GENETIC ALGORITHMS APPLIED TO A FASTER DISTANCE PROTECTION ... · PDF fileGENETIC ALGORITHMS APPLIED TO A FASTER DISTANCE PROTECTION OF TRANSMISSION LINES ... transmission line protection

GENETIC ALGORITHMS APPLIED TO A FASTER DISTANCEPROTECTION OF TRANSMISSION LINES

Denis V. Coury∗

[email protected]

Mario Oleskovicz∗

[email protected]

Silvio A. Souza∗

[email protected]

∗SEL-EESC-USP Sao CarlosAv. Trabalhador Sancarlense. 400 Centro

CEP 13566-590 - Sao Carlos – SP

RESUMO

Algorıtmos Geneticos Aplicados a uma Mais Ra-pida Protecao de Distancia de Linhas de Trans-missaoO principal objetivo deste trabalho e implementar umanova metodologia baseada em Algorıtmos Geneticos(AGs) para extracao de fasores fundamentais de tensaoe corrente em sistemas que possibilite uma protecao dedistancia mais rapida. Os AGs resolvem problemas deotimizacao baseados nos princıpios da selecao natural.Esta aplicacao foi formulada como um problema de oti-mizacao, tendo como principal objetivo o de minimizara estimacao do erro entre as formas de ondas em analise.Uma linha de transmissao de 440 kV, com 150 km deextensao foi simulada atraves do software ATP (Alterna-tive Transients Program) para testar a eficiencia do novometodo. Os resultados desta aplicacao mostram que odesempenho geral do AG foi altamente satisfatorio noque diz respeito a velocidade e a precisao na respostaquando comparado ao metodo tradicional utilizando aTransformada Discreta de Fourier.

PALAVRAS-CHAVE: Protecao de Distancia, Transfor-mada Discreta de Fourier, Linhas de Transmissao e Al-gorıtmos Geneticos.

Artigo submetido em 23/02/2010 (Id.: 01106)

Revisado em 20/08/2010, 09/12/2010

Aceito sob recomendacao do Editor Associado Prof. Julio Cesar Stacchini

Souza

ABSTRACT

The main purpose of this paper is to implement a newmethodology based on Genetic Algorithms (GAs) to ex-tract the fundamental voltage and current phasors fromnoisy waves in power systems to be applied to a fasterdistance protection. GAs solve optimization problemsbased on natural selection principles. This applicationwas then formulated as an optimization problem, andthe aim was to minimize the estimation error. A 440kV, 150 km transmission line was simulated using theATP (Alternative Transients Program) software in orderto show the efficiency of the new method. The resultsfrom this application show that the global performanceof GAs was highly satisfactory concerning speed and ac-curacy of response, if compared to the traditional Dis-crete Fourier Transform (DFT).

KEYWORDS: Distance Protection, Discrete FourierTransform, Transmission Lines and Genetic Algorithms.

1 INTRODUCTION

The increasing growth in power systems both in sizeand complexity has demanded higher speed relays in or-der to protect major equipment, as well as keeping itsstability. When a fault occurs on a transmission line,radical changes occur in the voltage and current wave-forms. The phase and magnitude of the 60 Hz voltage

334 Revista Controle & Automacao/Vol.22 no.4/Julho e Agosto 2011

and current signals are badly corrupted by noise, in theform of a DC offset (exponentially decaying transient),as well as harmonic components. Therefore, a protectiverelaying system has to detect them as soon as possibleand isolate the faulty region from the rest of the system,preventing the propagation of the fault.

Many research groups have been working on digital pro-tection of transmission lines. Much attention has beenpaid to distance relaying techniques lately (Osman andMalik, 2001; Sidhu et al., 2002). Among many ap-proaches considered, transmission line protection basedon the fundamental frequency signals is widely used. Ba-sically, the objective of a relaying scheme is to estimatethe fundamental frequency components from the cor-rupted voltage and current signals following the fault oc-currence. For distance relaying, these fundamental com-ponents are used to determine the apparent impedance(Phadke and Thorp, 1988). According to the calculatedimpedance, the fault is identified as internal or externalto the protection zone.

