The simulation of a.c. adjustable electric drive systems

MIHAIL-FLORIN STAN*, MARCEL IONEL**, OCTAVIAN-MARCEL IONEL*** *Automatics, Informatics and Electrical Engineering Department

**Electronic, Telecommunications and Energetically Engineering Department Valahia University Targoviste, Electrical Engineering Faculty

18-24 Unirii Blvd., 130082 Targoviste, ROMANIA *** Electrical Engineering Department, Politecnico di Torino,

Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY flo.stan@gmail.com, ionel.marcell@yahoo.com, ionel.octavian@yahoo.com,

www.valahia.ro, www.polito.it

Abstract: - Determination of the electric drive parameters (electric power, electromagnetic torque, angular speed, adaptability to almost any conditions of order etc.) requires a simulation system and fast and efficient control methods. SPICE simulation of induction machine controlled by AC inverters drive improves energy efficiency methods, to obtain a fast response, simplicity of control etc. and permits the possibility of operating in the generator regime.

Key-Words: - Energy conversion, electric motors, power electronics, electric drive systems, control, SPICE simulation.

1 Introduction Nowadays, electric drives use different types of motors and they have led to major changes in processing industry. In an industrialized country, more than 60% of generated electricity is used to electric drive with electric machines. Applicability of electrical drives has increased from low power applications for a small number of areas (various instruments, computer peripherals, machine tools and industrial robots, shareholders in the paper industry, textile industry, applications and blowers pumping stations, etc..) to megawatts power, lines air compressors, fans for boilers, pumps, water supply, cement, ships propulsion, metallurgy, etc [1]- [4].

2 The modeling of three-phase

induction motor For the study of the operation and computer-aided analysis of induction motors fed by three-phase AC voltage used to adjustable speed control systems is proposed the following model of motor. It is considered a symmetrical three-phase induction motor with stator windings supplied from a symmetrical three-phase voltage and source frequency is f1. [5]

Fig.1. Reflective to writing equations of the three-phase induction motor

It allowed these simplifying assumptions: saturation magnetic circuit is negligible (linear magnetic circuit), stator and rotor windings are sinusoidal currents crossed wires and winding resistances are independent of temperature. Applying the law of electromagnetic induction on some „Γ” curve which crosses one motor’s winding phase and close the air on a line corresponding phase voltage at the terminals (Figure 1) induction motor equations can be written in the fixed reference system [6]. Equation established in fixed to the stator reference system:

[ ] [ ] [ ] [ ]SSSS dt

dRiu ψ+⋅= (1)

Equation established in fixed to the rotor reference system:

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[ ] [ ] [ ] [ ]rrrr dt

dRiu Ψ+⋅= (2)

Knowing that between the power line frequency (same as the stator currents) number of pole pairs and induction motor synchronous speed relation is 60 fs = n1 ⋅ p, the stationary operating mode can be inferred (motor operation is based on the principle of power conservation) equivalent electrical diagram ferro-magnetic core losses account for homologous phase of stator and rotor of induction motor [7] (Figure 2).

Fig.2. Steady state equivalent circuit with core losses of induction motor

The components of the stationary model scheme are: Rs – Resistance of stator winding;

R

2

2w2

1w1

2

1r R

kw

kw

m

mR ⋅

⋅⋅

⋅= – Resistance of rotor

winding reported to stator winding. where:

m1 - number of phases of stator winding; m2 - number of phases of rotor winding; w1 - number of turns of a phase of rotor winding; w2 - number of turns of the rotor phase winding; kw1, kw2 - winding factors; RR - rotor winding resistance; XσS = ωs · Lσs - escape stator reactance; ωs = 2π · fs - stator current pulsation; LσS - escape stator inductance; Xσr = ωs · Lσr - escape rotor reactance reported to

stator;

R

2

2w2

1w1

2

1r X

kw

kw

m

mX σσ ⋅

⋅⋅

⋅= - escape rotor

reactance; Lσr - escape rotor inductance reported to stator; RFe - ferromagnetic core losses resistance; Xm = ωs · Lm - magnetization reactance.

Induction motor equations, written for one phase, in stationary regime:

EILjIRU SSsSSS −⋅ω⋅+⋅= σ (3)

EILjIs

R0 rrsr

r +⋅ω⋅+⋅= σ (4)

rSm III −= (5)

where:

SI - stator current phasors in stationary regime;

rI - rotor current phasors reported to the stator

current phasors, in stationary regime; s = (n1 – n)/n1 - slip of the induction motor at „n”

speed. Previous scheme can not be used for analysis of induction motor transient regimes. For their study it is used a phasors model in a spatial reference system rotated with angular velocity ωg. All vector spaces are fixed to a reference system generally rotated at angular velocity ωg to the stator (Figure 3). Rotor sizes are reported to the stator sizes.

