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Compensation of the current transformer saturation effects for transmission line fault location with impedance-differential relay
Electric Power Systems Research 182 (2020) 106223
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Compensation of the current transformer saturation effects for transmission line fault location with impedance-differential relay
T
J. Herlender, J. Iżykowski*, K. Solak Electrical Power Engineering Department, Wroclaw University of Science and Technology, 27 Wybrzeze Wyspianskiego st., 50-370 Wroclaw, Poland
A R T I C LE I N FO
A B S T R A C T
Keywords: Fault location Current transformer saturation Transmission line Simulation
In this paper, the impedance-differential protection dedicated to transmission lines is analysed. The considerations are focused on the extra function of such protection, namely the ability to accurately determine the fault location for an inspection-repair purpose. Measurements of current and voltage at both line ends allow to formulate a differential impedance which constitutes an efficient criterion for fault locating. However, the considered fault location may face a problem when faults with current transformers (CTs) saturation take place. Therefore, in this paper, the proposal aiming at improving fault location accuracy by compensating the CTs saturation effect is introduced. For this purpose, the compensated current was determined by using voltages from both line ends and current from not saturated side and then used in the proposed algorithm instead of the saturated current. The introduced algorithm enables for accurate fault location, even under deep CTs saturation condition. The developed solution has been thoroughly tested with the signals generated with the use of ATPEMTP program.
1. Introduction Published fault statistics [1–3] unambiguously indicate that a majority of a total number of power system faults occur on overhead power lines. Such faults have to be detected and then located by protective relays as well as by fault locators [3,4]. In order to prevent spreading out the fault effects, the identified fault has to be cleared by a circuit breaker tripped by a protective relay as quickly as possible. One of the very first protection principles that have been developed and put into service is the differential criterion [5–7]. The standard line current-differential protection compares currents flowing into the protected line with those flowing out of the protected line and requires a reliable communication link to compare currents at the transmission line terminals [8,9]. The recent development of optical fibre communication technology has made it possible to solve the problems of a digital communication channel for current differential protection [10,11]. Due to this simple principle, current differential protection is easy to apply [12]. Moreover, the current-differential protection scheme is sensitive, highly selective for all fault types, secure [13] and operates stably in the presence of both high-frequency AC and DC components occurred during system faults [14]. In power line applications, is characterised by good tolerance to high line loading [15] and its principle is slightly or even completely not affected by weak
⁎
terminals, series compensation, cross-country faults, power swings, and nonstandard short-circuit current sources like renewable energy sources [12]. Moreover, installation of differential protection in power lines exhibit beneficial performance on multi-terminal lines as well on lines of any length [12]. The traditional current-differential relays [12] apply measurements of three-phase currents at the line ends, while the impedance-differential protection concerned in this paper, primarily introduced in Ref. [16], utilises the measurements of both currents and voltages from the line ends. Thus, more information on the fault is provided in the case of impedance-differential protection. As a result, not only effective protection of transmission line is achieved but also the distance to fault can be accurately determined, what is the main interest of this paper. The protection principle based on differential current is quite robust; however, there are still situations when it may maloperate [17]. For instance, this may be caused by current transformers (CTs) errors that are due to the high value of fault current amplitude or/and decaying DC components in fault currents. In the literature [18–21] it can be found several methods that propose improving stabilisation under external faults with CT saturation. However, these solutions are only dedicated to current-differential protection and do not guarantee the desired effects for all situations. Therefore, the solution dedicated to impedance-differential protection, while CTs saturation takes place, is
Corresponding author. E-mail address: [email protected] (J. Iżykowski).
https://doi.org/10.1016/j.epsr.2020.106223 Received 29 May 2019; Received in revised form 13 December 2019; Accepted 11 January 2020 Available online 06 February 2020 0378-7796/ © 2020 Elsevier B.V. All rights reserved.
Electric Power Systems Research 182 (2020) 106223
J. Herlender, et al.
Nomenclature d dsup IF IF1,IF2, IF0 IS2, IR2 ISφ, IRφ i2(n)
i2e(n) VS2, VR2 VSφ, VRφ Z1L Z2S, Z2R
Calculated distance to a fault [p.u.] Supplementary distance to a fault [p.u.] Faulty current Positive, negative, zero sequence fault current Negative sequence current at the line terminal S, R Current in phase φ at the line terminal S, R Real sample of secondary current
ZLOC φ ϕ2
Estimated value of the secondary current sample Negative sequence voltage at the line terminal S, R Voltage in phase φ at the line terminal S, R Positive sequence impedance of the line Calculated negative sequence impedance of the equivalent system at the line terminal S, R Locational differential impedance Faulty phase (L1, L2, L3) Phase of the calculated negative sequence impedance
The aim of this paper is to analyse the fault location feature of the impedance-differential relay in case of CTs saturation. Several case studies are carried out to investigate the performance of the proposed method. In particular, a comprehensive evaluation of fault location accuracy with the use of the simulation data is presented. The examination of the algorithm was performed in MATLAB software using the fault data obtained from ATP-EMTP simulations [42]. In Section 2, the general structure of the considered impedancedifferential protective relay is presented. The main problems relevant for such protection are shortly described. The proposal for equipping a relay with off-line accurate fault location feature is also stated. Next, in Section 3, the concept of saturated current compensation in case of CT saturation for fault location purposes is introduced. Section 4 is devoted to presenting the testing results of the fault location feature incorporated into the impedance-differential relay, and a comprehensive evaluation of fault location accuracy is carried out. Finally, Section 5 contains the conclusions.
proposed by the authors in Ref. [22]. The introduced method is based on the phase angle calculation of the negative sequence impedances at both line ends. This solution enables to improve protection selectivity for external fault cases still maintaining sensitivity, reliability and speed of operation for all internal faults. However, the proposed solution is insufficient while taking into account the fault location function of the impedance-differential protective relay. In the case of CTs saturation, a secondary current signal which is used for fault location calculations can be distorted and thus causes inaccurate result in the distance to fault determination. In literature, many methods can be found [3,23,24] which allow for accurate calculation of the distance to the fault but they are designed for fault locators or require additional signals and therefore cannot be implemented in the investigated algorithm. Thus, in this paper, the proposal to solve the problem of inaccurate distance to fault calculation by the considered impedance-differential protection in case of CTs saturation is introduced. The proposal aiming at improving the analysed algorithm is based on the compensation of deeply saturated current signal by using voltages from both line ends and current only from not saturated side and then use the calculated compensated current instead of the saturated current signal to calculate the differential impedance and finally the fault location. However, to implement the proposed solution concerning usage of compensated current signal in case of CTs saturation for fault location purposes, there is a need to detect the CTs saturation effectively. Several approaches may be found in the literature [25–41] to detect CT saturation and to mitigate or eliminate the impact of saturation. Among others, three main groups of methods have been suggested. The first group concerns the determination of CT saturation based on normative recommendations [25] or CT model equations [26–29]. This group [26–29] attempts to compensate the saturated current of CT by approximation of CT model. As mentioned in Refs. [27 and 28], this method is based on analysing the magnetic flux at the beginning of the saturation in the instance of fault. The model-based methods suffer from starting point and inaccuracy of estimation due to noise condition [30]. The second approach dedicated to the detection of CT saturation refers to algorithmic methods. This group [18,31–36] deals with mathematical extraction of some features from the unsaturated interval of the faulty current. These methods depend on the current waveform and interval of saturation. In the third group, there are classified solutions which used artificial-intelligence techniques [37–40], including artificial neural networks (ANNs) for CT saturation detection and compensation [37,40]. For these solutions, large amounts of training data considering different systems and CT parameters is required. Finally, the algorithmic method [41] has been selected for CT saturation detection in the considered application. It is based on the assumptions that the third derivative of the secondary current from the previous sampling period may be taken to predict the value of the next sample. If the absolute value of the predicted sample is more significant than the measured one, it shows that saturation began [41]. The chosen method of doing that used for study in this paper is simple, efficient, and accurate. What is important, the information about saturation interval length is not required for accurate distance to fault determination by the algorithm described in this paper.
