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Power Systems & Transmission (Electrical Engineering) Solved Questions & Notes (2026) - Apex Rankers

Engineering & Technology > Electrical Engineering > Power Systems & Transmission

30 Total Solved Questions
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Power Systems & Transmission

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Q. 1 Electrical Engineering
Difficulty: Easy (1 Mark)
The Ferranti Effect in electrical power transmission lines refers to the phenomenon where:
A
The receiving-end voltage is higher than the sending-end voltage under no-load or lightly loaded conditions on long transmission lines
✓ Correct
B
The line voltage drops significantly during heavy inductive loading
C
Current concentrates on the outer surface of conductors
D
Corona discharge ionizes ambient air at high altitudes
💡 Step-by-Step Explanation & Concept Rationale
On long, lightly loaded or open-ended transmission lines, line charging current flowing through the line's distributed series inductance causes a voltage rise along the line, resulting in receiving-end voltage exceeding sending-end voltage (Vr > Vs). Shunt reactors are installed to absorb this reactive power.
Q. 2 Electrical Engineering
Difficulty: Easy (1 Mark)
Surge Impedance (or characteristic impedance Zc) of a lossless overhead transmission line with inductance L and capacitance C is given by:
A
Zc = sqrt(L / C)
✓ Correct
B
Zc = sqrt(C / L)
C
Zc = 1 / sqrt(L * C)
D
Zc = sqrt(L * C)
💡 Step-by-Step Explanation & Concept Rationale
For a lossless line (R=0, G=0), the surge impedance is Zc = sqrt(L / C). For typical overhead transmission lines, Zc ranges from 400 to 450 ohms, while for underground cables, Zc is around 40 to 50 ohms.
Q. 3 Electrical Engineering
Difficulty: Medium (1 Mark)
Surge Impedance Loading (SIL) of a transmission line with nominal line-to-line voltage V_LL and surge impedance Zc is:
A
SIL = V_LL^2 / Zc
✓ Correct
B
SIL = Zc / V_LL^2
C
SIL = sqrt(3) * V_LL * Zc
D
SIL = V_LL * Zc
💡 Step-by-Step Explanation & Concept Rationale
Surge Impedance Loading represents the power delivered by a transmission line to a load equal to its surge impedance: SIL = V_LL^2 / Zc (MW). At this loading, reactive power generated by line capacitance exactly balances reactive power absorbed by line inductance, yielding flat voltage along the line.
Q. 4 Electrical Engineering
Difficulty: Easy (1 Mark)
Corona discharge on high-voltage overhead transmission lines is accompanied by:
A
A violet-colored luminous glow, hissing noise, ozone gas production, and power loss
✓ Correct
B
Sudden freezing of line conductors
C
Complete cancellation of series line inductance
D
Zero power loss
💡 Step-by-Step Explanation & Concept Rationale
Corona occurs when the electrostatic field gradient at the conductor surface exceeds the dielectric breakdown strength of air (approx. 30 kV/cm peak or 21.2 kV/cm RMS). Ionization of air produces a faint violet glow, hissing acoustic noise, chemical production of ozone (O3), and power loss.
Q. 5 Electrical Engineering
Difficulty: Medium (1 Mark)
Bundle conductors are widely employed in Extra High Voltage (EHV) and Ultra High Voltage (UHV) transmission lines primarily to:
A
Increase the effective conductor diameter (GMR), thereby reducing surface electric field gradient, corona loss, and line reactance
✓ Correct
B
Make tower erection easier and cheaper
C
Eliminate the need for lightning arresters
D
Prevent mechanical sag in hot summers
💡 Step-by-Step Explanation & Concept Rationale
Using bundles of two, three, or four sub-conductors per phase increases the Geometric Mean Radius (GMR) of the phase conductor. This lowers the electrostatic surface stress below the critical disruptive threshold, substantially reducing corona loss, radio interference, and series inductive reactance.
Q. 6 Electrical Engineering
Difficulty: Medium (1 Mark)
The critical disruptive voltage of a transmission line decreases under which environmental condition?
A
High atmospheric pressure and dry air
B
Stormy, foul weather (rain, fog, or snow) and high altitude with low barometric pressure
✓ Correct
C
Sub-zero temperatures with dry breeze
D
Nighttime with clear skies
💡 Step-by-Step Explanation & Concept Rationale
Critical disruptive voltage Vd = m0 * g0 * delta * r * ln(D/r). At high altitudes or stormy weather, the air density factor delta decreases and the conductor irregularity factor m0 drops from 1.0 to ~0.8, causing corona to initiate at much lower voltages.
