Influence of frequency on the performance of integrated electric drive systems

Ion Voncila, Razvan Buhosu,

Control Systems and Electrical Engineering Departement „Dunarea de Jos” University

Galati, Romania ion.voncila@ugal.ro, razvan.buhosu@ugal.ro

Madalin Costin Research Centre „Integrated Conversion Systems and

Complex Process”, „Dunarea de Jos” University of Galati

Abstract—Based on the algorithm design of brushless synchronous motors (brushless DC), this paper presents the influence of input quantities frequency of the electrical gateway (voltage, current) - for constant values obtained from the gateway machine (speed, torque) – on the geometric dimensions, parameters and functional stability of this category of electric drives. The analysis used the Matlab programming environment to design and visualise modes of frequency quantity variation (geometric size, operation parameters, other characteristic values). The stated purpose of the paper is to show that, in modern adjustable drive systems, it is necessary to create harmony between sub-components, and between the frequency of control sizes (supplied by static converter) and the natural frequency of mechanical structures (in particular, the electromechanical converter).

Keywords—Brushless DC, functional stability, permanent magnets.

I.INTRODUCTION A careful analysis of modern integrated drive systems

reveals the following:

- The current electric drive system structure, particularly electromechanical converters and transmission systems from the drive motor to working machine, is made of high density materials (steel, copper, metallic permanent magnets, etc.);

- Due to the high density of such structures, its frequency of vibration (viewed at the extreme edge through its own resonance frequency) is relatively low. In particular, such structures can store relatively high amounts of energy but, unfortunately, can relay only small amounts of information;

- Under these conditions, the association within the integrated system of the electromechanic converter (of classic or particular topology but using largely the same material as the classic one) and the static converter is generally an inadequate solution because the electromechanical converter primarily stores energy, while the static converter primarily relays information [1], [10], through various control techniques. Between the two entities conveyed directly via the feedback system (specific to modern electrical drives) there is a big difference in terms of frequency. The feedback is, of course, mainly information so that discrepancies at the level of frequency are practically nonexistent.

Conclusions to be drawn from this small analysis:

- High harmonics occurring in energy curves (voltage, current) of the electromechanical converter are a natural consequence of the frequency differences in the two integrated subsystems: static converter (high frequency), and electromechanical converter (low frequency);

- These harmonics (usually, temporal ones) can generate spatial harmonics in the low-frequency structure of the electromechanical converter, which can inconvenience structural stability and is reflected, at first, in the functional instability of these converters;

- Integrated functional stability is achieved at present through an additional contribution of information, which creates a vicious circle of misunderstandings and leads to searches for new techniques and new physical control systems to relay information of increasing frequency. Of course, these structures also convey energy, but the information component is much stronger than the energy one.

In the end, we can formulate the following conclusion:

- A paradigm shift is necessary in integrated systems of modern electrical drive chains, a change that should take place starting with the electromechanical converter, so the new drive chains can achieve as much as possible of the harmony of classical chain drives which were mainly relaying energy in low frequency systems suitable for the electromechanical converter.

This paper presents the authors contribution regarding the influence of electrical power frequency quantities (voltage, current) on synchronous drives with brushless permanent magnets (Brushless DC) in terms of functionality, energy performance, and functional stability (static and dynamic stability).

II.DETERMINING GEOMETRIC DIMENSIONS AND PARAMETERS OF THE BRUSHLESS SYNCHRONOUS DRIVES (BRUSHLESS DC)

BASED ON THE DESIGN ALGORITHM AT DIFFERENT FREQUENCIES OF VOLTAGE SUPPLY

To see the effect frequency has on the potentiality of these drives, we used the class design algorithm for brushless, ferrite permanent magnet drives.

The design was done at three values of voltage frequency, 50 Hz, 100 Hz, 200 Hz (drive reference). The voltage was chosen so that the voltage-frequency dependence is linear. Thus, the specified frequencies were used following the line voltages 500 V, 400 V, 200 V (the reference drive).

Some characteristic parameters were kept constant for this class (in terms of permanent magnets), Table 1.

