Experimental investigations using quadratic-tripping characteristics based on alienation/coherence coefﬁcients of voltage and current signals for synchronous generators protection

A protection scheme is proposed using alienation method derived from coherence model which is a backup protection method for the differential overcurrent protection of synchronous generators. This scheme which is realized by the computational technique based on the alienation coefﬁcients estimated for generator voltage and current signals is considered to be mounted beside the main differential protection system, which operates in the cases that differential protection is unable to detect the internal faults. This novel protection algorithm operates by adjusting the alienation settings of the suggested relay that sends the trip signal to the three-phase circuit breaker of the protected generator. In the proposed method, fault occurrences can be determined regardless of variations of terminal voltage and current in different working states of synchronous generator. This is done by designing new quadratic-tripping characteristics based on alienation limits for the electrical signals. To demonstrate the proposed method, a motor-synchronous generator set with built instrument transformers, for measuring voltage and current data at the generator terminals, are used. Extensive experimental investigations validate the functionality of this novel protection scheme under different abnormal, unbalance and operating conditions for the generator under test.


INTRODUCTION
The most important element of a power system is the synchronous generator. As a result, many protection schemes were proposed to protect the synchronous generators against different types of series and shunt faults [1]. Several previous articles presented various schemes for protecting synchronous generators against various types of faults. These schemes were presented for inter-turn short-circuit fault detection, fault type classification or/and the fault location identification using different techniques such as: total harmonic contents, support vector machine, artificial neural network, fuzzy logic, finite element study and different statistical approaches [1][2][3][4][5][6][7][8][9][10] [1]. In [2], Gopinath et al. used Nuisance Attribute Projection (NAP) algorithm to improve the maximum fault classification accuracy for an inter-turn fault applied to a small working model of a synchronous generator, Pouya Mahdavipour et al. proposed a voltage-controlled overcurrent protection scheme which is a backup protection of differential relay in [3], while in [11], Coffele et al. suggested an adaptive overcurrent relay to reduce the mean operating time compared with conventional overcurrent schemes. Liang Che; Ustun, et al. considered sensing low fault currents and time delay in microgrids [12,13], respectively. Yadaiah et al. proposed a technique to detect and classify internal and external faults of synchronous generator in [14]. The sensitivity and operating time of protective relay become an issue when DGs are inserted [15]. Many authors discussed adaptive and AI techniques of overcurrent protection of DGs and microgrids [16][17][18][19][20]. The authors in [21] utilized the machine model for simulating stator internal faults and presented a 100% stator-ground protection based on the third harmonic voltage on the neutral and terminals of the machine. Paper [22] developed an analytical method to detect, classify, and locate the internal faults, namely phase-to-ground faults and turn-to-turn faults, in the synchronous generator stator winding based on harmonic components of the terminal voltage waveforms, where Decision Tree (DT) is employed to extract the third and the fourth harmonic components of the terminal voltage waveforms and the fundamental component of the residual voltage signal, which used not only all the turn-to-turn faults and the number of the shorted turns can be determined but also the faulty phase to-ground can be detectable. In [23], the authors suggested a new approach to interpret the voltage unbalance cases using the expression of voltage unbalance factor (VUF).
In [24], Shweta et al. proposed an analytical technique based on coherence coefficient and Lagrangian function to separate the out of step generator and to give information about the level of instability of the system. In [25], Vahidnia et al. used the coherence function and the angle of cross-spectral density function to assess whether the interconnected generators are positively or negatively coherent and assign them different machine groups. In [26,27], Elsadd et al. presented new adaptive techniques in the first article with the aim to increase the reliability of the generator-transformer unit overall differential protection with use of the capability curves, also presented formulas to calculate the reliability, dependability, and security percentage of the protective relay, while in the second article the authors proposed an adaptive optimum coordination for deregulated distribution networks considering the change in the network topology including parallel feeders. In this paper, a backup protection scheme for synchronous generator is proposed to operate and to send a trip signal to the generator breakers in conditions that the main protection scheme, which is the highspeed differential overcurrent protection, is unable to detect the internal fault. In this protection scheme, alienation coefficients derived from coherence coefficients, calculated for generator voltage and current signals, is used as the final decision maker and sets the alienation setting of the proposed relay that sends the trip signal to the generator breaker(s). This paper is organized as follows: In Section 2, the alienation-based protection scheme of the synchronous generator, with all the details, is given. In Section 3, the motor-generator set under test with its instrument transformers are presented. In Section 4, the experimental results are given. In Section 5, the proposed technique features have been listed. In Section 6, the conclusions have been made.

