Protection Scheme for Transmission Lines Based on Correlation Coefficients

Transcription

1 International Journal of Engineering and Advanced Technology (IJEAT) ISSN: , Volume-3, Issue-4, April 4 Protection Scheme for Transmission Lines Based on Correlation Coefficients R. Abd Allah Abstract In modern digital power system protection systems, statistical coefficients technique is recently used for analysis. A correlation technique is developed for s detection and discrimination. The proposed technique is able to accurately identify the condition of phase(s) involved in all ten types of shunt s that may occur in extra high-voltage transmission lines under different resistances, inception angle and loading levels. The proposed technique does not need any extra equipment as it depends only on the three line-currents measurements which are mostly available at the relay location. This technique is able to perform the detection, type and phase selection in about a half-cycle period. Thus, the proposed technique is well suited for implementation in digital protection schemes. The proposed methodology is applied for a part of 5 KV Egyptian network. Alternative transient program (ATP) and MATLAB programs are used to implement the proposed technique. Index Terms Power system, detection, classification, correlation coefficient. I. INTRODUCTION In modern power system protection, accurate, fast and reliable classification technique is an important operational requirement. On one hand, correct information of the type of is readily needed for location algorithms []. On the other hand, in digital distance protection schemes, for proper operation of the protective relays, correct determination of the type is a prerequisite []. A significant amount of research work has been directed to address the problem of an accurate classification scheme. Among the various techniques reported for classification in transmission system, Artificial-neural-network (ANN) approach is the most widely used techniques. Although the neural-network-based approaches have been quite successful in determining the correct type, the main disadvantage of ANN is that it requires a considerable amount of training effort for good performance, especially under a wide variation of operating conditions such as, system loading level, resistance, inception instance [3-9]. Similarly, Expert system-based approach effectiveness depends largely on the domain knowledge of the experts, which is often quite time-consuming to be obtained [-]. Fuzzy and fuzzy neural-network-based approaches also require extensive training of the ANN [3-4]. Recently, classification techniques suitable for a recorder has been proposed in [5], which can identify all ten types of short-circuit s. Some statistical coefficients techniques were used for analysis such as an alienation technique was developed for s detection and discrimination. The paper [6] presented protection scheme for transmission lines based on alienation coefficients for current signals; the scheme used another algorithm besides alienation coefficients to distinguish between double phase and double phase-to-ground s. In this paper, a detection and selection based on correlation technique is proposed which is able to determine accurately, during one cycle period of fundamental frequency, all types and phase selection. Also this technique takes into consideration the wide variations of operating conditions such a switching, pre- power level, resistance and inception angle. II. FAULT CLASSIFICATION STRATEGY The selection algorithm is based on the auto-correlation technique of two half successive cycles with the same polarity. For transmission lines protection, this method needs only three line-current measurements available at the relay location (i a, i b, i c ). A. Correlation Coefficients Calculation The auto-correlation coefficient is estimated as follows for any two dependant variables, y (x) and y (x) [7]. The auto-correlation coefficient calculated as follows: r s ( N N s x y ( x) y ( x) N y y ( x) N ( y ) )( s x x N s s y ( x) N ( y ) ) Where, N s = the number of samples per cycle used in the simulation r: empirical correlation coefficient of y (x), and y (x). y (x): is the initial instantaneous value of the current at time t. y (x): is the instantaneous value of the current at next cycle. y, y : arithmetic means of y (x) and y (x), respectively. N N s y y s x N N s y s x y ( x ) ( x ) y s () ( ) (3 ) The strength of linear association between two variables is quantified by the correlation coefficient, its value lies between - and + [7]. Manuscript received on April 4. R. Abd Allah, Electrical Power Department, Faculty of Engineering, Private Buraydah Colleges, Qassim Region, Kingdom of Saudi Arabia. 3

