A Novel, Single Stator Dual PM Rotor, Synchronous Machine: topology, circuit model, controlled dynamics simulation and 3D FEM Analysis of Torque Production Ion Boldea1, Marcel Topor1, Fabrizio Marignetti2, Sorin Ioan Deaconu1, Lucian Nicolae Tutelea1 1 Politechnica University of Timisoara, 2University of Cassino
[email protected],
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[email protected] Abstract-This paper introduces a novel brushless, single winding and single stator, dual PM rotor axial-air-gap machine capable to deliver independently torque at the two rotors by adequate vector control. The proposed topologies, the circuit model, controlled dynamics simulation and preliminary 3D FEM torque production on a case study constitute the core of the paper. The proposed dual mechanical port system should be instrumental in parallel (with planetary gears) or series hybrid electric vehicles (HEV) aiming at a more compact and efficient electric power system solution.
Ring Planet Engine shaft
Planet Ring ∼
I.
Driveline shaft
Motor
Generator
Sun
∼
=
=
INTRODUCTION
Vehicles equipped with internal combustion engine (ICE) have been in existence for over a hundred years. Although ICE vehicles (ICEVs) are being improved by modern automotive electronics technology, they need a major change to significantly improve the fuel economy and reduce the emissions [1]. Electric vehicles (EVs) and hybrid EVs (HEVs) have been identified to be the most viable solutions to fundamentally solve the problems associated with ICEVs [2]–[4]. Electric drives are the core technology for EVs and HEVs. The basic characteristics of an electric drive for EVs are the following [5]–[7]: 1) high torque density and power density; 2) very wide speed range, covering low-speed crawling and high-speed cruising; 3) high efficiency over wide torque and speed ranges; 4) wide constant-power operating capability; 5) high torque capability for electric launch and hill climbing; 6) high intermittent overload capability for overtaking; 7) high reliability and robustness for vehicular environment 8) low acoustic noise; 9) reasonable cost. On top of the aforementioned characteristics, the electric drive for HEVs needs additional ones as follows [8]–[10]: 1) high-efficiency generation over a wide speed range; 2) good voltage regulation over wide-speed generation.
a)
Windings
PMs Slip rings Engine shaft
Driveline shaft
∼
∼ =
=
b) Fig. 1. e-CVT existing systems a) with planetary gears (Toyota Prius); b) integral-electric (in proposition).
With the advent of high-energy permanent-magnet (PM) materials, PM motors are becoming more and more attractive. Being continually fueled by new machine topologies and control strategies, PM brushless (BL) drives have been identified to be the most promising to provide the aforementioned characteristics for modern EVs and HEVs [11].
Power battery Electric Generator
ICE
AC/DC Converter
DC/AC Bidirectional PWM Converter
Electric Propulsion Motor
Drive line
Fig. 2. Typical series HEV dual electric machines existing system.
Hybrid electric vehicles (HEV) are considered the way of the future for automobiles [1], to reduce energy consumption and air pollution. A key problem with HEV is the electric propulsion corroboration with the thermal engine (ICE) such that the latter is allowed to operate close to the sweet point (torque and speed for maximum efficiency or minimum emission) indifferent to the vehicle speed [12]. A so called continuously variable transmission (CVT) is to be obtained. Figure 1 identifies two existing e-CVT solutions for parallel HEVs (one commercial and one still a proposition) with two electric machines and two inverters one with planetary gears and one without it but the latter with full power slip-ring brush transfer instead [1]. A distinct electric generator and a propulsion electric motor, both with full power converters are typical for a series HEV (fig. 2). Ring Planet
ICE
NS slots with Gramme-ring AC coils
2p1 PM pole rotor
To drive line
Sun
Internal combustion engines, regardless of fuel type (gasoline, diesel, hydrogen), operate most efficiently at midrange speeds and high torque levels. It is one goal of the eCVT to match the vehicle road load to this engine optimal operating regime [12]. The present paper proposes a new, dual PM rotor SM drive with basically single stator and dual rotor with different pole counts and high winding factors, to reduce volume, weight and cost in either planetary-gear parallel HEV or in series HEV. It is organized as follows: Section 2: proposed dual PM rotor machine topology, Section3: the dual PM rotor single stator phase coordinate model, Section 4: dual frequency tooth- wound winding particularities, Section 5: mathematical model for (and) 3DFEM analysis, Section 6: torque production by 3D FEM, Section 7: proposed dual vector control and dynamic simulations, Section 8: conclusions. II.
