PMdrives part1

Advance AC Drives 2009

Department of Electrical and Electronic Engineering

Advanced AC Drives

Permanent Magnet Machine Drives

Dr. Chris [email protected]


Part I

Basics principles of Permanent Magnet (PM) Machines

Characteristics and application areasTypes of PM machines and drives– BLAC

– BLDC

Permanent MagnetsConcept of Armature ReactionSaliency Phasor Diagrams Torque and Maximum Torque per AmpereDynamic equations and Equivalent Circuit


Characteristics of PM machines

• PM motors have the fastest growing machine drive market share

• PM machine topologies are generally the Most Efficient and have the Highest Torque/Power Density of all machine types.

• Relatively simple construction, no brush gear.

• More flexible to design than induction machines - ex: high pole number machines, axial flux machines, transverse flux machines, concentrated wound machines….

• Permanent magnets offer a way of providing the magnetic field excitation without having an excitation winding.

• Hence : lower losses in the machine and converter, higher efficiency, improved power factor, better torque per amp ratio and a greater torque density.

• Power range from mW(small spindle motors) to MW(ship propulsion)

6-pole permanent magnet rotor


Application Areas

• High Performance / High Efficiency drives

• Industrial Drives

• More Electric Transport– Automotive– Aerospace– Marine

• Distributed Generation– CHP– Tidal generators

– Wind turbine generators

• White Goods– Air Conditioners– Washing Machines ….

Ship Propulsion : up to 18MW

Wind Generation : up to 5MW

Aerospace actuation : tens of kW

Electric & Hybrid Vehicles


Brushless PM Motor Drive types

• Two are two types of Brushless PM Drives– BLAC (brushless AC or PM

synchronous) : sinusoidlly excited and sinusoidal back-EMF

– BLDC (brushless DC) : square wave excited and trapezoidal back-EMF

• In BLAC machines all phases conduct current at the same time. They are fed from a multi-phase supply( in most cases 3) and operate on the principle of a rotating magnetic fields – just like Induction Machines.

• BLDC motors are also fed from a multi-phase supply (generally 3 –and shifted by 1200 one from another) but these wave shapes are rectangular. Only 2 phase windings out of 3 conduct current simultaneously. Such a control scheme (electronic commutation) is functionally equivalent to the mechanical commutation in d.c. machines. Thus the name BLDC.

BLAC BLDC


• The low power BLAC motors (in the range of kWs) are often supplied from d.c. link converters with a simple diode bridge rectifier as a line-side converter. IGBTs are most commonly used.

• For bi-directional power flow back to back converters are most commonly used with direct AC-AC converters (matrix converters) used in specialised applications such as aerospace where weight is at premium.

• BLAC motor drives are characterised by smooth torque production. The sinusoidal winding distribution and sinusoidal flux distribution ensures smooth “commutation”between active phases.

• Can be operated under V/F control however vector control is more commonly used to achieve high dynamic performances.

• Drive operation is similar to that of an induction machine however with zero slip. That is:

• Control electronics generally consist of a DSP and FPGA platform to perform the relatively complex control algorithms.

• High resolution encoder/resolver is generally needed for control purposes.

• Well suited for field weakening operation especially the salient type versions of the machines.

BLAC motor drives

2e rPω ω=


BLDC motor drives

• BLDC motor drives are often opted for due their simpler drive requirements (cheaper) when compared to BLAC drives.

• Control strategy can easily be implemented using analogue circuitry.

• BLDC output characteristics are however generally inferior to BLAC drives in terms of torque and current smoothness.

• Torque density is however high, potentially higher than BLAC due to better utilisation of the magnetic circuit.

• Hall effect devices mounted in the motor detect the position of the permanent magnet rotor. These are relatively crude and if greater resolution is required a more expensive resolver or encoder should be used.

• Field weakening is possible up to a certain point. Performance in this region is however considerably inferior to BLAC drives.


PM machines for BLAC and BLDC drives

• For BLAC drives the machine should have as much sinusoidally shaped BEMF as possible. This guarantees smooth torque output with minimum current distortion. This is generally achieved by :– Employing distributed windings. Chording and skewing often used to eliminate unwanted harmonics.

