I, R, X L , V R and cosϕR represent voltage regulation, line current, line resistance, line reactance, receivi

Question

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.

Examoogle · Accepted Answer

The correct answer is Option C: IR \cos\phi_R < IX_L \sin\phi_R. Voltage regulation is defined as the change in receiving end voltage from no-load to full-load expressed as a percentage of full-load receiving end voltage. Negative voltage regulation occurs when the receiving end voltage is greater than the sending end voltage ($V_R > V_S$), which typically happens under leading power factor conditions (capacitive loads).

Step-by-Step Solution & Concepts:
Voltage regulation is defined as the change in receiving end voltage from no-load to full-load expressed as a percentage of full-load receiving end voltage. Negative voltage regulation occurs when the receiving end voltage is greater than the sending end voltage ($V_R > V_S$), which typically happens under leading power factor conditions (capacitive loads).

Working Principle: The approximate voltage drop in a transmission line is given by $V_S \approx V_R + I(R \cos\phi_R \pm X_L \sin\phi_R)$. For a leading power factor, the reactive drop is subtractive ($V_S = V_R + IR \cos\phi_R - IX_L \sin\phi_R$). For the receiving end voltage to be greater than the sending end voltage ($V_R > V_S$), the expression must satisfy $V_S - V_R

Key Formulas: $$	ext{Voltage Regulation} = \frac{V_{NL} - V_{FL}}{V_{FL}} 	imes 100\%$$; $$V_S \approx V_R + I(R \cos\phi_R - X_L \sin\phi_R) \quad (	ext{for leading p.f.})$$

Key Points: Negative voltage regulation signifies $V_R > V_S$.; Leading power factor loads cause a Ferranti-like effect or voltage rise due to the capacitor effect.; The condition $IR \cos\phi_R

Advantages: Allows voltage boost at the receiving end without additional regulators.; Improves system efficiency for long lines by compensating for inductive reactance.

Disadvantages: Excessive voltage rise can damage insulation.; Difficult to control in varying load conditions.

Applications: Long EHV (Extra High Voltage) transmission lines.; Capacitive reactive power compensation systems.

Additional Info: The option C ($IR \cos\phi_R V_S$.. The provided images in the prompt show variants of the inequality; option C is the correct physical condition for this phenomenon.

Answer: C is correct — For the receiving end voltage to be greater than the sending end voltage, the resistive drop component must be less than the reactive rise component, expressed as $IR \cos\phi_R

Exam Tip: Remember that lagging power factor always leads to a drop in voltage, while leading power factor can cause a voltage rise at the receiving end.

Examoogle · Answer

Option A: IR \cos\phi_R >> IX_L \sin\phi_R

Examoogle · Answer

Option B: IR \cos\phi_R > IX_L \sin\phi_R

Examoogle · Answer

Option D: IR \cos\phi_R = IX_L \sin\phi_R

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