Download TRANSFORMERLESS STEP UP ALTERNATING VOLTAGE

TRANSFORMERLESS STEP UP ALTERNATING VOLTAGE REGULATORS WITH
SINUSOIDAL INPUT AND OUTPUT CURRENTS
G. S. Zinoviev, A.V. Udovichenko
Novosibirsk state technical university, Novosibirsk, K.Marx's avenue, 20, 630064, Russia
Abstract – The new transformerless step up alternating voltage regulators with a sinusoidal input
and output currents and ability of voltage increasing with the raised quality of formed an output
voltage and an input current are considered, which can be used as a three-phase alternating
voltage stabilizer, a transformerless devices of alternating voltage increasing, the regulable
source of stable alternating voltage for the purposes of reactive power of a network
compensation and the soft-starting devices for asynchronous motors. The results of mathematical
modeling and analytical calculation of effective values by first harmonics of currents and voltage
of a basic regulator are presented.
Work is executed under the state contract № 13.G36.31.0010 from 22.10.2010.
Keywords – alternating voltage stabilization, alternating voltage regulation, a regulator of
reactive power, the soft start of induction machine.
Introduction
The demand of alternating voltage stabilization at an input of electric network consumers is
actual, particular, in the overloaded and rural “weak” network. Traditionally, it is solved by
using of the tapped transformer and relay or thyristor switch of taps. Such system is inertial,
discrete and requires of transformer using. Well-known the fast-operating transistor two-zone
pulse-width regulator of alternating voltage, but it contains a transformer too [1]. Also wellknown the transistor pulse-width alternating voltage regulator allowing to increase of an output
voltage without transformer [2]. But it requires in an input filter, additionally, because it have the
discontinuous input current.
In the present paper, on the basis of suggested earlier [3, 4] a basic three-phase transistor
regulator of alternating voltage, which has 6 switches of alternating current, a simplified and a
simple regulator of alternating voltage (RAV) schemes are considered, having only in 3 or 2
switches.
Transformerless step up alternating voltage regulators
The simplified transistor transformerless alternating voltage regulator is considered, Fig. 1,
capable to support the stable output voltage with possibility of its regulation for the purposes of
reactive power of a network compensation or the purposes of the operated asynchronous electric
drive. The switches of alternating current at this regulator are located in the branches with the
ballast reactor L1. Figure 2 shows modeling results obtained by the PSIM program for a
simplified RAV. The input voltage with current, supplied impulses to the switch of alternating
current of capacitor branch and the output voltage with current are shown.
Fig. 1. A simplified three-phase transistor alternating voltage regulator with commutatable
reactor.
Fig. 2. Modeling results for a simplified RAV with commutatable reactor (the input voltage with
current, supplied impulses to the switch of alternating current of capacitor branch and the output
voltage with current).
The another version of a simplified regulator with halving a number of switches, as compared
with a basic regulator, is shown on Fig. 3. In this scheme the switches of alternating current are
located in branches with ballast capacitor C1. The same diagrams of its a currents and voltages
are shown in Fig. 4. Resistor R1 required for dampening of L1C1 loop.
Fig. 3. A simplified three-phase transistor alternating voltage regulator with commutatable
capacitor.
Fig. 4. Modeling results for a simplified RAV with commutatable capacitor.
Further decreasing a number of switches in the regulator can be obtain, if possess the ability to
access to both leads of power source phases, that can occur in an autonomous power-supply
system. The scheme of a simple regulator for this case is shown in Fig. 5 and the diagrams of the
same its currents and voltages are shown in Fig. 6.
By closing the transistor T1 serially with a power source and a load, capacitors C1 appear
switched through diodes of three-phase bridge M1, while by closing the transistor T2 serially with
a power source and a load, reactors L1 appear switched through diodes of three-phase bridge M2.
Fig. 5. A simple three-phase transistor alternating voltage regulator with divided source phases.
Fig. 6. The diagrams of a currents and voltages of a simple regulator with divided source phases.
The another version of the simple scheme of transformerless regulator is shown in Fig. 7. This
simple regulator differs from previous in that it has access to 6 leads of a load. In this scheme
only 2 switches of alternating current as compared with 6 in the basic scheme. The diagrams of a
currents and voltages of regulator are shown in Fig. 8. The patent application on the current type
of regulator is filled.
Fig. 7. A simple three-phase transistor alternating voltage regulator with divided load phases.
Fig. 8. The diagrams of a currents and voltages of a simple regulator with divided load phases.
From the data obtained in modeling by PSIM the quality of an output voltage and an input
current was estimated, which presented as a dependences its harmonics factor of voltage from
modulation depth, Fig. 9, and harmonics factor of current from modulation depth, Fig. 10.
Fig. 9. Harmonics factor of output voltage.
Fig. 10. Harmonics factor of input current.
The quality of an output voltage and input current remains high in the operational range at the
same time it worse with increasing of load current.
Analytical calculation and results
For the construction of regulator mathematical model on a smooth component (first harmonic)
use the direct method of calculation (ADE2) [5]. The equivalent circuit of one phase of regulator
is shown in Fig. 11.
Fig. 11. The equivalent circuit of one phase of transformless step up alternating voltage regulator
The differential equations of the circuit for both its states have the form:
di2
 R2i2  uc1  (1   )uc 2  e1 (1)
dt
di
(2)
L1 L1  R1iL1  uc1  uc 2  0
dt
du
(3)
C1 c1  i2  iL1  0
dt
du
(4)
C2 c 2  (1   )i2  iL1  0
dt
Here ψ – the switching function, equal to one when the switch S2 is tuned on and equal to zero
when the switch S1 is an enabled state.
The switching function spectrum looks like:
L2

