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 = \(P_{dev} \cdot \frac{p}{\omega_e} \)

**No-Load Test:**

**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.