A backup Protection Technique for Three- Terminal ... - IEEE Xplore

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TSG.2017.2693322, IEEE Transactions on Smart Grid

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REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < limited by the line asymmetry as the untransposed lines cannot be decoupled using symmetrical components transformation. In this paper, two main contributions are presented. First, a new technique is proposed to recognize the faulty branch for three-terminal multisection compound untransposed doublecircuit transmission lines. The derivation of the proposed technique is based on a distributed-parameter line model in the phase-coordinates without any assumptions. Comparing with the pervious method in [22], the faulty branch can be easily recognized in a simple manner with a low computational complexity and high efficiency. Second, an improved fault location technique is applied to untransposed parallel transmission lines as the proposed algorithm in [22] is limited by the line asymmetry. The proposed technique is robust against different fault resistances, different fault locations, different fault types, different fault inception angles and transmission line parameters errors, as well as synchrophasor errors. Also, the proposed technique takes into account the effect of non-linear high impedance faults and evolving faults. The paper is divided as follows. The proposed technique is presented in section two. The test results are discussed in section three. Finally, section four concludes the paper.

]

[

]

[ [

2

(

)

(

(

)

(

) ] )

where VR, Vk, Ik,R and IR,S are 6x1 voltage and current phasors at point k and bus R, respectively. Q(L) is the transformation matrix and is the distance between bus R and point k in per unit. The G, H, M and N are 6x6 transmission line parameters matrices and can be expressed in terms of infinite series as [23]: (

)

(

)

𝑧𝑦

(

) 𝑧𝑦

𝑧 𝑧𝑦

(

)

𝑧

𝑧𝑦 𝑧(

𝑧(

)

𝑧 𝑧𝑦

)

)

𝑧𝑦 𝑧

(

𝑧𝑦 (

(

)

𝑧(

)

)

II. PROPOSED BACKUP PROTECTION TECHNIQUE The proposed technique is developed based on the following assumptions: • Three-terminal synchronized measurements are available. • Communication channels are available. A. Review of Two-Terminal Untransposed Double-Circuit Transmission Lines Fault Location Algorithm Due to the mutual couplings between the adjacent circuits, symmetrical components transformation cannot be used for decoupling untransposed transmission lines. Reference [23] has been proposed a fault location technique for two-terminal untransposed single-circuit long transmission line. This technique can be extended to untransposed double-circuit long transmission line as explained below: Consider the double-circuit transmission line (S-R) shown in fig. 1 with line length L. The series impedance and shunt admittance matrices per unit length can be written as [24]:

𝑧

𝑦

𝑧 𝑧 𝑧 𝑧 𝑧 [𝑧

𝑧 𝑧 𝑧 𝑧 𝑧 𝑧

𝑧 𝑧 𝑧 𝑧 𝑧 𝑧

𝑧 𝑧 𝑧 𝑧 𝑧 𝑧

𝑧 𝑧 𝑧 𝑧 𝑧 𝑧

𝑦 𝑦 𝑦 𝑦 𝑦 [𝑦

𝑦 𝑦 𝑦 𝑦 𝑦 𝑦

𝑦 𝑦 𝑦 𝑦 𝑦 𝑦

𝑦 𝑦 𝑦 𝑦 𝑦 𝑦

𝑦 𝑦 𝑦 𝑦 𝑦 𝑦

𝑧 𝑧 𝑧 𝑧 𝑧 𝑧 𝑦 𝑦 𝑦 𝑦 𝑦 𝑦

(

where the dimensions of z and y are 6x6. The voltage and current phasors in the phase-coordinates at point k can be derived as [25]:

𝑧𝑦

𝑧(

)

k

f

Fig. 1. Faulted two-terminal double-circuit transmission line.

