An overview of various faults detection methods in synchronous generators

Synchronous generator (SG) plays a vital and critical role in the power system by sup-plying electric power to consumers. Various faults in SGs can cause some catastrophic events such as power disruption or blackout. These faults can be classified into two electrical and mechanical faults. Short circuit in stator windings and field winding are electrical fault while bearing, static/dynamic eccentricity, and broken damper bars faults are mechanical one. Unlike the induction machines, there are no much researches in SGs condition monitoring owing to its complex behaviour against the faults. Herein, the SG modelling approaches are presented briefly to elaborate shortcoming and challenging issues in the modelling, and then a comprehensive review of various electrical and mechanical fault detection methods is presented.


| INTRODUCTION
Synchronous generator (SG) is one of the most important apparatus in the power systems, which supply the electrical energy to consumers. The SGs are highly reliable equipment but the faults are unavoidable and can interrupt the electrical power supply. Since the SG reliability is a critical issue in the power systems, various protection techniques have been so far proposed to enhance the power system reliability. Although reliability enhancement improves by redundancy (adding another SG as the backup unit), it increases the cost, volume and weight of the power generation system. Hence, an appropriate approach uses a sensitive and accurate fault diagnosis method to detect the faults in the incipient level. In large SGs, the stator-winding fault is the most prevalent one, and the rotor-winding fault has second priority. Figure 1 shows the proportion of the faults which occur in large electrical machines [1]. Although, there are a lot of work on the fault diagnosis of induction machines, less attention has been paid to SGs faults detections. The reason includes complicated structure and difficult starting process of the generator. The failure modes can be classified into electrical and mechanical ones. The electrical faults include [2]: � Core insulation failure. � Stator winding or its insulation failure. � Rotor winding or its insulation failure and the mechanical faults include: � Bearing failure. � Broken damper bars. � Rotor mechanical integrity failure. � Stator mechanical integrity failure.
Creating a real fault on the SG and analysing its behaviour is mostly destructive and costly, because the SG cannot operate properly after such experiment. Moreover, a real fault can be dangerous and cause some problems. That is why modelling plays a major role in the SGs analysis by reducing costs and dangers.
Herein, various SGs modelling firstly are presented. Then, rotor/stator winding faults, as the most probable faults, are reviewed. Rotor eccentricity and broken damper bars faults are discussed in details. Finally, the last section provides the conclusions.
Each model has its own advantages and disadvantages. The simplest modelling method of the SG is the use of. the dq0 frame. Although, this modelling technique is applicable in symmetrical and balanced conditions, it cannot be recommended for asymmetrical systems [4]. Owing to the simplicity of this approach, its computations time is relatively short, and the parameters of the SG can be calculated quickly. The dq0 model is a useful tool for prediction of healthy SG behaviour. At this end, the dq0 parameters are calculated for stator/rotor windings and damper bars [5]. However, the dynamic model of the brushless SG has been presented in Ref. [6] which models the SGs with the turn-to-turn fault (TTF) using the dq0 frame. Simulation and experimental results show that this model is appropriate for a minor fault, but it is not preferred for severe faults such as phase-to-ground or phase-to-phase short-circuits. The reason is that the high severity faults can lead to asymmetrical and unbalanced system. It means that the dq0 model is not accurate for severe faults detection in the SGs. Moreover, the dq0 models used in the simulation of the SGs cannot account for the space harmonics of the winding [7]. To overcome this shortcoming winding function approach (WFA) has been proposed for modelling.
Although, the WFA is more complicated than the dq0 model, it is applicable to the asymmetrical systems. This model is able to estimate the inductances in various healthy and faulty conditions accurately. The WFA shows the air-gap magnetomotive force (MMF) distribution in the air-gap due to the winding [8], which takes into account the space harmonics, slotting, air-gap permeance and slot skewing effects [9,10]. The WFA is capable to model various electrical machines in different fault conditions and it only needs to consider the effect of fault in the estimated inductance matrix. The internal fault has been modelled in Ref. [11] based on the WFA, in which a new inductance estimation procedure is given, and it also integrate all space harmonics of the fault modelling. To apply this method the following assumptions must be considered: 1. Neglecting stator slots effects. 2. Ignoring magnetic hysteresis. 3. Neglecting iron saturation effects.