2 Protection Scheme for Transmission Lines Based on Correlation Coefficients B. Fault Detection and Faulty Phase Selection To implement our technique, three tasks are starting in parallel: detection, confirmation, and y phase selection as follows: () Fault Detection (Initiation) A transition is detected if: I > % I n, where I n is the line nominal current. () Faulty Phase Selection - Fault confirmation and y phase selection are done according to the following sequences. Three-phase current correlation coefficients values are calculated. If is detected, phase current correlation values are sorted in ascending order and compared. - If is detected, phase current correlation values are sorted into ascending order and compared. The possible cases are: (a) If the three-phase correlation coefficients are nearly equal and their values are less than.7, then the is three-phase fau - If r a r b r c <.7, the is three-phase (a-b-c ) (b) If the two-phase correlation coefficients are equal and their values are nearly, while the third phase correlation coefficient is less than.7, the is single-phase to ground. - If r a <.7, r b, r c, the is single phaseto-ground (a-g ) - If r b <.7, r a, r c, the is single phaseto-ground (b-g ) - If r c <.7, r a, r b, the is single phaseto-ground (c-g ) (c) If the two-phase correlation coefficients are equal and their values are less than.7, while the third phase correlation coefficient is nearly, the is double phase-to-ground. - If r a r b <.7, r c the is double phase-to-ground (a-b-g ) - If r b r c <.7, r a the is double phase-to-ground (b-c-g ) - If r a r c <.7, r b the is double phase-to-ground (a-c-g ) (d) If the three-phase correlation coefficients are not equal and their values: one phase is less than.3, second phase is less than.7, while the third phase alienation coefficient is nearly, the is phase-to-phase. - If r a <.7, r b <.7, r c the is phase-to-phase (a-b ) - If r b <.7, r c <.7, r a the is phase-to-phase (b-c ) - If r a <.7, r c <.7, r b the is phase-to-phase (a-c ) - To make sure of distinguishing between double phase and double phase-to-ground s, the cross-correlation between the two phase currents of the ed phases is calculated. If the value of cross-correlation is nearly -, the is double phase. - If r ab - the is phase-to-phase (a-b ) otherwise the is double phase-toground (a-b-g ). - If r bc - the is phase-to-phase (b-c ) otherwise the is double phase-toground (b-c-g ). - If r ac - the is phase-to-phase (a-c ) otherwise the is double phase-toground (a-c-g ). III. CASE STUDY POWER SYSTEM The proposed technique is applied on the power system shown in Fig. (). The system parameters are obtained from one-generation unit in El-kuriemat power station that produces 3 MVA [8]. The parameters of the selected system are as follows: Fig. () The simulated power system. Machine (sending source): Rated line voltage is 9 kv, Volt-Ampere rating is 3 MVA, Frequency is 5 Hz, Voltage phasor angle phase is and number of poles is. Machine (receiving source): Machine has the same parameters of Machine except the steady-state voltage phasor angle phase is. Main Transformers: At each side there is a step up transformer 34 MVA, 9.57/5 kv (Delta/Star earthed neutral), its primary impedance is.7 + j.84 ohm, its secondary impedance is j 6.8 ohm. Aux. Transformers: At each side there is an auxiliary transformer 3 MVA, 9.57/6.3/6.3 kv (Delta/Star/Star earthed neutral), its primary impedance is j.4894 ohm, its secondary impedance is.39 + j.6 ohm. Lines: Transmission line (T.L.) impedance is.7 + j.3 ohm/km with Km length for each circuit. Loads: Each load is represented as impedance of value. + j6. ohm. IV. SIMULATION RESULTS A (F) was considered at the middle of one circuit of the transmission line assuming that short circuit is temporary and not resistive. The developed technique was applied by calculating the auto-correlation coefficient (r x ) between two successive half cycles with the same polarity of current signals at the sending-end where relays would normally be installed. The proposed technique is capable to discriminate 4