Fig.3. Explanatory to the phasors setting of a spatial reference system which is rotated with ωg angular

speed In Figure3, Aref g - fixed reference axis of space phasors g, Aref FR - fixed reference axis of the rotor, Aref FS - fixed reference axis stator. To achieve the system model equations (1) is written in the reference speed ωg arbitrarily rotated to the stator as follows:

S

j

SgS

gS

jSSSS

dt

deRiu

edt

dRiu

g

g

Ψ⋅+⋅=⇒

⇒⋅Ψ+⋅=

θ−

θ−

(6)

gSg

SjgS j

dt

de

dt

d g Ψ⋅ω−Ψ

⋅=Ψ θ− (7)

So, for stator it can be written:

dt

djRiu

gSg

SgSgS

gS

Ψ+Ψω⋅+⋅= (8)

Similar, for rotor:

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( )dt

djRiu

grg

rrgrgr

gr

Ψ+Ψω−ω⋅+⋅= (9)

Equivalent circuit is presented in Figure 4.

Fig.4. Induction motor equivalent circuit with spatial phasors rotated with g angular speed

Sizes used in the equivalent circuit diagram are: gSΨ - Stator leakage flux vector; grΨ - Rotor leakage flux vector;

gSi - Corresponding stator current space vector; gri - Corresponding rotor current space vector; gSu - Appropriate stator voltage space vector; gru - Rotor voltage vector corresponding space.

Because qSdSgS ujuu ⋅+= and qSdS

gS ijii ⋅+= spatial

vectors that model can be decomposed into two equivalent circuits: an equivalent circuit mounted directly to the stationary reference system - the axis d and a fixed reference system in quadrature - axis q. For ωg = 0 results equivalent circuit „dq” in Figure 5.

Fig.5. „dq” model of three phase induction motor

Although the sizes decomposed from „dq” spatial phasors by real and imaginary components seem to be just mathematical sizes, however they are physically existing quantities.

„dq” flows can be measured directly in the air-gap of induction motor and „dq” currents and voltages occur in loops after field oriented speed control. Between phase voltages ua, ub, uc stator power and size is the correlation matrix udS and uqS and direct Park transformation:

⋅

−

−

=

c

b

a

S0

qS

dS

u

u

u

2

1

2

1

2

12

3

2

30

2

1

2

111

3

2

u

u

u (10)

where:

3

uuuu cba

S0

++= (11)

represents possible zero sequence component (homopolar component) of voltage. After processing the axes it results:

−−= cbadS u2

1u

2

1u

3

2u (12)

( )cbdS uu3

1u −= (13)

Voltage equations written by the stator „dq” axes:

dSsdSdS dt

dRiu Ψ+⋅= (14)

qSsqSqS dt

dRiu Ψ+⋅= (15)

Voltage equations written by the rotor „dq” axes:

qrrdrrdrdr dt

dRiu Ψ⋅ω+Ψ+⋅= (16)

drrqrrqrqr dt

dRiu Ψ⋅ω−Ψ+⋅= (17)

Last terms in relations (16), (17) and sizes

qrr ψ⋅ω and drr ψ⋅ω− are also called induced

electromotive forces by rotation. Leakage flows defined by two axes are:

dmmdSSdS iLiL ⋅+⋅=Ψ σ (18)

dmmdrrdr iLiL ⋅+⋅=Ψ σ (19)

qmmqSSqS iLiL ⋅+⋅=Ψ σ (20)

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qmmqrrqr iLiL ⋅+⋅=Ψ σ (21)

3 SPICE model of three-phase

induction motor

SPICE model of three phase induction motor drive is based on „dq” equivalent circuit diagram. Strong inductive stator phases are modeled as controlled current sources whose current values are obtained by the inverse Park transformation of the current „dq” components.