In the WFA, the general expression of the mutual inductance between winding "i" and winding "j" of electrical machine is given by: where μ 0 is the free space permeability, r is the air gap average radius, l is the axial stack length of the machine, and g À 1 (φ,θ) is the inverse air-gap length function which is constant in the case of uniform air gap. N i (φ,θ) and N j (φ,θ) are the winding functions of the windings i and j, φ is the angle along the inner surface of the stator, and θ is the angular position of the rotor with respect to the stator reference axis.
Referring to machine parameters, (1) is modified as follows: where L BA is the mutual inductance between circuit A and B, and L md and L mq are the d-axis and q-axis magnetising inductances, respectively. Moreover, w s is the amplitude of the fundamental harmonic of the stator phase winding function of a healthy machine, n B (φ,θ) is the total turns function of circuit B, N A (φ,θ) is the total winding function produced by circuit A and finally p is the number of pole pairs. By using (2), the stator inductance, rotor inductance, and mutual inductance between the stator and rotor of the healthy F I G U R E 1 Proportion of faults in large electrical machines [1] 392 -MOSTAFAEI AND FAIZ machine are easily calculated. However, in faulty machine, the following equation must be solved numerically.
This is a vector form of the voltage equation. The mentioned method of the inductance matrix calculation in the SG improves the accuracy of the SG model in an asymmetrical system such as phase-to-ground fault and phase-to-phase fault. The results reported in Ref. [11] illustrate that experimental and simulation waveforms are reasonably close.
Apart from severe short circuit faults, rotor misalignment is another failure that leads to an asymmetrical system and needs a more accurate model; however, it is slower than the dq0 frame model. The dynamic eccentricity fault has been modelled using WFA in Ref. [12], in which the saturation effect has been included.
To shorten the computation time of WFA and to improve the accuracy of the dq0 frame method, a hybrid modelling method has been proposed by merging the two modelling approaches. It means that the hybrid model [13] can work in both symmetrical and asymmetrical systems. As shown in Figure 2, for low severity fault (SC of 5% to 10% of stator winding turns), dq0 and hybrid method are accurate, but in saturation condition with more severe faults, the dq0 model cannot follow the real machine waveform and this error increases in a higher saturation level and more severe faults. In low severity fault, the faults such as turn-to-turn fault (TTF), stator core does not saturate, but in severe ones, saturation is common, and the dq0 model cannot work properly. In fact, the proposed hybrid method makes a compromise between the accuracy and speed, which can cover the entire fault region from low to high severity. The phase domain model (PDM) is more complicated than the dq0 model, but it does not require the sinusoidal winding distribution [8]. Besides, the dq0 model has constant inductance matrices [13]. The PDM uses voltage and flux-linkage equations in a reference phase to derive the fault model in the SGs [14][15][16].
The PDM can deal with the saturation conditions, as described in Ref. [17]. Some have presented a modified winding function approach (MWFA), which combines the WFA and PDM model for detecting the phase to ground faults [9,18,19]. The MWFA, as an extended version of the WFA, is used in a non-uniform air-gap machine [20]. The dynamic eccentricity (DE) fault causes the asymmetrical air-gap; therefore, the SGs must be modelled by MWFA [20][21][22].
The mutual inductance of two arbitrary windings x and y in respect to the winding distribution n x and n y is as follows [23]: where P is the permeance distribution of the air-gap.
Few modelling methods consider the saturation effect in the faulty SGs. In Ref. [23], the saturation effect has been taken into account in the induction motor with uniform air-gap. A robust non-linear model of the SGs has been introduced in Ref. [24] to overcome some non-linear phenomena such as the SGs saturation.
The MWFA model of the mixed eccentricity (ME) fault has been reported in Ref. [25] in which the self-and mutual-inductances are calculated precisely.
Last but not least, the finite element method (FEM) is the most accurate modelling approach that is able to model various electrical machines by considering different conditions such as saturation, core loss, and rotor and stator faults. In fact, FEM is able to validate other models when a real machine is not accessible, or an experiment is costly and challenging. Moreover, the magnetic flux pattern can be visualised in FEM software, which gives a clear viewpoint. Despite of the FEM modelling accuracy, it needs a powerful computer particularly for complex calculations. Hence, using this model for fault detection is difficult and time-consuming process, and it is only applicable for validation or optimisation of electrical machines. FEM has been applied to validate the MWFA modelling method in the saturation condition and eccentricity fault [26]. Table 1 shows a brief review of various SG modelling methods.