– Having a sinusoidal air gap flux density distribution (approx magnet span 1200). Different rotor topologies and magnet shapes are used to improve distribution.

• For BLDC drives the machine should have a flat topped, trapezoidally shaped BEMF waveform. This minimizes torque ripple and current distortion. This is generally achieved by :– Employing concentrated stator windings.

– Having a rectangular shaped flux density distribution in the air gap (approx magnet span 1800)

BLAC

BLAC Airgap Flux Density

BLDC0magnet span 120 electrical≈0magnet span 180 electrical≈

BLDC Airgap Flux Density


BLDC PM machine operation

• BLDC drive operation is characterised by torque ripple. This is the main price to pay for the control and sensing simplicity of this type of drive. Torque ripple has a number of sources, some machine related others due to the way the drive is operated. Sources of torque ripple are :

Simulated instantaneous torque waveform for a PMDC drive with PWM-regulated six-step current waveform.

– BEMF Harmonics (machine related). This is what causes the crest of the torque waveform (and BEMF) to be somewhat rounded during the intervals between commutations .

– Cogging Torque (machine related). The magnitude and frequency of these torque components are dependent on the number of poles and slots the machine has. A good slot-pole combination should be chosen to avoid excessive ripple. Skew and magnet pitch can be optimised to reduce this ripple. This ripple can also be eliminated through inverter control at the expense of current ripple.

– Switching Ripple (inverter related). This is directly proportional to the high-frequency (>5kHz typical) PMW ripple in the motor phase currents. This ripple is generally not a problem because the mechanical load inertia is typically large enough to filter out its effect on speed.

– Commutation Ripple (inverter related). This tends to be quite troublesome and is due to phase current commutations when current is transferred from an off-going inverter phase to the next on-coming active phase at the end of each π/3 interval.


BLAC PM machine operation

• BLAC drives are generally characterised by smooth torque. The sources of torque ripple are similar to the BLDC motor drive except for not having commutation ripple and having lower switching ripple.

3-phase BEMF waveforms

Torque produced for different rms phase currents

Increasing torque ripple with high current due to

saturation effects


IM vs BLDC vs BLAC

• In the rest of this course we will mainly focus on brushless AC machines.

IM BLDC BLAC

Motor Efficiency + +++ +++

Torque Smoothness +++ + +++

Torque Density + +++ +++

Open Loop Control +++ - -

Closed Loop Simplicity + +++ +

Minimum Control Sensors + +++ +

Machine design flexibility + ++ +++

Extended Speed Range ++ + +++

Motor Robustness +++ + ++

Cost - motor £ ££ ££ Cost – converter, sensors& control £££ (vector drive) £ £££


Permanent Magnet Excitation

• The permeability of a magnet is the slope of the straight line which intercepts the axis at the remenancepoint (Bm). The permeability for ferrite and rare earth magnets is approximately that of free space (mr ~1.05 to 1.07)

• Once off the linear part of the curve (knee-point), the magnet is wholly or partially demagnetised and must be re-magnetised.

cMMF H l= ⋅

r rB Aφ = ⋅

• Permanent Magnets are Hard magnetic materials – they retain considerable magnetisation when the external field is removed

Br – remanent flux density

Hc – coercive force


Permanent Magnet Properties

• All magnets are affected by temperature. For small temperature changes this effect is reversible.

• For NdFeB magnets the remanence reduces by about 0.1% per °C. For ferrite magnets the remenance reduces by 0.2% per °C and the coercivity reduces by 0.5%.

• However, at the Curie temperature the magnet loses all of its magnetism permanently unless re-magnetised at normal room temperature by an externally applied field.

• Magnets are more easily demagnetised as their temperature increases. The effect is that the knee point moves upwards (see chart on next slide)

• Obviously this is a potentially disastrous situation for an electrical machine and immediately rules out permanent magnet machines for some applications where the ambient temperature is very high.

• The maximum operating temperature for magnets can be quite low only 120-180 for NeFeBR.

• Magnetic steels in machines lose their Ferro-magnetic properties at temperatures about 600 to 800 degrees centigrade. Thus magnet temperature often imposes the limit on the maximum continuous torque developed by the machine.

