By increasing the transmission voltage to double of its original value the same power can be dispatched keepin

Question

By increasing the transmission voltage to double of its original value the same power can be dispatched keeping the line loss

Examoogle · Accepted Answer

Option D: One fourth of original value

Explanation & Concepts:
When the transmission voltage is increased while keeping the power transmitted ($P$) and the power factor ($cos \phi$) constant, the line current ($I$) decreases in inverse proportion to the voltage. Since line loss is proportional to the square of the current ($I^2R$), doubling the voltage leads to a reduction of line loss to one-fourth of its original value.

Working Principle: The power transmitted in a system is given by $P = V I \cos \phi$ for single-phase systems or $P = \sqrt{3} V_L I_L \cos \phi$ for three-phase systems. If $P$ is constant, $I \propto \frac{1}{V}$. Line power loss ($P_{loss}$) is defined as $P_{loss} = I^2 R$. By substituting the inverse relationship of current and voltage, we get $P_{loss} \propto (\frac{1}{V})^2$, which simplifies to $P_{loss} \propto \frac{1}{V^2}$. Thus, doubling the voltage ($2V$) results in $(1/2)^2 = 1/4$ of the original loss.

Key Formulas: $I = \frac{P}{V \cos \phi}$ — Current as a function of voltage; $P_{loss} = I^2 R$ — Power loss formula; $P_{loss} \propto \frac{1}{V^2}$ — Inverse square relationship with voltage

Key Points: High voltage transmission reduces line current, minimizing ohmic ($I^2R$) losses.; Higher transmission voltage allows for smaller conductor cross-section areas, saving material costs.; Increasing voltage beyond certain limits may increase corona loss and insulation costs.

Advantages: Higher efficiency due to reduced copper losses; Improved voltage regulation; Lower conductor material requirement

Disadvantages: Higher cost of insulation and switchgear; Increased risk of corona effect; Complexity in tower design due to increased clearance

Applications: HVDC and HVAC bulk power transmission; Inter-grid power interconnection

Additional Info: Option A is incorrect because current must change if voltage is scaled and power is constant.. Option C is incorrect because it implies power loss increases with voltage, which contradicts the $I^2R$ law.. The constant power transmission assumption is critical for this derivation.

Answer: D is correct — Because power loss is proportional to the square of the current, doubling the voltage reduces the current by half, resulting in one-fourth of the original line loss.

Exam Tip: Always verify if the power being transmitted is assumed constant, as $P_{loss} \propto \frac{1}{V^2}$ only holds true when $P$ remains constant.

Examoogle · Answer

Option A: Equal to original value

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Option B: Half the original value

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Option C: Double the original value

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