Rectifiers with a Combined Filtration of Primary

Current for High-Frequency Power Systems

Sokol E.I., Goncharov Yu.P., Eresko A.V., Ivakhno V.V., Krivosheev S.Yu., Zamaruiev V.V., Lobko A.V., Voytovich Yu.S.

National Technical University "Kharkiv Polytechnic Institute", Kharkov, Ukraine

Lobko-Andrey@mail.ru

Abstract - The article considers the ideology of connection of communal loads at low-voltage high-frequency power supply, which allows to create non-contact wide-range power control

loads and non-contact protection at emergency conditions

I. THE ANALYSIS OF THE PROBLEM STATE AND THE

DESCRIPTION OF THE WORK TASK

The present state of power electronics allows to start the

work on the development of one-phase low-voltage electric

distribution networks with an operating frequency of about

20 kHz, like in [1], instead of or in addition to the traditional

three-phase distribution networks of 380 V, 50 Hz [2], where

grid currents are large because of the low operating voltage

and therefore the great losses and heat release are

considerable that compels to increase a wire cross-section for

heat dissipation. The main effect, which can be achieved is to

reduce to 3 - 5 times consumption of the conductor on low-

voltage cable lines of electrical power supply (EPS) and the

loss of energy that now reaches 10% of the transmitted

energy. This is achieved by the separation of voltage levels in

EPS the order of 1 - 3 kV and low voltage allowable for the

electrical safety of consumers. This is accomplished by

installing compact high-frequency intermediary transformers

for either every individual consumer or a small closely-

located group of consumers. Herewith RMS current in the

cable EPS decreases by several times. Similar systems with

two-stage voltage have already got some application, but

they are ineffective at low frequency due to poor specific

characteristics of 50 Hz low power intermediary transformers.

The cardinal increase of frequency at low-voltage

distribution networks (which is dictated primarily by the

desire to get out of the sound frequency range), allows to

review the structure of energy consumption in order to

increase its effectiveness. Particularly, this applies to non-

linear loads, containing rectifiers. They consume non-

sinusoidal currents that can cause resonance phenomena in

the high frequency cable EPS.

In general, to prevent the appearance of such currents it is

possible to install the individual power factor correctors

(PFC) in a circuit at each of the loads. An alternative solution

is the use of non-traditional schemes of rectifiers with

resonant ballasts (RRB). Such ballasts are widely used in

resonant inverters for the improvement of the switching

conditions [3, 4]. This article focuses on the application of

another useful property of series LC - ballast. When it is

connected to an AC circuit, the rectifier generates little

number of higher harmonics. They can be suppressed by low-

power active filters (AF) that are installed at the output of

cable EPS and are connected through resonant ballasts. The

latter allows to use in AF fast-operating low-voltage

MOSFET of new generation, which has been announced by

manufacturers [5].

The aim of this work is to analyze the properties and

characteristics of rectifiers with combined filtration in a high-

frequency power supply system.

II. RRB BASIC CIRCUIT

The scheme contains an AC-voltage source, a resonant

ballast on the AC side, a diode bridge, an output filter Cd and

the equivalent of varying load in the form of a resistor with

variable resistance (Fig. 1). The comparison is made with

rectifier variants without the resonant ballast: with a pure

capacitive output filter Cd and with an output filter LdCd .

Fig. 2 shows the oscillograms of voltages and currents in the

scheme of Fig. 1 that are obtained on its Matlab model. The

improvement of the input current form is produced the ballast

inductance L which has great resistance on frequencies of

higher harmonics. Inductive resistance of the fundamental

frequency ω is set by the relative parameter

x*=ωL/RL (1)

where RL is the resistance of the nominal load, which is

reduced to the input of the commutator.

At high enough x* the input current does not contain zero

pauses, as it is shown in (Fig. 2,a).

Then the switching of diode pairs occurs at the current

transition points through zero value, which means a strong

relation between the input and output voltages u=±ud. In the

Fig. 1 Rectifier's scheme with a resonant ballast LC: K - commutator;

Cd - output filter; RL - the equivalent of varying load

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current zeros a change in polarity of the input voltage happens

and when voltage ripples ud are neglected (Fig. 2,c), the input

voltage has the form of an ideal rectangle (meander)

(Fig. 2,b). As it is known, meander has a full range of odd

harmonics, whose amplitudes decrease inversely

proportionally to the harmonic number k. If the resistance of a

capacitor at frequencies of higher harmonics is neglected, the

higher harmonics in the input current decrease inversely

proportionally to k2 as the inductance resistance of the

inductor is proportional to the frequency. The rapid decrease

of the current harmonics amplitudes differs this scheme from

the two others. In the LdCd output filter without a ballast input

current has the form of a meander.