PROPOSED DUAL PM ROTOR MACHINE TOPOLOGY
In an effort to simplify the planetary-geared e-CVT (Fig. 1a) for the parallel HEV or the series HEV (Fig. 2) we hereby propose to replace the basically two electric machines and their two power converters by a single axial-air-gap electric machine central stator, fed from a single PWM converter with dual frequency voltage output (V1(f1), V1(f2)) and two independent PM rotors with 2p1 and 2p2 poles placed on the sides of the central stator with Ns slots and a tooth-wound (or Gramme) winding (Fig. 3). The mixture of 2 frequencies in the inverter output voltage (with corresponding phase angles) leads to two different speeds ωr1 and ωr2 in the two rotors and different positive (or negative) torques as required.
2p2 PM pole rotor
S
N Single inverter with two frequency control
Clutch
SMC material
2
1
10
Battery
N S
N S
S N
5
PM rotor 2 2p’1 = 14 poles
Differential
PM rotor 1 2p1 = 10 poles
a)
b) SMC material (core)
1
Back iron magnetic field
C hcs
To “sun” gear shaft
Battery
b) Fig. 3. Proposed e-CVT with single electric machine stator and inverter a) for planetary geared parallel HEV; b) for series, HEV.
Mechanical clutch to engage ICE mechanically directly (the bidirectional dual switch in fig. 5f is turned off)
12
bearings To drive line shaft
A’
3 B
10 B
4 B’ × C A
8
A’ 7 NS = 12 slots
c)
2
×
9 B’ Through Gramme-ring winding
A
AC coils
11 C’
Power filter AC-DC Bidirectional inverter with two frequency control
S
N 6
7
Wheel
N
S
S
N
8
Transmission 4:1
S
N
Wheel
ICE
N
N
4
S 9
S
N S
S
Power filter
a)
SMC material section for easier flux weakening
3 N
C’
6
5
to power inverter
winding 2
winding 1
dual bidirectional static switch
d) 1
2
2 1
3 A’ C’
12
A
A
C
C
A’ B
11
4 C’ B’
5
B B
B’ B’
B C
10
B’ A C’ C’
6
A’ A’ C A
9
Though there will be ω2 - ω1 torque pulsations from one frequency (rotor) to the other, the torque stress on the stator will be reduced when one rotor is motoring and one is generating. The proposed e-CVT topology in detail is presented in figure 4. Though fig. 4 is rather self-explanatory, here are few remarks: - though the stator core magnetic circuit SMC material is suggested, a rolled-lamination magnetic core is also feasible, especially for the case of “non through” coils; the same rationale is valid for the rotor magnetic core. - either “through” or “non through” coil shapes may be adapted; it seems that if the number of coil turns is small, “non through” coils may be mounted easily. - it may be, however, possible to adopt double layer coils along tangential direction with opposite polarity on the two stator axial sides (fig. 4d). In this case a dual TRIAC switch might be used to disconnect one half winding when only (typical to average vehicle speeds) motoring or only generating is needed with one rotor only. The stator m.m.f. flux lines in the stator close circumpherentially in the back iron to avoid severe flux fluctuation in the two rotors, besides the PM flux fluctuation effects from one rotor to the other (2p1 ≠ 2p2), which should be small for surface PMs.
7 8
e) Fig. 4. Dual PM rotor (10 poles/14 poles) axial air-gap single stator (12 slots) PMSM proposed typical topology a) 10 PM poles rotor with SMC back iron and small-air-gap SMC zone for flux weakening; b) 14 PM poles rotor with SMC back iron c) SMC stator with machined slots and Gramme ring (“through”) AC coils; d) opening half of the winding in fig. 4e; e) two layers “non-through” coil winding.