2. Impedance-differential protective relay equipped with accurate fault location function In Fig. 1 the general structure for the considered impedance-differential protective relay is presented. Such a relay determines the phasors of three-phase voltages (VSφ, VRφ) and currents (ISφ, IRφ) from both line ends (S, R). It is considered that the phasors are determined synchronously, with the use of the DFT. To provide that the measurements from both line ends are synchronous, the use of the GPS has to be considered or one of the analytical methods for synchronisation can be applied [3]. The considered relay performs the protection function itself and in addition to that, it is proposed to equip the relay with accurate fault location function. In contrast to the protection function which is run on-line, the fault location is executed as off-line calculations, after the relay has identified a particular fault as occurring on the protected line. The protection function of the relay presented in Fig. 1 is performed with the use of the determined phasors. Firstly, a fault has to be detected and then an internal fault undergoes detecting, resulting in tripping the circuit-breakers at both the line ends. At the beginning, based on current signals from both sides of the protected line, the fault detection criterion is checked. This criterion is expressed in (1) where ISET is a threshold value:
| I Sϕ| + | I Rϕ | > ISET
(1)
Subsequently, the verification of a situation whether the fault is within zone or out-of-zone is done. It is achieved by calculating a distance to fault (d [p.u.]). The calculations of this value will be presented in Section 3, together with considering the introduced accurate fault location function. In order to have a reliable operation of the relay, different factors affecting the operation have to be investigated. Among them, CTs saturation appears as very important for that issue. However, the effect of CTs saturation does not affect the operation of the impedance-differential relay during internal faults, as it is described in Ref. [16] and presented in Section 4.2. Nevertheless, to prevent redundant tripping of the relay while the external fault with CTs 2
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Fig. 3. Schematic diagram of faulty current in case of the considered phase-tophase fault.
Z 2S (R) =
V 2S (R) I 2S (R)
(2)
Finally, the phase difference between phase angles of the negative sequence impedances is defined as:
ϕ2 = |arg ( Z 2S ) − arg ( Z 2R )|
(3)
Generally, if the value of phase difference (3) is close to zero degrees, this indicates that fault is within the protected zone. While it is near 180° the fault is out of the protected zone, and the relay should not operate. Therefore, the threshold value φ2SET is set to 90°. For symmetrical faults, the negative sequence impedance is replaced by the positive sequence impedance. Note, that for three-phase faults (especially when they are located near to the source) the terminal voltages may be close to zero. It means that positive sequence impedance is also close to zero. In such a case, the calculated phase difference (3) can give an incorrect result. Therefore, for such a situation, a memorised pre-fault positive sequence voltage is applied. The testing results [22] show that the described improved impedance-differential relay works appropriately even in the case of distinguishing external faults with CT saturation. Fig. 1. Impedance-differential protective relay equipped with accurate fault location function.
3. Accurate fault location with compensation of the CT saturation effects After the relay has identified that the fault occurs on the protected line, the off-line fault location procedure is executed. In the first step of this process, it is verified if CT saturation takes place or not. The method for this verification is described in Ref. [41]. The possible CT saturation may be determined through comparison of the predicted (estimated) value of the current sample and the real sample of the secondary current. If the secondary current sample is substantially smaller than the estimated value of the current, then one may conclude that the saturation took place. To predict the sample, which is unknown, one has to use previous samples taken during the undistorted section. For the algorithm investigated in this paper the third derivative of the secondary current from the previous sampling period is taken to predict the value of the next sample. According to formulas listed in Ref. [41] when the value of the third derivative during the two consecutive sampling instants is constant and using the first and second derivative calculations, the following formula to calculate the estimated value of the current can be presented:
Fig. 2. Equivalent transmission network circuit diagram for negative sequence component, where negative sequence impedance of the line is equal to positive sequence impedance Z2L = Z1L.
saturation occurs, the improved impedance-differential protective algorithm was introduced in Ref. [22]. According to the criterion presented in Ref. [22] a phase difference between phase angles of the calculated negative sequence impedances is checked – see Eqs. (2 and 3). The following equation gives the negative sequence impedance for side S or R:
i2e (n) = 4⋅i2 (n − 1) − 6⋅i2 (n − 2) + 4⋅i2 (n − 3) − i2 (n − 4) 3
(4)
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Fig. 4. ATP-EMTP model consisting of: 1 – faulted single-circuit transmission line; 2, 3 – equivalent systems with circuit breakers; 4 – fault model; 5, 6 – current transformers; 7, 8 – anti-aliasing filters in measurement of currents; 9, 10 – anti-aliasing filters in measurement of voltage. Table 2 Fault location results: 100 km line, L1-E fault, RF = 2 Ω, case I - SkS" = 8 GVA, SkR" = 4 GVA. Fault location [p.u]
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Max. Avg.
Fault location [p.u]
Table 1 Fault location results: 100 km line, L1-L2 fault, RF = 0.01 Ω, case I - SkS" = 8 GVA, SkR" = 4 GVA.
0.1 0.2 0.3 0.4 0.5a 0.6 0.7 0.8 0.9 Max. Avg. a
No saturation compensation
Saturation compensation
Side S
Side R
dcomp. [p.u]
Error [%]
dcomp. [p.u]
Error [%]
+ + + + – – – – – – –
– – – – – – + + + – –
0.1191 0.2296 0.3335 0.4235 0.5091 0.5957 0.6838 0.7756 0.8779 – –
1.9106 2.9574 3.3510 2.3477 0.9140 0.4271 1.6207 2.4418 2.2056 2.9574 2.4049
0.1010 0.1991 0.2982 0.3975 – – 0.7017 0.8007 0.8981 – –
0.1012 0.0852 0.1813 0.2544 – – 0.1675 0.0672 0.1939 0.2544 0.1501
Table 3 Fault location results: 100 km line, L1-L2 fault, RF = 0.01 Ω, case II - SkS" = 30 GVA, SkR" = 5 GVA.
Fig. 5. Magnetising characteristic of modelled CT.
Fault location [p.u]
CTs saturation
CTs saturation
No saturation compensation
Saturation compensation
Side S
Side R
dcomp. [p.u]
Error [%]
dcomp. [p.u]
Error [%]
+ + + + – – – – – – –
– – – – – – + + + – –
0.1276 0.2405 0.3405 0.4193 0.5019 0.5928 0.6841 0.7780 0.8830 – –
2.7618 4.0527 4.0532 1.9278 0.1856 0.7186 1.5888 2.2020 1.7048 4.0532 2.6130
0.0951 0.1945 0.2947 0.3950 – – 0.7038 0.8036 0.9018 – –
0.4851 0.5452 0.5293 0.5037 – – 0.3801 0.3569 0.1773 0.5452 0.4253
0.1 0.2a 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Max. Avg. a
The case presented in Figs. 6–9. 4
CTs saturation
No saturation compensation
Side S
Side R
dcomp. [p.u]
Error [%]
dcomp. [p.u]
Error [%]
+ + + + – – – – – – –
– – – – – – + + + – –
0.1304 0.2498 0.3508 0.4398 0.5094 0.5935 0.6838 0.7756 0.8818 – –
3.0418 4.9798 5.0795 3.9784 0.9389 0.6486 1.6245 2.4388 1.8196 5.0795 3.2803
0.0963 0.1962 0.2964 0.3965 – – 0.7019 0.8016 0.8998 – –
0.3741 0.3838 0.3648 0.3478 – – 0.1906 0.1616 0.0202 0.3838 0.2632
The case presented in Figs. 10–15.
Saturation compensation
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at the other terminal (S) can be derived analogously. The idea of current compensation is presented on the example of phase-to-phase fault (L1-L2). The calculations are aimed at determining the currents analytically from the side R since the measured currents are affected by the saturation. For current estimation, symmetrical components are used. For this purpose, the line model for negative sequence components (Fig. 2) is considered. In this circuit diagram, there is a supplementary distance to fault (dsup in p.u.), which will be applied for estimating the missing current. For the circuit of Fig. 2, the following formula can be obtained:
Table 4 Fault location results: 100 km line, L1-E fault, RF = 2 Ω, case II - SkS" = 30 GVA, SkR" = 5 GVA. Fault location [p.u]
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Max. Avg.
