Available online at www.sciencedirect.com

ScienceDirect Energy Procedia 90 (2016) 540 – 551

5th International Conference on Advances in Energy Research, ICAER 2015, 15-17 December 2015, Mumbai, India

Sensorless Speed Control of Induction Motor Driven Electric Vehicle Using Model Reference Adaptive Controller Abhisek Pala*, Rakesh Kumara, Sukanta Dasa a

Department of Electrical Engineering, Indian School of Mines, Dhanbad 826004, India

Abstract This paper proposes a new sensorless speed control technique for induction motor (IM) driven electric vehicle (EV) using a model reference adaptive controller (MRAC) with a basic energy optimization technique known as golden section method. The proposed MRAC for the vector controlled IM drive utilizes instantaneous and steady state values of a fictitious resistance (R) in the reference and adaptive models respectively. The proposed scheme is immune to the variation in stator resistance (Rs). Moreover, the unique formation of the MRAC with the instantaneous and steady-state reactive power completely eliminates the requirement of any flux estimation in the process of speed estimation. Thus, the method is insensitive to integrator-related problems like drift and saturation enabling the estimation at or around zero speed quite accurately. The proposed drive’s performance with the R-MRAC is validated for various speed ranges and patterns in Matlab/Simulink. Sensitivity of various motor parameters and stability studies are carried out using eigenvalues loci plots by first order eigenvalue sensitivity analysis. © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2016 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICAER 2015. Peer-review under responsibility of the organizing committee of ICAER 2015 Keywords: Drives; electric vehicles; estimation; induction motor; MRAC; optimization; sensorless; speed; stability

1.

Introduction

Electric Vehicles (EVs) are the future of automobile technology in context of depleting oil reserves. In coming years, EVs will have the potential to solve the problems associated with environment, energy resources, and people health [1]. However, to prove its dominance in the coming era, EVs should be more energy efficient over the wide

* Corresponding author. Tel.: (+91)-8900515980 E-mail addresses: [email protected]

1876-6102 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICAER 2015 doi:10.1016/j.egypro.2016.11.222

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

Nomenclature : d and q-axis components of stator and rotor current (A) : d and q-axis components of stator and rotor flux (Wb) : stator, rotor, mutual and stator leakage inductances (H) : stator and rotor resistance (Ω) : synchronous speed, rotor speed, and slip speed (rad/s) : total leakage factor : rotor circuit time constant (s) ^, * P

: estimated, reference quantities : time-derivative operator : error signal

speed and torque ranges. This can be achieved by a suitable choice of electric motor [2], [3]. However, induction motor (IM) drives are more rugged, compact, cheap and reliable in comparison to the other motors (e.g., DC motors or synchronous motors) of same capacity used for EV applications [4]. Vector Control or field oriented control (FOC) plays a critical role in extracting the drive’s high performance due to its simplicity and fast dynamic response [5], [6]. However, for implementation of FOC, knowledge of either the flux or speed is necessary. In this regard, digital shaft position encoders and shaft mounted tachogenerator are usually employed to detect the rotor speed [6]. The flux and speed sensors lead to the increased size of drive system with additional involvement in cost for the sensors. In addition, these degrade the mechanical robustness reducing the system reliability. The emergence of sensorless vector control [7] has reduced the cost and size of drive system with the reduction of the hardware complexity, increased reliability, better noise immunity and less maintenance requirements. In years, many improved speed estimation techniques such as sliding-mode observers, [7], extended Kalman filters [8], speed adaptive flux observer (Leunberger observer) [9] and model reference adaptive controller (MRAC) [10], [11] are reported in the literature. A brief review of different MRAC is available in [12]. Among all the strategies, MRAC based techniques have been proven to be as one of the best methods being proposed by the researchers due to its simple formulation, less computational complexity thereby ease in implementation [13]. Minimization of loss in the induction motor is directly related to the choice of the flux level. But extreme minimization causes a high copper loss [5]. For constant speed operation, if torque is variable then flux have to vary, to improve the drive efficiency. A number of energy optimization strategies such as simple state control [14], search control [15] and loss model based control [16] for IM drive are found in the literature. The on-line power search optimization controllers called search controllers (SCs) mainly works on the principle of optimization of a significant parameter (e.g., DC link power or DC-link current or stator current or drive losses) by trial and error method [17], [18]. Unlike other control strategies, the method does not depend upon the motor or converter parameters. However, the method suffers from the torque ripples and slow convergence rate. Nevertheless, the problem may be overcome using second order low-pass filter [19]. In the present work, golden section algorithm is used to minimize the drive loss. This also has a close relation to the Fibonacci search method [19]. However, the golden section technique has the edge over the Fibonacci search algorithm as the later needs to know a priori the number of evaluations in the minimum searching process, which is totally eliminated in former [20]. To achieve a minimal machine core loss, the golden section technique searches the optimal value of rotor flux reference using very fast convergence algorithm. In addition, a new fictitious d- and q-axis resistance error based MRAC (R-MRAC) is proposed for the estimation

541

542

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

of speed and rotor resistance for IM drive in this paper. The proposed scheme does not require any kind of flux computation and eliminates the derivative terms from the adaptive model. The drive system consists of an energy * and optimization algorithm based on the power loss of drive and speed error signal to generate optimal value of i ds hence, the optimal rotor flux. The stability analysis of R-MRAC has been carried out using linear time invariant system of equations by first-order eigenvalue sensitivity analysis and also by first-order perturbations of eigenvalues in Matlab/Simulink. The analysis proves the stability of R-MRAC in both the motoring and regeneration modes of drive’s operation. The paper is organized in six sections. In section-2, the formulation of new R-MRAC is presented. Section-3 discusses the efficiency optimization technique for IM drive. The system stability analysis through eigenvalue plots is detailed in section-4. Simulation results are presented in section-5. Finally, section-6 concludes the work carried out. 2. Formulation of R-MRAC The IM stator voltages in the synchronously rotating reference frame are expressed as [5] vds = Rsids + σLs pids +

L Lm pψ dr − σLsωeiqs − ωe m ψ qr Lr Lr

(1)

vqs = Rsiqs + σLs piqs +

Lm L pψ qr + σLsωeids + ωe m ψ dr Lr Lr

(2)

Dividing (1) by i ds , (2) by i qs and subtracting, the equation for reference model of R-MRAC is obtained as

R1 =

v ds v qs − i ds i qs

(3)

The dimension of R1 represents resistance or ohms which can be explained as the difference between d-axis and q-axis resistances. Hence, it is defined as fictitious resistance. Since, it is independent of rotor speed, it is used in the reference model. Substituting the values of v ds and v qs from (1) and (2) in (3), the new expression for instantaneous value of R1 that can be used as adaptive model becomes,

⎛ pi ⎛i ⎞ ⎛ piqs ⎞ Lm ⎛ pψ dr pψ qr ⎞ ψ ⎞ ⎟+ ⎜ ⎟ − σL ω ⎜ qs − ids ⎟ − ω Lm ⎜ ψ dr − qr ⎟ − R2 = σLs ⎜ ds − e s e⎜ ⎜ ids ⎟ ⎜ ⎟ ⎟ ⎜ iqs ⎠ Lr ⎝ ids iqs ⎠ Lr ⎝ iqs ids ⎟⎠ ⎝ ⎝ ids iqs ⎠

(4)

During steady state, as the derivative terms vanish, the expression becomes

⎛ iqs i ⎞ ψ qr ⎞ L ⎛ψ ⎟ R3 = − σLsωe ⎜ − ds ⎟ − ωe m ⎜ dr − ⎜ ids iqs ⎟ Lr ⎜⎝ iqs ids ⎟⎠ ⎝ ⎠

(5)

