Dynamic performance of the power differential relay for transmission line protection

Electrical Power and Energy Systems 32 (2010) 390–397

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

Dynamic performance of the power differential relay for transmission line protection Tamer A. Kawady a,*, Abdel-Maksoud I. Taalab a, Eman S. Ahmed b a b

Power System Protection Group (PSPG), Electrical Engineering Department, Faculty of Engineering, Minoufiya University, Shebin El-Kom 32511, Egypt Faculty of Engineering, Kafr El-shikh University, Kafr El-Shikh, Egypt

a r t i c l e

i n f o

Article history: Received 14 September 2007 Received in revised form 31 August 2009 Accepted 6 November 2009

Keywords: Differential relay Power swing MATLAB Transmission line Power system protection

a b s t r a c t Power differential relay was proposed recently as a practical relaying scheme for transmission systems. In this paper, the dynamic behaviour of the power differential relay is thoroughly investigated. These investigations are important to evaluate the overall performance of such relaying functions. For this target, a detailed simulation of a typical transmission system was developed via the MATLAB/SIMULINK package using detailed modeling for each power system element. Both stable and unstable power swings are considered. Moreover, single machine-infinite bus and double machine system operations are considered for all possible faulty and non-faulty conditions. All applied test results confirm the superiority of the power differential relay as an ideal candidate for transmission system protection applications. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction There is no doubt that differential relaying is one of the most important functions for protecting transmission lines. Their extra communication requirements may, however, postpone their expansion into the field. Moreover, requiring perfect synchronization of phase currents at both line ends arises as a technical difficulty [1]. The employment of Global Positioning Systems (GPS) or charging comparison schemes may partially represent solutions for these difficulties. On the other hand, GPS system is sophisticated and may suffer from service interruption, which is not under the control of power system protection engineers [2,3]. For eliminating most of the aforementioned problems, utilizing Phase Measurement Units (PMUs) in Conjunction with GPS systems for protection applications was presented in the literatures. This is, however, faced with the economic perspective. Also, charge comparison schemes were proposed as a solution for the aforementioned problems. However, depending on the current zero crossings may cause slow response under some fault conditions [4]. Non-conventional methods were also utilized for this target as well. Examples for these contributions were listed in the literatures as seen in [5,6]. In sympathy with these methods, a novel power differential concept has been recently proposed as reported in [7,8]. Similar efforts were also proposed using the power (en-

* Corresponding author. Tel.: +20 10 4151345; fax: +20 48 2235695. E-mail address: [email protected] (T.A. Kawady). 0142-0615/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijepes.2009.11.004

ergy) computation for protecting transmission lines as reported in [9,10]. The power differential concept relies on computing the active and reactive power loci during normal operation, switching, normal power swing and internal (external) faults. From these loci, discrimination of internal faults can be achieved. Adaptive setting of the power differential relay was also proposed in [8], providing a detailed description for its operation and features. Capability of the power differential relay to efficiently detect line faults occurring at the swing voltage center is an exclusive feature of this relay particularly at higher values of load angle and fault resistances. These faults may not be detected by any of the existing relay technology including the charge comparison scheme. Moreover, the universality of the proposed setting for different transmission systems has been justified as well. As reported in [7,8], the power differential relay corroborates an optimum performance through all applied steady state tests via the EMTP and MATLAB. Both software packages represent the most widely used simulation software for protective applications [11]. During these steady state conditions, the system operates typically close to their nominal frequency under a balance between the generated and the consumed active power. On the other hand, system faults and disturbances (line switching, generator disconnection, and the loss or application of loads, etc.) force to deviate the electrical power from the corresponding mechanical power input to generator. These system disturbances may consequently result in oscillations in machine rotor angle producing severe power swings. Depending on the severity of the disturbance and the actions of