CTs saturation
No saturation compensation
Saturation compensation
Side S
Side R
dcomp. [p.u]
Error [%]
dcomp. [p.u]
Error [%]
+ + + + – – – – – – –
– – – – – – + + + – –
0.1077 0.2155 0.3204 0.4196 0.5043 0.5996 0.6891 0.7789 0.8795 – –
0.7711 1.5473 2.0353 1.9639 0.4323 0.0394 1.0885 2.1100 2.0497 2.1100 1.6522
0.1004 0.2001 0.2997 0.3992 – – 0.7015 0.8009 0.8991 – –
0.0442 0.0142 0.0255 0.0769 – – 0.1538 0.0939 0.0860 0.1538 0.0706
The negative sequence current of the R side of the protected line (IR2) can be calculated based on the known S side current (IS2) and negative sequence faulty current (IF2). According to Voltage Kirchhoff’s law, one defines the equation for the circuit of Fig. 2:
V S 2 − d sup Z 1L I S 2 − (1 − d sup )_Z 1L ( I S 2 − I F 2) − V R2 = 0
where i2 - real sample of secondary current, i2e – the estimated value of the secondary current sample. The saturation is detected when the absolute value of the estimated sample becomes higher than the real measured sample, and the n-th sample is the first in the saturated period.
|i2e (n)| − |i2 (n)| > Δ⋅|i2e (n)|
(6)
I R2 = I F 2 − I S 2
(7)
After the simple mathematical operation, the negative sequence faulty current is transferred to the one side of the formula and finally is equal to:
I F2 =
(5)
where Δ. is the value which takes into consideration the maximum error of estimation. For the applied sampling frequency, which was equal to 1000 Hz, the level of Δ. ought to be about 0.02 [41]. When CTs saturation has been detected, a method enabling for compensating the impact of saturation for distance to fault calculation is started. In this part, an idea of fault location determination in case of CTs saturation is described in detail. For this aim, the saturated current compensation has been introduced. It was assumed that CTs could saturate only at one end of the protected line. This assumption has been proposed since in reality, for the majority of fault cases, the saturation cannot happen simultaneously at both ends [43]. In this paper, the case of CTs saturation at the receiving end (R) of the line (Fig. 2) is presented. However, the proposed procedure for the case of CTs saturation
V R2 − V S 2 + Z 1L I S 2 (1 − d sup ) Z 1L
(8)
For the considered L1-L2 fault (Fig. 3), the constraints in the phase domain can be expressed as:
I F = I FL1 = − I FL2 I FL3 = 0
(9)
Transforming to the sequence domain one gets:
1 ( I FL1 + aI FL2 + a2 I FL3) = 3 1 = ( I FL1 + a2 I FL2 + aI FL3) = 3 1 = ( I FL1 + I FL2 + I FL3) = 0 3
I F1 = I F2 I F0
1 (1 − a) I FL1 3 1 (1 − a2) I FL1 3
Fig. 6. Voltage waveshapes in case of L1-L2 fault at 50% line length, without CT saturation. 5
(10)
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Fig. 7. Current waveshapes in case of L1-L2 fault at 50% line length, without CT saturation.
Fig. 8. Current signal at phase L1 (L1-L2 fault at 50% of line, without CT saturation) and no detection of the saturation. 3
Replacing IF2 by the formula from (8):
where: a = exp j2π /3 = −0, 5 + j 2 - phasor rotation operator. Next, the relation of positive and negative sequence of faulty currents is determined:
I F1 = I F2
1 (1 − a) I FL1 3 1 − a2) I FL1 (1 3
(1 − a) = (1 − a2)
I F = (1 − a)
3 I F 2 = (1 − a) I F 2 (1 − a2)
(13)
To obtain the fault current in a sequence domain, first, the supplementary distance dsup to the fault should be calculated. For this purpose, calculations considering the fault loop model [3] were applied. Incomplete two-end measurements, i.e. three-phase voltages from both line ends, while three-phase current only from the end where there is no saturation, are utilised here. The fault loop model, in which the term
(11)
Then, the faulty current is as follows:
I F = I FL1 =
V R2 − V S 2 + Z 1L IS 2 (1 − d sup) Z 1L
(12) 6
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M = (1 − a)
V R2 − V S 2 + Z 1L I S 2 Z 1L
(18)
Splitting (16) into the real and imaginary parts can be written down as:
Re( V SL1 − V SL2) − d sup Re[ Z 1L ( I SL1 − I SL2)] − K Re( M ) = 0 Im ( V SL1 − V SL2) − d sup Im[ Z 1L ( I SL1 − I SL2)] − KIm ( M ) = 0
(19)
After transformation, the formula for the supplementary fault distance calculation can be expressed:
d sup =
Im( V SL1 − V SL2) Re ( M ) − Re ( V SL1 − V SL2) Im ( M ) Im[ Z 1L ( I SL1 − I SL2)] Re ( M ) − Re[ Z 1L ( I SL1 − I SL2)] Im ( M ) (20)
While applying the calculated supplementary distance (20) to (8), the negative sequence faulty current (IF2) can be determined. In the next step, according to the Eq. (6) the negative sequence current of the R side of the protected line (IR2) can also be calculated. After transformation from symmetrical components to phase domain the line com current at the R side, the compensated current: I Rφ can be found. Moreover, the compensation of saturated current of the protected line can be derived analogously for other types of faults (note: for symmetrical faults positive sequence network is utilised). However, for the sake of briefness, they are not explained here. com The compensated current signal I Rφ . can be applied for accurate fault location calculations as in the impedance-differential protective algorithm. For this purpose, one requires firstly to calculate the compensated differential impedance [16], which is now expressed as:
Fig. 9. Computed distance to fault (L1-L2 fault at 50% of line) – without CT saturation.
RFIF represents the voltage drop across the fault path resistance, is formulated as:
V S _P − d sup Z 1L I S _P − RF I F = 0
(14)
where VS_P, IS_P - protective (subscript P) distance relay voltage and current signals, at the sending (S) line end. For L1-L2 fault the fault loop model can be written as:
( V SL1 − V SL2) − d sup Z 1L ( I SL1 − I SL2) − RF I F = 0
mod Z diff = ⎛1 + ⎝
(15)
(21)
Substituting IF in the Eq. (15) by the formula (13) gives:
( V SL1 − V SL2) − d sup Z 1L ( I SL1 − I SL2) − KM = 0
where voltages ( V ′Sφ , V ′Rφ ) are calculated from (22), and indices 0, 1 mean zero and positive sequence components:
(16)
V ′Sφ = V Sφ −
where K and M are coefficients determined:
RF K= 1 − d sup
com dI Sφ − (1 − d ) I Rφ V ′Sφ − V ′Rφ ⎞ Y 1L Z 1L ⎞ ⎜⎛ = Z 1L com ⎟ com 2 I Sφ − I Rφ ⎠ ⎝ I Sφ − I Rφ ⎠
Z 0L − Z1L V S0 Z 0L
(22)
By subtracting Z1L from both sides of (21) and ordering, the locational differential impedance is obtained:
(17)
Fig. 10. Voltage waveshapes in case of L1-L2 fault at 20% line length, with CT saturation. 7
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Fig. 11. Current waveshapes in case of L1-L2 fault at 20% line length, with CT saturation.
Fig. 12. The saturated current signal at phase L1 (L1-L2 fault at 20% of line) and detection of the saturation. Note – the CT primary current is drawn with the dotted line. com I Sφ − I Rφ Z ⎞ = Z (2d − 1) mod Z LOC = 2 ⎛ Z diff − 1L ⎞ ⎛⎜ 1L com ⎟ 2 ⎠ ⎝ I Sφ + I Rφ ⎠ ⎝
occurs, was possible. The verification of distance calculation accuracy is carried out in Section 4.
(23)
Thereafter, the fault location can be determined using [16]:
1 Im( Z LOC ) d= +1 2 Im( Z 1L)
4. Testing results 4.1. Simulated transmission system
(24)
Based on the presented considerations, a formulation of the expression enabling to calculate the distance to fault, while CT saturation
For assessing the presented fault location algorithm, the model of the 400 kV transmission line supplied from both sides has been 8
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Fig. 13. Calculated distance to fault for the case of CTs saturation (L1-L2 fault at 20% of line).