The amplitudes of its harmonics decrease in inverse

proportion to k, that is slower. With Cd the output filter, the

input current has the form of a short impulse, which is located

in the vicinity of the voltage amplitude uS, when capacitor Cd

is recharging. It is known that infinitely short impulse has a

uniform frequency spectrum, in which all of the odd

harmonics are the same. Thus, for the relative amplitudes of

the harmonics in the schemes being compared:

IKm*=IKm/I1m∼1/k

2; IKm

* ∼1/k; IKm

*∼1/k

0=1 (2)

The role of ballast capacity C is the compensation of

voltage drop of the first harmonic on the inductor, for which,

the inductive and capacitive resistances at the fundamental

frequency should be equal

1/(ωC)=ωL=x (3)

This compensation improves the external characteristic of

rectifier, reduces the consumption of reactive power from

power line, and at large values of x* significantly improves

the use of electrical equipment on its installed capacity per a

unit of power load.

III. ANALYTICAL EVALUATION OF RRB PARAMETERS

It can be performed by the fundamental harmonics method.

Fundamental harmonics are first harmonics u1, i1, at the input

to the commutator К, and zero harmonics ud0, id0 (constant

component) at the output. The basic assumption is that the

interaction of higher harmonics through the commutator is not

taken into account, that is, at determining the input voltage u

we get ud=ud0, and at determined of the output current id we

assume i=i1.This assumption is justifies by the filtering action

of the elements Cd, L and gives the following relation

between the fundamental harmonics in the continuous current

mode

U1m=(4/π) ud0=US1m ; id0=(2/π )I1m; R=U1m/I1m=(8/π2) RL, (4)

where m is amplitude values of the first harmonics.

With the above assumptions, the input voltage u (Fig. 2,b)

is a perfect meander with the amplitude ud0. The capacitor C

resistance at the third harmonic frequency in comparison with

the inductor L resistance is also neglected and taking into

account (1) and (3) we get for the amplitude of the third

harmonic of the primary current with

I3m=I1m/(9⋅x*) or I3m

*= I3m /I1m=1/(9⋅x

*) (5)

For example, if x*=1 then I3m

*=1/9. In comparison with the

schemes without resonant ballast with LdCd and Cd output

filters we receive the reduction of the third harmonic of input

current, which has the largest amplitude by 3 and 9 times

respectively. Computer simulation confirms sufficient

accuracy of both the relations (5) and the more general

relation (2) for the continuous current mode. At the

discontinuous current mode, the analytical relations become

significantly inaccurate. However, this mode corresponds to

low-currents and therefore is not interesting.

The output current id coincides with the module of the input

current (Fig. 2,a). For its second harmonic and the capacity

value of the output filter:

Id2m=0.42⋅I1m, Cd=Id2m/(2ω⋅Kru⋅ud0) (6)

where Kru is the allowable ripples coefficient of the load

voltage. The required capacity Cd is reduced by nearly three

orders compared to that at 50 Hz.

IV. POWER ACTIVE FILTER (AF)

Fig. 3 shows its possible structure. The input of the system

is the basic converter (1 - 3) kV, that is installed in the

distribution substation. The entrance cables should be

considered as objects with multi resonance, which is caused

by the distributed capacitance and inductance. AF is set at the

termination points of load groups to PC. Intermediary

transformer is not shown at the scheme, and the parameters of

the basic converter and power cable are reduced to the turns

of its secondary winding. On the AF power input parallel LC

Fig. 2 Voltages and currents in the steady-state mode: i - the input current,

u - input voltage, ud - the output voltage, us - the mains voltage

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- ballast with resonance tuning at the fundamental frequency

ω according to (3) is installed. It prevents the delivery of the

first voltage harmonic to the subsequent elements of AF

scheme. Thanks to that, their voltage values consist only of

high harmonics and is reduced by a order. AF should act

primarily as an active compensator that generates current

harmonics in the grid, which are numerically equal and

opposite directed towards the higher harmonics of the load

current. It is made according to one or multi-level schemes of

the voltage source inverter.

