34
Int. J. Industrial Electronics and Drives, Vol. 1, No. 1, 2009
Efficiency optimisation based speed control of IPMSM drive M. Nasir Uddin* and Fasil Abera Dept. of Electrical Engineering, Lakehead University, P7B 5E1, Thunder Bay, ON, Canada Fax: 1-807-766-7243 E-mail:
[email protected] *Corresponding author
E-mail:
[email protected]
Abstract: A model based energy optimisation algorithm for speed control of interior permanent magnet synchronous motor (IPMSM) drive is proposed in this paper. The efficiency of variable speed drives can be optimised by either the proper design of the motor or selecting the appropriate control techniques or both. In this work, the efficiency of IPMSM is optimised online based on a developed control technique. The d-axis armature current is utilised to minimise the losses of the IPMSM in a closed loop vector control environment. The completed drive is successfully implemented in real-time using DSP board DS1104 for a laboratory 5 hp motor. It is found from both simulation and experimental results that the efficiency of the proposed IPMSM drive is improved significantly as compared to the conventional id = 0 control technique. Keywords: energy optimisation; permanent magnet synchronous motor; proportional-integral (PI) controller; speed control; vector control. Reference to this paper should be made as follows: Uddin, M.N. and Abera, F. (2009) ‘Efficiency optimisation based speed control of IPMSM drive’, Int. J. Industrial Electronics and Drives, Vol. 1, No. 1, pp.34–41. Biographical notes: M. Nasir Uddin received his BSc and MSc degrees both in Electrical and Electronic Engineering from Bangladesh University of Engineering and Technology, Bangladesh, and PhD in Electrical Engineering from Memorial University of Newfoundland, Canada in 1993, 1996, and 2000, respectively. Currently, he is a Professor in the Department of Electrical Engineering, Lakehead University, Canada. He has authored/co-authored over 85 papers. He is the recipient of the First Prize Paper Award from IEEE/IAS/IACC committee and both 2004 Contributions to Research and Teaching Awards from Lakehead University. He is a registered Professional Engineer in the Province of Ontario, Canada. Fasil Abera received his BSc in Electrical/Electronic Engineering from DeVry University, Phoenix, AZ, USA and MSc in Control Engineering from Lakehead University, Thunder Bay, ON, Canada, in 2003 and 2008, respectively. He has worked as a Test Engineer for Circuit Center Inc. and Celestica Electronics Manufacturing Companies, Canada from 2003 to 2005 and 2005 to 2006, respectively. His main research interests are in the areas of electric machines drives, power electronics, intelligent control and efficiency optimisation of electric machines.
1
Introduction
There have been growing concerns over energy consumption and the environment due to the soaring energy cost and tighter environment protection laws (Morimoto et al., 1990). Electric vehicle is a good example in this matter. Electric motor driven equipment utilises approximately 58% of the consumed electrical energy (Little, 1999). Thus, efficiency optimisation of motors utilised in industry becomes an important matter. Although, induction motors (IM) are widely utilised in the industry they have their own limitations regarding efficiency due to their inherent rotor copper loss that results in poor efficiency. Recently, as an alternative the interior permanent magnet synchronous motor (IPMSM) is becoming popular
Copyright © 2009 Inderscience Enterprises Ltd.
in variable speed drive applications due to some of its advantages such as high efficiency, high power density, high power factor low noise and robustness as compared to the conventional IM and other AC motors (Little, 1999). Since IPMSM has permanent magnets buried in the rotor core, it has no rotor copper loss and less heat is generated inside the motor. This avoids the additional need for cooling which is necessary in the case of IM (Little, 1999; Jahns et al., 1986). The operating efficiency of a motor drive can be improved in many ways such as optimum rotor structure design and intervening in the motor operation principle with different control techniques (Abrahamsen et al., 1996). Several control methods have been proposed in order to
Efficiency optimisation based speed control of IPMSM drive reduce the losses of IPMSM drives and improve their performances (Jahns et al., 1986). For example, copper loss can be minimised by the maximum torque-per-ampere (MTPA) current control technique (Little, 1999). Traditionally, the IPMSM has been controlled by keeping the d-axis component of the stator current, id = 0 in order to make the control task easier (Fernhndez-Bernal et al., 1998; Lau and Uddin, 2005; Vukosavi, 1998; Sousa et al., 1986; Nasar et al., 1993). However, with id = 0 control it is not possible to control the air gap flux and hence, the efficiency of the motor cannot be optimised (Fernhndez-Bernal et al., 1998). Moreover, with id = 0 controlling the reluctance torque of IPMSM cannot be utilised, which is an advantageous feature of IPMSM as compared to a surface mounted permanent magnet synchronous motor (Morimoto et al., 1990). Especially, at light load condition the motor flux becomes excessive for the developed torque resulting in higher iron loss and poor efficiency of the motor (Lau and Uddin, 2005; Vukosavi, 1998). The efficiency of IPMSM can be improved by reducing the air gap flux as the iron loss is roughly proportional to square of the air gap flux density. The loss minimisation algorithms can be developed in one of the two ways such as, a
search based
b
model-based loss minimisation techniques.