Assume that a fault occurred on point f which is Df in per unit away from the sending end (S). The voltage phasor at fault point f can be obtained by applying Kirchhoff voltage law from the two ends of the line as follows:

[ (

]

𝑧𝑦 𝑧

[ ( ]

𝑧

)

)

( )

)] [ (

] )] [

]

[ ] . If the where voltage and current phasors are known at both ends of the line, the fault distance will be the only unknown variable in the above equation. A and B are only expanded to three terms because the simulation results assure that expansion of more terms will not result in increasing the fault location accuracy. As a result, equation (9) is rewritten and six polynomial equations for fault distance are obtained as follows:

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TSG.2017.2693322, IEEE Transactions on Smart Grid

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][

]

where the dimensions of the coefficient matrices (X1, X2, X3, X4, X5, and X6) are 6x1and they are obtained from the following equations: 𝑧𝑦 𝑧𝑦 [ ] [ [

𝑧𝑦

𝑧𝑦

]

𝑧𝑦

𝑧𝑦

[

𝑧𝑦 𝑧

𝑧𝑦 𝑧

[

𝑧𝑦

𝑧𝑦 𝑧

]

] [

]

] 𝑧𝑦 𝑧

𝑧𝑦

]

] 𝑧𝑦 𝑧

𝑧𝑦 𝑧

[

]

𝑧𝑦 𝑧

𝑧𝑦 𝑧

]

]

𝑧𝑦 𝑧

𝑧

𝑧𝑦

[

[ [

]

𝑧

[ [

𝑧𝑦 𝑧

𝑧𝑦

[ [

𝑧

[

𝑧𝑦 𝑧

]

𝑧𝑦 𝑧

]

]

As a result, the fault distance is obtained by solving (10). The real part of fault distance is accepted as the correct fault location. Also, the current phasor at fault point f can be derived as: [ (

)

(

[ ( where

[

)] [ )

(

)] [

] ] ]

B. Fault Detection Unit Nowadays, distance relays are widely used as a main protection for transmission lines, while overreaching zones and earth fault overcurrent of distance relays are used as a backup protection. The operation of conventional backup protection depends on standalone decision according to local measurements. In addition, the conventional backup protection is not able to adapt with different operating conditions and it is affected by fault resistance. As a result, the conventional protective relays are not able to distinguish between symmetrical faults and other stressed normal conditions. Furthermore, Cascaded outages may occur due to maloperation of conventional backup protection. In this paper, an improved backup protection scheme is

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presented to replace the conventional backup protection. The proposed scheme is used as a backup protection based on the speed of communication system. The delay time associated with communication links is important issue and should be considered in power system protection. More information about delay time calculations is introduced in [26]. The delay time is in the range of 50-150 ms in digital microwave links and fiber-optic cables [27], [28]. The first step is to distinguish internal transmission lines faults inside the protected zone from different operating conditions or external faults outside the protected zone. To do so, consider the three-terminal nonhomogeneous transmission line shown in fig. 2. Three PMUs are connected to buses S, R, and T. Therefore, the synchronized voltage phasors and current phasors of all lines connected to these buses can be obtained utilizing the GPS technique. All data are collected in the central protection system through communication links. Assume that the number of line sections of line branches S-P, R-P, and T-P are respectively u, v, and w, where P is the teepoint. The length of each line section from terminals S, R, and T to tee-point P are respectively , and . Each line section is either underground cable or overhead line. In general, the line parameters of two successive sections are not identical. The proposed scheme for fault detection is divided into the three following steps: Step 1: The instantaneous value of voltage magnitude for each phase at buses S, R, and T is obtained using full cycle Discrete Fourier Transform [26], where subscript i denotes lines a1, b1, c1, a2, b2, and c2. The instantaneous value of voltage magnitude changes continuously due to load change conditions or fault conditions. For each periodic cycle, assume that the absolute difference between maximum and minimum instantaneous value of voltage magnitude for each phase at each bus is . The value of will be equal to zero, if no change in the network occurs. However, if any change in the network occurs, the instantaneous value of will change accordingly [26]. The method introduced in [26] compares positive-sequence voltage magnitude of buses to obtain the nearest bus to the faulty line. After this bus is identified, the faulty line is obtained by comparing the absolute difference of positive-sequence current angles at both ends of each line connected to the identified bus. However, in case of high fault impedance, the reduction of positivesequence voltage magnitude may be very low and the absolute difference of positive-sequence current angles at both ends of the faulty line may not be high enough. Consequently, the backup protection may not operate in such case. The threshold value of ΔV in [26] is equal to 0.05 per unit. In this paper, threshold value ( of is equal to 0.01 per unit so that transmission lines faults with high fault impedance can be detected. If the value of of each phase at each bus is less than , no fault is detected. While, if any value of of any phase at any bus is greater than , the next step is applied. It is important to note that the fault detection decision is not only based on the value of although the value of is only used as indication for power system change.