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power system controls, the system may remain stable and return to a new equilibrium state experiencing what is referred to as a stable power swing. Severe system disturbances may cause large separation of the generator rotor angle, large swings of power flows, large fluctuations of voltages and currents, and eventual loss of synchronism between groups of generators or between neighboring utility systems. Large power swings (even stable or unstable ones) can cause unwanted relay operations at different network locations, which can aggravate further the power system disturbance and cause major power outages or power blackouts. Large power system disturbances can lead to loss of synchronism among interconnected power systems. If such a loss of synchronism occurs, it is imperative that the system areas operating asynchronously are separated immediately to avoid wide area blackouts and equipment damage. An out-of-step tripping (OST) function is available in modern distance relays to differentiate between stable and unstable power swings. During unstable power swings, the OST initiates a controlled tripping of the appropriate breakers at predetermined network locations, to separate networks quickly and in a controlled manner in order to maintain power system stability and service continuity [12,13]. The objective of this paper is to thoroughly investigate the dynamic behaviour of the power differential relay covering a wide variety of faulty and non-faulty operating conditions. MATLAB (the widely used simulation software package) was employed for developing the required test cases with well prepared electromagnetic simulation with detailed modeled power system parts. This is an essential step to deeply evaluate the overall performance of the power differential relay as a candidate for transmission system protection. 2. Power differential relay with enhanced setting 2.1. Power differential relay description The basic mathematical core of the proposed power differential relay depends on the union action of the active and reactive power detectors providing a versatile and proper operation. As described in Fig. 1, the current and voltage measured are sampled and then fed to the ‘‘Phasor Estimation Module” for computing the fundamental components for current and voltage signals using the DFT routine. The filtered signals are then multiplied to produce the

instantaneous power and transmitted to the remote end via the adopted communication channels. The instantaneous power (indicated with subscript i) is computed for the active power at both transmission line ends on sample-by-sample basis. The DPi = P1i  P2i and Pi = (P1i + P2i)/2 are computed where P1i and P2i are the instantaneous power at the sending and receiving ends respectively. Then, the corresponding average active power quantities DPav and Pav are computed over a complete cycle. The corresponding schematic of the active power detector algorithm is described in Fig. 3. However in the reactive power algorithm, each of the instantaneous reactive power at the sending (Q1i) and receiving (Q2i) ends is computed by multiplication of voltage sample, after being delayed by a quarter of a cycle, by the current sample at the same end. The instantaneous reactive power is computed at both ends on sample-by-sample basis. The difference average (DQav) and reactive power through (Qav) are computed over a complete cycle for both ends in a similar manner to that for the active power algorithm shown in Fig. 1. Values of DPav, Pav, DQav, and Qav are employed to feed the overall fault detector scheme shown in Fig. 2. The output-tripping signal of the active power detector scheme is represented by the output of comparator 5. This signal is ORed with the output of the reactive power detector in conjunction with the three phase fault enable signal via 3-input OR2 gate. A similar fault detection scheme logic block diagram is used for the two other phases. As can be seen, DQav’s measured for the other two phases are made available at the input of the detector dedicated to each phase in addition to the setting value DQset. The reactive power setting of the proposed detector should cover all cases of external fault and power swings as well as detect all cases of internal fault, which the active power setting fails to detect. These cases namely are solid and low resistance (up to 1 X) internal SLG fault at line ends, solid SLG fault and low resistance (from 0 to 3 X) around the line midpoint for all value of d from 0° to 180°. Also, it should detect SLG faults with high fault resistance as well. A flow chart of this algorithm is given in Fig. 4. 2.2. Enhanced relaying setting As reported in [7,8], the corresponding settings for both active and reactive detectors were carefully adjusted fulfilling the maximum sensitivity for internal faults while keeping the maximum stability against external ones. Unfortunately, these settings face, however, some technical difficulties due to their profile complexities (such as involving an inverse sine function). These setting profiles can be, however, simplified while keeping the same sensitivity and stability requirements. This was achieved by describing the associated boundaries of both active and reactive power detectors with simple lines segments as shown in Fig. 5a and b respectively. The first line segment is described as,

DPset ¼ K 1 DP max þ

  DPmax 1  K 1  P for P 6 K 1 PðmaxÞ Pmax K1

ð1Þ

where DPmax is the difference power at power angle d = 180°. Pmax is the through power at power angle d = 90°, or 270°. P is the measured quantity of the through active power at relay location. K1 is a multiplier constant determines the maximum value of DPset at power angle d = 0°, 180°. The second line segment is expressed by the equation:

DPset ¼

K 2 DPmax DPmax þ P ðK 2  K 1 Þ Pmax ðK 1  K 2 Þ

for K 1 Pmax < P 6 K 2 Pmax ð2Þ

Fig. 1. Active power difference and average extraction diagram for phase a.

where K2 is the power through multiplier determining the horizontal setting limit of P.