Moreover, for vector control operation, ψ dr = Lmids and ψ qr = 0 , hence, the simplified expression of (5) which is independent of any rotor flux can be obtained as

543

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

⎛ i qs i ds R 4 = − σL s ω e ⎜ − ⎜ i ds i qs ⎝

⎞ ⎛ ⎟ − ω Lm ⎜ Lm i ds e ⎟ Lr ⎜⎝ i qs ⎠

⎞ ⎟ ⎟ ⎠

(6)

Substituting values of σ in (6), the modified expression for adaptive model of R-MRAC can be obtained as ⎛i i qs ⎞⎟⎛ R r i qs ⎞ ⎜ ⎟ R 4 = − L s ⎜ ds + σ ⎟⎜⎜ ω r + ⎟ ⎜ i qs ⎟ i L i ds r ds ⎠ ⎝ ⎠⎝

(7)

R iqs Where, ω e = ω r + ω sl and ωsl = r Lr ids * v ds

Reference Model

v*qs

R1 =

* ds * qs

i i

i ds i qs

v qs v ds − i ds (iqs + μ)

+

⎛ ids iqs +σ R4 = − Ls ⎜ ⎜ ( iqs + μ ) ids ⎝

−

⎞⎛ R i ⎞ ⎟⎜ ω ˆ + r qs ⎟ ⎟⎜ r Lr ids ⎟ ⎠ ⎠⎝

ε

Adaptive Model

PI

ˆr ω

Fig.1. R-MRAC structure for estimation of rotor speed.

Fig.1 shows the R-MRAC containing the reference and adaptive models. It is to be noted that a small value μ = 0.00001 is added to the d-q current components in the denominator to ensure satisfactory working of the algorithm, under no-load condition. Fig.2 shows the schematic diagram of the proposed vector controlled IM drive using R-MRAC with efficiency optimization scheme.

ω*r

+

Speed command/ Reference speed

Δωr

−

* iqs

ωsl calculation

+ +

ωe

∫

* i ds

θe

ˆr ω ids

ˆr ω

iqs

PI

Δωr Efficiency Optimization Algorithm

Adaptive Model

v*ds

v*qs

Reference Model

−

* i ds

+

PI

PI

−

Vector Rotation [5] v*ds

R1

+

s* vds

V

Adaptation Mechanism For ωˆ r

ˆr ω

I VI

SVPWM based pulse generation

PWM signals

3φ Inverter

3φ to 2φ and Inverse Vector Rotation [5]

i ds

−ε

II III

IV

θe

iqs

R4

s* vqs

v*qs

+

Ploss

* i ds

* iqs

* iqs

Ploss

Pout

+ −

IM

Pin

R - MRAC

Fig.2. Schematic diagram of vector controlled IM drive with R-MRAC and efficiency optimization scheme.

Pin

544

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

3. Efficiency Optimization of IM Drive In EV’s application, the improved dynamic performance with optimum efficiency are the important requirements. Therefore, an efficiency optimization scheme using golden section algorithm [21] has been incorporated in the outer loop of the control scheme. The vector control not only has the advantage of excellent dynamic performance, but also, enables decoupled control of torque and flux through d-axis (flux-producing) and q-axis (torque-producing) currents in the steady state. This makes the inclusion of the energy optimization algorithm very simple [19]. However, the present energy optimization algorithm using golden section technique for IM drive is based on power loss of the drive system. The drive loss is calculated from the difference between the power input to the inverter and the shaft power output. The reference flux current, i*ds is generated by the optimization algorithm, while the torque component of current is acquired from the speed control loop. In the transient state, when either the speed command or the load torque is changed, the nominal value of the i*ds comes into play. The transient speed is easily detected when the speed error signal ( Δωe ) reaches the maximum value 0.5 rad/s and the energy optimization algorithm starts settling the i*ds to the required optimal value. The optimal value of i*ds generates the optimized required flux without affecting the output power. The optimal value of flux reduces the power loss of the drive system, thus fulfilling the objective of proposed work. 4. System Stability Analysis To carry out the stability analysis of any system, the variables must be time-invariant [14]. The IM model in synchronously rotating (ω e ) reference frame can be expressed as [12], [13]: ⎡ids ⎤ ⎡− a1 ωe ⎢i ⎥ ⎢- ω − a qs ⎥ 1 =⎢ e p⎢ ⎢ψ dr ⎥ ⎢ a4 0 ⎢ψ ⎥ ⎢ 0 a4 ⎣ qr ⎦ ⎣

⎡ids ⎤ ⎡1 0 0 0⎤ ⎢i ⎥ = ⎢0 1 0 0⎥ ⎦ ⎣ qs ⎦ ⎣

where, a1 =

⎡1 a2 a3ωr ⎤ ⎡ids ⎤ ⎢ σLs - a3ωr a2 ⎥ ⎢⎢iqs ⎥⎥ ⎢ 0 ⎥ + - a5 ωsl ⎥ ⎢ψ dr ⎥ ⎢⎢ 0 ⎢ ⎥ - ωsl - a5 ⎥⎦ ⎣ψ qr ⎦ ⎢ ⎣ 0

0 ⎤ ⎥ 1 ⎥ σLs ⎥ 0 ⎥ ⎥ 0 ⎦

⎡vds ⎤ ⎢v ⎥ ⎣ qs ⎦

⎡ids ⎤ ⎢i ⎥ ⎢ qs ⎥ ⎢ψ dr ⎥ ⎢ψ ⎥ ⎣ qr ⎦

(8)

(9)

⎛1⎞ ⎛L ⎞ L2 ⎞ 1 ⎛⎜ 1 ⎛ Lm ⎞ 1 ⎛ Lm ⎞ ⎟ , a4 = ⎜ m ⎟ , a5 = ⎜ ⎟ ⎜ ⎟ , a3 = ⎜ Rs + m ⎟ , a2 = ⎜τ ⎟ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎜ ⎟ σLs ⎝ Lrτ r ⎠ σLs ⎝ Lrτ r ⎠ σLs ⎝ Lr ⎠ ⎝ r⎠ ⎝ τr ⎠

In the state space domain, (8) and (9) can be represented as px = Ax + Bu

(10)

y = Cx

(11)

where, x = ids iqs ψ dr ψ qr T , u = vds vqs T and y = ids iqs T

[

]

[

]

[

]

4.1 First-order perturbation of eigenvalues The eigenvalues of system matrix is sensitive to the perturbations. Small changes in the matrix elements can lead to large changes in the eigenvalues [22]. Let, matrix A is perturbed by P = eB , where, e (>0) is a small value, B is any

545

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

arbitrary matrix; eigenvalue λ i and right-eigenvector Φ i is perturbed as λi + Δλi and Φ i + ΔΦ i respectively. Then,

(A + P)(Φi + ΔΦi ) = (λi + Δλi )(Φi + ΔΦi )

(12)

The perturbed right-eigenvector is represented as a linear combination of other right-eigenvectors excluding itself as

ΔΦ i = e

where, aki =

n ∑ a ki Φ k k = 1, k ≠ i

(13)

βki , β ki = ψ iT BΦ i , sk = ψ kT BΦ k , Φ k = left-eigenvector and ψ iT = transpose of left(λi − λk ) sk

eigenvector. The first-order term in the perturbation of Φ i is given as [23]

ΔΦi = e

n β ki Φ k ∑ k = 1, k ≠ i (λi − λk )s k

(14)

⎡ β21Φ 2 β31Φ3 βn1Φ n ⎤ or, ΔΦi = e⎢ + + ⋅⋅⋅⋅ + (λ1 − λn )sn ⎥⎦ ⎣ (λ1 − λ2 )s2 (λ1 − λ3 )s3

(15)

