Experience in the Development of the Sine-Wave Filter for High-Power

Variable Voltage Variable Frequency Drive with Medium Voltage

Induction Motor

MIKHAIL PUSTOVETOV

Department of Electrical and Electronics Engineering,

Don State Technical University,

344000, Rostov region, Rostov-on-Don, Gagarin sq., 1

RUSSIA

Abstract: - The relevance of the work reflects the increased use in practice of variable frequency electric drive

additional options, which include sine-wave filter. The main aim of the study: is to develop guidelines for

choosing the parameters of the sine-wave filters and the correct selection of the elements in the current;

consider the phenomena occurring when the capacity is connected to terminals of the load with an induction

motor, such as: reactive power compensation and overcompensation, self-excitation. The methods used in the

study: test on a real process plant; and computer simulation of an electromechanical system with a

semiconductor converter based on a combination of circuit and operational principles for preparing the model.

The results: some of the results of experience in the design and testing of the sine-wave filter for high-power

variable voltage variable frequency drive with medium voltage induction motor with scalar control are

described. The comparative results of the computer simulation of processes at different sets of the sine-wave

filter and converter parameters are presented. Some recommendations for sine-wave filter design are suggested.

Key-Words: - frequency converter, pulse-width modulation of voltage, sine-wave filter, induction motor,

capacitance, reactive power, self-excitation, current.

Received: May 8, 2024. Revised: September 11, 2024. Accepted: November 10, 2024. Published: December 5, 2024.

1 Introduction

In order to smooth the pulse edges of the pulse-

width modulated (PWM) voltage supplied to the

terminals of induction motors (IM) from frequency

converters (FCs), output filters are used between the

FC and the IM, [1], [2], [3], [4], [5], [6], [7], [8], [9],

[10]. The negative impact of PWM voltage on

electrical equipment in the absence of an output

filter is expressed in: high-frequency noise of the IM

[11], [12], [13], increasing level of electromagnetic

interference [14], electro corrosion and destruction

of motor bearings and driven mechanisms [15],

[16], [17], [18], [19], [20], gradual degradation of

electrical insulation [21], [22], [23], accompanied

by intense generation of ozone, which is harmful to

personnel, [24], [25].

A solution to the problem is to use a sine-wave

filter (SF) (Figure 1). It brings the shape of the

output voltage of the inverter as close as possible to

a sinusoid, thereby minimizing the value of the total

harmonic distortion (THD) factor of the phase-to-

phase voltage

[26] and THD of the current

[26], [27].

Fig. 1: Electrical circuit diagram of SF

(alternatively, fuses can be connected in series with

the damping resistors RA, RB and RC)

It is advisable, in any case for the frequency of

the fundamental harmonic of the output voltage of

the inverter

150f

Hz, to require that the output

voltage after the SF correspond to the grid voltage:

the THD of the supply voltage (including all

harmonics up to the order 40) shall be less than or

equal to 8 %, [26], (

no more than 12% at

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380 V RMS grid’s rated voltage in accordance with

Russian State Standard, [28]). The complexity of

choosing SF parameters increases at the carrier

frequency of the PWM

car

f

kHz - a significant

capacitance is obtained (over 1000 μF). This

circumstance forces us to pay attention to possible

features, as well as the positive and negative effects

of connecting a capacitance to the terminals of a

load containing an IM. Let's look at a few specific

provisions below.

2 Problems Formulation

1. The current through the SF capacitors increases

as the load on the IM shaft decreases.

2. In addition to the function of the SF element, the

capacitance can also perform the function of

compensating the reactive power of the IM and the

step-up transformer.

3. A significant capacitance will most likely be

composed of several parallel-connected capacitors,

possibly of different ratings and with different

characteristics.

4. The SF capacitance can form resonant circuits

with inductances in various branches of the circuit

diagram.

5. If the voltage at the inverter output fails, the SF

capacitance, remaining connected to the load circuit

containing the IM, can lead to self-excitation of the

IM, accompanied by significant currents and

voltages.