3 International Journal of Engineering and Advanced Technology (IJEAT) ISSN: , Volume-3, Issue-4, April 4 between the two types of two -phase s either earthed or isolated. To confirm the two ed phase type, a cross-correlation coefficient is calculated for the ed phase. To implement the present technique, the studied power system configuration was simulated by using ATP software [9]. The generated and measured three phase line current signals are taken from the transmission line terminals at busbar '' BB '' side. Five simulation case studies are done to discriminate between the y phases, by using the proposed method, for classification. These cases are done under effects of different pre- power level, resistance, and inception angle located on the simulated power system. The current measured signals sampling rate is 5 samples per cycle, which means sampling time of.4 msec. The total simulation time is Sec (i.e. the total number of samples is 5). The inception time is.4 Sec and the clearing time is.5 Sec from the beginning of the simulation time. A. Three phase-to-ground (Case ) This case studies the performance of the proposed technique during the three phase-to-ground condition on the proposed technique. The operating power angle of generator (δ ) is degree. Figure shows the simulation results for case. Figures (a-c) present the instantaneous values for the three phase currents. In this case, it is noticed that the three phase currents during the are higher than the pre- currents; their values are nearly five times the pre- current. The correlation coefficients (r x ) are calculated between two successive half-cycles with the same polarity for the three-phase current signals. The three-phase current correlation coefficients r ia, r ib and r ic are shown in Figs. (d-f).the values of r ia, r ib, r ic are equal and close to one before inception and after clearing. At start they are equal and less than.4 while they are less than.4 at clearing. From the above results, it is clear that the correlation coefficient values at initiation are good detector to determine the ed phases; Their values are closely to one for current signals in case of normal operation and they are less than one in case of condition. Summary of the correlation coefficients for the measured current signals at the different periods are shown in Table (). Table () (δ = degree, three-phase to ground s (a-b-c-g) with R f = ohm). Fault type Thre e line-t o-gro und Signa ls pre-fa ult at start during at cleari ng post-f ault i a r ia =.4. i b r ib =..35 i c r ic =.3.4 B. Single line-to-ground (Case ) All parameters are kept as in case, except the type is changed from three lines-to-ground (a-b-c-g) to single line-to-ground (a-g). Figures 3 (a-c) present the instantaneous values for three-phase currents. The y phase current value is nearly six times the pre- current, while both the healthy phase currents are equal and nearly.35 times the pre- value. The three phase current correlation coefficients r ia, r ib, r ic are shown in Figs. 3 (d-f). Their values are equal and close to one before inception and after clearing. At start r ia is less than.74 while r ib and r ic are nearly one. At clearing, r ib is equal one while r ia, r ic are less than.74. From the above results, it is clear that the correlation coefficient value at initiation is good indicator to determine the ed phase A. Summary of the correlation coefficients for the measured signals at the different periods are shown in Table (). Table () (δ = degree, single phase-to-ground s (a-g) with R f = ohm). Faul t type Sin gle line -togrou nd Signa ls pre-fa ult at start durin g at cleari ng post-f ault i a r ia = i b r ib = i c r ic = C. Double line-to-ground (Case 3) This case studies the effect of double line-to-ground condition on the performance of the proposed algorithm. Therefore, all parameters are kept as in case, except the type is changed to double line-to-ground (a-c-g). Figures 4(a-f) show the simulation results for three-phase currents as the two y phases currents are nearly ten times the pre- values while the healthy phase current is nearly.35 times its pre- current value. The values of correlation coefficients r ia, r ib and r ic are equal and close to one before inception and after clearing. At starts, r ia and r ic are less than the value of.7, whereas r ib is nearly one. At clearing, r ia and r ic are less than.78 whereas r ib is nearly one. From the above results, it is clear that the correlation coefficient value at initiation can define the double line-to-ground. The cross-correlation coefficient r iac, calculated between the two ed phases (A and C), at start has a value of -.85; this value confirms the type of is double line-to-ground. Before inception, the value of cross-correlation coefficient r iac is equal to cos( ) =.5, which is considered a normal value. Summary of the correlation coefficients for the measured signals at the different periods is shown in Table (3). From the obtained results, it is clear that the correlation coefficient value at initiation is good detector to determine the ed phases (A and C). Table (3) (δ = degree, double phase-to-ground s (b-c-g) with R f = ohm). Faul t Type Signa ls pre-fa ult durin g post-f ault at faul t start at cleari ng Dou i a r ia =