T.A. Kawady et al. / Electrical Power and Energy Systems 32 (2010) 390–397

ΔQav(a) dQ /dt av

Comparator 1 dQ/dt(set)

Inhibit for PS

S

Comparator 2

&

ΔQset ΔQset Comparator 3 ΔQav(b)

&

ΔQset ΔQav(c)

&

Comparator 4

To Tri p

Inhibit for L-L fault OR1

& ΔPset ΔPav(a)

OR2

Enable for L-L-L fault

392

Comparator 5

Fig. 2. Block diagram of the proposed power fault detector for phase a.

Calculate the average of the difference and through of reactive power ΔQ av, Q av

Compute Δ Qset from (3)

No

Q av > Q av2/3

Yes

Compute Δ Q set from (5)

OR

Δ Q set Δ Q av

Δ Q av>Δ Qset

No

Yes Compute dQ/dt

dQ/dtset Fig. 3. Flowchart of the active power algorithm (P detector).

Similarly, the reactive power detector setting was described as shown in Fig. 5b by Eqs. (3) and (4) for both line segments respectively.

DQ set ¼ K 3 Q av þ K 4 DQ C DQ set ¼ 2=3DQ max

ð3Þ

2=3DQ max  1:1DQ C Q ð2=3Þ

No

Block

Yes

Trip Fig. 4. Proposed flowchart for the reactive power algorithm (Q detector).

ð4Þ

K3 is the first segment slop which can be determined from:

K3 ¼

dQ/dt > dQ/dt set

ð5Þ

K4 is arbitrary chosen as a multiple of DQc. DQmax is the maximum reactive power difference, which occurs at d = 180°, Q(2/3) is the reactive power corresponding to two-third the DQmax. As described in Fig. 3, the active power detector algorithm is started with calculating the average values DPav and Pav respectively. The measured value of Pav is compared with the value of K1Pmax. If it is less, DPset is computed from Eq. (1). However for K1Pmax 6 Pav 6 K1Pmax, the value of DPset is computed from Eq. (2). If the measured value of DPav is greater than the obtained DPset from Eq. (1) or Eq. (2), a trip signal is issued. However if DPav is less than DPset, a new cycle of calculation is started. It could be appreciated that the proposed active power relay algorithm allows the threshold to be adaptive according to the values of the actual

power flow Pav, maximum power transferred capability; Pmax, and maximum power difference between the line ends; DPmax. The reactive power detector algorithm is developed as shown in Fig. 4, based on the average quantities of the difference and through reactive power similar to the active power algorithm. Flow chart is started with the calculation of DQav and Qav. The algorithm contains two comparators. In the first comparator, the measured value of DQav is compared with the value of DQset computed from Eq. (3). If DQav is less than DQset, a new cycle is started. If it is greater, a trip signal is issued. In the second comparator, the measured value of DQav is compared with the value of 2/3 DQmax. If it is less, it is compared with the first comparator setting. However if it is greater than 2/3 DQmax, a trip signal is issued. Details of this detector mathematics are given in the aforementioned references. 3. Simulation system development Fig. 6 shows the one line diagram of the developed power system for the aimed study, whereas Fig. 7 illustrates the corresponding

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a

X 1= P(max) X 2= K 1P(max) X 3= K 2P(max) Y1= ΔP(max) A= K 1ΔP(max)

Pdif (pu)

0.4

A

Sub-system(1) Sending end

Sub-system(5) Line model

Sub-system(2) Receiving end

Pset

0.2 Y1

B

Sub-system(3)

Sub-system(4)

P&Q measurement(1)

P&Q measurement(2)

PS locus

C

0 0

1

0.5

X1

1.5

X2

X3 2

Sub-system(6)

P (pu)

b

Power differential relay

Qdif (pu)

5.33

Fig. 7. SimPower-based model blocks for the selected system.

2.66

E

D

the sub-systems 3 and 4, whereas sub-system 6 was assigned for developing the P and Q detectors for the power differential relay core.

Q set

4. Evaluation tests

QPS

0 0.001

0.01

0.1

1

10

Q (pu) Fig. 5. Enhanced setting profiles for P and Q detectors: (a) P detector setting compared to the power swing (PS) locus and (b) Q detector setting compared to the reactive power swing locus.

The dynamic performance of the power differential relay was thoroughly investigated via the collected real-time test cases prepared with the developed simulation with MATLAB. These test cases covered all the critical issues that may affect its dynamic performance such as the entire length of the line, load angle (d) variations and the fault inception angle. All types of faults including internal and external cases were addressed as well. Both single machine-infinite bus and double machine configurations were considered as describes in the following subsections. 4.1. Single machine-infinite bus configuration

Gen.

