Single-to-three phase induction motor sensorless drive system

Z.M.S. El-Barbary

OURNAL

Alexandria Engineering Journal (2012) 51, 77-83

FACULTY OF ENGINEERING ALEXANDRIA UNIVERSITY

Alexandria University Alexandria Engineering Journal

www.elsevier.com/locate/aej www.sciencedirect.com

ORIGINAL ARTICLE

Single-to-three phase induction motor sensorless drive system

Z.M.S. El-Barbary *

Department of Electrical Engineering, Kafrelsheikh University, Egypt Department of Electrical Engineering, King Khalid University, Saudi Arabia

Received 19 June 2011; revised 20 May 2012; accepted 27 May 2012 Available online 26 June 2012

KEYWORDS

Voltage Source Reversible Rectifier (VSRR); Four-Switch Three-Phase (FSTP) inverter; Six Switch Three-Phase (SSTP) inverter; Vector control; Digital Signal Processor (DSP)

Abstract This paper presented a single to three-phase induction motor drive system to provide variable output voltage and frequency. The proposed drive system employs only six IGBT switches, which form the front-end rectifier and the output inverter for the one step conversion from singlephase supply to output three-phase supply. The front-end rectifier permits bidirectional power flow and provides excellent regulation against fluctuations in source voltage. Moreover, it incorporates active input current shaping feature. The control strategy of the proposed drive system of three-phase induction motor is based on speed sensorless vector control technique. A low cost of motor drive and much more advantages can be achieved using the proposed drive system. Simulation and experimental results are carried out to analysis and explore the characteristics of the proposed drive system.

1. Introduction

In home domestic appliances, rural electric systems and remote areas the cost to bring three-phase power to a remote location is often high. This is due to high cost of a three-phase extension. Further, the rate structure of a three-phase service is higher than the single-phase service. A single-wire earth return transmission line has proved to be a cost-effective solution for

* Tel.: +966 0581352199.

E-mail address: z_elbarbary@yahoo.com

Peer review under responsibility of Faculty of Engineering, Alexandria University.

delivering power to rural communities. Single-phase power is adequate for many domestic applications such as lighting, heating and powering small appliances. However, problems arise as soon as applications demand the use of medium electric motors. These applications include pumps for irrigation or drinking water, air conditions, elevators, washing machines, machinery for mills or small industries.

The single-phase induction motor, up to sizes of 5 kW, has been a ubiquitous motor for many years in applications where a single-phase supply is readily available, such as in the household. These are used in refrigerators, washing machines, fans, food mixers, pumps and air conditioners. In most of these applications the motor is actually a two-phase motor. Usually the motor runs at one, two or at most three speeds obtained through manual intervention. Obviously, the motor operates at non-optimum efficiency and at low power factor. Variable

speed operation has been obtained through voltage control using triacs or back-to-back thyristors. However, these suffer from large harmonic injection into the supply network and low power factor.

Fixed speed operation often means that the process, which is not controlled to the desired extent, consequently cannot be made to respond well to what is desirable and adequate. A wide speed range, truly variable-speed motor, frees the designers to come up with better operating features. This can be achieved by using three-phase motor, which are more readily available. Therefore, single-phase to three-phase converters is a suitable solution for these situations where three-phase power is not available. Various methods, including static phase converter, rotary phase converters, reduced topology power electronic converters and novel motor designs have all been investigated [1-4].

Variable-speed drives using three-phase inverters and ac motors have already found widespread practical application in various forms. Certain applications, however, still require a further cost reduction for the drive. The reduction of the number of power semiconductor device components in the converter should be the main consideration for reducing the cost of the control subsystem. The use of transistors instead of thyristors eliminates the forced commutating components and presents distinct advantages for drives in the power range up to 50 kVA. A further reduction in components is possible by considering alternatives to the conventional three-phase bridge configuration for a voltage-fed inverter, since this circuit uses six switching devices and six reactive power diodes. These considerations lead to a bridge circuit with only four switching devices and four reactive power diodes. It has been shown that a two-level current control can be implemented to yield quasi-sinusoidal currents in the three-phase load [5,6].

