I, R, X_L, V_R and cosϕR represent voltage regulation, line current, line resistance, line reactance, receiving end voltage and load power factor of transmission line, respectively. Also, receiving end voltage is more than the sending end voltage. Identify the correct expression for the leading load power factor.

Concept of Voltage Regulation and Power Factor:

Voltage regulation (VR) is defined as the difference between the sending end voltage (V_S) and the receiving end voltage (V_R), expressed as a fraction of the receiving end voltage:

VR = (V_S - V_R) / V_R

For a leading power factor load, the voltage regulation can be affected by the inductive reactance (X_L) and the line resistance (R) of the transmission line. The expression for voltage regulation in terms of these parameters is:

VR = (I R cosϕ_R) - (I X_L sinϕ_R)

Where,

• I = Line Current
• R = Line Resistance
• X_L = Line Reactance
• V_R = Receiving End Voltage
• cosϕ_R = Load Power Factor (leading)
   

Given Condition:

• The receiving end voltage (V_R) is more than the sending end voltage (V_S), indicating a leading load power factor. This condition implies that the reactive component is capacitive, causing the voltage to rise.
• In a transmission line with a leading power factor, the voltage regulation is negative, meaning the receiving end voltage (VR) is higher than the sending end voltage. The leading power factor causes the capacitive reactance to dominate, which means the reactive component (IXL) plays a larger role than the resistive component (IR). This leads to the condition where IR COSϕR is less than IXLCOSϕR.
   

Correct Expression for Leading Power Factor: IR cosϕ_R < I X_L cosϕ_R

Conclusion:

Hence, the correct expression for the leading load power factor is:

IR cosϕ_R < I X_L cosϕ_R