40220140505010

International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 100-109 © IAEME
100
POWER FLOW BETWEEN TWO ASYNCHRONOUS GRIDS USING TWIN
STATOR INDUCTION MACHINES
A S Sindekar#
, B H Band*
#
Associate Professor, Electrical Engineering Department,
Government college of Engineering Amravati-444604, India
*
PG Research Scholar, Electrical Engineering Department,
Government college of Engineering Amravati-444604, India
ABSTRACT
Two identical wound rotor induction machines are used for power transfer between two
asynchronous grids. Also, mathematical equation of power flow between twin stator induction
machines is presented. The stators of two induction machines are connected to different frequency
grids. The two machines are made to run at predetermined operating speed. The simulation results on
two nominally identical wound rotor induction machines are presented.
Keywords: Power System Interconnection, Power Flow, Cascaded Induction Machine.
NOMENCLATURE
A. Main Variables
I RMS current (A)
j Imaginary operator
L Inductance (H)
N Mechanical speed (rpm)
p Differentiation with respect to time
P Number of pole
℘ Power (W)
ℜ Real part of complex quantity
R Resistance ( )
τ Instantaneous torque (N-m)
INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING &
TECHNOLOGY (IJEET)
ISSN 0976 – 6545(Print)
ISSN 0976 – 6553(Online)
Volume 5, Issue 5, May (2014), pp. 100-109
© IAEME: www.iaeme.com/ijeet.asp
Journal Impact Factor (2014): 6.8310 (Calculated by GISI)
www.jifactor.com
IJEET
© I A E M E

101
T Steady state torque (N-m)
V RMS voltage (V)
ω Angular velocity (rad/s)
Z Impedance ( )
λ Flux linkage (Wb)
B. Subscript and Superscript Variables
1 machine 1
e Electrical
g Air gap
i Instantaneous
l Leakage
m Mechanical
M Mutual
out output
in input
N Natural
2 machine 2
r Rotor
s Stator
* Complex conjugate
Bold lower case variable denotes instantaneous space phasor. Bold upper case variable
denotes rms space phasor.
I. INTRODUCTION
The AC link and DC link are two options available for large power system interconnections.
Since AC is the dominant mode of generation, transmission and distribution in power system, the AC
link is the “natural” way of interconnecting existing AC power systems. The interconnections have
been mostly realized by AC link since option is technically feasible and economically justified. Thus,
for electrical power flow from one power system network to another power system network; a
simple, reliable and low cost interconnection is needed. Therefore, a flexible AC link is desirable to
connect one power system network to another power system network reliably, such that either side is
least affected by the disturbances in them (for example, due to fault condition or switching
transients).
When an alternator or an asynchronous power system is directly connected to the grid, or one
asynchronous power system is connected to another power system, many problems may arise.
A severe transient inrush current flows in the system at the instant of switching-in. Thus, to
avoid this condition, asynchronous interconnection between power systems is achieved by high
voltage direct current (HVDC) link. But, HVDC conversion is complicated due to the need of
harmonic filtering, controls, and reactive compensation. Moreover, HVDC has performance limits
when the ac power system on either side has low capacity compared to the HVDC power rating.
Further, HVDC systems need conversion plants at both sides of the tie line which increases cost and
undesirably require significant space due to the large number of high voltage switches and filter
banks.
An arrangement with a tap-changing transformer and a phase-shifting transformer is used to
connect two different power systems and to control power flow along a transmission line. It has the

