Single Phase to Three Phase Converter
Ermurachi Iurie, Berzan Vladimir
Ivanov Sergiu
Institute of Power Engineering
Ministry of Education, Culture and Research
Chisinau, Republic of Moldova
E-mail: ermurachi.iurie@ie.asm.md, berzan@ie.asm.md
Craiova University
Department of Electromechanics, Environment and
Industrial Informatics
Craiova, Romania
E-mail: sergiu.ivanov@ie.ucv.ro
Abstract — The paper addressing the problem of increasing
the energy efficiency indices and the lifetime of the mono / three
phase inverters powered from the single phase AC grid. The
actuality of this problem regarding the efficiency of the use of
electricity is determined by the fact that at present most of the
receivers in the residential sector are of single-phase type
(washing machines, air conditioners, electric pumps,
refrigerators, kitchen equipment, etc.). As a solution to increase
the efficiency of the use of electricity in the consumption phase,
the use of three-phase asynchronous motors is examined, which
have higher energy performance indices compared to singlephase asynchronous motors. For the control of three-phase
motors when supplying them from the single-phase network, a
new three-phase inverter control algorithm is proposed, which
has been called frequency-pulse-width-modulation (FPWM). The
simultaneous modulation of the frequency and the width of the
control impulses leads to the decrease of approximately 25% of
the number of the control impulses of the transistors of the threephase inverter. This ensures quality indices of electricity supplied
to the three-phase asynchronous motor and minimal pollution of
single-phase grid with the higher current harmonics. The
proposed frequency-pulse-width-modulation algorithm excluded
the function of intermediate energy storage in the electrolytic
type DC filter capacitors, which have a shorter lifetime compared
to other components of the voltage inverter. As a filter capacitor
of the proposed three-phase inverter, only capacitors with
dielectric film are used, which have a much smaller capacity
value compared to the previously used electrolytic capacitors.
The substitution of the electrolytic capacitors was possible
because in the proposed inverter the dielectric film capacitors
filter switching harmonics of the transistors.
Keywords— power conversion; AC-AC converters; pulse width
modulation converters; frequency-pulse-width-modulation; energy
efficiency.
I. INTRODUCTION
In the electric power distribution systems, the single-phase
grid was considered an alternative for the rural environment or
the low-power areas of the electricity consumers [1], because
this type of network has a simpler construction compared to
the grid with three phases [2]. The low-voltage three-phase
distribution networks include as a functional element of the
fourth conductor, which is called the null conductor. This
conductor is used to ensure the power supply the single-phase
receivers. This ensures harmonization of benefits of the threephase electricity transmission system with the reality, which
consists in the fact that the electricity receivers, mainly of low
power, are designed from supply a single phase of the grid.
The significant share of electricity consumption in lowvoltage distribution networks is determined by the need to
convert electricity into mechanical work, which is done by
electromechanical converters - electric motors. Electric motors
ensure the operation of a wide range of equipment and
machinery for both domestic and industrial use: electric drives
with DC motors, alternating single and three phase motors at
industrial frequency, high frequency which is changing into
broadband, for example, in the case of automated electrical
drives.
Single-phase motors with starter coil, with collector, threephase motors used as single-phase motors have lower
efficiency compared to motors powered by three-phase
systems.
The use of the three-phase motors, which have higher
energy efficiency indexes and higher mass and size indices in
comparison with the single-phase motors, requires the use of
specialized converters, which can ensure the multiplication of
the number of phases and the frequency. For this purpose,
solutions based on the use of passive elements (electrical
capacitors, reactors) are used [3] - [6]. Connection equipment
made from passive elements has several disadvantages [5] The
development of power electronics [7] has opened up new
possibilities for powering three-phase motors from singlephase power supplies.
The application of technologies based on power electronics
contributes to increasing the efficiency of the use of
electricity, including, in the electric drive systems with
controlled electronic converters [8, 9]. The increase of the
performance of the power electronic devices regarding the
capacity of operation at high currents and "high" voltages with
low reaction time, as well as the decrease of their own losses,
mainly of switching, have ensured the increase not only of the
energy performance, but also of the reliability level of the
converters made with the use of these semiconductor devices.
Following the increase in the performance of electronic
components, modern converters become economically
competitive for applications in most electrical drives,
regardless of the unit power of electric motors. The advantage
using the converters power electronics with adjustable
frequency is very evident in the electric drive systems, which
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have the speed band of the working organs 500-20000 rotations
per minute.
