Proceedings of India International Conference on Power Electronics 2006
R. S. Bhide
Research Scholar
Department of Electrical Engineering
Indian Institute of Technology Bombay
Mumbai, Powai-400076
E-mail: ravib@ee.iitb.ac.in
S. V. Kulkarni
Associate Professor
Department of Electrical Engineering
Indian Institute of Technology Bombay
Mumbai, Powai-400076
E-mail: svk@ee.iitb.ac.in
Abstract— The parallel operation of two three-pulse controlled converters with interphase transformer (IPT) is modeled and analyzed. An IPT absorbs voltage difference between DC voltages of the two converters at any instant and ensures independent operation without any circulating current. It also results in sixpulse output voltage resulting in less harmonic distortions. The complete circuit is solved by using modified nodal analysis (MNA) and magnetic nonlinearity in the IPT core is taken into account by dynamic inductance model. Power electronic switches are modeled as small and large resistances during ON and OFF states. A code has been written to model and simulate the circuit under balanced and short circuit conditions.
I. I NTRODUCTION
Several converters are connected in parallel to meet high current requirements in all electrochemical, electrometallurgical and traction purposes. However, their parallel operation is more complicated due to fluctuations in DC voltages. Such systems can be connected in parallel without any circulating current, if their DC voltages are equal at any instant, i.e., if their average values are equal and ripple voltages coincide.
It is desired that the ripple voltages instead of coinciding be so displaced that the combination results in a system with a higher pulse number. The parallel combination must be then made in such a manner that it does not affect the operation of individual group. Two or more rectifier systems with displaced ripple voltages can be connected in parallel through an interphase transformer (IPT). It absorbs difference between DC voltages of individual systems and must be designed for the time integral of the differential voltage [1],
[2]. The system configuration is shown in Fig. 1, where,
1
,
L r
1
, r
2 and
L
2 are line resistances and inductances, respectively.
The converters connected in parallel are fed through rectifier transformer to get
180 o phase shift, for increasing the number of pulses at the output. The system in the present work consists of two three-pulse controlled converters (each of which supplies
3000
A), connected in parallel for six pulse operation at the output. Increasing the number of pulses reduces total harmonic distortion (THD) in the load voltage. To meet high current requirements, thyristors are used as power electronic devices since they offer best efficiency, reliability and robustness, improving the life of converters. An IPT is
415 V,
3− ph,
50 Hz
33 V, 3−ph vc1 va1 vb1
3 pulse controlled converter vb2
IPT
R load
Lload va2 vc2
33 V, 3−ph 3 pulse controlled converter
Fig. 1. The system configuration.
L 1
L 2 connected between the neutral points of two secondary star connections of the rectifier transformer and is housed in a common tank. Analog based constant current controller is simulated and implemented in the code.
Nonlinear effects in IPT are required to be taken into account for analysis of its effect on coupled power electronics circuit [3]. More accurate results are obtained if power electronic switches are modeled as low and high resistances
(instead of ideal switches) during ON and OFF states, respectively. The nonlinearity in magnetic material can be tackled by a dynamic inductance model [4]. Firing angle unbalance during parallel operation of controlled converters has significant effect on the IPT model [5]. Several such IPT models with different types can be used for connecting multiple power converters in parallel [6]. Such power electronic circuit consisting of coupled nonlinear magnetic circuit can be solved by modified nodal analysis (MNA) method [7].
The parallel operation of converters with interphase transformer is analyzed using modified nodal analysis (MNA) technique in the work. Commutation overlap and nonlinearity in magnetic material have also been considered. Closed loop current control block is implemented and the system is analyzed under balanced and short circuit conditions. Power
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Proceedings of India International Conference on Power Electronics 2006
is1 is
2 e
1 e
2 is
3 e
3
L
R sw1 e
4
R sw2
L
L e
5
R sw3
e7
Idc
1 r1
e6 r2
R sw4 e
9
R sw5
Idc
2 R sw6
L is
4
e 10
L
e 13 is
5
e 11
L
e 14 is
6
e 12
e 15
IPT Ldyn
e 8
L load
R load n ref
Fig. 2. Simplified system for MNA.
αH
B =
1 + β | H |
(2) where, values of
α and
β for CRGO material of type M4 can be calculated from provided
B − H curve as
0 .
2196
H/m and
0 .
1133 m/A, respectively. Above equation can be expressed in terms of mutual flux linkage
( λ ) and current difference
( I dif f
) with availability IPT geometry which is as shown in the Fig. 4.
v (t + d t ) i
L v (t + d t ) i (t) i (t + d t )
G eq d t
L
Fig. 3. Backward Euler companion model of an inductor in Norton form.
electronic switches in the converter circuit are modeled as low and high resistances during ON and OFF states, respectively.
