Benchmarking of a High-Speed Permanent Magnet Machine

Delvis Gonzalez-Lopez, Member, IEEE

Abstract—A 5.0 MW, high-speed permanent-magnet machine is extensively studied in this paper. The overall measured losses of the machine were segregated through a finite element (FE) analysis. Consequently, the FE model was used to determine the parameters of the per phase equivalent circuit. This paper proposes a FE analysis based procedure to calculate the parameters of permanent magnet machines based on a pre-defined set of test data.

Keywords-Permanent magnet; high speed electric machines; electric motor; electric generator

I. INTRODUCTION High-speed permanent-magnet (HSPM) machines are

characterized by high efficiency and significant reduction of the size and weight compared with conventional, wound field synchronous machines. These features makes HSPM preferred for applications where it is desired to improve reliability and efficiency by eliminating gearboxes. The direct coupling between the electric driver and the mechanical load allows an overall compact system.

For high speed operations, the robustness of the rotor represents a challenge for the mechanical design of the machine. A non-magnetic sleeve is commonly used to retain the magnets on permanent-magnet (PM) surface-mounted rotors [1]. At the same time, the retaining sleeve increases the magnetic gap affecting the electromagnetic performance of the machine.

The stators of HSPM and conventional synchronous machines are similar. However, for high speed applications, the size and shape of the wires for the stator coils must be selected carefully to minimize the alternate current (AC) contribution to the copper losses. The resistance per phase increases due to the proximity and skin effects. Extensive studies were published to quantify these effects for high frequency and inverter powered machines [2]-[5].

This paper is mainly focused on the experimental verification of the performance of a 5.0 MW and 15,000 rpm permanent magnet machine. Generally, any operating point of a PM machine can be reproduced by FE analysis, and accurate predictions can be determined if the model allows reliable description of the material properties used. The stator of the machine under study was built with HF-10 laminated silicon steel. A sample of this material was tested, and the resultant magnetic properties were used to model the stator lamination in the FE analysis. The magnets in the model match the B = f(H) magnetic curve provided by the manufacturer for different operational temperatures. In this section, the paper proposes a procedure to calculate the equivalent circuit parameters from the test data and provides a methodology to segregate the losses of the machine under study.

The second part of this paper discusses the test results of the presented HSPM machine on retardation test proposed in [1] and [6], and operating in generator mode. These operating points were reproduced by FE analysis in order to study the distribution of the electromagnetic losses in the machine.

II. PER PHASE VOLTAGE-DRIVEN EQUIVALENT CIRCUIT The voltage-driven equivalent circuit per phase, Fig.1,

allows an easy estimation of the perfomance of the machine in steady state. The open circuit voltage (VOC), synchronous inductance (Ls) and the resistance per phase (Rs) were calculated by FE and corroborated by test data.

Fig. 1. Per phase voltage-driven equivalent circuit

A. Open Circuit Voltage The separate drive test proposed in [1] and [6] can be

carried out in open circuit condition. The open circuit voltage can be measured directly at the terminals of the generator once the bearings reach stable temperature.

Table 1 summarizes the predicted and measured open circuit voltage in V/krpm. The demagnetization of the rotor with the temperature is 2.2 %, which is typical of SmCo magnets. The temperature of the rotor in the FE model was set to 120o C in order to match the stable temperature condition during test. However, the open circuit voltage obtained by FE solution is 6.4% higher, mainly because 2D analysis does not take into account the end effect of the rotor, resulting in more flux going to the stator and inducing voltage in the coils.

TABLE I. VOC PREDICTED BY FE & MEASURED ON SEPARATE DRIVE TEST

Voc [V/krpm] % Diff from Test (S. Temp)

FE Prediction 175.8 6.4%

Test (Cold) 168.9 2.2%

Test (Stable Temp) 165.3

2011 IEEE International Electric Machines & Drives Conference (IEMDC)

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B. Synchronous Inductance Generally, FE professional softwares have the feature to

calculate the synchronous inductance directly, by dividing the flux linkage by the current injected in the coils. Another method is calculate Ls from the ratio of the magnetic energy and the square of the current in the coil. However, in simulations of PM machines, most of the FE packages include the flux linkage due to the excitation of the magnets into the calculation, which produces a wrong result.

