Question

A 3-\(\phi\), 50 Hz synchronous motor is to be operated at constant flux by frequency control. If frequency is decreased by 4% of rated frequency at the same flux, then the voltage should be

• A. \( \text{Decreased by 4%} \)
• B. \( \text{Increased by 4%} \)
• C. \( \text{Decreased by 16%} \)
• D. \( \text{Constant} \)

Hint:

Constant flux operation means a direct linear relationship between voltage and frequency (\(V \propto f\)). Because it is a direct linear relationship, any percentage change applied to the frequency requires an identical percentage change in the voltage. - Frequency drops by 4% \(\rightarrow\) Voltage drops by 4%. No complex formulas needed!

Answer 1

The Correct Option is A

Concept: The internal air-gap magnetic flux ($\phi$) developed inside an AC electrical machine (such as a synchronous or induction motor) depends on the ratio of the applied stator voltage ($V$) to the operating frequency ($f$). This relationship is derived directly from the induced electromotive force (EMF) equation: \[ V \approx E = 4.44 \, f \, N \, \phi \, K_w \quad \Rightarrow \quad \phi \propto \frac{V}{f} \] To prevent core saturation and maintain optimum torque capacity, the internal magnetic flux must be held constant. This requires keeping the $V/f$ ratio constant: \[ \frac{V}{f} = \text{Constant} \]

Step 1: Expressing the constant flux condition using ratios.
Let the initial operating voltage and frequency parameters be $V_1$ and $f_1$. Let the new parameter values following the adjustment be $V_2$ and $f_2$. Since the flux remains unchanged, we can equate their ratios: \[ \frac{V_1}{f_1} = \frac{V_2}{f_2} \quad \Rightarrow \quad \frac{V_2}{V_1} = \frac{f_2}{f_1} \quad \cdots (1) \]

Step 2: Modeling the change in frequency.
The problem states that the operating frequency is decreased by 4% of its rated value. We can write this mathematically as: \[ f_2 = f_1 - 0.04f_1 = 0.96f_1 \] Therefore, the frequency ratio is: \[ \frac{f_2}{f_1} = 0.96 \]

Step 3: Calculating the corresponding change in voltage.
Substitute this frequency ratio back into Equation (1): \[ \frac{V_2}{V_1} = 0.96 \quad \Rightarrow \quad V_2 = 0.96V_1 \] Let's find the percentage change in voltage: \[ % \text{ Change in Voltage} = \frac{V_2 - V_1}{V_1} \times 100% = \frac{0.96V_1 - V_1}{V_1} \times 100% \] \[ % \text{ Change in Voltage} = -0.04 \times 100% = -4% \] The negative sign confirms that the voltage must decrease. Therefore, to maintain a balanced, constant magnetic flux link, the voltage must be decreased by exactly 4%. Hence, the correct choice is option (1).