Controllable resonant type converter development for capacitorcharging loads

Abstract

The paper investigates various controlling options for the selected resonant converter topology, which is optimized for capacitor charging systems. Several of the controlling algorithms were studied in depth, and one of them was practically verified. There are two major advantages about the system: full/partial soft-switching mode what allows to use higher switching without the system efficiency drop; controllable energy flow from the input to the output, without any additional sophisticated parts.

Full text

ISSN 1607-7970. Техн. електродинаміка. 2017. № 6 11
ПЕРЕТВОРЕННЯ ПАРАМЕТРІВ ЕЛЕКТРИЧНОЇ ЕНЕРГІЇ
CONTROLLABLE RESONANT TYPE CONVERTER DEVELOPMENT
FOR CAPACITOR CHARGING LOADS
I.V. Volkov*, S.V. Podolnyi
Institute of Electrodynamics National Academy of Sciences of Ukraine,
pr. Peremohy, 56, Kyiv, 03057, Ukraine. E-mail: dgp@ukr.net
The paper investigates various controlling options for the selected resonant converter topology, which is optimized for
capacitor charging systems. Several of the controlling algorithms were studied in depth, and one of them was
practically verified. There are two major advantages about the system: full/partial soft-switching mode what allows to
use higher switching without the system efficiency drop; controllable energy flow from the input to the output, without
any additional sophisticated parts. References 6, figures 9.
Key words: resonant converter, capacitor charging systems, soft-switching.
Introduction. Capacitor charging systems are widely used for various industrial, special, domestic,
science experiments electrical and power electronic applications, like pulse welding, laser technic, magneto-
impulse processing of metals, volume electro-erosion processing, etc. [3]. The major operational condition
for such system types is an economic charge of the storage capacitor according to some specific time-domain
law, and optimal interrelations between processes in the charging circuit and the power source (especially if
it’s autonomous one) [2, 3].
There are three main methods known for the storage capacitor charging: from constant voltage type
source, from constant current type source and from constant power type source [4, 6]. The first one has low
efficiency – below 50% due to the restricting input current requirement with a resistor. In the case of using a
current limiting inductor, its energy capacity (sizes and price accordingly) is relatively big, and contributes to
more than quarter to the device energy capacity [3].
The main drawback of the second type – the maximum power of the power source two times exceeds
the average power per cycle, required for the capacitor full charging. The constant power case has the
disadvantage of increased dynamical energy losses in its semiconductor devices, which create such a mode at
the first place.
There are numerous schematic methods exist for overcoming those disadvantages in each particular
case, and in this article we use quasi-separated schematic of two separate resonant tanks (Fig. 1) to facilitate
hard-switching energy losses and EMI-effects of conventional power converter equipment and improve
switching conditions for the semiconductors switches. For these purposes we utilize in the converter a
transitional “small” capacitor C0, that during the charging cycle of the “big” output capacitor Cout >> C0
repeatedly transfers small portions of energy (“quants”) until the system is fully charged.
In this article, we propose and compare possible algorithms for the converter switches, which would
provide optimal energy transfer with minimal dynamical losses in the transistors switches.
All the switches here are one directional. Several theoretical algorithms can be used for obtaining
different types of the converter behaviours. For this particular reason the Fig. 1 schematic includes K21 as a
controllable element, though in some cases this one can be substituted with a diode. We don’t consider static
losses at the beginning (Fig. 1 doesn’t contain resistive elements in order to simplify functional possibilities
of the device analytically).
The first resonant tank. This circuit
works during the switch K1 conductive state,
and closed K2 respectively. It has three
elements {Uin, L0, C0} with two possible
initial states on the C0. The transient
processes are described by well known
equations [1]
© Volkov I.V., Podolnyi S.V., 2017
ORCID ID:*http://orcid.org/0000-0002-0696-0382
Fig
. 1

12 ISSN 1607-7970. Техн. електродинаміка. 2017. № 6
   
t
L
U
tii
C
dt
id
Lin


sin0
1
00
2
2
0 , (1)
where 00 CLZ  is the wave impedance; 00
1CL

is the circular frequency.
The voltage C0
       


   
 
