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Co Huynh Liping Zheng Dipjyoti Acharya Calnetix, Inc.,
Cerritos, CA 90703
Microturbines are small combustion turbines with typical out- puts in the range of 20–500 kW. A typical system rotates over 40,000 rpm. One of the key enabling technologies for microtur- bines is the integral high speed electrical machines operating at the same speeds as the turbines, eliminating mechanical gear- boxes. The result is a very compact high efficiency system that allows for ease of onsite installation. High speed permanent mag- net PM machines are typically used in microturbine application due to their high power density and high efficiency characteristics. A good understanding of high speed PM machine characteristics, especially its losses, is critical to predict system performance and to ensure a reliable operation.
Losses in PM machines can be divided into three categories: a stator loss, b rotor eddy current loss, and c windage loss. The stator loss consists of copper loss and iron loss. The copper loss includes conventional I2R loss and stray load loss due to skin effect and proximity effect. This can be calculated based on finite element analysis FEA or using analytical methods. The stator iron loss is divided into hysteresis loss, classical eddy current loss, and excess eddy current loss. Empirical equations or time-step transient FEA with motion can be used to calculate iron loss. The rotor loss generated by induced eddy currents in the steel shaft and permanent magnets is not significant compared with a ma- chine’s total loss. However, removing the heat from the rotor to ensure reasonable operating temperatures of its components is more difficult than removing the heat from the stator. Thus, an accurate prediction of rotor loss becomes important especially at high speed. The major causes of the rotor loss are a space har- monics due to the existence of stator slot opening and winding distribution and b time harmonics of the phase currents due to pulse width modulation PWM . The rotor loss can be analyzed using analytical methods. However, simulations using FEA based on actual measured current waveforms or estimated current with total harmonics distortion THD provide a more accurate assess- ment. The windage loss as a result of the shearing action of the media that exists between the rotor and stator may also be signifi- cant at high speed, especially with small air gap and high cooling flow pressure in the air gap between the rotor and stator.
A spin-down test can be used to verify no-load loss, especially when the rotor’s inertia is large. Testing of a back-to-back con- figuration can verify a machine’s efficiencies and total losses at
Contributed by the International Gas Turbine Institute of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received April 1, 2008; final manuscript received May 9, 2008; published online December 23, 2008. Review conducted by Dilip R. Ballal. Paper presented at the ASME Turbo Expo 2008: Land, Sea and Air GT2008 , Berlin, Germany, June 9–13, 2008.
various loaded conditions. The thermal analysis model result com- pared with measured temperature mapping can also be used to verify machine losses.
2 Permanent Magnet Alternator Losses
The losses in PM alternators are grouped into a stator loss, b rotor eddy current loss, and c windage loss.
2.1 Stator Loss. The stator loss consists of copper loss and iron loss. Copper loss is the loss due to the current going through the armature windings. The copper loss consists of I2R loss and stray load loss. The I2R loss is given by
Pcu = m1I2R 1
where m1 is the number of phases, I is the armature current, and R is the dc armature resistance. The I2R loss can be significant when large current flows through the conductor with large Ohmic resistance.
The stray loss comes from a the skin effect resulting from the same source conductors and b the proximity effect resulting from the field induced from adjacent conductors sharing the same slot. The skin effect is caused by electromagnetic induction in the conducting material, which opposes the currents set up by the wave E-field. The skin depth is the distance in which an electro- magnetic wave entering a conducting surface is damped and re- duces in amplitude by a factor of 1/e, where e is equal to 2.71828.... The skin depth is given by
where is the angular frequency of the current and is the electrical conductivity of the conducting material.
In designing the stator winding, wire strand size is selected such that skin depth is much larger than the wire radius to mini- mize loss due to skin effect.
Stator windings are contained inside slots. Loss due to proxim- ity effects of conductors located in the slots of electric machines can be estimated based on the following equation 1 :
Losses in High Speed Permanent Magnet Machines Used in Microturbine Applications
High speed permanent magnet (PM) machines are used in microturbine applications due to their compactness, robust construction, and high efficiency characteristics. These ma- chines are integrated with the turbines and rotate at the same speeds. This paper dis- cusses in detail the losses in high speed PM machines. A typical PM machine designed for microturbine application is presented with its detailed loss calculations. Various loss verification methods are also discussed. DOI: 10.1115/1.2982151
Pstray = Pcu kd − 1 3 kd = + m2 − 1 − msin 2 4
= sinh 2 + sin 2 5
cosh 2 − cos 2
MARCH 2009, Vol. 131 / 022301-1
Journal of Engineering for Gas Turbines and Power
Copyright © 2009 by ASME
Downloaded 06 Jan 2009 to 220.127.116.11. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm
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