a novel technique for sing harmonics and reactive power with load

8/9/2019 A Novel Technique for sing Harmonics and Reactive Power With Load

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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, IEEEDepartmentof Electrical Engineering,

Indian Institute of Technology -Bombay,Powai, Mumbai - 400 076, India

sincy@ee. itb.ac.in

Abstract: Generally, conventional power factor correctionstechniques assume ideal conditions, viz. sinusoidal supplyvoltage and balanced load. But vast majority of the domesticand industrial loads present in the power distribution system arenon-linear and unbalanced. Under such conditions, attempt tomake the power factor unity result into a non-sinusoidal sourcecurrent, which increases total harmonic distortion (THD) in thesystem. On the other hand attempt to make harmonic freecurrent may not result in unity power factor because of theharmonics present in the supply voltage. Thus, there is a tradeoff between improvement in power factor and reduction inTHD. With the introduction of power quality norms by variousutilities, it has become unavoidable to optimize power factorwhile satisfying harmonics limits. I n this paper, a noveltechnique for optimisation of THD and power factor subject topower quality constraints is presented. The algorithm usesLagrange multiplier technique to optimise the non-linearequations. The algorithm calculates the control coefficients byNewton Raphson method and is used to compute the desiredsource current that balances the system besides optimisingpower factor satisfying the load power while meeting the THDlimits. Knowing the load current, the compensating current tobe supplied by the shunt active power filter to the power systemis calculated. This technique, besides satisfying the powerquality norms, also balances the imbalance in the system. It isapplicable for single-phase and multi-phase system undersinusoidal and non-sinusoidal supply conditions. The proposedscheme does not use the widely used p-q theory and use simplecomputational techniques. Simulation using MATLAB hasshown encouraging results. The scheme is being implemented inhardware using DSP.

Key words: Power Quality and Harmonics, Power factorcompensation, Active Power Filters, DSP Control.

LINTRODUCTION

In electrical power distribution system, most of the loadsare inductive in nature. Residential loads and vast majority ofother single-phase loads cause imbalance in the system. The

increased uses of power electronic devices also impair powerquality in the grid. These non-linear loads draw non-sinusoidal currents from the system consequently voltagedrops are produced across impedances of transmission line,transformer and generator causing non-sinusoidal voltages inthe system. This distorted voltage affects other linear or non-linear loads connected to the system. Effect of these

Vivek Agarwal, Member, IEEEDepartment 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 electronicequipment is explained in various papers [l ].

Harmonic contents vary randomly and consequently theconventional compensating techniques such as the use ofpassive LC filters to perform harmonic reduction areineffective [2]. Due to this many types of active filters havebeen developed to compensate current and or voltageharmonics viz. shunt active filter, series active filter or

combination of both [2-51. Controlling the injection ofcurrent harmonic by the non-linear load can eliminate non-sinusoidal operation of the system. This can be achieved bythe installation of shunt active filters. In this technique, acurrent source inverter is connected in parallel with the load.This injects compensating current into the system to cancelthe undesired components of load current that are responsiblefor harmonics and low power factor.

The quality and performance of these filters mainly dependon the method used to generate the reference current forcompensation [6]. Most of these methods use p-q or d-qtransformation theory and assume a sinusoidal supplyvoltage. Control methods adopted by others [7,8] assume anon-sinusoidal supply, but use only positive sequence voltage

at the fundamental frequency to generate sinusoidalreferences to ensure that the supply current is harmonic freeand power factor is unity. However, when the supply voltageis non-sinusoidal, perfect harmonic compensation (PFC) doesnot result into unity power factor (UPF) and vice versa. Insuch conditions, non-linear optimisation technique [9,IO] isfound to be an efficient method to optimise the power factorand total harmonic distortion (THD) satisfying the powerquality norms or guidelines. The method adopted in [9] alsouses p-q theory and is not applicable to single-phaseconditions. Also most of the proposed active filters are basedon analogue implementation.

In this paper, an improved control algorithm for thereference current to the inverter under non-sinusoidal supply

voltage and unbalanced load condition is presented. Thisalgorithm is based on a non-linear optimisation technique anddoes not use p-q or d-q transformation. This techniqueconsiders harmonics in supply voltage for power factorcomputation. It is more versatile and flexible and isapplicable to both single phase and multi-phase system withlinear, non-linear, balanced or unbalanced load conditions.