.cos1|cossin
11
0
000
tUtutUdtt
L
U
C
dtti
C
tu in
t
in
in


  (2)
In the case of considering the transient half-cycle, i.e. t= /

, UC0 =2 Uin.
The doubled voltage require two additional conditions: the active resistance is negligible; zero initial
condition U(C0) = 0.
Let’s consider the case


00
~
C
UCU , then (1) transforms to the following
   
t
Z
UU
ti Cin

sin
0

, (3)
and the voltage C0
   


 
 
tUUUdtti
C
Utu CinCC

cos1
~~
1
~
00
0
0 . (4)
As can be seen from (4), at the moment t = /



0000
~
2
~
2
~
CinCinCC UUUUUU  . (5)
That means the initial condition can both increase or decrease the transferring energy of the
converter per working cycle.
The second resonant tank. The circuit include three basic elements with its initial conditions. Fig. 2
bellow shows the above mentioned in Laplace domain. The operational circuit components are: the “large”
output capacitor Cout>>C0, the dosing “small” capacitor C0 with initial condition
V0=UC0 and Vout – variable part of the output capacitor voltage аt nth step of
charging. Normally, Lout initial current ILout(0)=0. The operational current I(p)
 


 
outout
out
outout
out
LpCC
VV
pLpCpC
pVpV
pM
pN
pI 2
0
0
0
0
11
11 




 . (6)
Inverse Laplace-transformation for I(p) according to the decomposition
theorem
 


 
,
22
00
2
1
tj
out
out
tj
out
out
kk
ke
Lj
VV
e
Lj
VV
p
dp
dM
pN
ti







 
where pk is the roots of the M(p) polynomial. Since


tjee tjtj


sin2
,
     
t
Z
VV
t
L
VV
ti out
out
out


sinsin 00



. (7)
Cout voltage
     


  tout
out
out
out
outout dtt
Z
VV
C
Vdtti
C
Vtu
0
0sin
11

    
t
ZC
VV
Vtu
out
out
outout


cos1
0

 . (8)
Note   CCCLCLCC outoutoutoutout 1

,


outout CCCCC 
00 , hence
      
tVV
C
C
Vtu out
out
outout

cos1
0 .
Let outC CC /



, then








tVVVtu outCoutout

cos1
0 . (9)
Since 1
0



C
CC

.
Fig. 2

ISSN 1607-7970. Техн. електродинаміка. 2017. № 6 13
Similarly capacitor C0 voltage
    
t
C
VV
CVdti
C
Vtu out
C

cos1
1
0
0
0
0
00 

 
.
Let 0
/CC
C


, then








tVVVtu outcC

cos1
000  . (10)
Due to 1
0



C
CC

.
At the moment



t
, or the full half-cycle, the residual voltage of the dosing capacitor


outcres VVVu  00 2

. (11)
The dosing capacitor is fully discharged 0

res
u only in one case
outut C
C
VV
V

2
00
0, (12)
or if 0
CCout

, then 0
5.0 VVout

.
For all other cases, it will have positive or negative residual voltage.
Generally speaking, in some real cases we could encounter not zero initial condition for the inductor
current


0
00 II Lout


.
By rewriting (6) implying this additional condition
 
outout
outout
outout
outout
LpCC
IpLVV
pLpCpC
ILpVpV
pI 2
0
00
0
00
11
11 






. (13)
The inverse Laplace-transformation for the I(p)
 


 













tIee
I
L
VV
jti m
tjtj
out
out sin
22
00 , (14)
where
 
Z
U
Z
VVZI
Z
VV
II m
out
out
m
~
~2
0
22
0
2
0
2
0








 ,
 
















 2
0
22
0
0
0
0arcsin
22 out
out
VVZI
IZ
IZ
VV
arctg


.
Respectively Cout voltage
       
 

 tZIVtI
C
Vtu mCL
t
m
out
Lout coscos
~
sin
1
0
. (15)
And C0 voltage
       
 

