Session H4B
Energy Conservation Study on Induction Motors Using MATLAB/Simulink for Enhancing Electric Machinery Courses Navneet Kumar, Thanga Raj Chelliah Department of Water Resources Development and Management Indian Institute of Technology Roorkee Roorkee, India
[email protected],
[email protected] Abstract—This paper describes MATLAB/Simulink implementation of optimal excitation control on a three-phase induction motor (IM) for energy conservation at light loads. This simulation model is developed to support and enhance Loss Minimization Control (LMC) on electric machinery education at the undergraduate and postgraduate level in electrical engineering. This study provides the saving of real, reactive and total power of the motor (1 hp) operating with mine-hoist load diagram.
S. P. Srivastava
Department of Electrical Engineering Indian Institute of Technology Roorkee Roorkee, India
[email protected]
redesigned or fed through an inverter [13]. Simply, the flux must be reduced, obtaining a balance between copper and iron losses [12].
Index Terms—education; energy conservation; induction motors; loss model control; MATLAB/Simulink
I.
INTRODUCTION
The energy sector faces twin challenges. The first is to make more energy available at affordable prices to enable all people. The second is to slow the world’s overall growth of energy consumption through conservation and energy efficiency improvement [1]. Due to emission of CO2 (from the large generating stations) in the atmosphere and hence global warming, so the policy makers, researchers and academician have an important role to play to improve the efficiency of electrical devices. Therefore, cheaper and more practical solution is the “energy conservation”, particularly for industrial consumers who account for more than 50 per cent of the total energy consumption. Interactive learning/teaching with computer models and simulations of induction motor is easy for undergraduate electric machinery course. In this area, low-cost personal computers and a variety of software packages have led to the concept of “computer-aided teaching or learning.” To illustrate steady-state operation of the motor under various loading conditions, these multimedia tools is increasingly popular in education and support the classroom teaching [2]–[7]. Three-phase induction motors (IMs) are the most frequently used machines in various electrical drives. About 70% of all industrial loads on a utility are represented by IMs [8]. So for energy conservation the major attention is paid to the efficiency of IM [9]. IM efficiency varies with load as shown in Fig. 1 [10]. However, at light loads, iron losses increase dramatically, reducing considerably the efficiency [11], [12]. The efficiency and power factor can be improved by making the motor excitation a monotone increasing function of the load. To achieve this goal, the induction motor should either be
Figure 1. Efficiency vs. load. [10]
The organization of this paper is as follows. Section II vector control of induction motor with LMC, Section III detailed discussion of MATLAB/Simulink model for energy conservation in induction motor, Section IV presents the simulation results of 1 hp motor and analyzes the operation of the motor for energy conservation, and finally Section V conclusion. II.
VECTOR CONTROL OF INDUCTOR MOTOR WITH LMC
In general, there are two different approaches to improve the induction motor efficiency especially under light-load conditions, namely, loss model controller (LMC) and search controller (SC). Many researchers have been reported several strategies using different variables to minimize losses in IM. Some algorithms use slip speed [11], [14], rotor flux [13], [15]–[17], power input [15], [16], and voltage [19]. The operation LMC offers ripples in load torque during the variable speed and load operation [20]–[21]. Vector control of the induction motor is running in a closed-loop with the speed sensor coupled to the shaft shown in Fig. 2. The input commands of a vector controlled induction motor drive are reference torque, reference speed, actual speed and three-phase stator currents. The torque command is generated from the speed controller, whereas the flux command is selected by LMC according to the requirements of load. This paper considers rotor flux as a variable and searches its optimum through LMC. The proposed efficiency optimization controllers in induction motor are simulated by using MATLAB/SIMULINK. Torque producing current (iqs) is generated by Proportional Integral (PI) controller and flux
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Session H4B
producing current (ids) is generated by energy controller shown in Fig. 3 and are converted into three phase quantities. PWM current controller generates the pulses for inverter triggering circuits according to the error in the currents between reference and actual values.