Basic principle
There are a number of parameters that change with fault occurrence in synchronous generator. RMS values of the terminal voltages will drop and RMS values of the terminal currents will increase under short-circuit and overload conditions. In addition, the fault event may lead to a disturbance in frequencies and phase angle shifts measured for three phase voltage and current signals. Moreover, the fault may cause a variation in the symmetry and shape of sinusoidal waveforms or an unbalance between the three-phase voltage/current signals [23]. This fact can be used to diagnose the fault in cases that none of the three phase currents contain a D.C. component. Because of the unpredictable time of the fault occurrence, and therefore unknown state of the voltage and current signals at that random time, RMS value of the voltage or current cannot be a reliable parameter for diagnosing the fault. For all types of possible faults of the generator stator windings, terminal currents may contain D.C. components or not. Hence, a numerical method, based on the alienation concepts, is proposed; besides novel closed-tripping characteristics is developed for synchronous generators protection. In this article, the alienation coefficients are computed using the measured three phase voltage and current signals, which are obtained from coherence coefficients. A coherence coefficient is a statistical method that can be used to investigate the relationship, as a function of frequency, between any two signals or data sets. The coherence coefficient, sometimes called Magnitude-Squared Coherence (MSC), estimated between the two signals is a real value that lies from '0' to '+1' [24,25]. Therefore, the alienation coefficient is ranged between the two values of '+1' and '0'. The alienation approach can be used for discriminating normal, abnormal, balance and unbalance conditions of three phase voltage and current signals measured at the load side of SG stator windings.

Coherence coefficients calculation
There are two types of coherence coefficients used in this paper. One coherence coefficient is used for the same electrical signal of each phase which is named as 'auto-coherence'. The auto-coherence can monitor the disturbance condition in each voltage/current signal. The other type of coherence coefficients is used for two different electrical signals of one phase or two phases which is denoted as 'cross-coherence'. The crosscoherence can compare the unsymmetrical condition between each two voltage or two current signals for two different phases or differentiate between voltage and current signals for the same phase.

2.2.1
Calculation of the cross-coherence coefficients for three phase voltage signals To estimate the cross-coherence coefficient (Cv sx (k)) between the two sampled voltage signals (v s (n) and v x (n)) of the two different phases 'S' and 'X', respectively, the following equation can be used: where, (2) 2.2.2 Calculation of the cross-coherence coefficients for three phase current signals The following equation can be used for estimating the crosscoherence coefficient (Ci sx (k)) between the two discrete current signals (i s (n) and i x (n)) of the two different phases 'S' and 'X', respectively: Where,

Calculation of the cross-coherence coefficient between phase voltage and current signals
The following equation can be applied for evaluating the crosscoherence coefficient (Cvi s (k)) beween the sampled phase voltage and current signals (v s (n) and i s (n)) for the phase 'S':

2.2.4
Calculation of auto-coherence coefficient for phase current signal The auto-coherence coefficient is computed for each phase current signal. The auto-coherence coefficient (Ci s (k)), calculated between each two successive data windows shifted from each other by one-cycle interval of the same current signal (i s (n − N s ) and i s (n)) for each 'S' phase, is formulated as follows: Where, 2.2.5 Calculation of auto-coherence coefficient for phase voltage signal The auto-coherence coefficient is computed for each phase voltage signal. The auto-coherence coefficient (Cv s (k)), computed between each two successive data windows shifted from each other by one-cycle interval of the same voltage signal (v s (n − N s ) and v s (n)) for each 'S' phase, is given in the following mathematical formula: Where,

Alienation coefficients calculation
The alienation coefficient is defined as the complement of Magnitude-Squared Coherence (MSC) or coherence coefficient, and its value is bounded between '+1' and '0' [24,25]. Thus, there are two types of alienation coefficients used in the suggested algorithm. The first type is auto-alienation coefficient that is derived from the auto-coherence coefficient, which is used for the same electrical signal of each phase. Whereas the other type of alienation coefficients is cross-alienation coefficient that is deduced from the cross-coherence coefficient, which is used for two different electrical signals of one or two phase(s).
As mentioned before, the coherence and alienation coefficients assess a relationship between any two variables in the frequency domain. In the following table, some properties of alienation/coherence coefficient are listed; where, the benefit of each property of the coefficient is mentioned next to each property of them in the table.
In this paper, nine cross-alienation coefficients (Av ab , Av bc , Av ca , Ai ab , Ai bc , Ai ca , Avi a , Avi b, and Avi c ) and six autoalienation coefficients (Av a , Av b , Av c , Ai a , Ai b , and Ai c ) are computed and applied in the developed algorithm. The 15 alienation coefficients based-proposed technique is able to identify the normal/balance operating (i.e. no-fault state) and