⋅

−−

−=

S0

qS

dS

c

b

a

i

i

i

12

3

2

1

12

3

2

1101

i

i

i

(22)

In the absence of zero sequence current components, current values through the three phases are:

dSa ii = (23)

qsdsb i2

3i

2

1i ⋅+−= (24)

qsdsc i2

3i

2

1i ⋅−−= (25)

Mechanical equation is:

MMdt

dJ e −=

Ω⋅ (26)

where: Me - electromagnetic torque; M - load torque to the motor’s arbor. The mechanical losses can be inserted into the machine mechanical equation via MF0 dry friction torque and the viscous friction torque: MFV = F·Ω, where F is the viscous friction coefficient. The operation of induction motor mechanical load equation becomes:

Ω⋅−−=Ω

⋅ FMMdt

dJ 0Fe (27)

Mechanical rotor angular speed is:

p/rω=Ω (28)

Using the „dq” components of current and flux results electromagnetic torque:

( )qrdmdrqme iip2

3M ⋅Ψ−⋅Ψ⋅⋅−= (29)

( )drqmqmqrdmme iiLiiLp2

3M ⋅⋅−⋅⋅⋅⋅−= (30)

Nominal data of motor are given in Table 1 and circuit parameters of motor are given in Table 2.

Table 1

Power Pn [kW]

1.1

Speed n [rpm]

1410

Efficiency h[%]

77

Power factor cosϕ = 0,78

Voltage U [V] 400

Current In [A] la

400V 2,6

Moment of inertia

J [Kgm2] 0,0021

Frequency fn [Hz]

50 n

p

I

I

5,6 n

p

M

M

2,4

Table 2 Rr

[Ω] 5,5

Rs [Ω] 7,5

RFe [Ω]

2000

Lm [Η]

0,35105

Lσr [Η]

0,0188

LσS [Η]

0,02643

4 SPICE simulation program of

three-phase induction motor *SPICE_NET .TRAN 0.1M 0.5 UIC .PRINT TRAN I(VA)V(11) V(7) .OPTIONS METHOD=GEAR ABST0L=1M

RELTOL=.01 ITL4=1000 *INCLUDE SYS.LIB .SUBCKT SINT#0 1 2 *PARAMS ARE GAIN=500.00 RIN 1 0 1E12 E1 3 0 0 1 500.00 C1 2 4 1U IC=0 R1 3 4 1MEG E2 2 0 0 4 1E6 .ENDS .SUBCKT SUM2#0 1 2 3 B1 3 0V = -1.0000*V(1) + 1.0000*V(2) .ENDS VB 2 0 SIN 0 230 50 0 0 240 VC 3 0 SIN 0 230 50 0 0 120 VQS 8 9 RQS 8 5 7.5 LQS 5 10 18.8M IC=0 B6 9 0 V=(V(2)-V(3))/SQRT(3) LQR 10 16 26.43M RQR 16 24 5.5 LQM 10 4 0.35105 VQM 0 4 RQF 0 10 2000

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87 12 0 V=l(VM)*2*[0.02643*l(VDR)+0.35* I(VDM))

VDS 6 15 RDS 6 17 7.5 LDS 17 18 18.8M IC=0 BB 15 0V=2/3*(V(1)-0.5*V(2)-0.5*V(3)) LDR 18 20 26.43M RDR 20 25 5.5 LDM 18 22 0.35105 VDM 0 22 RDF 0 18 2000 B9 13 0 V=-

l(VM)*2*(0.02643*l(VQR)+0.35105*l(VQM)) VQR 24 12 VDR 25 13 B10 7 0 V=-1.5*2*(0.35105*l(VDM)*l(VQR)-

0.35105*l(VQM)*l(VDR)) B12 1 23 I=I(VDS) B13 2 23 l=-0.5*l(VDS)+SQRT(3)/2*l(VQS) B14 3 23 l=-0.5*l(VDS)-SQRT(3)/2*l(VQS) R2 23 0 100MEG X1 14 11 SINT#0 *K=500 VM 19 11 RF19 0 0.86 X2 21 7 14 SUM2#0 *K1=-1 K2=1 VTE 21 0 5 VA 1 0 SIN 0 230 50 0 0 0 .END .END

The simulation results are presented in next figures:

Fig.6. Variation of stator phase currents and angular

speed at the no-load induction motor starting up

Fig.7. Variation of electromagnetic torque at the no-

load induction motor starting up

Fig.8. Variation of stator phase currents and angular

speed at the load induction motor starting up

Fig.9. Variation of electromagnetic torque at the load induction motor starting up

5 Simulation of induction motor fed

from three phase voltage variator Analysis of induction motor operation powered by alternating voltage variators involves using the model of the induction phase induction motor circuit with the light sequence 0 [8], [9]. To maintain constant output size (motor speed) and to ensure stable system operation, the converter

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can be provided with a feedback loop made with speed and current controllers connected in cascade. Current information will be provided by current transformer and speed information will come from a mechanical position and speed sensor.