{
Threephase AC
Rectifier and Inverter system
IM
Load
Figure 5. per unit induction motor equivalent circuit. [13]
Gate drive circuitry
Ref. speed w* r Ref. torque T * r
Vector Control With LMC
ia ib
B. Loss Model of IM The equivalent circuit of the IM is similar to that for a transformer and it is also called as rotating transformer. Moreover IM parameters are derived from no-load and blocked rotor tests and can be easily represented by per-unit quantities.
Speed sensor
w m Actual Speed
Figure 2. Vector control induction motor drive with LMC. Ref. speed w* r Ref. torque * Tr
Motor Loss Model with equivalent motor parameters
* i ds
The per-phase IM equations (2)–(5) are given in the perunit systems [13]:
∗ Figure 3. Optimal flux producing current 𝑖𝑖 calculation.
A. Loss Model Controller The Loss Model Controller is a feed-forward approach, which calculates the optimum set of variables of the machine, depending on the optimization (maximize or minimize) of an objective function, defined using the machine parameters [22]. The objective function used in the present work is the total loss of induction motor drive. The flow of model-based controller is shown in Fig. 4. The approach requires knowledge of the exact values of machine parameters which include core losses and main inductance flux saturation.
𝑎𝑎 =
𝐼𝐼 =
&i
≤ Φ ≤ Φmax
s
(2)
=
(3)
The rotor current reflected in to the stator in terms of the air gap flux is given by:
Read desired speed and torque values
min
𝐼𝐼 =
* loss model subject to Find optimal ids from * *
=
The magnetizing current in terms of the air-gap flux and the magnetizing reactance is given by:
Start
Φ
(4)
The stator current in terms of rotor current and magnetizing current neglecting magnetic saturation is given by:
≤ ismax
Filter optimal value of ids and do the field orientation *
𝐼𝐼 =
Reference current generating using PWM current controller
End
Figure 4. Flowchart of model-based control.
The flux producing current command for vector control of induction motor can be calculated from the optimal flux obtained from scalar model as shown in equation (1). Maximum levels of flux and stator currents are forced as constraints in the algorithm. It is noted that the motor’s optimum operation is normally below the rated flux and hence flux constraint is not very important in the algorithm. Once ∗ ) is calculated as in equation optimal flux producing current (𝑖𝑖 (1), it is given to the stator reference current generation block as shown in Fig. 5 and generates appropriate pulses for PWM inverter which results optimal operation of induction motor in terms of minimum loss or maximum efficiency.
∗ 𝜙𝜙
where 𝜏𝜏 -Rotor time constant.
+ 1+2
(5)
The individual loss equations in the IM are given by [13]:
Pulse generation and given to inverter
∗ = 𝑖𝑖
𝐼𝐼
(1)
Copper losses 𝑃𝑃 = 𝑅𝑅 𝐼𝐼 + 𝑅𝑅 𝐼𝐼 Iron losses 𝑃𝑃 = 𝐾𝐾 1 + 𝑠𝑠 𝑎𝑎 + 𝐾𝐾 1 + 𝑠𝑠 𝑎𝑎 𝜙𝜙 Stray losses 𝑃𝑃 = 𝐶𝐶 𝜔𝜔 𝐼𝐼 Mechanical losses 𝑃𝑃 = 𝐶𝐶 𝜔𝜔
(6) (7) (8) (9)
𝑃𝑃 = 𝑃𝑃 + 𝑃𝑃 + 𝑃𝑃 + 𝑃𝑃
(10)
The total losses in IM drive system is given by:
From equations (6)–(9), the total losses can be rewritten as:
𝑃𝑃 = 𝑅𝑅 𝐼𝐼 + 𝑅𝑅 𝐼𝐼 + [𝑘𝑘 1 + 𝑠𝑠 𝑎𝑎 + 𝑘𝑘 1 + 𝑠𝑠 𝑎𝑎 ∅ ) + 𝐶𝐶 𝜔𝜔 𝐼𝐼 + 𝐶𝐶 𝜔𝜔
(11)
The constant are assigned as ke=0.0380, kh=0.0380, Cstr=0.0150, Cfω=0.093 [13]. Equation (12) shows the formulated loss model, which is a function of flux, torque and speed. This equation is used to find the optimal flux at minimum losses for required torque and speed. Optimal flux is tabulated in Table I for different combination of speed and torque.
