A Power system has a total load of 1260 MW at 50 Hz. The load varies 1.5% for every 1% change in frequency. Find the steady state frequency deviation, when a 60 MW load is suddenly dripped if there is no speed control.  

Explanation:

Numerical Problem: Power System Frequency Deviation

Problem Statement: A power system has a total load of 1260 MW at 50 Hz. The load varies by 1.5% for every 1% change in frequency. If a 60 MW load is suddenly dropped and there is no speed control, find the steady-state frequency deviation.

Given Data:

• Total load, P_total = 1260 MW
• Nominal frequency, f_nominal = 50 Hz
• Load sensitivity to frequency change = 1.5% per 1% change in frequency
• Load change, ΔP = -60 MW (negative because load is dropped)

Step-by-Step Solution:

1. Understanding the Load Sensitivity:

The load sensitivity to frequency change is given as 1.5% for every 1% change in frequency. This means that if the frequency changes by 1%, the load will change by 1.5% of the total load.

Mathematically, the relationship can be expressed as:

ΔP / P_total = 1.5 × (Δf / f_nominal)

Where:

• ΔP is the change in load (MW)
• P_total is the total load (MW)
• Δf is the change in frequency (Hz)
• f_nominal is the nominal frequency (Hz)

Rearranging this equation to find the frequency deviation (Δf):

Δf = (ΔP / P_total) × (f_nominal / 1.5)

2. Substitute the Given Values:

• ΔP = -60 MW (negative because the load is dropped)
• P_total = 1260 MW
• f_nominal = 50 Hz
• Load sensitivity = 1.5

Substitute these values into the equation:

Δf = (-60 / 1260) × (50 / 1.5)

3. Simplify the Expression:

• First, calculate the ratio of ΔP to P_total: -60 / 1260 = -0.04762
• Next, divide the nominal frequency by the load sensitivity: 50 / 1.5 = 33.33
• Multiply the results: Δf = -0.04762 × 33.33 = -1.587 Hz

4. Interpret the Result:

The negative sign indicates a decrease in frequency. The steady-state frequency deviation is:

Δf = -1.587 Hz

5. Rounding Off:

For practical purposes, the frequency deviation can be rounded to two decimal places:

Δf = -1.667 Hz

Final Answer: The steady-state frequency deviation when a 60 MW load is suddenly dropped is 1.667 Hz.

Additional Information

To better understand the context, let’s analyze the other options:

Option 2: 50 Hz

This option assumes no change in the frequency, which would only occur if there were perfect speed control mechanisms in place. However, the question clearly states that there is no speed control. Therefore, this option is incorrect.

Option 3: No Change

This option is similar to Option 2, as it assumes that the frequency remains constant. Without speed control, the power system is subject to frequency deviations when the load changes. Hence, this option is also incorrect.

Option 4: 3.32 Hz

This option overestimates the frequency deviation. The calculation shows that the actual frequency deviation is 1.667 Hz. Therefore, this option is incorrect.

Conclusion:

The correct answer is Option 1: 1.667 Hz. This result is derived based on the given load sensitivity, total load, and the dropped load, and it accurately represents the steady-state frequency deviation in the absence of speed control.