An Open-Loop Operation Strategy for Induction Motors Considering ...

IEEE PEDS 2015, Sydney, Australia 9-12 June 2015

An Open-Loop Operation Strategy for Induction Motors Considering Iron Losses and Saturation Effects in Automotive Applications Oliver Wallscheid1, Michael Meyer2, Joachim B¨ocker1 1

Power Electronics and Electrical Drives, University of Paderborn, D-33095 Paderborn, Germany 2 Volkswagen AG, D-34219 Baunatal, Germany Email: [email protected], [email protected], [email protected]

Abstract— Induction motors (IM) are suitable traction drives for electric vehicles (EV). In comparison to permanent magnet synchronous motors (PMSM) the lack of power and torque density can be compensated by inferior production costs and a greater level of robustness. However, IM have to be operated at maximum efficiency since the amount of stored energy is still very limited in automotive applications and the driving energy demand is directly related to costs. To generate a certain torque with minimum losses a precise motor model considering the impact of saturation effects as well as iron losses is required. To consider these nonlinear effects a lookup table (LUT) based open-loop operation strategy (OS) in the rotor flux-oriented coordinate system is proposed. The presented approach allows a smooth transition between the constant torque and the flux weakening area as well as a high level of voltage utilisation above base speed. The LUTs can be generated offline using a maximum efficiency (ME) strategy based on finite element analysis or measured motor data. Efficiency enhancements in the range of 0.1-0.2 % for a 60 kW IM in contrast to the classical minimal copper losses (MCL) strategy can be achieved.

I. I NTRODUCTION Induction motors (IM) with squirrel-cage rotor can be used as an cheap and robust alternative to permanent magnet synchronous motor (PMSM) based traction drives in electric vehicles (EV), since the installation space requirements are not as strict as in hybrid electric vehicle [1], [2]. Due to the limited energy storage in automotive applications the installed motor has to be operated with minimum losses in the complete operation area. Since traction drives have to be highly utilised with respect to volume and weight nonlinear saturation and iron loss effects have to be taken into account. This contribution proposes a lookup table (LUT)-based operation strategy (OS), which represents one suitable way to consider these effects. Furthermore, any OS approach for EV have to be implemented in an open-loop manner, since the torque and the electrical power cannot be measured during operation due to cost and constructional reasons. Hence, an extended LUTbased IM model is used which can be parametrised offline with the help of extensive laboratory measurements or finite element analysis (FEA) calculations. This model will be the basis for an efficiency-optimal operation point selection in the fundamental wave domain regarding the constant torque as well as flux weakening area with a smooth transition between them. Moreover, a voltage controller guarantees maximum voltage utilisation in the flux weakening area to overcome the problems of fluctuating DC-link voltage (e.g. battery state

of charge) and varying motor parameters (e.g. temperaturedependent resistances). II. M ACHINE M ODEL In Fig. 1 the IM equivalent circuit diagram in an arbitrary coordinate system K is depicted [3], [4]. Here, underlined symbols denote complex quantities and superscripts represent the actual coordinate system. Furthermore, it should be noted that the iron losses are modelled by a frequency-dependent resistance Rf e . That resistance is located in parallel connection to the main inductance Lm , which is a function of the magnetizing current im to consider saturation effects. Both parameters can be identified due to experimental measurements or FEA and stored into LUTs to increase the model accuracy [5]. The identified Rf e curve for the investigated prototype motor is shown in Fig. 2. Furthermore, the stator and rotor stray inductances Lσs and Lσr are considered constant. In the following the K coordinate system shall be aligned to the rotor flux: ψrd = ψr = |ψ r |

(1a)

ψrq = 0

(1b)

The flux linkage differential equation is then given by: dψ ks dt dψ kr

= uks + jωsk ψ ks − Rs iks

(2a)

(2b) = jωrk ψ kr − Rr ikr dt Here, ψ s and ψ r are the stator and rotor flux, us is the stator voltage, ω is the angular frequency between two given coordinate systems, Rs and Rr are the stator and rotor iks

Rs

Lσr

Lσs ikf e

uks Rf e (ωks )

ikµ

Rr

ikm Lm (|ikm |)

jωrs ψ kr

jωks Lm ikm

jωsk ψ kσs

jωsk ψ kσr

Fig. 1. Equivalent circuit diagram in arbitrary K-coordinates

c 978-1-4799-4402-6/15/$31.00 2015 IEEE

ikr

operations with respect to maximum efficiency as well as to the drive system operation limits (e.g. current and voltage constraints). It is also responsible for a smooth transition between the constant torque (CTA) and the flux weakening area (FWA). To guarantee maximum voltage utilisation as well as save operation at the voltage limit (voltage reserve for current control), the DC-link voltage is measured, since it can vary significantly in automotive applications (e.g. due to battery state of charge).