 tZIVtI
C
Vtu mC
t
m
out
Ccoscos
~
sin
1
0
0
00 . (16)
The equation (9) shows that there are two variables for uout(t): V0 and t which can be controlled
dynamically. Both the tanks can be adjusted to influence these parameters to a certain degree. Consequently,
the full spectra of possible controlling algorithms, for the “large” capacitor charging, are predetermined by
these two variables.
Controlling algorithms. Let’s consider some of them in more details.
1.1: V0, t are not regulated.
In this case, both the input and the output resonant tanks work under pure soft-switching conditions,
so dynamic losses are zero. The residual voltage ures of the dosing capacitor rapidly increases on each
charging cycle, and the magnitude of the input current respectively, until the following condition Vout = Uin
takes place. After that knee point Vout > Uin, and the input current Iin decreases by the same rate, i.e. it’s
symmetrical respectively to the knee.
Theoretical charging limit for the case approaches doubled input voltage, or inout UV


2.
The case has a significant drawback, namely very high growing rate of the input current, which for
the practical schemes should almost always be limited to an upper maximum value.

14 ISSN 1607-7970. Техн. електродинаміка. 2017. № 6
Let’s consider the example Uin = 310 V, Z = 50 Ohm, C = 5e-3. Then the charging dynamic is
illustrated bellow (Fig. 3). The voltage Uout here is shown on a
scale 10:1.
The output voltage grows until the residual voltage on
the dosing capacitor 0

res
u (Fig. 3, a). If 0

res
uthen the
output does not get any new energy portion due to the circuit
conducts only in one direction, otherwise it would discharge
backwardly, CLC UU

0(Fig. 3, b).
1.2: V0 is regulated in the first link.
It can be shown that that the input link equations for its
current and the dosing capacitor voltage, under all non-zero
initial conditions, are similar to (14), (15)


     
 





,coscos
,sin)(
00


tZIVtu
tIti
mC
m (17)
 
Z
VVZI
Iout
m
2
0
22
0
 , 






0
0
2IZ
VV
arctg out


.
According to (17) V0 can be regulated with the getting
away from the full soft-switching concept and introducing
beforehand commutation of the input switch timing ton or the
input angle

on, i.e. ton < /

. Here we make a deal with the
trade-off of somewhat decreased scheme overall efficiency for
the ability to limit the input current.
Taking into account the aforesaid condition for ton/

on, let’s rewrite (17) as follow
 
   
 


 























ZI
VU
II
UtZIV
ItI
m
on
mon
m
m
0max
max
max0
max
cosarccos
arcsin
coscos
sin , (18)
where Umax is the dosing capacitor maximum voltage; Imax is the maximum magnitude of the input current for
all charging cycles.
The second equation of (18) adds limitation to the maximum residual voltage
 
1cos
max
max 

ZI
uU res

. (19)
Let’s consider the example, where Umax=2Uin, besides there’s a
complyance to all other restrictions. It should be noted, that for this type of
regulation we have to include additional energy return circuit for the
inductor energy not to be wasted while the switch commutation occurs,
otherwise the input circuit will have low efficiency with high EMC-noise
radiation.
By assuming the foresaid true, our system is simplified and before
each new cycle I0 = 0, hence
 
Z
VU
Z
VVZI
Iin
out
m
0
2
0
22
0


 . (20)
Let’s consider the second controlling algorithm to the same
parameters that we mentioned in the previous case. The corresponding
model output capacitor theoretical limit, under selected Umax=2Uin
condition, approaches Uout  1.2Uin. The output resonant tank works in the
soft-switching mode all the time. Total amount of charging cycles – 45,
what’s notably longer than the previous case (Fig. 4, a). The result is
obvious, since the system pumps less energy per cycle on average.
The upper limit Umax defines the maximum residual voltage of C0,
which in its turn sets the input current magnitude for the next charging
a
b
Fig. 4
a
b
Fig. 3

