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GENETIC ALGORITHMS APPLIED TO A FASTER DISTANCEPROTECTION OF TRANSMISSION LINES
Denis V. Coury∗
coury@sc.usp.br
Mario Oleskovicz∗
olesk@sc.usp.br
Silvio A. Souza∗
sasouza@cteep.com.br
∗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
336 Revista Controle & Automacao/Vol.22 no.4/Julho e Agosto 2011
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
Chromosome real representation
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 .
Revista Controle & Automacao/Vol.22 no.4/Julho e Agosto 2011 337
0.364 0.834
AC,1 AS,1
Chromosome real representation
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
338 Revista Controle & Automacao/Vol.22 no.4/Julho e Agosto 2011
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
Revista Controle & Automacao/Vol.22 no.4/Julho e Agosto 2011 339
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 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 9: R – X diagram for a SLG (AG) fault with 0, 50 and100 Ohms fault resistances and one cycle data window.
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 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
340 Revista Controle & Automacao/Vol.22 no.4/Julho e Agosto 2011
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.
Figure 13. R – X diagram for a double line (AB) fault with 1 Ohm
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.
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.
Figure 13. R – X diagram for a double line (AB) fault with 1 Ohm
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.
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.
Figure 13. R – X diagram for a double line (AB) fault with 1 Ohm
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.
Revista Controle & Automacao/Vol.22 no.4/Julho e Agosto 2011 341
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.
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Phadke, A. G. and Thorp, J. S. (1988). ComputerRelaying for Power Systems. John Wiley & Sons.
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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.
342 Revista Controle & Automacao/Vol.22 no.4/Julho e Agosto 2011
Table 5: Distance estimation for a SLG (AG) fault with one, half and quarter data windows.
10
SB
A C
on
tro
le &
Au
tom
açã
o V
ol. 0
0 n
o. 00 / J
an
., F
ev.,
Mar,
Ab
ril d
e 0
000
Ta
ble
V.
Dis
tan
ce e
stim
ati
on
for
a S
LG
(A
G)
fau
lt w
ith
on
e, h
alf
an
d q
ua
rter
da
ta w
ind
ow
s.
Targ
et
Targ
et
Targ
et
Targ
et
Targ
et
Targ
et
Rf
Zo
ne
Dis
tan
ce
DFT
Zo
ne
Err
or
GA
Zo
ne
Err
or
Rf
Zo
ne
Dis
tan
ce
DFT
Zo
ne
Err
or
GA
Zo
ne
Err
or
Rf
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
Revista Controle & Automacao/Vol.22 no.4/Julho e Agosto 2011 343
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
Av. Error 25.5609 Av. Error 25.3604
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
Av. Error 27.9779 Av. Error 11.6677
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
344 Revista Controle & Automacao/Vol.22 no.4/Julho e Agosto 2011
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