Q. 7 Electrical Engineering
Difficulty: Medium (1 Mark)
The proximity effect in transmission conductors refers to:
A
Current redistribution due to the magnetic fields of nearby conductors carrying current, increasing effective AC resistance
✓ Correct
B
Mutual capacitance between tower body and ground wire
C
The reflection of lightning traveling waves
D
Thermal heating of insulators
💡 Step-by-Step Explanation & Concept Rationale
Proximity effect occurs when alternating flux from an adjacent parallel conductor distorts the current distribution across the cross-section of a conductor. When currents flow in the same direction, current shifts away from adjacent sides; when in opposite directions, it concentrates on facing sides, raising AC resistance.
Q. 8 Electrical Engineering
Difficulty: Easy (1 Mark)
ACSR (Aluminum Conductor Steel Reinforced) conductors are standard for overhead transmission because:
A
The inner steel core provides high mechanical tensile strength, while outer aluminum strands provide high electrical conductivity and lighter weight
✓ Correct
B
Steel has higher electrical conductivity than aluminum
C
Aluminum prevents mechanical corrosion of steel completely
D
Steel reduces eddy current losses to zero
💡 Step-by-Step Explanation & Concept Rationale
Pure aluminum has high conductivity and low weight but low tensile strength. Combining a high-tensile galvanized steel core with surrounding aluminum strands gives ACSR high mechanical strength to permit long spans between towers with reduced sag.
Q. 9 Electrical Engineering
Difficulty: Medium (1 Mark)
String efficiency of a suspension insulator string on an overhead transmission tower is defined as:
A
Total flashover voltage / Breakdown voltage
B
Voltage across the whole string / (Number of insulator discs * Voltage across the disc nearest to the line conductor)
✓ Correct
C
Capacitance of top disc / Capacitance of bottom disc
D
Leakage resistance / Surface resistance
💡 Step-by-Step Explanation & Concept Rationale
Due to shunt capacitance between insulator metal pins and the grounded tower body, voltage distribution across the string is non-uniform, with the bottom disc (nearest the line conductor) experiencing the greatest electrical stress. String efficiency = V_total / (n * V_bottom) * 100%.
Q. 10 Electrical Engineering
Difficulty: Medium (1 Mark)
A guard ring (static shielding ring) is installed around the bottom disc of an insulator string to:
A
Improve string efficiency by introducing cross-capacitances that equalize the voltage distribution across all discs
✓ Correct
B
Provide mechanical support to line clamps
C
Prevent birds from perching on the line
D
Ground lightning strikes directly to the tower
💡 Step-by-Step Explanation & Concept Rationale
A guard ring introduces capacitance between the line conductor and the insulator pins. These currents counteract the pin-to-ground leakage currents, making the voltage distribution across all discs nearly uniform, raising string efficiency close to 100%.
Q. 11 Electrical Engineering
Difficulty: Easy (1 Mark)
In a transmission line model, lines classified as 'Short Transmission Lines' have a length and operating voltage of approximately:
A
Length < 80 km and Voltage < 20 kV (where shunt capacitance is completely neglected)
✓ Correct
B
Length 80 to 250 km and Voltage 20 to 100 kV
C
Length > 250 km and Voltage > 100 kV
D
Length < 1 km only
💡 Step-by-Step Explanation & Concept Rationale
Lines up to ~80 km operating below 20-25 kV have negligible charging currents. Their performance is analyzed by representing only series resistance and series inductive reactance, neglecting shunt capacitance entirely.
Q. 12 Electrical Engineering
Difficulty: Medium (1 Mark)
In the Nominal-T method of representing a medium-length transmission line (80 - 240 km):
A
Total shunt admittance is lumped in the middle, between two half-series impedances (Z/2 each)
✓ Correct
B
Total series impedance is lumped in the middle, between two half-shunt admittances (Y/2 each)
C
Capacitance is neglected entirely
D
Line resistance is doubled
💡 Step-by-Step Explanation & Concept Rationale
In the Nominal-T network, total line impedance is divided into two halves (Z/2 on the sending side and Z/2 on the receiving side), with the entire line capacitance (admittance Y) lumped at the center node.
