MODULE 1 — Basics of Power Transmission

1.1 Layout of Power System (Single Line Diagram)

Generating Station (11kV)Pri. Transmission (132/220/400kV)Sec. Transmission (33/66kV)
Pri. Distribution (11kV)Sec. Distribution (415/230V)
~ 11kV Gen Step-Up (11/220kV) Primary Trans. Step-Down (220/33kV) Secondary Trans. Step-Down (33/11kV) Pri. Dist. Consumer (415V)

1.3 Advantages of High Voltage

$$ \text{Volume of Cu} \propto \frac{1}{V^2} $$
$$ P_{loss} = I^2 R = \frac{P^2 R}{V^2 \cos^2\phi} $$
$$ \%V_{drop} \propto \frac{1}{V} $$

Low Voltage (11kV)

Thick Wire, High Loss

vs

High Voltage (400kV)

Thin Wire, Low Loss

Power Loss = 100% | Cu Volume = 100%

1.4 AC vs DC Transmission

$$ P_{AC} = \sqrt{3} V_L I_L \cos\phi $$
$$ P_{DC} = V_{DC} \cdot I_{DC} $$
$$ d_{break-even} \approx 600-800\text{ km (Overhead)} $$
DC has higher terminal cost, but lower line cost per km.
Break-even point is where total costs intersect.

1.5 Kelvin's Law (Economic Conductor Size)

Cost Equations

$$ C_1 = (a + bx) \quad \text{(Capital Cost)} $$
$$ C_2 = \frac{c}{x} \quad \text{(Energy Loss Cost)} $$

Optimum Size

$$ Total \, C = C_1 + C_2 $$
$$ x_{opt} = \sqrt{\frac{c}{b}} \quad \text{minimized when } bx = \frac{c}{x} $$
Annual Cost of Energy Wasted = Annual interest + depreciation of conductor.
x_opt = 10.00 mm²