The IM parameters and controller values considered for the analysis are given in Appendix A. Using the machine parameters, the eigenvalues are calculated from the state transition matrix (10) and plotted in the complex frequency plane (i.e. s-plane) as shown in Fig. 3 and Fig. 4. Fig. 3(a) and Fig. 3(c) show the loci of the eigenvalues for the low speed motoring mode of drive’s operation using R-MRAC for the nominal and 100% increase in Rs and Rr respectively. All the eigenvalues are lying on the left side of the s - plane confirming a stable drive operation. The stability in motoring mode is further confirmed in Fig. 3(b) and Fig. 3(d) by observing the loci of the eigenvalues of two arbitrary perturbed matrices with the state matrix for the nominal and 100% increase in Rs and Rr . The location of eigenvalues assuring the drive’s stability in the regenerating mode for the nominal and 100% increase in Rs and Rr is shown in Fig. 4(a) and Fig. 4(c). The stability is also preserved for the arbitrary disturbances as shown in Fig. 4(b) and Fig. 4(d). The results obtained are quite similar in the both modes of drive’s operation confirming stability. The

a

b 20

λ

10

15

1 3

0 -5

λ

-10

λ

-15 -20 -120

λ

10

λ

5

Imaginary part

Imaginary part

20

[A]

15

-100

λ

5 0

λ λ

-15

-60 -40 Real part

-20

0

20

3

-5 -10

4

2

-80

[A] [A+P1] [A+P1+P2]

1

-20 -120

-100

4

2

-80

-60 -40 Real part

-20

0

20

546

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

c

d

20

[A] [A+P1] [A+P1+P2]

15

λ

5

λ 1

10 3

Imaginary part

10 Imaginary part

20

[A]

15

0 -5 -10

λ

λ

2

λ

5

λ

3

0 -5 -10

4

-15

1

λ

λ

2

4

-15

-20 -120

-100

-80

-60 -40 Real part

-20

0

-20 -120

20

-100

-80

-60 -40 Real part

-20

0

20

Fig. 3. Plots of eigenvalues in complex frequency plane in motoring mode ( ωr = 10 rad/s and T = 8 Nm): (a) for L Rr = 4.01 Ω and Rs = 5.55 Ω , (b) with perturbation for Rr = 4.01 Ω and Rs = 5.55 Ω , (c) for Rr = 8.02 Ω and Rs = 11.1 Ω , and (d) with perturbation for Rr = 8.02 Ω and Rs = 11.1 Ω .

loci of the eigenvalues for R-MRAC lie in the left half of the s-plane for both the modes of operation and thus it can be concluded that the scheme is stable in the low speed motoring and regenerating modes of operation. It has been observed that the arbitrary generated disturbance does not affect the stability in both modes of drive’s operation.

a

b 20

20 [A]

λ

Imaginary part

10

1

15

λ

5 0 -5

λ λ

-10

4

[A] [A+P1] [A+P1+P2]

1

2

λ

3

5 0 -5

λ λ

-10

4

2

-15

-15 -20 -120

λ

10

3

Imaginary part

15

-100

-80

-60 -40 Real part

-20

0

20

c

-20 -120

-100

-80

-60 -40 Real part

-20

0

20

d 20

20

[A]

λ

Imaginary part

10

λ

1

0

λ

2

λ

-10

4

1

λ

3

5 0

λ

-5

2

λ

-10

4

-15

-15 -20 -120

λ

10

3

5

-5

[A] [A+P1] [A+P1+P2]

15

Imaginary part

15

-100

-80

-60 -40 Real part

-20

0

20

-20 -120

-100

-80

-60 -40 Real part

-20

0

20

Fig. 4. Plots of eigenvalues in complex frequency plane in regenerating mode ( ωr = 10 rad/s and T = -8 Nm): L (a) for Rr = 4.01 Ω and Rs = 5.55 Ω , (b) with perturbation for Rr = 4.01 Ω and Rs = 5.55 Ω , (c) for Rr = 8.02 Ω and Rs = 11.1 Ω ,and (d) with perturbation for Rr = 8.02 Ω and Rs = 11.1 Ω .

547

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

5. Simulation Results The performance of the proposed R-MRAC for speed sensorless vector controlled IM drive is verified in Matlab/Simulink for various test cases as follows. 5.1. Step change in rotor speed Result of the proposed drive using R-MRAC is studied in the motoring mode by a step change in the reference speed as shown in Fig.5. An increasing step change in the speed command is applied at every 5 s and the estimated speed is found to track the reference speed satisfactorily for whole speed range (0-120 rad/s), rated (100 rad/s) and above the rated speed (120 rad/s) as shown in Fig.5(a). Throughout the operation a constant torque of 2 Nm is maintained. The flux components of the stator current ( ids ) is shown in Fig.5(b). After every speed transient period,

ids is adjusted to the optimal value by golden section algorithm. The flux orientation is well maintained as shown in Fig.5(c). The loss of the drive shown in Fig.5(d) and it can be observed that without efficiency optimization algorithm in the transient period, the drive loss is on the higher side as compared to the duration after optimization algorithm becomes functional.

a

b

2.6

Reference Speed Estimated Speed Actual Speed

Speed (rad/s)

100

2.4 2.2

80

Field weakening

60

1.8

40

1.6

20

c

1.4

0

10

2.5

30

Field weakening

0.5 0 -0.5

10

20

30

d

1.5 1

0

Time (s)

d-axis rotor flux q-axis rotor flux

2

Rotor Flux (Wb)

Time (s)

20

400 350 Total Loss (W)

0

Field weakening

2

ids

120

Efficiency optimization starts

300 250 200 150

Field weakening

Area without Efficiency optimization

100

50 20 30 0 10 20 30 Time (s) Time (s) Fig.5. Performance of R-MRAC for step pattern: (a) reference, estimated, and actual speeds, (b) d-axis stator current, (c) d- and q-axis rotor flux in rotating reference frame, and (d) total drive loss.

0

10

5.2. Low Speed Operation The performance of the proposed estimator at low speed is shown in Fig.6. It is observed that the estimated speed follows the reference speed quite accurately even at a very low speed of 5 rad/s (Fig.6(a)). A constant speed deviation of 1.0 % is observed between the estimated and the actual speeds for low speed operation. The d-axis current is shown

548

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

in Fig.6(b). Initial 15 s, no optimization algorithm is initiated for low speed. However, initialization of optimization algorithm readjust ids to optimal value of 2.5 A. This results in the reduction of d- axis rotor flux without affecting the q-axis rotor flux as depicted in (Fig.6(c)). Consequently, the loss is also reduced as observed from Fig. 6(d).

a

b Reference Speed Estimated Speed Actual Speed

3

4 5 4.95 4.9

2

8 0

3.2

ids

Speed (rad/s)

6

3.4

0

9

10

20

2.8

With Efficiency optimization

2.6

10 30

0

Time (s)

c

10

Time (s)

20

30

d

500

d-axis rotor flux q-axis rotor flux

2 Efficiency optimization starts

1

With Efficiency optimization

400

Total Loss (W)

3

Rotor Flux (Wb)

Without Efficiency optimization

300

Without Efficiency optimization

200 100

0 0

0 10 20 30 20 30 Time (s) Time (s) Fig.6. Performance of R-MRAC in low-speed region: (a) reference, estimated, and actual speeds,(b) d-axis stator current, (c) d- and q-axis rotor flux in rotating reference frame, and (d) total drive loss.

