05462950genetic-algorithm-based design of passive filters

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 46, NO. 4, JULY/AUGUST 2010 1295

Genetic-Algorithm-Based Design of Passive Filtersfor Offshore Applications

Vishal Verma, Member, IEEE, and Bhim Singh, Fellow, IEEE

Abstract—With the proliferation of power electronics convert-ers and increased use of magnetics, power lines have becomehighly polluted. Both passive and active filters have been used nearharmonic-producing loads or at the point of common couplingto mitigate/block current harmonics. Shunt filters still dominatethe harmonic compensation at medium/high voltage level, whereasactive filters have been proclaimed for low/medium voltage rat-ings. With diverse applications involving reactive power togetherwith harmonic compensation, passive filters are found suitable.For offshore platforms, having multiple variable frequency drivesfor oil exploration and the power fed through submerged powercable reduces the reactive power requirement in the power system.Under such reduced reactive power requirement, the design ofpassive filter conforming to the IEEE 1531 standard is presentedin this paper. This paper utilizes genetic algorithm technique todesign the tuned harmonic filters to compensate current harmon-ics together with limited reactive power compensation. The mainidea behind the design is minimization of net source rms currentwith insertion of a passive filter. The formulation thus becomes acombinational optimization system with nondifferentiable objec-tive function. Other environmental and operational constraints arealso incorporated in the design technique to ensure their effectiveperformance. The performance and operation of the so-designedpassive filter has been studied through simulation under MATLABenvironment.

Index Terms—Harmonic compensation, harmonic filters, pas-sive filter, tuned filters, variable-frequency ac motor drive.

I. INTRODUCTION

POWER SYSTEM harmonics are a menace to electricpower systems with disastrous consequences. The line

current harmonics cause increase in losses, instability, and alsovoltage distortion when these harmonics travel upstream andproduce drop across line impedance [1]. Situation becomesmore critical when the power system is for offshore oil field,where the stiffness in the supply is never achieved [1]–[3]. Un-der such condition, voltage harmonics are more severe and aremore damaging to a variety of linear and nonlinear loads. Dueto distortion in voltage, even linear loads attached to the point of

Manuscript received February 18, 2009; revised July 7, 2009; acceptedOctober 17, 2009. Date of publication May 10, 2010; date of current versionJuly 21, 2010. Paper 2009-PCIC-008.R1, presented at the 2004 IEEE PCI IndiaConference, New Delhi, India, November 9–10, and approved for publicationin the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Petroleumand Chemical Industry Committee of the IEEE Industry Applications Society.

V. Verma is with the Department of Electrical Engineering, Delhi College ofEngineering, Delhi 110042, India (e-mail: [email protected]).

B. Singh is with the Department of Electrical Engineering, Indian Instituteof Technology Delhi, New Delhi 110016, India (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIA.2010.2049629

common coupling (PCC) are also treated to be derated. Typesof filters designed by different constraints have been reportedand tried to compensate the harmonics produced by nonlinearloads along with reactive power compensation. However, by far,among the passive and active filters, the passive filters remainedpopular and effective for offshore applications due to their lowcost, rugged structure, and higher efficiency [13]. Moreover,these filters do not deteriorate the PCC on account of thevoltage distortions. As reported in literature, passive filters aredesigned to incorporate harmonic compensation and reactivepower minimization [3]–[10]. However, passive filters designedfor consideration to minimize reactive power are actually nota major constraint for offshore application, as the submergedcable used for power transmission in offshore areas offersa capacitive reactance [3]. This additional capacitive reactivepower mitigates the lagging reactive power requirement offeredby thyristorized dc and ac drives, transformers, and other loadsof similar type. Some schemes have reported that passive filtersoperate such that damping and attenuation of harmonics whichare amplified due to series and parallel resonances (occurringbetween the line and capacitive impedances of passive filtersor capacitive impedance of the submerged cable and inductiveimpedance of transformer and inductance of passive filters) canbe achieved. Majority of applications at offshore petrochemicalindustries demand variable speed operation of motors. Thus,variable frequency drives (VFDs) have replaced the previouslyexisting conventional drives [1]–[3]. These VFDs have high dis-placement factor, and the requirement of lagging reactive powerby other thyristorized drives may be partially/fully quenchedby the leading reactive power provided by the submerged cablefor power transmission for offshore system [3]. Therefore, theadditional capacitive reactance offered by passive filters forcesthe system to draw more current from generator units. Thiscapacitive current creates problems of voltage regulation in thepower system. In addition to this, the increased rms currentincreases losses and derates the system. Therefore, there is aneed to change the design parameter of passive filters usedfor offshore power systems. Such a design needs to minimizethe additional capacitive reactance by forcing the system tohave minimum rms current as design parameter. To circumventthe problem of resonance, the design of passive filters has tobe done for dedicated application with the VFD unit, whichgets switched off along with the drive [2], [4]. The design ofsuch passive filter has to be done by optimizing the value ofcapacitance in the passive filter so that the criterion of minimumrms line current is achieved. This design shifts the range offrequencies undergoing resonance due to the capacitance ofthe cable with inductance of the passive filter, far away in the