102
drawbacks of stepwise operation and stability problem on the grid, also components wear out due to
repetitive action. When the phase-shifting transformers are used with power electronics, some of
these drawbacks are eliminated. However, they have their own limitations including problems of
harmonics, risk of torsional interactions, risk of rapid bypass for grid disturbance, and short overload
capability due to low thermal time constant.
Recently an asynchronous AC link, an alternative of HVDC link, has been developed for two
power systems. The requirement of HVDC link, phase shifting transformers and the problem of re-
switching are eliminated by putting a variable frequency transformer (VFT) in between two
asynchronous power systems. In fact, VFT is rotated at a particular torque and a particular speed. In
this scheme, a separate dc motor is used to control torque, speed and direction of rotation of VFT
which in turn controls the power transmission from one power system to another at a constant
frequency. However, this VFT based asynchronous link suffers from a serious drawback that it
requires a forced rotation of VFT. Moreover; a constant torque is required even at zero speed, when
the frequencies of both grids are same. The system also requires frequent shutdown and maintenance
due to replacement of carbon brushes of the high rating dc motor which is a part of the VFT system.
Moreover; when there is a fault in power system, VFT requires very large torque to compensate. This
leads to requirement of very high rating of dc drive as VFT has to handle bulk power. The VFT
connects two grids of the same frequency or frequencies of close values.
This entire drawback can be overcome by using two induction machines and connecting them
to the different frequency grids for power flow between them. Two induction machines provide
asynchronous power transmission between two independent power generating networks. This paper
presents link for power transfer between the two grids, without restriction on the grid frequencies.
The difference in the frequency of two grids can be of small value or large value.
II. THEORY OF OPERATION
The system consists of two induction motors, connected in cascade for power transfer
between the two asynchronous grids. The doubly fed twin stator induction machine (DFTSIM) is
being investigated as a variable speed drive. One of the benefits of the DFTSIM is it exhibits
synchronous behavior at a pre-determined, user settable, variable speed. The stators of the two
induction machines are connected to different values of frequency (grids) and the rotors are
connected mechanically. The rotors are also connected electrically for power transfer between the
two grids. The system contains two wound rotor induction machines in twin stator configuration. The
power is transferred between two generating networks through the electrical connection provided
between the rotors. The machine 1 rotor has an induced voltage and magnetic field of frequency fr1
due to its stator field. Similarly for machine 2, the rotor induced voltage and magnetic field have a
frequency fr2 due to its stator field. The rotors of the two machines are mechanically coupled and the
rotor windings are connected in reverse sequence so as to produce contra rotating fields. The rotating
fields produced by two rotors will rotate in opposite direction to each other. The two rotor
frequencies must be of the same value to obtain power transfer. Two rotors must be connected
electrically to satisfy this condition. Two induction machines provide asynchronous power
transmission between two independent power generating networks.
The stator magnetic field rotates with synchronous speed and it depends on number of poles
and supply frequency of the machines (Ns=120f/P). The rotor magnetic field of each machine
depends on machine number of poles and rotor frequency.

103
III. STEADY STATE EQUATIONS
In the analysis, the following assumptions are made:
(a) Balanced three phase windings are distributed to produce sinusoidal space variation of flux
density;
(b) Only the fundamental components of voltage and current are considered;
(c) The magnetic circuits are linear, i.e. the effects of saturation and hysteresis are neglected;
(d) Zero sequence quantities are not present;
(e) The only losses are copper losses;
The rotors of the two machines are mechanically coupled with their ‘a’ phases aligned and
the windings are connected in reverse sequence so as to produce contra rotating fields that are
coincident on the magnetic axis of the ‘a’ phase. The general equation for the DFTSIM, in the rotor
reference frame can be written as,
[v]= [z] [i] (1)
Fig. 1: Arrangement of DFSTIM
Where
[v] = [v1 v2
*
0] T
, [i] = [i1 i2
*
ir] T
, (2)
ሾZሿ ൌ ൦
R1s+ ൫p + jP1
ωm൯L1s 0 ൫p+jp1
ωm൯L1m
0 R2s+ ൫p- jP2
ωm൯L1s ൫p- jP2
ωm൯L2s
pL1m pL2m ሺRr+pLrሻ
൪
Rr = R1r + R2r, and Lr = L1r + L2r
The electromagnetic torque is given by,
τe = 3/2ℜ(jP1L1M i1s
*
i1r) + 3/2ℜ(-jP2L2Mi2s i1r) (3)
where, the first term represents the torque contributed by machine 1 and the second, torque
contributed by machine 2.

104
In steady state, (1) becomes; using rms values,
[V12] = [Z12] [I12] (4)
where,
[V12] = [V1 V2
*
0] T
, [I12] = [I1 I2
*
Ir] T
ሾZଵଶሿ ൌ ቎
(R1s
൅ jω1L1sሻ 0 jω1L1M
0 (R2s
- jω2L2sሻ െjω1L2M
jωrL1M jω୰L2M ሺRr+jωrLrሻ
቏
Equation (4) contains voltages and currents at three separate frequencies.
In steady state, the electromagnetic torque becomes; using rms values,
Te = 3 ℜ (jP1L1MI1Ir
*
) + 3 ℜ (-jP2L2MI2Ir) (5)
IV. POWER FLOW WITHIN DFTSIM
In power flow, per phase power will be discussed. To obtain the total power, per phase power
is multiplied by three. To understand the power flow into the DFTSIM, equation (4) is used. The first
row, relating to the machine 1 quantities, is at the frequency f1. The second row, relating to machine
2 is at frequency f2 and the third is at the rotor electrical frequency fr. Multiplying the first row of (4)
by I1
*
, and taking the real part only gives,
ℜ (V1I1
*
) - |I1|2
R1s - ℜ (jω1L1MIrI1
*
) = 0 (6)
The first term of (6) represents the power flowing into the machine 1 stator winding and it is
at the frequency f1. The second term represents the machine 1 stator winding copper loss and the
third term is machine 1 air gap power.
Multiplying the second row of (4) by I2, and taking the real part only gives,
ℜ (V2
*
I2) - |I2|2
R2s - ℜ (-jω2L2MIrI2) = 0 (7)
The first term of (7) represents the power flowing into the machine 2 stator winding and this
is at the frequency f2. The second term represents the machine 2 stator winding copper loss and the
third is the machine 2 air gap power.
Multiplying the third row of (4) by Ir
*
, and taking the real part only gives,
|Ir|2
Rr + ℜ (jωrL1MIr
*
I1) + ℜ (-jωrL2MIrI2) = 0 (8)
The electrical quantities in (8) are at the frequency of the rotor currents and voltages. Using
the slip relationships in Appendix A, (8) may be rewritten as,
-|Ir|2
Rr + [ℜ (jω1L1MI1
*
Ir) +ℜ (-jP2ωML2MIrI2)] –
- [ℜ (jP1ωmL1MI1Ir) + ℜ (-jω2L2MIrI2)] = 0 (9)
The first term in (9) is the rotor copper loss, the second is the machine 1 air gap power, the
third term is machine 2 air gap power and the final two terms represent the mechanical output power.