This paper presents single-to three-phase sensorless induction motor drive system. The proposed drive system employs only six IGBTs transistors converter for rectifier and inverter structure. This configuration incorporates front-end half bridge active rectifier. This rectifier provides the dc-link voltage with active input current shaping feature. A four-switch inverter with split capacitors in the dc-link provides a balanced three-phase output to the motor. The converter draws near sinusoidal current from the ac mains at close to unity power factor and therefore satisfies strict harmonic current standards. Bi-directional power flow is possible between the ac mains and dc-link. The four switches makes the inverter less cost, less switching losses, less chances of destroying the switches due to lesser interaction among switches, less complexity of control algorithms and interface circuits as compared to the conventional Six Switch Three-Phase (SSTP) inverter. The proposed sensorless speed control approach introduces more reduction such as, the computation for real time implementations. Also, the use of speed sensorless for induction motor drives besides being reducing bulky and increase the robustness, it reduces additional electronics, extra wiring, and extra space. Also, reduces extra cost to the drive system, speed sensor. It also, implies careful mounting which detracts from the inherent robustness of the drive. The proposed sensorless control method verifies the validity of model reference adaptive system (MRAS)-based speed estimator with the six switches converter fed induction motor drive system for cost reduction and other advantages such as reduced switching losses, reduced number of interface circuits to supply logic signals for the switches,

easier control algorithms to generate logic signals. Thus, the main issue of this paper is to develop a cost effective, simple and efficient high performance induction motor drive. A closed-loop vector control scheme of the proposed induction motor drive system incorporating the MRAS is simulated using the MATLAB/SIMULINK. Also, a laboratory drive system is built and tested using the six switches converter to explore the most important feature of the low cost drive.

2. Six switch converter

The single to three-phase converter is configured as shown in Fig. 1. The switches T1 and T2 form the front-end rectifier. Two split capacitors form the dc-link. The output inverter converts the dc-voltage to a balanced three-phase output with adjustable voltage and frequency. This inverter is configured with four switches T3, T4, T5 and T6, respectively. Two output phases are taken from the inverter legs directly where the third output is taken from the midpoint of the two capacitors.

2.1. Front-end rectifier

The front-end rectifier converts a single-phase utility ac supply voltage to dc-voltage. A boost inductor, Ls, is connected in series with the utility supply voltage. The power transistors T1 and T2 are switched on using current forced control (CFC) strategy that enables the device to operate with a sinusoidal line current. As a result, little distortion, unity power factor and regulated dc busbar voltage can be achieved. Moreover, this control strategy permits power transfer in either direction between ac mains and dc busbar voltage. So, this rectifier calls single-phase Voltage Source Reversible Rectifier (VSRR).

The two capacitors (designated Co) initially have to be charge up to the peak voltage of the utility supply via the inverse parallel diodes across the transistors. The two capacitors must be large enough to appear as an essentially constant dc voltage source with low ripple contents [7]. The large size of Co also means that some form of soft start must be included during the initial charge up to prevent transient inrush current from harming circuit components. Once the capacitors have fully charged and the diodes are reversing biased, it becomes virtually constant dc voltages. The output voltages Edc+ and Edc_ can be kept constant by connecting the capacitors in series with the voltage source, Vs, via the two transistor switches T1 and T2. Note that only one-transistor turn on at a time, or

Figure 1 Six switch converter configuration.

A■*■>

Calclation

l j, l

ds' os

Figure 2 MRAS speed estimation.

else a short circuit of the dc voltages will occur. If a transistor that conducting current is turned off, owing to the inductive nature of the circuit, the current instantaneously freewheels through the diode across complementary transistor. If the same transistor is turned back on, then the conducting diode will reverse biased and the current will switch to flow back through the transistor. In a CFC scheme, whenever a transistor is turned on the complementary transistor is always turned off. So, the two transistors/diodes essentially behave as a two pole bi-directional switch. This switch conveniently is represented as switching logic variable NS. Using this logic variable, the circuit differential equations can be written as:

(1) (2) (3)

This inverter is configured with four switches T1} T2, T3 and T4, respectively. Two output phases are taken from the inverter legs directly where the third output is taken from the midpoint of the two capacitors. A detailed comparison of the four-switch inverter with the conventional six-switch inverter configuration is given in [5,6]. Two control possibilities exist to control the four-switch bridge inverter, i.e., two-level current control to force the two controlled phases currents to sinusoidal, or using PWM to control the voltages applied to the three-phase quasi-sinusoidally. The two-level current control of the four-switch bridge inverter is used to control the load current by forcing it to follow a reference one. This is achieved by the switching action of the inverter to keep the current within the hysteresis band. The load currents are sensed and compared with respective command currents using two independent hysteresis comparators. The output signals of the comparators are used to activate the inverter power switches. This controller is simple and provides excellent dynamic performance.