Transformer

Transmission line

Infinite system V∠0o

Fig. 6. Selected system one line diagram.

schematic of the developed model into MATLAB [14]. Six different sub-systems were utilized comprising the associated elements of the considered network. The sending end was equipped with a 600 MVA, 13.8 kV synchronous machine with hydraulic turbine governor (HTG) and excitation control system. The relevant parameters for the utilized generation set were demonstrated in Tables A1–A3 respectively. Incorporating both the turbine governor and the excitation system is essential for performing dynamic simulations. A 600 MVA transformer (of 13.8/230 kV and delta/star connection) connected the sending end to the receiving end via a 158.4 km single circuit overhead transmission line. The line impedance and its shunt capacitance are (0.0243 + j0.29033) X/km and 12.6 nF/km respectively. Distributed parameter line model in MATLAB was employed for simulation purposes. The receiving end was connected to either infinite bus (single machine connection) or to another 600 MVA detailed synchronous machine (two machine system). MATLAB is competing nowadays strongly with other electromagnetic simulation programs with its promising GUI-based SimPower toolbox. It is equipped with an integrated library including a large variety of built-in models covering all power system elements. This facilitates to develop a detailed modeling of power system networks and consequently provides an optimum tool for such dynamic studies. The active and reactive power quantities are extracted at each line end via the built-in P-Q blocks with

Infinite bus was modeled in MATLAB with a stiff voltage source with fixed magnitude and angle. Different conditions were considered as follows. 4.1.1. Effect of power swing during internal faults The performance of the power differential relay was thoroughly investigated during internal fault conditions. Prepared cases covered a wide variety of fault conditions including different fault types (phase–ground, phase–phase and three phase), different locations (along the whole line length), different fault resistance (for ground faults), different loading and different inception angles. This is in order to insure its proper behaviour during the fault period as well as after the fault clearance. Fig. 8 illustrates the response for a three phase internal fault at the sending end for 0.1 s only, whereas Fig. 9 shows the profile of the load angle variation due to this event. This faulted case was successfully recognized during the fault period as noticed by the response of P and Q detectors in the aforementioned figure. Both responses were rapidly reset to a low state after the fault clearance. Repeating this test scenario with the whole test set for internal fault cases demonstrated the same successful manner with a sensitive operation up to 150 X for ground faults. This clearly emphasized the scheme sensitivity to the internal fault happening as well as the scheme immunity against mal-operation with swinging conditions. 4.1.2. Effect of power swing during external faults External fault condition, accompanied with dynamic power swing, represents a severe situation that may affect the performance

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Fig. 8. Scheme response and phase (A) current and voltage for three phase internal fault at the sending end.

Fig. 10. Scheme response to an external three phase fault at the sending end: (a) Q and P detector outputs, (b) DQ variation profile versus Qset during the fault period and (c) DP variation profile versus Pset during the fault period.

Fig. 9. Load angle variation for the internal three phase fault at the sending end.

of the protective relays remarkably. Thus, investigating the influence of such these situations on the stability of the power differential relay is significant. Fig. 10a shows the response of P and Q detectors for a three phase external fault occurring at the sending end having low DP and DQ ranges for both detectors during the fault period as well as the after the fault clearance. On the other hand, Fig. 10b and c illustrate the variation profile of both DQ and DP versus the computed active and reactive power respectively. Both aforementioned figures emphasized the scheme stability resulting from keeping the DP and DQ levels below their corresponding setting lines during the whole test period. Similarly, the scheme stability for external phase–ground and phase–phase fault was examined showing stable behaviour as well.

4.1.3. Scheme response to midpoint internal faults Internal faults occurring at the line midpoint represent a special issue for the power differential relay as reported in [7,8]. Hence the need to investigate its dynamic behaviour during these situations is obvious. The response of both P and Q detectors for a three phase fault at line midpoint is shown in Fig. 11a, whereas Fig. 11b shows the load angle variation profile for this situation. Similarly, the cor-

Fig. 11. Scheme response to a three phase fault at the line midpoint: (a) P and Q detector outputs compared to the scheme settings and (b) Load angle variations due to the occurred fault.

responding response for solid phase–ground and phase–phase faults are shown in Fig. 12a and b respectively. The results corroborate that the scheme keeps its superior performance even with accompanied power swig with the occurring fault. 4.1.4. Stable and unstable power swing with load addition Sudden addition of large loading may contribute into either stable or unstable power swing condition according to the amount of the added load. These situations represent a severe condition that may represent a challenge for some protection equipment. Thus, investigating the performance of the power differential through these is quite important. Two different loading addition cases with

