harmonics techniques

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A Novel Technique For Optimising Harmonics And Reactive Power With Load

Balancing Under Non-Sinusoidal Supply And Unbalanced Load Conditions

Sincy

George,

Member, IEEE

Department

of

Electrical Engineering,

Indian Institute of Technology -Bombay,

Powai, Mumbai

- 400

076, India

sincy@ee. itb.ac.

in

Abstract:

Generally, conventional power factor corrections

techniques assume ideal conditions,

viz.

sinusoidal supply

voltage and balanced load. But vast majority of the domestic

and industrial loads present in the power distribution system are

non-linear and unbalanced. Under such conditions, attempt to

make the power factor unity result into a non-sinusoidal source

current, which increases total harmonic distortion (THD) in the

system.

On

the other hand attempt to make harmonic free

current may not result in unity power factor because of the

harmonics present in the supply voltage. Thus, there is

a

trade

off between improvement in power factor and reduction in

THD. With the introduction of power quality norms by various

utilities, it has become unavoidable to optimize power factor

while satisfying harmonics limits. I n this paper, a novel

technique for optimisation of THD and power factor subject to

power quality constraints is presented. The algorithm uses

Lagrange multiplier technique to optimise the non-linear

equations. The algorithm calculates the control coefficients by

Newton Raphson method and is used to compute the desired

source current that balances the system besides optimising

power factor satisfying the load power while meeting the THD

limits. Knowing the load current, the compensating current to

be supplied by the shunt active power filter to the power system

is calculated. This technique, besides satisfying the power

quality norms, also balances the imbalance in the system. It is

applicable for single-phase and multi-phase system under

sinusoidal and non-sinusoidal supply conditions. The proposed

scheme does not use the widely used p-q theory and use simple

computational techniques. Simulation using MATLAB has

shown encouraging results. The scheme is being implemented in

hardware using DSP.

Key words: Power Quality and Harmonics, Power factor

compensation, Active Power Filters, DSP Control.

LINTRODUCTION

In electrical power distribution system, most of the loads

are inductive in nature. Residential loads and vast majority of

other single-phase loads cause imbalance in the system. The

increased uses of power electronic devices also impair power

quality in the grid. These non-linear loads draw non-

sinusoidal currents from the system consequently voltage

drops are produced across impedances of transmission line,

transformer and generator causing non-sinusoidal voltages in

the system. This distorted voltage affects other linear or non-

linear loads connected to the system. Effect of these

Vivek Agarwal,

Member, IEEE

Department of Electrical Engineering,

Indian Institute of Technology -Bombay,

Powai, Mumbai

- 400

076, India

agarwal@ee. itb.ac in

0-7803-7754-0/03/ 17.0002003 IEEE

1537

harmonics and voltage imbalance on electrical and electronic

equipment is explained in various papers [ l] .

Harmonic contents vary randomly and consequently the

conventional compensating techniques such as the use of

passive LC filters to perform harmonic reduction are

ineffective [2]. Due to this many types of active filters have

been developed to compensate current and or voltage

harmonics viz. shunt active filter, series active filter or

combination of both [2-51. Controlling the injection of

current harmonic by the non-linear load can eliminate non-

sinusoidal operation of the system. This can be achieved by

the installation of shunt active filters. In this technique, a

current source inverter is connected in parallel with the load.

This injects compensating current into the system to cancel

the undesired components of load current that are responsible

for harmonics and low power factor.

The quality and performance of these filters mainly depend

on the method used to generate the reference current for

compensation [6]. Most of these methods use p-q or d-q

transformation theory and assume a sinusoidal supply

voltage. Control methods adopted by others [7,8] assume a

non-sinusoidal supply, but use only positive sequence voltage

at the fundamental frequency to generate sinusoidal

references to ensure that the supply current is harmonic free

and power factor is unity. However, when the supply voltage

is non-sinusoidal, perfect harmonic compensation (PFC) does

not result into unity power factor (UPF) and vice versa. In

such conditions, non-linear optimisation technique [9 IO] is

found to be an efficient method to optimise the power factor

and total harmonic distortion THD) satisfying the power

quality norms or guidelines. The method adopted in [9] also

uses p-q theory and is not applicable to single-phase

conditions. Also most of the proposed active filters are based

on analogue implementation.