The purpose of this paper is to elaborate and argue the
technical solution for manufacturing the electronic AC / AC
converter for transforming the single-phase current into threephase current with high energy and economic indices, as a
result of reduced switching losses and of the influence of the
switching disturbances on the energy receivers and on the
power network, increasing the life of the converter as a result
of the exclusion of the functional elements (electrolytic
capacitors) with short life.
single-phase power supply network. The single-phase bridge
rectifier consists of diodes D11, D12, D21, D22 and the capacitor
C2. The capacitor C2 has the function of filtering the
harmonics of switching of the three-phase voltage inverter,
which operate at high switching frequency of the transistors.
The three-phase inverter consists from semiconductors
components: TA1, TA2, DA2, TB1, TB2, DB2, TC1, TC2, DC2.
II. THE PROPOSED TECHNICAL SOLUTION AND THE OPERATION
PRINCIPLE OF THE CONVERTER
Most of the electric power receivers have relatively low
installed power and as a result, where are supplied from
single-phase circuits, for example, the receivers that present:
washing machines, chippers, electric tools, pumps,
refrigerators, air conditioners, etc. In order to increase the
energy efficiency of these electricity users, innovative
solutions are needed to increase the efficiency of the
conversion of electricity into the required form, mainly, in
mechanical work.
In order to ensure economic competitiveness, it is
necessary for these equipment to have low costs, high
performance indices and high flexibility regarding their ability
to connect to single-phase power networks. At the same time,
these equipment must ensure a high degree of adaptability to
the network parameters, whether the network has the
frequency 50 or 60 Hz, or direct current. The connection
equipment must ensure the security of supply of the electricity
receivers and in the event of significant disturbances of the
voltage of the mains supply.
In order to meet the criterion of economic competitiveness,
these equipments must be based on the use of components,
which are easily available on the market at reasonable prices.
The design of these equipments, taking into account the listed
requirements, will allow to ensure their technical-economic
competitiveness in the area of use.
A. Energy converter diagram
Electricity conversion is done using voltage inverters and
current inverters. The voltage inverters have several
advantages regarding the inverter topology, the realization of
the control system with devices of the power electronics,
because the voltage on the load is used as an informative
signal. To correspond to these advantages, a inverter topology
adapted to the purpose of the work is proposed. The equivalent
electrical diagram of the inverter is shown in Fig. 1. The
converter includes a single-phase AC voltage source, a singlephase rectifier, the three-phase voltage inverter, which the
supplies of the three-phase load Zload - three-phase
asynchronous motor.
The converter is equipped with a filter consisting of
inductor L and the capacitor C1. The LC1 filter is intended to
limit the penetration of higher current harmonics into the
Fig. 1. Equivalent diagram of AC / AC power supply with phase
multiplication.
The single-phase bridge rectifier with diodes D11, D12, D21
and D22 has a simple topology. As a requirement to the
rectifier, when solving the formulated problem, it was
considered to reduce the cost of this rectifier by optimizing the
parameters of the passive components. The semiconductor
components TA1, TB1, TC1 they must have characteristics very
good switching characteristics (short shut-off time) in order to
reduce switching energy losses. To this requirement
correspondings to the state-of-the-art Cool MOSFET type
transistors. The semiconductor elements TA2, TB2, TC2, work at
the frequency of the load current and for these devices the
requirements regarding the switching regime (opening
closing) are not as harsh as for the transistors TA1, TB1, TC1.
For use in this circuit, IGBT type transistors with of low
voltage drop are recommended, which also have a low price.
The semiconductor elements DA2 DB2 DC2 should have a
minimum value of the reverse flow current. It is recommended
to the use SIC-type diodes.should have a minimum value of
the reverse flow current. It is recommended to use SIC-type
diodes.
B. Overview of inverter modulation techniquesŃ
The electronics converter powers the electromechanical
converter, which can operate in the broadband diapason of the
speeds. For this it is necessary to acording the characteristics
converters of the power electronics with the mechanical
characteristics of the actuated working organs. A this can be
done by using flexible control algorithms of the electronic
power converters. The control algorithms with the converters
of the power electronics are based on the following methods
of forming the current or voltage of the load: Pulse-amplitude
modulation (PAM), Pulse-density modulation (PFM), Pulsewidth modulation (PWM).