0

10

5.3. Regenerative mode operation 5.3.1. Second quadrant operation The performance of the proposed drive in second quadrant is shown in Fig.7 which shows the transition of the estimator from motoring mode and back keeping the load torque constant at 2 Nm. The estimated speed follows the actual speed which in turn tracks the reference speed as shown in Fig.7(a). The applied load torque and the machine torque are shown in Fig.7(b). 5.3.2. Fourth quadrant operation In the fourth quadrant, the estimated speed is also observed to follow the reference and the actual speeds as seen from Fig.8(a). The applied load torque and the machine torque are shown in Fig.8(b). In the second and fourth quadrant operations, (Fig.7(c) and Fig.8(c)) show that the total loss of the drive system without optimization algorithm is significantly higher as opposes to that when golden section algorithm is active (Fig.7(d) and Fig.8(d)).

549

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

a

b

20 15

2

Torque (Nm)

10

Speed (rad/s)

2.5

Reference Speed Estimated Speed Actual Speed

5 0 -5

1.5

0.5 0

-10 -15

0

10

Time (s)

20

-0.5

30

c

0

10

Time (s)

20

30

d

400 300

Without Efficiency optimization

200

300 Area without Efficiency optimization

200 100

100 0

Efficiency optimization starts

400

Total Loss (W)

Total Loss (W)

Load Torque Electromagnetic Torque

1

0

10

20

0

30

0

10

20

30

Time (s) Time (s) Fig.7. Second quadrant operation: (a) reference, estimated and actual speeds, (b) load and electromagnetic torques, and total drive loss:(c) without efficiency optimization, (d) with efficiency optimization.

a

b Reference Speed Estimated Speed Actual Speed

Load Torque Electromagnetic Torque

4

Torque (Nm)

Speed (rad/s)

15

10

5

2

0

-2

0

0

10

Time (s)

20

30

-4

0

10

Time (s)

20

30

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

c

d

400

400

300

Total Loss (W)

Total Loss (W)

550

Without Efficiency optimization

200

300 Area without Efficiency optimization

200 100

100 0

Efficiency optimization starts

0

0 10 20 30 Time (s) Time (s) Fig.8. Fourth quadrant operation: (a) reference, estimated and actual speeds, (b) load and electromagnetic torques, and total drive loss:(c) without efficiency optimization, (d) with efficiency optimization.

0

10

20

30

6. Conclusion Induction motor (IM) driven electric vehicle is preferred due to the small size, light weight, rugged and energy efficient characteristics of IM. This paper presents an application of energy optimization technique for an inverterfed IM drive, based on the drive’s power loss operating in wide speed range. A new MRAC based speed estimation technique for the vector controlled induction motor drive is utilized for implementation of the said optimization algorithm. The efficiency optimization algorithm generates the optimal value of i*ds . Hence, core loss of the drive system is minimized as the flux level is optimized. In this proposed scheme, the instantaneous and steady state values of fictitious resistance (R) are utilized in the reference and adaptive models respectively. The proposed scheme does not require any kind of flux computation, making it suitable for low speed operation. The proposed IM drive works satisfactorily in all the four quadrants of operation. Moreover, the first-order eigenvalue sensitivity analysis along with first order perturbation of eigenvalues ensure the stability of the IM drive system in the motoring and regenerating modes of operation. APPENDIX A A.1. Induction motor parameters Rating

2.2 kW, 3-phase, 415 V, 50 Hz, 4 pole

pf

0.75

Stator/rotor resistance

5.55 Ω , 4.01 Ω

Stator/rotor inductance

A.2. Induction motor controller parameters Proportional

Integral

controller

controller

Speed

0.25

2

0.7249 H

Flux

0.2

4

Mutual inductance

0.7 H

Current

1

700

Rotor inertia

0.0237 kg-m2

MRAC

0.18

0.8

Friction coefficient

0.001

Controller

References [1] Unnewehr L, Nasar S. Electric vehicle technology. New York: John Wiley & sons.;1982. [2] Haddoun A, Benbouzid M, Diallo D, Abdessemed R. A loss-minimization DTC scheme for EV induction motors. IEEE Trans. Veh. Technol., 2007; 56(1), 81-88. [3] Ta C, Chakraborty C, Hori Y. Efficiency maximization of induction motor drives for electric vehicles based on actual measurement of input power. The 27th Annual Conference of the IEEE Industrial Electronics Society. IECON, 2001; 3, 1692 -697. [4] Vas P. Sensorless vector and direct torque control. New York: Oxford University Press.;1998. [5] Bose BK. Modern power electronics and ac drives. New Delhi: Prentice Hall.; 2002. [6] Kennel RM. Encoders for simultaneous sensing of position and speed in electrical drives with digital control. IEEE Tran. Ind. Appl.,2007; 43(6).

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

[7] Holtz J. Sensorless control of induction machines-with or without signal injection? IEEE Trans. Ind. Electron., 2006; 53(1), 7-30. [8] Pongam S, Sangwongwanich S. Stability and dynamic performance improvement of adaptive full- order observers for sensorless PMSM drive. IEEE Trans. Power Electron., 2012; 27(2), 588–600. [9] Kubota K, Matsuse K, Nakano T. DSP-based speed adaptive flux observer of induction motor. IEEE Trans. Ind. Appl., 1993; 29(2), 344–348. [10] Gadoue SM, Giaouris D, Finch JW. Stator current model reference adaptive systems speed estimator for regenerating-mode low-speed operation of sensorless induction motor drives. IET Electric Power Applications, 2013; 7(7), 597 - 606. [11] Teja AVR, Chakraborty C. A novel model reference adaptive controller for estimation of speed and stator resistance for vector controlled induction motor drives. IEEE International Symposium on Industrial Electronics (ISIE), 2010; 1187 - 1192. [12] Kumar R, Das S, Syam P, Chattopadhyay AK. Review on model reference adaptive system for sensorless vector control of induction motor drives. IET Electric Power Applications, 2015; 9(7), 496-511. [13] Xiao J, Li B, Gong X, Sheng Y, Chai, J. Improved performance of motor drive using RBFNN-based hybrid reactive power MRAS speed estimator. IEEE International Conference on Information and Automation (ICIA), 2010; 588-593. [14] Benbouzid ME, Said NS. An efficiency-optimization controller for induction motor drives. IEEE Power Engineering Review, 1998; 18(5), 63-64. [15] Kirschen DS, Novotny DW, Suwanwissot W. Minimizing induction motor losses by excitation control in variable frequency drives. IEEE Trans. Ind. Appl., 1984; IA-20(5), 1244-1250. [16] Farasat M, Trzynadlowski A M, Fadali MS. Efficiency improved sensorless control scheme for electric vehicle induction motors. IET Electr. Syst. Transp., 2014; 4(4), 122-131. [17] Sousa GD, Bose BK, Cleland JG. Fuzzy logic based on-line efficiency optimization control ofan indirect vector-controlled induction motor drive. IEEE Trans. Ind. Electron., 1995; 42, 92-198. [18] Sadegh V, Rahman M. An on-line loss minimization controller for the Interior Magnet motor drives. IEEE Trans. Energy Convers., 1999; 14(4), 1435-1440. [19] Ta CM, Hori Y. Convergence improvement of efficiency-optimization control of induction motor drives. IEEE Tran. Ind. Appl., 2001; 37(6), 1746-1753. [20] Chakraborty C, Hori Y. Fast efficiency optimization techniques for the indirect vector-controlled induction motor drives. IEEE Tran. Ind. Appl., 2003; 39(4), 1070-1076. [21] Kalavathy S. Operations research. New Delhi: Vikas Publishing House Pvt. Ltd.; 2002. [22] Konstantinov M, Wei G, Mehrmann V, Petkov P. Perturbation theory for matrix equations (studies in computational mathematics). NorthHolland: Elsevier Science Ltd.;2003. [23] Wilkinson J. The algebraic eigenvalue problem. New York: Oxford University Press; 1998.