• Load current can also demagnetise magnets through armature reaction effect. This often imposes the limit on the maximum transient torque developed by the machine.

• Another challenge with using PM materials such as NeFeBr is their relitavely low corrosion resistance. Appropriate coating have to be used.


Permanent Magnet Materials

Example of temperature variation for a particular grade of NeFeBr magnets

There are three main types of magnets

• Metal magnets (Alnico)– Oldest and rarely used

• Ceramic magnets (Ferrites of Barium and Strontium)– Cheapest and widely used

– Max B around 0.45T

• Rear Earth magnets (NdFeB and SmCo)– Most modern and relatively expensive

– Best performance – max B around 1.25T


Permanent Magnet Circuits

• The magnetic circuit in which the magnet is placed is also a reluctance. The diagram show a simple magnetic circuit.

• Assuming the magnetic steel is infinitely permeable implies that only the air gap and the magnet have a reluctance.

• The air gap flux is then simply the mmf source divided by the sum of the two reluctances (magnet and air-gap )

source m cF l H= ⋅ mm

o recoil m

lAμ μ

ℜ =⋅ ⋅

gg

o g

lAμ

ℜ =⋅

m gA A A= =

0source m cg g

mm gg

recoil

F A l HB A

ll

μφ

μ

⋅ ⋅ ⋅= ⋅ = =

ℜ +ℜ +

0m cg

mg

recoil

l HB

ll

μ

μ

⋅ ⋅=

+

Given that the cross sectional area is uniform :

(1) (2)

Assuming that : 1recoilμ =m

g rg m

lB B

l l=

+

Thus, a maximum stator teeth flux density of 1.6T (steel saturation) implies an air gap Bg ~ 0.8T. Using rare earth magnets with Br ~ 1.1T, and an air gap of 1mm implies a magnet thickness, lm of ~ 3mm


Basic concept of Armature Reaction

( )2demagg m

IHl l

=+

To a simple approximation, the demagnetising field intensity is :

• Let us consider a current carrying conductor in the air gap. This, in effect represents a simple electrical machine.

• The flux due to the current is the armature flux. It opposes the magnetic field over part of the magnet and assists over the rest.

• This demagnetising MMF forces the magnet operating point down towards the knee of the B-H curve.

• Once off the linear part of the curve, the magnet is wholly or partially demagnetised and must be remagnetised.

Force acting on conductor

Demagnetisation effect of armature reaction

Flux Density Shaded Plot


“Burying the magnet” to avoid demagnetisation

• A way of avoiding demagnetisation is to move the magnet away from the current carrying conductor as shown above.

• Rather than using a ‘surface magnet form’ of an electrical machine, buried magnet types shield the magnet from the demagnetising MMF.

• The price to pay in the circuit above is that the demagnetising MMF is now considerably larger since lm is effectively 0 as far as the air gap region is concerned. The inductance of the conductor is also increased.

• When I is large there may be sufficient flux from the armature (conductor) to saturate the pole tips of the magnetic steel causing an increase in the reluctance of the magnetic path and a reduction of the main magnet flux, as can be observed from the flux density plot above when compared to the one on the previous slide.

2demagg

IHl

=To a simple approximation, the demagnetising field intensity is :

Uniform Flux Density

Lower core flux density due to higher armature flux

Saturated pole tips

Flux Density Shaded Plot


d-q rotating reference frame for PMSM

• In PMSM we usually orientate ourselves with the magnet flux. Unlike IM the magnet flux in PMSM rotates at the same speed as the rotor ie. wsl=0

• Thus the direct or d-axis is aligned with the permanent magnet flux linkage phasor , so that the orthogonal quadrature or q-axis is aligned with the resulting back-EMF phasor E.