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1296 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 46, NO. 4, JULY/AUGUST 2010

higher side of harmonic spectrum. In a nutshell, the designreduces the problem that is very much predominant in offshorepower systems. Thus, minimization of harmonics and supplyrms current has been adopted as the design parameters forpassive filters designed for dedicated applications with VFDsin accordance with IEEE-1531 [4].

Instead of the conventional design of the filter which hasbeen based on the experiences of the designer, the optimizationmethod to obtain improved performance from the filter maybe used instead. The traditional optimization methods mayundergo a step-by-step searching algorithm which locates thelocal optima, whereas genetic algorithms (GAs) with the abilityof parallel searching through the entire solution space can giveglobal optima [11]–[15]. By using GAs, designers can quicklyfind appropriate parameter values to meet the desired passivefilter performance as it reduces the number of calculations incomparison to the existing methods. At the same time, GAs areable to handle many constraints simultaneously, which are notdone at ease with other reported algorithms [11], [14], [15].

The objective of this paper is to propose a new approachfor passive filter design particularly for offshore petrochemicalindustries having a large number of VFDs. A new designmethodology using GAs is proposed in this paper which cangive a near-optimum solution. The optimization process isbased on the design of the passive filter for minimization ofharmonic contents and rms line current simultaneously. Theproposed design also considers the detuning effects due thetemperature and frequency variation, as well as manufacturingtolerances.

The proposed design is simulated under the MATLAB envi-ronment. Simulation results show that the filter designed by theproposed GAs can meet the desired power quality requirement.Moreover, parameters such as harmonics, reactive power, rmscurrent, and cost are all minimized, giving the full utilization ofan existing power system. Different cases of design examplesare shown in this paper to verify the performance of theproposed design methodology.

II. GENETIC ALGORITHM

GA utilizes a stochastic global search method based onthe principle of natural selection and genetically developedoffsprings [13], [15]. GA operates on a population of poten-tial solutions in accordance with Darvin’s “survival of thefittest” hypothesis to produce better and better approximationto a solution. Prior to the beginning of GAs, the individuals,or current approximations, are encoded as strings, known aschromosomes, composed over some alphabet(s), so that thegenotype(chromosome value) is uniquely mapped on the de-cision variable (phenotypes) domain. Each chromosome mayrepresent a possible solution to the problem and consists of aseries of genes, represented by binary codes. The set of suchchromosomes forms the basis of population of the next gen-eration. In GA, the chromosomes in a generation are forced toevolve into a better next generation on the basis of reproduction,crossover, and mutation, along with fitness function [12]–[15].

1) Reproduction: It deals with the process of selection of thefittest chromosomes that get inherited in the offspring. It

Fig. 1. Three basic operators of GAs. (a) Reproduction. (b) Crossover (“c” isthe crossover point). (c) Mutation (“m” is the mutation point).

determines the number of times a particular individualis chosen for reproduction and, thus, the number ofoffsprings that an individual will produce.