4 Protection Scheme for Transmission Lines Based on Correlation Coefficients ble lineto-gr ound 5 i b r ib =.7.78 i c r ic =.7.38 i b & i c r ibc = D. Double line (Case 4) This case studies the effect of double line Condition on the performance of the proposed algorithm. Therefore all parameters are kept as in case, except that the type is changed to double line (a-c). Figures 5(a-f) show the simulation results for the three-phase currents as the two y phases currents are nearly ten times the pre- values, whereas the healthy phase current is nearly.35 its pre- value. The values of correlation coefficients r ia, r ib and r ic are equal and close to one before inception and after clearing. At start, r ia, r ib and r ic have different values with values of -.55,.95 and.7, respectively. While at clearing, r ia, r ib, r ic have values of -.57,.95 and.38, respectively. The cross-correlation coefficient r ibc, calculated between the two ed phases (A and C), at start has a value of, whereas its value is equal to.5 before inception. The value of cross-correlation coefficient, at inception, confirms that the type is phase-to-phase. Consequently, our technique can determine the type whether double phase-to-ground or phase-to-phase by calculating the cross-correlation between the two ed phases. If r ac -, at starts, the type is phase-to-phase otherwise it is double phase-to-ground. Summary of the correlation coefficients for the measured signals at different periods is shown in Table (4). These results show that the correlation coefficient value at initiation is good detector to determine the ed phases and distinguish between phase phase isolated and grounded y without adding any extra measuring equipments. Table (4) (δ = degree, double-phase (b-c-g) with R f = ohm). Fault type Double line Signals pre- at start during at clearing post- i a r ia = i b r ib = i c r ic =.7.38 i b & i c r ibc = E. Three Phase-to-Ground Fault with High Resistance (Case 5) This case studies the effect of three-phase-to-ground with high resistance on the proposed technique. In this case, the applied resistance (R f ) is ohm. The operating power angle of generator (δ ) is degree. Figure 6 shows the simulation results for case 5. Figure 6 (a-c) present the instantaneous values for the three-phase currents. In this case, it is noticed that the three-phase currents during the are higher than the pre- currents; their values are nearly four times the pre- currents (these values are less than that are in case). The auto-correlation coefficients (r x ) are calculated between two successive half-cycle for the three-phase current signals. The three-phase current correlation coefficients r ia, r ib, r ic are shown in Fig. 6 (d-f).the values of r ia, r ib, r ic are equal and close to one before inception and after clearing. At start they are equal and less than.65 while they are less than.74 at clearing. From the above results, it is clear that the auto-correlation coefficient values at initiation are good detector to determine the ed phases with high resistance. Also, the correlation coefficient values at initiation are higher than that are in case.the correlation coefficient values are closely to one for current signals of healthy phase and they are less than one for y phase. Summary of the correlation coefficients for the measured current signals at the different periods are shown in Table (5). Table (5) (δ = degree, three-phase to ground (a-b-c-g) with R f = ohm) Fault Sign type al Three line-t o-gro und with high resist ance pre-fa ult at faul t start durin g at cleari ng post-f ault i a r ia = i b r ib = i c r ic = By the comparison between case and case 5 we deduce the following findings: (a) The greater the applied resistance (R f ) the lower the DC components in the current (because of the lower primary time constant of the power system, (τ p =X L /ωr). (b) (c) The greater the applied resistance (R f ) the greater the correlation coefficient values at initiation. The greater the applied resistance (R f ) the greater the degree of power system stability. V. SIMULATION RESULTS AND TECHNIQUE EVALUATION From the different case studies, we summarize the following: () Faults cause transient of the transmission line s currents and as a result cause collapse for power system voltage magnitude. () The proposed technique is based on the two types of algorithms for detection: Algorithm : Fault detection using superimposed quantities (delta algorithm) Algorithm : Fault detection using auto-correlation coefficient value (3) Three tasks are starting in parallel for detection, classifications and y phase selection. (4) Auto-correlation coefficient between two successive half-cycles with the same polarity for each phase current signal can be used to identify the ed phase 6