According to the theorem of Nyquist-Shannon, working

frequency range ωb in COMP is limited to half frequency of

pulse-width modulation (PWM). To take this fact into

consideration the feedback circuit must have the appropriate

control filter with rectangular amplitude-frequency and zero

phase-frequency characteristic. It is known that, in general,

this filter does not satisfy the conditions of physical

realization, as its reaction to external disturbance must begin

before the disturbance happens [6]. However, in this

application, the properties of this filter can be implemented to

the steady-state mode, since for the periodic signal future

values can be associated with the past ones [7]. This filter of

discrete frequencies (FDF) allows to use fully the working

frequency band of AC according to the theorem of Nyquist-

Shannon mentioned above. As the boundary frequency the

harmonic frequency ωb of the load current, for which the

relative current is less than 0.01 can be taken. In this example,

it is approximately equivalent to the 10-th harmonic. For the

rectifier with the output LdCd filter, it would be necessary to

raise the boundary frequency by over than five times, and

with Cd filter - even to a higher degree. For all harmonics of

the load current, including those which fall outside the range

of the operating band of AC, AF should have properties of a

damper that overwhelming resonant phenomena in

LC - ballast and cable EPS. The simplest damper is a resistor,

where active resistance should be equal to the resistance of

the nominal rectifier load.

The simplest, but not the most optimal solution, is to use a

parallel resonant ballast with the same relative reactive

resistance x*=1, as is in the scheme of RRB.

V. TRANSITIONAL AND EMERGENCY MODES. SIMULATION RESULTS

The traditional schemes of the low-power mains rectifiers

create serious problems at starting-up, when there is initial

charge of a filter capacitor at the output, as well as at short-

circuit at the output terminals. In schemes in Fig. 1 and Fig. 3

the problem of current limitation is greatly facilitated by the

presence of a series ballast inductor with large enough

inductance at AC side. However, additional resources are

needed for resonance damping in a series LC - ballast in the

indicated transitional modes.

One of them is to use a varistor in parallel to the ballast

capacitor. Another varistor can be connected in parallel to the

capacitor of output filter for limiting overvoltage during the

starting-up which can occur due to the oscillatory nature of

the process of the initial capacitor charging (Fig. 4).

Assuming a varistor as an ideal voltage limiter and the

amplitude of the first harmonic equal to the amplitude of

trapezoidal voltage uC we get

uC1m*=x

*⋅KU, I1m

*=UC1m

*/x

*=1/x

*+KU, (7)

where KU>1 is the voltage limitation threshold in relation

to the nominal voltage amplitude.

For example, at KU=1.3 and x*=1 get I1m

* is equal to 2.3

that is enough for current protection reliable functioning.

Thus, RRB creates small "stress" on the power line both at

starting-up and at short-circuit. The significant addition that

allows to implement a fast-acting non-contact protection at

short-circuit involves the replacement of two diodes with

thyristors. At short-circuit this protection removes a

permanent unlocking signal at the control electrodes. Thanks

to this, the circuit breaks after the current transition through a

zero value. Since the thyristors do not need to be locked up,

then they do not have to be high-frequency.

The relations for the relative amplitudes of the harmonics

of RRB at steady state mode were tested on a computer

model. The second row of Table 1 shows through fraction the

calculated and actual values of harmonics relative amplitudes

of the primary current at RRB at x*=1 (the actual values were

obtained from Matlab model). For comparison, the next row

of the table shows the calculated values for the circuit with

LdCd output filter without the ballast.

According to the data of the example being studied, the

Fig. 3. AF connection to single-phase low-voltage distributional network:

PC - power cable reduced to the secondary winding of the intermediary transformer; LC - parallel resonant ballast of active filter; D - damper;

COMP - active compensator; Lpwm - harmonic filter of PWM; FDF - control

filter of discrete frequencies; CC - current controller

Fig. 4 Half-controlled scheme of RRB with varistors to limit the overloads

at transition process (a) and the definition of the primary short circuit

current (b)

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scheme modeling with combined filtration was performed

(Fig. 3). Single-phase bridge circuit of the voltage source

inverter with unipolar PWM and with prognosticative current

control according to the work [8] is used. At constant

frequency of PWM 2ωb=20ω the controller monitors actual

frequency spectrum from the 3-rd to 9-th harmonic included,

which is separated from the primary current of RRB (Fig. 2,a)

with the help of FDF. The harmonic structure in the result

corresponds to the last row of Table 1. Fragment monitored

current waveform ia together with the output signal shown in

Fig. 5 FDF.

