Topic 4 PrinciplesMachines

8/17/2019 Topic 4 PrinciplesMachines

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Jan-May 2010 Electrical Machines & Drives - ECNG 3010 2 -

Basic Principles of ElectromechanicalEnergy Conversion

Electric Drive

Electrical

System

Electrical

Machine

Mechanical

System

Motoring Mode

Braking (Generating)Mode

Pelec Pmech

Pelec Pmech

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Magnetic Field

! Magnetic field produced by a current carrying conductor

! Ampere’s Law

!" H dl =Closed path

i

dl

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Flux Density

BsatBm

!0

!0

!m

HmHm

Bm

" Units : Weber/meter2 (Wb/m2)) or Tesla (T)

" In air B = !oH , !o = 4" x 107 Wb/A/m

" Ferro-magnetic materials (higher permeability)

# Linear approximation Bm = !mHm# Bsat~ 1.6 – 1.8 Tesla

# In saturation !m approaches !0

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Flux, Flux Linkage & MMF

! Flux !m (Wb)

(assuming uniform flux density)

!m = Bm A m

Bm= !mHm and Hm = Ni / l m

!m

= Ni

l m"mAm

= F

R

Am

!m

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Flux, Flux Linkage, and MMF

! Reluctance

! FluxLinkage

! MMF

" m = N !m

F = N i

m

=l m

"mAmR

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Analogy between Electric and MagneticCircuits

Electric Circuit Unit Magnetic Circuit Unit

Driving Force emf (V) V mmf (F) At

Response current (I) A flux (!) Wb

Impedance resistance (R) " reluctance ( R ) 1/H

Equivalentcircuit

Field intensityrelationship

# E . dl = V V # H . dl = I A

Potentialdifference

V = IR V At

V R +

_ I

V = IR

F+

_ !

F = !

F = !

R

R

R

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Inductance

! For linear magnetic conditions inductance depends only on magnetic circuit

Energy stored in

magnetic circuits

Energy density

"m = Lmi

i A m

!mN

!m

Lm=i

= N

l m

"mAm N# m

=

N2

l m "mAm

= N2

R

N2

l m

"mAm

Lm=

i Hm Bm !m ! m N l rx x (!m) x (A m) x (N)

volume

w = W = 1 B2m

volume 2"m

W= (1/2) L i2 = 1 B2 A ml m

2"m

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Rotating Machine

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Rotating Machine

Stator

Rotor

Air Gap

Two sets of windings: stator and rotor… why?

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Rotating Machine

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Basic Principles of Operation

! Force on a current carrying conductor subjected toan externally-established magnetic field (extensionof Lorentz law – motor equation)

$ f em = il xB

! emf induced in a conductor moving in a magnetic

field ( extension of Faraday law)$ e = B l u

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Electromagnetic Force

! Force Direction – Higher concentration field to lower.

External B field

f em f em

subtract add

f em

resultant

B

il

f em = B l i

[Nm] [Wb/m2] [m] [A]

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Electromagnetic Force

Torque produced by forcescaused by interaction ofcurrent-carrying conductors

and magnetic fields

ferromagnetic pieces

Principle of Alignment

Magnetic flux

lines

F

F

Principle of interaction

F F

F

F

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! Force on positive charges

f q = q ( u x B )

In this example a net positive chargeaccumulates at the top and a net

negative charge accumulates at thebottom (Lorentz force)

! Magnitude of induced emf

e = B l u

[V] [Wb/m2] [m] [m/s]

Polarity of induced emf is given by f q

and is independent of current flowingthrough the conductor.

Induced EMF

f q-

f q+

+

_

B

(into paper)

f q+

u

B

(into paper)

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Rotating Electrical Machine:Two windings

! One winding: producesmain magnetic field (couldbe replaced by magnets).

! Next winding: produces thetorque due to the “motorequation”. Carries thecurrent associated withtorque.

! Additional issues: inducedvoltages, more than onemagnetic field.

F

F

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Production of Magnetic Field

! Radial field (H,F,B) in the air gap

H positive if away from center

Rotorsurface

Nsis#02l g

-$/2 0 $ 2$

Statorsurface B s(t)

+ Nsis#

02l g

!

Magnetic

axis

!

" = $

r

is(t)

is(t) N s

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Application of Basic Principles

Assumptions

Uniform B s , radial in direction

- Rotor current of constant magnitudebut polarity changes with position

-

Counter- clockwise torque ispositive

Force acting on conductor

f em = B s (N r I) l

and torque on coil

T em = 2 f emr = 2 B s (N r I) l r

Emf induced in coil

er =2 econd = 2 N r B s l r"m r

i r

I

- I

er E

- E

0

0

0

1800

3600

T em

%

%

%

Magnetic

axisElectricalsystem

!

&m

Tem

+ _ er ir

stator

MotoringMode

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Topic 4 PrinciplesMachines