A novel wavelet approach to busbar protection during CT saturation and ratio-mismatch

Electric Power Systems Research 72 (2004) 41–48

A novel wavelet approach to busbar protection during CT saturation and ratio-mismatch M.M. Eissa Department of Electrical Engineering, Faculty of Engineering, Helwan University, Helwan, Cairo, Egypt Received 30 July 2003; accepted 15 March 2004 Available online 5 June 2004

Abstract This paper deals with the use of a continuous wavelet transform (CWT) to distinguish faults in a busbar protection zone from those outside the zone. The Morlet wavelets are used as the wavelet basis function. They are more efficient in monitoring fault signals as time varies. The differential current as the operating quantity and the sum of the current magnitudes as the stabilizing signal are computed. The magnitudes of the CWT of these currents are derived to obtain the operational and restraint signals. The CWT coefficient plots are given to precisely determine the scale of analysis. The proposed wavelet transform approach based on Morlet basis function is found to be an excellent discriminant for identifying the fault signals during the CT saturation and ratio mismatch. ATP simulations are used to test and validate the proposed CWT approach for model power system faults. © 2004 Elsevier B.V. All rights reserved. Keywords: Bus-bar faults; Transients; Morlet wavelet; CT saturation; Protective relaying

1. Introduction A bus is one of the most critical system elements. It is the connecting point of a variety of elements and a number of transmission lines and any incorrect operation would cause the loss of all of these elements. Protection of busbars demands high speed reliability and stability. Failure-to-trip on an internal fault, as well as false tripping of a busbar during service, or in case of an external fault, can both have disastrous effect on the stability of the power system, and may even cause complete blackout [1]. Numeric techniques in protective relay design are offering the opportunity to improve busbar protection schemes and hence overall power system availability and reliability [2,3]. A very few algorithms for protecting busbars have been published. A directional comparison and current differential scheme to protect complex bus arrangements was introduced by [4]. The technique switched current transformer (CT) secondary current signals for the differential schemes. The CT current switching may result in hazards in the protected zone due to an open CT secondary circuit. A medium impedance differ-

E-mail address: [email protected] (M.M. Eissa). 0378-7796/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2004.03.003

ential bus relay is improved by [5] to solve the hazards in the protected zone. A low impedance protective relay for stabilizing the performance during CT saturation is developed in [6]. Another scheme [7] is based on developing electronic detector to identify saturated CTs for busbar protection. The technique provides auxiliary relays in the protection scheme to represent the disconnect switches in bus arrangements. A half cycle bus differential relay that uses information from the inception of the fault to the onset of CT saturation is developed by [8]. The design of isolator replica to suit different bus configurations, its realization through hard-wired logic and subsequent testing, has been a major drawback of analog bus protection schemes [9]. A numerical bus protection described in [9] realizes the inequalities (criteria for trip) as well as the charging of the capacitor and its discharge with microprocessor based software using digitized line currents. A new method for protection zone selection and its implementation in microprocessor is developed in [10]. The technique uses the graph theory for simplifying a complex bus arrangement. In [11,12], a technique is proposed for protecting busbars during CT saturation. The technique uses the positive-and-negative sequence models of the power system. The phase voltages and currents are used to detect faults. A protection method in [13]

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is used to protect the busbar based on digital low-impedance differential relay that combines the differential and current directional protection principles within the frame work of an adaptive algorithm controlled by a dedicated CT saturation detection module. A training tool for neural networks and a set of typical distorted and undistorted current signals is applied in [14]. An enhanced decentralized numerical busbar protection relay utilizing instantaneous current values from high speed sampling is introduced in [15]. Some of the previous proposed methods prevent relay operation during CT saturation. This may result in longer trip times. The other methods cannot guarantee correct operation under heavy and early CT saturation conditions. However, some algorithms that use the voltage signals may fail to operate in case of voltage collapse. While, the availability of information about voltage signal is not generated. This paper describes an approach that distinguishes faults in a busbar protection zone from these outside the zone. The technique is based on the concept of CWT based basis function. The Morlet wavelet is used as the basis function. A Morlet wavelet basis function is embedded within a wavelet transform (WT) scheme to detect and discriminate faults in case of CT saturation. The phenomenon of CT saturation and its impact on the proposed technique has also been analyzed. Some test results are also presented. Stability of the proposed technique during the CT saturating and ratio mismatches are also provided. The studied configuration systemis is given in Fig. 1.

