UPSC IES/ESE (Engineering Services) Electrical Machines, Power Systems and Power Electronics Syllabus

Define the ABCD (transmission) parameters of a two-port network.

$\begin{pmatrix}V_1\\I_1\end{pmatrix} = \begin{pmatrix}A & B\\C & D\end{pmatrix}\begin{pmatrix}V_2\\-I_2\end{pmatrix}$. For a reciprocal network $AD-BC=1$; for a symmetrical network $A=D$.

State the reciprocity and symmetry conditions for Z-parameters of a two-port.

Reciprocity: $Z_{12}=Z_{21}$. Symmetry: $Z_{11}=Z_{22}$.

Define cutoff frequency of a filter and name the four basic ideal filter types.

Cutoff frequency $f_c$ is the half-power ($-3$ dB) frequency separating passband from stopband. Types: low-pass, high-pass, band-pass, band-stop (band-reject).

For a constant-k low-pass filter, give the cutoff frequency.

$f_c = \dfrac{1}{\pi\sqrt{LC}}$.

Write the EMF equation of a DC generator.

$E_g = \dfrac{P\phi N Z}{60 A}$, where P = poles, $\phi$ = flux per pole, N = speed (rpm), Z = total armature conductors, A = parallel paths (A = P for lap, A = 2 for wave).

Write the torque equation (electromagnetic torque) of a DC machine.

$T = \dfrac{P\phi Z}{2\pi A}\,I_a = 0.159\,\dfrac{P\phi Z}{A}I_a$, i.e. $T \propto \phi I_a$.

State the back-EMF equation of a DC motor and the voltage relation.

$E_b = \dfrac{P\phi N Z}{60 A}$ and $V = E_b + I_a R_a$, so $I_a = \dfrac{V - E_b}{R_a}$.

For a DC shunt motor, describe the speed–torque (N–T) characteristic.

Speed is nearly constant, dropping only slightly as load (torque) increases because $N \propto \dfrac{E_b}{\phi}$ and flux is constant. It is essentially a constant-speed motor.

For a DC series motor, why must it never run on no-load?

In a series motor $\phi \propto I_a$, so $N \propto \dfrac{1}{I_a}$. At no-load $I_a$ is very small, flux is small, and speed becomes dangerously high (it may race to destruction).

Name the three DC motor starting concerns and the device used to limit starting current.

At start $E_b = 0$, so $I_a = V/R_a$ is very high. A starter (e.g. 3-point or 4-point starter) inserts external resistance in the armature circuit to limit starting current; it is cut out as the motor speeds up.

List the methods of speed control of a DC shunt motor.

(1) Flux/field control (vary field current to change $\phi$) — gives speeds above base. (2) Armature/rheostatic control (series resistance in armature) — gives speeds below base. (3) Armature voltage control (Ward-Leonard method).

State the EMF equation of a transformer.

$E = 4.44\,f\,N\,\phi_m$, where f = frequency, N = number of turns, $\phi_m$ = maximum core flux.

Give the transformation (turns) ratio relations for an ideal transformer.

$\dfrac{V_1}{V_2} = \dfrac{N_1}{N_2} = \dfrac{I_2}{I_1} = k$ (turns ratio). Power is conserved: $V_1 I_1 = V_2 I_2$.

Distinguish core-type and shell-type single-phase transformers.

Core-type: windings surround the core, single magnetic path, used for high-voltage/low-output. Shell-type: core surrounds the windings, double magnetic path, better mechanical bracing, used for low-voltage/high-output.

Name the common three-phase transformer connections.

Star–Star (Y-Y), Delta–Delta ($\Delta$-$\Delta$), Star–Delta (Y-$\Delta$, step-down), Delta–Star ($\Delta$-Y, step-up for distribution), and the open-delta (V-V) connection.

Write the condition for maximum efficiency of a transformer.

Maximum efficiency occurs when copper (variable) losses equal iron (constant) losses: $I^{2}R = P_i$. The load fraction is $x = \sqrt{\dfrac{P_i}{P_{cu,\,full}}}$.

Define voltage regulation of a transformer.

$\%\,\text{Regulation} = \dfrac{V_{no\text{-}load} - V_{full\text{-}load}}{V_{full\text{-}load}} \times 100$. Approximately $\%R \approx V_R\cos\phi \pm V_X\sin\phi$ (+ for lagging, − for leading p.f.).

State the advantage of an auto-transformer over a two-winding transformer.

It uses a single tapped winding (part conducted, part transformed), so it requires less copper, has lower losses, higher efficiency, better regulation and is cheaper. Saving of copper $\propto (1-k)$ where $k=N_2/N_1$. Drawback: no electrical isolation between primary and secondary.

State the conditions for satisfactory parallel operation of single-phase transformers.

(1) Same voltage ratings / turns ratio. (2) Same polarity. (3) Same per-unit (percentage) impedance. (4) Same X/R ratio. For three-phase: also same phase sequence and same phase displacement (vector group).

Which two tests determine transformer losses, and which loss does each give?

Open-circuit (no-load) test gives core/iron losses (and shunt branch parameters); short-circuit test gives full-load copper losses (and series impedance).

Explain why the open-circuit test is done on the LV side and short-circuit test on the HV side.

OC test on LV side: rated low voltage is easier to apply and the meters carry small no-load current. SC test on HV side: rated current flows at a low applied voltage (a few percent of rated), convenient and safe for measurement.

State the working principle of a three-phase induction motor.

Three-phase currents produce a rotating magnetic field (rotating at synchronous speed). This field induces (by Faraday's law) EMF and currents in the rotor; the interaction of rotor currents with the field produces torque (Lenz's law) that drags the rotor along. It is essentially a rotating transformer.

