# Flux Weakening of Variable Speed Drives

Motors and generators with MotorSolve

Variable speed drives generally require electric machines to deliver constant power over a wide speed range and IPMs are known to have the best extended CPSR characteristics. Recent studies have shown that fractional slot surface mounted permanent magnet (SPM) synchronous machines may also exhibit large constant power speed regions (ratio of 1:10 is within possible range) by applying optimal flux weakening. In this example, using MotorSolve, design and comparisons of CPSR characteristics are made between a fractional slot (2/7 slot per pole per phase (SPP) SPM), a multi-layer IPM and and an integral slot (1 SPP) machine.

This example will show that optimal flux weakening condition can be realized in fractional winding SPMs allowing their CPSRs to be extended beyond expected levels. The models designed can generate high starting/accelerating torque and output constant power over a large speed range that is appropriate for starter-alternator type applications, as an example. A detailed comparison of this with a multi-layer IPM and an integer slot machine has been presented here.

## CONSTANT POWER SPEED RANGE (CPSR)

Three machines; a 42 pole 36 slot SPM (2/7 SPP), a 12 pole 72 slot double layer IPM and a 36 slot 12 pole (1 SPP) SPM have been designed and their performance are compared below. Their operating speed is set to 2500 RPM and 14 KW output power is demanded over a CPSR of 1:6. It is shown that the fractional slot SPM meet the optimal flux weakening condition which states that the characteristic current is approximately equal to the rated current of the machine.

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## MACHINE PARAMETERS

Each motor has been designed using the MotorSolve software. A summary of the designs are presented in the table shown here. Concentric windings (instead of distributed windings) are applied to fractional slot SPMs to achieve optimal flux weakening condition. The additional harmonics associated with the concentric winding may be used to understand why it is possible to satisfy the optimal flux weakening condition in these types of machine.

Parameter 36 Slot 42 Pole SPM 36 slot 12 Pole SPM 72 slot 8 Pole IPM
Slot/pole/phase 2 by 7 1 2
Outer Diameter (mm) 272 272 293
Stack Length (mm) 60 58 54
Air gap (mm) 0.635 0.635 0.635
Rated current (amps) 140 140 130
Copper mass (kg) 2.57 3.41 5.96
Iron mass (kg) 9.69 11.3 11.23
Magnet mass (kg) 1.86 1.59 1.48
Turn/Phase 26 24 36
Parallel paths 6 6 6
Slot fill factor 0.35 0.35 0.35

## RESULTS

The power versus speed characteristics of the three machines are presented here. Using MotorSolve and its' PWM dynamic simulation, the output power envelop at various advance angles are seen for each machine. The results prove the viability of achieving the desired CPSR for each machine type. The performance envelopes show clearly that CPSR value of 6 is possible with the fractional slot and IPM models while this is not the case with a similar integer slot machine. This can also be confirmed by computing the flux weakening index for each machine which can be obtained from MotorSolve.

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## TORQUE vs. SPEED

The torque versus speed results have been presented here. High starting torque is achievable by all three machines. However, it is clear that with the integer slot IPM, even with flux weakening, it is not possible to maintain reasonable output torque at high speeds as the back emf becomes significant and the machine operates as a generator.

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## MACHINE MASS

MotorSolve outputs the component masses of the machines being designed. A comparison of the masses of these three machines is presented here which show that the overall that the fractional winding SPM has the least mass.

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## LOSSES

Ohmic and core losses and loss distributions.

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#### REFERENCES

1. El-Refaie A. M., Jahns T.M., Comparison of synchronous PM machine types for wide constant-power speed range operation. COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, v 27, n 5, p 967-984, 2008.

2. Lovelace E.C., Design and experimental verification of a direct-drive interior PM synchronous machine using a saturable lumped-parameter model. Conference Record of the 2002 IEEE Industry Applications Conference. 37th IAS Annual Meeting (Cat. No.02CH37344), p 2486-92 vol.4, 2002