Fig. 2: An electric drive of the pump of type 14D6

(right side of the photo) as a part of WPS based on a

four-pole IM (left side of the photo) with a rated

phase-to-phase voltage of 6 kV and a rated shaft

power of

2630

rated

P

Further explanations will be given using the

example of a specific technological installation - an

electric drive of the pump of type 14D6 as a part of

a water pumping station (WPS), [29], based on a

four-pole IM with a rated phase-to-phase voltage of

6 kV and a rated shaft power of

2630

rated

P

(Figure 2). The calculated parameters of the IM

equivalent circuit are published in [30]. At the rated

operating mode of the pump, the load of IM is

0.73 rated

P

. The IM is powered using a two-

transformer circuit [9], [31] (Figure 3) from the FC

of type Vesper EI-7009-1000N (six-pulse diode

rectifier plus two-level voltage source inverter,

[32]), which has a range of PWM carrier

frequencies

1...2.5

car

f

kHz and the highest

permissible RMS output current of phase at

continuous running duty (operating mode S1), [33]

1 lim 1600I

A. The inductive branch of the SF in

each phase is represented by a pair of parallel-

connected current-limiting reactors RTST-820-

0.0505 U3 (Figure 4). The resistance of one reactor

is 1.65 mOhm. In those cases where the absence is

not specified, the presence in the diagram is implied

according to Figure 1 in the power lines of the

capacitive part of the SF damping resistors RA, RB,

and RC with a rated value of 0.013468 Ohm.

Fig. 3: The IM is powered using a two-transformer

circuit

During commissioning work with a capacitance

of the SF of 8360 μF per phase and absence in the

circuit in Figure 1 resistors RA, RB, and RC at a

frequency

of about 12 Hz, about 27 Hz and

especially 41.9-42 Hz there was a noticeable

increase in the current at the output of the inverter.

Around

142f

Hz, the inverter switched off due

to a “short circuit at the inverter output.” An

increase in current, current surges and fluctuations

in current magnitude were visible in a fairly wide

band of adjacent frequencies (bandwidth 7 Hz or

more). Therefore, using the frequency hopping IF

function will not be effective. In addition, the

current resonance frequency band may fall within

the range used for the operation and control of the

drive. By sequentially removing fuses on 1000 μF

capacitors symmetrically across the phases of the

SF, with a capacity of 3360 μF per phase, it was

possible to achieve a non-stop start of the drive with

a frequency increase rate from 0 to 50 Hz in 90 s

with the pump running on a closed gate valve, [34]

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(that is, with a reduced load). However, current

swings with a frequency of the order of several hertz

continued to be present, including at

150f

Hz.

When the capacity of the SF phase was reduced to

1360 μF, the fuse links burned out during the startup

of the IM without load.

Fig. 4: Pair of 3-phase current-limiting reactors

RTST-820-0.0505 U3

3 Problems Solution

The first position is illustrated in Figure 5, which

shows the calculated dependences of the SF currents

(determined by the power released at the active

resistance when current is passed through it)

according to the diagram in Figure 1 at

150f

Hz. When approximating the current graph

()I f P

of curve 6 in Figure 5 by the

expression y = 0.0000000001x4 - 0.0000003028x3

+ 0.0002864698x2 - 0.1487129951x +

375.429507481 the coefficient of determination,

[35], [36] is R² = 0.9999999995. On the contrary,

the current through the SF inductance increases with

increasing load on the IM shaft. All dependencies

shown in Figure 5, Figure 6, Figure 7, Figure 8,

Figure 9, Figure 10 and Figure 11, were obtained as

a result of computer simulation by means of

OrCAD, [37], [38], [39] of steady-state operating

modes of the electric drive.

When constructing the simulation model of an

electric drive, the following were used: approaches

and relationships for calculating SF parameters

given in [40], [41], [42], [43], [44], [45], [46], a

mathematical model of a three-phase IM, [47], [48],

[49], [50] and a three-phase transformer [51],

a computer model of autonomous voltage source

inverter, [40], [52].