In this paper, an improved control algorithm for the

reference current to the inverter under non-sinusoidal supply

voltage and unbalanced load condition is presented. This

algorithm is based on a non-linear optimisation technique and

does not use p-q or d-q transformation. This technique

considers harmonics in supply voltage for power factor

computation. It is more versatile and flexible and is

applicable to both single phase and multi-phase system with

linear, non-linear, balanced or unbalanced load conditions.


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The control signal is computed using TMS320LF2407A

DSP controller.

This paper is organized into the following sections. Section

I1 details basic concept of the proposed scheme. Section I11

presents the algorithm for the scheme under non-sinusoidal

supply conditions. The result of the computer simulations

using MATLAB is included in section IV. Section V details

conclusion.

I1

BASIC CONCEPTS

OF

THE PROPOSED STRATEGY

The block diagam of the proposed scheme is shown in

Fig.1. The power circuit of the scheme consists of a three-

phase non-sinusoidal supply voltage connected to an

unbalanced non-linear load.

Let the resulting three-phase supply voltage,

v,

contain a set

of harmonic components, n and n . For phase a,

and the corresponding unbalanced load current

i

contain a

set of harmonic current nl n3

where

aan

s the arbitrary angle of supply voltage and vans

the phase angle of nthharmonic component of current.

For unity power factor, currents drawn should be in phase

with, and

of

the same shape, as the source voltage. i.e.

y ~ , ,

0

and the harmonics in current and voltage are

of

the same

order and their ratios equal. However in this case, THD may

not be within the acceptable limit of the utility or power

quality norms. By controlling these harmonic ratios, THD can

be controlled but the power factor may deteriorate. In

general, the desired source current

ius

with displacement

angle set to zero, and making the order of harmonics in

source current same as that of supply voltage may be written

as:

*

(3)

l J

where,

I = K,,,.Va,.

Similarly for phase

b

and c

K ,

K b n K C n

he admittance of the compensating load,

are the control variable in phase a, b, and c respectively.

Therefore, the reference compensating current is calculated as

* .

:c

* *

* .

. *

iac

= ial - 1 , ; bc

= ib, -ibs lee

=IC

-1 ,

(4)

In the proposed scheme, a current source inverter is

connected in parallel with the load. The proposed algorithm

calculates the reference compensating current and generate

control pulses for the inverter using DSP. This compensating

current when injected into the system cancels the undesired

component of load current that are responsible for the low

power factor and high THD.

Fig. Block diagram

of

the proposed scheme

111

CONTROL STRATEGY UNDER N ON-SINUSOIDAL AND

UNBALAN CED CONDITIONS

Non- sinusoidal and unbalanced conditions are common in

a modern power system. In such conditions unity power

factor and power balance can be achieved by making the

source current identical in magnitude, in phase and of same

shape as that of voltage, in all phases. When the source

current is made to have the same shape as voltage, current

THD may not be with in the acceptable limit. To obtain

perfect harmonic compensation, current drawn

from

the

source need to be a perfect sine wave. In this case, unity

power factor is not obtained. By using the proposed optimal

strategy it is possible to optimise the power factor satisfying

power demand and harmonic limit. The relevant theory is

discussed below.

A . POWER UNDER NON-SINUSOIDAL

SUPPLY

AND

UNBALANCED

LOAD

CONDITIONS

When the supply voltage and unbalanced load current

contains harmonics, the complex apparent power is given by

the vector sum of active, reactive and distortion power. The

instantaneous power can be given as:

p t ) =

vu t).ja t ) Vb t).ib t ) vc t ) . i c

t )

p t ) = v t).i+ t )

+

v-

t).i-

t )

+

vo t).iO t )

5 )

These powers can be calculated by sequence component of

voltage and current as:

where

+,

0

0

represents positive, negative and zero

sequence components respectively.

Positive sequence component of power contains mean value

p +

and an alternating component

(p , )

with zero mean

value. Similarly negative sequence and zero sequence

6 )

-

-

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- -

components contain a mean value

p -

p o and an

alternating component(p - Po

- -

I

PO)

=

P+ +P++

P-+

P-+Po +Po

(7)

- - -

The average power is given by pdc = p + + p - + p o .