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The control signal is computed using TMS320LF2407ADSP controller.

This paper is organized into the following sections. SectionI1 details basic concept of the proposed scheme. Section I11presents the algorithm for the scheme under non-sinusoidal

supply conditions. The result of the computer simulationsusing MATLAB is included in section IV. Section V detailsconclusion.

I1 BASIC CONCEPTS OF THE PROPOSED STRATEGY

The block diagam of the proposed scheme is shown inFig.1. The power circuit of the scheme consists of a three-phase non-sinusoidal supply voltage connected to anunbalanced non-linear load.

Let the resulting three-phase supply voltage, v, contain a set

of harmonic components, nl and n2 . For phase a,

and the corresponding unbalanced load current i contain a

set of harmonic current nl ,n3

where aans the arbitrary angle of supply voltage and vansthe phase angle of nthharmonic component of current.

For unity power factor, currents drawn should be in phasewith, and of the same shape, as the source voltage. i.e. y ~ , , 0

and the harmonics in current and voltage are of the sameorder and their ratios equal. However in this case, THD may

not be within the acceptable limit of the utility or powerquality norms. By controlling these harmonic ratios, THD canbe 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 insource current same as that of supply voltage may be writtenas:

*

(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 = ia l - 1 , ; bc = ib, -ibs 'lee’ =IC1 -1 , (4)

In the proposed scheme, a current source inverter isconnected in parallel with the load. The proposed algorithm

calculates the reference compensating current and generatecontrol pulses for the inverter using DSP. This compensatingcurrent when injected into the system cancels the undesiredcomponent of load current that are responsible for the lowpower factor and high THD.

Fig.1 Block diagram of the proposed schem e

111CONTROL STRATEGY UNDER NON-SINUSOIDAL AND

UNBALAN CED CONDITIONS

Non- sinusoidal and unbalanced conditions are common ina modern power system. In such conditions unity powerfactor and power balance can be achieved by making thesource current identical in magnitude, in phase and of sameshape as that of voltage, in all phases. When the sourcecurrent is made to have the same shape as voltage, currentTHD may not be with in the acceptable limit. To obtainperfect harmonic compensation, current drawn from thesource need to be a perfect sine wave. In this case, unitypower factor is not obtained. By using the proposed optimal

strategy it is possible to optimise the power factor satisfyingpower demand and harmonic limit. The relevant theory isdiscussed below.

A . POWER UNDER NON-SINUSOIDAL SUPPLY AN DUNBALANCED LOAD CONDITIONS

When the supply voltage and unbalanced load current

contains harmonics, the complex apparent power is given bythe vector sum of active, reactive and distortion power. Theinstantaneous 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 zerosequence 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 averagepower demand equally among each of the phases as shown inFig. 2. The active filter supplies the balance power requiredby the load.

Fig.2 Pow er balance diagram

B. OPTIMSATION TECHNIQUE

Lagrangian-multiplier technique [11,121 is used tooptimise the non-linear equation for reactive volt-amperesubject to equality and inequality constraints [101.

I. Objectivefunction

Let the order of harmonics in supply voltage and desiredsource current be n. The objective is to minimise apparentinput Volt-Ampere, S, in each phase and can be written as:

Optimisation is applied to minimise Sas with controlvariableKan, o that power factor is maximum in each phase.

II. Equality constraints

The desired source current in each phase is calculated insuch a way that, it should supply only mean value ofcorresponding instantaneous real power demanded by the

load after compensation. The compensating circuit suppliesremaining power demanded by the load. Therefore theequality constraints for phase a can be written as:

III. Inequality constraints

Let the total current harmonic distortion be limited toTHDiH,, 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 equalityconstraint 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 , heunknowns can be found out. By using these unknowns thereference source current for optimum power factor withinacceptable THD limit [131 is determined.

rV SIMULATION RESULT UNDER NON-SINUSOIDAL AND

UNBAL ANCED CONDITIONS

To verify the proposed theory under unbalancedconditions, simulation studies have been carried out usingMATLAB on a balanced three-phase, SO&, 415V (rms.)trapezoidal voltage power supply system (THD 2 1.8%) withan unbalanced rectifier load of 30kW.