Rf e /Rs

4000 3000 2000 1000

udc

0

0

1200 1800 2400 3000 3600 4200 ωks in s−1

600

T∗

∗ ψr,lim

OS

i∗d ψr & T ∗ Control iq

∗ Tlim

Fig. 2. Normalized function Rf e (ωks ) received through FEA calculations

iabc

(3)

(4)

Hence, the torque is given as [3], [6]: T =

3 Lm ψrd (isq − if e,q ) p 2 Lr

(5)

The motor losses can be separated into copper losses in the stator and rotor   3 L2m 2 2 Pv,Cu = Rs isd + (Rs + Rr 2 )isq (6) 2 Lr as well as iron losses Pv,F e

3 ωks Lm |ikm | = 2 Rf e


2

(7)

Thus, the overall losses Pv = Pv,Cu + Pv,F e

= ≈

uabc

εˆks Flux Observer

IM ωme

Fig. 3. Rotor flux-oriented control structure

The OS structure is shown in Fig. 4 and will be briefly explained: For operating the IM at maximum efficiency, a loss-minimal combination of isd and isq for a given torque is calculated by solving the Lagrange multiplier equation: h i i h ! ∂Pv ∂Pv ∂T ∂T ∇Pv = ∂i = λ∇T (9) = λ ∂i ∂i ∂i sq sd sq sd This leads to suitable (fundamental wave) steady-state operation points in the constant torque area (CTA) which are depicted in Fig. 5. Since the motor losses are frequencydependent, (9) has to be evaluated for different motor speeds. For implementation purpose, the absolute rotor flux values for the found operation points in the stator current plane are calculated and are shown in Fig. 6. It is obvious that the loss-minimal amount of rotor flux for a given torque ∗ ψr,opt (T ∗ , ωks ) decreases with increasing motor speed n due to the impact of iron losses. For operating at higher speeds

(8)

and the torque become frequency-dependent, which have to be considered in the maximum efficiency OS.

udc |u∗s |

∗ ψr,max

ωks

III. O PERATION S TRATEGY The operation strategy (OS) is embedded in a rotor fluxoriented control structure, which is depicted in Fig. 3. The general LUT-based framework was first introduced in [7] for PMSM drives. Subsequently, it is adopted for IM applications. In contrast to the most other industrial applications a superimposed speed control loop is not required, since the desired torque for EV is stated by the actual accelerator pedal position. However, safety and comfort functions (e.g. active damping of drive trains oscillations [8]) can be superimposed on the torque OS. Its purpose is to select a suitable combination of reference torque and rotor flux values for steady-state

Voltage Control

∗ ψr,opt (T ∗ , ωks )

min

ikr + iks Lm 1 + jωks R fe

ψˆr

ω ˆ ks

Therefore, the effective magnetising current is directly depending on the frequency as well as on the iron loss resistance (assume dikm /dt = 0): ikm =

sa sb PWM s c ia ib ic

resistances, and j is the imaginary unit, respectively. In this modelling approach the sum of rotor and stator current iµ is not equal to the magnetising current im due to the presence of the iron loss resistance Rf e : ikr + iks = ikµ = ikf e + ikm

ua Current ub Control uc

∗ ψr,lim

ωks

∗ ∗ Tlim (ψr,lim , ωks )

T∗

∗ Tlim

Fig. 4. Structure of the LUT-based operation strategy (OS)

the voltage limitation has to be taken into account. Hence, the Lagrange multipliers are used to find operation points with minimal voltage demand for a given torque in steady-state

operations: ∂|us | ∂isd

∂|us | ∂isq

i

!