Fig. 15. Comparison of the imaginary part of the phasor for current (phase L1) at the terminal S.
and voltages phasors estimation is done using the DFT. 4.2. Evaluation results In order to test the studied fault location algorithm, short-circuit simulations were conducted inside the line as well as beyond it. The inner faults were simulated, referring to the S side at distances of d = 0, 0.1, 0.2, 0.3…1 [p.u.]. The faults applied outside the protected line were located behind the terminals S and R, respectively. While simulating faults three different line length were considered, namely 80 km, 100 km and 200 km. The studies included four different fault types: symmetrical faults (three-phase-to-earth fault) and different types of asymmetrical faults (phase-to-earth (L1-E), phase-to-phase (L1-L2), and phase-to-phase-to-earth (L1-L2-E) faults). In order to check the performance of the proposed method, the resistive earth faults have been simulated with the fault resistances which were equal to 0.01, 1, 2, 10, 50 Ω. For the remaining faults, resistance was equal to 0.01, 1, 2 Ω. Results presented in Tables 1 and 2 concerning the Case I and faults inside the protected line, for 100 km line, while the results for the Case II are put in Tables 3 and 4. Moreover, simulation results of L1-L2 faults are pointed out in Tables 1 and 3, whereas L1-E faults in case of fault resistance equals to 2 Ω are presented in Tables 2 and 4. In all tables, the calculated fault location based on the compensated current (the presented algorithm) is compared with the distance to fault calculation done by the usage of saturated current (the standard fault location algorithm). Calculated distance to fault is defined as an average of all obtained values within the third cycle of fault interval. The error of the fault location algorithm is defined as:
Fig. 14. Comparison of the real part of the phasor for current (phase L1) at the terminal S.
investigated. The simulation was performed in ATP-EMTP [42], while the fault location algorithm was implemented in MATLAB software. In Fig. 4 a single-circuit line model in ATP-EMTP utilised for the studies is presented. The overhead transmission line is modelled as a transposed one with distributed parameters. The line is supplied from both sides, regarding different systems strength:
• •
error (%) = (d − dactual )*100 Case I: SkS" = 8 GVA, SkR" = 4 GVA Case II: SkS" = 30 GVA, SkR" = 5 GVA.
(25)
where: dactual is the actual (used in simulation) distance to fault referring to the S side in [p.u.]. Moreover, when the fault occurs at the beginning or at the end of the line, the distance calculated by the proposed algorithm might be incorrect. It is caused by the fact that the terminal voltages, which are necessary to calculate locational impedance and distance to fault, are close to zero. In such a case, the real current signal is taken for fault distance calculation, instead of the compensated one. From all Tables, it can be observed that the effect of CTs saturation was observed for both line ends, but not simultaneously on them. Based on the obtained results, it can be concluded that in case of faults with CTs saturation, the standard fault location algorithm, based on the saturated current signal, enables to calculate the distance to a fault with
Additionally, the developed model includes CTs (1000/1 5P30 30VA) with adequate magnetising characteristic (Fig. 5), that are installed on the sending and receiving sides of the transmission line unit. The data of the considered transmission line for positive and zero sequences are respectively: Z1L = (0.0267 + j0.3151) Ω/km, C1L = 0.0130 μF/km, Z0L = (0.2750 + j1.0265) Ω/km, C0L = 0.0085 μF/km. The sampling frequency of 1 kHz has been adopted, what yields 20 samples per cycle under 50 Hz system frequency. The secondary currents and secondary voltages are filtered by anti-aliasing filters of 1 kHz/3 = 330 Hz cut off frequency. The currents 9
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primary level. For the chosen example from Table 3, where no saturation was obtained, the voltage and current waveshapes are presented in Figs. 6 and 7. In Fig. 8 no saturation detection is observed in the current signal at phase L1 and analogously it is for the faulted phase L2. Fig. 9 presents the distance to fault calculated according to the standard approach (without the usage of saturated current compensation). In this case, the error of fault location computation was equal to 0.19%, as indicated in Fig. 9. The voltage and current waveshapes concerning L1-L2 fault at 20% line length, with CT saturation, are presented in Figs. 10 and 11. From Fig. 11 it can be seen that the current is influenced by CT saturation in both faulty phases. From Fig.12, it can be observed that the CT saturation in phase L1 has started after one cycle, since the fault inception and was correctly detected what activates the proposed fault location algorithm. In Fig. 13 it is visualised how the calculated distance to fault was changed when CTs saturation has started. While using the standard fault location algorithm, i.e. without compensation of CTs saturation (the blue line), the obtained distance is calculated with the high error. While the application of the CTs compensation enabled to calculate the distance to a fault with high accuracy (green line). Figs. 14 and 15 show that after applying the compensation of saturation effect for distance calculation purposes, the obtained current in phase L1 (both real and imaginary part of the phasor) follows greatly the primary CT current, even when the transients are not yet finished.
high errors. Referring to the results (Tables 1–4), it can be seen that error of distance calculation, obtained from the standard approach using saturated current signal, is higher for the side of the line where the equivalent system is stronger. It is caused by the fact that CTs saturation effect is also deeper in case of faults occurring near the line terminal from the stronger system side. It means that the influence of CTs saturation on distance calculation depends on the short-circuit power of the equivalent system. For a strong system, as indicated in Table 3, the errors of distance calculation were the highest, i.e. exceeded 5%. While for the line side with the weak system, the maximal fault location error was approximately equal to 2.9%. Moreover, the calculated distance error in case of L1-L2 faults without saturation compensation (Tables 1, 3), was two times higher for the line side with the stronger system than for the side where there is a weaker equivalent system. Also, it can be concluded that the fault location error calculated by the standard fault location algorithm, in case of L1-E faults involving fault resistance equals to 2 Ω (Table 4), was at the same level for both line sides, regardless of the equivalent system strength. For all the considered cases, it is visible that in the area near to the middle of the line, CTs saturation effect is not observed. It means that in such cases, the standard impedance-differential fault location algorithm can be utilised. In the case of CTs saturation detection, the introduced algorithm with the compensated current, instead of saturated signal, for fault location calculation was used. Therefore, the error of distance computations was reduced in all cases (Tables 1–4). Taking into consideration different equivalent system short-circuit power in case of 100 km line, see Tables 1–4, it can be assessed that the proposed fault location algorithm enables to calculate the distance to fault for all simulated examples accurately. Based on the obtained results, it can be concluded that the average error obtained for the presented fault location algorithm is greater for phase-to-phase faults than for phase-to-earth faults. The average error obtained for all considered faults of 100 km line does not exceed 0.43% in any of the investigated cases. What is more, for phase-to-earth faults, the maximal average error is smaller than 0.16%. Generally accessing the fault location accuracy with the presented algorithm, one can conclude that the error is relatively small, and its maximal value is approximately equal to 0.5% in case of L1-L2 fault, arisen at the 20% of the line length (Table 1). In addition, the maximal error calculated using the presented algorithm, for L1-E investigated cases did not exceed 0.25% (Table 2). The different level of CTs saturation for different fault types is caused by the fact that the fault resistance was higher in the case of phase-to-earth faults than for phaseto-phase faults. The application of the proposed fault location algorithm enables to reduce the maximal distance calculation error approximately reaching the level of 5% to the value not exceeding 0.4% for the phase-to-phase fault occurring at 30% of line length (Table 3). While the standard algorithm was used, the maximal error for the L1-E fault, occurring at the 30% of the protected line length, was equal to 3.3%. With the use of the proposed fault location algorithm, this number was diminished to 0.18%. Summarising the quantitative evaluation of fault location accuracy for the presented algorithm, one can state that based on the results presented in Tables 1–4, it can be concluded that the improvement of the accuracy was achieved regardless of level for CTs saturation The following figures present testing results of the fault location algorithms (the standard fault location algorithm and the presented one), including selected analysis in case of CTs saturation and without it. In Figs. 6–9 the example of L1-L2 fault, occurring in the middle of the 100 km line, without the effect of saturation is depicted, while the case of CTs saturation for L1-E fault is presented in Figs. 10–13. Moreover, in Figs. 14,15 a comparison of the saturated and the compensated current of the S side of the line with current transformed by ideal CT is visualised. For this purpose, CTs secondary currents were recalculated to
5. Conclusions In this paper, an accurate fault location algorithm has been formulated for embedding it into an impedance-differential protective relay. It utilises voltage and current signals from both sides of the protected line and thus appears as an attractive solution. There are many fault location algorithms known for such input signals but it has been decided here to have a designed fault location compatible with the considered protection. It means that both the protection and fault location are based on the same way for calculating a distance to the fault. It has been shown that since the current signal can be distorted while CTs saturation occurs, the calculated fault location can be inaccurate. The aim of this paper was to present the concept enabling for improving the accuracy of the faults location calculation in case of CTs saturation at the one line end. For this purpose, the compensated current from this end was determined analytically and then used in the proposed algorithm, instead of the current affected by CT saturation. After a series of simulation tests, with use of the ATP-EMTP software, it can be concluded that the presented algorithm enables for accurate fault location, even under deep CTs saturation condition. The range for the improvement of accuracy has been shown in comparison to the cases with no CT saturation. Moreover, based on the presented results, it can be stated that the introduced fault location algorithm can be applicable for transmission lines of different lengths, as well as, is not affected by the fault resistance of different values. In the further investigations of the demonstrated fault location algorithm, a possibility of its application to double-circuit transmission lines has to be verified. Conflict of interest None. CRediT authorship contribution statement J. Herlender: Conceptualization, Methodology, Formal analysis, Writing - original draft. J. Iżykowski: Supervision. K. Solak: Software, Visualization. 10
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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Compensation of the current transformer saturation effects for transmission line fault location with impedance-differential relay
T
J. Herlender, J. Iżykowski*, K. Solak Electrical Power Engineering Department, Wroclaw University of Science and Technology, 27 Wybrzeze Wyspianskiego st., 50-370 Wroclaw, Poland
A R T I C LE I N FO
A B S T R A C T
Keywords: Fault location Current transformer saturation Transmission line Simulation
In this paper, the impedance-differential protection dedicated to transmission lines is analysed. The considerations are focused on the extra function of such protection, namely the ability to accurately determine the fault location for an inspection-repair purpose. Measurements of current and voltage at both line ends allow to formulate a differential impedance which constitutes an efficient criterion for fault locating. However, the considered fault location may face a problem when faults with current transformers (CTs) saturation take place. Therefore, in this paper, the proposal aiming at improving fault location accuracy by compensating the CTs saturation effect is introduced. For this purpose, the compensated current was determined by using voltages from both line ends and current from not saturated side and then used in the proposed algorithm instead of the saturated current. The introduced algorithm enables for accurate fault location, even under deep CTs saturation condition. The developed solution has been thoroughly tested with the signals generated with the use of ATPEMTP program.