Q. 13 Electrical Engineering
Difficulty: Medium (1 Mark)
The ABCD transmission matrix parameters for a symmetric, bilateral, reciprocal transmission network must satisfy which two fundamental identities?
A
A = D (symmetry) and A*D - B*C = 1 (reciprocity)
✓ Correct
B
A = B and C = D
C
A*D + B*C = 1 and B = C
D
A = 1 and D = 0
💡 Step-by-Step Explanation & Concept Rationale
For any passive bilateral two-port network, the reciprocity condition requires the determinant of the transmission matrix to equal unity: AD - BC = 1. If the network is identical viewed from either port (symmetrical), A = D.
Q. 14 Electrical Engineering
Difficulty: Easy (1 Mark)
Transposition of 3-phase overhead transmission line conductors at regular intervals along the route is performed to:
A
Equalize the line inductances and capacitances of all three phases, preventing voltage unbalance and telephone interference
✓ Correct
B
Increase the mechanical tensile strength of the line
C
Prevent bird strikes
D
Reduce corona discharge at terminal bushings
💡 Step-by-Step Explanation & Concept Rationale
When conductors are placed unsymmetrically on towers, mutual inductances and capacitances to ground differ per phase. Transposing (swapping conductor spatial positions at 1/3rd intervals) balances phase impedances and cancels electromagnetic induction into parallel communication lines.
Q. 15 Electrical Engineering
Difficulty: Medium (1 Mark)
In High Voltage DC (HVDC) transmission systems, which converter configuration is universally employed for bulk power transfer?
A
12-pulse line-commutated converter (LCC) using thyristors or Voltage Source Converter (VSC) using IGBTs
✓ Correct
B
Single-phase half-wave diode rectifiers
C
Rotary mechanical converters
D
Step-down autotransformers
💡 Step-by-Step Explanation & Concept Rationale
Modern HVDC uses 12-pulse Graetz bridge rectifiers/inverters (connecting two 6-pulse bridges in series via Star-Star and Star-Delta transformers to cancel 5th and 7th harmonics) or modern VSC-HVDC utilizing IGBTs for independent real and reactive power control.
Q. 16 Electrical Engineering
Difficulty: Medium (1 Mark)
The 'Break-Even Distance' beyond which HVDC transmission becomes more economical than HVAC transmission for overhead lines is approximately:
A
20 to 50 km
B
600 to 800 km for overhead lines (and 50 km for submarine cables)
✓ Correct
C
2000 km minimum
D
100 km
💡 Step-by-Step Explanation & Concept Rationale
HVDC terminal converter stations have high capital costs, but DC lines require only 2 conductors (bipolar) instead of 3, have no reactive power charging current limits, and cheaper towers. The cost curves intersect at 600-800 km for overhead lines and ~50 km for underwater cables.
Q. 17 Electrical Engineering
Difficulty: Medium (1 Mark)
In underground cables, dielectric breakdown stress in the insulation is maximum at:
A
The outer surface of the lead sheath
B
The surface of the inner metallic conductor core (r = r_conductor)
✓ Correct
C
Midway between conductor and sheath
D
The metallic armor outer boundary
💡 Step-by-Step Explanation & Concept Rationale
Electric field gradient in a single-core coaxial cable is g = V / [x * ln(R/r)], where x is radial distance from the center. Electric stress is highest at minimum radius x = r (conductor surface) and lowest at maximum radius x = R (inner surface of lead sheath).
Q. 18 Electrical Engineering
Difficulty: Medium (1 Mark)
The most economical ratio of sheath inner radius (R) to conductor radius (r) in an underground cable to minimize dielectric stress is:
A
R / r = 2.0
B
R / r = e ≈ 2.718
✓ Correct
C
R / r = pi ≈ 3.142
D
R / r = 1.414
💡 Step-by-Step Explanation & Concept Rationale
Maximum electric stress g_max = V / [r * ln(R/r)]. Minimizing g_max with respect to r gives d(g_max)/dr = 0, which occurs when ln(R/r) = 1, meaning R / r = e ≈ 2.718.
