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WELCOME

04/11/23 1Dept. of EEE

Department of Electrical and Electronics EngineeringSREE VIDYANIKETHAN ENGINEERING COLLEGE

Sri Sainathnagar,A.Rangampet,Tirupathi-517102

OPTIMUM CONTROL OF SELECTIVE AND TOTAL HARMONIC DISTORTION IN CURRENT AND VOLTAGE UNDER

NON-SINUSOIDAL CONDITIONSBy

Y. JANAKI PRASAD Roll No:08121DO707

II M.Tech, IV semester

Under the esteemed guidance of Mr.D.Sreenivasulu Reddy, M.Tech.,

ASSISTANT PROFESSOR,Department Of E.E.E


To limit the TOTAL and SELECTIVE Harmonic

Distortion in current or voltage under

non-sinusoidal supply voltage and current

conditions, using shunt or series active filter.

OBJECTIVE


Introduction• Methods of reducing harmonics.• Dis-advantages.• Lagrange’s Multiplier Optimization Technique.• Current distortion limit for equipment.• Generation of non-sinusoidal voltage at PCC.

Proposed technique for total and selective harmonic control

CONTENTS


• Generalized tecnique for shaping the waveforms.

• Application of the technique to shape voltage (or) current.

Objective function Equality constraintsInequality constraintsLagrange’s function

Simulation diagrams and results.

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HARMONICS:

Harmonics are currents, usually in multiples of the

supply fundamental frequency, produced by ‘non-

linear’ loads such as the AC to DC power conversion

circuits. HARMONICS EFFECTS:

Reduction of efficiency of power generation,

transmission, and utilization.

Overheating and failure of electric motors.

Excessive measurement errors in metering

equipment.

INTRODUCTION

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Total Harmonic Distortion(THD)

• THD is an rms value of the distortion component of

the fundamental frequency current or voltage wave

due to harmonics.

( )

Sum of the squares of all harmonic currentsTHD

Square of the fundamental current

Methods of Reducing Harmonics

1.Instantaneous-reactive power method

2. Id-Iq method

3. Unity power factor method

4. Fictious-power-compensation method

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DISADVANTAGES OF ABOVE METHODS

It is only applicable for 3-phase balanced sinusoidal voltage.

The computation is instantaneous but incurs time delays in filtering the dc quantities.

This method is only suitable for combined systems of VAR and current harmonic compensation.

Minimization of source current RMS values is only done UPF method.

It involves a large amount of computation.Constant active power from the source is not

obtained from these methods expect instantaneous p-q method.


Lagrange's optimization technique is applicable to

shunt or series active filters under non-sinusoidal

supply voltage and current conditions to achieve the

following objectives.

1. Restricting the individual harmonic components of

source current or load voltage according to the

requirements.

2. Limiting the THD in current or voltage waveforms

according to the requirements.

3. Optimization of PF in conjunction with (1) and (2).

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LAGRANGES’s multiplier optimization technique

Advantages of the Lagrange’s optimization techniques:

Lagranges optimization tecnique does not use p-q

theory.

It is applicable to both single phase and three phase

systems under sinusoidal or non-sinusoidal supply

voltage and load condition.

Non-linear optimization technique is an effective method

to optimize the power factor and total harmonics

distortion.

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TABLE 1CURRENT DISTORTION LIMIT FOR EQUIPMENT (> 16 A PER PHASE)

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Contd…

Generation of nonsinsoidal voltage at the PCCNon linear loads draw non

sinusoidal currents from the

power system consequently

voltage drops are caused

across the transmission line

and transformer impedances.

This results in non

sinusoidal voltages in the

system.

When supply voltage is non

sinusoidal harmonics are not

perfectly reduced and does

not reach unity power factor

and vice versa. There is a

trade off between two in such

condition some optimization

technique incorporated in

the control strategy.

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LAGRANGES MULTIPLIER OPTIMIZATION TECHNIQUE FOR

CONTROL TOTAL AND SELECTIVE HARMONIC DISTORTION

Lagrangian multiplier technique is used to optimize the nonlinear equations for reactive volt-ampere subject to equality and inequality constraints.

This technique is generalized for shunt and series active filter for the compensation of SHD and THD in current and voltage by using the Lagrange multiplier optimization technique.

These technique also optimizes the PF while ensuring THD with in the specified limit in addition to selective harmonic control.