• The q-axis bisects the section between the permanent magnets.

fψ

d-axis

q-axis

fψ

Flux plot of a 2-Pole PMSM with zero stator current

q-ax

is

d-axis

fψ

E

-axisα

rθ


Concept of Saliency

• Permanent magnet machines can be salient just like traditional wound rotor salient synchronous machines. This is due to the relatively low permeability of the magnets compared to that of magnetic steel. (permeability of magnets ~ permeability of air)

• In PMSM the inductance of a stator coil aligned with the rotor d axis is Ld and is smaller than the inductance of the same coil aligned with the rotor q axis, Lq. Ie. Ld<Lq

• Note that this is opposite to a wound field machine where Ld>Lq

• Not all PMSMs are salient. This depends on the rotor construction. Surface mount magnet machines are generally non salient. Most buried magnet machines have typical saliency ratios (Lq/Ld) of 3 to 4. However ,machines with ratios higher than 7 are sometimes used.


Phasor Diagrams of PM synchronous Machines

• If the magnets are on the motor surface and the shaft cross-section is circular then the motor is non salient, Ld = Lq. In steady state, with balanced sinusoidal phase currents the operation can be represented by :

A) Non Salient Machines

( )aV E I R jX= + +

a d qI I I= +

f

VEδγφΨ

Supply Voltage phasor

BEMF phasor

Load angle (between V and E) +ve in Fig.

Current Angle (between I and q-axis) –ve in Fig.

Power Factor angle

Magnet Flux Linkage



• For salient machines, where Ld is different form Lq : B) Salient Machines - positive id

a d d q qV E I R jI X jI X= + + +

( ) ( )d d q qV E I R jX I R jX= + + + +

a d qI I I= +

• For a positive d-axis component Id>0, the stator winding produces an MMF distribution around the airgap that tends to augment the d-axis flux produced by the magnet. The stator current is said to be “magnetising”.

• The flux produced by the MMF associated with Id induces a voltage jXdId in the q-axis, which adds to jE as shown in the phasor diagram.

• The d and q axis voltage magnitudes are equal to :

sind q q dV V I X I Rδ= = −

cosq d d qV V E I X I Rδ= = + +



B) Salient Machines - negative id

• For a negative d-axis component Id<0, the stator winding produces an MMF distribution around the airgap that tends to oppose the d-axis flux produced by the magnet. The stator current is said to be “demagnetising”.

• A net reduction in flux linking the stator windings results in a smaller terminal voltage.

• The voltage jXdId is now opposite in direction to jE as shown in the phasor diagram.

• The d and q axis voltage magnitudes are equal to :

sind q q dV V I X I Rδ= = +

cosq d d qV V E I X I Rδ= = − +

• The power factor angle is given by : φ δ γ= −

• The power factor angle is larger in magnitude when Id>0. On the other hand with negative Id the power factor is improved.


( )q d q d qe

kT I E I I X Xω

⎡ ⎤= + −⎣ ⎦

Torque production in PMSM

• The electromagnetic torque is generally given by : d q q dT k I Iψ ψ⎡ ⎤= −⎣ ⎦Where k depends on the transformation used.

32Pk = ⋅

23 2

Pk = ⋅For the 3/2 x peak convention:

For the rms convention: Where P is the number of poles

• From the phasor diagrams the d and q axis flux linkages are given by :

e d d dE X Iωψ = +

e q q qX Iωψ =

• Substituting in the torque Equation we get :

• The first term is called the “magnet alignment torque” and the second term, proportional to (Xd-Xq) is called the “reluctance torque”. Note is the angle from the q-axis to the current vector. (positive anticlockwise) For a negative id, gamma is positive and negative for a positive id.

Magnet alignment component

Reluctance component

γ



• It is useful to express the torque produced as a function of the armature current in order to determine the best operating point of the machine in terms of producing the torque with the minimum armature current and hence with optimal efficiency.

The armature current is equal to : 2 2da qI I I= +

( )cos sin2d a aI I Iπ γ γ⎛ ⎞= + = −⎜ ⎟

⎝ ⎠( )cosq aI I γ=

( ) ( ) ( )( )2cos sin cosa a d qe

kT EI I X Xγ γ γω

⎡ ⎤= − −⎣ ⎦

( ) ( )( )2

cos sin 22a

a d qe

IkT EI X Xγ γω

⎡ ⎤= − −⎢ ⎥

⎣ ⎦

• Now, if we substitute for Id and Iq, in the torque equation we get :

• The magnet and reluctance torque terms are still apparent in the equation above. It is clear that there is an optimal angle for which we can get maximum torque. If the machine is not salient, then the equation reduces to :

γ

( )cosa

e

kEIT

γω

=

Note : E is constant, defined by the magnet flux, and Xd and Xq are physical quantities dependent on the machine design. If we fix I, and vary , an optimum angle for maximum torque can be found.

