GATE Electrical Engineering Electrical Machines Syllabus

Electrical Machines syllabus — full chapter and topic list

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

1. 1

   Single Phase Transformer

   4 topics

   • Equivalent Circuit
   • Phasor Diagram
   • Open Circuit and Short Circuit Tests
   • Regulation and Efficiency
2. 2

   Three-Phase Transformers

   3 topics

   • Connections
   • Vector Groups
   • Parallel Operation
3. 3

   Auto-Transformer

   overview

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

4. 4

   Electromechanical Energy Conversion Principles

   overview

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

5. 5

   DC Machines

   4 topics

   • Separately Excited
   • Series and Shunt
   • Motoring and Generating Mode of Operation and Their Characteristics
   • Speed Control of DC Motors
6. 6

   Three-Phase Induction Machines

   7 topics

   • Principle of Operation
   • Types
   • Performance
   • Torque-Speed Characteristics
   • No-load and Blocked-Rotor Tests
   • Equivalent Circuit
   • Starting and Speed Control
7. 7

   Operating Principle of Single-Phase Induction Motors

   overview

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

8. 8

   Synchronous Machines

   4 topics

   • Cylindrical and Salient Pole Machines
   • Performance and Characteristics
   • Regulation and Parallel Operation of Generators
   • Starting of Synchronous Motors
9. 9

   Types of Losses and Efficiency Calculations of Electric Machines

   overview

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

Electrical Machines flashcards for GATE Electrical Engineering

18 of 51 cards from the Electrical Machines deck — real questions with worked answers.

1. What is the per-phase approximate equivalent circuit of a transformer referred to the primary?

   A series impedance $R_{eq1} + jX_{eq1}$ (where $R_{eq1}=R_1+R_2'$ and $X_{eq1}=X_1+X_2'$) carrying the load current, with the shunt magnetizing branch $R_0 \parallel jX_0$ connected across the primary input. The shunt branch carries the no-load (excitation) current.

2. In a transformer equivalent circuit, how are secondary resistance $R_2$ and reactance $X_2$ referred to the primary side?

   They are multiplied by the square of the turns ratio: $R_2' = a^{2}R_2$ and $X_2' = a^{2}X_2$, where $a = N_1/N_2$.

3. What do the two parallel elements of the transformer shunt (excitation) branch represent?

   $R_0$ (or $G_0$) carries the core-loss current and accounts for hysteresis and eddy-current losses; $X_0$ (or $B_m$) carries the magnetizing current that sets up the mutual flux in the core.

4. Write the EMF equation of a transformer.

   $$E = 4.44\, f\, N\, \Phi_{m}$$ where $f$ is frequency, $N$ the number of turns, and $\Phi_m$ the maximum core flux.

5. Describe the transformer phasor diagram at a lagging power factor load.

   Flux $\Phi$ is taken as reference; $E_1$ and $E_2$ lag $\Phi$ by $90^{\circ}$. Load current $I_2$ lags $V_2$ by angle $\phi_2$. $V_1$ is found by adding the drops $I_1 R_{eq1}$ (in phase with $I_1$) and $I_1 X_{eq1}$ (leading $I_1$ by $90^{\circ}$) to $-E_1$. $V_1$ leads $V_2'$.

6. On a transformer phasor diagram, what is the relationship between the no-load current $I_0$, the core-loss component, and the magnetizing component?

   $I_0$ has two components: $I_w = I_0\cos\phi_0$ (working/core-loss component, in phase with $V_1$) and $I_\mu = I_0\sin\phi_0$ (magnetizing component, lagging $V_1$ by $90^{\circ}$). Thus $I_0 = \sqrt{I_w^{2}+I_\mu^{2}}$.

7. What is measured by the Open-Circuit (No-Load) test on a transformer, and from which side is it conducted?

   It is performed on the LV side with the HV side open, at rated voltage. It gives the core (iron) losses and the parameters of the shunt branch $R_0$ and $X_0$, since the no-load current produces negligible copper loss.