Fig. 5: Calculated currents of the SF: 1 -

II

without capacitors at

2.5

car

f

kHz; 2 -

with

an SF capacity of 2200 μF per phase,

2.5

car

f

kHz; 3 -

at 2200 µF,

car

f

kHz; 4 -

8360 µF,

2.5

car

f

kHz and the absence of

damping resistors; 5 -

at 2200 µF,

2.5

car

f

kHz (the

curves for other cases are very close to

the one shown); 6 -

at 2200 µF,

2.5

car

f

kHz; 7 -

at 2200 µF,

2.5

car

f

kHz; 8 -

at 2200 µF,

car

f

kHz; 9 -

at 8360 µF,

2.5

car

f

kHz and no damping resistors

If it is necessary to determine the RMS value of

the current in a transient process, for example,

during frequency acceleration of the IM, you should

select the current curve for harmonic analysis over a

time interval equal to the period of the fundamental

harmonic. Having squared the current curve over a

period, we will then perform its harmonic analysis.

The resulting constant component will correspond to

the power that will be dissipated at the resistance of

1 Ohm when the current in question flows through

it. That is, the square root of the resulting constant

component is the RMS value of the current, taking

into account all harmonics over the selected time

interval.

The second position is also confirmed in Figure

5: with a capacitance per phase of the SF of 2200

μF, the current at the output of the SF (load current)

exceeds the current at the input of the SF (consumed

from the inverter) due to the compensation of the

reactive power of the load with the SF capacitors.

The phenomenon is known for capacitive reactive

power compensators IM, [53], [54], [55], [56], [57].

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From Figure 6 it can be seen that with increasing

capacity SF for

decreases

. All other things

being equal, this occurs with an increase in

capacitance due to an increase in the proportion of

the fundamental harmonic in the harmonic spectrum

of the current

, at which reactive power

compensation occurs.

Fig. 6: Calculated specific RMS current through the

SF capacitance and the THD of the

current at

150f

Hz and load on the IM shaft equal to

0.05 rated

P

. The curves were obtained with

connected damping resistors. In their absence, the

specific RMS current through the capacitance is

1.3–1.4 times higher. 1 – permissible specific RMS

current 0.16 A/μF for capacitors with a capacity of

1000 μF; 2 – permissible specific RMS current 0.25

A/μF for capacitors with a capacity of 160 μF and

200 μF; 3 – calculated specific RMS current through

the SF capacitance; 4 -

However, from the same Figure 5 it can be seen

that with a capacitance per SF phase of 8360 μF, the

output current of the inverter significantly exceeds

the load current and depends little on changes in the

power on the IM shaft. At the same time, the

curve is close to the case with a SF capacitance of

2200 μF. The calculation showed that to fully

compensate for the reactive power of the load when

the IM is operating in the rated mode, a SF

capacitance of 2564 μF is sufficient. That is,

“overcompensation” of the reactive power of the

load by overestimating the capacity of the SF leads

to a noticeable

increase. When simulating with a

SF capacitance of 8360 μF at a low load on the IM

shaft without damping resistances for

140f

and

2.5

car

f

kHz, the specific current through

the capacitance was 0.101 A/μF, while at

145f

Hz it was already 0.181 A/μF. Accordingly, the

RMS values of the output current of the inverter at

continuous duty is 972.3 A and 1995.6 A. Thus,

around

142f

Hz there is a sharp increase of

and the output current of the inverter exceeds the

value

1 lim 1600I

A with a further increase, to

which the inverter responds by shutting down on the

basis of “short circuit at the output”. The multiple

increase in the low load mode of IM with an SF

capacitance of 8360 μF compared to the case of no

capacitance has been confirmed by tests.

The third point is illustrated by a specific

example: the SF phase capacitance of 8360 μF,

calculated from the operating condition at

car

f

kHz, was practically obtained by combining

capacitors with ratings of 1000 μF, 200 μF, and 160

μF. Each capacitor is protected by a fuse. The

maximum RMS values of long-term current are 40

A for 160 μF, 50 A for 200 μF and 160 A for 1000

μF. Accordingly, the long-term permissible specific

RMS current per unit of capacitance is 0.25 A/μF

for the lower ratings of capacitors, and 0.16 A/μF

for the higher ratings. Thus, if we connect as shown

in Figure 5, per phase SF 2200 μF, then based on the

sum of currents through the fuses, 370 A per phase

is permissible for a long time, and on this basis, it

should be according to Figure 5 and Figure 7, expect

that at

150f

Hz,

2.5

car

f

kHz and a load on

the IM shaft of more than

0.05 rated

P

, the

capacitors will not be overloaded by current in long-

term operation. But the current through parallel-

connected capacitors is distributed in direct

proportion to their capacitances. It follows that the

admissibility of loading capacitors with current in

the presence of parallel-connected high and low

ratings should be assessed by a value of 0.16 A/μF.