551

ScienceDirect Energy Procedia 90 (2016) 540 – 551

5th International Conference on Advances in Energy Research, ICAER 2015, 15-17 December 2015, Mumbai, India

Sensorless Speed Control of Induction Motor Driven Electric Vehicle Using Model Reference Adaptive Controller Abhisek Pala*, Rakesh Kumara, Sukanta Dasa a

Department of Electrical Engineering, Indian School of Mines, Dhanbad 826004, India

Abstract This paper proposes a new sensorless speed control technique for induction motor (IM) driven electric vehicle (EV) using a model reference adaptive controller (MRAC) with a basic energy optimization technique known as golden section method. The proposed MRAC for the vector controlled IM drive utilizes instantaneous and steady state values of a fictitious resistance (R) in the reference and adaptive models respectively. The proposed scheme is immune to the variation in stator resistance (Rs). Moreover, the unique formation of the MRAC with the instantaneous and steady-state reactive power completely eliminates the requirement of any flux estimation in the process of speed estimation. Thus, the method is insensitive to integrator-related problems like drift and saturation enabling the estimation at or around zero speed quite accurately. The proposed drive’s performance with the R-MRAC is validated for various speed ranges and patterns in Matlab/Simulink. Sensitivity of various motor parameters and stability studies are carried out using eigenvalues loci plots by first order eigenvalue sensitivity analysis. © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2016 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICAER 2015. Peer-review under responsibility of the organizing committee of ICAER 2015 Keywords: Drives; electric vehicles; estimation; induction motor; MRAC; optimization; sensorless; speed; stability

1.

Introduction

Electric Vehicles (EVs) are the future of automobile technology in context of depleting oil reserves. In coming years, EVs will have the potential to solve the problems associated with environment, energy resources, and people health [1]. However, to prove its dominance in the coming era, EVs should be more energy efficient over the wide

* Corresponding author. Tel.: (+91)-8900515980 E-mail addresses: [email protected]

1876-6102 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICAER 2015 doi:10.1016/j.egypro.2016.11.222

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

Nomenclature : d and q-axis components of stator and rotor current (A) : d and q-axis components of stator and rotor flux (Wb) : stator, rotor, mutual and stator leakage inductances (H) : stator and rotor resistance (Ω) : synchronous speed, rotor speed, and slip speed (rad/s) : total leakage factor : rotor circuit time constant (s) ^, * P

: estimated, reference quantities : time-derivative operator : error signal

speed and torque ranges. This can be achieved by a suitable choice of electric motor [2], [3]. However, induction motor (IM) drives are more rugged, compact, cheap and reliable in comparison to the other motors (e.g., DC motors or synchronous motors) of same capacity used for EV applications [4]. Vector Control or field oriented control (FOC) plays a critical role in extracting the drive’s high performance due to its simplicity and fast dynamic response [5], [6]. However, for implementation of FOC, knowledge of either the flux or speed is necessary. In this regard, digital shaft position encoders and shaft mounted tachogenerator are usually employed to detect the rotor speed [6]. The flux and speed sensors lead to the increased size of drive system with additional involvement in cost for the sensors. In addition, these degrade the mechanical robustness reducing the system reliability. The emergence of sensorless vector control [7] has reduced the cost and size of drive system with the reduction of the hardware complexity, increased reliability, better noise immunity and less maintenance requirements. In years, many improved speed estimation techniques such as sliding-mode observers, [7], extended Kalman filters [8], speed adaptive flux observer (Leunberger observer) [9] and model reference adaptive controller (MRAC) [10], [11] are reported in the literature. A brief review of different MRAC is available in [12]. Among all the strategies, MRAC based techniques have been proven to be as one of the best methods being proposed by the researchers due to its simple formulation, less computational complexity thereby ease in implementation [13]. Minimization of loss in the induction motor is directly related to the choice of the flux level. But extreme minimization causes a high copper loss [5]. For constant speed operation, if torque is variable then flux have to vary, to improve the drive efficiency. A number of energy optimization strategies such as simple state control [14], search control [15] and loss model based control [16] for IM drive are found in the literature. The on-line power search optimization controllers called search controllers (SCs) mainly works on the principle of optimization of a significant parameter (e.g., DC link power or DC-link current or stator current or drive losses) by trial and error method [17], [18]. Unlike other control strategies, the method does not depend upon the motor or converter parameters. However, the method suffers from the torque ripples and slow convergence rate. Nevertheless, the problem may be overcome using second order low-pass filter [19]. In the present work, golden section algorithm is used to minimize the drive loss. This also has a close relation to the Fibonacci search method [19]. However, the golden section technique has the edge over the Fibonacci search algorithm as the later needs to know a priori the number of evaluations in the minimum searching process, which is totally eliminated in former [20]. To achieve a minimal machine core loss, the golden section technique searches the optimal value of rotor flux reference using very fast convergence algorithm. In addition, a new fictitious d- and q-axis resistance error based MRAC (R-MRAC) is proposed for the estimation

541

542

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

of speed and rotor resistance for IM drive in this paper. The proposed scheme does not require any kind of flux computation and eliminates the derivative terms from the adaptive model. The drive system consists of an energy * and optimization algorithm based on the power loss of drive and speed error signal to generate optimal value of i ds hence, the optimal rotor flux. The stability analysis of R-MRAC has been carried out using linear time invariant system of equations by first-order eigenvalue sensitivity analysis and also by first-order perturbations of eigenvalues in Matlab/Simulink. The analysis proves the stability of R-MRAC in both the motoring and regeneration modes of drive’s operation. The paper is organized in six sections. In section-2, the formulation of new R-MRAC is presented. Section-3 discusses the efficiency optimization technique for IM drive. The system stability analysis through eigenvalue plots is detailed in section-4. Simulation results are presented in section-5. Finally, section-6 concludes the work carried out. 2. Formulation of R-MRAC The IM stator voltages in the synchronously rotating reference frame are expressed as [5] vds = Rsids + σLs pids +

L Lm pψ dr − σLsωeiqs − ωe m ψ qr Lr Lr

(1)

vqs = Rsiqs + σLs piqs +

Lm L pψ qr + σLsωeids + ωe m ψ dr Lr Lr

(2)

Dividing (1) by i ds , (2) by i qs and subtracting, the equation for reference model of R-MRAC is obtained as

R1 =

v ds v qs − i ds i qs

(3)

The dimension of R1 represents resistance or ohms which can be explained as the difference between d-axis and q-axis resistances. Hence, it is defined as fictitious resistance. Since, it is independent of rotor speed, it is used in the reference model. Substituting the values of v ds and v qs from (1) and (2) in (3), the new expression for instantaneous value of R1 that can be used as adaptive model becomes,

⎛ pi ⎛i ⎞ ⎛ piqs ⎞ Lm ⎛ pψ dr pψ qr ⎞ ψ ⎞ ⎟+ ⎜ ⎟ − σL ω ⎜ qs − ids ⎟ − ω Lm ⎜ ψ dr − qr ⎟ − R2 = σLs ⎜ ds − e s e⎜ ⎜ ids ⎟ ⎜ ⎟ ⎟ ⎜ iqs ⎠ Lr ⎝ ids iqs ⎠ Lr ⎝ iqs ids ⎟⎠ ⎝ ⎝ ids iqs ⎠

(4)

During steady state, as the derivative terms vanish, the expression becomes

⎛ iqs i ⎞ ψ qr ⎞ L ⎛ψ ⎟ R3 = − σLsωe ⎜ − ds ⎟ − ωe m ⎜ dr − ⎜ ids iqs ⎟ Lr ⎜⎝ iqs ids ⎟⎠ ⎝ ⎠

(5)