Q. 19 Electrical Engineering
Difficulty: Medium (1 Mark)
Grading of underground cables (capacitance grading or intersheath grading) is performed to:
A
Increase conductor current-carrying capacity
B
Make the radial electrostatic stress distribution uniform throughout the dielectric insulation layer
✓ Correct
C
Reduce cable armor weight
D
Lower the supply voltage
💡 Step-by-Step Explanation & Concept Rationale
In ungraded cables, the dielectric near the conductor is heavily stressed while outer insulation is under-stressed. Capacitance grading uses dielectric layers of decreasing permittivity (epsilon1 > epsilon2 > epsilon3) from inside out, equalizing dielectric stress across the whole insulation.
Q. 20 Electrical Engineering
Difficulty: Easy (1 Mark)
The metallic lead sheath over the insulation of an underground power cable serves to:
A
Provide mechanical protection against stone impacts
B
Prevent ingress of soil moisture, acids, and gases into the paper or polymeric dielectric insulation
✓ Correct
C
Increase mutual inductance
D
Act as the primary return path for load current
💡 Step-by-Step Explanation & Concept Rationale
High-voltage cable paper insulation is hygroscopic; even tiny traces of moisture ruin its dielectric breakdown strength. An extruded lead or aluminum sheath forms an impervious moisture-proof seal around the insulation.
Q. 21 Electrical Engineering
Difficulty: Easy (1 Mark)
In power generation economics, the Load Factor of a power station is defined as:
A
Maximum demand / Average load
B
Average load over a given period / Maximum demand during that period (or kWh generated / [Max Demand * Time])
✓ Correct
C
Connected load / Maximum demand
D
Plant capacity / Maximum demand
💡 Step-by-Step Explanation & Concept Rationale
Load Factor = Average Load / Maximum Demand = (Total kWh generated in T hours) / (Maximum Demand in kW * T). A higher load factor means generating units operate near peak capacity consistently, lowering the cost of energy per unit (kWh).
Q. 22 Electrical Engineering
Difficulty: Easy (1 Mark)
The Diversity Factor of a power supply distribution system is defined as:
A
Sum of individual consumer maximum demands / Coincident maximum demand on the power station
✓ Correct
B
Coincident maximum demand / Connected load
C
Average load / Rated capacity
D
Always less than 1.0
💡 Step-by-Step Explanation & Concept Rationale
Diversity Factor = (Sum of individual maximum demands) / (Coincident maximum demand). Because different consumers reach peak demand at different times of the day, the diversity factor is always greater than 1.0 (typically 1.2 to 1.5).
Q. 23 Electrical Engineering
Difficulty: Easy (1 Mark)
A high diversity factor in an electrical power system is economically desirable because it:
A
Increases line copper losses
B
Reduces the peak coincident maximum demand on the power plant, thereby minimizing required installed generator capacity and capital investment
✓ Correct
C
Increases fuel consumption
D
Forces transformer oil to degrade faster
💡 Step-by-Step Explanation & Concept Rationale
A higher diversity factor means non-coincident consumer peaks. This flattens the station load curve and lowers peak demand on the generators, allowing a smaller power plant to serve a larger total connected customer base.
Q. 24 Electrical Engineering
Difficulty: Easy (1 Mark)
Plant Capacity Factor (or Plant Use Factor) of a generating station is defined as:
A
Actual energy produced (kWh) / (Installed Plant Rating * Total Operating Time)
✓ Correct
B
Maximum Demand / Installed Capacity
C
Reserve capacity / Maximum demand
D
Connected load / Plant capacity
💡 Step-by-Step Explanation & Concept Rationale
Plant Capacity Factor = (Actual kWh generated) / (Installed rating in kW * Time). The difference between Installed Capacity and Maximum Demand represents the spinning reserve capacity of the power plant.
Q. 25 Electrical Engineering
Difficulty: Medium (1 Mark)
Kelvin's Law states that the most economical conductor cross-sectional area for an overhead transmission line occurs when:
A
The annual cost of electrical energy lost in conductor resistance equals the annual interest and depreciation charges on the capital cost of the conductor
✓ Correct
B
Voltage drop along the line is strictly zero
C
Conductor temperature reaches 100 degrees Celsius
D
Insulation cost equals tower cost
💡 Step-by-Step Explanation & Concept Rationale
Kelvin's Law determines conductor sizing: Total Annual Cost = C1 * A + C2 / A. Differentiating with respect to conductor area A yields the minimum cost condition: Annual interest and depreciation on conductor capital outlay (P1 ∝ A) = Annual cost of energy wasted as I^2*R losses (P2 ∝ 1/A).
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