Researchers have used both loss minimisation techniques for vector-controlled IPMSM drives (Stefanovic, 1994; Bose, 1988). The search based loss minimisation technique is insensitive to parameter variations which are caused by temperature and magnetic saturation (Vukosavi, 1998). In this loss minimisation technique the flux is decremented in stepwise manner until the minimum point for the total loss of the IPMSM, is reached. However, there are outstanding disadvantages in its application. First, torque ripple appears each time as the flux is changed in a stepwise manner. Second, when the optimal operating point is found the electromagnetic torque reserve is low, so the motor is very sensitive to load perturbations. Third, convergence of the magnetising current to the optimum value is very slow and never reached its optimal value but oscillates around it. For the above mentioned disadvantages of the search based loss minimisation technique the model based efficiency optimisation algorithm (Nasar et al., 1993) is considered for this paper. The rapid evolution of powerful digital microcontrollers and power converters allows us to apply complex control strategies for vector control of motor drives in real-time, which makes the drives more economical and more robust (Sousa et al., 1986). One of the most important algorithms which can be implemented on digital microcontroller is a model based efficiency optimisation algorithm for speed control of IPMSM (Abrahamsen et al., 1996; Sousa et al., 1986). In this work, the efficiency is optimised based on the optimal value of d-axis current iod, which is calculated online. The value of the iron loss resistance Rc is calculated offline based on the motor model. The detailed derivations of these values are presented in the paper. Whereas, in the
35
existing research (Morimoto et al., 1990), Rc was estimated empirically and iod for IPMSM was not calculated, rather implied from the simplest surface mounted permanent magnet synchronous motor in order to minimise the mathematical burden and cost of the drive. Moreover, the speed response was not tested rigorously along with the efficiency, which is essential for a high performance drive. The complete simulation model for the closed loop vector control of IPMSM drive incorporating the proposed loss minimisation algorithm is developed using Matlab/Simulink software (Matlab, 2004). The complete drive is also successfully implemented in real-time using DSP board DS1104 for a laboratory 5 hp IPMSM (dSPACE, 2003). The proposed efficiency optimisation algorithm is tested at different operating conditions such as sudden change in load, command speed and parameter variations. It is found that the efficiency of the proposed IPMSM drive is improved significantly as compared to the conventional id = 0 control technique.
