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7.8 Operation of the Transformer at a Voltage Different from the Rated Voltage

V1↑=4.44·N1·Φ0·f

Now we analyze the case in which the rms value of the voltage supply increases, keeping the frequency constant. Under these conditions, we see a flux increase which leads to an increase in iron losses. These conditions mean that:

V1>V1N

Then, because:

f=cte→Φ0↑→PFe↑

PFe=PF+PH=KF·f²·B_max²+KH·f·B_max (7.38)

Then, we have to keep in mind that if we expose the insulators to a voltage higher than the design voltage, or if we apply a voltage higher than the rated voltage (at the same frequency), the transformer becomes at risk of saturation, with the associated risks we discussed in the previous section. It is worth saying that the transformer is not at risk if we apply a voltage lower than the rated voltage (at the same frequency).

Question: What happens if we apply to the transformer a voltage lower than the nominal voltage (of the same frequency)? In this case the flux is lower, its iron losses are lower, and there is no saturation risk. However, it cannot be used at the maximum power for which it was built.

练习题

A transformer is supplied with a voltage higher than its rated voltage while the frequency remains constant. What is the primary effect on the magnetic flux in the transformer core?

A. The flux decreases proportionally to the voltage increase

B. The flux remains unchanged because frequency is constant

C. The flux increases, leading to higher iron losses

D. The flux becomes zero due to magnetic saturation

When a transformer operates at a voltage lower than its rated voltage (at the same frequency), which statement correctly describes the consequences?

A. The flux increases and there is a risk of saturation

B. The flux decreases, iron losses are lower, but maximum power capability is reduced

C. The flux remains the same but iron losses decrease

D. The transformer can still deliver rated power without any limitations

Which of the following effects occur when a transformer is subjected to a voltage higher than its rated voltage while maintaining constant frequency? Select all that apply.

A. Magnetic flux in the core increases

B. Iron losses increase

C. There is a risk of core saturation

D. The transformer can deliver more than its rated power safely

E. Insulation may be exposed to voltages higher than design values

The iron losses in a transformer core consist of eddy current losses that vary with $f^{2} \cdot B_{ma x}^{2}$ and hysteresis losses that vary with $f \cdot B_{ma x}$ .

A transformer is at risk of saturation when operated at a voltage lower than its rated voltage at the same frequency.

When a transformer operates below its rated voltage at constant frequency, it can still deliver its full rated power output.

According to the transformer voltage equation $V_{1} = 4.44 \cdot N_{1} \cdot Φ_{0} \cdot f$ , when the supply voltage increases while frequency remains constant, the magnetic flux ___ in the core.

When a transformer operates at a voltage lower than rated voltage (at the same frequency), the flux decreases, iron losses decrease, and there is no saturation risk. However, the main disadvantage is that the transformer cannot deliver its maximum ___ power.

Explain why applying a voltage higher than the rated voltage to a transformer (at constant frequency) creates a risk of saturation, while applying a lower voltage does not.

Using the iron loss formula $P_{F e} = K_{F} \cdot f^{2} \cdot B_{ma x}^{2} + K_{H} \cdot f \cdot B_{ma x}$ , explain why iron losses increase when the transformer operates above rated voltage at constant frequency.

According to the transformer voltage equation $V_{1} = 4.44 \cdot N_{1} \cdot Φ_{0} \cdot f$ , what happens to the magnetic flux and iron losses when the supply voltage is increased while keeping the frequency constant?

A. The flux decreases and iron losses decrease

B. The flux increases proportionally and iron losses increase

C. The flux remains constant but iron losses increase

D. The flux increases with the square of voltage and iron losses remain constant

A transformer is designed for rated voltage $V_{N}$ and rated frequency $f_{N}$ . According to the rated conditions and voltage operating limits, which of the following statements are correct?

A. Operating at

V = 1.2 \cdot V_{N}

with

f = f_{N}

risks transformer saturation

B. Operating at

V = 0.8 \cdot V_{N}

with

f = f_{N}

is safe but limits maximum power output

C. Operating at rated voltage and rated frequency allows indefinite operation

D. Operating above rated voltage at rated frequency is safe if the load is reduced

When a transformer operates at a voltage lower than its rated voltage (at the same frequency), the efficiency $η = P_{2} / (P_{2} + P_{F e} + P_{C u})$ always increases because both iron losses and copper losses decrease.

An ideal transformer model assumes the magnetic circuit is unsaturated, but in a real transformer operating above rated voltage at constant frequency, the increased flux may cause ________, which poses operational risks including insulation stress and distorted magnetizing current.

Using the iron losses formula $P_{F e} = K_{F} \cdot f^{2} \cdot B_{ma x}^{2} + K_{H} \cdot f \cdot B_{ma x}$ , explain why both increasing voltage at constant frequency and decreasing frequency at constant voltage lead to increased iron losses.

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7.8 Operation of the Transformer at a Voltage Different from the Rated Voltage