ISSN 1607-7970. Техн. електродинаміка. 2017. № 6 15
cycle. Fig. 4, b illustrates ton /

on behaviour, as was mentioned before if

on  then additional switching
losses exist; they have the decreasing tendency over time. As can be seen after 32 cycles the systems works
in full soft-switching mode, what corresponds to the following condition Uout= Uin.
1.3: I0 is regulated in the first link.
In the previous case we took Umax as the main limitation from (18). Alternatively,


max
sin ItIm




can be selected for the same purpose. Similary to the case 1.2 an additional energy
return circuit for the inductor is needed.
Expression (20) gives us the following limitation on the peak current
 
 
min0
1
inininm UUVU
Z
I . (21)
Expression (21) shows that Im & Umax & ures eventually are the same thing from the selected
limitation point of view, linearly dependant on each other; i.e. we could select any limitation here suitable to
a specific task. The overall process does not change.
2.1: uout limitation in the second tank.
As shown on Fig. 1, by introducing K21 switching element, the output circuit gains the ability to limit
the residual voltage/input current by way of isolating C0 from the superfluous recharging current at an
appropriate moment of time.
The controlling algorithm for the case works in three stages: 1)
C0 charging from the input; 2) C0 discharging with the residual voltage
limiting; 3) waiting until the Lout magnetic energy will be fully
transferred to the output capacitor.
For such a scenario the total charging-discharging cumulative
time TC = t1 + t2 + t3 varies, due to Lout initial condition isn’t constant,
besides the residual magnetic energy transferring isn’t fast process,
0
,, CLoutCoutLout ff

, and at the beginning the situation when t3 > t1 + t2
rather possible. Consequently, the input impulses duty-cycle is not
uniform, changing from some maximum to its minimum – 50%.
Even though the charging process takes 28 cycles (Fig. 5), the
value

27 C
T is bigger than for the previous case with almost 50 cycles.
The output voltage approaches Uout  1.2Uin.
The output switch works in both modes, namely it has hard-
switching closing for the first seventeen cycles, and the full soft-
switching mode afterwards. The peak of residual magnetic energy Ires is
defined by both I0 / Umax / ures value and the system parameters. Fig. 6
shows the same process for the input/output currents dosing in time
domain.
The simplest practical implementation for the case is using a
diode as the K21 switch. An ideal diode will be automatically turned on when the dosing capacitor voltage
reaches zero, therefore the residual
voltage also stay zero and the system
works in full soft-switching mode for the
whole time. Besides the approach
simplifies the controlling system
implementation. If the full charging time
is a critical parameter – this will a
drawback, because of the limitation on
the maximum transferred energy per
cycle.
The diode switching time is
volatile, can be found as follow












0cos1
000 tVVVU LCC


a
b
Fig. 5
Fig. 6

16 ISSN 1607-7970. Техн. електродинаміка. 2017. № 6
 








LC VV
V
t
0
0
1arccos


. (22)
Fig. 7 shows the dynamic for the case of using a diode. After the 50th cycle the dosing capacitor has
residual positive voltage which respectively decrease input current until the final point. The process last
about two times longer in comparing to the controllable K21.
There is a possibility to simplify further the controlling algorithm by making the duty cycle constant,
however for the price – the current at the beginning will have higher magnitude (Fig. 8).
The average pumping energy her is higher, hence the
charging process is a bit faster. Special precautions should be
taken for the diode selection, otherwise its life-cycle could be
tangibly shortened.
This variant was investigated experimentally. On
estimation level, we confirmed dynamical characteristics of the
system, what is shown on the following pictures Fig. 9).
U
C
0
(t)
UCout
Iout
Fig. 9
Conclusion.
The proposed converter schematic with the intermediate dosing capacitor has notable advantages as
compared with the classical approaches, namely – low dynamical energy losses and algorithmic flexibility. If
the charging time isn’t the major parameter than the physical implementation of the converter, e.g. with an
additional diode, does not require complex feed-backs and tracking systems. The system doesn’t tend to
malefaction from external electromagnetic interferences due to its inbuilt properties, which induce
overvoltages and overcurrents. After more detailed analysis of the system energy efficiency behavior, first of
all with considering the reactors quality factor, we’ll cover the system possible practical applications.
a
b
Fig. 7
Fig. 8