Load balancing can be achieved by sharing the average

power demand equally among each of the phases as shown in

Fig.2. The active filter supplies the balance power required

by the load.

Fig.

2

Power balance diagram

B. OPTIMSATION TECHNIQUE

Lagrangian-multiplier technique [11,121 is used to

optimise the non-linear equation for reactive volt-ampere

subject to equality and inequality constraints [101.

I. Objectivefunction

Let the order of harmonics in supply voltage and desired

source current be n. The objective is to minimise apparent

input Volt-Ampere, S in each phase and can be written as:

Optimisation is applied to minimise Sas with control

variable

Kan,

o that power factor is maximum in each phase.

II. Equality constraints

The desired source current in each phase is calculated in

such a way that, it should supply only mean value of

corresponding instantaneous real power demanded by the

load after compensation. The compensating circuit supplies

remaining power demanded by the load. Therefore the

equality constraints for phase

a

can be written as:

III. Inequality constraints

Let the total current harmonic distortion be limited to

THDiH

The inequality constraint is given by

The inequality constraint

U

can be written as:

IV. Lagrange

unction

The objective is to minimise

S,

subject to the equality

constraint and the inequality constraint given by

9)

and

1 1)

respectively. The augmented hnction L is given by:

(12)

where2 and p are constants. Using the necessary and

sufficient condition for constraint local minima of L he

unknowns can be found out. By using these unknowns the

reference source current for optimum power factor within

acceptable THD limit [131 is determined.

rV SIMULATION RESULT UNDER NON-SINUSOIDAL AND

UNBAL ANCED CONDITIONS

To verify the proposed theory under unbalanced

conditions, simulation studies have been carried out using

MATLAB

on a balanced three-phase, SO , 415V (rms.)

trapezoidal voltage power supply system (THD 2 1.8%) with

an unbalanced rectifier load of 30kW.

I I I

- - a

- b

400

-400

I I

002

0025

0

03

0

035 0 04

Fio 3 fa\

l i m e se c )

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4/5

Waveforms of non-sinusoidal supply voltage considered

for simulation is shown in Fig 3(a) and unbalanced load

current is shown in Fig.

3(b).

Calculated 3-phase source

current at 5% THD after the compensation is shown in Fig.

3(c) and waveform of computed compensating current is

shown in Fig. 3(d). This compensating current is the

reference current for the inverter.

I

I

I

0.04

-100

0 02

0025

o

0.035

F , ~ .(b) Time sec1

W

I I I

By using hysterisis control for the inverter, the sample

system is simulated. The optimised source current computed

and the source current obtained after compensation for

5

THD case is plotted in Fig. 4 (a). Fig 4 (b) shows the

waveforms of source voltage, load current and source current

for phase

a of

the system.

(- Reference I

0

I

0 02

50

0 005

0.01

0.015

Fig

4 a)

Time sec)

-100

I

I

0.m

0 025 0.03

0 035

0 04

Fig, 3 cl Time sec1

Fig 4. Waveform of reference and actual source current,

supply vo ltag e, load current and source current after compensation.

40

I

I

0.02 10 025 0 03 0.035 0 04

Fig 3 Wave forms o f supply v oltage, load current, reference source

current and compensating current

Fig

3(d)

fime sec)

It may be noted from above figure that the source current

after compensation follows the computed current very

closely. Current harmonics in phase a, before and after

compensation is shown in Fig. 5(a) and Fig. 5(b) respectively.

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V CONCLUSIONS

Phase Load Voltage Current Average

current THD (in THD (in power

60

50

40

Q

E

a

3 30

.-

20

10

0

Power

factor

1 e f t * . * . . . . . . .

2

4

6

8 10 12 14 16 18

Order of harmonics

a

b

c

Fig. 5(a) Harmonic spectrum of source current

in phase a before compensation

(A) p.u) p.u) (kW)

60.201 0.2027 0.202 14.774 1.007

37.338 0.2113 0.210

9.122 0.997

26.998 0.2120 0.211 6.599 0.997

0

2

4 6 8 10 12 14 16 18

20

Order of harmonics

Fig.