Some filtering techniques found in the literature canbe applied to this problem. Various digital signal-processing techniques based on static and dynamic esti-mation have been suggested to evaluate the fundamentalfrequency (60 Hz). Some examples of static estimationare the Least-Squared Method (LSM) (Alfuhaid and El-Sayed, 1999) and the Discrete Fourier Transform (DFT)(Altuve et al., 1996). On the other hand, the KalmanFilter is an example of a dynamic estimation (Girgisand Brown, 1985). Genetic Algorithms (GAs) (Osmanet al., 2003a; Macedo et al., 2003) and Artificial Neu-ral Networks (ANNs) (Osman et al., 2003b) have alsobeen applied to the distance protection of power sys-tems. However, the DFT filter has been the most pop-ular for this purpose and has become a standard in theindustry. This is because its computational cost is lowand a good harmonic immunity can be reached. On theother hand, its performance can be adversely affected bythe DC component leading to erroneous estimations, de-pending on the window length utilized. A shorter datawindow would give a faster response but an unstableoutput. A longer data window would give a stable re-sult, but the response of the filter would be delayed.For protection purposes, a data window of one cycle hasbeen largely used (Chen et al., 2006).

The main purpose of this paper is to implement a newmethodology based on GAs to extract the fundamen-tal voltage and current phasors in power systems to beapplied to the distance protection. The optimizationprocedure follows an evolutionary strategy to find thebest solution for a search problem. In order to obtain

a faster distance protection decision, the window lengthfor the new methodology was analyzed in comparisonto the standard DFT filter, showing some advantagesconcerning the new approach.

2 BASIC CONCEPTS RELATED TO GE-NETIC ALGORITHMS

A Genetic Algorithm (GA) is a search algorithm basedon the mechanism of natural selection and natural genet-ics. Its fundamental principle is “the fittest member of apopulation has the highest probability for survival”. AGA operates in a population of current approximations,the individuals, initially drawn in a random order, fromwhich improvement is sought. Individuals are encodedas strings, the chromosomes, so that their values repre-sent a possible solution for a given optimization problem(Goldberge, 1989).

There is a fitness value associated to each chromosome.The better the solution the chromosome represents, thelarger its fitness and its chances to survive and produceoffspring. In this context, the objective function estab-lishes the basis of selection.

At the reproduction stage, a fitness value is derived fromthe raw individual performance measure given by the ob-jective function, as is used to bias the selection process.The selected individuals are then modified using geneticoperators. Afterwards, individual chromosomes are de-coded, evaluated, and selected according to their fitness,and the process continues for different generations. Bymanipulating a population of possible solutions simulta-neously, the GAs can explore various areas of the searchspace.

The GAs rely on two basic kinds of operators: geneticand evolutionary. Genetic operators, namely crossoverand mutation, are responsible for establishing how in-dividuals exchange or simply change their genetic fea-tures in order to produce new individuals. Evolutionaryoperators deal with determining which individuals willexperience crossover or mutation.

Essentially, a GA tries to minimize or maximize thevalue presumed by the fitness function. In many cases,the development of a fitness function can be based onthis return and can represent only a partial evaluation ofthe problem. Additionally, the algorithm must be fast,because it will analyze each individual from a populationand its successive generations.

Revista Controle & Automacao/Vol.22 no.4/Julho e Agosto 2011 335

3 THE REPRESENTATION OF THE ES-TIMATION PROBLEM

3.1 The mathematical model of the inputsignals

A periodic signal can be represented as a sum of itsexponential DC, the fundamental frequency, as well asits harmonic components. In order to estimate the har-monic components of a nonsinusoidal waveform, a math-ematical expression can be written as (Pascual and Ra-pallini, 2001):

xe (t) = x0 e−λ·t +

N∑i=1

Ac,i cos ( iw0t) +As,isin ( iw0t)

(1)

where x0 is the amplitude of the decaying DC compo-nent and λ is its time constant; and are the cosine andsine amplitudes of the ith harmonic respectively; is thefundamental frequency (377 rad/sec - 60 Hz) and N isthe number of harmonics used to represent x(t).

Assuming that the signal xs(t) is sampled at a pre-defined time interval ∆t, after (m − 1) ∗ ∆t secondsthere will be m samples, xs(t1), xs(t2). . . . .xs(tm), fort1, t2. . . . .tm, where t1 is an arbitrary time reference.The system of equations given by equation (2), wheree(tk), k = 1. . . . .m, is the equation error at time tk, andcan be written as:

xs(t1)xs(t2)

...xs(tm)

=

e−λt1 · · · cos(Nw0t1) sin(Nw0t1)e−λ2 · · · cos(Nw0t2) sin(Nw0t2)

.... . .