105
The power delivered to the rotor is the sum of the air gap powers from machine 1 and machine 2 and
is,
℘in = ℜ (jω1L1MI1
*
Ir) + ℜ (-jω2L2MIrI2) (10)
The total output power is the sum of the contributions from each part of the DFTSIM and is,
℘out = ℜ (jP1ωML1MI1Ir) + ℜ (-jP2ωML2MIrI2) (11)
Using the slip relationships in Appendix A, the output power may be represented as,
℘out = (1-S1) ℘1g + (1+ (S1/S)) ℘2g (12)
The first term in (12) is same as the power output of a singly fed induction machine. In a
standard induction machine, the air gap power ℘1gS1, becomes the I2
R loss.
In this system, machine 1 operated as a motor and machine 2 as generator. Therefore, rotor
frequency for machine 1 and machine 2 is,
fr1 = f1 [(ω1 – ω/ ω1) (13)
fr2 = f1 [(ω2 + ω/ ω2) (14)
The condition of power transfer between the rotors is fr1 = fr2. Substituting for the machines
number of poles and solving for the speed at which the rotor frequencies will be equal.
ω = 60 [(f1 – f2) / (P1 + P2)] (15)
Equation (15) gives driving motor speed and same speed is applied to the rotor of two
induction machines. The operating speed of two rotors is same, hence frequency is same. If the two
grids have the same frequencies, then the speed becomes zero and the system is acting as a stationary
transformer.
V. SIMULATION AND RESULTS
The simulation of the system is carried out using the Simulink software package. Two
induction machines are mechanically coupled and made to rotate at a predetermined speed. The
machine speciations used in the simulation is mention in Appendix B. The machine 1 has 2 pole
connected to 60 Hz frequency grid and machine 2 has 2 pole connected to 50 Hz frequency grid. The
two machines are driven at calculated speed of 150 rpm.To represent the electrical connection of the
two squirrel cage rotors, we use the wound rotor block to facilitate the rotor connections and to be
able to measure the rotor currents. Since the two machines are mechanically coupled, they are forced
to rotate at a predetermined speed.
Figure 2 shows the block diagram of the system. Figure 3 to figure 5 shows the simulation
results. The system is used to link a 50 Hz grid to 60 Hz grid. The 60 Hz grid is connected to the
machine 1(2-pole) and the 50 Hz grid is connected to the machine 2 (2-pole). The voltage at the
machine 1 is 220 V with an angle of -240°. The voltage at the machine 2 is 220 V with an angle of
0°. The angles of these two voltages cannot be related to each other due to difference in the
frequencies. Figure 4 shows steady state power at the system terminals. The system power at
machine 1 (60 Hz) is about -285.4 W and the system power at machine 2 (50 Hz) is around +285.3

106
W. The power is transferred from the 50 Hz grid to the 60 Hz i.e. from machine 2 to machine 1.The
simulation shows that the power has a constant value at the steady state.
Fig. 2: Simulink model of system
Fig. 3: The Power at the system terminals

107
Fig. 4: Stator currents
Figure 6 shows the rotor currents. The default direction of the rotor current is from the rotor
to the external circuit. So, ir1= -ir2. This means the two rotor currents have a phase shift of 180°. The
rotor currents contain no harmonics.
Both currents have the same frequency. Even that the stator currents have different
frequencies, the rotor currents have equal frequencies. So the condition for power transfer is satisfied
at the calculated speed.
Fig. 5: Rotor currents
VI. CONCLUSION
The system can be used to transfer the power between two asynchronous grids. The system
does not restrict to the frequency of grid. It connects two grids, with any two values of frequency.
This system does not require slip-rings as the two rotors are mechanically coupled with direct
electrical connections. The calculated speed operates two rotors at same speed and it leads to
generate same rotor frequency from either machine and rotor current contains no harmonics.

