Design and Analysis of Output Filter for 3-Phase UPS Inverter

8/10/2019 Design and Analysis of Output Filter for 3-Phase UPS Inverter

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Design and Analysis of Output Filter for 3 phase

UPS

Inverter

Byoungwoo Ryu*, Jaesik

Kim**,

Jaeho Choi , and Changho Choi

Chungbuk National University*

48 Gaesindong, Cheongju, Chungbuk

Phone: +82-43-261-2425, Fax: +82-43-276-7217

E-Mail: choi@,power.chunPbuk.ac.kr

POSCON Ltd., Seoul, S. KORE A**

361-763

S.

KOREA

Abstract

This paper proposes a design method of the

L-C

output filter for three-phase

UPS

inverter: The

harmonic components

of

the output voltages are

dependent

on

the

L-C

value and the system time

constant defined by the switching frequency, the

speed o f control processo< the controller gain, and

etc., but their characteristics are complicate and

entangled each othel: In this paper: the relation

between the

L-C

value and the system time constant

are described with the closed form and the filter

values can be calculated to meet the limit of voltage

THD considering the system time constant. The

schematic design procedure is given by a single f l ow

chart and the proposed filter design algorithm is

verified through the simulation an d experiments.

Key words: output filter design, UPS, zero-output

impedance

1 Introduction

There are two kinds of harmonic sources that make

the UPS output voltage waveform be distorted: One

is caused by the PWM switching of inverter and the

other is caused by the nonlinear characteristics of the

load. If any linear loads are connected to the inverter

output side, then the output voltage harmonics due to

the PWM switching can be eliminated by inserting

the L-C filter between the inverter and the loads, and

it

is well known how to design the optimal values of

the filter components [ l , 21. But the configuration of

the power circuit with L-C filter cannot meet the zero

output impedance at all. Therefore, the capacitor

voltage is usually collapsed in case of the sudden

load change or under the nonlinear load.

By using the fast feedback controller for the output

capacitor voltage, the harmonic distortion due to the

nonlinear load characteristics, such as the capacitor

input type rectifier load or transient load change, can

be complemented [3]. But the performance of the

feedback controller is dependent on the system time

constant defined by the switching frequency, the

speed of control processor, and the controller gain.

And the harmonics suppression characteristics of the

L-C filter and the feedback controller are entangled

each other and complicate to analyze. Therefore, it is

difficult to design the L-C filter considering the

system time constant with the conventional methods.

In this paper, the harmonics characteristics due to

the L-C filter value and the system time constant are

described with the closed form and L-C filter values

can be calculated to meet the given specification of

voltage THD, considering the system time constant.

It means that the harmonic components due to the

PWM switching of inverter and the nonlinear load

characteristics are decoupled separately, and the L-C

filter value and the performance of the feedback

controller are determined to meet each allotted ratio

of THD, for the harmonics suppression [4, 51.

The design procedure of the L-C filter for three-

phase UPS inverter is described. The transfer

function of the filter output voltage to the load

current is given as the closed form and it is possible

to get the L-C values by solving this closed form.

The capacitor value can be calculated with the given

system time constant defined by the performance of

the system controller. This procedure is more

practical to design the power circuit and control

circuit of inverter for UPS than the conventional one.

And also, the effect of the load current to the voltage

distortion can be calculated from the closed form, so

it is possible to analyzed the system how much the

voltage waveform is distorted under the nonlinear

load.

Finally, the schematic design procedure is given by

a single flow chart and the proposed filter design

algorithm is verified through the simulation.

2

Three phase PWM VSI system

The three-phase voltage and curren t equations of

0-7803-7156-9/02/ 10.000 2002 IEEE 941

PCC-Osaka 2002


2/6

P WM INVERTER

LC

FILTER LOAD

I

I

Fig.

1

Configuration of three-phase PWM-VSI power

circuit.

I

I

Fig.

2

Single-phase equivalent block diagram.

the input and output sides of the filters are transferred

to , he dq-values under the stationary reference frame

as (1) and ( 2 ) .