 1
sin  2 nM 1   cos  2 nft  
n 1   n
1


cos  2 nM 1   1  sin  2 nft   (5)

n

  M1   
Where f – a switching frequency of switches, M1=M–1, M – the modulation depth. When n=1
the calculation is made by first harmonic. Thus:
 (1)  M1 

1

1

sin  2 M 1   cos  2 ft  
 cos  2 M   1  sin  2 ft  (6)
1
As a result of this system of equations algebraization by the ADE2 approach obtain the following
system of equations for a sine and cosine components of first harmonics of a variables:
 R2 I 2(1) а   L2 I 2(1) р  U C1(1) а  1   (1) U C 2(1) а  E1(1) а

 R1I L1(1) а   L1I L1(1) р  U C1(1) а  U C 2(1) а  0

 I 2(1) а  I L1(1) а  С1U C1(1) р  0

1   (1)  I 2(1) а  I L1(1) а  С2U C 2(1) р  0

 R2 I 2(1) р   L2 I 2(1) а  U C1(1) р  1   (1) U C 2(1) р  0

 R1I L1(1) р   L1I L1(1) а  U C1(1) р  U C 2(1) р  0
 I
 I L1(1) р  С1U C1(1) а  0
 2(1) р
 1    I
(1)
2(1) р  I L1(1) р  С2U C 2(1) а  0

(7)
The matrix form of a system of equations of a regulator mathematical model:
R2
0
1  (1)  1  L2
0
0
0
0
R1
1
1
0
 L1 0
0
1
1
0
0
0
0 C1
0
1   (1) 1
0
0
0
0
0
C2
 L2
0
0
0
 R2
0
1 1   (1)
0
 L1 0
0
0
 R1 1
1
0
0 C1
0
1
1
0
0
0
0
0
C2  (1)  1 1
0
0
I 2(1) а
E1(1) а
I L1(1) а
0
U C1(1) а
0
U C 2(1) а
0


I 2(1) р
0
I L1(1) р
0
U C1(1) р
0
U C 2(1) р
0
By the solutions of these equations in the Mathcad environment using the following technique:
1) The matrix form looks like:
AX T  E T
(8)
Where ET   E1(1) а ,0,0,0,0,0,0,0  column matrix of the right side of equation (7).
T
2) The solution of this equation in matrix form looks like:
(9)
X T  A1ET
3) In the scalar form for each component of 8 unknown first harmonics of a decision variables
of the vector X the solution takes the form^
8
Xi 
i


 e Ad
j 1
j
ij
(10)

Where Adij – adjunct of an ij-element of the coefficient matrix A determinant Δ.
4) From the solution (10) formulas for first harmonics of the load current I2(1)a and I2(1)p
quadrature components are obtained. After that load current resulting first harmonic is found:
I 2(1) 
I   I
2
2(1) а
2(1) р