The modulated phases voltages of four switch inverter are introduced as a function of switching logic NA, NA1, NB and NB1 of power switches by the following relations [8].

is — L- J (v, - NS * Edc+-(1 - NS)* Edc)dt Edc+ — — J (NS * is - ii)dt Edc- — — J((1 - NS)*is + i,)dt

where ii is the load current which may be ia, ib or ic. NS = 1, if T1 or D1 is on and NS = 0, if T2 or D2 is on. From the above equations it can be seen that if T1 is on the supply current is will decrease. On the other hand, if T2 is on, the current will increase. Hence, the current can be forced to track a reference waveform ir simply by switching on T2 if the current is higher than ir, or by switching T1 on if the current is lower than ir. For the device to operate with a sinusoidal input current and unity power factor it is necessary to produce a sinusoidal-current reference waveform that is either in phase or 180° out of phase with ac utility supply voltage. In addition, the dc voltage Edc must be maintained equal to a reference Edcr under all load conditions. Both these can be obtained using the control scheme of Fig. 2. Comparing a dc reference, Edcr, with the actual dc-link voltage, Edc, the output error, e, is filtered and modified by a PI controller. The filter output, U, multiplied by a unit vector signal derived from the supply voltage to produce the required current reference ir. The current reference is then compared with the actual supply current to determine which transistor should be turned on. If Edc is too low then the error is positive and ir is produced in phase with Vs. The power is transferred from the ac to the dc side (rectifying) and consequently increasing Edc.

2.2. Output inverter

The four switch three phase inverter is configured as shown in x*i — Fig. 1. The inverter converts the dc-voltage to a balanced three-phase output with adjustable voltage and frequency. and

Va — (4NA + 2 ■ NB - 1) —

Vb — -3- (-2NA + 4 ■ NB - 1) E

Vc — -y (-2NA - 2 ■ NB + 2)

where NA1 and NB1 are complementary of NA and NB.

2.3. Induction motor model and vector control

The mathematical model of three-phase squirrel cage induction motor in de — qe is described as:

(me - Xr)Lm Rr + pLr

The electromechanical equations are given by

r Ve qs 'Rs + pLr LeLr PL

Vds —a-L0 Rs + pLr -Lei:

0 RrLm 0 Rr + pL r

_0 0 RrLm -(xe — Lr)L

r Ie qs

Ie Tds

TL — J—— + Brnr dt

— 3— Z^H (Te k e

— 2 ^ 2 Lr (lqsAdr

' Tds kqr )

Eq. (8) denotes that the torque can initially proportional to the quadrature component of the stator current FqS if the qe-axis component of the flux becomes zero (de-axis is aligned with the rotor flux axis), and the d^-axis component l*der is kept constant. This is the philosophy of the vector control technique. In accordance, Eq. (8) is linearized as:

Te — K,\kdr\Ieqs (9)

This equation is similar to that of the separately excited dc motor. The angular slip frequency command («*,) is:

qs kdr

4 = T (1 + s'rp)kedr

Angular frequency is obtained as follows:

x* — X + x'

e:= a>: ■dt

(12) (13)

The torque producing current component is calculated from:

f = K - Xr) Kps[1 + ScsS] (14) kt kA scsS

3. MRAS for the sensorless control of induction motor

Model Reference Adaptive Systems (MRAS) techniques applied in order to estimate rotor speed. This technique is based on the comparison between the outputs of two estimators. The outputs of two estimators may be (the rotor flux, back e.m.f. or motor reactive power). The estimator that does not involve the quantity to be estimated (the rotor speed xr) is considered as the induction motor voltage model. This model is considered to be the reference model (RM). And the other model is the current model, derived from the rotor equation, this model considered to be the adjustable model (AM). The error between the estimated quantities by the two models is used to drive a suitable adaptation mechanism which generates the estimated rotor speed [9].

In this paper, the state variable of MRAS technique is the stator current and rotor flux.

The speed estimating procedures from the stator current error are as follows: first, from the induction motor equation the stator current is represented as:

ids — 7-[kdr + XrTrkqr + Trpkdr]

iqs — Lm [v

Xr Tr kqr + Trpkqr\

From the relationship between the real stator current and the estimated stator current, the difference in the stator current is obtained as

is— Lm Mœ - _]

r \air — xj

• _ r ^

In Eq. (17), the difference of stator current is sinusoidal value because it is the function of rotor flux. Multiplying by the rotor flux and adding them together;

ids — i )kqr — Lm kqr [Xr —

Lm kdr>xr

-iqs jkdr — ^ ^r — X\

By summing the above two equations.

ids — i lki

i iqs } kdr r

k2qr + kdrr) [Xr — _] (19)

Hence, the error of the rotor speed is obtained as follows:

ids i } kqr I iqs i } kdr

where K — Lm ft + 4

The right hand term seems as the term of speed calculation from adaptive observer, so the speed can be calculated by the following Eq. (17):