A

1

vc i

o

c / s

The three-phase system can be described by the

two single-phase systems of 'd' and 'q' as shown in

Fig. 2 without the coupling terms. The dq single-

phase equivalent blocks are shown as the M I S 0

system with two inputs of the inverter output voltage

and the load current in Fig. 2 . We will deal with the

equivalent system of 'd' axis only in the equations

below and it can be applied to

q

axis equally.

From Fig. 2 , the transfer function of the capacitor

output voltage to the inverter output voltage and the

load current can be described in (3) neglecting the

resistance of inductor [ 5 ]

In conventional method of the filter design, the

second term is treated as the disturbance and only the

first term is considered to determine the L-C values.

Once the product of L,Cj is calculated from the

expecting cut-off frequency of the L-C filter, the

exact values of Lf nd Cf are determined at values that

minimize the cost function defined by the summation

of the reactive powers. This design procedure can be

applied to a linear load well. But under the nonlinear

load or transient load change, we cannot neglect the

harmonics components due to the second term.

If

the inductor value is minimized at almost zero in

(3),

the capacitor voltage can be independent on the

load current characteristics and it means that the UPS

system works as an ideal voltage source. To minimize

the inductor value, the capacitor value should be

maximized. But as the increase of the capacitor value,

the power rating of an inverter will be increased due

to the increase of the reactive power.

So

it is

permitted to increase the inductor value for the

decrease of the capacitor value as far as the harmonic

components of the capacitor voltage is controlled

with the help of fast feedback voltage controller. It is

clear from the above that the filter design value

should be compromised as the performance of the

system controller. But they are coupled each other

and the filter values are adjusted as the performance

of the controller by the try-and-error method in the

conventional methods.

3 Proposed filter design method

3.1

Transfer function of system controller

Figure 3 shows the system block diagram with

controller. The control system is designed based on

double regulation loops: the main feature is the inner

control loop of the current flowing through the filter

capacitor can be limited within a given range and a

second feedback has been performed using an outer

voltage loop which makes it possible to improve the

dynamics of the entire control system. The transfer

function is driven as

(4).

I 1

Fig. 3 System block diagram with controller

In (4), let's consider the input-output transfer

characteristics responding to the voltage command

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and the load current separately. For the analysis of

the effect due to the capacitor com mand voltage, the

effect due to the load current can be neglected by

putting zero, I,,=O. Then th e controller gains, Kp, Ki,

and

K ,

can be designed to m eet-the ideal controller.

For this, the gain of the transfer function satisfies unit

to make all the values of the nominator and the

denominator are same within the passing bandwidth.

From the above, (4) is simplified as (5).

If the inverter output L-C filter is designed well to

eliminate the harmonics included in the inverter

output voltage, then the command voltage of

5),

Vcd*

is substituted by the fundamental component of the

inverter output voltage, Vadl s in (6).

For the analysis of the effect due to the change of

load current only, the first term o f the right side of (6)

can be neglected and the transfer characteristics of

the capacitor voltage to the load current is given as

7).

7 )

c d ( j n o o ) L P ~ W , ~

IOd ( i n ) K , K ,

3.2

Design of con troller gain

For the design of controller gain, CDM(Coefficient

Diagram Method) controller with observer canonical

form is used [6]. The characteristic equation of (4) is

defined in

CDM

controller by (8) to meet the

robustness.

a

r 2

3 5 s 3 0 s

ao no

Y2YI

YI

With the comparison of the coefficients of two

equations, the transfer function of the capacitor

voltage to the load current given by (7) is described

as

(9).

( 9 )

If the specification of the capacitor voltage

harmonics caused by the nonlinear load current is

given arbitrary, then the relation between the system

time constant and the capacitor value

C

is given

as the closed form of (9). In this equation, the

stability factors of are used here as y , =2.5 and

y 2

2

which satisfy the Manabes recommendation

[5,61.

And also, from the same methods of comparison,

all the values of controller gains,

Kp,

Ki,nd

K ,

are

given as like the following equations.