From Figure 7 it can be seen that only when the

power on the IM shaft is above

0.4 rated

P

that we

have an acceptable current load on the capacitors at

continuous duty. Otherwise, since the calculated

specific RMS capacitance current exceeds the

permissible value of 0.16 A/μF slightly, the

protection (fuse links) will be triggered, first of all,

by capacitors rated 1000 μF due to overload current

(due to overheating at continuous duty). This was

observed during the commissioning of the SF on the

WPS, when a continuous duty was tested at

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150f

Hz and no load condition on the IM shaft

and capacitors on the SF phase of 2200 μF and 2000

μF (fuses’ elements melting within 10 - 15 minutes)

or 1000 μF (fuses’ elements melting within 5

minutes).

Fig. 7:

and the specific RMS capacitance current

as a function of the power on the IM shaft for the

case of capacitance in the SF phase of 2200 μF,

150f

Hz and

2.5

car

f

kHz: 1 - ; 2 – highest

permissible RMS current at continuous duty

4 lim 370I

A; 3 – specific RMS current through

capacitance at continuous duty; 4 - highest (equal to

0.16 A/μF) permissible specific RMS current

through capacitance at continuous duty

From Figure 6 it follows that with a shaft power

of IM equal to

0.05 rated

P

150f

Hz and

2.5

car

f

kHz, we have a permissible load of

capacitors by current in a continuous duty with a

capacitance in the SF phase of at least 7160 μF, if

damping resistors are connected.

With the adopted current-limiting reactors in the

inductive part of the IF output filter, it can perform

the functions of the SF with a capacitance value per

phase of at least 360 μF at

2.5

car

f

kHz. To

create a capacitance of 360 μF, only capacitors of

160 μF and 200 μF ratings with a large permissible

specific current are used. But in this case, the value

of the calculated specific RMS current is almost

twice as high as 0.25 A/μF (Figure 6). You should

expect rapid burnout of the fuses protecting the

capacitors due to inrush current such as short circuit

current. When carrying out commissioning work on

the SF with a capacity of 360 μF per phase, the

melting of the fuses’ elements occurred already

during the frequency start-up of an unloaded IM at

120...25f

Hz (approximately 40 s after the

start of the frequency acceleration of the IM). The

fuses’ bodies didn't even have time to heat up.

Figure 8 shows the calculated graphs of the

specific RMS currents of the SF capacitances at

continuous duty as a function of the frequency of

the output voltage of the inverter for three values of

capacitance in the SF phase at low loads on the IM

shaft in case of the presence of damping resistors

RA, RB and RC in the capacitive part of the SF.

Fig. 8: Specific RMS current at continuous duty

through capacitance and

as a function of the

frequency of the output voltage of the inverter for

cases of capacitance in the SF phase of 360 μF,

2200 μF and 8360 μF at

2.5

car

f

kHz, low loads

on the IM shaft and connected damping resistors: 1 -

10 / rated

(ratio of power on the IM shaft to

rated); 2 - specific RMS current at 360 μF; 3 -

specific RMS current at 2200 μF; 4 - specific RMS

current at 8360 μF; 5 – highest permissible specific

RMS current of capacitors with ratings of 160 μF

and 200 μF at continuous duty; 6 – highest

permissible specific RMS current of capacitors rated

1000 μF at continuous duty; 7, 8, 9 -

with a

capacity of 360 μF, 2200 μF and 8360 μF,

respectively

From Figure 6 it can be seen that with a

capacitance of 8360 μF, the specific RMS current

through capacitance is below the highest permissible

value at continuous duty in the entire range of

At 2200 µF the specific RMS current through

capacitance is below the highest permissible value

up to

149f

Hz, and at 360 µF - only up to the

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frequency of

125f

Hz. Moreover, at 360 μF,

the highest current load of the capacitors is observed

145f

Hz, and not at

150f

Hz, as in the

other two cases. In all cases, there is a decreasing

trend for

with increasing frequency. But at

8360 µF

increases slightly above 40 Hz, and at

2200 µF – above 45 Hz of fundamental frequency.

