ISSN 10683712, Russian Electrical Engineering, 2015, Vol. 86, No. 8, pp. 453–458. © Allerton Press, Inc., 2015. Original Russian Text © A.V. Pavlenko, I.V. Vasyukov, V.S. Puzin, V.P. Grinchenkov, A.V. Bol’shenko, 2015, published in Elektrotekhnika, 2015, No. 8, pp. 21–27.
Designing of the Output Stage of the Impulse Power Source A. V. Pavlenko, I. V. Vasyukov, V. S. Puzin, V. P. Grinchenkov, and A. V. Bol’shenko Platov SouthRussian State Polytechnic University (NPI), Novocherkassk, Russia email: journal
[email protected] Received July 22, 2015; in final form, August 5, 2015
Abstract—Issues in designing of the output stage of an impulse power source are considered based on a bridge with hard switching. The calculation formulas for the amplitude values of the throttle current and impulses of the voltage at the filter input in the mode of discontinuous and continuous currents taking into account the influence of leakage inductance of the transformer and voltage drop at the rectifier diodes are given. Two sub modes are defined in the mode of the throttle continuous currents—with a pause in the current of the sec ondary winding and without a pause. The peculiarity of the second submode is the independence of the out put voltage of the power source on the PWM fill factor. While deriving the calculated dependences, the mag netizing inductance of the transformer was not considered, leakage inductance was supplied to the secondary winding, and the active resistances of the elements of the equivalent circuit were assumed equal to zero. Based on the proposed formulas, the algorithm of calculation of the output filter of the power source of bridge topol ogy was modified. Experimental research on the breadboard model of the power source proved the effective ness of the suggested design algorithm. The errors of calculation of the amplitude values of currents and volt ages are significantly reduced as compared to the traditional method. As a result of the research that was car ried out, it was stated that the power source designed not taking into account the leakage inductance of the impulse transformer cannot provide the required parameters. Keywords: full bridge with hard switching, leakage inductance, impulse power source, output filter DOI: 10.3103/S1068371215080106
At present, most highpower supply sources repre sented in the market are constructed on the basis of bridge topology with phase control or different reso nance topologies providing “soft” switching of the power tongs. Such a mode provides low dynamic losses and more insignificant problems with electro magnetic compatibility. The developers of these sources have to put up with the complexity of provision of the mode of “soft” switching within the whole range of loads, presence of additional reactive components, and high requirements to the parameters of power tongs for the resonance circuits. In addition. there are areas of application in which the classical PWM with “hard” switching provides a low level of losses as com pared to the “soft” switching mode. Such areas of application are characterized by a positive interval of the operation time of the source upon a small load and periodic consumption of total output capacity by the load. For example, a highvoltage source of anode voltage of the output stage of the radio transmitter main amplifier, charging units of electric batteries which, after charging with heavy current. are sup ported in the charged condition by low current in the buffer mode and technological sources for different welding devices. An analytical review of scientific and technical lit erature showed that there are many calculation meth
ods of designing of the impulse power sources based on different assumptions. The most detailed calculation methods are given in [1–4], but there is no comparison of the design characteristics of the sources with exper imental ones. In [5], the authors made an attempt to create a generalized method of designing of the bridge converter with hard switching, but leakage inductance of the transformer and voltage drop at the output diodes were not taken into account. Experimental research on some samples of the power sources designed according to the aforementioned methods showed significant differences in the experimental and calculated characteristics of the sources. To find the influence of the parameters of the transformer and out put rectifying diodes on the output characteristics of the converter, its operation was modeled in the program LTspice for one of the source variants. The calculation equivalent circuit of the source is given in Fig. 1. The model was a bridge inverter on ideal switches SW with bypass diodes with the specified voltage drop in the straight direction. For the real transformer, a Tshaped equivalent circuit was used in the model, including leakage inductances of the primary and sec ondary windings and magnetizing inductance. The parameters of the transformer equivalent circuit were defined based on the measured values of inductances according to the methods [6].
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VD1 S1
VD5
VD3 S3
VD7
UVD5
Uin
a
Ls2
Ls1
UVD7 Uout C
T1 b VD8
VD6 S2
S4 VD2
UVD6
VD4
UVD8
Fig. 1. Equivalent circuit.