Kp I ids — i ) kqr

X — K

i \kq,

■ -A k

lqS I i kdr qs

Fig. 2 shows the MRAS system. 4. Overall drive system

Using Eq. (15), and estimated instead of measured speed, the stator current is estimated as follow:

i — 7-[kdr + X Trkqr + Trpkdr]

ds Lm dr r r qr r dr

i — 7-[kqr — X Trkqr + Trpkqr]

qs Lm r

The control scheme of low cost ac induction motor drive is shown in Fig. 3. It incorporates the speed controller which receives the error signal between the command speed and the actual observed speed of the motor shaft and then generates the torque command (T) through a PI speed controller. This torque command produces the quadrature current command in the rotor flux method described in Eq. (14).

COS; --J, OOe ——3

_ ¡NB1 Hy^terei is-Gurrent com roller

vb —e-w

vc —e—

abc to d!-qs Transformations

MRAS Speed Estimator

Figure 3 Block diagram of sensorless induction motor drive system.

The direct axis current component I*JS is set by the rotor flux level, k*r as described in Eq. (11). This flux level is calculated according to the reference frame (STRF) with the aid of the calculated command angle (h*). This command angle is calculated in such a way that aligns the de-axis of SYRF with the rotor flux axis. The two stator current commands, Iq*se and Id*se in the SYRF are then transformed to STRF and then transformed to three phase references current iar, ibr and icr [6]. Only, two currents reference iar and ibr required for the hysteresis current controller that generates the switching function for the pulse width modulated voltage source inverter.

5. Results and discussion

The proposed control system represented by Figs. 3 and 4 is designed and implemented for a simulation and experimental investigation. Simulation is carried out using the general purpose simulation package Matlab/Simulink, while experimental

Figure 4 Experimental set up for DSP-board control of induction motor.

study is implemented using a TMS320C31 floating-point Digital Signal Processor [10] (DSP1104) hosted on a personal computer as shown in Fig. 4. Simulation and experimental results are presented to show the effectiveness of MRAS speed estimation method at different operating conditions. These results are classified into two categories; the first represents start-up and steady-state while the second represents the dynamic performance.

5.1. Start-up and steady-state performance

Start-up and steady-state results are illustrated by Figs. 5-7. Fig. 5a shows measured speed signal obtained in real time where as, Fig. 5b shows its corresponding signal obtained off line from simulation. Fig. 6a shows estimated speed signals obtained in real time. where as, Fig. 6b shows its corresponding signal obtained off line from simulation. These results show a good correlation between the estimated speed signal and its corresponding measured as well as simulated speed signals. In the four figures, signals are almost correlated from startup point up to the steady state value, which is reached after about 200 ms. The motor phase current signals corresponding to start-up period is shown in Fig. 7a and b respectively. These current signals are of sine wave profiles on which controller switching transients are shown.

5.2. Dynamic performance

For studying the dynamic performances of proposed system, a series of measurements and simulations have been carried out. In this respect, the dynamic response of the proposed speed estimation algorithm is studied under speed step change under full load condition.

To study the dynamic response of the control system due to a step changes in the command of speed, the motor is subjected

Figure 5 Motor measured speed at start-up: (a) experimental and (b) simulation.

Figure 6 Motor estimated speed at start-up: (a) experimental and (b) simulation.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Time (Sec)

~ 2 I 0

<1) fi

ra -4 CL

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (Sec)

Figure 7 Motor phase current at start-up: (a) experimental and (b) simulation.

-5 -10

«1:1 Inl (Model Root/ij/lnl) I »1:2 Outl (Model Boot/PWMJijtalWOuH)

0.3 0.4 0.5 0.6 0.7 0.8 0.9

Time (Sec)

Figure 9 Motor phase current at speed step change: (a) experimental and (b) simulation.

■100

Reference speed

|#1:1*1:3

WUllHHlliltM

Estimated speed

Measured speed

#1:1 In 1 (Model RootWr/ln1)

#1:2 In1 (Model Root Estimated Vispeef rad/ftjir/lnl j

# 1:3 Vj lu e (Modtl ReotfCensl3nt3/Vjlue)

0.5 1 1.5 2 2.5 3

Time (Sec)

Figure 8 Motor speed at speed step change: (a) experimental and (b) simulation.

50 LAil

-100 — 0.9

I I I I I I I I ï I Ï I

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.1

Time (sec.)

Figure 10 Supply (voltage/5) and current (simulation).

o 800 —

H 600 —

! 400 -

A 200 —

1.2 1.3 1.4 1.5 Time (sec.)

