(SEM V) THEORY EXAMINATION 2023-24 POWER SYSTEM - I

SECTION A – Short Answers (2 × 10 = 20)

(a) Differentiate between renewable and non-renewable energy

(b) What is a diversity factor?

Diversity Factor=Sum of individual maximum demandsMaximum demand on system\text{Diversity Factor} = \frac{\text{Sum of individual maximum demands}}{\text{Maximum demand on system}}Diversity Factor=Maximum demand on systemSum of individual maximum demands​

It measures load variation among consumers.
Higher diversity factor → better system utilization.

(c) What is skin effect?

When AC current concentrates near the surface of a conductor, reducing effective cross-sectional area and increasing resistance with frequency.
Negligible in DC.

(d) Is corona more in AC or DC?

Corona is more pronounced in AC because:   Voltage changes polarity → ionization–deionization cycles.                                                              Higher effective voltage gradient at conductor surface.

(e) What do you mean by sag template?

A graphical tool used by engineers to determine sag and tension in overhead conductors over varying span lengths and tower heights.                             It ensures safe clearance and economical conductor length.

(f) Define the term sag.

Sag is the vertical distance between the highest point of the support and the lowest point of the conductor.

S=wL28TS = \frac{wL^2}{8T}S=8TwL2​

where
www = weight per unit length,                 LLL = span,                 TTT = tension in conductor.

(g) What do you mean by self GMD and mutual GMD?

Self GMD (GMR): Geometric Mean Radius of a single conductor bundle.

Mutual GMD (GMD): Geometric mean distance between conductors of different phases.
Used in inductance and capacitance calculation of transmission lines.

(h) Main causes of insulation failure            Over-voltage due to lightning or switching surge

Mechanical stress and vibration                  Moisture and dirt deposition

Thermal aging                                             Manufacturing defects or poor maintenance

(i) Underground cable losses                      Dielectric losses in insulation.

Conductor (I²R) losses.                             Sheath and eddy current losses.

Charging current losses at high voltage.

(j) Difference between overhead lines and underground cables

SECTION B – Descriptive Questions (Any 3 × 10 = 30)

(a) Equipments used in a substation                           Bus bars

Circuit breakers                                                           Isolators

Transformers                                                               Instrument transformers (CTs, PTs)

Surge arresters                                                            Control and protection relays

Grounding system

(b) Kelvin’s Law for Conductor Size

States that total annual cost = capital cost + energy loss cost, and is minimum when these two are equal.
Used to determine economic cross-section of transmission conductor.

(c) Factors affecting sag                                 Weight of conductor

Span length                                                  Tension applied

Wind and ice loading                                  Temperature variation (thermal expansion)

(d) Inductance of double circuit single-phase line

L=2×10−7H/mln⁡Dmr′L = \frac{2 \times 10^{-7}}{\text{H/m}} \ln\frac{D_m}{r'}L=H/m2×10−7​lnr′Dm​​

You substitute given D1,D2,D_1, D_2,D1​,D2​, and diameter values to compute per km inductance.

(e) Types of insulating materials                    Solid: Paper, mica, porcelain

Liquid: Mineral oil, silicone oil                      Gaseous: Air, SF₆ gas

Synthetic: Epoxy, Teflon, PVC

SECTION C – Long Questions (Any 1 from each)

3(a) Daily Load Curve Calculation

Given data allows:

Max Demand = 70 MW                                      Units Generated = Area under curve = Σ(P×t)

Average Load = Total Units / 24 hrs                  Load Factor = Average Load / Max Demand

4(a) Types of Supply Systems

DC 2-wire, DC 3-wire, AC 1-phase, AC 3-phase (3-wire and 4-wire)
Comparison: 3-phase 3-wire requires less conductor material for same power compared to DC 2-wire.

4(b) Medium Transmission Line (T-model)

Used for lines 80–250 km long.
Considers distributed R, L, C parameters as lumped halves at each end.
ABCD parameters derived using nominal T-circuit:

A=D=1+YZ2,B=Z(1+YZ4),C=YA = D = 1 + \frac{YZ}{2},\quad B = Z(1+\frac{YZ}{4}),\quad C = YA=D=1+2YZ​,B=Z(1+4YZ​),C=Y 

5(a) String Efficiency

Given: Vs=15kVV_s = 15 kVVs​=15kV, ratio k=CCs=8k = \frac{C}{C_s} = 8k=Cs​C​=8.
Use capacitive voltage distribution to find

Vtotal, η=nVmeanVmax×100V_{total},\ \eta = \frac{nV_{mean}}{V_{max}} \times 100Vtotal​, η=Vmax​nVmean​​×100 

6(a) Catenary Method for Sag

Sag curve forms a catenary under self-weight.
Equation:

y=T0w[cosh⁡(wxT0)−1]y = \frac{T_0}{w}\left[\cosh\left(\frac{wx}{T_0}\right) - 1\right]y=wT0​​[cosh(T0​wx​)−1]

Used for long spans where parabolic approximation isn’t accurate.

7(a) Inter-sheath Grading of Cables

Reduces dielectric stress by inserting metallic sheaths at intermediate potentials.

Practical difficulty: Complex manufacturing and insulation leakage between sheaths.

7(b) Economical Diameter of Cable

For 66 kV, 3-phase system with peak stress E=50 kV/cmE = 50\text{ kV/cm}E=50 kV/cm:

r=VmE,D=2rr = \frac{V_m}{E}, \quad D = 2rr=EVm​​,D=2r

Calculate for 66 kV (rms) → Vm=66×103×2/3V_m = 66 \times 10^3 \times \sqrt{2}/\sqrt{3}Vm​=66×103×2​/3​.