Three variants of the model were used for the trans former during simulation: (1) a model with the full Tshaped equivalent circuit; (2) a model not taking into account magnetizing inductance; and (3) a model with the ideal transformer not taking into account leakage and magnetizing inductances. The results of the experiment and simulation are given in the table. It is clear from the presented data that neglecting of leakage inductance leads to an intolerably significant error. The model in which magnetizing inductance is neglected introduces a considerable smaller error, but permits simplifying significantly the calculation method. This assumption is used in further derivations of the calculation formulas. The basic formulas on which the calculation algo rithm is based are the dependences of amplitude of the throttle current imax on amplitude voltage on the sec ondary winding U2, output current Iout, and output
voltage Uout. For the mode of the throttle discontinu ous current, 2T f I out ( U out + U VD ) ( U 2 – U VD – U out ) , U 2 L + U out L leakage + U VD L leakage
(1)
T f ( U out + U VD ) ( U 2 – U VD – U out ) i max = + I out , U 2 L leakage + U VD L leakage + U 2 L
(2)
i max =
where UVD is the drop on the diodes of the output rec tifier (sum of drops on two diodes for the bridge recti fier), L is the inductance of the throttle, Lleakage is the leakage inductance of the transformer supplied to the secondary winding, and Tf is the impulse repetition period at the input of the output LCfilter. To determine the required amplitude value of the voltage on secondary winding of the transformer U2, it is necessary to consider the processes in the filter in more detail.
Table Model Parameter
1
2
20.98
21.258
21.347
Throttle current amplitude ILmax, A
2.20
2.210
2.274
Throttle rootmeansquare current ILrms, A
1.33
1.326
1.341
Output voltage Uout, V
Error, %
Experiment 3
1
2
3
+1.32
+1.75
+20.29
2.560
+0.45
+3.36
+16.36
1.564
–0.28
+0.83
+17.62
25.24
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Fig. 3. Dependence of (a) t L
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t Fig. 2. Mode of continuous currents of the throttle: (a) without a pause, (b) with a pause; (1 and 2) PWM impulses of the control microchip, (3) secondary winding current, and (4) throttle current.
Depending on the initial data, the mode of contin uous currents of the throttle can be divided into two cases—without a pause of the current in the secondary winding of the transformer and with a pause. In the operation mode without a pause (Fig. 2a), after the end of the impulse, all diodes of the output rectifier open and the current in the throttle begins decreasing at the velocity defined by the output volt age. The voltage between the points of winding con nection (Figs. 1a and 1b) to the rectifying bridge comes to zero as the drops of voltages on the diodes VD2, VD4 and VD1, VD3 are mutually compensated. Thus, the energy stored in leakage inductance at actu ally shortcircuited points a and b returns to the power source through the transformer. The duration of the current drop in leakage inductance is calculated according to the formula L leakage I max t openLleakage = . U2 After the beginning of the PWM impulse, the cur rent in the circuit of leakage inductance increases from zero to the value of the throttle current decreasing at this moment. After all values of these current become equal, the energy begins again coming to the load and current in the throttle begins growing. At this stage, the duration of growth of the cur rents of leakage inductance is defined according to the formula L leakage I 0 t openLleakage = , U2 where I0 is minimum throttle current. RUSSIAN ELECTRICAL ENGINEERING
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, (b) ton_pwm,
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Therefore, in the aforementioned mode, after the end of the PWM impulse, within time t openLleakage , the PWM impulse of another polarity or absence does not influence the current in the throttle; i.e., during a change of the fill factor in a certain range, the output voltage does not change. Thus, in the mode of contin uous currents of the throttle, the fill factor of the PWM modulator will always be higher than the fill factor of the throttle current at t openLleakage in both the mode with a pause of the secondary winding current and that without a pause. The total time required for the value of the current in leakage inductance changes from Imax to I0 comes to 2L leakage I out t Lleakage.pause ( U 2 ) = . U2
(3)
The time of throttle current drop can be defined according to the formula LT f ( U 2 – U out – U VD ) t Lpause ( U 2 ) = . U 2 L + U out L leakage + U VD L leakage
(4)