The fourth position regarding the occurrence of

resonances of the SF capacitances with the AC grid

side of the drive is impossible due to the one-way

conductivity of the diodes of the input uncontrolled

rectifier (6 pulse, bridge type) of the FC. As can be

seen from Figure 7,

, consumed from the AC

grid by the electric drive (current of the high-voltage

winding of the step-down transformer) weakly

depends on the presence and parameters of the SF. It

should be noted that there is a slight increase of

in the presence of SF compared to its absence (by 1–

41%, higher values correspond to a lower IM load).

For the current consumed from the AC grid

also varies somewhat depending on the SF capacity

(Figure 9).

There is a possibility of resonance phenomena

occurring between the inductive elements of the FC

and the SF capacitors, as well as between the SF

capacitors and the load inductances.

In [58], in paragraph 3.4 regarding the SF it is

said: “The LC filter allows you to form a voltage

waveform close to a sinusoidal one in the motor. In

some cases, a dissipative element is added to the LC

filter - a resistor, the inclusion of which eliminates

the possibility of shock excitation processes

occurring due to cyclic energy exchange in the

“filter capacitance - motor inductance” circuit. In

order to dampen possible resonant current

oscillations in circuits containing SF capacitors, it

was decided to connect resistors RA, RB, and RC in

the capacitor power lines (Figure 1). Such technical

solutions are used by electrical engineering

companies, [59], [60]. Resistances of 0.013468

Ohms were selected, allowing for long-term

dissipation of up to 8 kW per SF phase at

continuous duty. Computer simulation has shown

that it is possible to satisfy the limitation on power

dissipation in resistors, taking into account the very

complex harmonic composition of the currents

through them, only with an SF phase capacitance of

no more than 2360 μF. The temperature of the

resistances during tests without blowing was 172

°C, which indicates the need for their forced

cooling. Figure 10 shows the calculated energy

characteristics of the SF with a capacity of 2200 μF

per phase at

150f

Hz,

2.5

car

f

kHz, and

32.3

k

% for the linear voltage at the input of

the SF. In the case of a

car

decrease, all other

things being equal, the energy characteristics of the

SF deteriorate.

Fig. 9: Current consumed from the AC grid by the

electric drive at

150f

Hz: 1 -

2.5

car

f

kHz, SF absence or in case a capacitance of 2200 μF

per phase and damping resistors connected; 2 -

2.5

car

f

kHz, capacitance 8360 μF per SF

phase without damping resistors; 3 -

car

f

kHz, capacitance 2200 μF per phase SF

and damping resistors connected; 4 -

СI

2.5

car

f

kHz and SF absence; 5 -

СI

car

f

kHz, capacitance 2200 μF per phase and

damping resistors connected; 6 -

СI

2.5

car

f

kHz, capacitance 8360 μF per phase

without damping resistors; 7 -

СI

2.5

car

f

kHz, capacitance 2200 µF per phase and damping

resistors connected

There is a possibility of resonance phenomena

occurring between the inductive elements of the FC

and the SF capacitors, as well as between the SF

capacitors and the load inductances.

Figure 11 indicates the effectiveness of the

influence of SF on the harmonic composition of the

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current. The largest parasitic current

harmonic is

the 5th.

According to Figure 10 and Figure 11, we can

conclude that the SF characteristics are quite

satisfactory at

150f

Hz and

2.5

car

f

kHz,

excluding excessive specific current through the

capacitance at low IM loads (Figure 6, Figure 7 and

Figure 8). In other words, such an SF can be

operated with a motor shaft power exceeding

0.4 rated

P

. It is impossible to carry out

commissioning work on a drive with such an SF

without a load on the shaft or with a low load at

continuous duty. It is quite possible to operate the

SF in the entire range of IM loads at

149f

and

2.5

car

f

kHz. At

car

f

kHz, operation of the

SF is impossible.