Both frequencies voltages and their currents travel the whole single stator winding coils sides, though only the left side (in fig. 3) produces torque at ωr1 speed and only the right side interacts to produce torque at ωr2 speed. This implies additional copper losses in the stator but if the end connections are kept small, part of this inconveniency is removed. On the other hand, the single inverter has to handle the entire apparent power related to the interaction of stator magnetic fields with both rotors at different speeds. Only when the two frequency are equal (and electric rotor speeds related by ωr1 = ωr2 (n1p1 = n2p2), a direct transfer of power directly through the winding, for say, one motoring and one generating operation modes, seems to be possible. Apart from the evident simplification and compactness of the proposed solution, attempts to reduce somewhat the inverter power rating based on motor/generator simultaneity are worth trying.
Fig. 5. Proposed configuration cross section
Fig. 6. Proposed configuration exploded view
The actual mechanical configuration is presented in figure 5. As one may notice the dimensions of the mechanical assembly are sensibly shorter than the radial configuration proposed in [13]. This is due the fact that the axial flux permanent machines with double rotor and single stator has smaller axial length than the corresponding solution with radial flux, for given larger than 6 number of poles and diameter, as it is mentioned in reference [14]. Figure 6 shows the two rotors with different number of permanent magnet poles. The different number of poles may impose a rather different amount of permanent material but if we select the arc pole ratio adequately it is possible to use the same amount of permanent magnet material on both rotors.
kdiff 1,2 – differential leakage inductance coefficients for the rotor with 2p1 and respectively 2p2 poles (which is known to be large in tooth-wound windings because the stator m.m.f. is rich in space harmonics). The e.m.f. per phase, produced by PMs is: N E1,2 abc = ωr 1,2 ⋅ φ PM 2 p1 (2 p2 ) ⋅ k w1 ⋅ S ⋅ nc ⋅ 6 . (5) 2π π ⎤ ⎡ ⋅ cos ⎢θ er 1,2 − (i − 1) + ⎥ 3 2⎦ ⎣ With ⏐LS⏐ a diagonal matrix with constant terms, the matrix stator voltage equations are straight forward: d iabc ⋅ RS − Vabc = − LS iabc − E1 abc + E2 abc , dt III. THE DUAL PM ROTOR SINGLE STATOR PHASE p (E ⋅ i + E1b ⋅ ib + E1c ⋅ ic ) J dωr 1 COORDINATE MODEL ⋅ = 1 ⋅ 1a a − T1 load , (6) p1 dt 2 ωr 1 The stator phase supply voltages Vs a b c contain 2 frequencies J dωr 2 p 2 (E 2 a ⋅ i a + E 2 b ⋅ i b + E 2 c ⋅ i c ) − T2 load . ⋅ = ⋅ Vs a b c = Vs*1 cos θer1 + γ 1 + Vs*2 cos θer2 + γ 2 , (1) p 2 dt 2 ωr 2 dθer1 dθer2 = ωr 1 , = ωr 2 , (2) IV. DUAL FREQUENCY OPERATING WINDING dt dt The three-phase winding could be characterized by its π π (3) γ 1 = + δ v1 , γ 2 = + δ v2 , number of slots per pole and phase. This is given by the 2 2 where δv1, δv2 are the voltage power angles (positive for following relation: NS q motoring, negative for generating); θer1, θer2 rotors 1 and 2 (8) q= = c , electrical position angles (PM rotor axes). m2 p qd The small SMC rotor pole parts (with some anisotropy) (Fig. where N stator slots, p pole pairs and m is the number of S 4a) are used to facilitate PM flux weakening and also to phases. facilitate rotor position estimation in case of sensorless control. Solely, q can not fully characterize a winding, since the q Let us neglect here the small rotor saliency (left in the parameter does not take into account the number of layers the rotors SMC pole section for easier flux weakening) and winding has. For this reason the number of coils per pole and discuss first the Gramme ring winding case. The total phase phase q should be defined. For a machine the following c