Why three-phase electric power is awesome

## The Unofficial ELEC3105 Final Exam Formula Sheet Edit

### Magnetic Circuits Edit

Ampere's Law

Magnetising current

Magnetising inductance

### AC Power Computation Edit

#### Single Phase Edit

Real power

Reactive power (in VAR)

Complex power

Apparent power

#### Three Phase Edit

where and are line-to-line voltage and current for delta-connected loads, and and are phase voltage and current for star-connected loads.

### Transformers Edit

Referring to primary side:

Efficiency

% Voltage regulation =

### Electromechanical Energy Conversion Edit

In a rotary system:

where:

= current

= inductance

= angle of displacement

### DC Machines Edit

where = (area of coil) x B x (number of coils)

where = (area of coil) x B x (number of coils)

The mechanical power used by the load is

and the power delivered to the load is

The total loop equation for the armature is

and the equation for the field coil is simply .

### Induction Machines Edit

Thevenin equivalent circuit:

but that is pretty bad, try and

Slip for maximum produced torque:

#### Power Edit

(Input power) - (Stator copper loss) = (Air gap power)

(Air gap power) - (Rotor copper loss) = (Developed mechanical power)

(Dev. mechanical power) - (Windage and friction losses) = (Output Power)

(Windage and friction losses) =

### Synchronous Machines Edit

As with induction machines,

The synchronous impedance is calculated from the open circuit test voltage and short-circuit test current: .

Often, so .

The important power equation is:

where is the load angle.

### Power Electronics Edit

For buck converter:

where D is the duty cycle.

For boost converter: