Question

Question:How would the value of H change if a generator’s assumed operating frequency is changed from 60-HZ to 55 HZ?

Short answer

Answer

The value of normalised inertia constant at 50-HZ frequency, H₅₀ will be${\text{H}}_{\text{60}}{\left(\frac{5}{6}\right)}^2\text{perunit}-\text{seconds}$ .

Step-by-step solution

Write the given data from the question.

Consider the operating frequency is changed from 60HZ to 55 HZ.

Step 2: Determine the formula of Normalised inertia constant and Angular velocity of rotor is related to frequency.

Write the formula of Normalised Inertia constant.

$\mathbf{H}=\frac{\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{J\omega }}_{\mathbf{msyn}}^{\mathbf{2}}}{{\mathbf{S}}_{\mathbf{rated}}}$ …… (1)

Here, J is moment of inertia, ${\mathbf{S}}_{\mathbf{rated}}$ is Volt-ampere rating of generator and ${\omega }_{\mathbf{msyn}}$ is angular velocity of rotor.

Write the formula of Angular velocity of rotor is related to frequency.

${\omega }_{\mathbf{msyn}}=\left(\frac{\mathbf{2}}{\mathbf{P}}\right)\left(\mathbf{2}\pi \mathbf{f}\right)\frac{\mathbf{rad}}{\mathbf{s}}$${\omega }_{\mathbf{msyn}}=\left(\frac{\mathbf{2}}{\mathbf{P}}\right)\left(\mathbf{2}\pi \mathbf{f}\right)\frac{\mathbf{rad}}{\mathbf{s}}$ …… (2)

Here, f is supply frequency and p is number of poles.

Determine the value of Normalised inertia constant and Angular velocity of rotor is related to frequency.

We may conclude that the normalized inertia constant is proportional to the frequency square from the two equations above.

$$\begin{gathered} H_{50}=H_{60}\left(\frac{{50}^2}{{60}^2}\right) \\ =H_{60}{\left(\frac{5}{6}\right)}^2\text{per}\text{unit}-\text{seconds} \end{gathered}$$

Here, H₅₀ is normalised inertia constant at frequency, H₆₀ is normalised inertia constant at frequency.

Therefore, the value of normalised inertia constant at 50 HZ frequency, H₅₀ will be${\text{H}}_{\text{60}}{\left(\frac{5}{6}\right)}^2\text{per}\text{unit}-\text{seconds}$ .