978-1-4673-2418-2/12/$31.00 ©2012 IEEE August 20–23, 2012, Hong Kong IEEE International Conference on Teaching, Assessment, and Learning for Engineering (TALE) 2012 H4B-11
(12)
Minimize 𝑃𝑃 (𝑇𝑇 , 𝜔𝜔 , 𝛷𝛷 )
TABLE I.
Speed (pu)
OPTIMUM FLUX (PU) FOR DIFFERENT SPEED (PU) AND LOAD TORQUE (PU)
0.2 0.4 0.6 0.8 1.0
0.2 0.5253 0.5055 0.4864 0.4689 0.4532
Load Torque(pu) 0.4 0.6 0.8 0.7099 0.8073 0.8731 0.6926 0.7959 0.8649 0.6743 0.7823 0.8547 0.6554 0.7677 0.8436 0.6368 0.7527 0.8318
1.0 0.9226 0.9167 0.9080 0.9011 0.8927
III.
Session H4B
MATLAB/SIMULINK MODEL FOR ENERGY CONSERVATION OF INDUCTION MOTOR
The detailed MATLAB/Simulink model with LMC operation for energy conservation in induction motor is shown in Fig. 6. The different blocks used for this study are explained separately. A. Rectifier and Inverter system Three-phase supply with peak amplitude 330V and frequency 50 Hz is connected to rectifier via measurement block. This provides DC voltage and connected to inverter system with DC link inductor and capacitor, respectively as shown in Fig. 7.
Figure 6. MATLAB/Simulink model for energy conservation in induction motor. TABLE II.
Figure 7. MATLAB model for rectifier and inverter system.
B. Induction Motor Stationary reference frame three-phase squirrel cage 1-hp, 420V and 50Hz induction motor is used. The motor parameters are used tabulated in Table II. Three-phase currents, speed and torque are measured using measurement block.
INDUCTION MOTOR PARAMETERS
Stator resistance (RS) Stator inductance (Lls) Rotor resistance (Rr’) Rotor inductance (Llr’) Mutual inductance (Lm) Inertia Friction Factor Pole Pair
11.124 ohm 33.36 mH 8.8938 ohm 33.36 mH 490.45 mH 0.0018 Kg.m2 0 N.m.s 1
C. Proportional Integral (PI) Speed Controller The PI controller is used to generate the value of reference torque according to the error shown in Fig. 8. Unit delay is used to generate the reference torque in this controller.
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Session H4B
speed (ωm(n)) and then a discrete integration is carried out to calculate the flux angle at the nth instant. The flux angle (ψ) is defined at the nth instant as: ∗ 𝛹𝛹() = 𝛹𝛹() + 𝜔𝜔() + 𝜔𝜔() ∆𝑇𝑇 where ΔT is the sampling time.
(17)
The MATLAB model for calculating the flux angle (ψ) is shown in Fig. 11.
Figure 8. MATLAB model for PI controller.
D. Optimal flux calculation by LMC The loss model controller is shown in Fig. 9. According to the Table I, the optimal flux in accordance to speed (pu) and torque (pu) is entered in Look-up table. The flux controller picked up the value of flux when the speed/torque changes. Step input controlled switch is for selecting the constant flux or optimal flux. (13)
𝑖𝑖 = 𝑘𝑘. 𝜑𝜑
Figure 11. MATLAB model for calculating the flux angle.
Two-phase rotating to three-phase stationary reference frame converter can be modeled as follows: ∗ ∗ ∗ 𝑖𝑖 = −𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆 𝛹𝛹 + 𝑖𝑖 𝐶𝐶𝐶𝐶𝐶𝐶 𝛹𝛹
∗ 𝑖𝑖 ∗ 𝑖𝑖
=
∗
−𝐶𝐶𝐶𝐶𝐶𝐶 𝛹𝛹 + √3𝑆𝑆𝑆𝑆𝑆𝑆 𝛹𝛹
∗ ∗ = −(𝑖𝑖 + 𝑖𝑖 )
+
∗
(18) 𝑆𝑆𝑆𝑆𝑆𝑆 𝛹𝛹 + √3𝐶𝐶𝐶𝐶𝐶𝐶 𝛹𝛹
(19) (20)
where ids* and iqs* is refer to decoupled components of the stator circuit is* in two-phase system with respect to rotor reference frame and ias* , ibs* and ics* are three phase currents in stator reference frame. The MATLAB model for calculating the three phase reference currents by Equations (18)–(20) is shown in Fig. 12.