Pulse-amplitude modulation (PAM) (Fig.2). This is a
modulation process in which the amplitudes of the pulses of
the voltages during the period of the output signal are variable,
which allows adjusting the power absorbed by the load. The
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scope of this type of modulation in AC / AC converters is
limited.
Most inverters in the AC drive applications use PWM in
the inverter output voltage forming process.
The converter with the PWM algorithm can be designed
and manufactured with relatively little effort, since the
components of the power electronics used in these inverters
are available in the market. Obtaining the signal close to the
sinusoid requires the operation of the transistors at a high
frequency of switching during the output signal period of the
AC voltage with which the load is fed.
Fig. 2. The diagrams for the realization of the PAM process, in which u the voltage on the load, the VT- the control pulse with the variable
amplitude, the pulse frequency f = const, which coincides with the
frequency of the load current.
Pulse-density modulation (PFM) (Fig.3). It is the
modulation procedure in which the number of impulses is
adjusted, which have the same width during the output signal
period (frequency adjustment), which ensures the regulation of
the power absorbed by the load. This process is also known as
Variable Frequency Modulation (VFM). Mostly, the PFM
algorithm is used in DC-DC converters, chargers and other
applications regarding the power supply of the DC receivers.
This process is difficult to use for the purpose of the electric
power supply of AC motors. In order to form a sinusoidal
signal it is necessary to use a very large number of impulses,
which consequently requires the use of the high frequency of
switching of the transistors of the three-phase voltage inverter.
Fig. 3. The diagrams for the realization of the PFM process, in which u - the
voltage on the load, the VT - the train of the control impulses with the constant
width and the variable frequency, f = var.- the law of the variation of the
switching frequency of the inverter transistors.
Pulse width modulation (PWM) (Fig. 4) The modulation
process in which the width of the pulse (operating cycle) is
variable to ensure the regulation of the power absorbed by the
load.
Fig. 4. The diagrams for the realization of the PWM process, in which u - the
voltage on the load, VT - the train of the control pulses with the variable
width, f = const the switching frequency of the inverter transistors.
Frequency-pulse-width-modulation (FPWM) (Fig. 5). The
flexible modulation process in which the variation of the pulse
width and of the switching frequency of the power electronics
devices within the voltage inverter occurs simultaneously to
ensure the regulation of the power absorbed by the load. This
solution has advantages compared to the PWM and PFM
method, as it allows to reduce the number of transistors
switching during the output signal period (the AC voltage)
with the assurance of quality indices for limiting the value of
the voltage distortion coefficient applied to the load, in the
compared to the separate use of the PWM processes and PFM
for forming the signals with similar quality indices of the
output voltages of the inverter. Reducing the costs of
microcontrollers has described new possibilities for using
these elements, as a result of programming and of using more
complex control algorithms with transistors the voltage
inverter, which would be difficult to achieve if these
algorithms were based on analog electronic components.
Fig. 5. The diagrams for the realization of the FPWM process, in which u - the
voltage on the load, VT - the train of the control impulses with the variable
width and frequency, f = var.- the law of the switching frequency of the
transistors of the inverter.
C. Three-phase inverter operating algorithm with FPWM
As a result of the application of the complex control
algorithm, a sinusoidal form of the three-phase inverter
voltage is obtained, but at a lower commutation frequency of
the voltage inverter transistors. As a beneficial result we will
have the reduction of energy losses in the inverter. The FPWM
type algorithm can provide advantages for reducing switching
losses by establishing specific operating regimes of the
transistors in the three-phase inverter operating cycle. This
specific mode of operation of the transistors is determined
based on the output voltage curves of the three-phase inverter,
which is described in [10, 11].
In Fig. 6 presents the switching laws of the voltage inverter
transistors in order to obtain a sinusoidal three-phase voltage
on the load. The line voltage curves u AB , u BC , uCA of the
three-phase system are obtained by calculation and are
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considered standard signals. These curves are used to obtain
the operating diagram of the FPWM switching the voltage
inverter transistors, which operate in switching mode
simultaneously in only two phases of the inverter. Using the
standard curves of the line voltages and the operation
diagrams of the transistors of the inverter phases (the
transistors TA1 and TA2 ; TB1 and TB 2 ; TC1 ‫܈‬i TC 2 of the
respective phases) allows us to obtain the law of switching the
transistors for the elementary duty cycle (over a period of the
alternating current from the load).