Moreover, for vector control operation, ψ dr = Lmids and ψ qr = 0 , hence, the simplified expression of (5) which is independent of any rotor flux can be obtained as

543

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

⎛ i qs i ds R 4 = − σL s ω e ⎜ − ⎜ i ds i qs ⎝

⎞ ⎛ ⎟ − ω Lm ⎜ Lm i ds e ⎟ Lr ⎜⎝ i qs ⎠

⎞ ⎟ ⎟ ⎠

(6)

Substituting values of σ in (6), the modified expression for adaptive model of R-MRAC can be obtained as ⎛i i qs ⎞⎟⎛ R r i qs ⎞ ⎜ ⎟ R 4 = − L s ⎜ ds + σ ⎟⎜⎜ ω r + ⎟ ⎜ i qs ⎟ i L i ds r ds ⎠ ⎝ ⎠⎝

(7)

R iqs Where, ω e = ω r + ω sl and ωsl = r Lr ids * v ds

Reference Model

v*qs

R1 =

* ds * qs

i i

i ds i qs

v qs v ds − i ds (iqs + μ)

+

⎛ ids iqs +σ R4 = − Ls ⎜ ⎜ ( iqs + μ ) ids ⎝

−

⎞⎛ R i ⎞ ⎟⎜ ω ˆ + r qs ⎟ ⎟⎜ r Lr ids ⎟ ⎠ ⎠⎝

ε

Adaptive Model

PI

ˆr ω

Fig.1. R-MRAC structure for estimation of rotor speed.

Fig.1 shows the R-MRAC containing the reference and adaptive models. It is to be noted that a small value μ = 0.00001 is added to the d-q current components in the denominator to ensure satisfactory working of the algorithm, under no-load condition. Fig.2 shows the schematic diagram of the proposed vector controlled IM drive using R-MRAC with efficiency optimization scheme.

ω*r

+

Speed command/ Reference speed

Δωr

−

* iqs

ωsl calculation

+ +

ωe

∫

* i ds

θe

ˆr ω ids

ˆr ω

iqs

PI

Δωr Efficiency Optimization Algorithm

Adaptive Model

v*ds

v*qs

Reference Model

−

* i ds

+

PI

PI

−

Vector Rotation [5] v*ds

R1

+

s* vds

V

Adaptation Mechanism For ωˆ r

ˆr ω

I VI

SVPWM based pulse generation

PWM signals

3φ Inverter

3φ to 2φ and Inverse Vector Rotation [5]

i ds

−ε

II III

IV

θe

iqs

R4

s* vqs

v*qs

+

Ploss

* i ds

* iqs

* iqs

Ploss

Pout

+ −

IM

Pin

R - MRAC

Fig.2. Schematic diagram of vector controlled IM drive with R-MRAC and efficiency optimization scheme.

Pin

544

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

3. Efficiency Optimization of IM Drive In EV’s application, the improved dynamic performance with optimum efficiency are the important requirements. Therefore, an efficiency optimization scheme using golden section algorithm [21] has been incorporated in the outer loop of the control scheme. The vector control not only has the advantage of excellent dynamic performance, but also, enables decoupled control of torque and flux through d-axis (flux-producing) and q-axis (torque-producing) currents in the steady state. This makes the inclusion of the energy optimization algorithm very simple [19]. However, the present energy optimization algorithm using golden section technique for IM drive is based on power loss of the drive system. The drive loss is calculated from the difference between the power input to the inverter and the shaft power output. The reference flux current, i*ds is generated by the optimization algorithm, while the torque component of current is acquired from the speed control loop. In the transient state, when either the speed command or the load torque is changed, the nominal value of the i*ds comes into play. The transient speed is easily detected when the speed error signal ( Δωe ) reaches the maximum value 0.5 rad/s and the energy optimization algorithm starts settling the i*ds to the required optimal value. The optimal value of i*ds generates the optimized required flux without affecting the output power. The optimal value of flux reduces the power loss of the drive system, thus fulfilling the objective of proposed work. 4. System Stability Analysis To carry out the stability analysis of any system, the variables must be time-invariant [14]. The IM model in synchronously rotating (ω e ) reference frame can be expressed as [12], [13]: ⎡ids ⎤ ⎡− a1 ωe ⎢i ⎥ ⎢- ω − a qs ⎥ 1 =⎢ e p⎢ ⎢ψ dr ⎥ ⎢ a4 0 ⎢ψ ⎥ ⎢ 0 a4 ⎣ qr ⎦ ⎣

⎡ids ⎤ ⎡1 0 0 0⎤ ⎢i ⎥ = ⎢0 1 0 0⎥ ⎦ ⎣ qs ⎦ ⎣

where, a1 =

⎡1 a2 a3ωr ⎤ ⎡ids ⎤ ⎢ σLs - a3ωr a2 ⎥ ⎢⎢iqs ⎥⎥ ⎢ 0 ⎥ + - a5 ωsl ⎥ ⎢ψ dr ⎥ ⎢⎢ 0 ⎢ ⎥ - ωsl - a5 ⎥⎦ ⎣ψ qr ⎦ ⎢ ⎣ 0

0 ⎤ ⎥ 1 ⎥ σLs ⎥ 0 ⎥ ⎥ 0 ⎦

⎡vds ⎤ ⎢v ⎥ ⎣ qs ⎦

⎡ids ⎤ ⎢i ⎥ ⎢ qs ⎥ ⎢ψ dr ⎥ ⎢ψ ⎥ ⎣ qr ⎦

(8)

(9)

⎛1⎞ ⎛L ⎞ L2 ⎞ 1 ⎛⎜ 1 ⎛ Lm ⎞ 1 ⎛ Lm ⎞ ⎟ , a4 = ⎜ m ⎟ , a5 = ⎜ ⎟ ⎜ ⎟ , a3 = ⎜ Rs + m ⎟ , a2 = ⎜τ ⎟ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎜ ⎟ σLs ⎝ Lrτ r ⎠ σLs ⎝ Lrτ r ⎠ σLs ⎝ Lr ⎠ ⎝ r⎠ ⎝ τr ⎠

In the state space domain, (8) and (9) can be represented as px = Ax + Bu

(10)

y = Cx

(11)

where, x = ids iqs ψ dr ψ qr T , u = vds vqs T and y = ids iqs T

[

]

[

]

[

]

4.1 First-order perturbation of eigenvalues The eigenvalues of system matrix is sensitive to the perturbations. Small changes in the matrix elements can lead to large changes in the eigenvalues [22]. Let, matrix A is perturbed by P = eB , where, e (>0) is a small value, B is any

545

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

arbitrary matrix; eigenvalue λ i and right-eigenvector Φ i is perturbed as λi + Δλi and Φ i + ΔΦ i respectively. Then,

(A + P)(Φi + ΔΦi ) = (λi + Δλi )(Φi + ΔΦi )

(12)

The perturbed right-eigenvector is represented as a linear combination of other right-eigenvectors excluding itself as

ΔΦ i = e

where, aki =

n ∑ a ki Φ k k = 1, k ≠ i

(13)

βki , β ki = ψ iT BΦ i , sk = ψ kT BΦ k , Φ k = left-eigenvector and ψ iT = transpose of left(λi − λk ) sk

eigenvector. The first-order term in the perturbation of Φ i is given as [23]

ΔΦi = e

n β ki Φ k ∑ k = 1, k ≠ i (λi − λk )s k

(14)

⎡ β21Φ 2 β31Φ3 βn1Φ n ⎤ or, ΔΦi = e⎢ + + ⋅⋅⋅⋅ + (λ1 − λn )sn ⎥⎦ ⎣ (λ1 − λ2 )s2 (λ1 − λ3 )s3

(15)