1. Introduction Published fault statistics [1–3] unambiguously indicate that a majority of a total number of power system faults occur on overhead power lines. Such faults have to be detected and then located by protective relays as well as by fault locators [3,4]. In order to prevent spreading out the fault effects, the identified fault has to be cleared by a circuit breaker tripped by a protective relay as quickly as possible. One of the very first protection principles that have been developed and put into service is the differential criterion [5–7]. The standard line current-differential protection compares currents flowing into the protected line with those flowing out of the protected line and requires a reliable communication link to compare currents at the transmission line terminals [8,9]. The recent development of optical fibre communication technology has made it possible to solve the problems of a digital communication channel for current differential protection [10,11]. Due to this simple principle, current differential protection is easy to apply [12]. Moreover, the current-differential protection scheme is sensitive, highly selective for all fault types, secure [13] and operates stably in the presence of both high-frequency AC and DC components occurred during system faults [14]. In power line applications, is characterised by good tolerance to high line loading [15] and its principle is slightly or even completely not affected by weak
⁎
terminals, series compensation, cross-country faults, power swings, and nonstandard short-circuit current sources like renewable energy sources [12]. Moreover, installation of differential protection in power lines exhibit beneficial performance on multi-terminal lines as well on lines of any length [12]. The traditional current-differential relays [12] apply measurements of three-phase currents at the line ends, while the impedance-differential protection concerned in this paper, primarily introduced in Ref. [16], utilises the measurements of both currents and voltages from the line ends. Thus, more information on the fault is provided in the case of impedance-differential protection. As a result, not only effective protection of transmission line is achieved but also the distance to fault can be accurately determined, what is the main interest of this paper. The protection principle based on differential current is quite robust; however, there are still situations when it may maloperate [17]. For instance, this may be caused by current transformers (CTs) errors that are due to the high value of fault current amplitude or/and decaying DC components in fault currents. In the literature [18–21] it can be found several methods that propose improving stabilisation under external faults with CT saturation. However, these solutions are only dedicated to current-differential protection and do not guarantee the desired effects for all situations. Therefore, the solution dedicated to impedance-differential protection, while CTs saturation takes place, is
Corresponding author. E-mail address: [email protected] (J. Iżykowski).
https://doi.org/10.1016/j.epsr.2020.106223 Received 29 May 2019; Received in revised form 13 December 2019; Accepted 11 January 2020 Available online 06 February 2020 0378-7796/ © 2020 Elsevier B.V. All rights reserved.
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Nomenclature d dsup IF IF1,IF2, IF0 IS2, IR2 ISφ, IRφ i2(n)
i2e(n) VS2, VR2 VSφ, VRφ Z1L Z2S, Z2R
Calculated distance to a fault [p.u.] Supplementary distance to a fault [p.u.] Faulty current Positive, negative, zero sequence fault current Negative sequence current at the line terminal S, R Current in phase φ at the line terminal S, R Real sample of secondary current
ZLOC φ ϕ2
Estimated value of the secondary current sample Negative sequence voltage at the line terminal S, R Voltage in phase φ at the line terminal S, R Positive sequence impedance of the line Calculated negative sequence impedance of the equivalent system at the line terminal S, R Locational differential impedance Faulty phase (L1, L2, L3) Phase of the calculated negative sequence impedance
The aim of this paper is to analyse the fault location feature of the impedance-differential relay in case of CTs saturation. Several case studies are carried out to investigate the performance of the proposed method. In particular, a comprehensive evaluation of fault location accuracy with the use of the simulation data is presented. The examination of the algorithm was performed in MATLAB software using the fault data obtained from ATP-EMTP simulations [42]. In Section 2, the general structure of the considered impedancedifferential protective relay is presented. The main problems relevant for such protection are shortly described. The proposal for equipping a relay with off-line accurate fault location feature is also stated. Next, in Section 3, the concept of saturated current compensation in case of CT saturation for fault location purposes is introduced. Section 4 is devoted to presenting the testing results of the fault location feature incorporated into the impedance-differential relay, and a comprehensive evaluation of fault location accuracy is carried out. Finally, Section 5 contains the conclusions.
proposed by the authors in Ref. [22]. The introduced method is based on the phase angle calculation of the negative sequence impedances at both line ends. This solution enables to improve protection selectivity for external fault cases still maintaining sensitivity, reliability and speed of operation for all internal faults. However, the proposed solution is insufficient while taking into account the fault location function of the impedance-differential protective relay. In the case of CTs saturation, a secondary current signal which is used for fault location calculations can be distorted and thus causes inaccurate result in the distance to fault determination. In literature, many methods can be found [3,23,24] which allow for accurate calculation of the distance to the fault but they are designed for fault locators or require additional signals and therefore cannot be implemented in the investigated algorithm. Thus, in this paper, the proposal to solve the problem of inaccurate distance to fault calculation by the considered impedance-differential protection in case of CTs saturation is introduced. The proposal aiming at improving the analysed algorithm is based on the compensation of deeply saturated current signal by using voltages from both line ends and current only from not saturated side and then use the calculated compensated current instead of the saturated current signal to calculate the differential impedance and finally the fault location. However, to implement the proposed solution concerning usage of compensated current signal in case of CTs saturation for fault location purposes, there is a need to detect the CTs saturation effectively. Several approaches may be found in the literature [25–41] to detect CT saturation and to mitigate or eliminate the impact of saturation. Among others, three main groups of methods have been suggested. The first group concerns the determination of CT saturation based on normative recommendations [25] or CT model equations [26–29]. This group [26–29] attempts to compensate the saturated current of CT by approximation of CT model. As mentioned in Refs. [27 and 28], this method is based on analysing the magnetic flux at the beginning of the saturation in the instance of fault. The model-based methods suffer from starting point and inaccuracy of estimation due to noise condition [30]. The second approach dedicated to the detection of CT saturation refers to algorithmic methods. This group [18,31–36] deals with mathematical extraction of some features from the unsaturated interval of the faulty current. These methods depend on the current waveform and interval of saturation. In the third group, there are classified solutions which used artificial-intelligence techniques [37–40], including artificial neural networks (ANNs) for CT saturation detection and compensation [37,40]. For these solutions, large amounts of training data considering different systems and CT parameters is required. Finally, the algorithmic method [41] has been selected for CT saturation detection in the considered application. It is based on the assumptions that the third derivative of the secondary current from the previous sampling period may be taken to predict the value of the next sample. If the absolute value of the predicted sample is more significant than the measured one, it shows that saturation began [41]. The chosen method of doing that used for study in this paper is simple, efficient, and accurate. What is important, the information about saturation interval length is not required for accurate distance to fault determination by the algorithm described in this paper.
