The change in reactive power Q produces large effect on receiving end voltage because

Question

Examoogle · Accepted Answer

The voltage drop associated with this change is in phase with reference voltage

Explanation: In electrical power systems, the voltage drop across an inductive transmission line is primarily caused by reactive power flow. Because the line resistance $R$ is typically much smaller than the reactance $X$ ($X >> R$), the voltage drop component resulting from reactive power flow aligns almost perfectly in phase with the sending and receiving end voltages.

Working Principle: The approximate voltage drop $\Delta V$ in a transmission line is given by $\Delta V \approx I_R R + I_X X$. Since $I_X$ (reactive current) carries the bulk of reactive power $Q$, and the phase shift between the receiving end voltage and the voltage drop component due to $X$ is small, this drop contributes directly to the magnitude of the receiving end voltage. Consequently, variations in $Q$ lead to significant fluctuations in the terminal voltage magnitude.

Key Formulas: $\Delta V \approx \frac{RP + XQ}{V_R}$ — Approximate voltage drop in a transmission line; $Q = VI \sin(\phi)$ — Definition of reactive power

Key Points: Transmission lines are highly inductive ($X >> R$).; Reactive power $Q$ flow directly impacts the voltage magnitude $V_R$.; Active power $P$ flow primarily impacts the phase angle $\delta$ between voltages.; Voltage stability is maintained by compensating reactive power using capacitors or reactors.

Advantages: Improved voltage regulation; Enhanced power transfer capability

Disadvantages: Requires reactive power compensation equipment (SVC, STATCOM); Increased system complexity

Applications: Grid voltage control; Transmission line stability enhancement

Additional Info: The component of the voltage drop due to $Q$ is proportional to $IX$, which is nearly in phase with the reference voltage vector in high-voltage lines.. Option B is incorrect because a quadrature component of the voltage drop would primarily affect the power angle $\delta$ rather than the voltage magnitude $V$.

Answer: A is correct — The voltage drop produced by reactive power flow in an inductive transmission line acts directly on the magnitude of the receiving end voltage due to the phase alignment of the reactive voltage drop component.

Exam Tip: Always remember the rule of thumb: Active power $P$ controls the load angle $\delta$, while reactive power $Q$ controls the voltage magnitude $V$.

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