The IM parameters and controller values considered for the analysis are given in Appendix A. Using the machine parameters, the eigenvalues are calculated from the state transition matrix (10) and plotted in the complex frequency plane (i.e. s-plane) as shown in Fig. 3 and Fig. 4. Fig. 3(a) and Fig. 3(c) show the loci of the eigenvalues for the low speed motoring mode of drive’s operation using R-MRAC for the nominal and 100% increase in Rs and Rr respectively. All the eigenvalues are lying on the left side of the s - plane confirming a stable drive operation. The stability in motoring mode is further confirmed in Fig. 3(b) and Fig. 3(d) by observing the loci of the eigenvalues of two arbitrary perturbed matrices with the state matrix for the nominal and 100% increase in Rs and Rr . The location of eigenvalues assuring the drive’s stability in the regenerating mode for the nominal and 100% increase in Rs and Rr is shown in Fig. 4(a) and Fig. 4(c). The stability is also preserved for the arbitrary disturbances as shown in Fig. 4(b) and Fig. 4(d). The results obtained are quite similar in the both modes of drive’s operation confirming stability. The

a

b 20

λ

10

15

1 3

0 -5

λ

-10

λ

-15 -20 -120

λ

10

λ

5

Imaginary part

Imaginary part

20

[A]

15

-100

λ

5 0

λ λ

-15

-60 -40 Real part

-20

0

20

3

-5 -10

4

2

-80

[A] [A+P1] [A+P1+P2]

1

-20 -120

-100

4

2

-80

-60 -40 Real part

-20

0

20

546

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

c

d

20

[A] [A+P1] [A+P1+P2]

15

λ

5

λ 1

10 3

Imaginary part

10 Imaginary part

20

[A]

15

0 -5 -10

λ

λ

2

λ

5

λ

3

0 -5 -10

4

-15

1

λ

λ

2

4

-15

-20 -120

-100

-80

-60 -40 Real part

-20

0

-20 -120

20

-100

-80

-60 -40 Real part

-20

0

20

Fig. 3. Plots of eigenvalues in complex frequency plane in motoring mode ( ωr = 10 rad/s and T = 8 Nm): (a) for L Rr = 4.01 Ω and Rs = 5.55 Ω , (b) with perturbation for Rr = 4.01 Ω and Rs = 5.55 Ω , (c) for Rr = 8.02 Ω and Rs = 11.1 Ω , and (d) with perturbation for Rr = 8.02 Ω and Rs = 11.1 Ω .

loci of the eigenvalues for R-MRAC lie in the left half of the s-plane for both the modes of operation and thus it can be concluded that the scheme is stable in the low speed motoring and regenerating modes of operation. It has been observed that the arbitrary generated disturbance does not affect the stability in both modes of drive’s operation.

a

b 20

20 [A]

λ

Imaginary part

10

1

15

λ

5 0 -5

λ λ

-10

4

[A] [A+P1] [A+P1+P2]

1

2

λ

3

5 0 -5

λ λ

-10

4

2

-15

-15 -20 -120

λ

10

3

Imaginary part

15

-100

-80

-60 -40 Real part

-20

0

20

c

-20 -120

-100

-80

-60 -40 Real part

-20

0

20

d 20

20

[A]

λ

Imaginary part

10

λ

1

0

λ

2

λ

-10

4

1

λ

3

5 0

λ

-5

2

λ

-10

4

-15

-15 -20 -120

λ

10

3

5

-5

[A] [A+P1] [A+P1+P2]

15

Imaginary part

15

-100

-80

-60 -40 Real part

-20

0

20

-20 -120

-100

-80

-60 -40 Real part

-20

0

20

Fig. 4. Plots of eigenvalues in complex frequency plane in regenerating mode ( ωr = 10 rad/s and T = -8 Nm): L (a) for Rr = 4.01 Ω and Rs = 5.55 Ω , (b) with perturbation for Rr = 4.01 Ω and Rs = 5.55 Ω , (c) for Rr = 8.02 Ω and Rs = 11.1 Ω ,and (d) with perturbation for Rr = 8.02 Ω and Rs = 11.1 Ω .

547

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

5. Simulation Results The performance of the proposed R-MRAC for speed sensorless vector controlled IM drive is verified in Matlab/Simulink for various test cases as follows. 5.1. Step change in rotor speed Result of the proposed drive using R-MRAC is studied in the motoring mode by a step change in the reference speed as shown in Fig.5. An increasing step change in the speed command is applied at every 5 s and the estimated speed is found to track the reference speed satisfactorily for whole speed range (0-120 rad/s), rated (100 rad/s) and above the rated speed (120 rad/s) as shown in Fig.5(a). Throughout the operation a constant torque of 2 Nm is maintained. The flux components of the stator current ( ids ) is shown in Fig.5(b). After every speed transient period,

ids is adjusted to the optimal value by golden section algorithm. The flux orientation is well maintained as shown in Fig.5(c). The loss of the drive shown in Fig.5(d) and it can be observed that without efficiency optimization algorithm in the transient period, the drive loss is on the higher side as compared to the duration after optimization algorithm becomes functional.

a

b

2.6

Reference Speed Estimated Speed Actual Speed

Speed (rad/s)

100

2.4 2.2

80

Field weakening

60

1.8

40

1.6

20

c

1.4

0

10

2.5

30

Field weakening

0.5 0 -0.5

10

20

30

d

1.5 1

0

Time (s)

d-axis rotor flux q-axis rotor flux

2

Rotor Flux (Wb)

Time (s)

20

400 350 Total Loss (W)

0

Field weakening

2

ids

120

Efficiency optimization starts

300 250 200 150

Field weakening

Area without Efficiency optimization

100

50 20 30 0 10 20 30 Time (s) Time (s) Fig.5. Performance of R-MRAC for step pattern: (a) reference, estimated, and actual speeds, (b) d-axis stator current, (c) d- and q-axis rotor flux in rotating reference frame, and (d) total drive loss.

0

10

5.2. Low Speed Operation The performance of the proposed estimator at low speed is shown in Fig.6. It is observed that the estimated speed follows the reference speed quite accurately even at a very low speed of 5 rad/s (Fig.6(a)). A constant speed deviation of 1.0 % is observed between the estimated and the actual speeds for low speed operation. The d-axis current is shown

548

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

in Fig.6(b). Initial 15 s, no optimization algorithm is initiated for low speed. However, initialization of optimization algorithm readjust ids to optimal value of 2.5 A. This results in the reduction of d- axis rotor flux without affecting the q-axis rotor flux as depicted in (Fig.6(c)). Consequently, the loss is also reduced as observed from Fig. 6(d).

a

b Reference Speed Estimated Speed Actual Speed

3

4 5 4.95 4.9

2

8 0

3.2

ids

Speed (rad/s)

6

3.4

0

9

10

20

2.8

With Efficiency optimization

2.6

10 30

0

Time (s)

c

10

Time (s)

20

30

d

500

d-axis rotor flux q-axis rotor flux

2 Efficiency optimization starts

1

With Efficiency optimization

400

Total Loss (W)

3

Rotor Flux (Wb)

Without Efficiency optimization

300

Without Efficiency optimization

200 100

0 0

0 10 20 30 20 30 Time (s) Time (s) Fig.6. Performance of R-MRAC in low-speed region: (a) reference, estimated, and actual speeds,(b) d-axis stator current, (c) d- and q-axis rotor flux in rotating reference frame, and (d) total drive loss.