...e−λtm · · · cos(Nw0tm) sin(Nw0tm1)

·

·

x0Ac,1As,1

...Ac,NAs,N

+

e(t1)e(t2)

...e(tm)

(2)

In this work, the system (2) is solved using GAs. Solvingthe system of equations given by (2), we would be ableto find, λ, x0, and , i = 1, . . . , N . However, concern-

ing the distance protection application, only the funda-mental phasors are required to calculate the apparentimpedances seen by a local relay during a faulty situa-tion. Therefore, equation (1) was drastically simplifiedconsidering only the cosine and sine amplitudes of thefundamental component, and, respectively. Taking thisinto account, a real-coded GA scheme was used to repre-sent the cosine and sine amplitudes of the fundamentalvoltage and current, as illustrated in Figure 1. Consid-ering this approach, the GA worked as a filter for thevoltage and current inputs, which is well known for be-ing corrupted by noise (as mentioned before).

0.364 0.834

AC,1 AS,1

Chromosome real representation

Figure 1: Individual representation.

3.2 The fitness function

The evaluation function (FA) is responsible for deter-mining the fitness of each individual. Its objective is toevaluate the estimation error (e), in (3) . The coded pa-rameters in equation (2) are compared to the measuredvalue in each time step in order to calculate the error(e) (Figure 2).

e(tk) = xs(tk) − xe (tk) k = 1.....m (3)

The error represented in (4) was used in this work.

ET =

√√√√√∣∣∣∣ m∑i=1

ei

∣∣∣∣m

(4)

As the objective of the GAs is to maximize the chro-mosome’s fitness, it is necessary to transform ET intoa fitness function (F). This is done using equation (5), where ∆ is a very small positive constant, 0.00001,aimed to avoid overflow problems.

FA =1

ET + ∆(5)

Concerning the reproduction process, some of the pa-rameters should be mentioned, such as: population of


Figure 2: The estimation error evaluation.

100 individuals, chromosomes with real representation,the tournament operator; the considered crossover andmutation rates of 90% and 10%, respectively. The stopcriterion in each run was 5,000 generations or 100 gen-erations without improvement.

3.3 The Discrete Fourier Transform

Traditionally, the Fourier technique is widely used toanalyze currents and voltage waveforms from an electricpower system. In this work, the DFT technique is usedin order to compare it to the new methodology proposed.

Considering the Fourier filter, the real and imaginarycomponents of the fundamental frequency phasor (forone cycle of data with Nc samples per cycle), aregiven by the following equations (Pascual and Rapallini,2001):

∧x or =

2

Nc

Nc−1∑n=0

x(n) cos

(2π n

Nc

)(6)

∧x oi = − 2

Nc

Nc−1∑n=0

x(n) sin

(2π n

Nc

)(7)

where and are the peak value of the real and imaginarycomponents of the fundamental frequency phasor of theinput signal x(n), respectively. For a half cycle and onequarter of a cycle, 2/Nc should be replaced by 4/Nc and8/Nc in equations (4) and (5) , respectively.

4 TEST RESULTS

4.1 Transmission line simulation

In order to obtain the voltage and current signals, whichwill be applied to distance protection, transmission lineswith source equivalents at the ends were simulated (Fig-ure 3). This work makes use of a digital simulator offaulted EHV (Extra High Voltage) transmission linesknown as the Alternative Transients Program - ATP(ATP, 1987).

A typical 440 kV transmission line, illustrated in Figure4, from CESP (Companhia Energetica de Sao Paulo – aBrazilian utility) was utilized.

It should be mentioned that although the technique de-scribed is based on Computer Aided Design (CAD),practical considerations such as the Capacitor VoltageTransformer (CVT) and Current Transformers (CT),anti-aliasing filters and quantisation on system faultdata were also included in the simulation. The dataobtained was very close to that found in practice. Thetechnique also considered the physical arrangement ofthe conductors in the structure (Figure 4), the char-acteristics of the conductors, mutual coupling, and theeffect of earth return path. Perfect line transpositionwas assumed.

0.364 0.834

AC,1 AS,1


Figure 1. Individual representation.

Figure 2. The estimation error evaluation.

~ ~TL1 TL2 TL3

80 km 150 km 100 km

10 GVA 9 GVA

D E F G

440 kV

Relay

Figure 3. Power system simulated using ATP software.

11,93m

7,51m

24,07m 9,27m

0,40m

PHASE 1

PHASE 0

PHASE 3

PHASE 2

3,60m

Figure 4. Transmission line structure (440 kV).

Figure 3: Power system simulated using ATP software.