2. Impedance-differential protective relay equipped with accurate fault location function In Fig. 1 the general structure for the considered impedance-differential protective relay is presented. Such a relay determines the phasors of three-phase voltages (VSφ, VRφ) and currents (ISφ, IRφ) from both line ends (S, R). It is considered that the phasors are determined synchronously, with the use of the DFT. To provide that the measurements from both line ends are synchronous, the use of the GPS has to be considered or one of the analytical methods for synchronisation can be applied [3]. The considered relay performs the protection function itself and in addition to that, it is proposed to equip the relay with accurate fault location function. In contrast to the protection function which is run on-line, the fault location is executed as off-line calculations, after the relay has identified a particular fault as occurring on the protected line. The protection function of the relay presented in Fig. 1 is performed with the use of the determined phasors. Firstly, a fault has to be detected and then an internal fault undergoes detecting, resulting in tripping the circuit-breakers at both the line ends. At the beginning, based on current signals from both sides of the protected line, the fault detection criterion is checked. This criterion is expressed in (1) where ISET is a threshold value:
| I Sϕ| + | I Rϕ | > ISET
(1)
Subsequently, the verification of a situation whether the fault is within zone or out-of-zone is done. It is achieved by calculating a distance to fault (d [p.u.]). The calculations of this value will be presented in Section 3, together with considering the introduced accurate fault location function. In order to have a reliable operation of the relay, different factors affecting the operation have to be investigated. Among them, CTs saturation appears as very important for that issue. However, the effect of CTs saturation does not affect the operation of the impedance-differential relay during internal faults, as it is described in Ref. [16] and presented in Section 4.2. Nevertheless, to prevent redundant tripping of the relay while the external fault with CTs 2
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Fig. 3. Schematic diagram of faulty current in case of the considered phase-tophase fault.
Z 2S (R) =
V 2S (R) I 2S (R)
(2)
Finally, the phase difference between phase angles of the negative sequence impedances is defined as:
ϕ2 = |arg ( Z 2S ) − arg ( Z 2R )|
(3)
Generally, if the value of phase difference (3) is close to zero degrees, this indicates that fault is within the protected zone. While it is near 180° the fault is out of the protected zone, and the relay should not operate. Therefore, the threshold value φ2SET is set to 90°. For symmetrical faults, the negative sequence impedance is replaced by the positive sequence impedance. Note, that for three-phase faults (especially when they are located near to the source) the terminal voltages may be close to zero. It means that positive sequence impedance is also close to zero. In such a case, the calculated phase difference (3) can give an incorrect result. Therefore, for such a situation, a memorised pre-fault positive sequence voltage is applied. The testing results [22] show that the described improved impedance-differential relay works appropriately even in the case of distinguishing external faults with CT saturation. Fig. 1. Impedance-differential protective relay equipped with accurate fault location function.
3. Accurate fault location with compensation of the CT saturation effects After the relay has identified that the fault occurs on the protected line, the off-line fault location procedure is executed. In the first step of this process, it is verified if CT saturation takes place or not. The method for this verification is described in Ref. [41]. The possible CT saturation may be determined through comparison of the predicted (estimated) value of the current sample and the real sample of the secondary current. If the secondary current sample is substantially smaller than the estimated value of the current, then one may conclude that the saturation took place. To predict the sample, which is unknown, one has to use previous samples taken during the undistorted section. For the algorithm investigated in this paper the third derivative of the secondary current from the previous sampling period is taken to predict the value of the next sample. According to formulas listed in Ref. [41] when the value of the third derivative during the two consecutive sampling instants is constant and using the first and second derivative calculations, the following formula to calculate the estimated value of the current can be presented:
Fig. 2. Equivalent transmission network circuit diagram for negative sequence component, where negative sequence impedance of the line is equal to positive sequence impedance Z2L = Z1L.
saturation occurs, the improved impedance-differential protective algorithm was introduced in Ref. [22]. According to the criterion presented in Ref. [22] a phase difference between phase angles of the calculated negative sequence impedances is checked – see Eqs. (2 and 3). The following equation gives the negative sequence impedance for side S or R:
i2e (n) = 4⋅i2 (n − 1) − 6⋅i2 (n − 2) + 4⋅i2 (n − 3) − i2 (n − 4) 3
(4)
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Fig. 4. ATP-EMTP model consisting of: 1 – faulted single-circuit transmission line; 2, 3 – equivalent systems with circuit breakers; 4 – fault model; 5, 6 – current transformers; 7, 8 – anti-aliasing filters in measurement of currents; 9, 10 – anti-aliasing filters in measurement of voltage. Table 2 Fault location results: 100 km line, L1-E fault, RF = 2 Ω, case I - SkS" = 8 GVA, SkR" = 4 GVA. Fault location [p.u]
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Max. Avg.
Fault location [p.u]
Table 1 Fault location results: 100 km line, L1-L2 fault, RF = 0.01 Ω, case I - SkS" = 8 GVA, SkR" = 4 GVA.
0.1 0.2 0.3 0.4 0.5a 0.6 0.7 0.8 0.9 Max. Avg. a
No saturation compensation
Saturation compensation
Side S
Side R
dcomp. [p.u]
Error [%]
dcomp. [p.u]
Error [%]
+ + + + – – – – – – –
– – – – – – + + + – –
0.1191 0.2296 0.3335 0.4235 0.5091 0.5957 0.6838 0.7756 0.8779 – –
1.9106 2.9574 3.3510 2.3477 0.9140 0.4271 1.6207 2.4418 2.2056 2.9574 2.4049
0.1010 0.1991 0.2982 0.3975 – – 0.7017 0.8007 0.8981 – –
0.1012 0.0852 0.1813 0.2544 – – 0.1675 0.0672 0.1939 0.2544 0.1501
Table 3 Fault location results: 100 km line, L1-L2 fault, RF = 0.01 Ω, case II - SkS" = 30 GVA, SkR" = 5 GVA.
Fig. 5. Magnetising characteristic of modelled CT.
Fault location [p.u]
CTs saturation
CTs saturation
No saturation compensation
Saturation compensation
Side S
Side R
dcomp. [p.u]
Error [%]
dcomp. [p.u]
Error [%]
+ + + + – – – – – – –
– – – – – – + + + – –
0.1276 0.2405 0.3405 0.4193 0.5019 0.5928 0.6841 0.7780 0.8830 – –
2.7618 4.0527 4.0532 1.9278 0.1856 0.7186 1.5888 2.2020 1.7048 4.0532 2.6130
0.0951 0.1945 0.2947 0.3950 – – 0.7038 0.8036 0.9018 – –
0.4851 0.5452 0.5293 0.5037 – – 0.3801 0.3569 0.1773 0.5452 0.4253
0.1 0.2a 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Max. Avg. a
The case presented in Figs. 6–9. 4
CTs saturation
No saturation compensation
Side S
Side R
dcomp. [p.u]
Error [%]
dcomp. [p.u]
Error [%]
+ + + + – – – – – – –
– – – – – – + + + – –
0.1304 0.2498 0.3508 0.4398 0.5094 0.5935 0.6838 0.7756 0.8818 – –
3.0418 4.9798 5.0795 3.9784 0.9389 0.6486 1.6245 2.4388 1.8196 5.0795 3.2803
0.0963 0.1962 0.2964 0.3965 – – 0.7019 0.8016 0.8998 – –
0.3741 0.3838 0.3648 0.3478 – – 0.1906 0.1616 0.0202 0.3838 0.2632
The case presented in Figs. 10–15.
Saturation compensation
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at the other terminal (S) can be derived analogously. The idea of current compensation is presented on the example of phase-to-phase fault (L1-L2). The calculations are aimed at determining the currents analytically from the side R since the measured currents are affected by the saturation. For current estimation, symmetrical components are used. For this purpose, the line model for negative sequence components (Fig. 2) is considered. In this circuit diagram, there is a supplementary distance to fault (dsup in p.u.), which will be applied for estimating the missing current. For the circuit of Fig. 2, the following formula can be obtained:
Table 4 Fault location results: 100 km line, L1-E fault, RF = 2 Ω, case II - SkS" = 30 GVA, SkR" = 5 GVA. Fault location [p.u]
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Max. Avg.