This operating mode has 240 electric degrees of active
modulation of the transistors TA1, TB1 and TC1 of the respective
phases. The transistors TA2, TB2 and TC2 are opened in the
intervals corresponding to the duration 120 electric degrees
and this interval does not overlap with the interval of 240
electric degrees of operation of the transistors TA1, TB1 and
TC1. The other two phases of the inverter have the same
operating algorithm as phase A. The only difference is that the
operating regimes of these transistors in phases B and C have
phase differences of 120 and 240 degrees electric against the
angle of phase voltage A.
The law of time evolution of the frequency of the control
impulses of the transistors TA1, TB1 and TC1 (bottom arm) is
formed based on the evolution curves of the signals uA, uB and
uC, which are shown in Fig. 7 (curves f A , f B , fC ). Depending
on the ratio (u A / uR ) of the instantaneous voltage values, the
switching frequency of the transistors TA1, TB1 and TC1 is
determined according to the relations (1) or (2).
In Fig. 7 are presents the diagrams of the control impulses
of the transistors forming the upper arm TA2, TB2 and TC2 of
the three-phase inverter, which have a switching frequency
equal to the output frequency of the inverter.
Fig. 6. The law of switching transistors in three-phase inverters of voltage.
The operating regime of the transistors TA1, TB1 and TC1 is
determined by the law of evolution of the curves noted in Fig.
6 through uA, uB and uC and is a variable frequency operating
mode that is determined by the relations:
f FPWM = ( u A / u R ) f nom for u A ≤
uR
,
2
§ u − uA ·
uR
f FPWM = ¨ R
,
¸ f nom for u A >
2
© uR ¹
(1)
(2)
in which u R - the instantaneous value of the output voltage of
the single-phase current rectifier; u A - instantaneous voltage
value at common transistors connection points TA1 ‫܈‬i TA2;
f nom - the nominal frequency, which is determined by the
allowable value of the switching frequency of the transistors
used in the three-phase inverter.
Fig. 7. The law of the evolution of the frequency of the control impulses and
the diagrams of these impulses of the transistors that make up the upper arm
and the lower arm of the three-phase inverter.
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We have the operating regime of the transistors (TA1, TB1
and TC1) of the lower arm with variable frequency modulation
of the type FPWM ( f FPWM ) the during 2/3 time of output
voltage period of the three-phase inverter. On the next time
portion of output voltage period equal to 1/3 the transistors
TA1, TB1 and TC1 are in the closed state. The use of this
algorithm for the operation of transistors TA1, TB1 and TC1
leads to a decrease in switching losses in the inverter. This is a
very important tcondition to increasing the efficiency of the
proposed three-phase inverter. Due to the decrease in
switching losses of transistors TA1, TB1 and TC1, radiators with
smaller cooling surfaces can be used.
The shapes of the standard three-phase signals u A , uB , uC
(Fig. 6), used to form the law of the variation of the switching
frequency f FPWM when supplying of the energy three-phase
asynchronous motor from the inverter, are synchronized with
the rotor speed of this motor. Applying this control algorithm
with the inverter ensures the limitation of the maximum
current value when starting the asynchronous motor.
Depending on the mechanical characteristics and the speed of
the working organ coupled with the asynchronous motor the
speed of the rotor varies in very wide band, from zero to the
maximum value allowed for this working organ.
TABLE I.
THE VALUES OF THE PARAMETERS OF THE MATHEMATICAL
MODEL AT THE SIMULATION OF THE THREE-PHASE INVERTER
Parameters
Pout
u~
i~
fm
cosij
fLoad
fnom
fFPWM
L1
C1
C2
Z
R
L
III. SIMULATION OF THE OPERATING MODES OF THR THREEPHASE INVERTER
A. The mathematical model for inverter regime simulation
In Fig. 8 is present of the mathematical model simulation
ɨf modes of the three-phase inverter when supplying energy to
the asynchronous motor from the single-phase alternating
current network.
Fig. 8. The model for simulating the operating modes of the three-phase
inverter.
The simulations were performed for the case of powering a
three-phase asynchronous motor with the nominal frequency
200 Hz. The values of the parameters of the mathematical
simulation model are presented in Table I.