The transmission line parameters are presented in Ta-ble 1. Tables 2 and 3 show the equivalent parametersconcerning the generators and data from D and G ter-minals, respectively.

For this approach, the voltage and current fault valuesfrom busbar E were utilised as inputs. A sampling fre-quency of 2.400 Hz to distance protection calculationswas used.

The simulated data were obtained applying differentfaults in the TL2 transmission line (150 km) betweenbusbars E and F .


0.364 0.834

AC,1 AS,1


Figure 1. Individual representation.

Figure 2. The estimation error evaluation.

~ ~TL1 TL2 TL3

80 km 150 km 100 km

10 GVA 9 GVA

D E F G

440 kV

Relay

Figure 3. Power system simulated using ATP software.

11,93m

7,51m

24,07m 9,27m

0,40m

PHASE 1

PHASE 0

PHASE 3

PHASE 2

3,60m

Figure 4. Transmission line structure (440 kV).

Figure 4: Transmission line structure (440 kV).

Table 1: Transmission line parameters

Positive SequenceR (ohms/km) L (mH/km) C (uF/km)

3.853E-02 7.410E-01 1.570E-02

Negative SequenceR (ohms/km) L (mH/km) C (uF/km)

1.861E+00 2.230E+00 9.034E-03

Table 2: Equivalent parameters from D and G generation ter-minals

Generation Terminal DPositive Seq. Negative Seq.

R (ohms/km) 1.6982 0.358L (mH/km) 5.14E+01 1.12E+01

Generation Terminal GPositive Seq. Negative Seq.

R (ohms/km) 1.7876 0.4052L (mH/km) 5.41E+01 1.23E+01

Table 3: Data from D and G Generation Terminals

GenerationTerminal D

GenerationTerminal G

Power (GVA) 10 9Voltage (pu) 1.05 0.95Phase (grade) 0 -10

Figures 5 and 6 show a typical situation of an a-phase-to-earth fault in the TL2 transmission line at 75 kmfrom busbar E.

Figure 5: Voltage waveforms at the TL2 transmission line.

Figure 6: Current waveforms at the TL2 transmission line.

The obtained data (voltage and current waveforms) werefiltered using a 2nd order Butterworth filter with a cut-off frequency of 360 Hz in order to eliminate some of thehigh frequency components, as well as to prevent thealiasing effect. Moreover, the voltage and current wave-forms were digitalized using a 12 bit analog to digitalconverter (ADC).

4.2 Distance protection algorithm results

Impedance relays are from the family of distance relays.They are used to calculate the apparent impedance upto the fault point by measuring voltages and currents atone single end. As is known, they compare the apparentimpedance/fault distance measured to a protection zoneto determine if a fault is inside or outside it.

A complete scheme for a distance protection relay isshown in Figure 7. The voltage and current signals come


from the power system shown in Figure 3, simulatedin the ATP software. The first step of the algorithmwas the fault detection. Samples of current signals werestored in the memory. When a new sample came, it wascompared to the corresponding sample one cycle earlier.If the change was bigger than 0,05 p.u and this changewas confirmed by a counter four consecutive times, thefault situation was detected.

The next step was digital filtering. In this work, the tra-ditional DFT, as well as an alternative method, GeneticAlgorithms (GA), were utilized in order to estimate thefundamental frequency phasors, as shown in 7 . Bothmethodologies were used to appropriately estimate thesephasors as discussed in section 3.

The fault classification was also implemented becauseof the need to choose the voltages and currents involvedin a fault adequately in order to correctly calculate theapparent impedance seen by the distance relay. Themethod adopted in the design consists of calculating thepeak value of the three line currents and zero sequencecurrent from the estimated states from the filters, asmentioned in Girgis and Brown (1985). Table 4 showthe equations for fault impedance calculation accordingto the fault type (IEEE Std. C37.114TM , 2004).

Figure 5. Voltage waveforms at the TL2 transmission line.

Figure 6. Current waveforms at the TL2 transmission line.

Current and

Voltage

Signals

Fault Detection

Digital Filtering

Fault

Classification

Apparent

Impedance

(Fault Distance)

Fault Zone

(Trip Decision)

Discrete

Fourier

Transform

and

Genetic

Algorithm

S

A

M

P

L

E

S

P

H

A

S

O

R

S

Figure 7. A basic diagram for a distance protection relay.

Figure 7: A basic diagram for a distance protection relay.