2) Crossover: Crossover swaps the chromosomes of ran-domly selected subsection of parents to produce off-springs.

3) Mutation: In mutation, randomly selected genes of theparent chromosomes are altered by a probability deter-mined by mutation rate. Fig. 1 shows the schematicillustration of aforesaid GA operations on chromosomeswith 8-b genes.

The objective function describes the methodology to demar-cate the bad chromosomes out of the lot and to select the fittestfor the reproduction. The fitness function is normally usedto transform the objective function into a measure of relativefitness [15]. Thus,

F (x) = g {f(x)} (1)

where f is the objective function, g transforms the value ofthe objective function to a nonnegative number, and F is theresulting relative fitness. Only a certain number of chromo-somes are selected according the fitness function value andare passed to the next generation. The termination of GA iscommonly done after a prespecified number of generations andthen test quality of the best member of the population againstthe problem definitions.

GA differs substantially from traditional search and op-timization methods. The most significant differences are asfollows.

1) GAs search a population of points in parallel, not a singlepoint.

2) GAs do not require derivative information or other aux-iliary knowledge; only the objective function and corre-sponding fitness levels influence the directions of search.

3) GAs use probabilistic transition rules, not deterministic.4) GAs work on an encoding of the parameter set rather

than the parameter set itself (except in where real-valuedindividuals are used).

VERMA AND SINGH: GENETIC-ALGORITHM-BASED DESIGN OF PASSIVE FILTERS FOR OFFSHORE APPLICATIONS 1297

Fig. 2. System configuration.

III. PROBLEM FORMULATION

The objective is to find an optimal selection of componentsof passive filter dedicated for each VFD shown in Fig. 2 sothat the total harmonic distortion (THD) of the source currentgets minimized along with minimized sinking of fundamentalfrequency current through the filter section. The dedicatedfilters are in accordance with IEEE 1531 standard for the designof harmonic filters. The configuration enables the system toreduce net voltage distortion at the PCC due to a very lowimpedance path provided by these harmonic filters. Even fornonstiff power system, voltage distortion can be minimized,which, of course, is very prominent in the offshore systems.The design has been carried out by GA, which optimizes thesolution for multiple constraints. The objective function alsoensures the optimal solution to fulfill various operational andenvironment constraints.

A. System Configuration

The filter harmonic admittance (in per unit) for a first-orderseries single tuned passive filter is represented as follows [5]:

YFmh =∑

n=5,7

QFh

V 2

[h(n2

h − 1)h2 − n2

h

](2)

where QFh represents the filter capacity, h represents theharmonic index, and nh is the filter resonant point. The filteradmittance (in per unit) for a second-order high-pass filter(HPF) with corner frequency as the 11th harmonic frequencycan be represented as [5]

Y ′F11h =

1[hR2

11XL

R211+(hXL)2

− XC

h

] (3)

where

XC =V 2n2

h

QF11h (n2h − 1)

(4)

XL =XC

n2h

. (5)

Since the value of admittance due to resistive portion ofimpedance is very small, it has been neglected for the currentdesign purpose.

Therefore, the net admittance offered by a filter bank consist-ing of series tuned filters at resonant points n5 and n7, together

Fig. 3. Equivalent circuit for any hth order harmonic distortion where h =5, 7, . . ..

with a second-order damped HPF, is given by

Y ′′Fmh = YFmh + Y ′

F11h. (6)

The equivalent source admittance Ysh shown in Fig. 3 cor-responds to the admittance offered by the source, the cable,and the transformers in the line. Ih represents the current at hthharmonic frequency from the load which is acting as a harmoniccurrent source in the aforementioned equivalent circuit. Ihh

represents the harmonic current for which the passive filtersare designed during test conditions, and Ish represents theharmonic current data corresponding to source current duringtest conditions. Therefore, the harmonic current I ′sh escapingto the source side at the PCC can be represented as

I ′sh = Ish ×(

Ih

Ihh

). (7)

Equation (5) can further be expressed in a more generalizedform that is valid for any number of filters by the followingequation:

I ′sh =Ysh × Ih

Ysh + Y ′′Fmh

. (8)

The main goal is to minimize I ′sh, which is subjected to thesystem constraints.