Properties of alienation/coherence coefficient
The benefit of each property of alienation/coherence coefficient 1-The coherence coefficient is a real number in the range from '0.0' to '+1', while the alienation coefficient value is in the range of '+1' to '0.0'. (I) If the coherence coefficient takes values closer to 0.0, the coherence is weak and the relationship between the two variables is non-linear, while it will become stronger and the relationship between the two variables is linear when it is close to +1.0.
(II) If the alienation coefficient takes values closer to +1.0, the coherence is weak and the relationship between the two variables is non-linear, while it will become stronger and the relationship between the two variables is linear when it is close to 0.0.
-This information is useful for designing quadrilateral and closed-tripping characteristics of the proposed protection technique. Each quadrilateral operating characteristic includes two regions as follows: first is the tripping region, which can be divided into sub-regions according to the severity levels of voltage and current disturbances and unbalances, and second is the blocking region that prevent the operation (tripping) of SG CBs.
2-The coherence and alienation coefficients are not affected when the two variables are interchanged.
-This concern is useful for selecting any order or arrangement of electrical signals for calculating these coefficients.
3-The coherence and alienation coefficients are pure numbers without any effect of measurement units because they are scale invariants.
-This concern is useful for selecting various types of electrical signals (with different measurement units) for calculating these coefficients.

4-
The auto-coherence/auto-alienation function describes the relation of the same variable at two different time intervals. whereas the cross-coherence/cross-alienation function describes the relation between two different variables during the same time interval.
-This is useful for discrimination between normal and abnormal states for each phase voltage or current signal using the auto-alienation function, while the cross-alienation function is useful for discrimination between balance and unbalance conditions for three phase voltage or current signals.
5-When the two variables are at equilibrium, the coherence and alienation functions are stationary. They are independent on the absolute values of observations.
-This information is useful for normal and balance operating condition detection of three phase voltage and current signals, and differentiation between normal and abnormal or balance and unbalance situations.
6-When fluctuations for any variable around its average value are observed, the coherence and alienation functions can be defined in terms of the deviation from this average.
-This information is useful for severity level assessment of disturbance and unbalance for three phase voltage and current signals; which is resulting in estimate of the disturbance and unbalance indices of three phase system. 7-When the power quality parameters (magnitude, symmetry, shape and frequency) of electrical signals remain constant, the coherence and alienation functions for these signals are also fixed. The coherence/alienation functions will drop/rise, respectively, with any disturbance occurrence.
-This information is useful for detecting any power quality disturbance for phase voltage or current signal. This means that it is not restricted for determining overcurrent conditions. abnormal/unbalance conditions (such as overload, series and shunt faults, and CT saturation situation) using the rules listed in Table 2.

Protection algorithm procedure
As shown in Figure 1, the flow chart of the proposed protection algorithm, based on the fifteen alienation factors deduced from the coherence factors, works as explained below: operating the proposed protection algorithm for isolating the protected element) in the case of unbalance state. Figure 2(b) develops closed-tripping characteristics for the voltage and current disturbance, respectively. Each characteristic is based on the setting deviations of their auto-alienation coefficients compared to their ideal values. They are bounded between the two values of (0.0 Δu) and (0.0 Δw) in the case of normal operation for the voltage and current signals, respectively, measured at the three terminals of synchronous generator stator windings. Also, each characteristic possesses two zones: (I) a blocking zone in the case of normal operating condition, and (II) a tripping zone in the case of abnormal/fault condition. In the operating characteristics, shown in Figure 2(a) and (b), the index 'A' denotes to alienation coefficient, 'v' is voltage variable, 'i' is current variable, 'r, s and x' are the designation of three different phases, and the selected values of the alienation setting deviations (Δu, Δw, Δx, Δy and Δz) are 0.1, 0.1, 0.1, 0.1 and 0.75, respectively. These deviations are carefully selected according to the prevailed conditions, the acceptable overload currents, decent harmonics and temporary faults which occur in power system to prevent incorrect operation of the protection function. It is noted that the setting deviation (Δz) is large because of the low power factor of the used load in a system under test.