| STATOR WINDING FAULTS
According to Figure 1, 60% of the faults are dedicated to the stator winding. The most probable causes for winding fault are high temperature, short circuit, electrical discharge, mechanical stress, magnetic force and insulation deterioration [27]. Generally, stator winding fault diagnosis methods use magnetic flux, current and voltage or a combination of them.
Although the phase-to-phase and phase-to-ground faults are more severe than the inter-turn winding fault, they can be detected easier by protection relays in a fraction of second. Detection of the inter-turn fault is difficult at the incipient stage because it does not significantly influence the terminal currents. Therefore, condition monitoring is essential for interturn faults to diagnose the fault at starting point and prevent the following problems. There is a widespread belief that many phase-to-ground or phase-to-phase faults started as undetected TTF, which grew and propagated until disaster finally occurs [28]. Here, the stator winding fault detection methods are briefly reviewed in transformers and induction motors, and then the methods are extended to the SGs. In the incipient stage, the insulation failure is not dangerous, but if it is not detected earlier, it may lead to a severe fault. In fact, the TTF in the winding induces a high-induced current, which flows in the shorted loops and causes the winding failure [29]. Detecting the fault at an early stage decreases the machine damage, and the machine can be put back into service by rewinding the stator [30].
Differential relays cannot detect the TTF due to instrumental transformers saturation, which reduces its sensitivity. Hence, other methods such as negative or zero sequence-based methods should be used for the TTF diagnosis, beside the differential relay. To detect the stator-winding fault in the SGs, various quantities such as current, voltage, and magnetic flux can be utilised. The following techniques can be applied for stator fault detection.

| Magnetic flux
Most electrical and mechanical faults in electrical machines including stator-winding fault change the magnetic flux pattern. As shown in Figure 3, the stator-winding fault reduces the magnetic flux near the fault region, and the stray flux increases adversely. Therefore, flux monitoring can be an effective choice for fault diagnosis. Generally, sensors through measuring the leakage or air-gap flux in different parts monitor the magnetic flux. For flux monitoring in electrical machines, some sensor such as fluxgate magnetometer, Hall Effect sensors, and the search coil (SC) magnetometer can be used [31]. Each sensor has its frequency range, and the search coil is the simplest sensors for magnetic flux measurement with highfrequency range.
The magnetic flux sensors are used for TTF detection in transformers by measuring the leakage flux [32,33], and fluxlinkage [34][35][36][37] with high sensitivity. Besides, the air-gap and stray magnetic flux monitoring are enthusiastic methods in induction motors [38][39][40][41][42][43][44], which are used for stator TTF detection. Four different search coils mounted in various parts of induction motor have been introduced in Ref. [39] to measure the magnetic flux.
The MMF near the shorted turns has been decreased in the TTF case [45]. In the healthy case, the MMF is sinusoidal in space and time, but in faulty case, air-gap MMF is distorted as shown in Figure 3 [46].
The search coil can measure total harmonic distortion (THD) of the air-gap magnetic flux; the THD of the flux increases the fault in the stator winding; the saturation and loading conditions can be also taken into account. In addition, the fault location is identified using the ANN and wavelet transform [46].
Although the magnetic flux sensor is mostly inexpensive, reliable, and sensitive, its main drawback is practical limitations

F I G U R E 3
Magnetic field density distribution in a synchronous generator: (a) healthy condition, (b) inter-turn short circuit in stator winding [46] MOSTAFAEI AND FAIZ -395 during installation [46][47][48]. In fact, the stray flux sensors are non-invasive and inside/in the vicinity of the SG stator housing, but the stray flux is so small even in the faulty case and decreases the condition monitoring sensitivity.
In the large SGs, the stator winding fault is mostly severe, and the TTF is more probable in small ones. Therefore, conventional protection devices can detect the stator fault in a large SG without any problems, but the TTF in a small SG can be diagnosed by novel methods like air-gap flux or stray flux monitoring. Although the mentioned methods are sensitive and accurate, the current/voltage-based methods are more popular because they do not need additional sensors.