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TSG.2017.2693322, IEEE Transactions on Smart Grid

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REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < to or . It is supposed that the bus R is selected as a reference point. The algorithm for fault location estimation can be described in the following three steps: Step 1: It is assumed that each line section between bus R and tee-point P is the faulty line section. For the first line section (LR1), the voltage and current phasors at both ends of LR1 are needed to be determined in order to calculate the corresponding fault distance. The voltage and current phasors at the end R are known because a PMU is installed at this end while the voltage and current phasors at the other end of LR1 can be obtained from: [

]

[

]

As a result, the fault distance corresponding to first line section can be obtained by solving (10). Similarly, this is repeated for each line section connected between bus R and tee-point P and the estimated fault distance corresponding to each line section is calculated. Step 2: Starting from the first line section, if its corresponding estimated fault distance is within the interval [0, 1] and the other estimated fault distances are less than zero, the first line section is accepted as the faulty line section and the estimated fault distance is accepted as the estimated fault location. While, if the estimated fault distance corresponding to first line section is greater than 1, the next line section is verified. Step 3: For the second line section, if its corresponding estimated fault distance is within the interval [0, 1] and the next estimated fault distances are less than zero, the second line section is accepted as the faulty section and the estimated fault distance is accepted as the estimated fault location. While, if the estimated fault distance corresponding to second line section is greater than 1, the next line section is verified in similar way. By repeating this step, the faulty line section and the corresponding estimated fault location can be obtained. Similarly, the faulty line section and fault location can be obtained if the faulty branch is S-P or T-P. The flow chart of the proposed technique is shown in fig. 3. E. Fault Classification Unit After the faulty line section and fault location are determined, the fault type can be classified. As the voltage and current phasors at both ends of the faulty line section are obtained, the current phasor at fault point is calculated by solving (17). Based on Kirchhoff current law, the value of current phasor at fault point is ideally equal to zero for healthy phases and is greater than zero for faulty phases. In addition, to distinguish between line-to-line fault and double-line-toground fault, the current phasors of the two faulty phases are not equal for double-line-to-ground fault [29] while the current magnitudes of faulty phases are equal to each other with angle difference 180º for line-to-line fault [29]. III. PERFORMANCE EVALUATION To assess the performance of the proposed algorithm, it is applied to three-terminal multi-section untransposed double-

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circuit transmission line consisting of three branches (S-P, RP, and T-P) as shown in fig. 4. The line branch (S-P) consists of two transmission line sections with lengths LS1and LS2. The line branch (R-P) consists of three transmission line sections with lengths LR1, LR2, and LR3. Also, the line branch (T-P) consists of two transmission line sections with lengths LT1and LT2. The transmission lines (1-S), (2-R), and (3-T) have the same line parameters and they are used for simulating external faults. Loads are connected to buses S, R and T to simulate various loading conditions. All lines parameters, all lines lengths, and generator data are given in Appendix A. Three PMUs are connected to buses S, R, and T and all measurements are collected in the central protection system through communication links. The obtained current and voltage measurements are passed through a low-pass second order Butterworth filter with cut-off frequency 400 Hz. Consequently, the output data are sampled at 2500 Hz and a digital mimic filter is utilized to remove the dc component [30]. The 50 Hz fundamental component is extracted using full cycle Discrete Fourier Transform. To evaluate the accuracy of fault location, the percentage error in fault location is defined as [31]: | | 𝑢

start Read time data of voltage and current phasors at buses S, R, and T Calculate (∆Vi ) at buses S, R, and T No fault No

Is ∆Vi >

1?