Tripping characteristics
In the case of acceptable unbalance due to the overload condition, the RMS value of the terminal currents rises and and v a (n) Module (2) to detect the current unbalance condition using the cross-alienation coefficients for the current signals Unbalance and abnormal power factor and i c (n) Module (4) to detect the voltage disturbance condition using the auto-alienation coefficient and v a (n) Module (5) to detect the current disturbance condition using the auto-alienation coefficient and i a (n) FIGURE 1 Flow chart of the proposed alienation-based algorithm for synchronous generator protection voltages drop to approximately %90 of the nominal value, besides the phase shifts between the three phase angles are slightly changed with respect to the ideal phase shifting. Regarding these facts, the conventional overcurrent relay sends the trip signal to the generator circuit breaker(s) because of the increment of the RMS value of the terminal currents. So, the setting of the traditional relay must be suitable, and the isolation of the generator must be avoided through the overcurrent protection. Also, this problem can be prevented via the convenient values of the alienation setting deviations of the proposed protection scheme. Thus, the following important points should be considered about the proposed protection method: I. In the overload condition, the proposed method improves the security of the protective system by increasing both the data window size and the blocking zone in the proposed characteristics (which is equivalent to increase of the pickup current of the conventional overcurrent relay). II. In the fault condition, the proposed method improves the sensitivity of the protective system by decreasing both the data window size and the blocking zone in the proposed characteristics (which is equivalent to decrease of the pickup current of the conventional overcurrent relay).

EXPERIMENTAL MODEL UNDER TEST
In order to investigate the proper performance of the proposed algorithm for three phase Synchronous Generator (SG) protection, an experimental system model is constructed. The system under test consists of a three-phase synchronous generator, which is processed via a prime-mover (single phase induction motor), and a load of three phase induction motor that is connected at three phase SG terminals, as shown in Figure 3(a) and (b). In addition to that three phase voltage transformers (VT 1 , VT 2 and VT 3 ) and three phase current transformers (CT 1 , CT 2 and CT 3 ) are connected at SG load terminals. CT 4 is considered a neutral current transformer for neutral current signal, and CT 5 represents a residual current transformer for three-phase current signals. The model has parameters given in Table 3. The three phase VTs and CTs signals, measured at the generator load ends, are transformed to digital signals using Data Acquisition Card (DAC), then the proposed algorithm is designed and analysed in LABVIEW platform. The analog signals are sampled at 50 Hz with a sampling frequency of 2.5 kHz; this means that the sampling time is 0.4 ms and the number of samples per cycle is 50. Personal computer (PC) and DAC are used to virtually simulate the intelligent digital relay. The National Instruments USB-6008/6009 is data acquisition device which is adjusted to operate in differential mode. Extensive tests of abnormal and unbalance conditions are examined and analysed by application of different types of series and shunt faults at the SG output.

EXPERIMENTAL RESULTS
The DAC and LABVIEW software package are used for testing the proposed algorithm for protecting the three-phase synchronous generator against abnormal and unbalance situations. In this study, the selected size of data window is one cycle (i.e. 50 samples per cycle), and the full time of display is 0.2 s (i.e. the total number of samples (N t ) per the display time is 500 samples). The following section offers experimental results for different cases of normal operating and fault types.  In this case, the generator is working properly without any faults. Initially, the RMS values, measured using a digital multi-meter, of three phase primary currents for the generator are: I a = 2.  Figure 4(c) with slight deviation due to the decent unbalance of instrumentation CTs of the three phases. The crossalienation coefficients for three phase voltage signals are shown in Figure 4(d). All the above cross-alienation factors are approximately equal to +0.75 at normal operation with the acceptable unbalance for current/voltage curves. Figure 5(a) and (b) shows the auto-alienation coefficients for three phase current signals and three phase voltage signals, respectively, with a value of zero. Whereas the cross-alienation coefficients between each phase voltage and current signals are shown in Figure 5(c) with a value close to +0.75 at normal operation and no trip command as shown in Figure 5(d). In this case, it is evident clear that the fifteen alienation coefficients affirm the healthy condition, and their values are settled in the blocking zones of the operating characteristics.

Case 2: 'C' phase series fault condition) (MCB 5 opening)
In this case, "C" phase is manually open circuited, while all other conditions are the same as case 1. The three phase current and voltage waveforms are shown in Figure 6(a) and (b). Figure 6(c) shows the cross-alienation coefficients between each two phase currents; it is clear that the cross-alienation coefficient between the two currents of the healthy phases is zero, while the crossalienation coefficient between any of them and the faulty phase current is nearly +1. Figure 6(d) presents the cross-alienation coefficients between each two phase voltages with a slight difference due to the open circuit of the "C" phase and the unbalance of instrumentation VTs. It is seen that the cross-alienation coefficient between the two voltages of the healthy phases is +0.6, while the cross-alienation coefficient between any of them and the faulty phase voltage is nearly +0.85. In Figure 7(a) and (b), the auto-alienation coefficients for the three phase currents and the three phase voltages are shown, respectively, revealing the only different value of roughly +1 for the faulty "C" phase current, while the remaining auto-alienation coefficients are about zero. The cross-alienation coefficients between each     phase voltage and its current are shown in Figure 7(c), also with a distinguished value for the faulty phase. Their values are approximately +1 for the two healthy phases, while the crossalienation coefficient is about +0.4 for the faulty phase. In Figure 7(d), the trip order is high, indicating the detection of the series fault for "C" phase. In this test, it is clear that some alienation coefficients confirm the faulty state, and their values are located inside the tripping zones of the operating characteristics.