inductance LS (considering both rotors with all phase coils in definitions hold: series) are rather straightforward (as for constant air gap AC N q (9) qc = C = cn , machines): m 2 p qcd ( N S ⋅ nc ⋅ k w1 / 3) LS ≅ 6 ⋅ 2 ⋅ where NC – number of coils. π ⋅ g m (1 + k S ) ⋅ k c In our case the winding for each side of the stator is a 1 + k diff 2 ⎤ ⎡ 1 + k diff 1 double layer winding qc = q = 0.40 for the 10 poles side, and ⋅⎢ + ⎥ + Lls + LlEC , (4) qc = q = 0.29 for the 14 poles side. p1 p2 ⎣ ⎦ The winding layouts can be represented by means of two (N ⋅ n / 3) ⋅ lcoil ⋅ j RS = ρ co ⋅ S c , matrices as in [15]. First matrix will contain information on co rated I rated the ingoing coil sides of the coils while the second matrix of g m = g + hPM , the outgoing coils sides. The matrices are referred to as M1 and M2 for the ingoing and outgoing coil sides respectively. with Lls – slot leakage inductance; Both matrices have n columns and m rows. In addition, the LlEC – end connection inductance; number of columns equals the number of stator slots and the ρco – copper resistivity; rows are equal to the number of phases, thus m = 3 and n = NS – number of stator slots; N . The matrices can be expressed as: nc – number of turns/coil; S ' ' lcoil – coils length; ⎡ m11 m1n ⎤ ⎡ m11 m12 m12 m1' n ⎤ ⎢ ⎥ ⎢ ⎥ g – air gap; m21 m22 m2n ⎥ m'21 m'22 m'2n ⎥ ⎢ ⎢ M , M = = , (10) hPM – PM axial thickness; 1 ⎥ ⎢ ⎥ 2 ⎢ RS – stator phase resistance; ⎢ ' ⎥ ⎢ ⎥ ' mmn ⎦ m'mn ⎦⎥ jco rated – rated copper current density; ⎣mm1 mm2 ⎣⎢mm1 mm2 Irated – rated current;
(
(
)
) (
(
)
)
where mij and mij' are 1 (for the ingoing coils) or -1 (for the outgoing coils) if the n phase is placed in the m slot; otherwise it is zero. The winding in matrix form is very compact and has advantages in machine analysis [16]. The matrix contains all the information of the winding arrangement in the stator slots. This allows the construction of the voltage phasor which is necessary to calculate the winding factor. In addition, the slot m.m.f. can be obtained from the column data. The properties of the matrix are summarized as follows: - if the winding is symmetrical, the number of assigned elements in all rows are equal; - the number of columns is equal to the number of stator slots; - the number of rows is equal to the number of phases; - for a single layer winding there is only one nonzero element in a column; - a double layer winding has two nonzero elements in a row; - the matrix is valid for both a fixed and variable slot pitch. The winding matrix is used to calculate the winding factor and the slot m.m.f. A vector is assigned to the centre of each stator slot (fig 7). The exponential representation of a vector is used, i.e.: e jνα = cos(να ) + j sin(να ) . (11) The variables ν and α are the harmonic order and slot peripheral angle, respectively. All the vectors as shown in are represented as a column matrix vν. The number of rows is equal to the number of slots, i.e.
vν = ⎡e jνα1 ⎣
e jνα n 2
… e
jνα N S
⎤ ⎦
T
1 ≤ n2 ≤ N S .(12)
With M1 and M2 assigned, the winding factor for any harmonic can be calculated as the product between the matrices and the slot vector as given in [17]. This means that a row of the winding matrix is multiplied by the slot vector column matrix. The matrix product means that all the vectors
belonging to the same phase are added where the α accounts for both regular and irregular distributed stator slots. The winding factors for the two sides (12- slots 10 poles) and (12 slot -14 poles) windings results as ξ1 = 0.966 for the first and for the second side. The matrix product means that all the vectors belonging to the same phase arc added and for the case ν = p equals
(m
1,i1
(
+ m2,i1 ) e jpα1 + ( m1,i 2 + m2,i 2 ) e jpα 2 + …
)
+ m1,iN S + m2,iN S e
jpα N S
.