108
REFERENCES
[1] Arezki Merkhouf, Pirre Doyon, and Sanjoy Upadhyay, “Variable Frequency Transformer—
Concept and Electromagnetic Design Evaluation”. IEEE Transaction on nergy Conversion,
vol.23, no.4 December 2008.
[2] N.G. Hingorani and L. Gyugyi, “Understanding FACTS: Concepts and Technology of
Flexible AC Transmission Systems,” IEEE press/Standard Publishers Distributors, Delhi,
2001.
[3] H.Wang and M.A. Redfern, “The advantages and disadvantages of using HVDC to
interconnect AC networks,” in Proc. IEEE 45th Int.UPEC, Cardiff, Wales, Aug. 31- Sept. 3,
2010, pp.1-5.
[4] Rob O’Keefe and David Kidd. “United States and Mexico Cross-Border. Variable Frequency
transformer to reinforce power transfer between countries”. Controls & Automation,
pp. 20-26,August 2006.
[5] Kilgore et al. United States Patent 3, 975, 646, August 17th, 1976.
[6] M. S. Vicatos and J. A. Tegopoulos, L., “Doubly-fed induction motor differential cascade
Part I - configuration and analysis in the steady state”. IEEE Transactions on Energy
Conversion, Vol. 14, No. 3, September 1999,pp. 361-366.
[7] Mohamed Ashraf Mahmoud Abdulla, “New System for Power Transfer between Two
Asynchronous Grids Using Twin Stator Induction Machine”. IEEE International Electric
Machines & Drives Conference (IEMDC), 2011,pp.1658-1663.
[8] Kostyantyn Protsenko and Dewei Xu, “Modelling and Control of Brushless Doubly-Fed
Induction Generators in Wind Energy Applications”. IEEE Transaction on Power Electronics,
Vol. 23, No.3, May 2008, pp.1191-1197.
[9] D. Picovici, D. Levy, A.E. Mahdi, T. Coffey, “The cascade induction machine: a Reliable
and controllable motor or generator”. journal of Electric Power Systems Research 68 (2004),
pp.193-207.
[10] Q. P. Ha, J. G. Zhu, and G. Boardman, “Power ﬂow in doubly fed twin stator Induction
machines,” AUPEC 2001, pp. 37–42.
[11] Prabha Kundur, “Power System Stability and Control”. McGraw Hill, 1994, ISBN0-07-
035958-X.
[12] Jagadanand G, Lalgy Gopi, Saly George and Jeevamma Jacob, “Inter-Turn Fault Detection in
Induction Motor using Stator Current Wavelet Decomposition”, International Journal of
Electrical Engineering & Technology (IJEET), Volume 3, Issue 2, 2012, pp. 103 - 122,
ISSN Print: 0976-6545, ISSN Online: 0976-6553.
[13] Haider M. Husen , Laith O. Maheemed and Prof. D.S. Chavan, “Enhancement of Power
Quality in Grid-Connected Doubly Fed Wind Turbines Induction Generator”, International
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[14] B.Sivaprasad, O.Felix, K.Suresh, G.Pradeep Kumar Reddy and E.Mahesh, “A New Control
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& Technology (IJEET), Volume 4, Issue 2, 2013, pp. 305 - 323, ISSN Print : 0976-6545,
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ISSN Online: 0976-6553.

109
APPENDIX A. DEFINITIONS OF SLIP
In a single stator induction machine, the slip S, is defined as,
S ൌ
Synchronous speed െ Rotor speed
Synchronous speed
ሺA1ሻ
By this definition, the slip for machine 1 can be expressed consequently as
S1 = [(ω1 – P1 ωm) / ω1] (A2)
and the slip for the machine 2,
S2 = [(ω2 – P2 ωm) / ω2] (A3)
The slip for the DFTSIM is defined to be,
S = - (S1 / S2) (A4)
= [(ω1 – P1 ωm) / ω1] / [(ω2 – P2 ωm) / ω2]
= ω2 / ω1
Because
ωr = ωr1 = ω1 – P1 ωm (A5)
and
ωr = -ωr2 = -(ω2 – P2 ωm) (A6)
We have,
P1 ωm = ω1 (1- S1) (A7)
P2 ωm = ω2 [1+ (S1/S)] (A8)
APPENDIX B. Doubly-Fed Machine Data
Two similar 1.5 kW, three phase, wound rotor induction machines are used with following data:
Name Plate Data Machine Parameters
Stator voltage 220 V Stator resistance 3.4
Stator full load
current
7.8 A
Stator leakage
reactance
3.7
Rotor voltage 85 V Rotor resistance 0.2
Rotor full load
current
12.5 A
Rotor leakage
reactance
0.2
Number of poles 2
Magnetizing
reactance
10

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