Yes

Apply vector sum of all current phasors at each bus (ΣӀi)

Yes

Is abs(ΣӀi) At any bus >

Bus fault at the bus Corresponding to abs(ΣӀi) > 2 end

Calculate Ip

No

Load change conditions or external fault

end

2?

No

Is Ip >

3?

Yes

Calculate the value of F and identify the faulty branch Calculate the fault distance of each line section determine the faulty section and fault location

Fig. 3. Flowchart of the proposed technique.

All simulations are developed by MATLAB software on a 2.1 GHz Core 2 Duo CPU with 2 GB of RAM. The estimated computational time for fault detection and faulty branch identification is less than 1ms while the total computational time including fault location calculations is about 19 ms. Various loading conditions, Generator outages, external

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TSG.2017.2693322, IEEE Transactions on Smart Grid

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < transmission lines faults, bus faults, and internal transmission lines faults are simulated in the following sections considering different fault resistances, different fault locations, transmission line parameters errors, different fault types and fault inception angles, as well as synchrophasor errors. Also, the effect of non-linear high impedance faults and evolving faults have been verified. Again, the values of , , and are respectively equal to 0.01, 0.05, and 0.1 per unit. Central Protection System

PMU S

1

𝐆𝐒

PMU R 𝑆1

Line (1-S)

𝑅3

𝑆2

𝑅2

𝑅1

Line (2-R)

Circuit 1

2

𝐆𝑹

P Circuit 2

Load S

𝑇2

𝐕𝑺

𝐕𝑹 Load R

𝑇1

PMU

T Line (3-T)

3

𝐕𝐓 Load T

𝐆𝑻

6

considering three different fault locaiton at 10%, 50%, and 90% of the line length, all fault types, 3 different fault resistances having 1, 50 and 100 ohm, and 90º fault inception angle . A total of 108 fault cases (3x3x4x3x1) are conducted on the three lines. In all simulated cases, the maximum obtained value of is equal to 0.0244 per unit. As this value is less than 0.1 per unit, the results of the fault detection unit are EF or LCC for all simulated cases. To show the performance of the proposed technique for very low and very high fault impedance, Table 2 summarizes the results for different fault types and different fault location. As observed, the maximum value of is equal to 0.03164 per unit. Therfore, the results of the fault detection unit are EF or LCC for all cases in Table II. In addition, phase a to ground fault at bus S is simulated with Rf =0.01 Ω and δf = 0º. The instantaneous value of at bus S for different phases is shown in fig. 6. As expected, the instantaneous value of voltage magnitude for phase a is decreased while the instantaneous value of voltage magnitude for other phases is increased. The absolute value of vector sum of phase a at bus S ∑ is equal to 12.134 per unit so that bus fault is detected.

Fig. 4. Simulated three-terminal double-circuit nonhomogeneous transmission lines.

A. Various Loading Conditions Different cases are tested by connecting different loads at buses S, R and T at different switching angles. Also, the outages of all generators and sudden loss of all loads are simulated to verify the robustness of the suggested technique. The results are shown in Table I. the load values are selected to be 100 and 200 MVA at each bus. The vector sum of all current phasors at buses S, R, and T is not shown due to space restrictions. However, these values are less than 0.05 per unit. For example in case 1, 100 MVA load is connected to bus S at switching angle 180º. The maximum values of at buses S, R, and T are respectively equal to 0.0113, 0.0021, and 0.0021 per unit. The maximum value of is less than 0.1 per unit and it is equal to 0.0039 per unit so that no transmission line fault is detected inside the protected zone. Also, the last case is generator (GT) outage. The maximum values of at buses S, R, and T are respectively equal to 0.0067, 0.0053, and 0.0337 per unit. The maximum value of is equal to 0.00053 per unit. Therefore, the result of the fault detection unit is external fault (EF) or load change conditions (LCC). In addition, sudden loss of all loads at buses S, R, and T are simulated at 90º switching angle. The instantaneous value of corresponding to the phases of maximum at buses S, R, and T are shown in fig. 5. The maximum value of is equal to 0.004 per unit so that the result of the fault detection unit is EF or LCC. As a result, it is clear that the proposed scheme can discriminate all external events correctly. B. External faults cases Different external faults are conducted on transmission lines (1-S), (2-R), and (3-T). The three lines are simulated with

Fig. 5. The instantaneous value of maximum at buses S, R, and T.