TABLE 1

Characteristics drive sizes Characteristics sizes Ferrite drives(FS4)

Nominal torque - NM [Nm] 10

Nominal speed [rpm] -

Nn [rot/min] 1000

Number of the stator phases, m 3 Isolation class F Protection level IP 44 Nominal power- NP [W] 1046.66

For each value of the supply voltage frequency we obtain a

different number of pole pairs. For the three values of the frequency mentioned above, we obtain the number of poles in Table 2, values determined by the relation:

N

N

nf

p60

= (1)

TABLE 2

Frequency - Nf [Hz]

Number of pole pairs, p Ferrite drives (FS4)

50 3 100 6 200 12

Following the design algorithm presented in [7] and [12],

we obtained the geometric dimensions of the drives for each voltage and frequency value, and we determined drive parameters (resistance, inductance) for losses and functional characteristics (angular characteristic and so on).

The values of interest for the comparative analysis proposed in this paper are shown in Table 3.

TABLE 3

Geometric dimensions and parameters Ferrite drive(FS4)

50[ ]Nf Hz= 100[ ]Nf Hz= 200[ ]Nf Hz=

Volume of permanent magnets, VPM [m3] 0.001893 0.000946 0.000473 Rotor diameter, Dr [mm] 204.98 162.69 129.13 Inner placement diameter of the permanent magnets, DiPM [mm] 61.49 48.81 38.74 Width of permanent magnets, bPM [mm] 71.74 56.94 45.19 Height of permanent magnets, hPM [mm] 21.45 8.51 3.38 Length of permanent magnets, lPM [mm] 204.98 162.69 129.13 Size of air gap, g [mm] 0.5 0.5 0.5 Number of stator slots, Zs 18.00 36.00 72.00 Stator pole step at level with the air gap, Sτ [mm] 107.79 42.83 17.03 Pole surface, Sp [m2] 0.017676 0.005575 0.001759 Surface of permanent magnet corresponding to a pole, SpPM [m2] 0.029411 0.018528 0.011672

Magnetic induction in air gap, Bg [T] 0.24 0.37 0.34 Magnetic flux per pole, pΦ [Wb] 0.004215 0.002054 0.000605 Step stator tooth, ts [mm] 35.93 14.28 5.68 Number of spires in series per phase, Ns 36.00 84.00 264.00 The total height of stator teeth, hs [mm] 4.00 7.00 17.00 The minimum width of stator teeth, bcsmin [mm] 26.91 8.74 3.62 Opening of the stator slot towards the air gap, b0s [mm] 16.15 5.24 2.17 Stator yoke height, hjs [mm] 14.00 9.00 4.00 Magnetic voltage drop in air gap, Umg [Asp] 140.25 193.09 170.86 Saturation coeficient, ksat 1.13 1.06 1.08 Resistance per stator phase, Rfs [ Ω ] 0.62 0.86 1.95

D-axis synchronous reactance, Xd [ Ω ] 3.51 3.24 10.11

Q-axis synchronous reactance, Xq [ Ω ] 8.85 7.83 17.25 Ferromagnetic core stator losses, PFes [W] 216.58 117.60 80.63 Induced emf per phase at rated speed, Eef [V] 23.335 53.058 98.176

The study shows that the frequency magnitudes of the

electrical gateway have a great influence on the geometric dimensions and functional parameters of electric drives (particularly, on the brushless excited synchronous motors with permanent magnets ferrite). Some remarks apply: a) increasing the frequency leads to a strong reduction of the overall size of the engine, due to the drastic reduction in the volume of the permanent magnet (4-fold reduction of the amount of permanent magnet to a 4-fold increase in frequency) b)

increasing the frequency leads to a strong increase of phase induced emf at rated speed (4-fold increase in frequency also increases 4-fold the emf). These observations lead to the following conclusions, also drawn by the literature [8], [9], [11]: using an increasingly higher frequency in modern adjustable electric drive systems is primarily aimed at drastically reducing its overall size, with an increase of its structure potentiality [2], [3].