Figure 11 Dc-link voltage (simulation).

to step increase in the speed command to evaluate its performance. At t = 0.9 s. The motor speed command is changed from 90 rad/s to 120rad/s. Fig. 8a and b shows the motor speed signals corresponding to these step changes. It can be seen that the motor speed is accelerated smoothly to follow its reference value with nearly zero steady state error. Fig. 8a shows measured and estimated speed signals obtained in real time. Fig. 8b shows the estimated speed signal and its

corresponding signal obtained off line from simulation. These results show a good correlation between the estimated speed signal and its corresponding measured as well as simulated speed signals. Phase current corresponding to this speed step changes are shown in Fig. 9a and b) respectively. Fig. 9a represents the phase current and its reference command also with a good correlation between them. These results ensure the effectiveness of the proposed controller and shows good

behavior of its dynamic response. Fig. 10 shows the supply current with supply voltage. It is noticed that the supply current is in phase with supply voltage even during the period of speed changes. This means that unity power factor can be achieved irrespective of the motor dynamics. Fig. 10 shows that the dc-link voltage is not affected by speed changes. This is one aim of rectifier design. It is shown that the control of the rectifier works independently (see Fig. 11).

List of symbols: Lr — Ls — , r — 1 — -¡¡L, Vqse, Vdse is the qe — de - axis stator voltage, Iqse, Idse the qe — d - axis stator current, Xqse, Xdse the qe — de - axis stator flux linkage, Rs, Rr the stator and rotor resistances, J, B the moment of inertia and viscous friction coefficients and Ls, Lr, Lm is the stator, rotor and mutual inductances.

References

6. Conclusion

This paper has presented a single-phase to three-phase converter for low cost induction motor drives. This converter provides variable output voltage and frequency. The proposed converter has maintained sinusoidal input current with unity input power factor and Bidirectional power flow has been achieved. Based on sensorless speed of vector control technique, a control strategy of the proposed converter to drive induction motor has been implemented. The performances of the proposed MRAS-based six switches converter fed induction motor drive has been investigated. The low cost ac drive has been ensured using the proposed system. A laboratory drive system has been built and tested to verify the most important features of the proposed drive system. The results have been shown the efficacy of the low cost ac drive system.

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[2] M.N. Uddin, T.S. Radwan, M.A. Rahman, Performance analysis of a 4-switch, 3-phase inverter based cost effective IPM motor drives, in: Canadian Conference on Electrical and Computer Engineering, 2004, pp. 85-88.

[3] C.B. Jacobina, E.R.C. da Silva, A.M.N. Lima, R.L.A. Ribeiro, Vector and scalar control of a four switch three phase inverter, in: Conference on Rec., IEEE-IAS Annu. Meeting, 1995, pp. 2422-2429.

[4] C.B. Jacobina, M.B. de Rossiter Correa, E.R.C. da Silva, A.M.N. Lima, A general PWM strategy for four-switch three-phase inverters, IEEE Trans. Energy Convers. 21 (4) (Dec. 2006) 832-838.

[5] J. Klima, Analytical investigation of an induction motor fed from four-switch VSI with a new space vector modulation strategy, IEEE Trans. Power Electron 21 (6) (2006), 1618-1617.

[6] R.J. Cruise, C.F. Landy, Phase converter for rural applications, in: Symposium on Power Electronics, Industrial Drives, Power Quality and Traction systems, Capri, Italy, June, 1996.

[7] J.T. Boys, A.W. Green, Current forced single - phase reversible rectifier, in: IEE Proceeding, vol. 136, Pt. B. no. 5, September 1989.

[8] Nalin Kant Mohanty, Ranganath Muthu, Microcontroller based PWM controlled four switch three Phase inverter fed induction motor drive Serbian, J. Electric. Eng. 7 (2) (2010) 195204.

[9] Chul-Woo Park, Woo-Hyen Kwon, Simple and robust speed sensorless vector control of induction motor using stator current based MRAC, Electric Power Syst. Res. 71 (2004) 257-266.

[10] DSP-Hardware, dSPACE Digital Signal Processing and Control Engineering GmbH, Germany, 1993.

Appendix A

Machine parameters of the applied induction

Rated power 1.1 kw

Rated load torque 7.5 Nm

No. of poles 4

Stator resistance 7.4826 X

Rotor resistance 3.6840 X

Rotor leakage inductance 0.0221 H

Stator leakage inductance 0.0221 H

Mutual inductance 0.4114 H

Motor speed 1500 r.p.m.

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