CTs saturation
No saturation compensation
Saturation compensation
Side S
Side R
dcomp. [p.u]
Error [%]
dcomp. [p.u]
Error [%]
+ + + + – – – – – – –
– – – – – – + + + – –
0.1077 0.2155 0.3204 0.4196 0.5043 0.5996 0.6891 0.7789 0.8795 – –
0.7711 1.5473 2.0353 1.9639 0.4323 0.0394 1.0885 2.1100 2.0497 2.1100 1.6522
0.1004 0.2001 0.2997 0.3992 – – 0.7015 0.8009 0.8991 – –
0.0442 0.0142 0.0255 0.0769 – – 0.1538 0.0939 0.0860 0.1538 0.0706
The negative sequence current of the R side of the protected line (IR2) can be calculated based on the known S side current (IS2) and negative sequence faulty current (IF2). According to Voltage Kirchhoff’s law, one defines the equation for the circuit of Fig. 2:
V S 2 − d sup Z 1L I S 2 − (1 − d sup )_Z 1L ( I S 2 − I F 2) − V R2 = 0
where i2 - real sample of secondary current, i2e – the estimated value of the secondary current sample. The saturation is detected when the absolute value of the estimated sample becomes higher than the real measured sample, and the n-th sample is the first in the saturated period.
|i2e (n)| − |i2 (n)| > Δ⋅|i2e (n)|
(6)
I R2 = I F 2 − I S 2
(7)
After the simple mathematical operation, the negative sequence faulty current is transferred to the one side of the formula and finally is equal to:
I F2 =
(5)
where Δ. is the value which takes into consideration the maximum error of estimation. For the applied sampling frequency, which was equal to 1000 Hz, the level of Δ. ought to be about 0.02 [41]. When CTs saturation has been detected, a method enabling for compensating the impact of saturation for distance to fault calculation is started. In this part, an idea of fault location determination in case of CTs saturation is described in detail. For this aim, the saturated current compensation has been introduced. It was assumed that CTs could saturate only at one end of the protected line. This assumption has been proposed since in reality, for the majority of fault cases, the saturation cannot happen simultaneously at both ends [43]. In this paper, the case of CTs saturation at the receiving end (R) of the line (Fig. 2) is presented. However, the proposed procedure for the case of CTs saturation
V R2 − V S 2 + Z 1L I S 2 (1 − d sup ) Z 1L
(8)
For the considered L1-L2 fault (Fig. 3), the constraints in the phase domain can be expressed as:
I F = I FL1 = − I FL2 I FL3 = 0
(9)
Transforming to the sequence domain one gets:
1 ( I FL1 + aI FL2 + a2 I FL3) = 3 1 = ( I FL1 + a2 I FL2 + aI FL3) = 3 1 = ( I FL1 + I FL2 + I FL3) = 0 3
I F1 = I F2 I F0
1 (1 − a) I FL1 3 1 (1 − a2) I FL1 3
Fig. 6. Voltage waveshapes in case of L1-L2 fault at 50% line length, without CT saturation. 5
(10)
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Fig. 7. Current waveshapes in case of L1-L2 fault at 50% line length, without CT saturation.
Fig. 8. Current signal at phase L1 (L1-L2 fault at 50% of line, without CT saturation) and no detection of the saturation. 3
Replacing IF2 by the formula from (8):
where: a = exp j2π /3 = −0, 5 + j 2 - phasor rotation operator. Next, the relation of positive and negative sequence of faulty currents is determined:
I F1 = I F2
1 (1 − a) I FL1 3 1 − a2) I FL1 (1 3
(1 − a) = (1 − a2)
I F = (1 − a)
3 I F 2 = (1 − a) I F 2 (1 − a2)
(13)
To obtain the fault current in a sequence domain, first, the supplementary distance dsup to the fault should be calculated. For this purpose, calculations considering the fault loop model [3] were applied. Incomplete two-end measurements, i.e. three-phase voltages from both line ends, while three-phase current only from the end where there is no saturation, are utilised here. The fault loop model, in which the term
(11)
Then, the faulty current is as follows:
I F = I FL1 =
V R2 − V S 2 + Z 1L IS 2 (1 − d sup) Z 1L
(12) 6
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M = (1 − a)
V R2 − V S 2 + Z 1L I S 2 Z 1L
(18)
Splitting (16) into the real and imaginary parts can be written down as:
Re( V SL1 − V SL2) − d sup Re[ Z 1L ( I SL1 − I SL2)] − K Re( M ) = 0 Im ( V SL1 − V SL2) − d sup Im[ Z 1L ( I SL1 − I SL2)] − KIm ( M ) = 0
(19)
After transformation, the formula for the supplementary fault distance calculation can be expressed:
d sup =
Im( V SL1 − V SL2) Re ( M ) − Re ( V SL1 − V SL2) Im ( M ) Im[ Z 1L ( I SL1 − I SL2)] Re ( M ) − Re[ Z 1L ( I SL1 − I SL2)] Im ( M ) (20)
While applying the calculated supplementary distance (20) to (8), the negative sequence faulty current (IF2) can be determined. In the next step, according to the Eq. (6) the negative sequence current of the R side of the protected line (IR2) can also be calculated. After transformation from symmetrical components to phase domain the line com current at the R side, the compensated current: I Rφ can be found. Moreover, the compensation of saturated current of the protected line can be derived analogously for other types of faults (note: for symmetrical faults positive sequence network is utilised). However, for the sake of briefness, they are not explained here. com The compensated current signal I Rφ . can be applied for accurate fault location calculations as in the impedance-differential protective algorithm. For this purpose, one requires firstly to calculate the compensated differential impedance [16], which is now expressed as:
Fig. 9. Computed distance to fault (L1-L2 fault at 50% of line) – without CT saturation.
RFIF represents the voltage drop across the fault path resistance, is formulated as:
V S _P − d sup Z 1L I S _P − RF I F = 0
(14)
where VS_P, IS_P - protective (subscript P) distance relay voltage and current signals, at the sending (S) line end. For L1-L2 fault the fault loop model can be written as:
( V SL1 − V SL2) − d sup Z 1L ( I SL1 − I SL2) − RF I F = 0
mod Z diff = ⎛1 + ⎝
(15)
(21)
Substituting IF in the Eq. (15) by the formula (13) gives:
( V SL1 − V SL2) − d sup Z 1L ( I SL1 − I SL2) − KM = 0
where voltages ( V ′Sφ , V ′Rφ ) are calculated from (22), and indices 0, 1 mean zero and positive sequence components:
(16)
V ′Sφ = V Sφ −
where K and M are coefficients determined:
RF K= 1 − d sup
com dI Sφ − (1 − d ) I Rφ V ′Sφ − V ′Rφ ⎞ Y 1L Z 1L ⎞ ⎜⎛ = Z 1L com ⎟ com 2 I Sφ − I Rφ ⎠ ⎝ I Sφ − I Rφ ⎠
Z 0L − Z1L V S0 Z 0L
(22)
By subtracting Z1L from both sides of (21) and ordering, the locational differential impedance is obtained:
(17)
Fig. 10. Voltage waveshapes in case of L1-L2 fault at 20% line length, with CT saturation. 7
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Fig. 11. Current waveshapes in case of L1-L2 fault at 20% line length, with CT saturation.
Fig. 12. The saturated current signal at phase L1 (L1-L2 fault at 20% of line) and detection of the saturation. Note – the CT primary current is drawn with the dotted line. com I Sφ − I Rφ Z ⎞ = Z (2d − 1) mod Z LOC = 2 ⎛ Z diff − 1L ⎞ ⎛⎜ 1L com ⎟ 2 ⎠ ⎝ I Sφ + I Rφ ⎠ ⎝
occurs, was possible. The verification of distance calculation accuracy is carried out in Section 4.
(23)
Thereafter, the fault location can be determined using [16]:
1 Im( Z LOC ) d= +1 2 Im( Z 1L)
4. Testing results 4.1. Simulated transmission system
(24)
Based on the presented considerations, a formulation of the expression enabling to calculate the distance to fault, while CT saturation
For assessing the presented fault location algorithm, the model of the 400 kV transmission line supplied from both sides has been 8
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Fig. 13. Calculated distance to fault for the case of CTs saturation (L1-L2 fault at 20% of line).
Fig. 15. Comparison of the imaginary part of the phasor for current (phase L1) at the terminal S.
and voltages phasors estimation is done using the DFT. 4.2. Evaluation results In order to test the studied fault location algorithm, short-circuit simulations were conducted inside the line as well as beyond it. The inner faults were simulated, referring to the S side at distances of d = 0, 0.1, 0.2, 0.3…1 [p.u.]. The faults applied outside the protected line were located behind the terminals S and R, respectively. While simulating faults three different line length were considered, namely 80 km, 100 km and 200 km. The studies included four different fault types: symmetrical faults (three-phase-to-earth fault) and different types of asymmetrical faults (phase-to-earth (L1-E), phase-to-phase (L1-L2), and phase-to-phase-to-earth (L1-L2-E) faults). In order to check the performance of the proposed method, the resistive earth faults have been simulated with the fault resistances which were equal to 0.01, 1, 2, 10, 50 Ω. For the remaining faults, resistance was equal to 0.01, 1, 2 Ω. Results presented in Tables 1 and 2 concerning the Case I and faults inside the protected line, for 100 km line, while the results for the Case II are put in Tables 3 and 4. Moreover, simulation results of L1-L2 faults are pointed out in Tables 1 and 3, whereas L1-E faults in case of fault resistance equals to 2 Ω are presented in Tables 2 and 4. In all tables, the calculated fault location based on the compensated current (the presented algorithm) is compared with the distance to fault calculation done by the usage of saturated current (the standard fault location algorithm). Calculated distance to fault is defined as an average of all obtained values within the third cycle of fault interval. The error of the fault location algorithm is defined as:
Fig. 14. Comparison of the real part of the phasor for current (phase L1) at the terminal S.
investigated. The simulation was performed in ATP-EMTP [42], while the fault location algorithm was implemented in MATLAB software. In Fig. 4 a single-circuit line model in ATP-EMTP utilised for the studies is presented. The overhead transmission line is modelled as a transposed one with distributed parameters. The line is supplied from both sides, regarding different systems strength:
• •
error (%) = (d − dactual )*100 Case I: SkS" = 8 GVA, SkR" = 4 GVA Case II: SkS" = 30 GVA, SkR" = 5 GVA.