5 b)

Harmonic spectrum of source current

in

phase

a

after compensation

a

b

c

Summary of load current, voltage

THD,

current

THD,

average power and power factor is shown in Table 1.

Table 1.

Summary of measured values before and after compensation

42.099 0.2027 0.050

10.136 0.988

41.906 0.2113 0.050

10.136 0.987

41.898 0.2120

0.050

10.136 0.987

From the results of the simulation detailed in section IV, it

is evident that the proposed control strategy is well suited for

balancing the power system besides reactive and harmonic

compensation to optimise the power factor satisfying the

THD. The technique presented here is verified under

various conditions of input supply and load viz. linear, non-

linear and its combination under balanced and unbalanced

conditions. For implementation

of

the algorithm, a non-

sinusoidal

3

phase, 60 V , 50Hz supply source is made by

clipping of sine wave using diodes and batteries. Control

algorithm is developed by an inter list of assembly and C

language. The compensating current is injected into the

system using 3-phase inverter Semikron SKH160. This is

being implemented using

DSP

controller TMS320LF2407A.

REFERENCES

[I] V.E Wagner Effect of Harmonicson Equipment Report of IEEE Task

force

on

The effect of Harmonics on Equipment,

IEEE Transactions on

Power Delivery, Vo1.8, No.2, April 1993.

[2] F.Z.Peng, H.Akagi, A.Nabae A Novel Harmonic Power Filter

[3] Hirofumi Akagi New

trends

in Active Filters for Improving Power

Quality, Power

Electronic Drives and Energy System

or

Industrial Growth,

1996, Proceedin gs of 1996 Intemationa l conference Vol.1, pp. 417 -425.

[4]Hirofumi Akagi Trends in Active Power Line Conditioners IEEE

Transaction on Pow er Electronics,

Vo1.9, No. 3, May 1994,pp263-268

[5] Mauricio Aredes, Edson H. Watan abe New control algorithm for

series and shunt 3 phase 4 wire active power filters,

IEEE Tran sactions on

PowerDelivery,

VolO, No.3, July 19 95, pp. 1649-165 6.

[6] Juan W Dixon, Jaime J Garcia and Luis Moran Control System for

Three-phase Active Power Filter Which Simultaneously Compensates Power

Factor and Unbalanced Loads,

IEEE Transactions on Industrial Electronics,

Vo1.42, No.6, Decemb er 1995, pp. 636-641

[7] Cheng-Che Chen, Yuan-Yih Hsu A Novel approach to the design of a

shunt active filter for an unbalanced 3-phase 4-wire system under non-

sinusoidal condition,

IEEE Transactions

on

Power Delivery,

Vo15, No.4,

October 2000, pp. 1258-1264.

[8] Mauricio Aredes, Edson H. Watanabe New control algorithm for

series and shunt 3 phase 4 wire active power filters,

IEEE Transactions on

Power Delivery,

VolO, No.3, July 199 5, pp. 16 49-1656.

[9] S.Mohammad-Reza Rafiei, Hamid A. Toliyat, Reza Ghani and Tilak

Gopalarathnam An optimal and Flexible control strategy for active filtering

and power factor correction under non-sinusoidal line voltages

IEEE

Transactions on Power Delivevy,

Vo1.16, No.2, April 2001, pp. 297-30 5.

[IO] Sincy George, Vivek Ag ama l A Novel Technique for optimising the

Harmonics and Reactive Power under Non-sinusoidal voltage conditions,

Accepted for presentation in

IECONOZ,

o be held in November, 5-8,2002,

in Sevilla, Spain

[I I] A Ravindran, Don T. Phillips, James J. Solberg, Operations Research

Principles and Practice,

John Wiley Sons, pp. 524-542

[I21 Hadi Saadat,

Power System Analysis,

McGraw-Hill Company, pp.258-

266

[I31 IEEE Std 519-1992 IEEE Recommended Practice and Requirements for

Harmonic Control in Electrical Power Systems.

PESC88,April

1 9 8 8 , ~ ~151-I156

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