The most economic load on an underground cable is

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Option B: Less than the natural load

Explanation & Concepts:
The most economic load on an underground cable is typically lower than the natural load (surge impedance loading) to ensure the dielectric stress, thermal limit, and voltage regulation constraints are maintained within safe operational limits. Operating significantly above this level leads to excessive heat generation, which degrades the insulation rapidly, leading to permanent cable failure.

Working Principle: Underground cables have a much higher shunt capacitance compared to overhead transmission lines. This results in a higher charging current. The natural load, or Surge Impedance Loading (SIL), is defined as $P_{SIL} = \frac{V^2}{Z_0}$, where $Z_0$ is the surge impedance $\sqrt{\frac{L}{C}}$. Because cables have a high capacitance ($C$), their $Z_0$ is very low, making the theoretical SIL very high. However, loading the cable to its theoretical SIL would result in thermal breakdown due to resistive losses ($I^2R$), so they must be operated at a load lower than the natural load to preserve insulation life.

Key Formulas: $SIL = \frac{V^2}{Z_0}$ — Surge Impedance Loading definition; $Z_0 = \sqrt{\frac{L}{C}}$ — Surge impedance of the transmission line/cable

Key Points: Underground cables possess significantly higher capacitance ($C$) compared to overhead lines.; Higher capacitance lowers the surge impedance ($Z_0$), leading to a high theoretical SIL.; Thermal limitations and insulation degradation due to dielectric stress prevent operating at SIL.; Economic load factor accounts for both capital expenditure (CAPEX) and operational losses (OPEX).

Advantages: Lower operational temperatures extend insulation lifespan.; Improved voltage regulation under steady-state conditions.; Reduction in cumulative dielectric stress on cable insulation.

Disadvantages: Under-utilization of the cable's current-carrying capacity.; Higher cost per unit of power transmitted.

Applications: Submarine power transmission; High-density urban underground distribution networks

Additional Info: Option A is incorrect because operating above the natural load increases losses significantly.. Option C is incorrect because the cable would operate beyond its thermal safety threshold.. The economic load is determined by Kelvin's Law, which balances the cost of energy loss against the interest and depreciation on the capital investment.

Answer: B is correct — The most economic load on an underground cable is typically less than the natural load to maintain thermal stability and insulation integrity.

Exam Tip: Always remember that for underground cables, the thermal limit is the primary constraint, unlike overhead lines where stability (SIL) is often the dominant constraint.

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Option A: Greater than the natural load

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Option C: Equal to the natural load

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Option D: None of above

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