Fig. 6. The instantaneous values of fault.

corresponding to the phases of

at bus S for different phases due to bus

C. Internal faults cases To verify the performance of the proposed technique against very low impedance and very high fault impedance,

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> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < the results for various fault cases are depicted in Table III for different line sections. The maximum values of for buses S, R, and T are not shown in the tables. However, these values are greater than 0.01 per unit. The last column in the table shows the percentage fault location error (F.L error %). For example, case 1 is phase a1 to ground fault at 15% of with 0.001 ohm fault resistance and 0º fault inception angle. All values of are less than 0.1 per unit except the value corresponding to phase a1. Therefore, transmission line fault is detected. To identify the faulty branch, the value of F is equal to 0.0030 per unit which is equal to the value of . Therefore, the voltage phasors and are approximately equal and the faulty branch is S-P. Accordingly, the calculated fault distances corresponding to and are respectively equal to 0.1457 and -0.277 per unit so that is accepted as the faulty line section and the estimated fault location is equal to 0.1445 per unit. The percentage error in fault location is equal to 0.1375% in this case. Statistical results for several fault cases conducted on each line section are shown in fig. 7. Each line section is tested with considering five different locations at 10%, 30%, 50%, 70%, and 90% of the line section length, all fault types and 3 different fault resistances having 1, 50 and 100 ohm, as well as fault inception angle at 90º. A total of 60 fault cases for each line section are simulated. In all cases, the transmission line faults inside the protected zone are correctly detected and the faulty line branch and the fault type are correctly identified. As observed in fig. 7, the maximum percentage error is equal to 0.214% and the total percentage average error is equal to 0.039%.

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D. Influence of Line Parameters Errors The variations of lines parameters have been considered in the proposed algorithm. Therefore, 1%, 5%, and 10% increasing and decreasing in impedances and admittances of all line sections have been considered at the same time to assess the performance of the proposed method. Each line section is tested under various fault conditions considering four different locations at 20%, 40%, 60%, and 80% of the line section length, all fault types and 3 different fault resistances having 1, 50 and 100 ohm, as well as 180º fault inception angle. A total of 48 fault cases are simulated for each line section. The maximum and average estimation errors in fault location for each line section are shown in fig. 8 considering variations of -1%, -5%, -10%, 1%, 5%, and 10% in all lines parameters at the same time. As observed, the maximum and average percentage error are respectively equal to 4.267% and 1.055% for 10% decreasing in all line parameters of all line sections at the same time. While the maximum and average percentage error are respectively equal to 3.696% and 0.904% for 10% increasing in all line parameters of all line sections at the same time. In all simulated cases, the faulty branch and faulty line section are correctly identified.

Fig. 8. Effect of errors in line parameters on the fault location estimation.

Fig. 7. The maximum and average percentage error in fault location for all line sections

In addition, the results of fault classification unit are shown in Table IV. For example, the third case in the table is line-toline fault (a2c2) in . As shown, the value of current phasor at fault point is very small except the values of phase a2 and phase c2. The fault current Ia2 is approximately equal to -Ic2. Therefore, the result of fault classification unit is line-to-line fault. As a result, it can be concluded that the proposed technique yields acceptable results for all fault cases.

E. Effect of Synchrophasor Errors To meet IEEE standard accuracy requirements, a maximum of 1% total vector error must be considered in synchronized measurements [32]. Therefore, a maximum of ±31° time error for a 50 Hz system and ±1% magnitude error are introduced in voltage and current phasors measurements. A total of 48 fault cases are simulated for each line section. The maximum and average estimation errors in fault location for each line section are shown in fig. 9. As observed, the maximum percentage error is equal to 0.5154% and the total average error in all cases is equal to 0.0997%. In all simulated cases, the faulty branch and faulty line section are correctly recognized. The obtained results assure that the proposed technique provides acceptable performance even with considering the synchrophasor errors.

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TSG.2017.2693322, IEEE Transactions on Smart Grid

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REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT)
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