A quick solution could be to replace the magnet by air and then calculate the inductance per coil, but this procedure is not totally correct. In [7] it is demonstrated that the saturation of the magnetic circuit can vary the inductance of the machine. A good approach to estimate the inductance, taking in account the saturation due to the residual flux density of the magnets is to calculate the total flux linkage (λtotal) in the coil and subtract the flux linkage due to the magnet (λpm) only: L λtotal-λpm (1)

The total flux linkage results from FE model solved with magnets and rated current in the coils, and λpm can be found by solving the FE model in open circuit (Is = 0). Similar concept can be applied if L is calculated from the magnetic energy in the coil.

The machine under study is a form-wound and the coils are made with six rectangular strands in parallel. Fig. 2 shows the layout of the slot and the characteristics of the coils. In a form-wound machine with n strands, the inductance per coil can be calculated by the parallel sum of the inductance of every strand (Lstd),

∑ _ (2)

Lstd is obtained from its self and mutual components, which are calculated by (1) from the FE analysis. Since the presented machine has four parallel circuits, the synchronous inductance per phase is,

(3)

Fig. 2. Slot layout of the presented machine

Several tests can be performed to calculate the synchronous inductance of a PM machine. The goal on every test is to determine the reactance per phase (Xs) from the measurements of current and terminal voltage. Then, the synchronous inductance can be calculated by,

· (4)

The frequency (f) is found from the current or voltage waveform, or from the speed measurement. Because the inductivity of the coils in the machine under study is quite large, the resistance of the stator winding was not taken in to account in the estimation of Xs.

The calculation of the unsaturated synchronous reactance (Xus) from a sudden three-phases short-circuit test is proposed in [1] and [6]:

(5)

Under stable short-circuit condition, the short-circuit current (Isc) is limited only by the synchronous reactance. The magnitude and frequency of Isc can be measured once the short-circuit reaches steady state. The armature reaction flux is in d-axis in opposite direction of the excitation flux, resulting in zero voltage at the terminal of the machine. Because this condition causes low saturation on the magnetic circuit, the resultant inductance is called unsaturated synchronous inductance. Due to the linear dependency of VOC and Xus with the frequency, the rms value of the stable short-circuit current is independent of the speed.

Fig. 3. Vector diagram of a PM motor under electric input test for Id >> Iq.

The synchronous inductance can be calculated by the electric input test proposed in [1] and [6]. The vector diagram of Fig. 3 describes the relation of the voltages and currents in an unloaded PM motor under field weakening operation. The magnitude of the q-axis component of the current (Iq) and the angle of torque (δ) depend only on the no-load losses of the

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motor. For large PM motors, both Iq and δ are typically low under no load condition. But the magnitude of the component of the current in the direct-axis (Id) can be increased by moving the vector of the stator current toward d-axis. For the condition where Id >> Iq and assuming that the angle of torque is very small (δ ≈ 0), a linear approximation can be used to calculate the synchronous inductance.

(6)

The synchronous inductance can also be obtained by operating the machine as a generator with inductive or resistive load. If a PM generator is feeding a “pure” inductive load, the active power delivered by the generator is very small compared to the reactive power. Therefore, the angle of torque is close to zero. While the reactive power delivered by the generator increases, the vector of the current moves toward d-axis [7]. Operating at high current the Id >> Iq and δ ≈ 0. Then, Xs can be solved from the voltage equation as, Xs -VtIs (7)

Fig. 4 depicts the vector diagram of a PM generator operating with unity power factor [8]. φpm, φs and φg are the excitation flux, the armature reaction flux and the resultant flux in the airgap, respectively.

Fig. 4. Vector diagram of a PM generator operating under unity power factor

When a “pure” resistive bank is used as a load, the angle between the terminal voltage and the current is zero and the generator does not deliver reactive power [2].

· 0 (8)

Then, the torque angle can be solved as,

(9)

Now, the synchronous reactance can be calculated by,

·· sin (10)

Where Pph is the active power per phase measured at the terminals of the generator.

Fig. 5 compares the synchronous inductance predicted with FE analysis by following the procedure explained above, with Ls obtained by test. The calculation from the electric input method lost accuracy at low current because Iq is comparable with Id and so, the relation between voltages is not linear. Therefore, it is recommended to perform this test at high current. The synchronous inductance obtained by (7) from testing as a generator with inductive load is valid only if the active power demanded by the load can be disregarded. Therefore, it is recommended to run this test at low speed to avoid inaccurate results due to the increment of the resistance of the load with frequency.

Fig. 5. Synchronous inductance estimated by FE and calculated from testing

The average value of the synchronous inductance calculated from test is compared in Table II with Xs predicted by FE analysis. In 2D FE analysis the end turns are not modeled. The inductance per phase from FE analysis corresponds just to the active length of the machine, resulting in smaller inductance per phase.