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Generalized Technique for Shaping the Waveforms x(t) and y(t) represent two nonsinusoidal waveforms

of different shapes with a certain phase angle between them

1

11

1sin2h

h thXtx

2

2

h

122h hthsinY2ty

……………1

……………2

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Xh1 and Yh2 RMS value of hth order harmonic component of x and y.

To shape y(t) the same as x(t), without any phase shift between them, the following conditions need to satisfied.

1. Similar order of harmonics should be present in both the waveforms x(t) and y(t).

2. Ratio of the rms value of each harmonic component of one waveform to the corresponding component in the other waveform should be equal.

3. Phase angles corresponding to similar harmonic components in the two waveforms should be zero.

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Contd…

y(t) should be modified to Ynew(t) as follows:

…….(3)

…….(4)

Where

…….(5)

By controlling the values of Kh the shape can be

controlled.

This concept is used to shape the current or voltage to the desired one.

1

11

1sin2h

newnew thYtyh

hhnew X.KYh

h

newh X

YK

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DESIRED CURRENT FROM SHUNT ACTIVE FILTER

Shunt active filter is used for limiting the SHD and THD in current.

The desired source current (i*des) is obtained from vs(t) and

is (t) by setting h = 0.

)8(sinsin21 2

2111 1

221*

h h

hdeshdesdes thIthIihh

shshuntdes VKIhh.

is a control variable admittance of the hth-order harmonic component.

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hshuntK

1 3

3h11h

h

1

h

13h3desh1des

*des thsinIthsinV2v

hdesV shseries I.K

h

DESIRED VOLTAGE FROM SERIES ACTIVE FILTER

series AF can be used for the compensation of voltage harmonics.

The desired load voltage (v*des) is obtained that the current

is(t) is in phase with supply voltage vs(t) by setting n= 0.

(9)

is a control variable impedance of the hth-order

harmonic component.04/11/23 19Dept. of EEE

hseriesK

Lagrangian-multiplier technique is used that optimizes the PF while limiting the SHD and THD in current or voltage.

According to the Lagrange optimization technique, an augmented Lagrange function can be written as

L = f + g + µu + w + y + z+… (10)

Objective Function (f):

PF can be improved by minimizing the total apparent input power S.

S is the objective function in case of both series and shunt Active Filters.

Where

(11)

rmsrms I.VS

h

hrms VV1

2 h

1

2hrms II

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h

1

h

1

2sh

2shunt

2sh

2shunt .VKVSf

h

h

1

h

1

2sh

2series

2sh

2series .IKISf

h

Objective function (fshunt) for shunt AF is given by

Objective function (fseries) for series AF is given by

………12

………13

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Equality Constraint: It states that relationships should exactly match a resource value.These are more

difficult to handle and therefore need to be avoided whenever possible. Necessary condition to form equal constrained (g) is mean value of instantaneous

power demand before and after compensation should be equal. Mean value of the instantaneous real power with shunt active filter is given by

(14)

Pdc is the power demand which supplies for compensation.

h h

shuntshhdesshdc hKVIVP

1 1

2 ..

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01

2 h

shuntshdcshunt hKVPg

h

1series

2shdcseries .0KIPg

h

For a shunt active filter, equality constraint (gshunt) is given by

(15)

For a series active filter, equality constrained (gseries) is given by

(16)

INEQUALITY CONSTRAINT:

It states the relationships among design variables are either greater than, smaller than or equal to a resource value.

There are two inequality constraints:

1) Total harmonic distortion.

2) Selective harmonic distortion.

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Total harmonic distortion: THD is the rms value of distortion component of the

fundamental frequency current (or) voltage due to harmonics.

THD limit in current be ITHD

221

2

2

THDs

h

des

II

I

2THD2

1s2shunt

h

2

2sh

2shunt

IVK

Vk

1

h

h

2

2sh

2shuntshunt VKu

h 0VKI 21s

2shunt

2THD 1

0IKVIKu 21s

2series

h

2

2THD

2sh

2seriesseries 1h

The inequality constraint for shunt active filter (fshunt) is

The inequality constraint for series active filter (fseries) is

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(19)

(20)

Selective harmonic distortion

SHD is the ratio of magnitude of the corresponding harmonic component to the fundamental component of the current.