Fig. 10: Calculated energy characteristics of the SF:

1 -

; 2 – SF’s total losses; 3 - THD of phase-to-

phase voltage at the load

; 4 – per phase power

losses on the damping resistance; 5 – voltage drop

from the fundamental harmonic in the SF phase

While allowing for reliable, trouble-free start of

the drive, the introduction of damping resistors did

not completely eliminate low-frequency current

fluctuations (on the order of several hertz) at the

inverter output at some output voltage frequencies.

During tests with a SF capacitance of 2000 μF per

phase, fluctuations in the effective current value

were up to 17% of the average value at

150f

and over 11% at

138f

Hz. An increase in

current during acceleration is noted to

approximately

130f

Hz. Above a frequency of

30 Hz, a decrease in

current values followed.

Since during the tests the rate of increase in

frequency by the converter was set to 50 Hz for 90

s, the phenomena of the inrush current of the IM

should have ended before reaching a frequency of

30 Hz.

Fig. 11: Calculated THDs for SF currents: 1 -

;

2 -

; 3 -

34II

kk

Therefore, it is possible that there are resonance

phenomena in the amplitudes of the FC and IM

currents. During the analysis of the results of

computer simulation, it was noted that with the

power of

0.05 rated

P

on the IM shaft at various

values, there are fluctuations in the rotor speed with

a frequency of approximately

5...7.25

f

(arithmetic mean 6.125 Hz). Their presence in the

simulation results is not related to the size or

absence of SF capacity. Under low load conditions,

during oscillations of the rotor speed, periodic

outputs of the IM into generator mode are possible.

The amplitude of the IM phase current

and the

amplitude of the output current of the inverter

have the same oscillation period. There are also

fluctuations in the power released at the resistances

of the reactors and damping resistors, the same

frequency as the fluctuations in the rotation speed of

the IM rotor. Power fluctuations are most noticeable

125f

Hz and 35 Hz. Accordingly, the

oscillation frequencies are about 5 Hz and 6.67 Hz.

The same frequencies of amplitude oscillations are

recorded in the results of modeling the drive

network current. An increase in the mains current as

a result of such fluctuations could explain the

isolated cases of tripping of the step-down

transformer protection recorded during testing. The

frequency values of the inverter output voltage, for

which an increase in

amplitude was observed

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during testing and simulation, namely: 12 Hz, 25

Hz, 27 Hz, 35 Hz, 38 Hz, 42 Hz, 47 Hz, 50 Hz, are

close to numbers that are multiples of

In [61], it is indicated that for powerful IM

the occurrence of self-oscillations of current and

rotation speed is possible. In other words,

manifestations of

current resonant phenomena

are possible. There is no mention in [61] of the

presence or absence of FC’s output filters in the

circuit. The main criterion for the propensity of the

IM to enter resonance in [61] is the value of the

magnetic flux transmission coefficient between the

stator and the rotor

0.95k

  

/k L L L L L

    

  

(1)

For IM used on the WPS, the components of (1)

have the values indicated in Table 1.

It is obvious that a particular IM meets the

criterion of propensity to enter into resonance, since

the calculated

0.955 0.95k

. It is possible

that the presence of a capacitive energy storage

device at the load terminals contributes to the

aggravation of the manifestations of this tendency

since no noticeable low-frequency

current

swings were recorded during tests when starting the

drive without an SF.

The fifth position is reflected, for example, in

[54], [62], where a correspondence is established

between the rated power of the IM at 0.4 kV line

voltage with a synchronous rotation speed of 1500

rpm and the maximum reactive power of

compensating capacitors, kVAr, connected to the

motor terminals, guaranteeing the absence of self-

excitation of IM (Table 2 in Appendix). From Table

3 (Appendix) it follows that the capacitances of

powerful SFs for operation at

car

f

kHz of

known manufacturers [63], [64], [65] meet the

requirements of Table 2 (Appendix). Low

capacitance in the SF is achieved by increasing the

inductance, which in some cases leads to a voltage

drop across the inductance of more than 10%.

However, [54], [62] do not deny the possibility of

using capacitances larger than those recommended.