2
Loss model based control algorithm
An equivalent d-q axis model of IPMSM in rotor reference frame with simplified loss representation is given in Figure 1. The mathematical equations (1)–(4) are derived based on Figure 1 (Fernhndez-Bernal et al., 1998). Figure 1
D-q axis model of IPMSM incorporating iron loss
(a)
(b)
⎡ vd ⎤ ⎢v ⎥ = Ra ⎣ q⎦
⎞ ⎡ vod ⎤ ⎥ ⎟⎢ ⎠ ⎣⎢ voq ⎦⎥
(1)
−ω ρ Ld ⎤ ⎡iod ⎤ ⎡ 0 ⎤ ⎥ ⎢i ⎥ + ⎢ωψ ⎥ 0 ⎦ ⎣ oq ⎦ ⎣ a ⎦
(2)
⎡iod ⎤ ⎛ R a ⎢i ⎥ + ⎜ 1 + ⎣ oq ⎦ ⎝ R c
⎡ Vod ⎤ ⎡ 0 ⎢⎣ Voq ⎥⎦ = ⎢ω L d ⎣
36
M.N. Uddin and F. Abera
iod = id − icd , ioq = iq − icq icd = −
ω ρ ioq Ld Rc
, icq =
(3)
ω ( ψ a + Ld iod )
(4)
Rc
(
)
0.5
(5)
(
Va = ⎡ R a id − ω ρ Ld ioq ⎢⎣
) + ( R a iq + ω( ψa + Ld iod ) ) 2
(
Te = Pn ψ a ioq + (1 − ρ ) Ld iod ioq
Where, ρ =
2 ⎤ 0.5
⎥⎦
)
(6) (7)
Lq
Pn is number of pole pairs, Ia is rms value Ld′ of the line-to-line stator current and Va is rms value of stator voltage. The first term in (7) represents the magnetic torque and the second term is the reluctance torque. Copper and core losses are the two controllable losses in electric motors (Sneyers et al., 1985). Core loss is the combined effect of eddy current and hysteresis losses. Eddy current losses are caused by the flow of induced currents inside the stator core. On the other hand, hysteresis losses are caused by the continuous variation of flux linkages in the core (Jahns, 1987; Abbondanti, 1977). Based on equations (3), (4) and Figure 1, the copper loss WCu, the iron loss WFe and the mechanical loss WM are expressed as (8), (9) and (10) respectively.
(
Wcu = R a id2 + iq2
) 2
ω ρ ioq Ld ⎞ ⎛ ω ( ψ a + Ld iod ) ⎞ ⎛ = R a ⎜ iod − ⎟⎟ ⎟ + ⎜⎜ ioq + Rc Rc ⎝ ⎠ ⎝ ⎠
(
2 2 WFe = R c icd + icq ⎛ ω ρi L oq d =⎜ ⎜ R ⎜ c ⎝
(
WM = TM ωr
)
)
2
(
)
(
2 2 2 2 WE = R a icd + i cq + R c icd + icq
Where, id and iq are d-axis and q-axis stator currents, vd and vq are the d-axis and q-axis armature voltages, iod and ioq are the d-axis demagnetising and q-axis torque generating currents, icd and icq are d-axis and q-axis core loss currents, Ra and Rc represents the stator copper and core loss resistances and Lq and Ld are q-axis and d-axis self inductances, respectively, ψa is magnet flux linkage and ωr is the rotor speed. The harmonics in the back EMF also generate an iron loss. However, the harmonic generated iron loss is not controllable therefore its effect is not considered in this paper. The stator current Ia, the stator voltage, Va and the developed torque Te are expressed in (5), (6) and (7), respectively. Ia = id2 + iq2
dependent WM is not controllable by the loss minimising algorithm. The output power Pout and efficiency of the IPMSM drive η are expressed as (13) and (14).
2
(8)
)
(11)
WL = WM + WE
(12)
Pout = Te ωr
(13)
η=
Pout ∗100 Pout + WL
(14)
Efficiency can be improved by minimising the controllable electrical losses WE of the IPMSM drive (Stefanovic, 1994). The loss minimisation condition that has to be fulfilled, at steady state, is derived by partially differentiating (11) with respect to iod and equating the result to zero as shown in (15). ∂WE = 0, ∂iod
T, ω = constant
(15)
As a result, the loss minimisation condition is given as XY − T 2 Z = 0
(16)
Where, X, Y and Z are given by (17) and T is given by equation (7) respectively.
{
}
X = Pn 2 R a R c2 iod + ω2 Ld ( R a + R c )( Ld i od + ψ a ) Y = ⎡⎣ ψ a + (1 − ρ ) Ld iod ⎤⎦
3
{
Z = R a R c2 + ( R a + R c )( ω ρ Ld )
2
} (1 − ρ) L
17 d
For given torque T and speed ω the optimal d-axis current iod is derived from (16) and shown by below.
(
2 4 iod = −A −1 Biod + Ci3od + Diod −E
)
(18)
Where, A, B, C, D and E are given by (19).