4 Filter design procedure

Before proceeding of the filter design, the UPS

specification and the system parameters are given as

followings:

1) Total harmonic distortion factor of voltage,

THD,

is below 5% in case of both

0.8

linear

lagging load and nonlinear rectifier load with the

crest factor,

CF=1.

2 ) Modulation index,

my

is given as

0.7

considering

the variation range of DC link voltage and load.

The flowchart of filter design procedure is shown

in Fig.

4.

In the design process, if the calculated total

harmonic distortion factor of the output voltage THD,

doesnt meet the specification, then it repeats the

routine after decreasing the rate of voltage harmonics

due to the dominant load current harmon ics [4,5].

4.1

Define the harmonics

of SPWM VSI

voltage

and

load

current

The voltage harmonics of

SPWM-VSI

is defined

ideally as (13) and the fundamental component and

dominant harmonics of inverter output voltage

normalized by DC input voltage

is

given as Table

I.

Under the assumption of ideal voltage waveform,

the nonlinear load current harmonics of capacitor

input type rectifier with the crest factor, CF=3 is

analyzed using the computer simulation. Table I

shows the Fourier coefficients of load current

normalized by the fundamental component.

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Table I. Normalized inverter voltage harmonics,

v a d ~ v d ~s the change of mo dulation index, mp

mf

Order

1

F S W

f7 2

1 0.9 0.8 0.7 0.6 0.5

1.00 0.90 0.80

0.70

0.60

0.50

0.60 0.71 0.82 0.92 1.01 1.08

0.32 0.27 0.22 0.17 0.13

0.09

n

Mag.

4.2 Determine the impedance ratio of inductor

and capacitor

The impedance ratio

of

inductor and capacitor is

determined to satisfy the condition that the ratio of

output voltage to input voltage at the specific

harmonic order shown

in (14)

can be smaller than

3[ ]

of the fundamental component of the output

voltage as shown in (15). The specific harmonic

order will be given as the same value of switching

frequency.

1 3

5

7 9 11 13

1.00 0.73

0.35

0.07 0.04

0.02 0.01

(14)

4.3 Determine the capacitance value based on the

cost function

The upper limit of the capacitance is determined

at the value that minimizes the cost function defined

by the total kVA

of

the filter L-C components as

shown in (16).

In (16),

W

is the w eighting coefficient determined

due to the relative cost of inductor to the capacitor.

4.4 Determine the system time constant and

capacitance value

The system time constant zi s selected 3 times

longer than the switching time considering the

system stability and the dynamics empirically. Then

the capacitance value is calculated using the given

values of system time constant and the rate of

permitting voltage harmonics due to the load current

from (8). The permission level of the harmonics due

to the nonlinear load current is initially selected 1 A]

considering the remaining harmonics after

eliminating with

L-C

filter. If the THD, canno t meet

the specification finally, then the calculation of the

capacitance value should be repeated after decreasing

this level.

0.01 y2y,2 1

xc

~

n 2 w i I o n

5

4.5

Determine the gains of controller

Using

1

0) to (1 2), all values of controller gains

K,,,

Ki,

nd K, are determined with the given value of

the stability factor and the determined values of the

system time constant and capacitance.

4.6

Calculation of the output voltage harmonics

The total harmonic distortion factor of the output

voltage THD,is calculated from (4) as described in

(1 8). The determined values of controller gains and

the L-C parameters are used for this calculation.

After the calculation of THD,, if it does not meet

the specification, then the above process should be

repeated from the top after modifying the condition

as followings: 1 ) In case o f linear load, repeat the

calculation process after decreasing the impedance

ratio

of

inductance and conductance from

3[ ].

2 ) In

case of nonlinear load, repeat it after decreasing the

harmonics ratio caused by the load current from

1

?I.

