The relationship between the steady state change in frequency with respect to change in load is

Question

Examoogle · Accepted Answer

Option B: $\frac{-1}{B + \frac{1}{R}}$

Explanation & Concepts:
In a power system, the steady-state frequency response to a load change is governed by the system damping constant (B) and the governor speed regulation (R). The relationship is derived from the linearized steady-state power balance equation, where the frequency deviation (\Delta f) is determined by the total load change (\Delta P_L) divided by the total system frequency sensitivity (B + 1/R).

Working Principle: When a load change occurs, the governor automatically adjusts the generation to restore balance. The total change in power is balanced by the load frequency sensitivity B (due to motor load variation with frequency) and the speed governing system sensitivity 1/R. The steady-state frequency deviation is expressed as \Delta f = - \frac{\Delta P_L}{B + 1/R}, making the sensitivity factor equal to -1 / (B + 1/R).

Key Formulas: $\Delta f = - \left( \frac{1}{B + \frac{1}{R}} \right) \Delta P_L$ — Steady state frequency deviation equation; $D = B + \frac{1}{R}$ — Total system frequency response characteristic

Key Points: R represents the governor speed regulation or droop characteristic.; B is the frequency-sensitive damping constant of the load.; A larger value of (B + 1/R) results in a smaller frequency deviation for a given load change, indicating a more stable system.; The negative sign denotes that an increase in load leads to a decrease in frequency.

Advantages: Provides inherent stability to the power system frequency.; Allows for automated primary frequency control without manual intervention.

Disadvantages: Steady-state frequency error exists unless secondary control (AGC) is applied.; Sensitivity depends heavily on the droop settings of connected generators.

Applications: Load Frequency Control (LFC) modeling.; Determination of system stability margins during load disturbances.

Additional Info: The parameter B is often referred to as the system damping factor, and 1/R is the governor speed regulation parameter in p.u. MW/Hz.. If the frequency bias B is ignored, the sensitivity reduces to -R.

Answer: B is correct — The steady state sensitivity of frequency change to load change is given by the negative reciprocal of the sum of the load damping and the governor response coefficients.

Exam Tip: Always remember that the denominator is the sum of the damping factors (B + 1/R). If the question asks for frequency deviation per unit load, the answer is the negative of the total sensitivity.

Examoogle · Answer

Option A: $\frac{-B}{B + \frac{1}{R}}$

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Option C: $\frac{-R}{B + \frac{1}{R}}$

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Option D: None of above

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