(
2 A = ψ 3a λ + ω2 − 2ioq ρ2 ψ a L4d αλω2 ( R a + R c
B C D E
(
2
(
) (
)
= 3 (ω L3d R a + R c ψ a2 α) (1 + α) + Ld ψ a2 αλ 2 −2ioq ρ2 ψ a L5d α3λω2 R a + R c = 3L2d ψ a α 2 λ + 3ω2 L4d α 2 R a + R c ψ a 1 + α = L3d α3λ + L5d α3ω2 R a + R c 2 = −ioq ρ2 ψ a2 L3d λω2 α
(
(
)
)
)
(
)
) (19)
Where, λ = R a R c2 , α = (1 − p). 2 ⎞ ⎞ ⎛ 2 ⎟ + ⎜ ω ( ψ a + Ld iod ) ⎟ ⎟ ⎜ ⎟ Rc ⎟ ⎝ ⎠ ⎠
The current ioq can be calculated from (20). (9) ioq =
(10)
Where, TM is the frictional torque of the motor and ωr = ( ω p n ) is the angular velocity of the motor where ω is the electrical speed. Unlike Wcu and WFe,, the speed
T 2
Pn (ψ a + ω Ld iod (1-α))
20
However, if the motor under consideration is non-salient,
(
i.e., Lq = Ld ψ 3a
) then Z term will be 0, the Y term becomes
and then the condition X = 0 will give the optimal d-axis current iod as shown in (21). In this case, the optimal
Efficiency optimisation based speed control of IPMSM drive current iod is independent of the torque and easier to calculate. iod = −
ω2 Ld ( R a + R c ) ψ a
R a R c2 + ω2 L2d ( R a + R c )
(21)
The values of the motor parameters are given in Table 1. The value of Rc in Table 1 is calculated at the rated speed and torque from (8) and (9). First, the iron loss WFe is calculated by subtracting the mechanical loss WM, the copper loss Wcu and the output power Pout from the input power. The value of Rc is considered constant. Based on the above mentioned loss minimisation algorithm, the block diagram of the proposed IPMSM drive is developed and shown in Figure 2. For vector control purpose, the speed controller is implemented using a classical proportion and integral (PI) controller because of its simplicity and faster response (Fernhndez-Bernal et al., 1998). The PI controller has speed error as its input and the command current, i∗q as its output. The PI speed controller is given by,
∫
i∗q = K p Δωr + K i Δωr dt
(22)
Where Kp is the proportional gain and Ki is the integral gain and Δωr = ( ω − ωr ) is speed error. The PI controller is tuned based on Ziegler-Nichols tuning chart and found to be Ki = 17 and Kp = 10. The command phase currents i∗a , i∗b and i∗c generated from i∗q , which is the output of the speed
37
actual phase currents with corresponding command currents to generate PWM logic signals. These signals trigger the IGBT gates of the inverter in order to supply the IPMSM with appropriate voltage and frequency. The complete closed loop vector controlled IPMSM drive with the proposed loss minimisation algorithm is simulated using Matlab/Simulink as shown in Figure 2. For real-time implementation the control algorithms are implemented through developing a real-time Simulink model. Then the model is downloaded to the DSP board utilising ControlDesk software and real time workshop (RTW) (dSPACE, 2003). The sampling frequency used in the work is found to be 5 kHz. Table 1
IPMSM parameters
Number of poles
6
Ra
0.242 ohm
Lq
6.42 mH
ψa
0.24 Wb
Ld
5.06 mH
Rc
7.5 ohm
Rated frequency
87.5
Ia
14.2 A
Va
183
T
19.1 Nm
Tmech
0.001
Prated
5 hp
i∗d ,
controller and which is the output of the loss minimisation algorithm utilising the inverse park’s transformation. The hysteresis controller compares the Figure 2
Block diagram of the proposed loss model based efficiency optimisation of IPMSM drive (see online version for colours)
Simulated responses of the proposed loss minimisation based IPMSM drive (a) speed (b) torque and iq (c) torque and id (d) speed and efficiency (see online version for colours) Speed responce with loss minimization algorithm with constant load 200 180 command speed
160 140 speed (rad/sec)