In Table 4, A, B and C indicate the phases involved, G isfor ground, V and I are voltage and current phasors, k =

Table 4: Fault impedance equations for different types of faults.

Fault Type Equation

AG VA/(IA + 3kI0)

BG VB/(IB + 3kI0)

CG VC/(IC + 3kI0)

AB or ABG (VA −VB)/(IA − IB)

BC or BCG (VB −VC)/(IB − IC)

CA or CAG (VC −VA)/(IC − IA)

ABC The same as a phase-to-phase

(Z0˘Z1)/Z1, Z0 and Z1 correspond to zero and positive-sequence line impedance, respectively, and I0 is the zero-sequence current.

Finally, after the apparent impedance calculation, thatis proportional to the distance to the fault, the protectedzone is inferred.

Considering the power system shown in Figure 3, alltypes of faults were simulated in order to test the pro-posed technique compared to the traditional DFT fil-tering method. For brevity, the results presented areconcentrated in line-to-ground faults (AG) and phase-to-phase faults. The system behavior for the other faulttypes is similar to those presented.

These different kinds of faults were obtained consideringthe TL2 transmission line in Figure 3. The distancesconsidered from busbar E were: 15, 45, 75, 105, 135 and145 km. The apparent impedances and fault distanceswere calculated for all kinds of faulty situations, takinginto account not only the DFT but also the GA method.Windows of one, half and quarter of a cycle, i.e., 40,20 and 10 samples from voltage and current waveformswere used as input for both methodologies. The faultinception angles for the simulations presented here wereconsidered to be 0o and 90o. Moreover, fault resistancesof 0, 50 and 100 Ohms were also included. Zone 1 wasset to 80 % of the total line length. Consequently, faultdistances of 15, 45, 75 and 105 km corresponded to thefirst zone and 135 and 145 km to the second zone.

Figure 8 shows the impedance trajectory from the pre-to the post-fault data, considering the use of a DFT filter(one and half cycle windows), as well as a GA filter of aquarter cycle. A single line to ground (SLG) fault waslocated in the middle of the line with no fault resistancefor this case study.

Figures 9 to 14 show the stabilized values for theimpedance calculation for different faults located alongthe line and different types of faults, considering theDFT and AG filtering methods. A standard quadrilat-eral characteristic for the first zone was adopted in the


Figure 8. Impedance trajectory for a SLG (AG) fault considering DFT and AG filters.

Figure 9. R – X diagram for a SLG (AG) fault with 0, 50 and 100 Ohms fault resistances and one cycle data window.

Figure 10. R – X diagram for a SLG (AG) fault with 0, 50 and 100 Ohms fault resistances and half cycle data window.

Figure 8: Impedance trajectory for a SLG (AG) fault consideringDFT and AG filters.

figures as well as a representation for the positive se-quence line in question.

Figure 9 illustrates the estimated apparent impedancesusing both DFT and GA filters, considering the dis-tances described earlier along the line length versus thefault resistance variation for a single line to ground fault.The results show a good and correct estimation for bothmethods with one cycle data window.

Figure 10 illustrates the same situation using a half cycledata window. It can be observed that both methodspresented similar results.

Finally, Figure 11 shows the same situation for a quar-ter cycle window. Considering the quarter cycle windowof data, the use of GA shows a better result, especiallybecause it kept the same type of response of the pre-vious cases. The same did not happen with the DFTtechnique, as already expected.

The fault distance estimations, as well as the zone inwhich the faults are located (1- inside the primary zoneand 0- otherwise), for the cases illustrated in Figures 9,10 and 11 are shown in Table 5. The results are shownin function of the error calculated according to 8:

e (%) = |destimated−dactual|L ∗ 100 (8)

where, destimated is the fault distance estimated by theGA; dactual is the actual fault distance; and L is thetotal length of the transmission line.

It can be observed in Table 5 that generally the GAmethodology shows a better performance (in terms of

errors) if compared to the DFT method. This can bebetter observed in the cases using a quarter data win-dow. For these cases, the fault distance estimations,as well as location zones, were on average much moreprecise, if compared to the traditional method, provid-ing better conditions to the new method to distinguishdifferent relay zones with this very short window.




Figure 9: R – X diagram for a SLG (AG) fault with 0, 50 and100 Ohms fault resistances and one cycle data window.




Figure 10: R – X diagram for a SLG (AG) fault with 0, 50 and100 Ohms fault resistances and half cycle data window.