Case 3: 'A and C' phases series fault condition) (MCB 3 and MCB 5 opening)
In this case, both phases "A" and "C" are manually open circuited. Figure 8(a) and (b) depicts the three phase currents and the three phase voltages, respectively, at the instants of fault occurrence and clearing. It is noted that the open circuit of the two phases is done manually which explains the time delay between the current signals and the voltage signals of the two faulty phases, this effect is equivalent to a DL series fault followed by a SL series fault. Figure 8(c) and (d) presents the cross-alienation coefficients between each two phase currents and the cross-alienation coefficients between each two phase voltages, respectively. The auto-alienation coefficients of the three phase currents and three phase voltages are shown in Figure 9(a) and (b) with variation of the coefficients during the fault period. The cross-alienation coefficients between each phase voltage and its current are represented in Figure 9(c) while the trip command is shown in Figure 9(d) indicating that the algorithm managed to detect the series fault condition in both phases "A" and "C". In this case, it is seen that all

Case 4: SLN (B-N) shunt fault condition
In this test, the fault type is SLN (B-N) shunt fault. The fault is located at the load ends of the synchronous generator under test. Figures 10 and 11 present the practical results for case 4. Figure 10(a) illustrates the three phase secondary current signals at the SG load terminals. Figure 10 and close to +0.75 during the period of the first two cycles, but their values are not constant during the remaining display time. Figure 10(d) introduces the three phase cross-alienation coefficients calculated between each two phase voltage signals. Also, it is seen that the values of these coefficients are fixed and close to +0.75 during the distance of the first two cycles, while their values are not stationary during the fault time. Figure 11(a) exhibits the three phase auto-alienation coefficients computed for each phase current signals. Figure 11(b) plots the three phase auto-alienation coefficients calculated for each phase voltage signals. As shown in Figure 11(a) and (b), it is clear that the six auto-alienation coefficients computed for current and voltage signals are steady during the normal operation (i.e. the first two cycles), while they rise instantaneously with the fault starting. Figure 11(c) describes three phase cross-alienation coefficients calculated between each phase voltage and current signals. It is seen that the values of the three phase coefficients change suddenly at the instant of fault inception, as presented in Figure 10(c), where they are constant and close to +0.8 during the normal operation condition; whereas their values are changed from +1.0 to +0.2 during the fault time. Figure 11(d) displays the tripping signal which is a high value of +1 in the case of SLN shunt fault. In this case, it is noticed that all alienation coefficients prove the faulty situation, and their values are inside the tripping zones of the closed-operating characteristics.
The experimental results confirm that the proposed protection algorithm is accurate, fast and reliable for identifying the abnormal/unbalance condition for three phase voltage and current signals.

Case 5: SLN (C-N) shunt fault condition with arc
In this case, a shunt fault is conducted between phase "C" and the neutral "N" at the output terminals of the synchronous generator. Figures 12 and 13 clarify the generated results from the protection algorithm for case 5 (SLG (C-N) shunt fault). Figure 12(a) and (b) show the three phase current and three phase voltage signals, respectively. Figure 12(c) illustrates the cross-alienation coefficients between each two phase currents while the cross-alienation coefficients between each two phase voltages are shown in Figure 12(d) with the clear variation of the calculated coefficients at the instant of fault occurrence. Figure 13(a) and (b) depicts the auto-alienation coefficients of the three phase currents and the three phase voltages, respectively. The variation of the calculated coefficients before and after fault occurrence indicates that the relay detected the fault/unbalance successfully. Figure 13(c) shows the crossalienation coefficient calculated between each phase voltage and its current. Whereas the trip signal is showing high value, as seen in Figure 13(d), to indicate that the proposed algorithm managed to identify the fault/unbalance condition. In this case, it is intelligible that all alienation coefficients affirm the fault occurrence, and their values are stable inside the tripping zones of the quadratic tripping characteristics.

