# H63EMA Electrical Machine

University of Nottingham H63EMA Electrical Machine Note

## Electromagnatic Basics

$$B = \mu H$$

$$MMF = H l$$

$$R = \frac{l}{\mu \cdot S}$$

Energy Stored , $$W_f = \frac{B^2 \cdot volume}{2 \mu_0 }$$

Force by Virtual Displacement, $$F = \frac{B^2 \cdot A}{2 \mu_0 } \quad [N]$$

Force on conductor, $$F = B \cdot i \cdot L \quad [N]$$

EMF by Faraday’s law, $$e = B \cdot l \cdot u \quad [V]$$

Losses:

• Core loss is made up of hysteresis and eddy current loss.
• Hysteresis loss is proportional to the frequency while eddy current losses are proportional to the frequency squared
• They both vary approximately in a quadratic fashion with B.
• Losses can be reduced by using a high resistivity core material
• A laminated core also increases the effective resistance to eddy currents.
• Materials with narrower hysteresis loops will reduce hysteresis losses.

## Electrical Machine

Torque = k * Electrical Loading * magnetic loading * Volume , $$T = 2 \cdot V \cdot B \cdot A$$

Electrical loading , $$A = \frac{N \cdot Z \cdot I_{rms} }{2 \pi R} \quad [A/m]$$

Lap winding: No. of parallel path = No. of poles

Wave winding: No. of parallel path = 2

Power: $$P = E_a \times I_a = T \times \omega$$

Increase Torque per volume.

• The current loading might be increased provided that suitable cooling is possible.
• Or B may be increased by using higher grade magnetic material with higher saturation flux density.

## DC Machine

$$V_a = R_a i_a + 2V_{brush} + E_a$$

### Winding connection

problem with shunt connection

• Particular problem in shunt-connected motors
• Assume the machine is operating from a fixed DC voltage source
• Reducing field flux causes speed increase
• Speed increase causes an increase in the mechanical load power
• This requires more armature current
• Hence further reduction in field flux!

Permanent Magnet DC motor

• Better performance and power density due to the fact that they do not have an associated magnetising current as with IM. This improves PF.
• Losses are consequently also lower improving efficiency and allowing for a smaller machine.
• Magnet temperature limits
• Demagnetisation
• more expensive

Interpoles

The interpoles aid current commutation. The flux generated by these poles, situated on the q-axis of the machine neutralises the q-axis armature winding flux linking the coils undergoing commutation in the armature circuit and furthermore generate surplus flux to induce an emf which aids commutation.

## Induction Machine

• A relatively cheap, robust and reliable machine in its squirrel cage
version.
• It does not need a commutator and hence has a simpler structure
• It is able to produce a high torque to volume ratio and requires little maintenance

Slip:

$$\frac{\omega_s – \omega_r}{\omega_s}$$

Stall: s = 1, sync speed: s= 0

Simple Equivalent Circuit:

Power

Developed power = $$3 \cdot I_r ^2 \cdot \frac{R_r (1-s) }{s}$$

Torque = $$P_{dev} \cdot \frac{p}{\omega_e}$$

Locked Rotor Test:

On-line vs Converter

• Induction motors can be operated directly on-line without the need of any power electronics for most industrial applications
• Though this is a very cheap way of operating an IM, the transient response is very poor, generally characterised by high currents and low torque, when compared to rated values.
• However, high performance operation is also possible if supplied by a power electronic converter and controlled using vector controlled algorithms where the machine dynamics are controlled in a similar way to a separately excited dc
machines

Starting Torque

For a wound rotor machine the rotor resistance can be varied through an external variable resistance. A high resistance at start up would ensure a high starting torque while a low resistance at rated speed keeps the rotor copper losses down. For a squirrel cage IM a similar effect can be achieved by using a deep bar or double cage. Skin effect due to the high frequency rotor currents at start up increase the effective rotor resistance and hence improve starting torque.

When operating from a variable voltage variable frequency source a high torque at start up can be achieved by increasing the supply frequency up to rated frequency, keeping V/f constant.

Double cage rotor

• One at the top of the rotor slot with a high resistance
• The other at the bottom of the slot with a lot of slot leakage reactance
• At high rotor current frequency, (low speed) most current will go through the outer cage due to its lower impedance. This gives a high rotor resistance and a low leakage.
• At low rotor current frequency (high speed) current is distributed evenly in the slot and thus the rotor resistance is lower and leakage inductance higher.

## Synchronous Machine

Saliency

• A salient rotor has a short air gap section for each pole round which the field winding is wound
• When the stator peak mmf is aligned with the D-axis the inductance is greatest.
• The synchronous reactance is then Xsd
• When the peak stator mmf is aligned with the Q-axis the stator inductance is a minimum.
• The synchronous reactance is then Xsq
• The output torque is made up of two components. One is the electromagnetic torque due to the excitation and the other is a reluctance torque do to the rotor saliency

Synchronous Machine vs Induction Machine

• In both machines, torque is produced based on the interaction of a current distribution and an air-gap field distribution synchronously rotating and ideally in phase with each other.
• In synchronous machines the field is supplied via slip rings and is DC.
• Rather than induced through transformer effect from the stator windings as is the case in IM.
• Thus SM operates only at synchronous speed whilst IM produce zero Torque at synchronous speed.