The proposed loss minimisation control algorithm for IPMSM drive is tested in both simulation and experiment under different operating conditions such as sudden change in command speed, load and parameter. Sample results are presented below. Figures 3 and 4 show the simulated responses of IPMSM drive with proposed loss minimisation and id = 0 control, respectively, in order to see the responses for a step increase of speed and load conditions. Initially, a step input of speed from zero to 100 rad/s with a load of 10 Nm is applied and then at t = 0.5 s the load is increased from 10 Nm to 19 Nm. Again, at t = 0.6 s, the command speed is increased from 100 rad/s to 180 rad/s while a constant load of 19 Nm is applied. Figure 3(a) shows the speed response of the IPMSM drive with the proposed loss minimisation controller and Figure 3(b) shows the speed response with the conventional id = 0 control. It is seen from Figure 3(a) that the actual motor speed follows the command speed smoothly without any overshoot/undershoot and steady-state error for the proposed loss minimisation algorithm. Whereas, for the conventional id = 0 control the speed response suffers from overshoot/undershoot and exhibits slight steady-state error, which is not acceptable for high performance drive applications. The increase in load at t = 0.5 s can be seen from the increase in torque and iq from Figures 3(b) and 4(b). The speed response for the proposed control is almost insensitive whereas, for the conventional id = 0 control there is dip in speed when the load is increased. For the proposed control, d-axis current is adjusted with the changing load condition to optimise the efficiency, which can be seen from Figures 3(c) and 3(d). Whereas, for the conventional control as id always remains zero, the efficiency drops with the step change in command speed which can be seen from Figures 4(c) and 4(d). It is found in Figures 3(d) and 4(d), that an efficiency improvement of about 4% can be achieved with the proposed loss minimisation algorithm as compared to the conventional id = 0 control technique. The change in parameter, particularly, the change in value of Lq is a common phenomenon for IPMSM drives due to magnetic saturation. In order to see the responses of the proposed loss minimisation algorithm with parameter variation, the simulation results are presented in Figure 5. The value of Lq is decreased by 50% at t = 0.5 s while the motor was running at rated speed (183 rad/s) and rated load (19 Nm) conditions. It is seen from Figure 5(a) the speed response is insensitive to the parameter change. Figures 5(b) and 5(c) show the corresponding variations in d and q axes currents, respectively. It is found from Figure 5(d) that the efficiency is decreased slightly with the step decrease in Lq. However, in practice the value of Lq will decrease slowly and hence, the efficiency will not be affected that much. Therefore, the proposed loss minimisation based controller is found to be robust while maintaining the efficiency at its optimal level against different operating conditions such as sudden load change, step change of speed and parameter variations.
Figure 3
120 100 80 60 rotor speed
40 20 0
0
0.1
0.2
0.3
0.4
0.5 time(sec)
0.6
0.7
0.8
0.9
1
(a) q-axis current responce for load change with loss minimization algorithm 40
30 torque load
20
m agnitude
Simulation and experimental results
X: 0.8431 Y: 13.61
10
0
q-axis current
-10
-20
-30
0
0.1
0.2
0.3
0.4
0.5 time(sec)
0.6
0.7
0.8
0.9
1
(b) d-axis current respoc for 50% load change 25
20
15 torque load 10 magnitude(amper-Nm)
3
M.N. Uddin and F. Abera
5
0 optimal d-axis current -5
-10
-15
-20
0
0.1
0.2
0.3
0.4
0.5 time(sec)
0.6
0.7
0.8
0.9
1
(c) efficiency responce for speed change 200
180 rotor speed 160
140
120 magnitude
38
X: 0.8431 Y: 92.88
100
80 efficiency 60
40
20
0
0
0.1
0.2
0.3
0.4
0.5 time (sec)
(d)
0.6
0.7
0.8
0.9
1
39
Efficiency optimisation based speed control of IPMSM drive Figure 4
Simulated responses of IPMSM drive with id = 0 control technique (a) speed (b) torque and iq, (c) torque and id (d) speed and efficiency (see online version for colours)
Figure 5
Simulated responses for the proposed loss minimisation based IPMSM drive with a step decrease in Lq (a) speed (b) iq (c) id (d) efficiency (see online version for colours)
id=0 speed rresponce for sudden load change
speed 200
200 180
150 speed(rad)
command speed 160
100 50
120
0
100
0
0.1
0.2
0.3
0.1
0.2
0.3
-3
80 rotor speed
40 20 0
x 10
7