2
(11)
5) Voltage first harmonic on the load U2(1) is determined by the (11):
U 2(1)  I 2(1)
 R2   L2 
2
2
(12)
6) The adjusting characteristic U 2(1)  f1  M  is determined by the equation (12), Fig. 12, and
the external (load) characteristic of a regulator U 2(1)  f 2  I 2(1)  , Fig. 13.
7) Also dependence of the input current shear coefficient by first harmonic relatively of an
input voltage is possibly to calculate:
I
(13)
1(1)  arctg 2(1) р
I 2(1) а
The family of adjusting characteristics, external characteristics of a basic regulator and a
dependence its input power factor from modulation depth, Fig. 14, is plotted, which presented
simultaneously with the corresponding characteristics obtained in the model of the PSIM
program.
Fig. 12. The family of adjusting characteristics.
As seen from the characteristics, the operational range of an increasing voltage is located in the
range M=[0;0,5], with the output voltage maximal value more to 1,4 times at the sufficiently
high quality.
Fig. 13. The family of external characteristics.
E1
. The raised voltage is reached in the range of modulation depth M=[0;0,5],
L1 C1
at the higher levels of modulation depth the stabilized reduced voltage can be obtained, as shown
in Fig. 13.
Where I b 
Fig. 14. Input power factor.
M
Il(1)(A)
Ul(1)(V)
χ
theory (practice)
A comparison of first harmonics effective values of load current and voltage and power factor,
obtained experimentally in the Mathcad environment and analytically using the Mathcad
program is presented in Tab. I.
TABLE I
A COMPARISON OF FIRST HARMONICS EFFECTIVE VALUES OF LOAD CURRENT
AND VOLTAGE AND POWER FACTOR
E1
Il Ib  0,12 , I b 
L1 C1
1
0,75
12,1 12,8
(12,1) (12,1)
193,7 212,6
(193,7) (202,2)
0,74 0,812
(0,739) (0,773)
0,625
12,8
(12,4)
213,6
(206,2)
0,816
(0,788)
0,25
0
11,7 13,6
(12,2) (12,2)
208,5 251,5
(218) (224,9)
0,797 0,859
(0,833) (0,859)
Conclusion
1. The transformerless alternating voltage regulators with a practically sinusoidal input and
output currents are offered with the capability to increase per unit the voltage conversion
coefficient. In the case when the load or independent three-phase source are executed with
divided phases then a regulator contains only two regulated switches and two diode bridges.
2. The stabilization of output voltage in the offered transformerless regulators is realized with
the sufficiently high quality of voltage form, at the same ability of its increasing remains.
3. The expansion of the calculation direct method of a converters energy indicators on their
model with variable parameters leading to differential equations with the periodical
discontinuous coefficients is constructed. The accounting of first terms in the expansion of
variable coefficients in a Fourier series allowed to obtain an analytical solutions in a closed form
for all state variables and output variables first harmonics and for all regulator general
characteristics: external, adjusting and energy. As seen from Tab. I and the family of adjusting
characteristics, Fig. 12, an error of obtained mathematical model, generally, in the range of 10%,
a differences are minimal at the edges of ranges and high value of load current, at low currents
the difference of currents and voltages values theoretically obtained does not exceed 5% of
difference compared to data obtained by modeling in the PSIM environment.
References
[1] Divan D., Sastry J., Prasai A., Johal H. Thin AC Converters –A New Approach for
Making Existing Grid Assets Smart and Controllable. Proc. PESC 2008, CD, pp. 16951701.
[2] Zinoviev G.S., Obuhov A.E. Step-up pulse-width regulators of alternating voltage.
Nauchni vestnik NGTU, 1997. №3. P. 111-120. (in Russian)
[3] Zinoviev G.S., Udovichenko A.V. Regulator of alternating voltage. Patent application RF
№ 2011146812, 2011. 8p. (in Russian)
[4] Zinoviev G.S., Udovichenko A.V. Transformless step-up regulators of alternating voltage
with sinusoidal currents for soft-starting devices for asynchronous motors //
Electroprivodi peremennogo toka – EPPT-2012, March 12-16. – P. 55-58.
[5] Zinoviev G.S. Fundamentals of power electronics, Novosibirsk, NGTU, 4izd. 2009.
672p. (in Russian)
Gennady S. Zinoviev – student, postgraduate student, senior lecturer, doctoral candidate of the
Novosibirsk Electrotechnical Institute, professor of the Industrial Electronics Department of the
Novosibirsk State Technical University (NSTU), research supervisor of the Research Laboratory
“Optimization of Energy in Converting Systems”. Author of the textbook on power electronics,
two monographies devoted to electromagnetic compatibility of gated converters, 90 patents and
over 200 publications.
Udovichenko A.V. born in Novosibirsk in 1987 year. Second year postgraduate student of
Novosibirsk State Technical University.