Define slip of an induction motor and give synchronous speed.

$N_s = \dfrac{120 f}{P}$ (rpm). Slip $s = \dfrac{N_s - N}{N_s}$, often as a percentage. Rotor frequency $f_r = s f$.

Give the condition for maximum torque in a three-phase induction motor.

Maximum (pull-out) torque occurs when rotor resistance equals standstill rotor reactance referred per phase: $\dfrac{R_2}{s} = X_2$, i.e. slip at maximum torque $s_m = \dfrac{R_2}{X_2}$. Maximum torque is independent of $R_2$.

List the common starting methods for three-phase induction motors.

Squirrel-cage: Direct-On-Line (DOL), Star–Delta starter, Auto-transformer starter, Soft starter / rotor-resistance for slip-ring. Slip-ring motors: add external rotor resistance to boost starting torque and limit current.

Explain speed control of induction motors by varying supply frequency (V/f control).

Since $N_s = \dfrac{120f}{P}$, varying f changes speed. To keep flux constant and avoid saturation, voltage is varied proportionally so that $\dfrac{V}{f}$ is held constant — the basis of VFD/V-f control.

Name methods of braking an induction motor.

(1) Regenerative braking (rotor driven above synchronous speed, machine acts as generator). (2) Plugging (reverse phase sequence). (3) Dynamic (rheostatic) braking — DC injected into stator.

Write the voltage regulation expression for an alternator (synchronous generator) and define it.

$\%\,\text{Reg} = \dfrac{E_0 - V}{V}\times100$, where $E_0$ is no-load (excitation) EMF and V is terminal voltage at full load. $E_0 = \sqrt{(V\cos\phi + I R_a)^{2} + (V\sin\phi \pm I X_s)^{2}}$ (+ lagging, − leading).

List methods of finding voltage regulation of a synchronous generator.

(1) Synchronous impedance / EMF method (gives pessimistic value). (2) Ampere-turn / MMF method (gives optimistic value). (3) Zero power factor / Potier method. (4) ASA method.

How is power factor of a synchronous motor controlled, and what is a synchronous condenser?

By varying field (DC) excitation: over-excitation makes it draw leading current (capacitive), under-excitation makes it draw lagging current. The V-curves show this. A synchronous condenser is an over-excited synchronous motor running on no-load used to supply leading reactive power and improve system power factor.

State the synchronization conditions for connecting an alternator to the grid.

(1) Same voltage magnitude. (2) Same frequency. (3) Same phase sequence. (4) Same phase (in phase) at the instant of paralleling.

Define load factor, demand factor and diversity factor in power systems.

Load factor $= \dfrac{\text{average load}}{\text{maximum demand}}$. Demand factor $= \dfrac{\text{maximum demand}}{\text{connected load}}$. Diversity factor $= \dfrac{\text{sum of individual max demands}}{\text{coincident max demand of group}}\ (\geq 1)$.

What is the most economical conductor cross-section for a transmission line (Kelvin's law)?

Kelvin's law: the most economical conductor size is that for which the annual cost of energy loss (variable, $\propto$ area) equals the annual interest plus depreciation on the capital cost of the conductor (fixed, $\propto$ area).

Define inductance and capacitance per phase of a transmission line (single conductor).

Inductance per phase $L = 2\times10^{-7}\ln\dfrac{D}{r'}\ \text{H/m}$ (with $r' = r e^{-1/4}$ = GMR). Capacitance per phase $C = \dfrac{2\pi\varepsilon_0}{\ln(D/r)}\ \text{F/m}$, where D = spacing between conductors.

Compare short, medium and long transmission line models.

Short ($<80$ km, $<$ 11–66 kV): only series R and L; capacitance neglected. Medium (80–250 km): capacitance included as lumped (nominal-T or nominal-$\pi$). Long ($>250$ km): distributed parameters, solved with hyperbolic functions / ABCD constants.

For a long transmission line, give the characteristic impedance and propagation constant.

Characteristic (surge) impedance $Z_c = \sqrt{\dfrac{z}{y}} = \sqrt{\dfrac{R+j\omega L}{G+j\omega C}}$; propagation constant $\gamma = \sqrt{zy} = \alpha + j\beta$. For a lossless line $Z_c = \sqrt{L/C}$.

Define the Ferranti effect.

On a long or medium transmission line under no-load or light-load conditions, the receiving-end voltage rises above the sending-end voltage due to the line's charging (capacitive) current flowing through the line inductance.

What is corona, and give Peek's formula for critical disruptive voltage.

Corona is the luminous discharge (ionization of air) around a conductor when the surface electric field exceeds the breakdown strength of air, causing power loss, hissing and ozone. Critical disruptive voltage $V_d = m_0\,\delta\,g_0\,r\ln\dfrac{D}{r}$, where $g_0\approx30\ \text{kV/cm}$, $\delta$ = air density factor, $m_0$ = conductor surface factor.

List factors affecting corona loss and ways to reduce it.

Affected by: supply voltage, frequency, conductor diameter, spacing, air density, and surface condition. Reduced by using larger-diameter conductors, bundled conductors, hollow/ACSR conductors, and increasing spacing. Peek's corona loss $\propto (f+25)(V-V_d)^{2}$.

Define string efficiency of a suspension insulator and how to improve it.

$\text{String efficiency} = \dfrac{\text{voltage across the whole string}}{n \times \text{voltage across the disc nearest the conductor}}$. Improved by using a guard/grading ring, longer cross-arms, and capacitance grading. Ideal string efficiency is $100\%$ (equal voltage on all discs).