The prototype stator to be built 12 slots with 5 pole pairs for one side and 7 pole pairs on the other side. This is a double layer winding and the number of slots is equal to the number of coils. Both q and qc and the basic winding has 6 slots. The lowest harmonic has 5 pole pairs which is the same as the working harmonic. Therefore, the winding has no subharmonics as it is presented in figure 10 and 11 where kd is distribution factor, kp is pitch factor, ks is skewing factor and k1 is winding factor. The matrix elements of the basic winding are: ⎛0 1 0 0 0 0 1 0 0 0 0 0 ⎞ ⎜ ⎟ M1,b = ⎜0 0 0 0 0 1 0 0 0 0 1 0 ⎟, ⎜1 0 0 0 0 0 0 0 0 1 0 0⎟ ⎝ ⎠ (14) ⎛−1 0 0 0 0 0 0 −1 0 0 0 0 ⎞ ⎜ ⎟ M2,b = ⎜ 0 0 0 0 − 1 0 0 0 0 0 0 − 1⎟, ⎜ 0 0 0 −1 0 0 0 0 0 0 −1 0 ⎟ ⎝ ⎠ the absolute value of the winding factor as a complex number is [17]:
ξν =
3 [ M 1vν + M 1vν ] ∈ C . 2 Nc
Fig. 8. Coil placement in slots. αn = 150
o
Fig. 7. The voltage vector graph of the 12 slot 10 pole nonoverlapping winding.
(13)
Fig. 9. Winding Configuration used for simulation.
(15)
lower over-all outer diameter of the frame. However the total synchronous inductance is not small due to the rather large differential leakage components attributed. Because we have a different pole number for each side, the resulting m.m.f. harmonics will be different as it can be seen from figures 10 and 11. The 10 pole and 14 pole, however, have the same winding factor for a 12 slot stator (this fact is present also in several papers both for axial flux and radial flux machines [14]). The two rotor machine is supplied from a single inverter supply. The machine winding is assumed to be star connected with no neutral connection. Therefore the six current components should add up to zero. V.
MATHEMATICAL MODEL FOR ( AND ) 3D FEM ANALYSIS
For a three-phase machine the flux linkages can be expressed in matrix form as: ⎡ ψ 1 ⎤ ⎡ L11 L12 L13 ⎤ ⎡i1 ⎤ ⎢ψ ⎥ = ⎢ L ⎥⎢ ⎥ (17) ⎢ 2 ⎥ ⎢ 21 L22 L32 ⎥ ⎢i2 ⎥ , ⎢⎣ψ 3 ⎥⎦ ⎢⎣ L31 L32 L33 ⎥⎦ ⎢⎣i3 ⎥⎦ where L11, L22, L33 represent the self-inductance of each phase. The off-diagonal terms in the matrix represent the mutual inductances between the phases. In order to identify by FEM the self- and mutual inductances, the following two steps need to be executed: 1. A nonlinear magneto-static solution is generated with the sources at values for a given operating point. This establishes the permeability that varies with each mesh element, because of the variable saturation throughout the machine. 2. In the second step one ampere is applied to a phase and zero to the remaining phases. A linearized solution (using the saved permeability from the first step) is performed to calculate the self-inductance of the phase where one ampere is flowing. This procedure is repeated for each of the phases. For each of the solutions as described here, the remnant flux density in the permanent magnets is set equal to zero. This means that the flux linkages as a result of only the currents are taken into account. The self-inductances are calculated as follows:
Fig. 10. Side 1 winding MMF.
Fig. 11. Side 2 winding MMF.