B. System Constraints

With the minimization of net harmonic current flow towardthe source side, determined by minimizing the harmonic fil-ter impedance, as compared to the source impedance, andmaximizing the filter impedance at fundamental frequency,the addition of a passive filter would result in the net rmscurrent reduction, due to more reduction in harmonic currentcontents in the source currents than an increase of fundamentalfrequency current sinking in the passive filters.

1) Minimizing Harmonic Source Current: The harmoniccurrent minimization is the prime objective of the algorithm.The minimization of harmonic current has been ensured byminimizing the net harmonic current contents in the sourcecurrent. This can be represented by a summation of all harmoniccurrent contents at different harmonic frequencies as

I ′h =√ ∑

h=5,7,...

(I ′sh)2. (9)

2) Minimizing Fundamental Current in Passive Filters: Theconstraint of maximizing the passive filter impedance at funda-mental frequency is given by

Max.

[ |Z1|γ

]or Min.

[γ · 1

|Z1|]

(10)


Fig. 4. Impedance–frequency plot of the designed set of passive filters of oneof the phases.

where γ is a multiplication factor (≥ 1) that represents thesensitivity of the filter to the influence of the impedance atfundamental frequency.

C. Reactive Power

The other operational constraint is to accumulate a reserveof reactive power for stable operation of the power system. Thesummation of the filter’s reactive power has been kept equal orless than the total reactive power compensation required for thesystem ∑

m=5,7,11...

QFm = Qc (11)

where m denotes the filter legs tuned at resonant points.The impedance versus frequency characteristic of optimally

designed single tuned passive filter incorporating all the systemconstraints is shown in Fig. 4.

D. Environment Conditions

The environment conditions play an important role in thedetermination of the smooth operation of filters while in oper-ation. It therefore becomes mandatory to evaluate the passivefilter performance due to changes in environment conditionsbefore installation of filters as per IEEE 1531 standard [4]. Thefollowing section deals with the evaluation of the design underchanges in frequency, capacitance, and inductance of the filterbanks. Frequency variation in power system is reported to beabout ±1% [8]

−1% <Δf

f< +1%. (12)

The capacitors change their values due to temperature andtolerance specified by the manufacturing process. It has a ±2%error due to the change of temperature and 0% ∼ +10% errordue to manufactures. Therefore, the total errors that can beincorporated against manufacture can be given, for capacitance,as [4]

−2% <ΔC

C< +12% (13)

and, for the inductance, as [4]

−3% <ΔL

L< +3%. (14)

The common resonant point of the filter bank unit consistingof series tuned filter of fifth and seventh harmonic frequen-cies and HPF at 11th harmonic frequency corner frequency isgiven by

nh =1

2πf√

LC. (15)

From the aforementioned considerations, the possible re-gion of variation of the common resonant point nh can beexpressed as

h

1.01 ×√1.03 × 1.12

<nh <h

0.99 ×√0.97 × 0.98

0.92h <nh < 1.036h. (16)

For h = 5, the variation of the resonant point would be de-fined between 4.60 < n5 < 5.18. The variation in the resonantpoint indicates the range within which harmonic over load offilter is possible due to series resonance. It means that, to designa filter suppressing the fifth-order harmonic, a compromise hasto be made on detuning the filter to avoid series resonance dueto distorted mains.

E. Constitution of Objective Function for GA

Incorporating the main objective, i.e., minimization of har-monic currents in mains along with the system constraintsof maximizing the filter impedance at fundamental frequencyand net reactive power requirement, constitutes the objectivefunction as

ObjF =√ ∑

h=5,7,11

(I ′sh + αP1 + βP2)2 (17)

where

P1 =[γ · 1

|Z1|]

(18)

P2 =

(Q −

∑m=5,7,11,...