| Current/voltage signature
Current or voltage is the most common quantity for fault diagnosis, because they are accessible through a current transformer (CT), potential transformer (PT), or probes. Unlike the magnetic flux-based methods, the current/voltagebased ones do not need additional sensors, and they are more reliable. For the SGs with multi-branch winding, comparison of the different branches currents is common, which is known as differential TTF protection. In. this method, currents in different branches of stator winding are compared. In healthy condition, the difference of the currents is almost zero, but for TTF in the SG, the difference increases, and differential current circulates between the windings [49].
Another approach is the residual winding voltage applicable in all SGs. To measure the residual voltage, an additional open delta PT is used. In the healthy generator, phase voltage of the winding is almost the same, therefore, the sum of fundamental voltage harmonics in secondary is zero, while in the TTF, the faulty winding voltage drops, and the residual voltage is no longer zero. In this method, the sum of other harmonics such as third harmonics is non-zero, and all must be removed to prevent unwanted tripping [50]. In the abovementioned detection method, an additional PT is necessary, it may cause some installation problems, and in some cases, it is not economical. To solve this problem (required additional PT), a novel protection scheme shown in Figure 4 has been proposed which calculates zero-sequence voltage (ZSV) instead of measuring it [51]. In this method, the ZSV is calculated as follows.
where V ON is the ZSV and V AN , V BN and V CN are as follows:

<
: In faulty case ZSV ¼ 0, but due to the intrinsic asymmetry of the electrical machine, the ZSV is generally non-zero even in the healthy condition. Hence, a threshold should be considered. When the ZSV is higher than the threshold (k), a TTF has been occurred in the winding.
Time-harmonic of the stator current and rotor current can be used for stator winding fault detection. The interaction between the electrical quantities at the supply frequency and different space harmonics produce additional time-harmonic components in the stator and rotor currents [39]. The TTF of the stator winding produces some even harmonics in the rotor field current, which is noticeable to define a fault detection method. In this case, some even harmonics increase in the faulty case [52] and this validates the simulation results [53,54]. For instance, when the TTF occurs in the stator winding, the eighth-order harmonic is generated in the rotor of a 4-pole SG; however, it is noted that even harmonics are also produced in the unbalanced supply conditions in synchronous motors [55]. The third harmonic of the rotor current can be used for fault diagnosis, but it has no acceptable sensitivity. Therefore, by a search coil in the rotor and measuring its 90 Hz component (for fundamental frequency of 60 Hz) can significantly improve the protection without any correction factor [56].
In transient and steady state modes, for stator TTF in a brushless SG, the third harmonic of the positive sequence stator voltage is selected as an indicator [57]. Most stator TTF detection methods in induction motors can be extendedto the SGs, because of the similarity of the stator in both machines. Therefore, the extended Park's vector approach (EPVA) has been presented for the SGs and induction motors in Ref. [58], which uses the spectral analysis of the decomposed current by Park's transform.
The second harmonic in the EPVA spectrum is sensitive to the stator TTF and it is a good indication for fault diagnosis. However, the mentioned method of performance is ambitious in the unbalanced supply. Negative sequence impedance is also another indicator to detect the TTF in the stator winding of electrical machines. The proposed method has an appropriate performance against the TTF, but it is not so in minor faults and unbalanced supply [59,60]. A modified negative sequence impedance method uses a voltage mismatch detector to solve the mentioned problems [61]. Negative sequence voltage (NSV) can be also used for this purpose as introduced in the large SGs [62].
Recently, slope measurement for condition monitoring has become popular. The slope of a Lissajous curve has been used in Ref. [63] for short-circuit fault diagnosis in turbo-generators. In Figure 5, a turbo-generator with a short-circuit fault in phase has been connected to the power grid A. According to the figure, the fault current is written as follows:

-
where γ is the phase difference between V A_grid , V A_Gen and β is the phase difference between the healthy and faulty current.
The fault currents in three phases can be classified into two categories according to β. When β < 90°, the fault current is called class I and else is called class II. In this case, the current in the faulty phase (IF A ) has a reverse direction, and when β > 90°, it is the class II.
To determine the current class, the Lissajous curve is used for the phase difference between the two time-dependent signals. In this curve, two time-dependent signals are plotted versus each other. For two sinusoidal signals with amplitude A, their equations can be written as follows: Therefore, by solving (8): where x(t) is the current sample in a specific time and y(t) is the current sample in the previous cycle. Since the frequency change is negligible over a short time, by assuming ω x ¼ω y , (9) is simplified as follows: The slope of the Lissajous curve is an appropriate factor to determine the current class, where the positive slope means the class I and negative slope means the class II. The sign of Δx/ Δy determines the sign of the large axis slope of the ellipse in this curve.
To distinguish the internal fault from other disturbances and faults, the difference between the SG phase currents is estimated. In the internal fault, the difference between the phase currents of F I G U R E 4 Proposed protection scheme for TTF detection using zero-sequence voltage [51] F I G U R E 5 Schematic model of a generator with an internal fault in phase A MOSTAFAEI AND FAIZ -397 the two healthy phases is negligible, but the difference between the currents of the faulty phase and two healthy phases is large. If the difference of instantaneous current of phase A and phase B in the faulty case is ΔFAB and in healthy case, just in the previous cycle is ΔHAB, the ratio ΔFAB/ΔHAB can help to distinguish the internal fault from other disturbances and faults. Figure 6 shows the flow-chart of fault diagnosis methods which can detect the fault in different phases. Table 2 shows a brief review of the various SG winding fault detection methods.
Frequency response analysis (FRA) is another well-known technique in detecting the various defects such as winding short circuit, core deformation, and winding movement in power transformers and it is now a standard method. It uses the equivalent impedance for fault diagnosis in the frequency domain [64]. Figure 7 presents the equivalent scheme for the rotor winding.
A novel approach uses the FRA in a rotating machine, especially SGs with static excitation [65]. It is able to detect both ground fault and TTF. Moreover, FRA can be applied while the rotor is turning at full speed with no excitation. [65]. The disadvantages of the FRA are the difficulties in interpreting the results and unavailability of the healthy results for on-service machines.
Despite the transformer, the rotor winding of the SG (similar to the secondary winding of transformer) is rotational, and its position changes the FRA results. However, Figure 8 shows that the differences between the various rotor positions are negligible.

| ROTOR FAULTS
Owing to the rotor rotation, both mechanical and electrical faults can take place in the rotors. Detection of the electrical failure in the rotor, that is the SG short-circuit.
winding is quite different from the stator, because the DC current flows in the rotor winding and the faults cannot be detected by sinusoidal waveform-based approaches. To discriminate rotor electrical and mechanical faults, symmetrical component monitoring can be considered as an appropriate method [66]. In the proposed method, the current spectrum and voltage have been analysed to discriminate against the rotor faults. The results show that the rotor TTF increases the positive, negative, and zero sequences of the rotational frequency of the first right sideband, while the mechanical fault increases only the positive sequence of the rotational frequency [66]. Furthermore, vibration can be used to diagnose both winding and eccentricity faults.

| Rotor winding faults
The TTF in the rotor winding is caused by the insulation failure due to ageing, thermal, and mechanical stresses [67]. As a result of short-circuit turns, the total ampere-turn is reduced in the affected pole, and consequently, the air-gap magnetic flux density distribution becomes asymmetrical [68]. Magnetic flux and vibration are two major quantities, measured by sensors, which can be used for the rotor winding fault diagnosis. For this purpose, magnetic flux probes were used in the 1970s for the first time and developed up to now [69]. Some methods focus on the stray flux or leakage flux measured by stator wedge-mounted sensors; however, its magnitude is small and not recommended for condition monitoring [70,71]. A new flux probe introduced in Ref. [72] has been mounted on the stator core tooth to measure the main magnetic flux passing through the core tooth. These probes can be removed easier than the conventional flux probes [71].
A non-invasive method has been proposed in Refs. [73,74], which uses the external search coil to sense the stray magnetic flux in the SGs. Analysing both the stray flux and frame vibrations can detect the rotor TTF in SGs.
The search coil near the frame is firstly applied to induction motors for fault detection [75]. Similar search coil can be also used in the SGs. The frequencies in the magnetic flux spectrum and signal spectrum of vibration define the healthy and faulty SGs. In the faulty condition, the magnitude of some frequencies increases compared with the healthy case. It is noted that although there are amplitude changes every 25 Hz in the vibration spectrum, the most significant modification appears at low frequencies, especially at 225 Hz, but the healthy frequencies remain unchanged [73].
As shown in Figure 9, to diagnose the rotor-winding fault in turbo-and hydro-SGs, the flux probe is installed in the stator slot. The flux probe is sensitive to the of the air-gap radial flux change.

