In load frequency control the area control error is negative if: 

Explanation:

Load Frequency Control and Area Control Error (ACE):

Definition: In power systems, Load Frequency Control (LFC) is a mechanism used to maintain the frequency of the power grid within permissible limits and to manage the power exchange between interconnected areas. The Area Control Error (ACE) is a measure used in LFC to determine the deviation in frequency and the net power flow from a specific control area compared to a scheduled value.

Concept of Area Control Error (ACE):

The ACE is mathematically defined as:

ACE = ΔP + βΔf

• ΔP: The deviation of net power flow from the scheduled value. It represents the mismatch between the actual and scheduled power exchange with neighboring areas.
• β: The frequency bias coefficient, which is a system-specific parameter used to relate frequency deviation to power imbalance.
• Δf: The frequency deviation from the nominal frequency.

The ACE can be positive or negative, depending on the direction and magnitude of the deviations. A negative ACE indicates that corrective action is required to restore the system balance by increasing generation or reducing load.

Correct Option Analysis:

The correct option is:

Option 2: Net power flow out of an area is low.

This option correctly explains the scenario where the ACE becomes negative. When the net power flow out of an area is lower than the scheduled value (ΔP is negative), it implies that the area is not exporting as much power as required, or it may even be importing power. If the frequency bias coefficient (β) and the frequency deviation (Δf) are also considered, the overall ACE can be negative, indicating a need for corrective measures like increasing generation within the area or reducing its demand to maintain system stability.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: Frequency has increased.

While an increase in frequency (Δf > 0) could potentially contribute to a negative ACE (depending on the β value and the net power flow deviation ΔP), this alone does not necessarily imply that the ACE is negative. The net power flow out of the area (ΔP) must also be considered to determine the ACE. Hence, this option is incomplete and not the most accurate explanation.

Option 3: Net power flow out of an area is high.

If the net power flow out of an area (ΔP) is higher than the scheduled value (i.e., positive ΔP), it would contribute to a positive ACE rather than a negative one. This scenario indicates that the area is exporting more power than required, which is contrary to the condition needed for a negative ACE. Therefore, this option is incorrect.

Option 4: Net power flow out of an area is zero.

If the net power flow out of an area is zero (ΔP = 0), the ACE would depend solely on the frequency deviation (Δf) and the frequency bias coefficient (β). A zero net power flow does not inherently cause a negative ACE unless the frequency deviation is sufficiently negative. However, this option does not directly explain the condition for a negative ACE, making it incorrect.

Conclusion:

Load Frequency Control (LFC) and Area Control Error (ACE) are critical concepts in maintaining the stability and reliability of power systems. The correct understanding of ACE and its components is essential for effective system operation. In this case, the negative ACE is correctly explained by option 2, as it directly relates to the scenario where the net power flow out of an area is lower than the scheduled value. This condition highlights the need for corrective actions to restore the balance and ensure stable system operation.