0

10

5.3. Regenerative mode operation 5.3.1. Second quadrant operation The performance of the proposed drive in second quadrant is shown in Fig.7 which shows the transition of the estimator from motoring mode and back keeping the load torque constant at 2 Nm. The estimated speed follows the actual speed which in turn tracks the reference speed as shown in Fig.7(a). The applied load torque and the machine torque are shown in Fig.7(b). 5.3.2. Fourth quadrant operation In the fourth quadrant, the estimated speed is also observed to follow the reference and the actual speeds as seen from Fig.8(a). The applied load torque and the machine torque are shown in Fig.8(b). In the second and fourth quadrant operations, (Fig.7(c) and Fig.8(c)) show that the total loss of the drive system without optimization algorithm is significantly higher as opposes to that when golden section algorithm is active (Fig.7(d) and Fig.8(d)).

549

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

a

b

20 15

2

Torque (Nm)

10

Speed (rad/s)

2.5

Reference Speed Estimated Speed Actual Speed

5 0 -5

1.5

0.5 0

-10 -15

0

10

Time (s)

20

-0.5

30

c

0

10

Time (s)

20

30

d

400 300

Without Efficiency optimization

200

300 Area without Efficiency optimization

200 100

100 0

Efficiency optimization starts

400

Total Loss (W)

Total Loss (W)

Load Torque Electromagnetic Torque

1

0

10

20

0

30

0

10

20

30

Time (s) Time (s) Fig.7. Second quadrant operation: (a) reference, estimated and actual speeds, (b) load and electromagnetic torques, and total drive loss:(c) without efficiency optimization, (d) with efficiency optimization.

a

b Reference Speed Estimated Speed Actual Speed

Load Torque Electromagnetic Torque

4

Torque (Nm)

Speed (rad/s)

15

10

5

2

0

-2

0

0

10

Time (s)

20

30

-4

0

10

Time (s)

20

30

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

c

d

400

400

300

Total Loss (W)

Total Loss (W)

550

Without Efficiency optimization

200

300 Area without Efficiency optimization

200 100

100 0

Efficiency optimization starts

0

0 10 20 30 Time (s) Time (s) Fig.8. Fourth quadrant operation: (a) reference, estimated and actual speeds, (b) load and electromagnetic torques, and total drive loss:(c) without efficiency optimization, (d) with efficiency optimization.

0

10

20

30

6. Conclusion Induction motor (IM) driven electric vehicle is preferred due to the small size, light weight, rugged and energy efficient characteristics of IM. This paper presents an application of energy optimization technique for an inverterfed IM drive, based on the drive’s power loss operating in wide speed range. A new MRAC based speed estimation technique for the vector controlled induction motor drive is utilized for implementation of the said optimization algorithm. The efficiency optimization algorithm generates the optimal value of i*ds . Hence, core loss of the drive system is minimized as the flux level is optimized. In this proposed scheme, the instantaneous and steady state values of fictitious resistance (R) are utilized in the reference and adaptive models respectively. The proposed scheme does not require any kind of flux computation, making it suitable for low speed operation. The proposed IM drive works satisfactorily in all the four quadrants of operation. Moreover, the first-order eigenvalue sensitivity analysis along with first order perturbation of eigenvalues ensure the stability of the IM drive system in the motoring and regenerating modes of operation. APPENDIX A A.1. Induction motor parameters Rating

2.2 kW, 3-phase, 415 V, 50 Hz, 4 pole

pf

0.75

Stator/rotor resistance

5.55 Ω , 4.01 Ω

Stator/rotor inductance

A.2. Induction motor controller parameters Proportional

Integral

controller

controller

Speed

0.25

2

0.7249 H

Flux

0.2

4

Mutual inductance

0.7 H

Current

1

700

Rotor inertia

0.0237 kg-m2

MRAC

0.18

0.8

Friction coefficient

0.001

Controller

References [1] Unnewehr L, Nasar S. Electric vehicle technology. New York: John Wiley & sons.;1982. [2] Haddoun A, Benbouzid M, Diallo D, Abdessemed R. A loss-minimization DTC scheme for EV induction motors. IEEE Trans. Veh. Technol., 2007; 56(1), 81-88. [3] Ta C, Chakraborty C, Hori Y. Efficiency maximization of induction motor drives for electric vehicles based on actual measurement of input power. The 27th Annual Conference of the IEEE Industrial Electronics Society. IECON, 2001; 3, 1692 -697. [4] Vas P. Sensorless vector and direct torque control. New York: Oxford University Press.;1998. [5] Bose BK. Modern power electronics and ac drives. New Delhi: Prentice Hall.; 2002. [6] Kennel RM. Encoders for simultaneous sensing of position and speed in electrical drives with digital control. IEEE Tran. Ind. Appl.,2007; 43(6).

Abhisek Pal et al. / Energy Procedia 90 (2016) 540 – 551

[7] Holtz J. Sensorless control of induction machines-with or without signal injection? IEEE Trans. Ind. Electron., 2006; 53(1), 7-30. [8] Pongam S, Sangwongwanich S. Stability and dynamic performance improvement of adaptive full- order observers for sensorless PMSM drive. IEEE Trans. Power Electron., 2012; 27(2), 588–600. [9] Kubota K, Matsuse K, Nakano T. DSP-based speed adaptive flux observer of induction motor. IEEE Trans. Ind. Appl., 1993; 29(2), 344–348. [10] Gadoue SM, Giaouris D, Finch JW. Stator current model reference adaptive systems speed estimator for regenerating-mode low-speed operation of sensorless induction motor drives. IET Electric Power Applications, 2013; 7(7), 597 - 606. [11] Teja AVR, Chakraborty C. A novel model reference adaptive controller for estimation of speed and stator resistance for vector controlled induction motor drives. IEEE International Symposium on Industrial Electronics (ISIE), 2010; 1187 - 1192. [12] Kumar R, Das S, Syam P, Chattopadhyay AK. Review on model reference adaptive system for sensorless vector control of induction motor drives. IET Electric Power Applications, 2015; 9(7), 496-511. [13] Xiao J, Li B, Gong X, Sheng Y, Chai, J. Improved performance of motor drive using RBFNN-based hybrid reactive power MRAS speed estimator. IEEE International Conference on Information and Automation (ICIA), 2010; 588-593. [14] Benbouzid ME, Said NS. An efficiency-optimization controller for induction motor drives. IEEE Power Engineering Review, 1998; 18(5), 63-64. [15] Kirschen DS, Novotny DW, Suwanwissot W. Minimizing induction motor losses by excitation control in variable frequency drives. IEEE Trans. Ind. Appl., 1984; IA-20(5), 1244-1250. [16] Farasat M, Trzynadlowski A M, Fadali MS. Efficiency improved sensorless control scheme for electric vehicle induction motors. IET Electr. Syst. Transp., 2014; 4(4), 122-131. [17] Sousa GD, Bose BK, Cleland JG. Fuzzy logic based on-line efficiency optimization control ofan indirect vector-controlled induction motor drive. IEEE Trans. Ind. Electron., 1995; 42, 92-198. [18] Sadegh V, Rahman M. An on-line loss minimization controller for the Interior Magnet motor drives. IEEE Trans. Energy Convers., 1999; 14(4), 1435-1440. [19] Ta CM, Hori Y. Convergence improvement of efficiency-optimization control of induction motor drives. IEEE Tran. Ind. Appl., 2001; 37(6), 1746-1753. [20] Chakraborty C, Hori Y. Fast efficiency optimization techniques for the indirect vector-controlled induction motor drives. IEEE Tran. Ind. Appl., 2003; 39(4), 1070-1076. [21] Kalavathy S. Operations research. New Delhi: Vikas Publishing House Pvt. Ltd.; 2002. [22] Konstantinov M, Wei G, Mehrmann V, Petkov P. Perturbation theory for matrix equations (studies in computational mathematics). NorthHolland: Elsevier Science Ltd.;2003. [23] Wilkinson J. The algebraic eigenvalue problem. New York: Oxford University Press; 1998.

551