Commutation and turn ON processes are modeled as linearly changing resistances from 1 mΩ to 1
MΩ and vice versa.
Differential equations are solved by backward Euler method and nonlinearity in the equations is tackled by using Newton-
Raphson method.
II. C ONVERTER M ODELING
Two three-pulse controlled converters are connected in parallel by an IPT. The circuit constitutes nonlinear mutual inductance between IPT windings. Fig. 2 shows the simplified circuit diagram where the line inductances included are representing reactances of rectifier transformer or line impedances. Mutual inductance of the IPT is modeled as dynamic inductance
( L dyn
)
, whose value depends on the fluxcurrent relation in the IPT core at every time instant. The circuit system is solved by the MNA method where, currents through the IPT windings,
I dc 1 and
I dc 2 state variables along with node voltages ( e
, are also treated as currents ( i s 1 to i s 6
1 to e
15
) and source
). All the inductances are modeled by their backward Euler companion models in Norton form [8] as shown in the Fig. 3. The current i ( t + d t ) in the inductor is given as i ( t + d t ) = i ( t ) + d t v ( t + d t )
L
(1)
A. Nonlinearity in Magnetic Material
The IPT core is made up of CRGO material of type M4 which has nonlinear characteristics. The
B − H curve of the material can be approximated as [9]:
Fig. 4. IPT geometry (all dimensions are in mm).
I dif f
λ
= | I
=
0 .
dc 1
− I
0 .
0275 I dif f
055 + 0 dc 2
.
|
4532 I dif f
(3)
(4)
It is to be noted that only the current difference
( I dif f contributes to the core saturation.
)
B. Dynamic Inductance
The dynamic inductance can be defined as a derivative of the mutual flux linkage
( λ ) with respect to the current difference
( I dif f
) in both the windings. The expression is linearized by the backward Euler method and the value of dynamic inductance in terms of the mutual flux linkage
( λ ) and current difference
( I dif f
)
( L dyn
) at any time instant
( t + d t ) is calculated
. The expression for
( L dyn
) can be given as:
L t +d t dyn
=
λ t +d t − λ t
I t +d t dif f
− I t dif f
(5) where, the values of
( λ ) are calculated from Eq. 4. This value of
( L dyn
) is then used in the MNA method to solve the circuit.
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Proceedings of India International Conference on Power Electronics 2006
C. Constant Current Control
The converters have been operated with constant current control such that the full load current of
6000
A is supplied at firing angle
( α ) of
60 o during normal operation. As the load on the converters increases, control circuitry sets the new firing angle to maintain the load current at a constant value.
Under the load short circuit condition, the firing angle is set almost equal to
90 o
. An analog control circuitry implemented in practical systems can be simulated as shown in Fig. 5.
The current error
(d I ) is calculated by comparing total load current
( I dc
) with the reference current
( I current error
(d I ) as formulated below.
ref
)
. Proportionality controller calculates the firing angle corresponding to the
Iref Idc
π
2
Converter 1 e
7
Iref
Idc
Kp
(proportionality constant)
α
1 r1 + sL1
Idc
1 e
9
1 r2 + sL2
Idc
2
Converter 2
Idc
Fig. 5. Control block diagram.
currents are equal to
3000
A and coincide with each other due to presence of the IPT. In such a case, the value of
I dif f is negligibly small and the operation is mainly on the linear part of the
B − H curve. The load current and voltage waveforms obtained from the simulation are as shown in the Fig. 6 and
Fig. 7.
7000
6000
5000
4000
3000
2000
1000
Total load current
Individual currents coincide
0
0 10 20 30
ω
t (rad)
40 50 60
Fig. 6. Current waveforms under balanced operation.
70 d I
α = − K p d I +
π
2
Thus, even in the short circuit condition the load current does not exceed the safe limit of the reference current
( I ref
)
.
(6)
(7)
The modeling and simulation of the work have been carried out by developing an algorithm for dynamic inductance model and MNA method. The system is analyzed under balanced and load short circuit conditions. The operating parameters are as shown in Table I. For obtaining more accurate results, turning ON and OFF processes of switching thyristors are considered as linear transitions from 1
MΩ to 1 mΩ and vice versa, respectively.
TABLE I
O
PERATIONAL PARAMETERS
Input voltage to rectifier transformer 415 V, 50 Hz, 3 ph
Input voltage to each converter (L-L) 33 V
Rated load current
Load and internal inductance 1.8
6000 A mΩ
, 10
µ
H
A. Balanced Operation
= I ref
− I
III. R ESULTS dc
The parallel operation of converters with IPT remains in the balanced condition till their input voltages, firing angles and commutating inductances are equal. The normal load current is maintained at
6000
A and firing angle is set at
60 o
. Both the
25
20
15
10
5
0
−5
−10
−15
42 44 46 48
ω
t (rad)
50 52 54
Fig. 7. Voltage waveforms under balanced operation.