The ampere-turns in each slot can be obtained from the matrix winding columns. Since the matrices M1 and M2 contain the coil side information for the ingoing and outgoing coil sides respectively, the total ampere-turns of a coil side is the product of its value in the winding matrix with the number of coil turns nc. For a three-phase winding the slot m.m.f. Fslot of the kth slot is calculated as: Fslot ,k = N t ∑ in (m1,1k + m2 ,1k ) . 3
n =1
L11 = l Fe ∫S B 1 H 1 da (i1 = 1,i2 = i3 = 0 ) L22 = l Fe ∫S B 2 H 2 da (i2 = 1,i1 = i3 = 0 ) ,
(18)
L33 = l Fe ∫S B 3 H 3 da (i3 = 1,i1 = i2 = 0 ) where the remnant flux density of the permanent magnet is Br=0 and μ = μ saved . In order to calculate the mutual inductances the solutions for B and H must be saved. (16) The mutual inductances are then calculated as:
The windings of the sides are the same since the stator is double sided. On each side we have a double layer nonoverlapping winding with tooth concentrated coils as it can be noticed in figs. 8 and 9. The tooth-wound coils have short end connections and thus end-up in lower copper losses and
⎧Bi due to current in the i th phase ⎪ th ⎪ Lij = lFe ∫S Bi H i da where ⎨H j due to current in the j phase.(19) ⎪i = j ⇒ self − inductance ⎪i ≠ j ⇒ mutual− inductance ⎩
Table I. Parameters and machine dimensions machine Frequency (f) Number of poles rotor 1 (2p) Number of poles rotor 2 (2p) Current density (Js) Air-gap length (g) Pole-arc-ratio rotor 1 (αi1) Pole-arc-ratio rotor 2 (αi2) Outer diameter (Do) Inner diameter (Di ) Slot depth (hss) Axial length of stator core (hcs) Axial length of rotor core (hcr) Magnet axial length (hPM) Permanent magnet material
50 Hz 10 poles 14 poles 4.33 A/mm2 1 mm 0.6944 1 300 mm 180 mm 30 mm 90 mm 10 mm 5 mm NeFeBr40
1.5 Airgap 1 (10 pole rotor -stator) Bn [T] Airgap 2 (stator -14 pole rotor) Bn [T]
1.0
Normal Flux desity Bn [T]
A complete 3D FEA model has been developed to yield reasonable predictions of the torque quality and 3D field distribution of flux density for the proposed configuration. Only a full 3D Finite Element Analysis (FEA) can accurately analyze the complex geometry models involving permanent magnets of any shape and material [18]. However this requires a large amount of computation power. There is no need to calculate the reluctances and inductances using circuit type analytical methods since these values can simply be extracted from the finite element analysis as inferred above. One important advantage of using FEA is the ability to calculate the torque variations such as cogging torque, ripple torque and total torque for various rotor positions. The main purpose of this analysis is to find out torque in the proposed axial flux machine using 3D field analysis method. The principal parameters of the model are given in table I.
0.5
0.0
-0.5
-1.0
-1.5 0
20
b)
60
80
100
Airgap Length for R=240 mm
140
160
[mm]
A full scale model using a commercial software is built for the 3D nonlinear magneto-static solution. Using a full scale model with an average mesh of 500 000 nodes the flux density solution was obtained. The flux density vectors are presented in figure 12 for the main parts of the machine. Figure 13 shows the PM air-gap flux density of the machine. It can be seen from the plot that maximum air-gap flux density is nearly 0.8T and the average air-gap flux density is 0.55 T. It can also be noted from the air-gap flux density plot that the flux density becomes greater at the edges of the magnets because of the fact that the leakage flux between the magnets gains importance and causes some concentration of flux. 3D FEM TORQUE ANALYSIS
In general, the total torque of a PM machine has three torque components: average torque, ripple torque and cogging torque. Since the considered prototype has a slotted topology, pulsating torque comprises both cogging and ripples torque components. The two output torques for constant amperturns (3744 Aturns per slot) is presented in fig 14. The torque for each rotor was computed by means of Maxwell stress tensor for each rotor separately. As the calculations in fig. 14 have bean done at standstill with DC currents the torque pulsations created by one frequency voltage in both rotors are not yet visible.
c) Fig. 12. The flux density vector in: 10 pole rotor a) central stator b) full machine c).