8. What is measured by the Short-Circuit test on a transformer, and from which side is it conducted?

   It is performed on the HV side with the LV side shorted, at reduced voltage to circulate rated current. It gives the full-load copper losses and the equivalent series parameters $R_{eq}$ and $X_{eq}$, since the core loss at reduced voltage is negligible.

9. From the open-circuit test readings $V_0$, $I_0$, $W_0$, how are $R_0$ and $X_0$ found?

   $\cos\phi_0 = \dfrac{W_0}{V_0 I_0}$, $I_w = I_0\cos\phi_0$, $I_\mu = I_0\sin\phi_0$, then $R_0 = \dfrac{V_0}{I_w}$ and $X_0 = \dfrac{V_0}{I_\mu}$.

10. From the short-circuit test readings $V_{sc}$, $I_{sc}$, $W_{sc}$, how are $Z_{eq}$, $R_{eq}$, $X_{eq}$ found?

    $Z_{eq} = \dfrac{V_{sc}}{I_{sc}}$, $R_{eq} = \dfrac{W_{sc}}{I_{sc}^{2}}$, and $X_{eq} = \sqrt{Z_{eq}^{2}-R_{eq}^{2}}$ (all referred to the side on which the test was done).

11. Define voltage regulation of a transformer.

    $$\%\text{Reg} = \frac{V_{2,\text{no-load}} - V_{2,\text{full-load}}}{V_{2,\text{full-load}}}\times 100$$ It is the per-unit drop in secondary voltage from no-load to full-load at constant primary voltage.

12. Give the approximate per-unit voltage regulation formula in terms of equivalent resistance and reactance.

    $$\text{Reg} \approx I_2\big(R_{eq2}\cos\phi \pm X_{eq2}\sin\phi\big)/V_2$$ with $+$ for a lagging power factor and $-$ for a leading power factor load.

13. At what power factor is transformer voltage regulation zero or negative?

    At a leading power factor. Regulation becomes zero/negative when $\tan\phi = X_{eq}/R_{eq}$ (leading), because the reactance drop is offset by the leading current, making the no-load voltage less than or equal to the full-load voltage.

14. State the efficiency expression of a transformer.

    $$\eta = \frac{V_2 I_2 \cos\phi}{V_2 I_2 \cos\phi + P_i + I_2^{2}R_{eq2}}$$ where $P_i$ is the constant iron loss and $I_2^{2}R_{eq2}$ is the variable copper loss.

15. What is the condition for maximum efficiency of a transformer?

    Maximum efficiency occurs when the variable copper loss equals the constant iron (core) loss: $I_2^{2}R_{eq2} = P_i$. The load fraction is $x = \sqrt{P_i/P_{cu,\text{FL}}}$.

16. Define and give the formula for all-day efficiency of a distribution transformer.

    $$\eta_{\text{all-day}} = \frac{\text{energy output in 24 h (kWh)}}{\text{energy input in 24 h (kWh)}}$$ It is based on energy over 24 hours; iron loss runs continuously while copper loss varies with load, so distribution transformers are designed with low iron loss.

17. Name the common three-phase transformer connection types and a key feature of each.

    Star-Star (Y-Y): no phase shift, needs neutral, third-harmonic issues. Delta-Delta ($\Delta$-$\Delta$): allows open-delta operation, good for large unbalanced/heavy currents. Star-Delta (Y-$\Delta$): step-down with $30^{\circ}$ shift. Delta-Star ($\Delta$-Y): step-up, neutral available on secondary, $30^{\circ}$ shift.

18. What is the line-to-line voltage ratio of a star-delta connected three-phase transformer with per-phase turns ratio $a$?

    $$\frac{V_{L,\text{primary}}}{V_{L,\text{secondary}}} = \sqrt{3}\,a$$ because the star primary line voltage is $\sqrt{3}$ times the phase voltage while the delta secondary line voltage equals its phase voltage.

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