=λ

h

∂T ∂isd

∂T ∂isq

i

= λ∇T

The found operation points are depicted also in Fig. 5. They constitute the maximum torque which can be realised for a given voltage constraint. Note, that at the boundary points of the CTA and FWA lines the maximum positive respectively negative torque is produced. For implementation purpose in the rotor flux-oriented control structure the function of the maximum achievable torque for a given rotor flux amount ∗ ∗ Tlim (ψr,lim , ωks ) along the FWA line is calculated and is shown in Fig. 7. Here, the motor speed respectively frequency has only a minor impact for high torque values. Note also, that the gray-shaded area in Fig. 5 contains all suitable steady-state operation points in the stator current plane for the complete torque and speed range. 1

0.9

(10)

0.8 ∗ ψr,opt /ψr,max

∇|us | =

1

h

0.7 0.6 0.5 0.4 0.3

0 min−1 3000 min−1 6000 min−1 9000 min−1 12000 min−1

0.2 0.1 0

−1

−0.5

0 T ∗ /Tmax

0.5

1

Fig. 6. Efficiency optimal rotor flux as a function of T ∗ and n in the constant torque area (CTA)

Tmax

1

0.8

0.8 0.6

0.6

0.4 ∗ Tlim /Tmax

0.4 n

isq /is,max

0.2 0

0 min−1 3000 min−1 6000 min−1 9000 min−1 12000 min−1

0.2 0 −0.2 −0.4 −0.6

−0.2

−0.8

n −0.4

−1 0

−0.6 −0.8

Tmin

is,max CTA FWA

−1 0

0.2

0.6 0.4 isd /is,max

0.8

1

Fig. 5. Selection of operation points in the stator current plane

The functional principle of the OS in Fig. 4 can be summarised as follows: For the actual reference torque T ∗ the ∗ efficiency-optimal absolute rotor flux ψr,opt is provided by the first LUT. Next, this value is compared with the maximum fea∗ sible rotor flux ψr,max calculated by a superimposed voltage controller. This controller is typically of PI-type and computes the allowed rotor flux maximum by comparing the current control output voltage |u∗s | to the actual DC-link voltage udc . Here, a safety margin regarding the maximum voltage utilisation should be considered to guarantee the functionality of the inner control loops with respect to disturbances and transient operations. Since the focus of this contribution lies on the steady-state selection of suitable operation points details of the voltage controller design are not discussed. For ∗ more details on this topic [9] is recommended. If ψr,opt is ∗ smaller or equal to ψr,max the IM is operated with maximum efficiency in the CTA, otherwise the rotor flux has to be ∗ reduced to ψr,max to satisfy the voltage limitation in the FWA.

0.2

0.4 0.6 ∗ /ψr,max ψr,lim

0.8

1

∗ and n in the flux Fig. 7. Maximum feasible torque as a function of ψr,lim weakening area (FWA)

∗ ∗ In this case the second LUT Tlim (ψr,lim , ωks ) may reduces the reference torque, if T ∗ cannot be realised within the actual operation limits. Therefore, the proposed OS structure allows a smooth transition between CTA and FWA and the output ∗ ∗ quantities Tlim and ψr,lim can be realised safely within the current and voltage limitation. It should also be noted that the proposed method does not cause any additional time delay since all time-consuming numeric computations are done in the control design phase. This is particularly important since the torque dynamics may be reduced in low load cases due to the reduced rotor flux in combination with the typically large rotor time constant. Moreover, the OS’s scope is not limited to field-oriented control schemes and thus it can be used in direct torque control approaches without any further adjustments. For Rf e = ∞ the proposed ME strategy becomes the classical minimal copper loss (MCL) strategy neglecting the iron losses [10], [11]. If additionally Rr = 0 is assumed, the proposed approach can be simplified to the maximum torque per current (MTPC) strategy [12]. Here, it should also be mentioned that the MTPC strategy is often called ’maximum torque per ampere (MTPA)’ strategy in literature which is inherently wrong, since a

1 1.8 0.8

20 0

0.4 0.2

1.0

0

0.8

−0.2 −0.4

0.6

−0.6

0.4

−0.8

0.2

∆η in %

1.2

∆Pv in W

1.4

Pme in kW

1.6

0.6

T /Tmax

40 v in m/s

physical quantity (torque) cannot be compared meaningfully with a dimensional unit (ampere).