Case 6: DL (A-B) shunt fault condition
In this case, both phases "A" and "B" are shorted. Figure14 (a) and (b) shows the three phase currents and three phase voltages, respectively. The cross-alienation coefficients between each two phase currents are shown in Figure 14(c), while the crossalienation coefficients between each two phase voltages are shown in Figure 14(d). The auto-alienation coefficients of the three phase currents and the three phase voltages are shown in Figure 15(a) and ;(b) with changes in the values of calculated coefficients at the instant of fault occurrence. In Figure 15(c), the cross-alienation coefficients between each phase voltage and its current are shown with distinguished values of the coefficients for the two faulty phases. Figure 15(d) offers the tripping

FIGURE 13
Experimental results for case 5 (continue). (a) Three phase auto-alienation coefficients calculated for three phase current signals, (b) three phase auto-alienation coefficients calculated for three phase voltage signals, (c) three phase cross-alienation coefficients calculated between three phase voltage and current signals, (d) tripping signal in shunt fault state.

FIGURE 14
Experimental results for case 6. (a) Three phase currents in shunt fault state, (b) three phase voltages in shunt fault state, (c) three phase cross-alienation coefficients calculated for three phase current signals, (d) three phase cross-alienation coefficients calculated for three phase voltage signals.

FIGURE 15
Experimental results for case 6 (continue). (a) Three phase auto-alienation coefficients calculated for three phase current signals, (b) three phase auto-alienation coefficients calculated for three phase voltage signals, (c) three phase cross-alienation coefficients calculated between three phase voltage and current signals, (d) tripping signal in shunt fault state.

Case 7: DL shunt fault (A-C) with CT saturation condition
In the following case, also the two phases "A" and "C" are shorted, but this time the instrumentation CTs and VTs are saturated as could be seen in Figure 16(a) and (b). In spite of CT saturation, the cross-alienation coefficients could detect the abnormal/unbalance condition between each two phase cur-rents, as depicted in Figure 16(c) and between each two phase voltages, as given in Figure 16(d). Figure 17(a) and (b) shows the auto-alienation coefficients for the three phase currents and the three phase voltages, respectively. In Figure 17(c), the cross-alienation coefficients between each phase voltage and its current are shown with clear deviation from the normal operation condition which means that the algorithm detected a fault/unbalance condition and sent a trip order to the circuit breaker as shown in Figure 17(d). In this experiment, it is plain that all alienation coefficients ascertain the fault event, and their values are settled in the tripping zones of the closed-tripping characteristics.
From the above practical results and other experimental verifications, it is concluded that all alienation coefficients are located inside the blocking zones of the closed-operating characteristics during the normal operating conditions, while most these coefficients are concentrated inside the tripping zones during the abnormal/unbalance conditions (such as series faults, shunt faults and CT saturation). Moreover, the proposed protection scheme based on the alienation/coherence method is an acceptable solution in detection and assessment of the different operating, unbalance and abnormal conditions for the synchronous generator under test. Hence the performance of the proposed protection algorithm is investigated as a backup relay for generators protection using the alienation coefficients (derived from the coherence coefficients) computed for three phase voltage and current data.
In this study, the performance of the proposed protection scheme was monitored over a period of nearly 3 months. It was found that the protection scheme operated 85 times, out of which 82 were correct trips. The relay failed to issue trip decision on two occasions. In all cases of normal operating conditions, the protection scheme was hold/blocked 35 times without any maloperation time. The percentages of accuracy, dependability, security and reliability of the proposed protective relay can be computed under both faults and measurement errors utilizing the formulae presented in articles [26,27], as given in Table 4: Note that even though dependability and security are individually above 95%, overall reliability is lower than 95% (only 4.25%).

ALIENATION/COHERENCE-BASED PROTECTION ALGORITHM FEATURES
The developed protection technique based on the alienation derived from coherence concept has the following merits: 1. The abnormal and unbalance conditions, for the three phase voltage and current signals, can be continually monitored and identified quickly and accurately using the alienation coefficients estimated for the electrical signals, 2. The size of data window can be tuned to get fast response, where it is selected to be one cycle or sub-cycle for most cases; the data window size affects the detection time of abnormal and unbalance conditions, 3. The severity degrees of voltage/current can be assessed, for all possible contingencies and unbalances, using the alienation coefficients; thus, the developed method is a useful tool in mitigation techniques applied to compensate voltage and current unbalance effects in power systems, 4. It is characterized by being accurate, reliable and robust; and it can be applied in generation, transmission, distribution and utilization systems with various voltage levels, besides It can be a crucial solution of unbalance detection and assessment for traditional, smart grids and digital substations, 5. Its sensitivity and security can be controlled via selecting the alienation/coherence deviation settings and the size of the coherent data window, 6. The setting values of alienation can be adaptive based on the prevailed conditions of power grids and the acceptable unbalance for voltage and current signals, 7. The approach develops new closed and quadratic-tripping characteristics based on alienation/coherence limits, 8. It is independent on the parameters data of power system elements and instrument transformers (such as voltage and current transformers), 9. The proposed algorithm can be a base for digital fault recorders, protective relays, besides voltage and current disturbances detectors, and 10. It could be used in adaptive protection relays and systems to make adaptation of tripping characteristics (such as differential overcurrent relays and voltage-controlled time overcurrent relays). Table 5 presents a comparison between the proposed protection scheme and the other conventional backup protection methods. This comparison describes the effectiveness of the developed scheme from various viewpoints, such as tripping characteristics, pre-setting values, speed, reliability, security, sensitivity, simplicity, multi-functions, low pass filter, and so on.