Using specific measuring instrument, it was possible to

determine the relative power of losses in the damper Rd in the

steady state mode, which is about 0.25%. Next, the ±7%

deviation from the terms of the resonance tuning (3) in the

parallel ballast was introduced, which led to the appearance of

the fundamental harmonic currents in the damper. As a result,

the relative losses increased to 0.53%.

Then, the introduction of the high-frequency power cable

with air insulation (ε=ε0) at changing length lk from 0 to

1.25 km was simulated. Cable wave resistance was equal to

RL, that corresponds to the agreed nominal load mode.

While introducing the cable, the distortion power supply

voltages appear, which for the considered range of variation lk

have the larger value when lk=1.25 km, since in this case

resonant frequency of the cable coincides with the frequency

of the third harmonic current of the load. The current value of

the third harmonics of power supply voltage was thus 4.5%,

which is acceptable (Fig. 2,d). This has been facilitated to use

low-power resistive damper in the active filter scheme.

The obtained results allow to recommend the reviewed

rectifier system as the basis of non-contact protection and the

wide-range contactless regulation of power of communal

loads provided the replacement of traditional low-voltage

distribution network of 380 V, 50 Hz for the proposed single-

phase distribution system (1 ÷ 3) kV 20 kHz [2]. In order to

do this, rectifiers are complemented by simplest step-down or

buck-boosters, based on power MOSFET technology [5].

VI. CONCLUSIONS

1. At frequency of about 20 kHz it is effective to use

resonant filtering method of the primary current harmonics of

rectifier in combination with a low-power active filter for a

group of consumers, eliminating the need for individual

power factor correctors (PFC), and simplify the protection.

2. In comparison with the traditional rectifier scheme with

capacitive filter without PFC, the rectifier scheme with

resonant ballast reduces the amplitude of the generated

spectrum of harmonics by the order, provides a strong

external characteristic and limitation current impulse of

power line at the twofold level at transitional and emergency

work modes.

3. The use of low-power resistive damper in the active

filter scheme allows to reduce significantly the distortion of

input voltage due to the distributed inductance and cable

capacitance.

4. The reviewed structures can be considered as the basis

for the creation of the low-voltage high-frequency electrical

distribution networks with non-contact wide-range power

regulation of communal loads and non-contact high-speed

protection under emergency conditions.

REFERENCES

[1] Hansen I. G. Status of 20 kHz space station power distribution

technology. – National Aeronautics and Space Administration, Cleveland,

OH (USA). Lewis Research Center, 1988. – №. N-88-15838; NASA-TM-

100781; E-3951; NAS-1.15: 100781; CONF-880248-.

[2] Sokol E.I., Goncharov Yu.P., Eresko A.V. The use of power

electronics in low-voltage distribution networks of the communal objects //

Proceedings of the Institute of Electrodynamics of NAS of Ukraine.

Collected works. Spec. Release. Kiev, 2011. Part 1, pp. 101-111 / in Russian

[3] Mohan N., Underland T.M., Robbiens W.P. Power Electronics //

Third Edition. John Wiley, 2003

[4] Schröder D. Power electronic circuits // Springer, 2008/ in

German

[5] McDonald T. GaN Based Power Technology Stimulates

Revolution in Conversion Electronics. International rectifiers

Www.bodospower.com, 2009

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McGraw-Hill Science Engineering, 2000

[7] Goncharow Yu.P., Zamaruev V.V., Krivosheev S.Yu. et al.

Restriction spectrum of periodic signals of feedback in power active filters

for power supply systems of contact networks // The scientific and technical

collection «Hirnycha elektromekhanika ta avtomatyka» the Issue 84, 2010,

Dnepropetrovsk, pp. 28-37 / in Russian

[8] Sokol E.I., Goncharow Yu.P., Eresko A.V. et al. Semiconductor

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TABLE I CALCULATED AND ACTUAL VALUES OF RELATIVE HARMONIC AMPLITUDES

OF RRB PRIMARY CURRENT

K 1 3 5 7 9

RRIkm* 1/1 0.11/0.125 0.04/0.041 0.02/0.02 0.011/0.012

Ikm* 1 0.33 0.25 0.14 0.11

Ikm* 1 0.012 0.008 0.004 0.001

Fig. 5 Output signal FDF (if) and the tracking current (ia) in the active filter

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