(25)
where: dactual is the actual (used in simulation) distance to fault referring to the S side in [p.u.]. Moreover, when the fault occurs at the beginning or at the end of the line, the distance calculated by the proposed algorithm might be incorrect. It is caused by the fact that the terminal voltages, which are necessary to calculate locational impedance and distance to fault, are close to zero. In such a case, the real current signal is taken for fault distance calculation, instead of the compensated one. From all Tables, it can be observed that the effect of CTs saturation was observed for both line ends, but not simultaneously on them. Based on the obtained results, it can be concluded that in case of faults with CTs saturation, the standard fault location algorithm, based on the saturated current signal, enables to calculate the distance to a fault with
Additionally, the developed model includes CTs (1000/1 5P30 30VA) with adequate magnetising characteristic (Fig. 5), that are installed on the sending and receiving sides of the transmission line unit. The data of the considered transmission line for positive and zero sequences are respectively: Z1L = (0.0267 + j0.3151) Ω/km, C1L = 0.0130 μF/km, Z0L = (0.2750 + j1.0265) Ω/km, C0L = 0.0085 μF/km. The sampling frequency of 1 kHz has been adopted, what yields 20 samples per cycle under 50 Hz system frequency. The secondary currents and secondary voltages are filtered by anti-aliasing filters of 1 kHz/3 = 330 Hz cut off frequency. The currents 9
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primary level. For the chosen example from Table 3, where no saturation was obtained, the voltage and current waveshapes are presented in Figs. 6 and 7. In Fig. 8 no saturation detection is observed in the current signal at phase L1 and analogously it is for the faulted phase L2. Fig. 9 presents the distance to fault calculated according to the standard approach (without the usage of saturated current compensation). In this case, the error of fault location computation was equal to 0.19%, as indicated in Fig. 9. The voltage and current waveshapes concerning L1-L2 fault at 20% line length, with CT saturation, are presented in Figs. 10 and 11. From Fig. 11 it can be seen that the current is influenced by CT saturation in both faulty phases. From Fig.12, it can be observed that the CT saturation in phase L1 has started after one cycle, since the fault inception and was correctly detected what activates the proposed fault location algorithm. In Fig. 13 it is visualised how the calculated distance to fault was changed when CTs saturation has started. While using the standard fault location algorithm, i.e. without compensation of CTs saturation (the blue line), the obtained distance is calculated with the high error. While the application of the CTs compensation enabled to calculate the distance to a fault with high accuracy (green line). Figs. 14 and 15 show that after applying the compensation of saturation effect for distance calculation purposes, the obtained current in phase L1 (both real and imaginary part of the phasor) follows greatly the primary CT current, even when the transients are not yet finished.
high errors. Referring to the results (Tables 1–4), it can be seen that error of distance calculation, obtained from the standard approach using saturated current signal, is higher for the side of the line where the equivalent system is stronger. It is caused by the fact that CTs saturation effect is also deeper in case of faults occurring near the line terminal from the stronger system side. It means that the influence of CTs saturation on distance calculation depends on the short-circuit power of the equivalent system. For a strong system, as indicated in Table 3, the errors of distance calculation were the highest, i.e. exceeded 5%. While for the line side with the weak system, the maximal fault location error was approximately equal to 2.9%. Moreover, the calculated distance error in case of L1-L2 faults without saturation compensation (Tables 1, 3), was two times higher for the line side with the stronger system than for the side where there is a weaker equivalent system. Also, it can be concluded that the fault location error calculated by the standard fault location algorithm, in case of L1-E faults involving fault resistance equals to 2 Ω (Table 4), was at the same level for both line sides, regardless of the equivalent system strength. For all the considered cases, it is visible that in the area near to the middle of the line, CTs saturation effect is not observed. It means that in such cases, the standard impedance-differential fault location algorithm can be utilised. In the case of CTs saturation detection, the introduced algorithm with the compensated current, instead of saturated signal, for fault location calculation was used. Therefore, the error of distance computations was reduced in all cases (Tables 1–4). Taking into consideration different equivalent system short-circuit power in case of 100 km line, see Tables 1–4, it can be assessed that the proposed fault location algorithm enables to calculate the distance to fault for all simulated examples accurately. Based on the obtained results, it can be concluded that the average error obtained for the presented fault location algorithm is greater for phase-to-phase faults than for phase-to-earth faults. The average error obtained for all considered faults of 100 km line does not exceed 0.43% in any of the investigated cases. What is more, for phase-to-earth faults, the maximal average error is smaller than 0.16%. Generally accessing the fault location accuracy with the presented algorithm, one can conclude that the error is relatively small, and its maximal value is approximately equal to 0.5% in case of L1-L2 fault, arisen at the 20% of the line length (Table 1). In addition, the maximal error calculated using the presented algorithm, for L1-E investigated cases did not exceed 0.25% (Table 2). The different level of CTs saturation for different fault types is caused by the fact that the fault resistance was higher in the case of phase-to-earth faults than for phaseto-phase faults. The application of the proposed fault location algorithm enables to reduce the maximal distance calculation error approximately reaching the level of 5% to the value not exceeding 0.4% for the phase-to-phase fault occurring at 30% of line length (Table 3). While the standard algorithm was used, the maximal error for the L1-E fault, occurring at the 30% of the protected line length, was equal to 3.3%. With the use of the proposed fault location algorithm, this number was diminished to 0.18%. Summarising the quantitative evaluation of fault location accuracy for the presented algorithm, one can state that based on the results presented in Tables 1–4, it can be concluded that the improvement of the accuracy was achieved regardless of level for CTs saturation The following figures present testing results of the fault location algorithms (the standard fault location algorithm and the presented one), including selected analysis in case of CTs saturation and without it. In Figs. 6–9 the example of L1-L2 fault, occurring in the middle of the 100 km line, without the effect of saturation is depicted, while the case of CTs saturation for L1-E fault is presented in Figs. 10–13. Moreover, in Figs. 14,15 a comparison of the saturated and the compensated current of the S side of the line with current transformed by ideal CT is visualised. For this purpose, CTs secondary currents were recalculated to
5. Conclusions In this paper, an accurate fault location algorithm has been formulated for embedding it into an impedance-differential protective relay. It utilises voltage and current signals from both sides of the protected line and thus appears as an attractive solution. There are many fault location algorithms known for such input signals but it has been decided here to have a designed fault location compatible with the considered protection. It means that both the protection and fault location are based on the same way for calculating a distance to the fault. It has been shown that since the current signal can be distorted while CTs saturation occurs, the calculated fault location can be inaccurate. The aim of this paper was to present the concept enabling for improving the accuracy of the faults location calculation in case of CTs saturation at the one line end. For this purpose, the compensated current from this end was determined analytically and then used in the proposed algorithm, instead of the current affected by CT saturation. After a series of simulation tests, with use of the ATP-EMTP software, it can be concluded that the presented algorithm enables for accurate fault location, even under deep CTs saturation condition. The range for the improvement of accuracy has been shown in comparison to the cases with no CT saturation. Moreover, based on the presented results, it can be stated that the introduced fault location algorithm can be applicable for transmission lines of different lengths, as well as, is not affected by the fault resistance of different values. In the further investigations of the demonstrated fault location algorithm, a possibility of its application to double-circuit transmission lines has to be verified. Conflict of interest None. CRediT authorship contribution statement J. Herlender: Conceptualization, Methodology, Formal analysis, Writing - original draft. J. Iżykowski: Supervision. K. Solak: Software, Visualization. 10
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