QFm

)2

(19)

represent the penalty functions P1 and P2 for maximization/minimization of constraints described in (10) and (11). Thevalues of these penalty functions depend upon the degree towhich constraints are violated. α and β, the multiplicationconstants which will control the influence of the penalty func-tions over the objective function, optimize the design againstmajor constraints for smoother operation of passive filters.The optimization of parametric values thus meets the primeobjectives in addition to near-amicable conformity with othertwo constraints, which enhances the performance of the design.


Fig. 5. MATLAB block diagram of test bench consisting of power system and VFD loads for passive filters.

F. Steps in Algorithm

Step 1) Read the system data, base parameters, SCC, andsource-side reactance, and compute the per-unitvalues.

Step 2) Study the system, and measure the harmonic con-tent of source current in per unit (Ish, where h =5, 7, . . .); based on that, decision is to be made aboutthe harmonic order of the filters. Assess the VArrequirements (Q).

Step 3) Formulate the objective function in terms of individ-ual filter admittances in terms of resonant points, andreturn through function the net rms current sinkingin the filter bank.

Step 4) Initialize a population of individuals (generation ofuniformly distributed random binary strings denot-ing system variables, i.e., QF5, QF7, QF11, n5, n7,n11, and R11).

Step 5) Evaluate initial population. [Binary strings are con-verted to real-valued phenotypes, and then, objectivefunction value is calculated according to (17).]

Step 6) Assign fitness values to the entire population. (Therank-based fitness assignment with a selective pres-sure of two and linear ranking is used in this paper[14], [15]. This means giving the fit individual afitness value of two and the least fit individual afitness value of zero.)

Step 7) Select individuals for breeding. (In this paper, se-lection of individual for reproduction is done usingstochastic universal sampling [14].)

Step 8) Recombine individuals. (The design uses thesingle-point crossover with crossover probabilityPc = 0.7.)

Step 9) Apply mutation.Step 10) Evaluate offspring, and call objective function.Step 11) Reinsert offspring into population. (The design uses

a generation gap of 0.9.)Step 12) If the iterations do not converge, go to Step 6);

otherwise, go to Step 13).Step 13) Calculate the filter parameter through system

variables.

IV. MATLAB-BASED SIMULATION

The power source, including cable, transformer, VFDs, andpassive filter bank, is modeled in MATLAB using the PowerSystem Blockset. Fig. 5 describes the test bench to estimatethe performance of the passive filters under equivalent offshorepower system conditions though MATLAB simulation. Thesource block consists of a three-phase power source, with Πsection cable and transformer that produce finite impedance,making the source nonstiff. The performance of the designedset of passive filters with the aforementioned placement hasbeen studied. The set of passive filters includes bank of passivefilters consisting of tuned passive filter at the fifth and seventhharmonic frequencies and a second-order damped HPF whosecorner frequency is kept at 11th harmonic frequency as perIEEE 1531 standard. The VFD has been modeled with a dioderectifier with a smoothing capacitance of 200 μF and an ac


Fig. 6. Impedance–frequency plot with variation of capacitance in individuallegs in the set of passive filters for one of the phases.

drive as equivalent resistance which represents the real powerconsumed by the load. This equivalent resistance correspondsto a 9.25-kW drive. The performance of the designed passivefilter has been simulated for its placement at two positions. Oneis at a common place on the bus where it caters to all the VFDsconnected on the bus, and other topology places the passivefilter dedicated for each VFD. The simulated results have beenstudied for analyzing the cases of parallel and series resonancesalong with the THD of current and voltage at PCC.

V. DISCUSSION OF RESULTS

Fig. 4 clearly shows that the passive filter is tuned to nearfifth and seventh harmonic frequencies by GA, incorporatingaforesaid constraints, besides minimization of harmonics inthe source current. The passive filters are subjected to variouschanges in their component values and other system varia-tions due to which their performance is severely affected. Astudy over their performance has been shown in Figs. 6 and7 for changes in component values due to manufacture toler-ance/aging and due to change in temperature for capacitancealone and inductance alone, respectively. Fig. 6 clearly showsthat a large change in capacitance value shifts the resonantpoint slightly toward the lower side and slightly detunes thefifth and seventh tuned filters. These changes, on the contrary,would entail the passive filter to block series resonance dueto distorted voltage supply condition at PCC more effectively,without much sacrificing the shift of resonant point. Hence, thisstrengthens the design carried out in the present work. Fig. 7shows that the performance of the passive filters does not differat all for changes in the value of inductance as per IEEE-1531guidelines.