Figure 9. MATLAB model for optimum flux by LMC. ∗ ∗ E. Vector Controller [Estimator for 𝑖𝑖 , 𝑖𝑖 𝑎𝑎𝑎𝑎𝑎𝑎 𝜔𝜔∗ ]
This section calculates the direct and the quadrature axis stator current components (ids* and iqs*) and reference slip frequency of the rotor ω2*. Mathematically, the equations for calculating these quantities are given blow [23]: ∗ 𝑛𝑛 = 𝑖𝑖 𝑛𝑛 + 𝜏𝜏 𝑖𝑖
∗ 𝑖𝑖
𝑛𝑛 =
𝜔𝜔∗ 𝑛𝑛 =
∗ ()
∗ () ∗
∗ ()
∗ ()
(14) (15) (16)
The MATLAB model for the estimation of ids*, iqs* and ω2* with Equations (14)–(16) is shown in Fig. 10.
Figure 12. MATLAB model for the three phase reference current generation.
G. PWM Current Controller The current error for each phase is difference between the reference current and the sensed (actual) winding current for that phase. Hence the current errors in the three phases at the nth instant are modeled as below: ∗ ∗ 𝑖𝑖() = 𝑖𝑖() − 𝑖𝑖 ∗ ∗ 𝑖𝑖() = 𝑖𝑖() − 𝑖𝑖 ∗ ∗ = 𝑖𝑖() − 𝑖𝑖 𝑖𝑖()
Figure 10. MATLAB model the estimation of ids*, iqs* and ω2*.
F. Field orientation and reference current generation This block converts the two-phase reference currents (ids* and iqs*) in rotating frame into three phase reference currents (ias*, ibs* and ics*) in stationary reference frame. The flux angle (ψ) at which the synchronously rotating reference frame is to be inclined is also calculated as given below. First the reference slip frequency of the rotor (ω2*(n)) is added to the sensed rotor
(21) (22) (23)
These current errors in each phase are processed through a proportional controller to generate a modulating signal for each phase. This modulating signal is then compared with a triangular carrier waveform to generate a switching signal. The frequency of the modulating signal is the fundamental frequency of the inverter output voltage and the frequency of the carrier wave is the switching frequency of the inverter. The MATLAB model for calculating the current errors required for the PWM current controller is shown in Fig. 13. The model of pulse generation for PWM inverter is shown in Fig. 14. Model for triangular wave is shown in Fig. 15.
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Session H4B
1.0pu and at point L2 (separated by region T2, T3) the load is further reduced to 0.14pu but the speed is decreased to 0.5pu from 1.0pu. Load points L1 and L2 are consider at 1.5 sec and 3 sec respectively, for simulation.
Figure 13. MATLAB model for the three phase reference error generation.
(a)
Load Torque
(b)
Speed
Figure 17. Mine hoist load diagram.
1 Flux (pu)
1
Torque (N.m)
H. Three-phase instantaneous power measurement Real and reactive Power is measured by PQ measurement block available in MATLAB with input of three-phase voltages and currents. Total power is vector addition of real and reactive power shown in Fig. 16.
0.8 0.6
5
5
0
A mine hoist load diagram [24] is used in the present study to illustrate the importance of the LMC for energy conservation. A motor normally 2000-hp rated is employed with mine hoist and is operated with variable load and speed as shown in Fig. 17(a) and Fig. 17(b). These diagrams are separated by three regions (T1, T2, and T3) with respect to the load and speed [25]. In the present study, authors mainly concentrate energy saving in region T3 (light load region 0.14pu). At point L1 (separated by region T1, T2) the load is reduced to 0.87pu from 1.5pu, speed is increased from 0.5pu to
-5
350
300
300
250 200 150 100
(a)
0
350 Speed (rad/sec)
SIMULATION RESULTS AND DISCUSSION
Speed (rad/sec)
IV.