2. Wavelet transform The main problem with the windowed Fourier transform WFT is the inconsistent treatment of different frequencies: at low frequencies there so few oscillations within the window that the frequency localization is lost, while at high frequencies there are so many oscillations that the time localization is lost. Finally, the WFT relies on the assumption that the signal can be decomposed into sinusoidal components. WT has been introduced rather recently in mathematics, even though the essential ideas to this development have been around for a long period of time. It is a linear transformation much like the Fourier transform, however with one important difference: it allows time localization of different frequency components of a given signal. WFT achieves this same goal, but with a limitation of using a fixed width windowing function. As a result, both frequency and time resolution of the resulting transform will be fixed. In the case of the WT, the analyzing functions, which are called wavelets, will adjust their time-widths to their frequency in such a way that, higher frequency wavelets will be very narrow and lower frequency ones will be broader. This property is very useful for analyzing fault transients during CT saturation. The WT of a time dependent signal, f(t), consists in finding a set of coefficients WTa,b . These coefficients measure the similarity between the signal f(t) and a set of functions

Fig. 1. Studied bus configuration system.

ψa,b (t). All the functions, ψa,b (t), are derived from a chosen mother wavelet ψ(t) as follows [16]:
 t−b ψa,b (t) = |a|−1/2 ψ (1) a where, a and b are the scaling (dilation) and translation (time shift) constants respectively. The WT can be defined as:  ∞   ¯ a,b (t) dt f(t)ψ (2) WTa,b = ψa,b (t), f(t) = ∞

The signal f(t) can be expressed as a linear superposition of ψa,b (t) called wavelets:  ∞ ∞ 1 dadb f(t) = WTa,b ψa,b 2 (3) Cψ −∞ −∞ a ψ(t) must be chosen to satisfy the following conditions: 

∞



2

|ψ(ω)| Cψ = ∞ −∞ |ω| or 

ψ(0) =



∞ −∞

f(t)dt = 0

(4a)

(4b)

2.1. Wavelet basis function The paper introduces a method of applying the Morlet wavelet transform to detect the bus-bars faults particularly

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in case of CT saturation based on selecting the proper frequency. A Morlet wavelet basis function is embedded within a wavelet transform scheme to detect various events of faults. The formulation of this basis function is [17]: ψ(t) = π−1/4 (ejkt − e−k

2 /2

)e−t

2 /2

(5)

where k helps in determining the shape of the wavelet. The main features of the method are: 1. It is effective in monitoring faults, which generated the signals as time varies. During time intervals where the current changes rapidly (case of CT saturation), the method can zoom the area of interest for better visualization of signal characteristics. 2. The approach has automatically adjusted time windows that can be used to capture and analyze different kinds of faults induced transients. 3. The approach leads to accurate frequency resolution and poor time location at low frequency. However, it provides accurate time location and bad frequency resolution at high frequency. This behavior is very appropriate for real signals such as sudden changes in case of CT saturation. 2.2. Scale-varying basis functions The wavelet analysis is a measure of similarity between the basis functions (wavelets) and the faulted signal. The similarity is in the sense of having similar frequency components. So, the mother wavelets must be highly selective in time and frequency in order to have good detecting properties. A basis function varies in scale by chopping up the same function or data space using different scale sizes. The Morlet wavelet is used as a scale varying basis function. The scale-varying with the time is used to detect the actual scaling factor and consequently the suitable frequency needed in WT analysis process. Fig. 2(a) shows the faulted current signal for a fault F1 at the bus-bar located in zone 1. Fig. 2(b) shows the continuous wavelet transform coefficients produced at different scales by different sections of the signal. The coefficients constitute the results of a regression of the fault signal performed on the wavelets. Fig. 3(a) and (b) shows the same analysis for a fault current signal produced by out of bus-zone fault at F2 in case of CT3 saturation. As shown in Figs. 2 and 3, projections appearing at different scales between 0.02 and 0.03 s indicate the presence of a sudden change in the signal. The scale value between times 0.02 and 0.03 s can be localized superbly. To capture the sudden changes in case of faults and CT saturation, a scaling factor equal to 46 is selected here. Consequently, the wavelet transform using an accurate scale value for the fault generated transients can be accurately computed. For this reason the Morlet wavelet offers the best frequency localization. Using this scale value in the proposed approach tends to successful detection for the fault even during the CT saturation.

Fig. 2. Faulted current signal and the corresponding coefficients for a bus fault at F1.