TABLE II. SYNCHRONOUS INDUTANCE: AVERAGE VALUE FROM TEST AND ESTIMATED BY FE

Ls [mH] Average from Test 0.69

Finite Element Analysis 0.55

C. Stator Resistance per Phase The direct current resistance per phase is a parameter that

can be measured directly at the machine terminals and easily estimated by FE analysis. However, on high speed operation, the resistance of the coil increases with the frequency. The

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distribution of the current inside the conductor changes with the speed due to the proximity and skin effects reducing the net area where the current is flowing [2]-[5].

In order to measure the resistance of the coils at high frequency, stator-alone test was carried out. The rotor was removed and AC voltage was applied to the stator coils. The input power and current were measured at different frequencies. The resistance was calculated by dividing the power per phase by the square of the rms current. Note that the measured power also includes the iron losses in the stator core due to the AC excitation [1]. Then, the AC resistance (RAC) has a component due to the iron losses, which is relatively low because of the low flux density in the stator lamination.

The stator-alone test was reproduced by FE analysis and the resistance per phase was calculated from the copper loss in the coils. Fig. 6 shows the variation of the resistance with the frequency. RAC estimated by FE analysis is lower because it does not include the iron loss component.

Fig. 6. Vector diagram of a PM generator operating under unity power factor

III. TESTING AND PERFORMANCE

A. Open-Circuit Retardation Test The retardation test on open-circuit condition is proposed

in [1] and [6]. The deceleration rate is recorded during the coast down from rated speed is used to determine the no-load losses (WNL)

· (10)

In (10), JR is the moment of inertia of the rotary parts and ω is the angular velocity in rad/s. The components of the no-load losses are the iron loss in the magnetic circuit, mechanical losses and the copper loss due to the Eddy currents induced in the coil by the rotary magnetic flux. Note that the magnets only induce Eddy current in the slot section of the coils and there is no loss in the end-turns on open-circuit condition. Therefore, the 2D FE analysis captures the total electromagnetic losses of the machine.

Because the excitation flux cannot be removed, the losses cannot be segregated from retardation test. However, the components of WLN can be estimated analytically in order to match its total with the total no-load losses calculated from experimental data.

The copper and iron losses can be predicted accurately by FE analysis. The mechanical losses are composed of windage in the airgap and friction in the bearings. The windage loss was calculated using the dimensions of the airgap and the temperature recorded during the retardation test. The loss in the bearing was estimated using the mass-flow rate and the inlet and outlet temperatures of the coolant.

Fig. 7. No load losses from retardation method

Fig. 7 depicts the no-load losses calculated from test measurements and its analytical segregation. As was expected, the iron loss is the most significant component due to the high flux density imposed by the magnets in the magnetic circuit. The mechanical losses have a quadratic dependency with the speed. The copper losses generated by the Eddy currents induced inside the stator bars become significant at high frequency. At 15 krpm the losses are segregated as a percent of the total no-load losses as,

- Iron loss: 59.6 % - Mechanical losses: 27.2 % - Copper loss: 13.2 %

B. Generator with Unity Power Factor Load The presented machine was tested in generating mode with

unity power factor (PF) load. The vector diagram showed in Fig. 4 describes the relationship between voltages under this condition. An adjustable resistor bank was used as load, in such a way that the power delivered by the generator could be adjusted up to 3.0 MW. The output power was calculated at thermal steady state from the recorded waveforms of the current and terminal voltage.

In order to reproduce the operation of the machine by FE analysis, the model was adjusted by setting the temperature recorded during testing, and external resistors were added to obtain the measured rms current. Table III compares the

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No Load Loss (Test)No Load Loss (Estimated)Iron Loss (FE)Copper Loss (FE)Mechanical (Analytical)

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predicted and measured powers, and provides the analytical segregation of the losses. The mechanical losses were calculated by the same method used on retardation test. The magnetic loss in the iron and the copper loss in the slot section of the motor were taken from 2D finite elements analysis. However, the loss in the end-turns (WCu_end) cannot be obtained directly from FE model.

The components of the copper loss in the slot section are the Joule loss (Is

2·RAC), where RAC is the AC resistance resulting of the current distribution due to the skin and proximity effects, and the loss generated by Eddy currents induced inside the copper conductors by the rotary magnetic flux of the rotor. The end-turns are not under the influence of the magnets flux, and so, only the Joule loss is present in the end-turns. Then, WCu_end can be estimated by,

_ _ _ · (11)

Where lact and lend are the length of the active section of the machine and the longitude of the end-turn, respectively. WCu_sl is the total copper loss under load condition, and WCu_NL is the copper loss in the active section obtained by solving the FE model in open circuit (no load) condition.

