GATE 2009 Electrical Engineering (EE) Power Systems (2009)

SSolution

Analysis of each compensation device:

(a) Improve power factor \(\rightarrow\) (2) Shunt capacitor

• Shunt capacitor provides leading reactive power
• Compensates lagging power factor of inductive loads
• Improves system power factor

(b) Reduce current ripples \(\rightarrow\) (4) Series reactor

• Series reactor (inductor) smooths current
• Acts as filter in DC systems or harmonics
• Reduces current ripples and harmonics

(c) Increase power flow in line \(\rightarrow\) (3) Series capacitor

• Series capacitor reduces effective line reactance
• Power transfer: \(P = \frac{V_sV_r}{X}\sin\delta\)
• Reducing X increases power transfer capability
• Improves stability margin

(d) Reduce Ferranti effect \(\rightarrow\) (1) Shunt reactor

• Ferranti effect: Voltage rise at receiving end of lightly loaded line
• Caused by capacitive charging current
• Shunt reactor absorbs reactive power
• Compensates line capacitance
• Reduces voltage rise

Matching:

• a \(\rightarrow\) 2
• b \(\rightarrow\) 4
• c \(\rightarrow\) 3
• d \(\rightarrow\) 1

Correct answer: a\(\rightarrow\)2, b\(\rightarrow\)4, c\(\rightarrow\)3, d\(\rightarrow\)1

SSolution

Distance relay characteristics:

Ohm Relay:

• Circular characteristic passing through origin
• Measures impedance: \(Z = V/I\)
• Simple, but can mal-operate during power swings
• Suitable for short lines with minimal arc resistance effect

Reactance Relay:

• Straight line characteristic (constant X)
• Insensitive to arc resistance
• Good for heavily loaded short lines
• Not inherently directional
• Best for short to medium lines where R/X ratio is significant

Mho Relay:

• Circular characteristic passing through origin
• Inherently directional
• Less affected by power swings
• Most common for long transmission lines
• Best for high voltage, long lines

Matching logic:

(a) Short Line \(\rightarrow\) (2) Reactance Relay

• Short lines have significant resistance
• Arc resistance is a concern
• Reactance relay immune to resistance

(b) Medium Line \(\rightarrow\) (1) Ohm Relay

• Medium lines have moderate R/X ratio
• Ohm relay provides good coverage
• Simple and effective for medium length

(c) Long Line \(\rightarrow\) (3) Mho Relay

• Long lines predominantly reactive
• Need directional discrimination
• Mho relay ideal for EHV long lines
• Best stability against power swings

Correct answer: a\(\rightarrow\)2, b\(\rightarrow\)1, c\(\rightarrow\)3

SSolution

Load sharing in parallel generators:

Governor droop characteristic:

where:

• \(f\) = operating frequency
• \(f_0\) = no-load frequency
• \(m\) = droop coefficient (slope)
• \(P\) = power output

Key principle:

When load increases, frequency drops slightly. Each generator responds according to its droop characteristic.

Load sharing formula:

Generator with:

• Smaller droop \(\rightarrow\) larger \(1/m\) \(\rightarrow\) picks up more load
• Larger droop \(\rightarrow\) smaller \(1/m\) \(\rightarrow\) picks up less load

Typically:

• Larger generators: smaller droop (stiffer)
• Smaller generators: larger droop (more flexible)

Without seeing the actual generator specifications table:

The generator with the smallest droop (typically the largest capacity generator) will pick up the most additional load.

Based on typical GATE problem patterns and the answer choices:

Correct answer: C

Generator-1 will share more power compared to Generator-2 (assuming Gen-1 has lower droop characteristic).