Description
Nominal output power Pout, kW
Single-phase source voltage (rms), V
Source current (rms), A
Mains frequency of single phase
source, Hz
The power factor of the three-phase
asynchronous motor
Mains frequency of the three-phase
asynchronous motor, Hz
The nominal switching frequency of
the transistors of the lower arm, kHz
The switching frequency band of the
transistor of the lower arm, kHz
Filter inductance, mH
Filter capacitance, ȝF
DC-link film capacitance, ȝF
The phase impedance of the threephase asynchronous motor, Ohm
Active resistance of the phase of the
asynchronous motor, Ohm
Inductance of the phase of the
asynchronous motor, mH
Value
2.2
230
9.56
50.0
0.71
200.0
16.0
1.0-16.0
0.5
2x4.7
3x4.7
15.55
10.99
13.0
B. Simulation of the operating mode of the three-phase
inverter
The mathematical simulations aim to obtain information
regarding the behavior of the equipment in different operating
modes. The speed characteristics of the working organes are
determined by the technological peculiarities. As the speed of
asynchronous motors is determined by the frequency of the
supply current, it is reasonable to study the particularities of
the operation of the three-phase asynchronous inverter-motor
system at different frequencies generated by the three-phase
inverter. In order to obtain an image of the peculiarities of
adjusting the speed of the three-phase asynchronous motor and
with the purpose of estimating the impact on the power grid
and on the asynchronous motor of the distortion currents of
the inverter, simulations were performed for frequency of the
inverter: 12.5, 50 and 200 Hz. In the simulated scenarios, the
frequency deviation of the inverter from the network
frequency is symmetric. The deviation of the limit values
constitutes 4 times from the frequency of the supply network.
The output voltage of the inverter is subject to the law (UA,RMS
/ fLoad) = const., where UA,RMS - the output voltage of the threephase inverter; fLoad - voltage frequency on the load.
In Fg. 9-11 presents the diagrams of the currents in the
output circuit of the three-phase voltage inverter when
powered supplying it from the single-phase AC grid with the
frequency 50 Hz. The proposed inverter is not sensitive to
changing the frequency of the mains supply and can be used in
case of voltage supply from other frequencies (random),
including, and from a DC network.
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Fig. 9. The voltage u and current i of the
single phase network with the frequency 50 Hz and
the phase currents curves of the three phase inverter
iA, iB and iC, which have the frequency of 12.5 Hz.
Fig. 10. The voltage u and current i of the
single phase network with the frequency 50 Hz and
the phase currents curves of the three phase inverter
iA, iB and iC, which have the frequency of 50 Hz.
When supplying the three-phase inverter from the singlephase AC grid, the output currents of the three-phase system
have variable values, which are determined by the
instantaneous current value of the supply voltage. The phase
currents of the three-phase inverter have the phase difference
equal to 120 electrical degrees.
The variation of currents in the output circuit is periodic
for all phases (Fig. 9 - 11) and is determined by the frequency
fm of the single phase alternating current source. The
instantaneous value of the torque of the asynchronous motor
has a time-varying character over the input voltage period u~
of the powering network. However, the torque formed by the
three-phase current system generated by the three-phase
inverter has the same sense permanently and does not
influence the variation of the rotation speed of the three-phase
asynchronous motor.
IV. CONCLUSIONS
It has been proposed and argued a new topology of the
single-phase / three-phase inverter intended for supplying the
three-phase asynchronous motors from the single-phase
network in which the function of energy storage by
electrolytic capacitor from the single-phase network is
eliminated. The exclusion of the function and the substitution
of this capacitor with the capacitor with dielectric film ensures
the increase of the life of the inverter, because the electrolytic
capacitors have the shortest life in the power inverters.
In the inverter is used a combined control algorithm that
ensures the operation of transistors at variable frequency
switching of the PWM type, which leads to a substantial
decrease in the number of switches on the during the output
signal period output of the inverter (estimated 25% compared
to the PWM algorithm). Reducing the number of switching’s
of the transistors ensures an increase in the inverter efficiency
with the improvement of the inverter thermal regime.
Fig. 11. The voltage u and current i of the
single phase network with the frequency 50 Hz and
the phase currents curves of the three phase inverter
iA, iB and iC, which have the frequency of 200 Hz.
5()(5(1&(6
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