This is possible only through the use of magnetic materials (particularly permanent magnets) and isolators with technical characteristics superior to those used previously [4], [5], [6]. Based on this assumption / trend, this paper chose to use as reference the high frequency drive.

On the other hand, the electric motor operation is strongly affected by increasing frequency. The angular feature is representative for the synchronous engine and allows viewing of its functional stability. Figures 1-3 present the angular characteristics of the designed engine for the three frequencies shown in Table 3. The engine is designed with shape anisotropy (with apparent poles). In order to get the design data characteristic as close as possible to the theoretical angular characteristics, we have used data interpolation polynomials (a 2nd degree polynomial or a 3rd degree polynomial).

It was found that the 3rd degree polynomial provides a good approximation of the real angular feature.

Fig. 1. Angular characteristic of synchronous brushless drive for an input frequency of 50 Hz

Fig. 2. Angular characteristic of synchronous brushless drive for an input frequency of 100 Hz

Fig. 3. Angular characteristic of synchronous brushless drive for an input frequency of 200 Hz

Based on figures 1 – 3, we conclude: increased input frequency into the drive leads to a drastic reduction of its overload capacity, and also to a substantial reduction in the reserve of stability (static and dynamic). Also, the maximum torque of the designed drive falls practically from 440 Nm at a frequency of 50 Hz, to only 54 Nm at a frequency of 200 Hz. Also, the nominal torque of 10 Nm is obtained for the increasingly heightened internal angle at only 10 degrees for a frequency of 50 Hz and at 22 degrees for a frequency of 200 Hz.

III. RESULTS. DISCUSSION To visualize how the frequency increase affects both size

and functional parameters of the brushless synchronous drive (brushless DC), we have studied (in Matlab) the frequency variation of the main quantities of interest (representative). The results were summarized in Table 4, and corresponding variation modes are presented in Figures 4-10. It is worth noting that the design (and the size correlation) was done following the same linear law of variation of voltage and frequency (assumption used to determine the quantities of table 3).

Thus, figure 4 presents the frequency variation of the permanent magnet volume. Figure. 5 presents the frequency variation of the rotor diameter. Frequency-caused changes in the air gap induction, respectively in the flux per pole re shown in figures 6 and 7.

40 60 80 100 120 140 160 180 200 2200.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2x 10

-3

volu

me

of p

erm

anen

t m

agne

t (V

PM

) [m

3]

frequency (f) [Hz] Fig. 4. Frequency variation of the permanent magnet volume VPM

40 60 80 100 120 140 160 180 200 220120

130

140

150

160

170

180

190

200

210

Rot

or d

iam

eter

, (D

r) [

mm

]

frequency (f) [Hz] Fig. 5. Frequency variation of rotor diameter Dr

TABLE 4

Geometric dimensions and parameters Frequency [Hz]

50 70 90 110 130 150 170 190 210

Volume of permanent magnets , VPM [m3] 0.001893 0.001352 0.001052 0.000860 0.000728 0.000631 0.000557 0.000498 0.000451

Rotor diameter, Dr [mm] 204.98 183.23 168.51 157.60 149.07 142.12 136.32 131.35 127.04

Magnetic induction in air gap, Bg [T] 0.24 0.31 0.35 0.38 0.39 0.38 0.37 0.35 0.33

Magnetic flux per pole, pΦ [Wb] 0.004215 0.003100 0.002348 0.001801 0.001392 0.001085 0.000852 0.000676 0.000542

Magnetic voltage drop in air gap, Umg [Asp] 140.25 170.44 188.12 195.94 196.56 192.29 184.93 175.79 165.80

Resistance per stator phase, Rfs [ Ω ] 0.62 0.66 0.71 0.90 0.97 1.20 1.45 1.72 2.01

D-axis synchronous reactance, Xd [ Ω ] 3.51 2.87 2.54 3.16 3.17 4.21 5.72 8.01 11.57

Q-axis synchronous reactance, Xq [ Ω ] 8.85 7.14 6.16 7.46 7.02 8.78 11.05 14.12 18.49