A possible compromise solution for using SF in

a two-transformer circuit for powering a medium-

voltage IM from a low-voltage inverter is to install

medium-voltage capacitors [66] on the terminals of

the high-voltage winding of a step-up transformer,

the leakage inductance of which in this case serves

as the inductance of the SF.

Table. 1 Values of the components of (1), [58]

Main

inductance

of the IM

L

, H

Stator

winding

phase

leakage

inductance

L

, H

Leakage

inductance

of the rotor

squirrel cage

reduced to

the stator

phase

L

, H

Magnetic

flux

transfer

coefficient

between

stator and

rotor

p.u.

IM of rated shaft power 630 kW, synchronous speed

1500 rpm, rated linear RMS voltage 6 kV

0.277214

0.01084367

0.01518114

0.955

The advantages of this solution: the capacitance

of the SF is small and is formed by a single

capacitor per phase, the recommendations of Table

2 (Appendix) are satisfied (if we assume that the

maximum reactive power of capacitors that can be

connected to the IM terminals without the risk of

self-excitation does not depend on voltage). The

disadvantage will be the lack of protection through

the SF step-up transformer. For WPS, in some

cases, this option is acceptable, since the

phenomenon of ozonation needs to be eliminated in

rooms where people are. IM with pumping units

installed in the machine room where personnel

work. Transformers are installed in separate boxes

where public access is limited.

In the case under consideration with a medium-

voltage IM with a power of 630 kW, medium-

voltage capacitors KEK1-6.3-75, connected in a star

configuration, can be used (Figure 12 in Appendix).

The capacitor capacity is 6 µF. Each capacitor is

connected to the rated phase voltage

6300 / 3 3467

Cphrated

V

V. The rated

current of the capacitor is calculated from the rated

reactive power and rated voltage:

75000 11.905

6300

Crated

Сrated

Crated

  

A. The

capacitor allows a current overload of 30%. At rated

current and phase voltage, the reactive power of the

three phases of the SF capacitors will be

33 3 3467 11.905

C ph Cphrated Crated

Q V I    

123823.9

VAr, that is, 123.8 kVAr, which is

slightly more than the limit value (123 kVAr) from

the Table 2 (Appendix). The nature of the

dependence of the current through the capacitor on

the load on the IM shaft is the same as with low-

voltage capacitors: at a constant voltage frequency,

as the load increases, the current through the SF

capacitors decreases. That is, the capacitor current

for no load mode will be greatest. By simulating

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Volume 23, 2024

with the IM

0.05 rated

P

loaded, the RMS value

of the current through the capacitor SF in a steady

state is 11.439 A, which is lower than the rated

current. RTST reactors in this case are practically

not a significant part of the SF inductance - mainly

its function is performed by the leakage inductances

of the windings of the TSZGLF 1250/10 U3

transformer, used as a step-up, for which, in a first

approximation, the sum of the leakage inductances

of the windings is

2 0.0036 0.0072LL



   

Then

/ 2500 / 765.7 3.265

car r

ff

4 Conclusions

1. When using SF capacitances composed of

parallel-connected capacitors with different

characteristics, the smallest possible value of the

specific RMS current through the capacitor should

be taken as a current limit.

2. When using SF capacitors made up of a specific

set of parallel-connected capacitors with different

ratings, it should be possible for the consumer to use

different combinations of capacitor ratings, allowing

the SF capacitor to be adjusted for specific operating

conditions. It should be possible to operate the SF

both without and with damping resistors in the

capacitive part.

3. SF capacitors are most loaded with current in case

of the no-load mode of IM (or another load device).

The SF must provide the ability to operate at

continuous duty with real no-load mode, for

example, IM, over the entire range of output voltage

and frequency of the inverter. This is very important

for commissioning work.

4. In the SF, you should not use a capacitance larger

than that suitable to ensure full compensation of the

reactive power of the load. Violation of this rule

leads to an unjustified increase in the output current

of the inverter and the current through the SF

capacitors.

5. The method for calculating the RMS value of the

current through the capacitance of the SF should

ensure correct consideration of the contribution of a

wide range of higher temporal harmonics. It is

advisable to carry out a computer simulation of

the steady-state operating modes of the drive to

calculate the RMS value of the current through the

capacitance, and dynamic modes to identify the

maximum instantaneous current values. Calculation

of the RMS value of the current through the SF

capacitance using the method described in [67] (for

example: Trace expression-> SQRT(S(I(R5)*

I(R5))/Time), based on the results of the dynamic

modes of the drive simulation, can lead to

underestimated values if the long-range steady-state

cycle has not been reached.