Fig. 8 shows the performance of the passive filter bankin time domain, for dedicated passive filter (DPF) for eachVFD. Fig. 8 also shows the load current drawn by each VFD(Ivfd1, Ivfd2, Ivfd3), net load current (IL), net source current(IS), and line voltage at PCC (Vpcc). It is clearly shown inFig. 8 that the power system is very weak. Even with very lowharmonic contents in the source current, the voltage waveform

Fig. 7. Impedance–frequency plot with variation of inductance in individuallegs in the set of passive filters for one of the phases.

Fig. 8. Response of passive filters with VFDs under undistorted mains.

is highly distorted at PCC. With the application of passivefilters, the THD of the source current under such condition hasbeen improved from 38.1% to 1.2%, and the THD of the voltagewaveform has been improved from 27.5% to 6.9%. Figs. 9 and10 show the THD of the load and source currents and voltageat PCC, without application of passive filters and with passivefilters at two different placements for VFDs. It is quite evidentfrom Figs. 9 and 10 that, with the application of passive filter,independent of its placement, the THDs of the source currentand voltage at PCC dynamically improve.

One very important aspect of the design corresponding tonet reduction in rms supply current holds true for both types ofplacements of passive filters in the power system. Table I clearlyshows that the application of passive filters reduces the net rmssource current from 73.3 to 66.6 A for a single common passive


Fig. 9. Harmonic spectrum of load current and source current with CPF andDPF under undistorted mains.

Fig. 10. Harmonic spectrum of voltage at PCC without passive filters and withCPF and DPF under undistorted mains.

TABLE IPERCENTAGE THD AND RMS VALUE OF LOAD AND SOURCE CURRENT

AND VOLTAGE AT PCC WITH AND WITHOUT PASSIVE FILTER (FOR

BOTH PLACEMENTS) UNDER UNDISTORTED MAINS

filter (CPF) at the bus and to 72.8 A for multiple DPFs for eachVFD. The details are shown in Table I; while comparing thetwo different placements, it can be clearly seen that the THDsof current and voltage have been improved further with DPFsover CPF for all VFDs at the cost of increased value of rmscurrent and voltage at PCC due to the use of multiple resistivelegs of HPF in each dedicated filter and increase in net reserveof reactive power, respectively. Since light-load conditionsrarely occur at offshore power system, the problems raised byincreased reserve of reactive power do not affect much. Thedistributed passive filters also ensure the system to operate withminimum chances of parallel resonance due to their isolationwith respective VFDs [4]. It can also be seen from Fig. 9that the harmonic spectrum does not show any evidence ofparallel resonance until 35th harmonics in accordance withIEEE-1531.

Fig. 11 shows the performance of the passive fil-ter bank under distorted mains conditions {5th harmonic(7.5%) and 7th harmonic (5%)}, for dedicated placement ofpassive filter with VFDs. The THDs of the source current andvoltage at PCC have been maintained for 5.97% and 6.93%,respectively, under such condition of mains. Figs. 12 and 13and Table II show the details of THDs of load, source current,

Fig. 11. Response of passive filters with VFDs under distorted mains.

Fig. 12. Harmonic spectrum of load current and source current with CPF andDPF under distorted mains.