ISSN 1607-7970. Техн. електродинаміка. 2017. № 6 17
1. Demirchyan K., Neyman L. Theoretical Foundations of Electrical Engineering. Vol. 2. – SPb.: Piter, 2006. –
576 p. (Rus)
2. Milyakh A.N., Volkov I.V. Stabilized current systems based on inductive-capacitive converters. − Kiev:
Naukova Dumka, 1974. – 216 p. (Rus)
3. Pentegov I.V. Fundamentals of the charging circuits theory for capacitive energy storage devices. − Kiev:
Naukova Dumka, 1982. – 420 p. (Rus)
4. Polishchuk Yu.A. To the study of charging systems of capacitive storage devices from a source of limited
power / Ustroistva preobrazovatelnoi tekhniki, vypusk 1. − Kiev: Naukova Dumka, 1969. − Pp. 10-16. (Rus)
5. Rashid M.H. Power Electronics Handbook. − N.-Y.: Academic Press, 2002. − 895 p.
6. Shcherba A.A., Suprunovska N.I. Electric energy loss at energy exchange between capacitors as function of
their initial voltages and capacitances ratio // Tekhnichna Elektrodynamika. – 2016. – No 3. – Pp. 9-11.
УДК 621.314
КЕРОВАНИЙ ПЕРЕТВОРЮВАЧ РЕЗОНАНСНОГО ТИПУ ДЛЯ ЄМНІСНИХ
ЕЛЕКТРОРОЗРЯДНИХ НАВАНТАЖЕНЬ
І.В. Волков, чл.-кор. НАН України, С.В. Подольний, канд.техн.наук
Інститут електродинаміки НАН України,
пр. Перемоги, 56, Київ, 03057, Україна, e-mail: dgp@ukr.net
Розроблено декілька способів керування вибраною структурою резонансного перетворювача, що працює на
ємнісне електроразрядне навантаження. Деякі методи розглянуто детально, один із них − з практичною пере-
віркою. Така система має дві основні переваги: повний/частковий режим софт-світчінгу, який дозволяє вико-
ристовувати її на більш високих частотах без суттєвого зниження ККД; керована передача енергії без
суттєвих ускладнень силової частини/системи керування. Бібл. 6, рис. 9.
Ключові слова: резонансний перетворювач, ємнісне електророзрядне навантаження, софт-світчінг.
1. Демирчян К., Нейман Л. Теоретические основы электротехники. T.2. – СПб.: Питер, 2006. – 576 c.
2. Милях А.Н., Волков И.В. Системы стабилизированного тока на основе индуктивно-емкостных преоб-
разователей. − Киев: Наукова думка, 1974. – 216 с.
3. Пентегов И.В. Основы теории зарядных цепей емкостных накопителей энергии. − Киев: Наукова думка,
1982. – 420 с.
4. Полищук Ю.А. К исследованию систем заряда емкостных накопителей от источника ограниченной мощ-
ности / Устройства преобразовательной техники, вып. 1. − Киев: Наукова думка, 1969. − С. 10-16.
5. Rashid M.H. Power Electronics Handbook. − N.-Y.: Academic Press, 2002. − 895 p.
6. Shcherba A.A., Suprunovska N.I. Electric energy loss at energy exchange between capacitors as function of their
initial voltages and capacitances ratio // Технічна електродинаміка. – 2016. – № 3. – С. 9-11.
УДК 621.314
УПРАВЛЯЕМЫЙ ПРЕОБРАЗОВАТЕЛЬ РЕЗОНАНСНОГО ТИПА ДЛЯ ЕМКОСТНЫХ
ЭЛЕКТРОРАЗРЯДНЫХ НАГРУЗОК
И.В. Волков. чл.-корр. НАН Украины, С.В. Подольный, канд.техн.наук
Институт электродинамики НАН Украины,
пр. Победы, 56, Киев, 03057, Украина, e-mail: dgp@ukr.net
Разработан ряд способов управления выбранной структурой резонансного преобразователя, работающего на
емкостную электроразрядную нагрузку. Некоторые методы рассмотрены детально, один из них − с прак-
тической проверкой. Данная система обладает двумя основными преимуществами: полный/частичный режим
софт-свитчинга, что позволяет использовать её на более высоких частотах без существенного снижения
КПД; управляемая передача энергии без существенных усложнений силовой части/системы управления.
Библ. 6, рис. 9.
Ключевые слова: резонансный преобразователь, емкостная электроразрядная нагрузка, софт-свитчинг.
Надійшла 24.05.2017
Остаточний варіант 03.08.2017