6. Reducing the specific RMS current through the

SF capacitance by increasing the resistance of

damping resistors is impractical. For example, a

twofold increase in resistance leads to an increase in

losses on it by 83% while the specific RMS current

through the SF capacitance decreases by only 4%.

7. As a rule, capacitors of type “AC filtering” are

suitable for composing the SF capacitance. The

main characteristics for selection will be the voltage

amplitude on the capacitor and the amplitude of the

current through the capacitor. It is also necessary to

take into account the RMS voltage across the

capacitor and the RMS current through the

capacitor. In order to prevent an overcurrent when

choosing a capacitor, it is recommended that, having

calculation or simulation result on the amplitude of

the current through the capacitor, calculate the RMS

value of the current from its amplitude as for a

sinusoidal waveform, i.e. dividing the calculated

amplitude value of the current through the capacitor

. The RMS value of the current through the

capacitor obtained as a result of the calculation

should be further used to select a capacitor from the

catalog [68], [69], [70] if it also indicates the RMS

value under the name Imax, acting on the principle

“select a value from the catalog that is not less than

the calculated one”. Maximum current

max

– the

maximum permissible RMS value of the current

through the capacitor in continuous operation, this

value is usually given in the technical specifications,

it determines the maximum power dissipated by the

capacitor. Also, when choosing a capacitor, you can

focus on the peak repeating current

- this is the

permissible current amplitude in a repeating mode.

The current

exceeds

max

from 3 to 40 and more

times. For the selected capacitors, you should select

a suitable protection device against overcurrents and

overload currents.

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Mikhail Pustovetov

E-ISSN: 2224-266X

231

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Mikhail Pustovetov

E-ISSN: 2224-266X

235

Volume 23, 2024

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Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

The author equally contributed to the present

research, at all stages from the formulation of the

problem to the final findings and solution.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

Conflict of Interest

The author has no conflicts of interest to declare that

are relevant to the content of this article.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en

_US

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236

Volume 23, 2024

APPENDIX

Table 2. Recommended correspondence between the rated power of the IM and the maximum reactive power

of the capacitors

Rated power of the IM,

Maximum reactive power of

capacitors, kVAr

C, µF (per phase) when connected according

to a delta circuit for a RMS voltage of 0.4

113

146

166

110

192

132

239

160

272

200

312

250

378

280

418

355

504

400

544

450

617

Subsequent values are obtained by extrapolation

500

102

675

630

123

816

800

150

994

Table. 3. Characteristics of powerful SF in accordance with [63], [64], [65] for an RMS linear voltage of 0.4 kV

Rated power of the IM, kW

C, µF (per phase) when

connected according to a delta

circuit

L, mH

Resonant frequency of SF fr,

Carrier frequency of PWM

inverter fcar, Hz

car

Voltage drop at a frequency of

50 Hz across the SF inductance

in % of 380 V

Inverter output current, A

250

0.11

903.6

3000

3.3

4.4

480

400

165

0.2

505.8

2000

4.0

12.4

750

450

188

0.11

639.0

2000

3.1

8.0

880

500

188

0.11

639.0

2000

3.1

8.0

880

560

282

0.075

631.8

2000

3.2

7.4

1200

630

282

0.075

631.8

2000

3.2

7.4

1200

800

330

0.1

505.8

2000

4.0

12.4

1500

WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS

DOI: 10.37394/23201.2024.23.23

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237

Volume 23, 2024

Fig. 12: Dry step-up power transformer 0.4/6 kV TSZ-1250/6/0.4 Y/Δ in an individual box. At the bottom right

you can see medium-voltage cosine capacitors KEK1-6.3-75 to 6.3 kV, 75 kVAr, connected according to the Y

circuit, acting as capacitive elements of the SF

WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS

DOI: 10.37394/23201.2024.23.23

Mikhail Pustovetov

E-ISSN: 2224-266X

238

Volume 23, 2024