3. Detection method Traditional power signals analysis tools, currently used in digital relays, have been efficient and useful in power system steady state analysis [18,19]. The analysis of non-stationary signals measured by the protection devices using the conventional techniques is very limited. The proposed technique is based on extracting the windowed wavelet transform of fault generated transients so as to distinguish between faults in a busbar protection zone from those outside the zone, particularly in case of early and severe CT saturation. The faults generated transients are extracted from the differential current (DIFF) as the operating quantity and the sum of the current magnitudes (SUM) as the stabilizing signal. The magnitude values of wavelet transform based on Morlet basis function are applied on the DIFF and SUM signals. The mathematical notations of these values are described in terms of two quantities CWTD and CWTS based on Eq. (2). The discrete time computations of the real part in Eq. (2) use the equivalent Riemann sum as: CWTD(kT, a)     1 [(nT − kT)]   = DIFF(nT) · √a · T · ψ  a n

(5)

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and reliability, a trip signal is calculated as: Trip(kT) = Trip(kT − 1) + R• CWTS(kT, a) − CWTD(kT, a)

(7)

Trip(kT) is the trip signal, and can be identified as the sum of the differences between the R × CWTS and CWTD values up to the kTth samples. R is the restraining factor. The final performance of the technique is identified as follows; if the Trip(kT) signal goes lower than some negative threshold value, the technique will distinguish that the faults inside the bus zone. On the other hand, if Trip(kT) goes higher than a positive THRESHOLD value, outside the bus zone fault is identified.

4. CT saturation and ratio mismatch

Fig. 3. Faulted current and the corresponding coefficients in case of an external fault at F2 and CT3 saturation.

CWTS(kT, a) 
   SUM(nT) · √1 · T · ψ (nT − kT)  =   a a n

(6)

where CWTD and CWTS are the magnitude values of the continuous wavelet transform of the DIFF and SUM respectively. T is the sampling period. k and n are integers. Finally, a is the scaling factor. 3.1. Use the data windows for computing the magnitude of the CWT At each sampling instant, the magnitude values CWTD and CWTS of the corresponding phases are computed using a data window of fixed length of the wavelet basis function. The wavelet window shifts continuously to the right so that at every sampling instant a new sample is included and the oldest sampling is discarded. 3.2. Criteria for tripping A comparison of the CWTD and CWTS values computed by the relay for Eqs. (5) and (6) distinguishes the fault as being inside or outside the protection zone of the busbar. For a bus fault, the CWTD is greater than the restraining factor times the CWTS value. To improve the relaying integrity

Current transformer is a basic component that is used in relaying schemes. It generally produces a waveform that faithfully represents the primary current until the CT core saturates. The saturation distorts the waveform of the secondary current. The extent of distortion depends on the magnitude of the remnant flux in the CT core and presence of CT offset in the primary current. Gradually, the CT comes out of saturation and the waveform of its secondary current starts to faithfully represent the primary current [11]. As discussed earlier, the transient behavior and discontinuities in the signals can be easily detected using the proposed approach. If an instantaneous drop in current magnitude happens at a certain time interval (CT saturation) it may lose the current value but it contributes a time and frequency information. For CWTD and CWTS based on basis function such as Morlet wavelet, the time and frequency information can be obtained rather than the current value. Therefore, the CT saturation does not affect the performance of the approach. The impact of CT saturation on the computed values has been studied. Important conclusions drawn from the analysis and an explanation of the effect of CT saturation on the proposed technique are provided. The CTs give the same secondary current for the same primary current, even if the CTs are commercially identical. A change in the CT ratio installed at a particular location results in a different magnitude of the current signals. An error current can occur during fault conditions. This difference in secondary current will flow in the relay. This is one of the shortcomings in the conventional low impedance relays based on current values. The proposed approach is used to monitor various events of faults generated signals as time varies rather than monitoring the current values. The approach described presents both frequency and time information simultaneously. Consequently, computed CWTD and CWTS value have not a significant effect rather than the current values based conventional techniques. This leads to the fact that the change of CT ratio does not affect the

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fault decision made by the relay. The impact of the ratio mismatch on the proposed technique is provided.

5. Power system modelling The model shown in Fig. 1 has been simulated. The substation includes 230 kV busbar. Data for verifying the proposed technique was generated by modeling the selected system by using the Alternative Transient Program (ATP) [20]. The transmission line parameters are given in [21]. Each source was modeled as three separate generators with an equivalent circuit in which positive sequence can be calculated from the fault level. The C800 (1200:5, Rs = zero) CT is used for the case studies presented here. The λ/i curve with a saturation point (1A, 3.53 Vs) is used with the CT model.

6. Simulation results The system shown in Fig. 1 was subjected to various events of faults. ATP program is used to generate data to test the performance of the proposed technique. The results obtained from the tests, when a sampling frequency of 20 kHz was used are given here. A scaling factor with optimum value equal to 46 is selected for the study. Simulated waveforms of the currents provided by unsaturated and saturated CTs are also given. The proposed approach was tested by computing the CWTS, CWTD and Trip values of single phase-to-ground, two phase-to-ground, phase-to-phase and balance three-phase faults. The performance of the proposed technique was evaluated for different types of internal and external faults.

