Permanent Magnet Alternator theory session for ITDG windpower course

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Permanent Magnet Alternator theory session for
ITDG windpower course Hugh Piggott HAMBANTOTA
DECEMBER 2003 Properties of electric and magnetic
circuits Permanent magnet alternator
configurations Connection of coils and
rectifiers Design calculations
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Electrical circuit
EMF E is the internal voltage source driving
the circuit
POWER (WATTS) PIV OHMS LAW IV/ R also RV/ I
and V IR RESISTANCES R1 IS INTERNAL
RESISTANCE, R2 IS LOAD RESISTANCE CURRENT I
E/R E/(R1 R2) So VOLTAGE V I/R2 ER2
/(RI R2) EFFICIENCY POWER OUT /POWER IN
VI/EI V/E R2 /(RI R2)
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Magnetic circuit

ELECTRICAL TERMS Voltage Current Resistance
MAGNETIC TERMS Magnetomotive force Fm Flux
F Reluctance Rm
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Advantages of permanent magnets over wound field
coils

• No need to supply current to the magnet rotor
• Better efficiency at low power
• No problems with brushes and sliprings
• Cheaper to manufacture
• Permanent magnet materials are constantly
  improving
• NdFeB neodymium magnets are more and more
  powerful
• Also cheaper as royalty agreements expire

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Magnet material specifications

• Remanence Br is flux density in a short
  circuit.
• Coercivity Hc is Field Strength in an open
  circuit (with no flux). Similar to EMF.
• Maximum Energy Product BHmax is the point on the
  curve where you get the most effective use of the
  magnet.
• Similar to R1 R2 in the electrical circuit.
• Flux density at BHmax (about half of Br ).
• Field strength at Bhmax (about half of Hc).

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Magnet data from the web site of Magna in
Tokyo www.magna-tokyo.com (This is typical of
data available on many similar web sites.)
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Sample demagnetisation curves
The NdFeB material (neodymium) has the highest
field strength H and highest flux density B. The
energy product (B x H) reaches a maximum at the
mid point of the line. The energy product
depends on the reluctance of the magnetic
circuit. In cases where the air gap area matches
the magnet face area, it happens that BHmax
coincides with the circuit reluctance where air
gap length is the same as magnet length. This
applies to both neodymium and ferrite
materials. Alnico has much lower field strength,
and so this rule does not apply.
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Simple alternator
EMF (volts) induced in a loop of wire E
-dF/dt If F is the flux in the magnetic circuit,
and N is the rpm, then dF/dt 2 FN /60 FN
/30 Hence the average EMF is FN /30
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• Voltage depends on rate of flux cutting wires
• Amount of flux
• Rate of rotation (rpm)
• Number of turns per coil

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TWO EXAMPLES OF POSSIBLE ALTERNATOR CONFIGURATIONS
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A TYPICAL PERMANENT MAGNET ALTERNATOR
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Axial Flux alternator
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Axial Flux alternator
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5-phase Version of Axial Flux alternator
This alternator has ten coils The magnets pass
the coils at different times The output has 5
phases
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An induction motor body can be adapted to make an
alternator
This is the commonest mass-produced electrical
machine on earth. Magnets can be fitted to the
rotor, and the stator can be rewound.
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Toroidally wound axial alternator
Another possible configuration North magnet pole
faces north magnet pole on the two rotors. The
stator core is made from a strip of suitable
low-silicon grade steel wound into a laminated
core Coils are wound around the toroidal
core. The flux passes through the coils into the
core and then along the core tangentially to the
next pair of poles. This configuration is used by
Proven Wind Turbines of Scotland.
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Advantages and disadvantages of using a laminated
core in the stator.

• DISADVANTAGES
• Magnetic loss and drag cause problems with
  start-up
• Cogging torque causes vibration.
• The self inductance of the stator winding limits
  the maximum output current
• Short circuit switches can only be used for
  braking up to a certain windspeed because of
  this current limiting
• Laminations are difficult to manufacture in a
  small workshop.

• ADVANTAGES
• Reduced air gap has lower reluctance and lower
  leakage, and hence offers higher flux density, at
  reduced magnet volume and costs.
• The self inductance increases the shaft speed
  range. This helps the blades to maintain a more
  constant tip speed ratio.

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Power/speed curves
Air gap alternator without core
Ferrite magnet alternator with slotted, laminated
core and small air gap.
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Single phase windings
If a single coil gives 1 volt then two coils in
series give 2 volts
2 coils in parallel give one volt, but the
resistance is only half compared to one coil
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3-phase windings
Star
Coils in different 3 phases connected star give
root(3) times higher voltage (x 1.73) than they
would connected delta
Delta
Resistance in star is 2 x coil resistance in
delta is 2/3 x coil resistance
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Series-star and series-delta
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Converting AC to DC with a rectifier
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5-phase stator wiring to battery
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Calculation of EMF
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Voltage Waveform Effects
Once we know the mean voltage, we can estimate
peak voltage. We assume that the waveform is
sinusoidal although it may not be. We subtract
the diode voltage from the peak to estimate DC
output.
Cut-in rpm (Vbat1.4)60/(1.562nA B)
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Calculation of internal resistance
Internal resistance is easy to calculate, using
the dimensions of the coils and the conductivity
of copper. R (ohms )L/Aw0.022(10.004(temp-70
)) where L is the length of copper wire in
the coils of one phase in metres, Aw is the wire
cross sectional area in mm (pi()square(diameter)/
4), and temp is wire operating temperature in
degrees C. Length L Mean turn length number
of turns Aw Cross sectional area of coil
Space factor / number of turns Space factor
depends on insulation and on skill of winding. A
good figure to use is about 0.5 - 0.6. Winding
wire is specified by metric diameter or by wire
gauge. Diameter (Aw4/pi()).5 AWG gauge
LOG(53.5/Aw,1.261) Wire is available is standard
sizes and therefore the choice of size will
dictate the space factor and the resistance in
the end.
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Computing the power/speed characteristic
You can use E and R to predict the output
current. There is no current until EdcgtVbat.
After that, current Idc will be Idc
(amps)(Edc-Vbat)/R (in theory) However this
neglects ripple. I In practice a more accurate
result is obtained by using this equation Idc
(amps)(Edc-Vbat)/R/1.3 NB The equation neglects
reactive effects (self induction) Where the
coils are wound on laminations, the inductance is
strong and it is hard to predict output current.
The current will be limited by the inductive
reactance at higher speeds. But with air-core
coils in a stator which does not contain iron, we
can look at the resistance R in ohms as the main
impedance. Using this equation in a spreadsheet
we can go ahead and calculate current at each of
a series of different speeds. Multiplying Idc by
Vbat we arrive at output power at each rpm. We
can also use Copper Loss (watts) (Idc)2R
and Diode Loss Idc 1.4 to estimate input
power before copper and diode losses.