CONCLUSIONS
The proposed technique is considered as an adaptive backup relay, against the disturbances of power quality parameters, used to protect the synchronous generator which is one of the important elements of the power system. The power quality parameters represent variations of frequency, amplitude, waveform shape, and symmetry. The tripping time of the algorithm is set to be at least one cycle to assure that the main protective relay has failed to operate. This tripping time depends on the severity degree of unbalance or disturbance in the three-phase voltage and current signals which gives the adaptive action to the suggested algorithm. The tripping action is based on 15 alienation coefficients derived from the coherence coefficients for these phase voltage and current signals. Extensive experimental investigations have been implemented and evaluated using the alienation-based protection algorithm. The developed algorithm has been proven that it is fast, stable, robust, adaptive, accurate (95.83%), dependable (97.62%), secure (96.47%) and reliable (94.25%). It can be applied in generation, transmission, distribution and utilization systems with various voltage levels for traditional, smart grids and digital substations. The superiority of this approach is the determination of the various series and shunt fault and unbalance conditions utilizing the proposed closed-tripping characteristics dependent on the alienation boundary. Moreover, it is able to modify the alienation threshold settings to control the sensitivity and security of the proposed relay.

2.Tripping characteristics type
-The method develops new closed-tripping characteristics, which are based on alienation/coherence coefficients with restricted values between the two values of '0' and '+1' that are similar to per unit magnitudes.
-Most of them have open tripping characteristics, which are without restriction values for voltage and/or current variables, even though they are in per unit values. This is except the tripping characteristic of the impedance relay that functions as a backup protection for synchronous generator.

Operating time delay (relay speed)
-The operating time delay is controllable using the suitable data window size, and it can be chosen to be less than one cycle (i.e. sub-cycle). if the algorithm selects a sub-cycle of the data window, this accelerates relay operation.
-The operating time delay is greater than one cycle because some of the conventional methods depend on calculating the RMS values of voltage and/or current, which requires at least a period of one cycle.

Multi-algorithms and multi-functions
-The proposed technique can be used to carry out various protection functions such as: • Voltage and current disturbance detector, • Voltage and current unbalance detector, • Assessment of voltage and current unbalance, and • Assessment of voltage and current disturbance, -Moreover, it can be used as a base for digital synchro-check relay, and power factor meter/relay.
-Some of them perform only one protection function in the protective relay.
-Other relays carry out a variety of protection algorithms to perform multi-functions protection, which require different types of mathematical formulas.

Data synchronization system
-The proposed novel protection scheme requires no data synchronization system.
-Most of them require no data synchronization system when transmitting data.

Relay properties
-It is simple, accurate, dependable, secure, reliable, sensitive, and stable system.
-Some of them are complex, accurate, dependable, secure, reliable, sensitive, and stable system.

Criteria simplicity
-It is simple system in maintenance, installation and operation. The simpler the protection system it will more reliable.
-Some of them are complex systems because they are difficult while maintenance and installation.

Cost of implementation
-Need DAC (Data Acquisition Card) to convert the analog signals to the digital signals. -Need software for processing the DAC. -The suggested protective relay processes only one algorithm for calculating the alienation/coherence factors.
-Need DAC (Data Acquisition Card) to convert the analog signals to the digital signals. -Need software for processing the DAC. -Some conventional protective relays process multi-algorithms for calculating the RMS values of voltage and current signals, as well as the relay operating time besides other criteria elements.

Digital low pass filter
-The selected data window size, used in calculation of alienation/coherence factors, is considered as a digital low pass filter.
-Some of them need an additional digital low pass filter. In the case of harmonic distortion, the Fourier Transform filters harmonics, and therefore it is recommended to use it to calculate the Root Mean Square (RMS) value.

CT saturation detection
-The alienation/coherence concept can be used for CT saturation detection and assessment.
-Most conventional methods require an additional CT saturation detector.

