Energy conversion and the two rules behind every machine
Every electrical machine works because of two facts you already know:
- A moving magnet (or a moving coil) makes a voltage in a coil. This is electromagnetic induction. It is how a generator works.
- A current in a magnetic field feels a force. This is how a motor works.
A stator is the part that stays still. A rotor is the part that turns. The gap between them is small, so the magnetic field passes easily. Generators and motors are very similar; the same machine can often do both jobs.
Synchronous machines
In a synchronous machine the rotor is a magnet (a permanent magnet or an electromagnet fed by DC). It turns at exactly the speed of the rotating magnetic field of the supply. That speed is the synchronous speed:
Ns = 120 × f / P (rpm), where f is frequency in hertz and P is the number of poles.
As a generator (alternator), a turbine or engine spins the magnet and the stator coils give AC with frequency f = P × N / 120. Power stations and ship generators are synchronous machines. As a motor it runs at constant speed whatever the load, so it is used in clocks and in big, steady drives. It is not self-starting; it needs help to reach speed first.
Induction machines
The induction motor is the most used motor in the world. The stator has coils fed by three-phase AC. These coils switch on one after another and make a rotating magnetic field. The field cuts the rotor bars and induces current in them. That current feels a force in the field, so the rotor turns the same way as the field.
The rotor can never catch the field. If it did, no bars would be cut and there would be no force. So the rotor runs slower than synchronous speed. The difference is the slip:
s = (Ns − N) / Ns (often written as a percentage; 2 to 6 % at full load).
Why it is popular: no brushes, no DC supply, strong, cheap and self-starting. Single-phase induction motors power fans and pumps at home; three-phase ones power factory machines and ship pumps.
DC machines
A DC machine has a stator that makes a steady magnetic field (field magnets or field coils) and a rotor called the armature. A commutator (a split ring) and brushes (carbon blocks) feed current into the armature. Every half turn the commutator reverses the current in the coil, so the force always pushes the same way and the armature keeps turning.
- DC motor: speed rises with the voltage. It is easy to control, so it is used in cranes, trains, lifts and toys.
- DC generator: the commutator turns the coil's alternating voltage into DC output.
Disadvantage: brushes wear out and spark, so they need maintenance.
Transformers
A transformer changes AC voltage with no moving parts. It has two coils, the primary (input) and the secondary (output), wound on one laminated iron core. The changing current in the primary makes a changing magnetic field in the core, which induces voltage in the secondary.
Vs / Vp = Ns / Np. More turns on the secondary: higher voltage (step-up). Fewer turns: lower voltage (step-down). A good transformer wastes little, so power in is almost power out: Vp × Ip ≈ Vs × Is. When voltage goes up, current goes down.
Uses: power stations step voltage up for transmission, because low current means low loss in the lines. Substations and ships step it down for factories and rooms. A transformer works only on AC, never on steady DC. Transformers need cooling; big ones sit in oil.
Emergency power supplies
Hospitals, ships, lifts and factories need light and power even when the main supply fails. An emergency (standby) power supply has two layers:
- Battery bank and UPS (uninterruptible power supply): a battery with an inverter that turns DC back into AC. It switches over in a fraction of a second, but can run the load only for minutes or hours.
- Engine generator: a diesel engine drives a synchronous generator. It needs several seconds to start, then can run for many hours while there is fuel.
An automatic changeover switch senses mains failure, starts the engine, and joins the generator to the load when it is ready. It also stops the generator from feeding power back into the dead mains. Emergency batteries must be charged and tested regularly. The generator must be run on test every week or month.
Try it: see the ratio yourself
In the 3D transformer, the primary has 15 turns and 230 V. Predict the output voltage when the secondary has 30 turns, then move the slider and check. Next, set the secondary to 5 turns: is it step-up or step-down? In the induction motor, move the slider and watch the rotor fall behind the field. At home, look at your phone charger: the label shows the input (230 V AC) and the output (like 5 V DC). A transformer inside gives the lower voltage.
Key formulas and definitions
- Synchronous speed Ns = 120 × f / P (rpm)
- Generator frequency f = P × N / 120 (Hz)
- Slip s = (Ns − N) / Ns; rotor speed N = Ns × (1 − s)
- Transformer: Vs / Vp = Ns / Np
- Ideal transformer power: Vp × Ip = Vs × Is
- Battery run time ≈ (battery voltage × amp-hours) / load power in watts
Worked examples
1. Find the synchronous speed of a 4-pole motor on a 50 Hz supply.
Ns = 120 × 50 / 4 = 1500 rpm.
2. A 6-pole generator is turned at 1000 rpm. What is the frequency?
f = P N / 120 = 6 × 1000 / 120 = 50 Hz.
3. A 4-pole, 50 Hz induction motor runs at 1440 rpm. Find the slip.
Ns = 1500 rpm. s = (1500 − 1440) / 1500 = 60 / 1500 = 0.04, so slip = 4 %.
4. A transformer has 1000 primary turns and 100 secondary turns. The primary is on 230 V. What is the secondary voltage?
Vs = Vp × Ns / Np = 230 × 100 / 1000 = 23 V (step-down).
5. A transformer steps 11000 V down to 440 V. The secondary has 100 turns. How many primary turns?
Np = Ns × Vp / Vs = 100 × 11000 / 440 = 2500 turns.
6. An ideal transformer gives 8 A at 110 V. The primary voltage is 440 V. Find the primary current.
Vp Ip = Vs Is, so Ip = 110 × 8 / 440 = 2 A.
7. A 12 V, 100 Ah battery runs a 500 W emergency load through an ideal inverter. For about how long?
Energy = 12 × 100 = 1200 Wh. Time = 1200 / 500 = 2.4 hours (real batteries give less, so test it).
Common mistakes
- Thinking an induction motor runs at synchronous speed. It always runs a little slower, because without slip no current is induced in the rotor.
- Using a transformer on a DC battery. Only a changing current makes a changing field, so DC gives no output (and can burn the primary).
- Mixing up step-up and step-down. Look at the secondary turns: more than the primary is step-up, fewer is step-down.
- Forgetting that current goes the other way: a step-up transformer raises voltage but lowers current.