44


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Harmonics analysis o f

PWM voltage and no nlinear load current

Calculating frequency transfer function of

filter input to filter output vo ltage

1

Determine the impedance ratio of

filter inductor and capacitor

,

output

Power

output

Voltage

Considered

Controller

Making closed form of filter capacitance and system equivalent time

constant using transfer function with contvoller

using closed form for load current harmonics

of the amplitude of dominant

30[kVA] Switching 9.54[kHz]

Frequency

22O[V] Controller 2OO[us]

time constant

f

4o[uH]

Considered L /

165[uH]

Cost function

c/ =100[uF]

c 25[uF]

R/

0 05f 0.05

calculated by cost function

Retune to the system

1

the impedance ratio of

I

equivalent time constant

Selecting controller gains

satisfying the system response

4

Analyzing output voltage harmonics under the linear and nonlinear load

using transfer function considering the system performance

of

controller

Calculating DC link voltage

I

Fig. 4 Flowchart o f filter design procedure

5 Simulation results

Table I shows the system parameters and the

design values of

L-C

filter and the controller gains

using the filter design flowchart as show n in Fig.

4.

In

case of the linear R-L load, the THD, of

capacitor output voltage is

3.2[ ]

when the

L-C

filter

is

designed by the conventional method based

on

the

cost function and 3.7[ ] when it is designed by the

proposed method, respectively. From the results, it is

verified that both methods are us ef d under the linear

load.

From Fig. 5 to Fig.

8,

the output voltage and

current waveforms and the harmonic spectra of the

output voltage waveform under the capacitor input

type three-phase rectifier with

CF=

re shown

Table 111. System parameters for simulation

945


6/6

300

300

I I

0.00

0 01 0 02

0 03

T i m sec]

-300

0.00 0 01 0.02 0.03

Tims [sec]

Fig.

5

Output voltage and current waveforms with L-

C filter designed by the conventional method.

Fig. 7 Output voltage and current waveforms with L-

C filter designed by the proposed method.

.

2 4 6 8 1 12 14 16

Order

..

_ _ _ .

h

2

4 6

8 1 12 14

16

Order

Fig.

6

Harmonic spectrum of output voltage in

conventional method. proposed method.

Fig.

8

Harmonic spectrum of output voltage in

When the filter is designed by the conventional

method, the voltage waveform is distorted a little and

the its

THD,

is 8.5[ ] with the given system time

constant. Therefore, to meet the specification of

THD,, the inductor value should be reduced and the

capacitor value should be larger. And the inverter

power rating will be increased due to the increase of

the reactive power.

On the other hand, if the filter is designed by the

proposed method, then the output voltage waveform

is almost sinusoidal and the THD, comes within the

specification with 4.6[%].

6.

Conclusion

References

[ l ] S .

Dewan and

P.

Ziogas, Optimum filter design for a

single phase solid-state UPS system,

IEEE Trans. Ind.

Appl.,

vol.

IA-15, no. 6, pp. 664-669, 1979.

[2] T. G. Habetler

and

D. M. Divan, Rectified Inverter

reactive component minimization, in Conf. Rec. of

IEEE PESC87, pp. 648-657, 1987.

[3] A.

Kusko, D. Galler, and

N.

Medora, Output

impedance of PWM UPS inverter-feedback vs. filters,

in Con Rec. of IEEE IAS90, p p .

1044-1048,

1990.

[4]

. Kim,

J.

Choi, and

F.

Blaabjerg, Design and analysis

of

output filter for UPS, in ConJ: Rec. of EPE2001,

DS3.1, 2001.

This paper proposes a filter design procedure for

three-phase

UPS

inverter. By using the proposed

closed form under the given system time Constant.

Therefore, the L-C filter value can be determined

using any try and error method.

[51

J Kim, Design of output filter and controller fo r UPS

inverter, Ph. D thesis in Chungbuk National University,

2001.

[6] S. Manabe, C oefficient diagram m ethod, in ConJ Rec.

o IFAC symposium

on

Automatic Control in Aerosp ace,

method, the filter values can be calculated from the

quickly through the systematic procedure without

pp. 199-210, 1998.

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Documents

Design and Analysis of Output Filter for 3-Phase UPS Inverter