If dependences (3), (4) are constructed in one dia gram, then crossing of these curves shall be obtained in point 1, as is shown in Fig. 3. Therefore, when there are voltages on the secondary winding lower than the point of intersection, the power source cannot provide the required parameters upon the specified values Uout, Iout, UVD, Lleakage, L, and Tf as the throttle current drop time shall be less than the time of changing of the cur rent in leakage inductance, which is impossible. However, having constructed in the same diagram (Fig. 3), the dependences of the calculated time of the PWM impulse and level of the maximum possible duration of the impulse for the PWMcontroller, it is possible to find the second limitation—by the maxi mum filling—in point 2. The PWM impulse time is defined as the sum of time of the current rise of the
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throttle and time of the current rise in leakage induc tance from zero to the value i0: t impulse.PWM ( U 2 ) L leakage I out LT f ( U 2 – U out – U VD ) = T f – + (5) U2 U 2 L + U out L leakage + U VD L leakage
and t Lpause (U2). After transformation of this equality, the following quadratic equation is obtained: (6)
with the coefficients a = LTf; b = –L(Tf(Uout + UVD) + 2Lleakageiout), 2
c = – 2L leakage i out ( U out + U VD ). The positive root of quadratic equation (6) defines required voltage U2 for the mode of continuous cur rents of the throttle without any pauses in the second ary winding current. To define required voltage U2 for point 2, the for mula was obtained for fill factor γf of the impulses at the filter input: γf ( U2 ) L ( U 2 – U out – U VD ) L leakage i out = 1 – + (7) U2 Tf U 2 L + U out L leakage + U VD L leakage L leakage ( U out + U VD ) ( U 2 – U out – U VD ) – . U 2 2 ( U 2 L + U out L leakage + U VD L leakage ) Having transformed dependence (7) and substi tuted the maximum fill factor into it, the following quadratic equation is obtained: 2
aU 2_ccm + bU 2_ccm + c = 0,
+ T f L leakage ( U out + U VD ) – 2T f L ( U out + U VD ), 2
c = – ( 2L leakage I out ( U out + U VD ) 2
If point 2 in the diagram is located to the right of point 1, then the required voltage on the secondary winding is defined by the maximum fill factor and out put stage will operate in the mode of continuous cur rents of the throttle with a pause in the secondary winding current. If point 2 is to the left of point 1, then the output stage will operate in the mode of continuous currents of the throttle without a pause in the secondary wind ing current. Therefore, two different expressions are necessary to define the voltage amplitude on the secondary winding for points 1 and 2. Required voltage U2 to provide operation in point 1 can be obtained from the equality of time t Lleakage.pause (U2)
2
b = ( γ fmax – 1 )2T f L leakage ( U out + U VD ) – 2L leakage I out L
+ T f L leakage ( U out + U VD ) ).
L leakage T f ( U out + U VD ) ( U 2 – U out – U VD ) – . U 2 2 ( U 2 L + U out L leakage + U VD L leakage )
aU 2_ccm + bU 2_ccm + c = 0 ,
where a = 2TfLγfmax;
(8)
Having defined the positive root from solution (8), required voltage U2 is obtained for the mode of contin uous currents of the throttle with a pause in the sec ondary winding current. Carrying out similar calculations for the mode of discontinuous currents of the throttle, the formula of definition of required voltage U2 is obtained: ( U out + U VD ) ( L + L leakage ) U 2 = U out + U VD – 2L 8LT f I out (9) 2 2 ( U out + U VD ) ( L + L leakage ) γ fmax T f + U out + U VD + . γ fmax T f 2L Taking into account the obtained expressions, the algorithm of calculation of the output stage of the source can be represented in the following form: (1) The initial data for calculation is Uout—output voltage; Iout—output current; kpulsation—pulsation coefficient; fpwm—conversion frequency; γpvmmax—PWM maximum filling. (2) Frequency ff and fill factors of the impulses are calculated at the input of the output filter γfmax as the double values of the relevant PWM parameters, and period Tf is calculated as a halved PWM period. (3) The minimum product of LCmin is calculated based on the condition of the permissible pulsation coefficient [3]. (4) Values L and C are selected meeting the condi tion: LC ≥ LCmin. Resonance frequency of the filter Fres is calculated, and the condition fres ≠ ff is checked. (5) Voltage U2_ccm is defined according to the condi tion of time of leakage inductance reversal for the mode of continuous currents of the throttle from the solution of Eq. (6). (6) The fill factor is calculated for this value U2_ccm according to formula (7). (7) If the obtained fill factor is less than the speci fied maximum (γf < γfmax), the found value U2_ccm is assumed as a final result for the continuous current mode of the throttle. (8) If γf > γfmax, the value U2_ccm for the continuous current mode should be calculated for the condition of the maximum fill factor solving solution (8).