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alternating machines during the swing case. It is sometimes considered a challenge for some protection equipment leading to false tripping issues. The investigation of the power differential relay against these circumstances is, therefore, quite interesting. For this target, the same MATLAB-based simulation was rearranged replacing the infinite bus with another similar 600 Mw, 13.8 kV synchronous generator. Similarly with the testing scenario in the aforementioned subsection, the following test cases were considered. 4.2.1. Scheme performance during internal faults Fig. 15a shows the response of both P and Q detectors for a three phase internal fault at the sending end, whereas the corresponding

Fig. 12. Scheme response to solid L-G and L-L faults at the line midpoint: (a) solid LG fault at midpoint and (b) solid L-L fault at midpoint.

200 and 300 Mw were considered. For each case, the load was suddenly added at the sending end. As noted from Fig. 13a, the first case referred to a stable power swinging recognized from its decreasing load angle. The latter case referred to unstable power swinging recognized from its increasing load angle as described in Fig. 13b. For each case, the corresponding active power difference (DP) and reactive power difference (DQ) were plotted versus their associated active and reactive power as shown in Fig. 14a and b respectively. Comparing the power setting edges for both quantities (shown in Fig. 5) with the resulted profiles of the varying load angle for each cases, these profiles were localized blow their relevant setting edges. Thus, the superior stability of the power differential relay against both stable and unstable power swings was certified. 4.2. Double machine configuration

Fig. 14. DP and DQ variation profiles during –– stable and — unstable power swings (a) (DP) versus the computed three phase active power and (b) (DQ) versus the computed three phase reactive power.

Double machine systems show different behaviours through the dynamic studies due to the dynamical interaction between both

Fig. 13. Load angle variation during stable and unstable power swing: (a) stable power swing due to 200 Mw load addition and (b) unstable power swing due to 300 Mw load addition.

Fig. 15. Scheme response to three phase internal fault at the sending end for double machine system configuration: (a) P and Q detector outputs compared to the scheme settings and (b) load angle variations for both line ends.

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load angle variations of both line ends were demonstrated in Fig. 15b. The results clearly highlighted the scheme sensitivity during the fault period as well as its stability after the fault clearance. Other prepared cases covering all internal fault possibilities were recognized successfully revealing the same sensitive performance realized with single machine systems.

Fig. 18. DP and DQ variation profiles for –– stable and — unstable power swings for double machine system configuration (a) stable power swing due to 200 Mw load addition and (b) unstable power swing due to 300 Mw load addition.

Fig. 16. Scheme response to three phase external fault at the sending end for double machine system configuration: (a) DP profile compared to the DP setting line and (b) DQ profile compared to the DQ setting line.

4.2.2. Scheme stability against external faults A three phase external fault was applied at the sending end just prior to the relay CTs. The proposed scheme presented the similar stability for such faults. This was clear from Fig. 16a and b showing the profiles of both computed active power difference (DP) and reactive power difference (DQ) as compared with their relevant setting edges. Other possibilities of external fault conditions were examined revealing the perfect stability of the power differential relay against all external fault conditions with double machine configurations as well. 4.2.3. Scheme sensitivity to midpoint internal faults As mentioned earlier for single machine-infinite bus configuration, midpoint internal faults represent a special issue for the power differential relay. Fig. 17a–c illustrate the outputs of both P and Q detectors for three phase, phase–ground and double phase faults respectively, in which all of the applied faults were successfully recognized. Similar performance was also realized for non-solid ground faults with fault resistance up to 150 X. These results corroborate the superior sensitivity of the power differential relay for all internal fault types along the whole line length. 4.2.4. Stable and unstable power swing with load addition Fig. 18a and b illustrate the variations of both active power difference (DP) and reactive power difference (DQ) as compared with their relevant setting lines for adding 200 and 300 Mw respectively at the sending end. As revealed from the shown result, both detectors kept their stability obviously with a sufficient margin below their setting edges. 5. Conclusions

Fig. 17. Scheme response to internal faults at the line midpoint for double machine system configuration: (a) P and Q detector outputs for three phase fault, (b) P and Q detector outputs for phase–ground fault and (c) P and Q detector outputs for phase– phase fault.

