The expression of critical receiving end voltage is

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\frac{E}{2 \cos (δ_{c r i})}

Explanation: The critical receiving end voltage is defined in the context of power system stability, specifically relating to the power-angle characteristic curve of a synchronous machine or transmission line. It represents the point where the power transfer limit is dictated by the voltage profile at the receiving end relative to the sending end excitation. Working Principle: In a simple two-bus system, the power transfer is governed by the relation $P = \frac{E V}{X} \sin(\delta)$. The stability limit often involves the relationship between the sending end voltage $E$, receiving end voltage $V$, and the power angle $\delta$. When considering the steady-state stability limit conditions where the receiving end voltage is critical for maintaining synchronization, it is derived that $V_{cri} = \frac{E}{2\cos(\delta_{cri})}$. Key Formulas: $V_{cri} = \frac{E}{2\cos(\delta_{cri})}$ — Formula for critical receiving end voltage; $P = \frac{EV}{X}\sin(\delta)$ — Power-angle equation of a transmission line Key Points: This relation is derived from the steady-state stability limit analysis.; It assumes a lossless line represented by its reactance $X$.; The term $\delta_{cri}$ refers to the critical power angle at the limit of stability. Advantages: Provides a direct estimation of voltage stability limits.; Helps in designing reactive power compensation schemes. Disadvantages: Assumes a simplified model ignoring line resistance.; Only applicable for steady-state stability analysis. Applications: Power system load flow studies.; Determination of static voltage stability margins. Additional Info: Option A: Incorrect, introduces a factor of 2 in the numerator.. Option B: Incorrect, represents a different limit condition.. Option D: Incorrect, mathematically inconsistent with power system stability equations. Answer: C is correct — The critical receiving end voltage is mathematically expressed as $\frac{E}{2\cos(\delta_{cri})}$. Exam Tip: Always verify if the system model assumes a lossless line ($R=0$) before applying these simplified stability formulas, as inclusion of resistance significantly alters the voltage-angle relationship.

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