0

50

100

150

200

0

50

100

150

200

0

50

100

150

200

0

50

100 150 t in s

200

20 0 −20 0

−100 −200

−1

0 0

2/12

4/12

6/12

8/12

10/12

1

2 ∆η in %

nme /nme,max Fig. 8. Difference of efficiency in the torque-speed-plane between ME- and MCL-strategy (∆η = ηM E − ηM CL )

1 0

ANALYSIS FOR

EV

The proposed operation strategy was investigated for a 60 kW IM prototype used in automotive applications. Therefore, the presented LUT-based motor model was parametrised with the help of extensive test bench measurements to consider the nonlinear iron loss and saturation effects. The OS based on the ME-strategy was compared to the MCL-strategy. The efficiency difference ∆η = ηME − ηMCL

Fig. 9. Improvement of motor efficiency regarding the New European Driving Cycle (NEDC)

30 v in m/s

IV. E FFICIENCY

20 10

(11)

Fa = mv˙

(15)

(12) (13) (14)

∆Pv in W

0

500

1000

1500

0

500

1000

1500

0

500

1000

1500

0

500

1000 t in s

1500

20 10 0 0

−100 −200 2 ∆η in %

Fv = Fd + Fr + Fw + Fa 1 Fd = cd ρa Ad v 2 2 Fr = mgcr cos(γ) Fw = mg sin(γ)

Pme in kW

0 in the entire speed-torque-plane is depicted in Fig. 8. It can be seen that significant efficiency improvements can be achieved from medium to high speeds at low load levels. For these operation points a loss-minimal flux can be selected within the drive limits (voltage and current constraints) using the degree of freedom between stator and rotor copper as well as iron losses (see Fig. 6). For higher speeds or torque that degree of freedom cannot be utilised since the operating point has to be chosen with respect to the current and voltage constraints. Consequently, the operating points chosen with the ME- and MCL-strategy become identical. To evaluate the OS under standardised conditions a longitudinal car model for a subcompact EV was set up. The longitudinal vehicle force Fv is given as the sum of aerodynamic drag force Fd , rolling friction force Fr , weight force Fw and the acceleration force Fa :

1 0

Fig. 10. Improvement of motor efficiency regarding the Federal Test Procedure 75 (FTP75)

Here, cd is the drag coefficient, ρa the air mass density, Ad the vehicle reference area, v the vehicle velocity, m the vehicle mass, g the gravitational acceleration, cr the rolling resistance coefficient and γ the gradient angle, respectively. The mechanical shaft power is than given as Pme = vFv . As a basis of comparison the New European Driving Cycle (NEDC) and the Federal Test Procedure 75 (FTP75) were chosen. The focus of the investigation was to clarify to what extent the motor efficiency changes, if either the OS considers iron losses or not (ME- vs. MCL-strategy). The simulation results regarding the NEDC and the FTP75 are shown in Fig. 9 and 10. It can be seen that the amount of efficiency improvement strongly depends on the actual driving situation. In some cases the maximum achievable improvement of up to 1.8 % is realised, in other cases the current and especially voltage limitation lead to identical loss behaviour. The average efficiency improvements regarding both strategies and driving cycles are shown in Tab. I. TABLE I AVERAGE EFFICIENCY IMPROVEMENT FOR SUBCOMPACT EV APPLICATION

OS

NEDC

FTP75

MCL

94.03 %

93.53 %

ME

94.13 %

93.73 %

It is shown that the IM’s average efficiency can be increased by 0.1 % for the NEDC and 0.2 % for the FTP75 by considering iron losses within the operation strategy. This is an interesting result if one elucidate that the efficiency improvement can be achieved just by changing the control software regarding the optimal choice of fundamental wave steady-state operating points. V. C ONCLUSION

AND

O UTLOOK

The proposed operation strategy for IM can be favourably applied in automotive traction drives. Its main features are: • • • • •

consideration of varying DC-link voltage high degree of motor utilisation while satisfying the current and voltage limit smooth transition between constant torque and flux weakening area avoiding of additional time delay since all optimisation calculations are done offline efficiency enhancement due to iron loss consideration in the range of 0.1 − 0.2 % under standardised conditions

However, the proposed control strategy was designed with the implicit understanding of perfect model parameter knowledge. Here, varying parameters (e.g. temperature-dependent stator and rotor resistance) have been neglected for this investigation as well. For future research in this field, these essential induction motor characteristics have to be taken into account. Also, loss influences apart from the selection of motor operation points in the fundamental wave domain, e.g. inverter losses or iron losses due to pulsating and harmonic currents, should be investigated [13].

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