving-end voltage.

9. State the approximate real power transferred over a short AC line in terms of the power (load) angle $\delta$.

   $$P=\frac{|V_S||V_R|}{X}\sin\delta$$ where $X$ is the line series reactance and $\delta$ is the angle by which $V_S$ leads $V_R$. Maximum (steady-state) power transfer occurs at $\delta=90^{\circ}$.

10. Why are AC transmission lines usually loaded well below their thermal limit on long lines?

    For long lines the limit is stability, not thermal heating. Since $P=\dfrac{|V_S||V_R|}{X}\sin\delta$ and $X$ grows with length, the maximum transferable power falls; the line must be operated at a low $\delta$ to keep an adequate steady-state stability margin.

11. What is the corona effect in AC transmission lines and which factors increase corona loss?

    Corona is the partial ionisation of air around a conductor when the surface voltage gradient exceeds the breakdown strength, causing a hissing sound, violet glow, ozone, and power loss. It increases with higher voltage, smaller conductor radius, rough/dirty conductors, and humid or rainy weather.

12. Why does skin effect occur in AC conductors and what is its consequence?

    In AC, alternating flux induces eddy currents that force current toward the conductor surface, so current density is highest at the periphery. This reduces the effective cross-section and increases the AC resistance above the DC resistance; the effect grows with frequency and conductor diameter.

13. What is meant by 'bundled conductors' in EHV AC transmission and give two benefits.

    Bundled conductors use two or more sub-conductors per phase spaced apart. Benefits: (1) reduced surface voltage gradient, lowering corona loss and radio interference; (2) reduced effective inductive reactance (higher GMR) which increases the line's power-transfer capability and SIL.

14. For a single-phase two-wire line, give the formula for loop inductance per unit length (including internal flux).

    $$L=\frac{\mu_0}{\pi}\left(\frac{1}{4}+\ln\frac{D}{r}\right)\ \text{H/m}$$ Equivalently $L=\dfrac{\mu_0}{\pi}\ln\dfrac{D}{r'}$ with $r'=r\,e^{-1/4}=0.7788\,r$ being the GMR of a solid round conductor.

15. Define Geometric Mean Radius (GMR) and Geometric Mean Distance (GMD) as used in line-parameter calculations.

    GMR (self-GMD) is the radius of an equivalent hollow conductor with no internal flux, $r'=0.7788\,r$ for a solid round wire; it accounts for internal plus external flux. GMD is the geometric mean of the distances between phase conductors, used as the equivalent spacing $D_{eq}=\sqrt[3]{D_{ab}D_{bc}D_{ca}}$ for a 3-phase line.

16. Why is transposition of conductors used in three-phase AC lines?

    Transposition periodically rotates the positions of the three phase conductors so each occupies every position for one-third of the length. This equalises the average inductance and capacitance of all three phases, balancing the line and reducing electrostatic/electromagnetic interference with nearby communication lines.

17. Give the per-phase inductance formula for a transposed three-phase line.

    $$L=2\times10^{-7}\ln\frac{D_{eq}}{r'}\ \text{H/m}$$ where $D_{eq}=\sqrt[3]{D_{ab}D_{bc}D_{ca}}$ is the GMD and $r'=0.7788\,r$ is the conductor GMR.

18. Give the per-phase capacitance-to-neutral formula for a transposed three-phase line.

    $$C_n=\frac{2\pi\varepsilon_0}{\ln\dfrac{D_{eq}}{r}}\ \text{F/m}$$ where $D_{eq}=\sqrt[3]{D_{ab}D_{bc}D_{ca}}$ and $r$ is the actual conductor radius (not the GMR—capacitance uses the true radius).

19. What is meant by the 'charging current' of an AC transmission line and why does it matter?

    Charging current is the capacitive current $I_c=\omega C V$ drawn by the line's shunt capacitance even at no load. It causes the Ferranti effect, contributes to reactive power, and limits the practical length of AC cables (high $C$), since charging current can approach the conductor's rated current.

20. List the three classifications of transmission lines by length and the model used for each.

    Short line (< ~80 km): series impedance only, shunt capacitance neglected. Medium line (~80–250 km): nominal-$\pi$ or nominal-T model with lumped shunt admittance. Long line (> ~250 km): distributed-parameter model using hyperbolic ($\cosh,\sinh$) functions.

21. What is a key reason AC won the early 'war of currents' over DC for transmission?

    AC voltage can be easily stepped up and down using transformers, allowing transmission at high voltage (low current, low $I^{2}R$ loss) and distribution at safe low voltage. Early DC had no economical voltage-conversion device, limiting it to short distances.

22. Why is power transmitted at high voltage in AC systems? Quantify the loss dependence.

    For a fixed power $P=VI$, raising $V$ lowers the current $I$. Line loss is $P_{loss}=I^{2}R=\left(\dfrac{P}{V}\right)^{2}R$, so doubling the voltage cuts the line loss to one-quarter. High voltage therefore minimises copper loss and conductor cross-section.

23. State the fundamental principle of HVDC (DC) transmission for moving bulk power.

    In HVDC, AC is rectified to DC at the sending end (converter station), transmitted as DC at high voltage over the line/cable, and inverted back to AC at the receiving end. Power flow and direction are controlled by adjusting the converter firing angles and DC voltage.

24. List three major technical advantages of HVDC over HVAC transmission.

    (1) No reactive power / charging-current limit, so very long overhead lines and especially underground/submarine cables are feasible. (2) Asynchronous interconnection of two AC systems possible (different frequencies). (3) Full, fast control of power flow; no stability angle limit and lower line losses (no skin effect, fewer conductors).

25. What is the 'break-even distance' in the HVDC vs HVAC economic comparison?

    It is the line length at which the total cost of HVDC equals that of HVAC. Below it AC is cheaper; above it DC is cheaper. DC has higher terminal (converter) cost but lower per-km line cost, so the two cost-vs-distance lines cross — typically ~600–800 km for overhead lines and much shorter (~50 km) for cables.

See more Power Systems flashcards →

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