SHD limit in current be ISHD

0.1 nSHDssn III

0I.V.KV.Kn1n SHD1sshuntsnshunt

Inequality constraint for shunt active filter

nSHDs

sn II

I

1

0... 11

nnSHDsshuntsnshuntshunt IVKVKW

0... 11

nnSHDsseriessnseriesseries VIKIKW

Inequality constraint for series active filter

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(21)

(22)

(23)

h

1

h

1h

2hdc

2h

2h

h

1

2h KXPXKXL

h

1

21

21

2lim

2h

2h XKTHDXK.µ

lim11hh SHD.X.KX.K

Lagrange Function: The objective is to minimize S, given the equality constraint g = 0

and the inequality constraints u0, and w 0.

In order to shape x(t) to a desired value, using x(t) and ynew(t), the

augmented function is written as

(24)

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PROBLEM:

• Balanced 3-phase,4-wire,415V,50HZ,trapezoidal voltage supply, having 21.02%THD and 20.5% third harmonic distortion is considered.

• To verify the performance of the algorithm, simulation studies have been carried out for two cases.

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Case1: To limit THD and SHD in current by using shunt active filter.

Case2: To limit THD and SHD in voltage using series active filter.

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Contd…

• Total harmonic distortion (ITHD) is limited from 21.48% to 16% and fifth harmonic distortion(I5sHD) is limited from 16.83% to 14% by using a shunt active filter .

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CASE 1

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Reducing the harmonics by using shunt active filter

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Lagrange’s multiplier technique applied for

shunt active filter

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Generating pulses

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Output of case 1

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V,I

time

Waveform of supply voltage and load current

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Waveforms of supply voltage,source current and load current

Is

Il

time

Vs

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Before Compensation

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After compensation

Reducing harmonics by using series active filterCase2

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Lagrange’s multiplier technique applied for

series active filter

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Generating pulses

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Output of case2

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Waveforms of supply voltge and load voltage

Vs

time

VL

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Power factor of before and after compensation

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Before compensation

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After compensating

Comparison of power factor and voltage THD before and after compensation

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compensation Voltage THD(%) 3rd harmonic distortion(%)

Power factor

Before compensation 21.02 20.5 0.9397

After compensation 8.0 5 0.9677

• Total and individual harmonic distortion is limited and optimizes the power factor under non-sinusoidal supply voltage and current conditions by using shunt or series active filter.

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CONCLUSION

Future Scope

• Use of hybrid active filters in place of conventional active filters will improve the power factor and limit the Total Harmonic Distortion(THD) and Selective Harmonic Distortion(SHD).

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1. Sincy George and Vivek Agarwal, “Optimum Control of Selective and Total Harmonic Distortion in Current and Voltage Under Non-sinusoidal Conditions“ IEEE Trans. Power Del., Vol.23, no.2, pp.937-944, APRIL 2008.

2. H. Akagi and H. Fujita, “A new line conditioner for kharmonic compensation in power systems,” IEEE Trans. Power Del., vol.10, no.3, pp.1570-1575, Jul, 1995.

3. F.Z. Peng, “Application issues of active power filters,” IEEE Ind. Appl. Mag., vol.4, no.5, pp. 21-30, Sep./Oct.1998.

4. V.E. Wagner, “Effect of harmonics on equipment,” IEEE Trans. Power Del., vol.8, no.2, pp.672-680, Apr. 1993.

5. A. Cavallini and G.C. Montanari, “Compensation strategies for shunt active-filter control,” IEEE Trans. Power Electron., vol.9, no.6, pp.587-593, Nove.1994.

6. S. George and V. Agarwal, “A novel technique for optimising the harmonics and reactive power under non-sinusoidal voltage conditions”, in Proc. 28th Annu. Conf. IEEE Industrial Electronic Society, 2002,pp.858-863.

REFERENCES

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Contd…7. IEEE Recommended Practice for Powering and Grounding Sensitive

Electronic Equipments, IEEE Std. 1100-1992.

8. IEEE Recommended Practice for Electric Power Distribution for IndustrialPlants, IEEE Std. 141-1993.

9 . M. S. Lancarotte and A. de A Penteado, Jr., “Estimation of core lossesunder sinusoidal or non-sinusoidal induction by analysis of magnetizationrate,” IEEE Trans. Energy Convers., vol. 16, no. 2, pp. 174–179,Jun. 2001.

10. Electromagnetic Compatibility (EMC)—Part 3–4 Limits—Limitationof Emission of Harmonic Current in Low-Voltage Power Supply Systemsfor Equipment With Rated Current Greater Than 16 A, IEC Std.61000-3-4-1998.

11. IEEE Recommended Practice and Requirements for Harmonic Controlin Electrical Power Systems, IEEE Std. 519-1992.

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