60
inductance(H)
m agnitude
140
0
0.1
0.2
0.3
0.4
0.5 time(sec)
0.6
0.7
0.8
0.9
0.8
0.9
1
0.8
0.9
1
0.8
0.9
1
0.8
0.9
1
0.8
0.9
1
0.8
0.9
1
0.8
0.9
1
0.8
0.9
1
6 5 X: 0.5998 Y: 0.00321
4 3
1
0.4 0.5 0.6 0.7 time(sec) 50% decrease in Q-axis inductance
0
0.4
(a)
0.5 time(sec)
0.6
0.7
(a)
q-axis current responce for load change in id=0 control . 40
Q.axis current responce for 50% change in Lq 40
torque load
20
m ag nitu de
20
current (A)
30
0
10
-20
0
0
0.1
0.2
0.3
0.1
0.2
0.3
-3
7
q-axis current inductance(H)
-10 -20 -30
X: 0.4982 Y: 3.963
0
0.1
0.2
0.3
0.4
0.5 time(sec)
0.6
0.7
0.8
0.9
0.4 0.5 0.6 0.7 time(sec) 50% decrease in Q-axis inducatnce
6 5 4 3
1
x 10
0
0.4
(b)
0.5 time(sec)
0.6
(b)
id=o current responce for sudden load change
D-axis currrent responce for 50% change in Lq
25
5 0 currrent(A)
20 torque load
magnitude
15
X: 0.6216 Y: 0.8981
-5 -10 -15 -20
10
0
0.1
0.2
0.3
0.1
0.2
0.3
-3
7
5
inductane(H)
d-axis current
0
-5
0.7
0
0.1
0.2
0.3
0.4
0.5 time(sec)
0.6
0.7
0.8
0.9
1
x 10
0.4 0.5 0.6 0.7 time(sec) 50% decrease in Q-axis inductane
6 5 4 3
0
0.4
(c)
0.5 time(sec)
0.6
0.7
(c)
efficiency responce for id=0 control and speed change 200
Efficiency 100
180
efficiency(%)
rotor speed
160
120 100
70 60 0
0.1
0.2
0.3
0.1
0.2
0.3
-3
80
7
60 efficiency
40 20 0
X: 0.647 Y: 90.91
80
50
X: 0.9067 Y: 87.2
inductance(H)
m agnitude
140
90
0
0.1
0.2
0.3
0.4
0.5 time(sec)
(d)
0.6
0.7
0.8
0.9
1
x 10
0.4 0.5 0.6 0.7 time(sec) 50% decrease in Q-axis inductance
6 5 4 3
0
0.4
0.5 time(sec)
(d)
0.6
0.7
40
M.N. Uddin and F. Abera
A sample experimental steady-state speed response and corresponding efficiency for the proposed loss minimisation based IPMSM drive is shown in Figure 6. The motor was running at 100 rad/s with 20% of rated load condition. It was tested at light load condition as the efficiency becomes poor at light load condition and hence considered as main concern in the paper. It is found that the drive efficiency is almost 92% in steady-state with the proposed loss minimisation control. For comparison purpose, the steady-state efficiency response for the same drive with identical condition but id = 0 control is shown in Figure 7. It is seen from this figure that the efficiency is around 90% with conventional id = 0 control. Therefore, the effectiveness of the proposed algorithm to optimise the efficiency of the drive in real-time is verified. The detailed experimental investigation and the results will be presented in the near future. Figure 6
Experimental steady-state speed response and corresponding efficiency for the proposed loss minimisation based IPMSM drive % Efficiency
Speed, rad/s Efficiency
Time, s
Figure 7
Experimental steady-state efficiency response of the IPMSM drive with conventional id = 0 control (see online version for colours)
Time, s
4
Conclusions
In this paper, a model based efficiency optimisation control algorithm for vector-controlled IPMSM drive has been developed, simulated and experimentally implemented. The developed efficiency optimisation control algorithm determines the optimal d-axis current of the drive for a given speed and torque command, it is as fast as the vector-control and it has no torque ripple. This developed efficiency optimisation algorithm is more generalised one as it can also be used for surface mounted PM motor with
Lq = Ld and for synchronous reluctance motor with ψa = 0. The performance of the proposed optimisation algorithm has been tested in both simulation and experiment at different operating conditions such as sudden load change, command speed change, parameter change, etc. The proposed algorithm has also been compared with the conventional id = 0 control scheme. It is found from the results that the proposed efficiency optimisation control algorithm can improve the efficiency as compared to the conventional id = 0 control scheme. The proposed loss minimisation algorithm has been found to be robust, efficient and hence it can be utilised as a potential candidate for high performance and highly efficient variable speed drive applications.