Another way to estimate the copper loss in the end-turns is solving the FE without rotor and stator, just the coils surrounded by air and carrying the load current. The length of the coil must be adjusted to the length of the end-turn. Both methods gave similar results. The copper loss in Table III includes the loss in the active length of the machine and the loss in the end-turn section.

IV. SUMMARY AND CONCLUSIONS In this work, the performance of a HSPM machine is

widely studied. Finite element analysis was used as tool to reproduce the tests carried out and segregate the losses. There are some practices to follow in order to effectively predict the performance of the machine by FE analysis. The temperature must be set correctly to take into account the weakening of the magnets and the increase of the resistivity of copper in the stator windings. The electromagnetic properties of the materials of the lamination, magnets and coils in the FE model must be adjusted such that they match the characteristics of the materials used to build the machine. On coils made with rectangular solid bars, it is important to model the real shape and size of the conductors, and properly select the dimensions of the elements of the FE mesh to capture the displacement of the current with the frequency. In order to reduce the solving time and the size of the FE file, the detailed modeling of the coil could be applied only to one slot. Then, average value of the copper losses in the slot over a complete cycle can be multiplied by the number of slots to find out the total copper loss.

Several tests can be performed to determine the parameters of the machine. Retardation test and operation in generating mode are preferred to avoid the impact of the harmonics associated with the power electronic drive during the electric input test. The calculation should be done post-processing the waveforms of the voltage and current and not from rms values directly measured during the test.

TABLE III. PERFORMANCE OF THE HSPM MACHINE IN GENERATING MODE WITH PF =1: TEST VS. FE ANALYSIS

Ope. Point 1 Ope. Point 2 Ope. Point 3 Ope. Point 4

Test FE Test FE Test FE Test FE Voltage L-L [V] 4527 4589 4368 4434 4348 4474 4180 4265 Current [A] 139 140 205 207 301 301 376 375 Output Power [kW] 1090 1117 1551 1592 2270 2333 2722 2768 % Diff. from Test 2.5% 2.6% 2.8% 1.7% Total Losses [kW] 76.0 81.2 88.7 97.2 Iron Loss [kW] 40.8 43.2 44.9 47.0 Copper Loss [kW] 17.3 20.1 25.9 32.3 Mech. losses [kW] 17.9 17.9 17.9 17.9

REFERENCES

[1] D. Saban, D. Gonzalez-Lopez and C. Bayley “Beyond IEEE 115 and API 546: Test procedure of for High-Speed Multimegawatt Permanent-Magnet Synchronous Machines,” IEEE Trans. On Industry Appl., vol. 46, no. 5, pp. 1769-1777, Sep/Oct 2010.

[2] M. J. Islam, J. Pippuri, J. Perho and A. Arkkio, “Time-harmonic Finite-element analysis of eddy currents in the form-wound stator winding of a cage induction motor,” IET Electr. Power Appl., vol. 1, no. 5, Sep 2007.

[3] S. Iwasaki, R. P. Deodhar, Y. Liu, A. Pride, Z. Q. Zhu and J. J. Bremner, “Influence of PWM on the Proximity Loss in Permanent-Magnet Brushless AC Machines,” IEEE Trans. On Industry Appl., vol. 45, no. 4, pp. 1359-1367, Jul/Aug 2009.

[4] A. D. Podoltsev, I. N. Kucheryavaya and B. B. Lebedev, “Analysis of Effective Resistance and Eddy-Current Losses in Multiturn Winding of High-Frequency Magnetic Components,” IEEE Trans. On Magnetic, vol. 39, no. 1, Jan 2003.

[5] C. R. Sullivan, “Optimal choice for number of strands in a Litz-wire transformer winding,” IEEE Trans. Power Electronic, vol. 14, no. 2, pp. 283-289, Mar 1999.

[6] IEEE Std 115-1995, IEEE Guide: Test Procedures for Synchronous Machines, IEEE Std., December 1995.

[7] D. A. Gonzalez, J. A. Tapia, R. Wallace and A. Valenzuela “Design and Test of an Axial Flux PM Machine with Field Control Capability”. IEEE Trans. On Magnetics

[8] I. Boldea, Synchronous Generators (The Electric Generator Handbook), CRC Press; 1st ed. 2005.

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