B. Short Circuit Operation
Load short circuit during the operation is a severe condition and is often treated as one of the standard testing procedures in industries. This test checks the capability of the system to operate in safe mode during such conditions. The control circuitry sets the firing angle of the converters almost equal to
90 o so that the average load voltage is automatically set nearly equal to zero, which ensures that the load current is below the reference value. The condition is balanced but the total current increases and the system operation can move on the nonlinear part of the
B − H curve. Fig. 8 shows the variation of load voltage with firing angle
( α ) clearly indicating controlling effect on the system. Voltage gradually decreases when firing angle
( α ) is increased to
90 o
. Fig. 9 shows the simulated load voltage waveforms in which the peak to peak voltage is found
195

Proceedings of India International Conference on Power Electronics 2006
25
20
15
10
5
0
−5
−10
−15
0 10 20 30 40
ω
t (rad)
50 60 70
Fig. 8. Load short circuit voltage with firing angle.
80
4
2
0
−2
−4
−6
−8
−10
10
8
6
42 44 46
ω
t
48 50 52
Fig. 9. Load short circuit voltage: simulation.
54
0
−20
40
20
80
60
−40
−60
−80
40 42 44 46 48
ω
t (rad)
50 52
Fig. 10. Simulated IPT voltage.
54 56 procedures. Further improvement can be obtained if the complete system is considered as coupled circuit-field problem and is solved with the aid of finite element method (FEM); the improvement in accuracy, however, may require large computational time and increase system complexity.
V. A CKNOWLEDGMENT
Authors thankfully acknowledge assistance of Mr. J. P. Koria, Deputy General Manager (Design) of Hind Rectifiers Ltd,
Bhandup, Mumbai, for the fruitful discussion and technical data.
to be
5
V. The approximate representation of power electronic devices introduces some inaccuracies in the simulations. Voltage across the IPT obtained from the simulation is also shown in Fig. 10. Maximum voltage is found out to be 26 V.
IV. C ONCLUSION
In the presented work, a parallel operation of two threepulse controlled converters with interphase transformer (IPT) is analyzed under balanced and load short circuit conditions.
Nonlinear mutual inductance of the IPT has been taken into account. The circuit is solved by modified nodal analysis
(MNA). The magnetic nonlinearity is represented by dynamic inductance model. As both the converter currents are of same magnitude but in opposite direction under balanced condition, the system operation is mainly observed on linear part of the
B − H curve. The load current increases effectively in short circuit condition and the system may operate on nonlinear part of the
B − H curve. The control loop sets the firing angle
α almost equal to
90 o and the average load voltage is set nearly equal to zero.
The MNA code has been developed in MATLAB which solves the circuit with backward Euler and Newton-Raphson
R EFERENCES
[1] J. Schaefer,
Rectifier Circuits: Theory and Design
.
New Jersy: John
Wiley & Sons, 1965.
[2] S. V. Kulkarni and S. A. Khaparde,
Transformer Engineering: Design and Practice
. New York: Marcel Dekker, 2004.
[3] A. M. Cross, A. J. Forsyth, and B. Cooper, “Modelling, simulation and validation of a twelve pulse autotransformer rectifier for aerospace applications,”
International Conference on Power Electronics, Machines and Drives
, vol. 2, no. 31, pp. 528–533, Mar. 2004.
[4] S. Kanerva, S. Seman, and A. Arkkio, “Inductance model for coupling finite element analysis with circuit simulation,”
IEEE Trans. Magn.
, vol. 41, no. 5, pp. 1620–1623, May 2005.
[5] D. J. Perreault and J. G. Kassakian, “Effects of firing angle imbalance on 12 pulse rectifiers with interphase transformer,”
IEEE Trans. Magn.
, vol. 10, no. 3, pp. 257–262, May 1995.
[6] I. G. Park and S. I. Kim, “Modelling and analysis of multi-interphase transformers for connecting power converters in parallel,”
Power Electronics Specialists Conference
, vol. 2, no. 22-27, pp. 1164–1170, June
1997.
[7] A. L. Naikodi and D. H. Mistry, “Modified nodal analysis; a comprehensive technique for drive modelling and simulation,”
TENCON 2003.
Conference on Convergent Technologies for Asia-Pacific Region
, vol. 1, pp. 255–258, Oct. 2003.
[8] L. T. Pillage, R. A. Rohrer, and C. Visweswariah,
Electronic Circuit and
System Simulation Methods
. New York: McGraw-Hill, Inc, 1995.
[9] D. Jiles,
Introduction to Magnetism and Magnetic Materials
. New York:
Chapman and Hall, 1991.
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