References Abbondanti, A. (1977) ‘Methods of flux control in induction motors driven by variable frequency, variable voltage supplies’, Int. Semiconductor Power Converter Conf. Record. Abrahamsen, F., Pedersen, J.K., Blaabjerg, F. (1996) ‘State-of-art of optimal efficiency control of low cost induction motor drives’, Proceedings of PESC’96, pp.920–924. Bose, B.K. (1988) ‘A high-performance inverter-fed drive system of an interior permanent magnet synchronous machine’, IEEE Trans. Ind. Appl., November–December, Vol. IA-24, pp.987–997. dSPACE (2003) Digital Signal Processing and Control Engineering Manual Guide, GmbH, Paderborn, Germany. Fernhndez-Bernal, F., Garcia-Cerrada, A. and Faure, R. (1998) ‘Loss-minimization control of synchronous machines with constant excitation’, IEEE Power Electronics Specialists Conf (PESC’98), May, Vol. 1, pp.132–138. Jahns, T.M. (1987) ‘Flux-weakening regime operation of an interior permanent-magnet synchronous motordrives’, IEEE Trans. Ind. Appl., July–August, Vol. IA–23, pp.681–689. Jahns, T.M., Kliman, G.B. and Neumann, T.W. (1986) ‘Interior permanent magnet synchronous motors for adjustable-speed drives’, IEEE Trans. Ind. Applicat., July–August, Vol. IA-22, pp.738–747. Lau, J. and Uddin, M.N. (2005) ‘Non linear adaptive backstepping based control for IPMSM drive’, International Electric Machines and Drives Conference, San Antonio TX, USA, 2005, pp.1689–1694. Little, A.D. (1999) ‘Opportunities for energy savings in the residential and commercial sectors with high-efficiency electric motors’, Final report, United Kingdom Environmental Protection Agency, pp.1–15. Matlab (2004) Simulink User Guide, The Math Works Inc. Morimoto, S., Takeda, Y., Hirasa, T. and Taniguchi, K. (1990) ‘Expansion of operating limits for permanent magnet motor by current vector control considering inverter capacity’, IEEE Trans. Ind. Applicat., September–October, Vol. 26, pp.866–871. Morimoto, S., Tong, Y., Takeda, Y. and Hirasa, T. (1990) ‘Loss drives minimization control of permanent magnet synchronous motor’, IEEE Trans. Industrial Electronics, September–October, Vol. 41, No. 5, pp.866–871. Nasar, S.A., Boldea, I. and Unnewehr, L.E. (1993) Permanent Magnet, Reluctance and Self-Synchronous Motors, Boca Raton, FL, CRC.
Efficiency optimisation based speed control of IPMSM drive Sneyers, B., Novotny, D.W. and Lipo, T.A. (1985) ‘Field weakening in buried magnet ac motor drives’, IEEE Trans. Ind. Appl., March–April, Vol. IA-21, pp.398-407. Sousa, G.C.D., Bose, B.K., Cleland, J.G. (1986) ‘Fuzzy logic based on-line efficiency optimization of an indirect vector-controlled induction motor drive’, IEEE Trans. Ind. Elec., Vol. 42, No. 2. Stefanovic, V.R. (1994) ‘Static and dynamic characteristics of induction motors operating under constant air-gap flux control’, presented at the IEEE IAS Annu. Meeting, 1976, October, pp.511–517. Uddin, M.N. and Rahman, M.A. (2000) ‘Fuzzy logic based speed control of an IPM synchronous motor drive’, Journal of Advanced Computational Intelligence, Vol. 4 No. 3, pp.212–219. Vukosavi, S.N. (1998) ‘Controlled electrical drives – status of technology’, Zbornik XLII Konf. ETRAN-a,rnja~ka Banja, 2–5 Juna, Sveska 1, pp.3–16.
41