Investigating the dynamic performance of new protective equipment is important since simple network models with stiff voltage sources and simple machine models do not represent the actual behaviour of the proposed relaying function under real field operation. For this target, a full dynamic power system model was developed with the MATLAB package considering both single

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phase. Thus the suitability of the power differential relay for providing the transmission lines with the proper protection is obvious.

Table A1 Parameter list for the utilized 600 MVA generator. Nominal power Nominal voltage Rs Ld Lq Inertia coefficient (H)

600 MVA 13.8 kV 0.003 p.u. 0.9176 p.u. 0.2176 p.u. 3.125 s

Table A2 Parameter list for the governor unit utilized with the 600 MVA generator. Servo-motor constant, Ka Servo-motor constant, Ta Initial mechanical power

10/3 0.07 s 0.8355 p.u.

Table A3 Parameter list for the exciter unit utilized with the 600 MVA generator. Low pass filter time constant Regulator gain Regulator time constant Initial value for terminal voltage Initial value for field voltage

397

20  103 300 0.001 1 p.u. 1.417

machine-infinite bus and double machine configurations. MTLAB package with its SimPower toolbox represent a powerful simulation environment for simulation power system networks as well as modern digital protection equipment. In order to evaluate the performance of the power differential relay, a complete test set of fault examples were prepared covering all possibilities of internal and external faults were prepared. The results corroborated the superior relay sensitivity for all internal fault types even at the midpoint of the line. All non-solid ground faults were successfully discovered up to 150 X of fault resistance. Also, the scheme shows a perfect stability against all external fault conditions as well as against both stable and unstable power swings. Realizing sensitive and stable operation is the essential issue for a successful unit protective relay. Moreover, a new setting profile was proposed for realizing a reliable and simple development in the implementation

Appendix A The relevant parameters of the 600 MVA generator and its associated governor and exciter units are listed below in Tables A1–A3 respectively. References [1] Russell Mason C. The art and science of protective relaying. John Wiley & Sons; 1984 [Fourth Wiley Eastern Reprint]. [2] IEEE Committee Report. Synchronized sampling and phasors measurements for relaying and control. IEEE Trans Power Deliver 1994;9(1):442–52. [3] Li HY, Southern EP, Crossley PA, Potts S, Pickering SDA, Caunce BRJ, et al. A new type of differential feeder protection relay using the global positioning system for data synchronization. IEEE Trans Power Deliver 1997;12(3):1090–9. [4] Ernst LJ, Hinman WL, Quam DH, Thorp JS. Charge comparison protection of transmission lines – relaying concepts. IEEE Trans Power Deliver 1992;7(4):1835–52. [5] Valsan Simi P, Swarup KS. Wavelet transform based digital protection for transmission lines. Int J Electr Power Energy Syst 2009;31(7–8):379–88. [6] Dash PK, Samantaray SR. A novel distance protection scheme using time– frequency analysis and pattern recognition approach. Int J Electr Power Energy Syst 2007;29(2):29–137. [7] Darwish HA, Taalab AI, Ahmed ES. Investigation of power differential concept for line protection. IEEE Trans Power Deliver 2005;20(2):617–24. [8] Taalab AI, Darwish HA, Ahmed ES. Performance of power differential relay with adaptive setting for line protection. IEEE Trans Power Deliver 2007;22(1):45–78. [9] Aziz Mohamed Mamdouh Abdel, Zobaa Ahmed Faheem, Ibrahim Doaa Khalil, Awad Mohammed Mohammed. Transmission lines differential protection based on the energy conservation law. Electr Power Syst Res 2008;78(11):865–1872. [10] Namdari F, Jamali S, Crossley PA. Power differential based wide area protection. Electr Power Syst Res 2007;77(12):1541–51. [11] So KH, Heo JY, Kim CH, Aggarwal RK, Kim JC, Jang GS. An implementation of current differential relay and directional comparison relay using EMTP MODELS. Int J Electr Power Energy Syst 2006;28(4):261–72. [12] Power System Relaying Committee, WG D6 power swing and out-of-step consideration on transmission lines, Power System Relaying Committee (PSRC) Report, IEEE-PES, Issued on the Published Reports Homepage on July 19, 2005. [13] Soman SA, Nguyen TB, Pai MA, Vaidyanathan R. Analysis of angle stability problems: a transmission protection systems perspective. IEEE Trans Power Deliver 2004;19(3):024–1033. [14] The MathWorks Inc., MATLAB, Ver. 7.01, 2005, .