0.6 0.4
-5
Figure 16. MATLAB model for power measurement.
0.8
0.4
Torque (N.m)
Figure 15. MATLAB model for triangular wave generation.
The motor operating with the given load diagram is considered for the analysis of energy conservation. Constant flux operation and LMC operation are performed for the comparison of real, reactive and total power. The complete MATLAB/Simulink model of system is shown in Fig. 6. In The comparison in flux, torque and speed for different region of load diagram are shown in Fig. 18. Power saving is possible in region T3 due to light load region. The comparison for real, reactive and total power is shown in Fig. 19. The real power, reactive power and total power are reduced by 75W, 14VAR and 77VA, respectively in LMC operation compared to constant flux operation.
Flux (pu)
Figure 14. MATLAB model for pulse generation for PWM inverter.
0
1
2
Constant flux operation
3
4
250 200 150 100
0
1
(b)
2
3
LMC operation
Figure 18. Simulation results for flux, torque and speed.
978-1-4673-2418-2/12/$31.00 ©2012 IEEE August 20–23, 2012, Hong Kong IEEE International Conference on Teaching, Assessment, and Learning for Engineering (TALE) 2012 H4B-14
4
[8] 2500
2000
2000
1500
Real Power (w)
Real power (W)
2500
1000 455 W
500
[10]
380 W
500 0
500
500
Reactive Power (VAR)
600
400 300 200
64 VAR
100
200 100
2500
2500
2000
2000
1000 460 VA
500 0
1
2
3
4
[12]
300
0
1500
[11]
400
0
0
(a)
1000
600
Total Power (VA)
Total Power (VA)
Reactive Power (VAR)
0
[9]
1500
[13]
50 VAR
[14]
1500 1000
0
[15]
383 VA
500 0
Constant flux operation
1
(b)
2
3
4
LMC operation
Figure 19. Simulation results for real power, reactive power and total power.
V.
CONCLUSION
The use of multimedia tools for modeling and simulation is essential for modern teaching. The purpose of this paper is to attract undergraduate as well postgraduate students for energy conservation in induction machines. The students are also having difficulties for laboratory experiments. To overcome this, the author proposes a pedagogic approach based on the use of the MATLAB/Simulink software for understanding the concept of energy conservation in induction motor at light load. This study investigated the influence of LMC for the energy conservation of a 1-hp squirrel cage induction motor in mine hoist applications. Considerable real and reactive power saving are achieved. But LMC offers ripples in load torque at the point of reduction in flux which can be minimized by a low pass filter. Since the rating of the actual mine hoist motor is normally higher than 2000 hp, actual energy saving is very much higher. REFERENCES [1] [2]
[3] [4] [5] [6] [7]
[16]
M. Madrigal et al., “Surmounting the global challenges of energy for all and greener, more efficient electricity services,” IEEE Power & Energy Mag., pp. 21–29, 2012. S. Ayasun and C. O. Nwankpa, “Induction motor tests using MATLAB/Simulink and their integration into undergraduate electric machinery courses,” IEEE Trans. Educ., vol. 48, no. 1, pp. 165–169, Feb. 2005. K. A. Nigim and R. R. DeLyser, “Using MathCad in understanding the induction motor characteristics,” IEEE Trans. Educ., vol. 44, no. 2, pp.165–169, May 2001. M. W. Daniels and R. A. Shaffer, “Re-inventing the electrical machines curriculum,” IEEE Trans. Educ., vol. 41, no. 2, pp. 92–100, May 1998. M. H. Nehrir et al., “Computer modeling for enhancing instruction of electric machinery,” IEEE Trans. Educ., vol. 38, no. 2, pp. 166–170, May 1995. T.-F. Chan, “Analysis of electric machines using Symphony,” IEEE Trans. Educ., vol. 35, no. 1, pp. 76–82, Feb. 1992. H. A. Smolleck, “Modeling and analysis of the induction machine: A computational/experimental approach,” IEEE Trans. Power Syst., vol. 5, no. 2, pp. 482–485, May 1990.