7. Impact of ct saturation and ratio mismatch Fig. 4(a) shows the waveforms of the fault currents provided by saturated CT3 and an external fault located at F2. Fig. 4(b) shows the computed CWTS and CWTD values during CT saturation. The proposed criterion indicates that the CWTS is higher than CWTD value. This properly identifies that the fault is out of the protected zone. Fig. 4(c) shows another case study for the same condition of fault but using different scaling factor. In this case the relay does not perform well and is highly affected in the CT saturation zone. This identifies that the proper selection of scaling factor is very essential in identifying the CT saturation conditions. Fig. 5(a) shows the waveforms of the fault currents for an external fault located at F2 without CT saturation. A change in the CT3 ratio is taken to give +20% error. This change gives a different magnitude of the current signals. Fig. 5(b) shows the computed CWTS and CWTD values. As shown in the figure, the computed CWTD value is not affected in any significant manner due to this error. So, the CT ratio

Fig. 4. Waveforms of currents from saturation and not-saturated CT and the CWT values at two different scale values.

mismatch does not affect the performance of the technique. Another case study is provided in Fig. 5(c) and (d) for an error (−20%) in the CT3 ratio.

8. Test results The performance of the proposed technique was evaluated for different types of internal and external faults. The proposed technique was tested by calculating the trip signal

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Fig. 6. CWT values and the Trip signal for a 3L-G fault at F1 (Zone-1).

CWTS and CWTD values and the Trip signal. The results are shown in Fig. 7. The figure shows that the Trip signal has a positive value. This led to the final decision that the fault is outside the bus protection zone. 8.3. Bus fault-out of zone-1 The effect of CT2 saturation and bus-2 fault at Zone-2 is also investigated. A 3LG fault in the second zone is located.

Fig. 5. Waveforms of currents and the CWT values in case of ratio-mismatch.

given by Eq. (7) with a restraining factor given by 80%. Some test results are included in the next sections. 8.1. Internal fault A three-phase-to-ground fault in the bus-protection zone at F1-Zone-1 was simulated. The performance of the algorithm is shown in Fig. 6. The performance of Trip signal moves as a function of time. The computed trip signal has a negative value that indicates the fault is in the protection zone of the busbar (Zone-1). 8.2. External fault A wide variation of external fault boundaries and fault resistance were investigated. For the power system shown in Fig. 1, consider that a single phase-to-ground fault outside the bus-bar protection zone (F2). The relay computed the

Fig. 7. CWT values and the Trip signal for a 1L-G fault at F2 out of protection zone.

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Fig. 8 shows the computed CWTS and CWTD values before and after saturation. The corresponding Trip signal has a positive value recognizing properly that the fault is out of the protection zone. 8.4. Early and severe CTs saturation The proposed technique can also be used to detect and discriminate successfully early and severely ct saturations. For an early and severely saturation the current goes to zero almost immediately after the fault inception. To analyze this concerns a phase-A to phase-B fault outside the bus–protection zone at F2 was examined. As shown in Fig. 9, the waveforms of the fault currents and the corresponding performance of the Trip signal. The Trip signal moves directly with a positive value after fault inception, thus recognizing the fault is out of bus-zone.

9. Conclusions

Fig. 8. CWT values and the Trip signal for a 3L-G fault on bus-2 (Zone-2) out of protection zone.

This paper presents a novel, wavelet transform based bus-bar protection. The wavelet transform coefficients at different scales are used to precisely determine the scale value. A wavelet transform approach using Morlet basis function was applied to discriminate the bus protection zone from those outside the zone. From the test results, the proposed technique was successful in detecting and discriminating the faults during CT saturation, ratio-mismatch, early CT saturation and at different events of faults. This is found to have many advantages over the existing methods. This reveals the feasibility of the method as a potential alternative in the area of power system relaying applications. Studies also show that the proposed technique is able to offer a very high accuracy and a very fast action in all cases of fault conditions.

References

Fig. 9. Waveforms of the currents during early and severe CT saturation and the corresponding Trip signal for an external fault located at F2.

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Moustafa Mohammed Eissa (M’ 96-SM’ 01) was born in Helwan, Cairo, EGYPT on May 17, 1963. He received the B.Sc. and M.Sc. degrees in Electrical engineering from Helwan University in 1986 and 1992 respectively. In 1997 he received the Ph. D. from KFKI-Mszki Institute of Hungary. He is at present an associate Professor at Helwan University. His interests are in digital relaying, application of neural networks to power systems, dispatcher training simulators and local area applications in power system.