Figure 12 presents a R – X diagram for a double linefault (AB) with fault resistance of 1 Ohm, consideringa one cycle data window. A good estimation for bothmethods can be seen.

Figure 13 shows the same situation for a half cycle datawindow. Once more, both methods had approximatelythe same performance.

Finally, Figure 14 presents the same situation for a quar-ter data window. As shown, a better performance can be


Figure 11. R – X diagram for a SLG (AG) fault with 0, 50 and 100 Ohms fault resistances and quarter cycle data window.

Figure 12. R – X diagram for a double line (AB) fault with 1 Ohm

fault resistance and one cycle data window.


fault resistance and half cycle data window.

Figure 11: R – X diagram for a SLG (AG) fault with 0, 50 and100 Ohms fault resistances and quarter cycle data window.

observed considering the GA technology. This behaviorcan also be found considering the distance estimationspresented in Table 6 where the GA technique with aquarter cycle data window presented much smaller av-erage errors if compared to the DFT.

It must be emphasized that, the GA methodology canpresent different results depending on its initialization.Considering this, in order to have a realistic result, eachtest was run individually 30 times and its average per-formance is presented in the tables.

The average running times for the proposed algorithm,considering fault detection, classification and locationare 19.17 ms, 10.84 ms and 6.67 ms considering one,half and quarter cycle data windows, respectively.





fault resistance and half cycle data window.

Figure 12: R – X diagram for a double line (AB) fault with 1Ohm fault resistance and one cycle data window.





fault resistance and half cycle data window. Figure 13: R – X diagram for a double line (AB) fault with 1Ohm fault resistance and half cycle data window.

Figure 14. R – X diagram for a double line (AB) fault with 1 Ohm fault resistance and quarter cycle data window. Figure 14: R – X diagram for a double line (AB) fault with 1Ohm fault resistance and quarter cycle data window.

4.3 Practical implementation

This work has been developed on a simulation basis.However, it should be mentioned that an embeddedmethodology using FPGAs (Field-Programmable GateArrays) would be very suitable for this application. Thesystem on chip concept makes intelligent digital distancerelays possible in practice. A similar approach was im-plemented in Souza et al. (2008) for on-line applica-tion of a frequency relay (estimating frequency devia-tion, phasor magnitude and phase angle) with very goodresults, facing all the restraints concerning an on-line re-lay application.


5 CONCLUSIONS

This work presented an efficient technique based on Ge-netic Algorithms applied to distance protection of powersystems. Considering the study, the proposed method-ology performed better compared to the traditional Dis-crete Fourier Transform method.

A basic algorithm for distance protection was tested andsituations such as different types of faults, fault resis-tances, fault distances and size of the input data windowwere considered.

It can be concluded that the size of the window is veryimportant for a good estimation. As far as distanceprotection is concerned, a shorter data window wouldgive a faster response. In this context, the deprecia-tion of the results when the size of the data windowwas made shorter could particularly be observed in thecase of the DFT technique. The use of one, half andquarter cycle data windows showed an interesting com-parison between the Genetic Algorithm and DiscreteFourier Transform with better performances in favor ofthe GA methodology. This is particularly important ifwe have in mind the times normally required for com-mercial relays (between one and two cycles) concerningthe fault detection, classification and location for trans-mission lines.

ACKNOWLEDGEMENT

The authors acknowledge the Department of ElectricalEngineering – Engineering School of Sao Carlos - Uni-versity of Sao Paulo (Brazil), for the research facilitiesprovided to conduct this project. Our thanks also toFAPESP - Fundacao de Amparo a Pesquisa do Estadode Sao Paulo for the financial support.

REFERENCES

Alfuhaid, A. S. and El-Sayed, M. A. (1999). A re-cursive least-squares digital distance relaying algo-rithm. IEEE Trans. Power Delivery, v. 14, n. 4,pp. 1257-1262.

Altuve, F. H. J.; Diaz, V. and Vazquez, M. E. (1996).Fourier and Walsh digital filtering algorithms fordistance protection. IEEE Trans. Power Delivery,v. 11, n. 1, pp. 457-462.

ATP (1987). Alternative Transient Program. LeuvenEMTP Center – Rule Book.

Chen, C. S.; Liu, C. W. and Jiang, J. A. (2006). Appli-cation of combined adaptive Fourier filtering tech-

nique and fault detector to fast distance protection.IEEE Trans. Power Delivery, v. 21, n. 2, pp. 619-626.