120
Fig. 13. No load air-gap flux density variation from finite element analysis.
VI.
a)
40
Fig. 14. 3D Analysis torque for the two rotors.
Fig. 15. Cogging torque from 3D analysis.
The cogging torque may affect the torque quality of the permanent magnet machines. In our case the two rotors are decoupled one from each one. We have analyzed the cogging torque by rotating each rotor simultaneously and we have evaluated the torque in the central stator. The resulting cogging torque presented in figure 15, is the summation of the two cogging torques produced by each rotor which obviously do not overlap. It is fairly small. VII.
PROPOSED VECTOR CONTROL STRATEGY. DYNAMIC SIMULATION
The proposed dual vector control strategy is illustrated in fig. 16, for the speed control mode. The objective of the dynamic simulation is to evaluate the dynamic and steady state operation of the dual vector control algorithm using two frequency modulation operations. Fig. 16 illustrates in fact an indirect DC current control vector control strategy with open loop (voltage) PWM strategy after rotor coordinates transformations at and back for ωr1 and ωr2. The PI + SM speed and current controllers (with chattering elimination by the addition of a PI signal applied to the sliding mode functional which is active only close to the target) provide for robust control without e.m.f. compensation, so usual with DC current regulators. Based on machine circuit model in paragraph 3, the dual vector control strategy dynamic behavior is simulated here via a dedicate Matlab Code. The complete sets of parameters used in simulation are given in table II.
Fig. 16. Generic dual vector control strategy.
Table II Dual vector control drive system parameters Motor Parameters Phase Resistance 2.87Ω Phase inductance 8.50E-003H Rotor PM flux 1 0.18 Wb Rotor PM flux 2 0.13 Wb Pole pairs rotor 1 5 Pole pairs rotor 2 7 Inertia (including reduction of translating mass) 0.018kgm2 Power (rotor 1) 2.5kW Power (rotor 2) 1.7kW IGBT Inverter Snubber resistance 1.00E+005Ω Ron 2.00E-004Ω Tf 1.00E-006s Tt 2.00E-006s Control parameters of PI controllers controller 1 Kp speed 1 Ki speed 1 Kp current 0.06 Ki current 0.3 Controller 2 Kp speed 1 Ki speed 5 Kp current 0.06 Ki current 0.3
Load step at 1s
Fig. 17. Rotor 2 speed for startup (0 -110rad/s) with load variation (from no load to 15 Nm) at 1s and three phase currents.
Fig. 18. Torque of rotor 2 operating motor mode.
REFERENCES [1]
Fig. 19. Torque of rotor 1 operating in generator mode at 1500 rpm.
The case evaluated is the drive startup behavior for rotor 2 with the speed ramp from 0 to 1000rpm at no load with a step load of 20Nm at t = 1s. Rotor 1 is driven by the IC engine in controlled generator mode (-30N⋅m). The fig. 17 is presenting the inrush current for the startup of rotor 2 and the machine current for the 15 Nm step load which occurs at 1s from startup. The torque for rotor 2 at startup and step load is present in figure 18 and negative (generating) torque of rotor 1 in fig.19. The torque pulsations (of the two frequency current m.m.f.s. in the two rotors) are mild in this particular case but not so for all situations. VIII.
CONCLUSIONS
In this paper, a drive system to produce dual, independent, electromechanical torque output using an axial-air-gap machine with a single stator and winding and two different PM rotors has been introduced in terms of topologies, circuit model, control method, and preliminary 3D-FEM torque production analysis. A rather extended simulation for two cases was considered (steady state and dynamic). The dual vector control for the independent rotors with one common stator is presented and proven to be effective. These preliminary results prove the concept quantitatively but further studies, which are already under way, in relation to prototyping, dynamic model, control and optimization design are needed to fully prove the practicality of the proposed system.
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