Ferromagnetic core stator losses, PFes [W] 216.58 155.48 124.20 113.04 94.98 88.05 83.38 84.35 81.70

Induced emf per phase at rated speed, Eef [V] 23.335 33.636 42.111 56.288 60.783 72.061 81.832 90.101 97.008

40 60 80 100 120 140 160 180 200 2200.24

0.26

0.28

0.3

0.32

0.34

0.36

0.38

0.4

0.42

Air

gap

flux

dens

ity,

(Bg)

[T

]

frequency (f) [Hz] Fig. 6. Frequency variation of magnetic induction of the air gap Bg

40 60 80 100 120 140 160 180 200 2200.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

-3

Pol

e m

agne

tic f

lux

[Wb]

frequency (f) [Hz] Fig. 7. Frequency variation of magnetic flux per pole pΦ

Figures 8 and 9 present frequency variations of magnetic voltage drop in the air gap respectively, the variation of the stator’s phase resistance.

40 60 80 100 120 140 160 180 200 220140

150

160

170

180

190

200

Air

gap

mag

netic

for

ce (

Um

g) [

Asp

]

frequency (f) [Hz] Fig. 8. Frequency variation of magnetic voltage drop of the air gap Umg

40 60 80 100 120 140 160 180 200 220

0.8

1

1.2

1.4

1.6

1.8

2

2.2

Res

ista

nce

per

phas

e (R

fs)

[ohm

]

frequency (f) [Hz] Fig. 9. Frequency variation of the stator’s phase resistance Rfs

Figures 10 and 11 present the frequency variations of the D and Q axis synchronous reactance, while Figures 12, 13 reveal changes induced by frequency changes in the iron core loss, respectively, induced electromotive force to the rated speed.

40 60 80 100 120 140 160 180 200 2202

3

4

5

6

7

8

9

10

11

12

D-a

xis

sync

hron

ous

reac

tanc

e (X

d) [

ohm

]

frequency (f) [Hz]

Fig. 10. Frequency variation of synchronous reactance on D-axis, Xd

40 60 80 100 120 140 160 180 200 2206

8

10

12

14

16

18

20

Q-a

xis

sync

hron

ous

reac

tanc

e (X

q) [

ohm

]

frequency (f) [Hz] Fig. 11. Frequency variation of synchronous reactance on Q-axis, Xq

40 60 80 100 120 140 160 180 200 22080

100

120

140

160

180

200

220

Fer

rom

agne

tic s

tato

r co

re lo

sses

(P

Fes

) [W

]

frequency (f) [Hz]

Fig. 12. Frequency variation of stator iron-core losses PFes

40 60 80 100 120 140 160 180 200 22020

30

40

50

60

70

80

90

100

Indu

ced

emf

per

phas

e at

rat

ed s

peed

(E

ef)

[V]

frequency (f) [Hz] Fig. 13. Frequency variation of phase induced emf at rated speed Eef

All studied variations highlight the significant effects of voltage frequency change on the potentiality of integrated drives with brushless synchronous motors (brushless DC).

IV. CONCLUSIONS The following conclusions can be drawn for brushless

synchronous motors (brushless DC):

- Use of materials that have adequate technical characteristics (permanent magnets, insulation, etc.) allows the increase of voltage frequency;

- Increased voltage frequency drastically reduces overall dimensions;

- For a given structure (electromechanical converter with constituent materials and topology) there is a frequency of control signals which allows operation with high induction in the air gap and, as a last resort, with specific forces (area where there is little gradient change in motor parameters, iron losses in the stator, and induced emf per phase). It is noteworthy that, for the structure of the electromechanical converter under review, in case of use of strontium ferrite magnets (medium density), their particular frequency is 120 Hz (lower to the one used as a practical reference: 200 Hz);

- Because structures have a frequency for best response and good stability reserve, it is recommended that, in practice, this analysis is done a priori to determine the optimum value of the control signal frequency (supplied by static converter) so that the integrated system (static converter - electromechanic converter) enjoys smooth operation.

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