Girgis, A. A. and Brown, R. G. (1985). AdaptiveKalman filtering in computer relaying: fault classi-fication using voltage models. IEEE Trans. PowerApparatus Systems, v. 104, n. 5, pp. 1167-1177.

Goldberge, D. (1989). Genetic algorithms in search.in: optimization and machine learning. Addison-Wesely.

IEEE Std. C37.114TMm (2004). IEEE Guide for de-termining fault location on AC transmission anddistribution lines. IEEE Publish, New York.

Macedo, R. A.; Silva, D. F.; Coury, D. V. and Carneiro,A. A. F. M. (2003). An evolutionary optimizationapproach to track voltage and current harmonics inelectrical power systems. IEEE Power Eng. Soc.Gen. Meet., v. 2, pp. 1250-1255.

Osman, A. H. and Malik, O. P. (2001). Wavelet trans-form approach to distance protection of transmis-sion lines. IEEE Power Eng. Soc. Summer Meet.,1, pp. 15-19.

Osman, A. H.; Abdelazim, T. and Malik, O. P. (2003a).Genetic algorithm approach for adaptive data win-dow distance relaying. IEEE Power Eng. Soc.Gen. Meet., v. 3, pp. 1862-1867.

Osman, A. H.; Abdelazim, T. and Malik, O. P. (2003b).Adaptive distance relaying technique using on-linetrained neural network. IEEE Power Eng. Soc.Gen. Meet., v. 3, pp. 13-17.

Pascual, H. O. and Rapallini, J. A. (2001). Behaviourof Fourier, cosine and sine filtering algorithms fordistance protection, under severe saturation of thecurrent magnetic transformer. IEEE Porto PowerTech Conf.

Phadke, A. G. and Thorp, J. S. (1988). ComputerRelaying for Power Systems. John Wiley & Sons.

Sidhu, T. S.; Ghotra, D. S. and Sachdev, M. S. (2002).An adaptive distance relay and its performancecomparison with a fixed data window distance re-lay. IEEE Trans. Power Delivery, v. 17, n. 3, pp.691-697.

Souza, S. A.; Oleskovicz, M.; Coury, D. V.; Silva, T.V.; Delbem, A. C. B. and Simoes, E. V. (2008).FPGA Implementation of genetic algorithms forfrequency estimation in power systems. IEEE PESGen. Meet., Pittsburgh.


Table 5: Distance estimation for a SLG (AG) fault with one, half and quarter data windows.

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Zo

ne

Dis

tan

ce

DFT

Zo

ne

Err

or

GA

Zo

ne

Err

or

(Ω

)(k

m)

(km

) (

%)

(km

) (

%)

(Ω

)(k

m)

(km

) (

%)

(km

) (

%)

(Ω

)(k

m)

(km

) (

%)

(km

) (

%)