5 International Journal of Engineering and Advanced Technology (IJEAT) ISSN: , Volume-3, Issue-4, April 4 status. The cross-correlation coefficient between the two ed phases is useful for determining the type of either double phase-to-ground or phase-to-phase. (5) An extensive simulation studies are done to study the effects of different loading levels, resistances (R f ) and inception angle on the performance of the proposed technique. The results show that our technique has high accuracy and efficiency for detection and classification with a wide range of resistances from zero value up to 5 ohm. VI. CONCLUSION In this paper, a correlation technique of transmission line for identification and y phase selection has been proposed. The main achievements of this work are as follows:. Three line current measurements are sufficient to implement this technique.. It is accurate to identify all ten types of short-circuit s. 3. It is efficient to distinguish between phase phase isolated and grounded y without needing any extra equipment. 4. The reliability of the proposed method is quite high. 5. It is quite effective over a wide range of a pre- power level, resistance, and inception angle. 6. Fast and simple method, as the time taken by this method is about ms (for a 5-Hz power system). 7. The effects of DC components and harmonics are eliminated with estimation of correlation coefficients. 8. The ed phases can be determined by using correlation technique. 9. The technique does not use the data of power system element but it needs only three phase current measurements available at the relay location. REFERENCES [] M. M. Saha et al., A new accurate location algorithm for series compensated lines, IEEE Trans. Power Delivery, vol. 4, pp , July 999. [] A. G. Phadke, Computer Relaying for Power Systems. New York: Wiley, 988. [3] R. K. Aggrawal, Q. Y. Xuan, R. W. Dunn, and A. Bennett, A novel classification technique for double-circuit line based on a combined unsupervised/supervised neural network, IEEE Trans. Power Delivery, vol. 4, pp. 5 5, Oct [4] W.-M. Lin, C.-D. Yang, and J. H. Lin, A classification method by RBF neural network with OLS learning procedure, IEEE Trans. Power Delivery, vol. 6, pp , Oct.. [5] T. Dalstein and B. Kulicke, Neural network approach to classification for high speed protective relaying, IEEE Trans. Power Delivery, vol., pp., Apr [6] D. K. Ranaweera, Comparison of neural network models for diagnosis of power system, Elect. Power Syst. Res., pp. 99 4, 994. [7] K. H. Kim and J. K. Park, Application of hierarchical neural networks to diagnosis of power system, Int. J. Elect. Power Energy Syst., vol. 5, no., pp. 65 7, 993. [8] A. L. O. Fernandez and N. K. I. Ghonaim, A novel approach using a FIRANN for detection and direction estimation for high voltage transmission lines, IEEE Trans. Power Delivery, vol. 7, pp , Oct.. [9] A. Poeltl and K. Frohich, Two new methods for fast type detection by means of parameters fitting and artificial neural networks, IEEE Trans. Power Delivery, vol. 4, pp , Oct [] A. A. Girgis and M. B. Johns, Ahybrid expert system for ed section identification, type classification and selection of location algorithms, IEEE Trans. Power Delivery, vol. 4, pp , Apr [] C. A. Protopapas, K. P. Psatiras, and A. V. Machias, An expert system for substation diagnosis and alarm processing, IEEE Trans. Power Delivery, vol. 6, pp , Apr. 99. [] H. T. Yang, W. Y. Chang, and C. L. Huang, On line diagnosis of power substation using connectionist expert system, IEEE Trans. Power Syst., vol., pp , Feb [3] A. Ferrero, S. Sangiovanni, and E. Zapitelli, A fuzzy set approach to type identification in digital relaying, IEEE Trans. Power Delivery, vol., pp , Jan [4] H.Wang andw.w. L. Keerthipala, Fuzzy neuro approach to classification for transmission line protection, IEEE Trans. Power Delivery, vol. 3, pp. 93 4, Oct [5] T. Adu, An accurate classification technique for power system monitoring devices, IEEE Trans. Power Delivery, vol. 7, pp , July. [6] M.E. Masoud, M.M.A. Mahfouz, Protection scheme for transmission lines based on alienation coefficients for current signals, IET Gener. Transm. Distrib., Vol. 4, Iss., pp March. [7] W. Hauschild, and W. Mosch, Statistical Techniques for High Voltage Engineering, hand book, English edition published by peter pere grinus Ltd., London, United Kingdom, chapter, pp , 99. [8] Instruction Manual for Generator Electrical Equipment, Upper Egypt Electricity Production Company, Elkureimat П 75 MW Combined Cycle Project, Steam Turbine Generator & Auxiliaries (Generator Electrical Equipment), Hitachi, Ltd., Tokyo Jaban. [9] ATP - version 3.5 for Windows 9x/NT//XP - Users' Manual Preliminary Release No.. - October. PERSONAL PROFILE R. Abd Allah, Assistant professor, Chairman of Electrical Power Department, Private Buraydah Colleges, Saudia Arabia. First University Degree : () Bachelor of Science (B.Sc.), Graduation year, Electrical Machine & Power Department, graduated from Faculty of Engineering, Cairo University, Highest University Degree: () The Master of Science Degree (M.Sc.), June 7, Helwan University, Faculty of Engineering, Department of Electrical Machines& Power Engineering, Cairo, Egypt. M.Sc. thesis under the following title: '' A Digital Busbar Protection Scheme Avoiding Current Transformer Saturation Effects '' (3) Degree of Doctor of Philosophy (Ph.D.), October, Helwan University, Faculty of Engineering, Department of Electrical Machines& Power Engineering, Cairo, Egypt. PHD thesis under the following title: ''Multifunction Digital Relay for Large Synchronous Generators Protection'' LIST OF RECENT PUBLICATIONS. ADVANCED DETECTION AND COMPENSATION SCHEME FOR CURRENT TRANSFORMERS SATURATION (Power Systems Conference, 6, MEPCON 6).. CT SATURATION CLASSIFICATIONS USING CORRELATION TECHNIQUE (Power Systems Conference, 6, MEPCON 6). 3. A NEW SCHEME BASED ON CORRELATION TECHNIQUE FOR GENERATOR STATOR FAULT DETECTION (Power Systems Conference,, MEPCON ). 4. EXPERIMENTAL RESULTS AND TECHNIQUE EVALUATION BASED ON CORRELATION FOR GENERATOR STATOR FAULT DETECTION (Power Systems Conference,, MEPCON ). 7

