Final answer:
To calculate the efficiency of transmission in a power system, the resistance and reactance per phase must be determined for the length of the transmission line, then used to compute line current and power losses. Subtracting the percentage of power loss from 100% yields the efficiency of transmission.
Step-by-step explanation:
To calculate the efficiency of transmission, we need to first determine the actual power losses in the line and compare it to the total power transmitted. Given the resistance (R) of 0.2 ohm/km, the reactance (X) of 0.5 ohm/km, and the transmission line length (L) of 100 km, the total resistance and reactance per phase are R₁ = 0.2 × 100 = 20 ohms and X₁ = 0.5 × 100 = 50 ohms, respectively.
The sent power (P₁) is 25 MW at 0.8 power factor (pf), which means the line current (I₁) can be calculated using P₁ = √3 × V₁ × I₁ × pf. Given V₁ is the phase voltage, we can calculate I₁. Then the power losses due to resistance (Pᴅ₁) will be Pᴅ₁ = 3 × I₁² × R₁. Finally, the efficiency (η) can be found by subtracting the percent of power loss from 100%, where percent of power loss is (Pᴅ₁/P₁) × 100%.