115

13.2

037

11.1

975

13.1

824

11.2

117

115

7.6

565

14.8

957

8.1

092

14.5

939

115

5.2

484

16.5

011

8.0

714

14.6

191

145

39.7

938

13.4

708

43.7

172

10.8

552

145

23.5

645

114.2

903

24.5

134

113.6

577

145

15.8

598

119.4

268

23.9

893

114.0

071

175

65.6

629

16.2

247

66.7

624

15.4

917

175

40.4

049

123.0

634

42.3

854

121.7

431

175

23.8

415

134.1

057

42.6

866

121.5

423

1105

91.7

993

18.8

005

101.1

645

12.5

570

1105

56.6

612

132.2

259

59.8

820

130.0

787

1105

33.6

484

147.5

677

62.3

094

128.4

604

0135

117.4

943

111.6

705

128.2

942

04.4

705

0135

71.9

300

142.0

467

75.6

420

139.5

720

0135

38.3

164

164.4

557

73.8

130

140.7

913

0145

126.6

266

012.2

489

134.5

082

06.9

945

0145

77.9

294

144.7

137

82.1

065

141.9

290

0145

41.2

405

169.1

730

85.9

315

139.3

790

Av. Err

or

7.2

688

Av. Err

or

3.5

968

Av. Err

or

26.8

726

Av. Err

or

25.2

624

Av. Err

or

40.2

050

Av. Err

or

24.7

999

115

22.3

692

14.9

128

22.3

633

14.9

089

115

21.6

517

14.4

345

21.9

736

14.6

491

115

15.6

403

10.4

269

21.5

082

14.3

388

145

49.2

981

12.8

654

52.2

037

14.8

025

145

46.4

780

10.9

853

48.8

420

12.5

613

145

26.2

432

112.5

045

43.5

535

10.9

643

175

76.0

861

10.7

241

74.7

398

10.1

735

175

71.4

740

12.3

507

73.0

954

11.2

697

175

37.3

313

125.1

125

65.6

395

16.2

403

1105

104.1

978

10.5

348

106.9

469

11.2

979

1105

98.3

654

14.4

231

103.4

606

11.0

263

1105

45.3

913

139.7

391

91.4

845

19.0

103

0135

131.3

115

02.4

590

133.6

485

00.9

010

0135

125.3

974

06.4

017

129.6

986

03.5

343

0135

54.2

055

153.8

630

114.5

856

113.6

096

0145

142.8

411

01.4

393

145.3

518

00.2

345

0145

135.0

332

06.6

445

137.0

275

05.3

150

0145

57.5

727

158.2

849

127.7

832

011.4

779

Av. Err

or

2.1

559

Av. Err

or

2.0

530

Av. Err

or

4.2

066

Av. Err

or

3.0

593

Av. Err

or

31.6

551

Av. Err

or

7.6

069

115

30.9

651

110.6

434

30.1

534

110.1

023

115

31.0

961

110.7

307

31.2

065

110.8

043

115

23.8

147

15.8

765

31.8

320

111.2

213

145

59.5

809

19.7

206

59.8

051

19.8

701

145

58.7

096

19.1

397

58.9

060

19.2

707

145

33.7

967

17.4

689

59.9

363

19.9

575

175

88.4

821

18.9

881

88.3

220

18.8

813

175

87.3

271

18.2

181

88.9

817

19.3

211

175

44.5

670

120.2

887

84.5

603

16.3

735

1105

116.7

607

17.8

405

115.9

602

17.3

068

1105

114.9

460

16.6

307

117.4

552

18.3

035

1105

55.9

241

132.7

173

115.5

594

17.0

396

0135

145.1

406

06.7

604

143.0

772

05.3

848

0135

144.0

050

06.0

033

144.4

114

06.2

743

0135

64.8

132

146.7

912

140.4

982

03.6

655

0145

154.1

422

06.0

948

153.2

651

05.5

101

0145

153.1

298

05.4

199

153.9

517

05.9

678

0145

68.0

160

151.3

227

151.0

829

04.0

553

Av. Err

or

8.3

413

Av. Err

or

7.8

426

Av. Err

or

7.6

904

Av. Err

or

8.3

236

Av. Err

or

27.4

109

Av. Err

or

7.0

521

0 50

100

Es

tim

ate

Fau

lt D

ista

nce

One Cycle

0 50

100

Half of a Cycle

0

One Quarter of a Cycle

50

100

Es

tim

ate

Fau

lt D

ista

nce

Es

tim

ate

Fau

lt D

ista

nce


Table 6: Distance estimation for a double line (AB) fault with one, half and quarter data windows.

Target Target

Rf Zone Distance DFT Zone Error GA Zone Error

(Ω) (km) (km) (%) (km) (%)

1 15 25.4585 1 6.9723 28.3264 1 8.8843

1 45 40.7422 1 2.8385 41.8901 1 2.0733

1 75 56.5220 1 12.3187 60.3663 1 9.7558

1 105 99.0110 1 3.9927 111.3835 1 4.2557

0 135 133.4565 0 1.0290 140.4249 0 3.6166

0 145 149.9801 0 3.3201 151.1982 0 4.1321

Av. Error 5.0785 Av. Error 5.4529

1 15 18.2905 1 2.1937 18.0957 1 2.0638

1 45 27.0539 1 11.9641 24.7307 1 13.5129

1 75 29.4580 1 30.3613 31.9811 1 28.6793

1 105 58.4590 1 31.0273 58.0636 1 31.2909

0 135 78.5676 1 37.6216 78.5758 1 37.6161

0 145 84.7035 1 40.1977 86.5001 1 38.9999


1 15 30.5322 1 10.3548 18.8957 1 2.5971

1 45 30.5676 1 9.6216 22.9438 1 14.7041

1 75 34.0375 1 27.3083 67.5402 1 4.9732

1 105 50.2944 1 36.4704 83.8399 1 14.1067

0 135 72.9268 1 41.3821 109.6211 1 16.9193

0 145 80.9051 1 42.7299 119.9412 1 16.7059


Estimate Fault Distance

1

1

1

On

e C

ycle

H

alf

of

a C

ycle

O

ne Q

uart

er

of

a C

ycle


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