6 Protection Scheme for Transmission Lines Based on Correlation Coefficients 4 current signal ia correlation coefficient(ria) -.8 ia(amp) c o rr (r i a ) Fig. (a) the current i a for case Fig. (d) r ia for the current i a for case current signal ib correlation coefficient(rib) 4.8 ib(amp) c o r r ( r ib ) Fig. (b) the current i b for case Fig. (e) r ib for the current i b for case current signal ic correlation coefficient(ric) ic(amp) - -4 c o rr (r ic ) Fig. (c) the current i c for case Fig. (f) r ic for the current i c for case Fig. (a-f) the simulation results for case, δ = degree, Three-phase to ground s (a-b-c-g). 8

7 International Journal of Engineering and Advanced Technology (IJEAT) ISSN: , Volume-3, Issue-4, April 4 3 current signal ia. correlation coefficient(ra)).8 ia(amp) - - corr(ra)) Fig.3 (a) the current i a for case Fig.3 (d) r ia for the current i a for case current signal ib correlation coefficient(rb)) ib(amp) c o rr (rb ) ) Fig.3 (b) the current i b for case Fig.3 (e) r ib for the current i b for case current signal ic. correlation coefficient(rc)) ic(amp) c o rr (rc ) ) Fig.3 (c) the current i c for case Fig.3 (f) r ic for the current i c for case Fig.3 (a-f) the simulation results for case, δ = degree, single line-to-ground (a-g). 9

8 Protection Scheme for Transmission Lines Based on Correlation Coefficients 3 current signal ia. correlation coefficient(ra)).8 ia(amp) - - corr(ra)) Fig.4 (a) the current i a for case 3 Fig.4 (d) r ia for the current i a for case 3 current signal ib correlation coefficient(rb)) 8. 6 ib(amp) 4 corr(rb)) Fig.4 (b) the current i b for case 3 Fig.4 (e) ri b for the current i b for case 3 current signal ic. correlation coefficient(rc)) ic(amp) c o rr(r c )) Fig.4 (c) the current i c for case 3 Fig.4 (f) r ic for the current i c for case correlation coefficient(ribc) corr(ribc) Fig.4 (g) r iac for the currents i a & i c for case 3 Fig.4 (a-g) the simulation results for case 3, δ = degree, double line-to-ground (a-c-g).

9 International Journal of Engineering and Advanced Technology (IJEAT) ISSN: , Volume-3, Issue-4, April 4 4 current signal ia. correlation coefficient(ria) ia(amp) c o rr(ria) Fig.5 (a) the current i a for case 4 Fig.5 (d) r ia for the current i a for case 4 current signal ib. correlation coefficient(rib) ib(amp) corr(rib) Fig.5 (b) the current i b for case 4 Fig.5 (e) r ib for the current i b for case 4 current signal ic. correlation coefficient(ric) 6 4. ic(amp) corr(ric) Fig.5 (c) the current i c for case 4 Fig.5 (f) r ic for the current i c for case correlation coefficient(ribc) corr(ribc) Fig.5 (g) r iac for the currents i a & i c for case 4 Fig.5 (a-g) the simulation results for case 4, δ = degree, double line (a-c).

10 Protection Scheme for Transmission Lines Based on Correlation Coefficients 8 current signal ia. correlation coefficient(ria) ia(amp) - -4 corr(ria) Fig.6 (a) the current i a for case 5 Fig.6 (d) r ia for the current i a for case 5 current signal ib. correlation coefficient(rib) ib(amp) corr(rib) Fig.6 (b) the current i b for case 5 Fig.6 (e) r ib for the current i b for case 5 current signal ic. correlation coefficient(ric) ic(amp) corr(ric) Fig.6 (c) the current i c for case 5 Fig.6 (f) r ic for the current i c for case 5 Fig.6 (a-f) the simulation results for case 5, δ = degree, Three-phase to ground s (a-b-c-g) with resistance (R f ) = ohm.