NOMENCLATURE
3LN Three line-to-neutral fault, Ai a The auto-alienation coefficient calculated between the two successive data windows of phase voltage signal (i a (n) and i a (n-N s )) for the phase ' A', Ai ab The cross-alienation coefficient calculated between the two current signals (i a (n) and i b (n)), The auto-alienation coefficient calculated between the two successive data windows of phase voltage signal (i b (n) and i b (n-N s )) for the phase 'B', Ai bc The cross-alienation coefficient calculated between the two current signals (i b (n) and i c (n)), Ai c The auto-alienation coefficient calculated between the two successive data windows of phase voltage signal (i c (n) and i c (n-N s )) for the phase 'C', Ai ca The cross-alienation coefficient calculated between the two current signals (i a (n) and i c (n)), Ai s The auto-alienation coefficient calculated between the two successive data windows of phase voltage signal (i s (n) and i s (n-N s )) for the phase 'S', Ai sx The cross-alienation coefficient calculated between the two current signals (i s (n) and i x (n)) for the two phases 'S' and 'X', respectively, Av a The auto-alienation coefficient calculated between the two successive data windows of phase voltage signal (v a (n) and v a (n-N s )) for the phase ' A', Av ab The cross-alienation coefficient calculated between the two voltage signals (v a (n) and v b (n)), Av b The auto-alienation coefficient calculated between the two successive data windows of phase voltage signal (v b (n) and v b (n-N s )) for the phase 'B', Av bc The cross-alienation coefficient calculated between the two voltage signals (v b (n) and v c (n)), Av c The auto-alienation coefficient calculated between the two successive data windows of phase voltage signal (v c (n) and v c (n-N s )) for the phase 'C', Av ca The cross-alienation coefficient calculated between the two voltage signals (v a (n) and v c (n)), Avi a The cross-alienation coefficient calculated between the voltage and current signals (v a (n) and i a (n)), Avi b The cross-alienation coefficient calculated between the voltage and current signals (v b (n) and i b (n)), Avi c The cross-alienation coefficient calculated between the voltage and current signals (v c (n) and i c (n)), Avi s The cross-alienation coefficient calculated between the voltage and current signals (v s (n) and i s (n)) for the phase 'S', Av s The auto-alienation coefficient calculated between the two successive data windows of phase voltage signal (v s (n) and v s (n-N s )) for the phase 'S', Av sx The cross-alienation coefficient calculated between the two voltage signals (v s (n) and v x (n)) for the two phases 'S' and 'X', respectively, Ci a (k) The auto-coherence coefficient, on a given frequency (k), calculated between each two successive data windows shifted from each other by one-cycle interval of the current signal (i a (n) and i a (n -N s )) of the ' A' phase, Ci ab (k) The cross-coherence coefficient calculated between the two current signals (i a (n) and i b (n)), Ci b (k) The auto-coherence coefficient, on a given frequency (k), calculated between each two successive data windows shifted from each other by one-cycle interval of the current signal (i b (n) and i b (n -N s )) of the 'B' phase, Ci bc (k) The cross-coherence coefficient calculated between the two current signals (i b (n) and i c (n)), Ci c (k) The auto-coherence coefficient, on a given frequency (k), calculated between each two successive data windows shifted from each other by one-cycle interval of the current signal (i c (n) and i c (n -N s )) of the 'C' phase. Ci ca (k) The cross-coherence coefficient calculated between the two current signals (i c (n) and i a (n)), Ci s (k) The auto-coherence coefficient, on a given frequency (k), calculated between each two successive data windows shifted from each other by one-cycle interval of the current signal (i s (n) and i s (n -N s )) of the 'S' phase, Ci sx (k) The cross-coherence coefficient calculated between the two sampled current signals (i s (n) and i x (n)) for the two different phases 'S' and 'X', respectively, on a given frequency (k); the coefficient is a real value, CT Current Transformer, CT 1 , CT 2 , CT 3 , Current Transformers no. 1, 2, 3, 4 and 5, CT 4 and CT 5 CTR Current Transformer Ratio, Cv a (k) The auto-coherence coefficient, on a given frequency (k), calculated between each two successive data windows shifted from each other by one-cycle interval of the voltage signal (v a (n) and v a (n -N s )) of the ' A' phase, Cv ab (k) The cross-coherence coefficient calculated between the two voltage signals (v a (n) and v b (n)), Cv b (k) The auto-coherence coefficient, on a given frequency (k), calculated between each two successive data windows shifted from each other by one-cycle interval of the voltage signal (v b (n) and v b (n -N s )) of the 'B' phase, Cv bc (k) The cross-coherence coefficient calculated between the two voltage signals (v b (n) and v c (n)), Cv c (k) The auto-coherence coefficient, on a given frequency (k), calculated between each two successive data windows shifted from each other by one-cycle interval of the voltage signal (v c (n) and v c (n -N s )) of the 'C' phase,