Fig.10. SPICE model of three phase induction motor and frequency converter

The simulation results are shown in Figure 11.

Fig.11. Angular speed variation of the induction motor and the stator current phase of the circuit for a

30° angle control of variators

6 Conclusions

Evolution of power inverters and static frequency converters is a key factor in the development of advanced applications. Availability of energy sources with adjustable frequency AC motors allowed to reach a new horizon in the field of research and technical applications, a horizon likely completely untapped today. However, the inherent advantages of adjusting the frequency of operation can not be fully exploited without adopting a proper control strategy, which is essential in characterizing the performance of a system. One reason for variable frequency systems applications compared to other power electronic systems is the variety of implications that the controls they produce an electric drive. Control techniques to ensure a fair and efficient operation of the drive during normal operation. Nominal data of the motor and inverter must be met and ensuring that optimum motor performance is in areas of maximum torque (current and speed). Under overload or in the presence of a defect is preferable instead to redesign the application components to be adopted advanced control strategies. Even if one adopts a vector control strategy and obtain a similar behavior of a DC motor, still remain many unresolved issues due to the particular structures of the motor and converter and the load and source interactions [10]. To prevent undesirable situations it appeals to the simulations using different types of software. Torque pulses, the existence of higher frequency harmonics, application optimization, increased energy efficiency, optimal parameters change, the rapid response to orders quickly just some of the many issues that must be solved by SPICE simulation. References:

[1] IONEL, M., STAN, M.F., VÎRJOGHE., E.O., Techniques of Induction Machine Vectorial Order Simulation, Proceedings of the 9th WSEAS/IASME International Conference on

Electric Power Systems, High Voltages, Electric

Machines, Genova, Italy, October 17-19, 2009, pp.202-207, ISSN: 1790-5117, ISBN: 978-960-474-130-4;

[2] IONEL, M., STAN, M.F., SĂLIŞTEANU I.C., IONEL, M.O., Advanced command techniques of electrical induction machines, Proceedings of

the 9th WSEAS International Conference on

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ISSN: 1792-4235 649 ISBN: 978-960-474-214-1

Power Systems (PS '09), Budapest, Hungary, September 3-5, 2009, pp.176-180, ISSN 1790-5117;

[3] M.F., VÎRJOGHE E.O., Current Trends on Command, Control, Modeling and Simulation of the Induction Machines, Proceedings of 5th IASME / WSEAS International Conference of

Energy & Environment (EE 10), Cambridge, UK, February 23-25, 2010, pp.271-276, ISSN: 1790-5095, ISBN: 978-960-474-159-5;

[4] VLĂDESCU, C., STAN, M.F., IONEL, M., Supple electrical drives optimization for

metallurgical industry, Bibliotheca Publishing House, Târgovişte, 2009, ISBN 978-973-712-300-8.

[5] STAN, M.F., VÎRJOGHE, E.O., IONEL, M., Electrical Engineering Treaty, vol. I, Bibliotheca Publishing House, Târgovişte, 2005, ISBN 973-712-099-X;

[6] IONEL, M., STAN, M.F., Electrical machines and electrical drive system. Electronic converters

commands, Bibliotheca Publishing House, Târgovişte, 2005, ISBN 973-8413-648;

[7] IONEL, M., STAN, M.F., Electrical Engineering Treaty, vol. II, Bibliotheca Publishing House, Târgovişte, 2006, ISBN 978-973-712-191-2.

[8] IONEL, M., STAN, M.F., DOGARU, V., IONEL, M.O. Posibilities of Diminishing the Distortions Introduced by Superior Harmonics of Electric Current, Proceedings of 6th WSEAS International Conference on Simulation,

Modelling and Optimization, Lisbon, Portugal, September 22-24, 2006, pp. 689-692, ISSN 1790-5117;

[9] STAN, M.F., IONEL, M., IONEL, O.M., Modern automatic system for the optimization of the electrical drives for working machines with mechanical branches, Proceedings of 8th WSEAS International Conference on Mathematical

Methods and Computational Techniques in

Electrical Engineering, Bucharest, Romania, October 16-17, 2006, pp. 5-8, ISSN 1790-5117;

[10] ENESCU, D., COANDA H.G., VIRJOGHE E.,O. and CACIULA, I., Numerical investigation by means of polynomial regression method for determining the temperature fields in a medium with phase transition, The 8

th WSEAS

International Conference Systems Theory and

Scientific Computation (ISTASC 08), Rhodos, Grecia, August 20-22, 2008, pg.88-93, ISSN: 1790-2769, ISBN: 978-960-6766-96-1;

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