[17] [18] [19]
[20] [21] [22] [23] [24] [25]
Session H4B
Z. Maljkovic et al., “The impact of the induction motor on short-circuit current,” IEEE Ind. Applic. Mag., vol. 7, no. 4, pp. 11–17, Jul./Aug. 2001. M. K. Yoon et al., “Efficiency increase of an induction motor by improving cooling performance,” IEEE Trans. Energy Conversion, pp. 1–6, 2002. C. Burt et al., “Electric motor efficiency under variable frequencies and loads,” Irrigation Training and Research Center, California Polytechnic State Univ., San Luis Obispo, CA, Rep. R 06-004, 2006. R. H. A. Hamid et al., “New technique for maximum efficiency of induction motors based on PSO,” in Proc. IEEE Int. Symp. Ind. Electron., Montreal, Canada, pp. 2176–2181. D. H. Kim, “GA-PSO based vector control of indirect three phase induction motor,” Appl. Soft Comput., vol. 7, no. 2, pp. 601–611, 2006. I. Kioskesidis and N. Margaris, “Loss minimization in scalar controlled induction motor drives with search controller,” IEEE Trans. Power Electron., vol. 11, no. 2, pp. 213–220, 1996. M. Cacciato et al., “Efficiency optimization technique via constant optimal slip control of induction motor drives,” in Proc. Int. Symp. Power Electronics, Electric Drives, Automation and Motion, Taormina, Italy, 2006, pp. 32–42. B. Pryymak et. al., “Neural network based flux optimization using a model of losses in induction motor drives,” Math. & Comput. in Simulation, vol. 71, no. 4–6, pp. 290–298, Jun. 2006. S. Limand and K. Nam., “Loss minimization control scheme for induction motors,” IEE Proc. Electron. Power Applic., vol. 151, no. 4, pp. 385–397, Jul. 2004. C. T. Raj et al., “Differential evolution based optimal control of induction motor serving to textile industry,” Int. J. Comput. Sci., vol. 35, no. 2, pp. 201–208, 2008. S. Ghozzi et al., “Energy optimization of induction motor drives,” in Proc. IEEE Int. Conf. Ind. Technol., Hammamet, Tunisia, 2004, vol. 2, pp. 602–610. K. Sundareswaran et. al, “Artificial neural network based voltage controller for energy efficient induction motor drives,” in IEEE Region 10 Int. Conf. Global Connectivity in Energy, Computer, Communication and Control, New Delhi, India, 1998, pp. 552–554. C. T. Raj et al., “Particle swarm and fuzzy logic based optimal energy control of induction motor for a mine hoist load diagram,” Int. J. Comput. Sci., vol. 36, no. 1, pp. 17–25, 2009. N. Kumar et al., “Economical analysis of induction motor for a mine hoist load diagram,” in Proc. World Congr. Information and Communication Technologies, Mumbai, India, 2011, pp. 1310–1315. P. Gnacinski, “Energy saving work of frequency controlled induction cage machine,” Energy Conversion & Managem., vol. 48, no. 3, pp. 919–926, Mar. 2007. P. C. Krause et al., Analysis of Electric Machinery and Drive Systems, 2nd ed. Hoboken, NJ: Wiley-IEEE Press, 2002. M. Chilikin, Electric Drives. Moscow, Russia: MIR Publishers, 1976. C. T. Raj et al., “Particle Swarm optimized Induction Motor for a Textile Mill Load Diagram”, in Proc. IET Int. Conf. Information and Communication Technology in Electrical Sciences, Chennai. India, 2007, pp. 379–383.
NOMENCLATURE Rs Rr' Xls Xlr Xm ω Te Φm E a, ωe s as ωr ωb Is
Stator resistance Rotor resistance Stator leakage reactance Rotor leakage reactance Magnetizing reactance Speed Electromagnetic torque Air-gap flux Air-gap voltage Supply frequency Slip Slip frequency Rotor speed Base speed Stator current
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Ir' Im Pc Pi Pstr Pm
Rotor current Magnetizing current Copper losses in Stator and Rotor Iron losses Stray losses Mechanical losses
Pconv Pcable Ploss ke, kh Cfw Cstr
Session H4B
Converter losses Cable losses Total losses Eddy current and hysteresis coefficients Mechanical loss coefficients Stray loss coefficients
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