Fig. 13. Harmonic spectrum of voltage at PCC without passive filters and withCPF and DPF under distorted mains.

and voltage at PCC for both the aforesaid placements of passivefilter. The increase in THD of the source current is nearly equalin both placements, due to the flow of harmonics from thesource side. The dedicated system of passive filter offers wideroperation as distributed harmonic current sink which eases theprotection of filters due to overloading, whereas CPF wouldbe subjected to series resonance much early. Thus, it can beseen that the GA-designed passive filter offers superior perfor-mance under multiple constraints and that dedicated topologyoffers wide applicability under uncertainties in offshore powersystems


TABLE IIPERCENTAGE THD AND RMS VALUE OF LOAD AND SOURCE CURRENT

AND VOLTAGE AT PCC WITH AND WITHOUT PASSIVE FILTER (FOR

BOTH PLACEMENTS) UNDER DISTORTED MAINS

TABLE IIIPARAMETERS OF THE CONSIDERED SYSTEM

VI. CONCLUSION

This paper has presented a new technique to design seriestuned and second-order bandpass passive filters. The design hasbeen emphasized for reduction of harmonic current togetherwith minimization of rms source current and reactive require-ment. The observed performance, through analyzing the result,has demonstrated the ability of the proposed designed passivefilters to compensate the current harmonics effectively alongwith the reduction of the net rms source current. Analysis hasalso been carried out to study the effect of change of filterparameters due to environment and manufacturing conditions.It has been observed that the design does not differ much andensures a proper operation even under extreme conditions. Theplacement of the designed passive filter has been studied fortwo different places. It has been found that the DPF for eachVFD reduces the THD of source current and voltage at PCCmore than a CPF at the bus. Moreover, the DPFs, which draw alittle more current and slightly increase the voltage at PCC, arerecommended for safer operation because of increased overloadcapacity to work under series resonance carried by distortedmains, which is prominent in offshore systems. It has beenfound that the problem of parallel resonance does not occurfor designed passive filter for the nonstiff power system up to aharmonic spectrum of 35th harmonic frequency. In a nutshell, itis recommended that the distributed scheme of DPF designed asper the proposed scheme may serve the offshore power systemapplication in a better way.

APPENDIX

The parameters of the considered system of the study aregiven in Table III.

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Vishal Verma (M’04) was born in Bareilly, India, in1966. He received the B.E. degree in electrical engi-neering from the G. B. Pant University of Agricultureand Technology, Pantnagar, India, in 1989, and theM.Tech. and Ph.D. degrees from the Indian Instituteof Technology Delhi, New Delhi, India, in 1998 and2006, respectively.

In 1991, he became an Assistant Professor in theDepartment of Electrical Engineering, G. B. PantUniversity of Agriculture and Technology. Since2004, he has been with Delhi College of Engineer-

ing, Delhi. His fields of interest include power electronics, drives, active filters,and power quality issues.

Dr. Verma is a member of the Indian Society for Technical Education and aLife Member of the Continuing Education Society of India.


Bhim Singh (SM’99–F’10) was born in Rahamapur,India, in 1956. He received the B.E. degree in elec-trical engineering from the University of Roorkee,Roorkee, India, in 1977, and the M.Tech. and Ph.D.degrees in electrical engineering from the Indian In-stitute of Technology (IIT) Delhi, New Delhi, India,in 1979 and 1983, respectively.

In 1983, he joined the Department of ElectricalEngineering, University of Roorkee, as a Lecturerand became a Reader in 1988. In December 1990,he joined the Department of Electrical Engineering,

IIT Delhi, as an Assistant Professor and became an Associate Professor in 1994and a Professor in 1997. He has received the Khosla Research Prize of theUniversity of Roorkee, JC Bose and Bimal K Bose awards of The Institution ofElectronics and Telecommunication Engineers (IETE) and PES Delhi ChapterOutstanding Engineer Award for the year 2006. He has been the General Chairof the IEEE International Conference on Power Electronics, Drives and EnergySystems (PEDES 2006) held in New Delhi. His current research interestsinclude power electronics, electrical machines and drives, active filters, flexibleac transmission system (FACTS), high-voltage dc (HVDC), and power quality.

Dr. Singh is a Fellow of the Indian National Academy of Engineering(INAE), the National Academy of Science, India (NASI), the Institution ofEngineers (India) (IE (I)), and the Institution of Electronics and Telecom-munication Engineers (IETE). He is a Life Member of the Indian Societyfor Technical Education (ISTE), the System Society of India (SSI), and theNational Institution of Quality and Reliability (NIQR).

05462950genetic-algorithm-based design of passive filters

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