γ



• The plot below shows how torque varies as a function of , with Ia held constant and its decomposition into the two components.

γ

• Maximum torque/amp occurs in a salient pole PMSM machines at values of which are >0

• When =0 , Ia is in phase with E, ie Ia=Iq and reluctance torque is zero.

• Also note that if Xd=Xq, reluctance torque component is zero throughout.

• If there is saliency, the angle required to produce maximum torque per amp, varies with current since the saliency torque increases with Ia2 while the magnet torque increases with Ia

• The relative amplitudes of the magnet and reluctance torque terms are set during the machine design process by choosing the rotor topology and adjusting the magnet and rotor saliency dimensions in order to vary the relative amplitudes of and (Ld-Lq).

γγ



• The plot below shows how torque varies as a function of , for various values of Ia. γ

• It can be observed that the higher the current the greater the angle of advance needs to be to operate at maximum efficiency.

• In order to determine the maximum torque point we can differentiate the torque equation with respect to and equate to zero as shown in the following slide.γ


Maximum Torque per Ampere (MTPA)

• In order to find the angle of maximum torque for a given current we can differentiate the torque equation as follows :

• This variation can be more complex than that indicated by the equation above, because the reactances Xd and Xq are subject to saturation and thus vary with loading. In some motor configurations this variation can be quite severe especially in Xq.

• We will revisit this equation in the last part of the course when we will look at the control methodologies for BLAC drives which exploit the saliency torque component to achieve optimum drive operational efficiency.

( ) ( )( )2sin cos 2 0a a d qe

dT k E I I X Xd

γ γγ ω

⎡ ⎤= − ⋅ − ⋅ − =⎣ ⎦

d qX X XΔ = − ( ) ( )2sin cos 2 0a aE I I Xγ γ⋅ ⋅ + ⋅ ⋅Δ =

( ) ( )2 2sin 1 2sin 0a aE I I Xγ γ⋅ ⋅ + ⋅Δ − =

( )2 2 22 sin sin 0a a aI X E I I Xγ γ− ⋅ ⋅Δ ⋅ + ⋅ ⋅ + ⋅Δ =

( )2sin sin 0a b cγ γ⋅ + ⋅ + =

Let :

Which is in the form : Thus :2 2 2

1max

8sin

4a

Ta

E E I XX I

γ −⎡ ⎤− ± + ⋅ ⋅Δ⎢ ⎥=

− ⋅Δ ⋅⎢ ⎥⎣ ⎦


PMSM Dynamic model

• The most convenient manner of describing sinusoidal BLAC machines for control purposes is through instantaneous current, voltage and flux linkage vectors in a synchronously rotating reference frame locked to the rotor flux, just like in induction machines.

• The coupled equivalent circuits for the d and q axis are shown below. The magnet flux source is represented by an equivalent current source If, which appears in the d-axis circuit while the resulting back-EMF appears as a dependent voltage source in the q-axis circuit.

D-axis equivalent circuit Q-axis equivalent circuit

dd d d e q

dIV I R Ldt

ωψ= + ⋅ − qq q q e d

dIV I R L

dtωψ= + ⋅ +

q lq mqL L L= +

d ld mdL L L= +

ld lqL L=

( )q lq mq qL L iψ = + ( )d ld md d md fL L i L Iψ = + +

e md fE L Iω=Where :


What’s next?

• In Part 1 we went over the basic properties of PM machine operation and the different types of drive configurations. We looked at the principles of torque production and are now able to evaluate the machine’s performance characteristics from its electrical parameters.

• In the next part of the course we will look at the relationships between the electrical parameters and machine geometry. We will also look at what limits the machine’s operation and maximum torque produced.

• In the last Part of the course we will look at methods of controlling BLAC drives over a wide speed range.

PMdrives part1

Documents

Transcript of PMdrives part1