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(9) The required value U2_ccm for the discontinuous current mode of the throttle is found according to for mula (9). (10) The throttle operation mode is defined. For this purpose, the following condition is checked:
40 0 –40 –80
If it holds, the throttle operates in the discontinu ous current mode and U2 = U2_dcm; otherwise, the con tinuous current mode takes place and U2 = U2_ccm. (11) The amplitude value of the throttle current is calculated. If the throttle operates in the discontinu ous current mode, it is calculated according to formula (1); if in the continuous current mode, according to formula (2). To confirm the validity of the developed algorithm, experimental research on the breadboard model was carried out. The breadboard model is a station inverter on field transistors control of which was carried out from square wave generators through optically isolated drivers. The frequency of the control impulses was assumed equal to 40 kHz with a strictly fixed fill factor of 0.44. A constant voltage 16 V of was supplied to the bridge input. A stepup transformer with transforma tion coefficient 2 was connected to the bridge inverter made on the magnetic circuit Sh20*16 M2000NM. The number of turns of the primary winding is 6, while there are 12 on the secondary winding. The experi mentally defined parameters of the transformer are as follows: primary winding inductance 200 uH, primary winding inductance upon the closed secondary wind ing 5.4 uH, secondary winding inductance 833.2 uH, and primary winding inductance upon the closed pri mary winding 21.4 uH. The throttle of the output filter had an inductance of 16.79 uH. The voltage drop at the output rectifier diode was 1.4 V. The following parameters were measured upon the maximum fill fac tor depending on the load current: voltage amplitude on the primary winding, output voltage, current amplitude of the throttle, and actual current value of the throttle. Precisely these parameters were calcu lated using the proposed method for the specified ini tial data: output current, output voltage, transforma tion coefficient, inductance of the throttle of the out put filter, capacity of the condenser of the output filter, drop at the output rectifier diodes, and leakage induc tance of the transformer brought to the secondary winding. The measurements were made using the following devices: —output voltage by an APPA71 multimeter instru ment; —load resistance by an E722 RLCmeter; —output current by a MASTECH MY61 multi meter instrument; and Vol. 86
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δ, % 80
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Fig. 4. Calculation errors: (a) voltages on the primary winding, (b) current amplitudes of the throttle, and (c) rootmeansquare current of the throttle. 䊉—calcula tion not taking into account, 䊏—calculation taking into account leakage inductance.
—amplitude and actual current value of the throt tle by a DS01014A oscillograph at a resistor with a resistance of 0.095 Ω. In Fig. 4, the values of the relative error of defini tion of the voltage on the primary winding, amplitude, and actual current value of the throttle are presented that were obtained during the experiment and as a result of calculation according to the method given in this article. For comparison, analogous values are shown in this figure calculated according to the method of [5]. The negative error values correspond to the underrated results of calculation as compared to the experiment. CONCLUSIONS (1) As a result of the research that was carried out, the algorithm of designing of the output stage of the impulse power source was improved, permitting taking into account the influence of the transformer leakage inductance and voltage drop at the output diodes.
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(2) The effectiveness of the developed method has been experimentally proven. The calculation error for the voltage amplitude on the primary winding was 1⎯4%, for the throttle current amplitude –3…+54%, and for the actual current value of the throttle ⎯12…+13%. The high error in determining the low value of the throttle current amplitude is connected with the faults of the measuring instruments. For com parison, the error during determination of the voltage amplitude on the primary winding of the transformer calculated according to the method of [5] is 43%. (3) The obtained results show that the power source designed not taking into account leakage inductance of the power transformer and drop at the output diodes will not provide the required parameters. ACKNOWLEDGMENTS The work was supported by project no. 2829 carried out in the framework of the basic part of state assign ment no. 2014/143 and a President of the Russian fed eration scholarship for young scientists and graduate students carrying on promising scientific research and development in a highpriority direction of modern ization of the Russian economy no. SP6459.2013.1.
REFERENCES 1. Naivel’t, G.S., Mazel’, K.B., and Khusainov, Ch.I., Istochniki elektropitaniya radioelektronnoi apparatury: Spravochnik (Power Sources for Radioelectronic Devices. Handbook), Moscow: Radio i svyaz’, 1985. 2. Erickson, R.W. and Maksimovic, D., Fundamentals of Power Electronics, Univ. of Colorado Boulder, 2004. 3. Meleshin, V.I., Tranzistornaya preobrazovatel’naya tekhnika (Transistor Transducing Equipment), Mos cow: Tekhnosfera, 2005. 4. Eranosyan, S.A., Setevye bloki pitaniya s vysokochastot nymi preobrazovatelyami (Network Power Sources with High Frequency Transducers), Leningrad: Energoat omizdat, 1991. 5. Pavlenko, A.V., Vasyukov, I.V., and Puzin, V.S., The way to design outlet filter for high voltage pulse power source, Izv. Vyssh. Uchebn. Zaved., Elektromekh., 2014, no. 1, pp. 59–62. 6. Berdnikov, D., The way to measure scuttering induc tion in transformers of pulse converters by means of RLCmeter, Sovr. Electron., 2006, no. 8.
Translated by Yu. Bezlepkina
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