I I I - - a

- b

400

-400 I 1 I

002 0025 0 03 0 035 0 04

Fio 3 fa\

l i m e (sec)

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Waveforms of non-sinusoidal supply voltage consideredfor simulation is shown in Fig 3(a) and unbalanced loadcurrent is shown in Fig. 3(b). Calculated 3-phase sourcecurrent 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 thereference current for the inverter.

I II I I

0.04-1000.02 0025 o m 0.035

F , ~ .(b) Time (sec1

1W I I I

By using hysterisis control for the inverter, the samplesystem is simulated. The optimised source current computedand the source current obtained after compensation for 5%THD case is plotted in Fig. 4 (a). Fig 4 (b) shows thewaveforms of source voltage, load current and source currentfor phase a of the system.

(- Reference I0

I

0.0250

0.005 0.01 0.015Fig 4(a) Time (sec)

-100I I0.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 ltage , load current and source current after compensation.

-40 I I

0.02 10.025 0.03 0.035 0.04

Fig 3 Wave forms of supply voltage, load current, reference source

current and compensating current

Fig 3(d) fime (sec)

It may be noted from above figure that the source currentafter compensation follows the computed current veryclosely. Current harmonics in phase a, before and aftercompensation is shown in Fig. 5(a) and Fig. 5(b) respectively.

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V CONCLUSIONS

Phase Load Voltage Current Averagecurrent THD (in THD (in power

60

50

40

Q

E

a3

3 30.-

20

10

0

Powerfactor

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 currentin 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 currentin phase a after compensation

a

bc

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 0.98841.906 0.2113 0.050 10.136 0.98741.898 0.2120 0.050 10.136 0.987

From the results of the simulation detailed in section IV , itis evident that the proposed control strategy is well suited forbalancing the power system besides reactive and harmonic

compensation to optimise the power factor satisfying theTHD. The technique presented here is verified undervarious conditions of input supply and load viz. linear, non-linear and its combination under balanced and unbalancedconditions. For implementation of the algorithm, a non-sinusoidal 3 phase, 60 V , 50Hz supply source is made byclipping of sine wave using diodes and batteries. Controlalgorithm is developed by an inter list of assembly and Clanguage. The compensating current is injected into thesystem using 3-phase inverter Semikron SKH160. This isbeing implemented using DSP controller TMS320LF2407A.

REFERENCES

[I] V.E Wagner “Effect of Harmonics on Equipment” Report of IEEE Task

force on Th e effect of Harmonics on Equipment, IEEE Transactions onPower 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 PowerQuality“, Power Electronic Drives and Energy System or Industrial Growth,

1996, Proceedin gs of 1996 Intemational conference Vol.1, pp. 417 -425.[4]Hirofumi Akagi “Trends in Active Power Line Conditioners” IEEETransaction on Pow er Electronics, Vo1.9, No. 3, May 1994,pp2 63-268[5] Mauricio Aredes, Edson H. Watan abe “New control algorithm forseries and shunt 3 phase 4 wire active power filters”, IEEE Tran sactions onPowerDelivery, VolO, No.3, July 1995, pp. 1649-165 6.[6] Juan W Dixon, Jaime J Garcia and Luis Moran ”Control System forThree-phase Active Power Filter Which Simultaneously Compensates Power

Factor and Unbalanced Loads”, IEEE Transactions on Industrial Electronics,Vo1.42, No.6, Decem ber 19 95, pp. 636-6 41[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 onPower Delivery, VolO, No.3, July 1995 , 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 filteringand power factor correction under non-sinusoidal line voltages” IEEE

Transactions on Power Delivevy, Vo1.16, No.2, April 2001, pp. 297-305.[IO] Sincy George, Vivek Ag ama l “A Novel Technique for optimising theHarmonics and Reactive Power under N on-sinusoidal voltage conditions”,Accepted for presentation in IECON’OZ, o be held in November, 5-8,2002,in Sevilla, Spain[I I] A Ravindran, Don T. Phillips, James J. Solberg, Operations ResearchPrinciples 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.

PESC’88,April 1 9 8 8 , ~ ~151-I156

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a novel technique for sing harmonics and reactive power with load

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