VA Ratings
Volt-ampere (VA) is a measurement of power in a direct current electrical circuit.
Th e VA specifi cation is also used in alternating current circuits, but is less precise in this application, because it represents apparent power, which oft en diff ers from true power. In a DC circuit, 1 VA is the equivalent of one watt (1 W). Th e power, P (in watts) in a DC circuit is equal to the product of the voltage V (in volts) and the current I (in amperes):
P = VI
In an AC circuit, power and VA mean the same thing only when there is no
reactance. Reactance is introduced when a circuit contains an inductor or capacitor.
Because most AC circuits contain reactance, the VA fi gure is greater than the actual dissipated or delivered power in watts. Th is can cause confusion in specifi cations for power supplies. For example, a supply might be rated at 600 VA. Th is does not mean it can deliver 600 watts, unless the equipment is reactance-free. In real life, the true wattage rating of a power supply is 1/2 to 2/3 of the VA rating.
A transformer is not considered a load, therefore the power rating allocated to a transformer is called apparent power (Papp) and is measured in kVA (kilo-volt-ampere).
Th e apparent power is the vector sum of real and reactive power. Th e apparent power is the magnitude of the complex power.
Real power (Pact)
Figure 4.20: Power relationship in transformers Summary on power
• Power dissipated by a load is referred to as true power. True power (Pact
)
is symbolised by the letter P and is measured in the unit of watts (W or kW).• Power merely absorbed and returned in load due to its reactive properties is referred to as reactive power. Reactive power (Preac
)
is symbolised by the letter Q and is measured in the unit of Volt-Amps-Reactive (VAr or kVAr).• Total power in an AC circuit, both dissipated and absorbed/returned is referred to as apparent power. Apparent power (Papp
)
is symbolised by the letter S and is measured in the unit of Volt-Amps (VA or kVA).• Th ese three types of power are trigonometrically related to one another. In a right triangle, P = adjacent length, Q = opposite length, and S = hypotenuse length.
Power factor
Th e ratio between real power and apparent power in a circuit is called the power factor. It is a practical measure of the effi ciency of a power distribution system. For two systems transmitting the same amount of real power, the system with the lower power factor will have higher circulating currents due to energy that returns to the source from energy storage in the load. Th ese higher currents produce higher losses and reduce overall transmission effi ciency. A lower power factor circuit will have a higher apparent power and higher losses for the same amount of real power.
Pact
Preac Papp
Preac
Th e power factor is normally a number between 0 and 1. Th is is just a dimensionless number. A high power factor is generally desirable in a transmission system to reduce transmission losses and improve voltage regulation at the load. It is oft en desirable to adjust the power factor of a system to near 1. Th e power factor is normally represented by the following formula:
cos θ = Pact ____
Papp Example
An inductive load works at a power factor of 0.6 lagging. Th e load draws a current of 12 amperes from a transformer with output voltage of 500 volt. Calculate:
a) the rating of the transformer.
b) the power consumed by the load.
c) the reactive power.
1. Th e turns ratio of a single-phase transformer is 75:3. Calculate the
secondary voltage when the transformer is connected to 220 V AC supply.
2. A single-phase step-down transformer is rated at 100 kVA and has a turn ratio of 10:1. Neglect losses and calculate:
2.1 secondary voltage if the primary voltage is 2 600 V.
2.2 secondary current is primary current is 30 A.
3. A 11 kV /220 V single-phase step-down transformer has 3 000 primary turns.
Neglect losses and calculate:
3.1 the transformer ratio.
3.2 number of secondary turns.
3.3 the primary current if the secondary of the transformer
draws 1 500 amperes.
4. How are eddy currents limited in transformers?
5. Name 4 types of cores used in transformers.
6. Draw a neatly labelled diagram of a single-phase transformer connected to Remember
cos θ = 0,6 Never substitute cos 0,6 into the formula.
7. Defi ne induction.
8. Describe mutual induction with reference to transformers.
9. Why are transformers not 100% effi cient?
10. Name four types of losses associated with transformers.
11. Name three types of transformers and an application for each one.
12. Calculate the voltage output by the secondary winding of a transformer if the primary voltage is 35 volts, the secondary winding has 4 500 turns, and the primary winding has 355 turns.
Vsecondary =
13. Calculate the load current and load voltage in this transformer circuit:
Iload = Vload =
14. Calculate the number of turns needed in the secondary winding of a
transformer to transform a primary voltage of 300 volts down to a secondary voltage of 180 volts, if the primary winding has 1 150 turns of wire.
Nsecondary =
15. Predict how all component voltages and currents in this circuit will be aff ected as a result of the following faults. Consider each fault
independently (i.e. one at a time, no multiple faults):
• Transformer T1 primary winding fails because of an open circuit.
• Transformer T1 primary winding fails because of a short circuit.
• Transformer T1 secondary winding fails because of an open circuit.
• Load fails shorted because of a short circuit.
For each of these conditions, explain why the resulting eff ects will occur.
16. Suppose 1 200 turns of copper wire are wrapped around one portion of an iron hoop, and 3 000 turns of wire are wrapped around another portion of that same hoop. If the 1 200-turn coil is energized with 15 volts AC (RMS), how much voltage will appear between the ends of the 3 000-turn coil?
17. Calculate the voltage output by the secondary winding of a transformer if the primary voltage is 230 volts, the secondary winding has 290 turns, and the primary winding has 1 120 turns.
Vsecondary =
Fuse T1
V1 Load
18. Calculate the source current and load current in this transformer circuit:
Isource = Iload =