MOSTAFAEI AND FAIZ
As each rotor slot passes the flux probe, a difference in the induced voltage waveform in a search coil caused by magnetic poles is detectable. An inter-turn fault in a coil reduces the peaks associated with the two opposite slots containing the faulted coil, thus, the presence of shorted turns could be detected [76].
Discrete wavelet transform (DWT) is alternative way for the rotor winding fault detection, which provides a set of decomposed signals in independent frequency bands, including the independent dynamic information due to the orthogonality of wavelet function [77]. Herein, the. rotor current in cylindrical SG is used as DWT input, and the results show that the fifth detail level gives useful information about the rotor winding fault.

| Rotor eccentricity fault
Rotor eccentricity is a mechanical fault in rotational machines related to the rotor. Generally, the air gap is distributed homogeneously, but the rotor eccentricity is defined as asymmetric air-gap that exists between the stator and rotor [78]. Figure 10 shows the static eccentricities (SE) and dynamic eccentricity (DE) faults. In the case of the SE fault, the position of the minimal radial air-gap length is fixed in space. The TA B L E 2 Various SG stator and stator fault detection methods

Method
Advantages Disadvantages F I G U R E 9 Position of flux probe around stator tooth near air-gap [76] MOSTAFAEI AND FAIZ DE occurs when the centre of the rotor is not at the centre of the rotation, and the position of minimum air-gap rotates with the rotor [79]. These faults are critical for electrical machines and must be detected in the early stage. Different methods have been presented for the eccentricity fault detection in induction motors but less in SGs. Therefore, the detection methods for induction motors are presented firstly, and then some proposed approaches in SGs are discussed. The eccentricity fault can be detected in large induction motors using line current and motor frame vibration [80]. Besides, based on a new theoretical analysis [81] has presented to diagnose SE and DE faults simultaneously. Search coil installation in stator slots is another approach for detecting the SE fault [82], which is not practical because the sensors must be fixed in the machine during the manufacturing process [21].
The current harmonic analysis has been presented in Refs. [22,23] for eccentricity fault diagnosis. The volunteer harmonic components are the 17 th and 19 th . However, the mentioned harmonics depend on the structure and geometry of the SGs. Moreover, these harmonics are similar to power network harmonics [83]. Rotor current double-frequency ripple can be used for the SE fault detection [84], where the impact of the regulator has been ignored.
The mixed eccentricity (ME) fault may occur in electrical machines, where both symmetrical and rotor rotation axes are displaced with respect to the stator rotation axis. In fact, all stator, rotor, and rotational symmetrical axes are displaced with respect to each other [26]. The SE, DE, and ME faults in SGs are discussed in Ref. [26]. The ME fault diagnosis method has been also introduced for permanent magnet synchronous motors in Refs. [85,86].

| BROKEN DAMPER BARS FAULTS
Damper bars are used in large SGs. These bars are located axially into the pole face slots, and two ends are connected. At starting, the rotor speed and synchronous speed differ, and currents are induced in the damper bars and developed the torque, which called the asynchronous operation of the SG [78,87]. Damper bars in SG are used to counteract an asynchronous air-gap flux causing by electrical and mechanical transients [88,89]. Moreover, they are used in direct-online applications to bring the SG to synchronous speed [90]. In fact, the damper bars damp the transient power and torque oscillations. The rotor speed oscillates around the synchronous speed in transition, and this oscillation should be damped by the damper bars [91].
The damper bars in a steady-state mode are quite different from the fault condition. Hence, the damper bar fault detection methods in SGs is proposed here. The correlation of the broken bars fault in induction motors and the damper bars in SGs has been considered in Ref. [92].
Although the current and thermal stress are considered for designing the damper bars, failure is possible due to the deficient construction of damper cage [93] or frequent and hard duty cycle [94,95]. This kind of fault is not common in SGs, but it occurs in some SGs and leads to severe damages [94].
Due to the similarity of the damper bars and induction motors cage bars and the probability of the broken damper bars fault, proposing the novel detection methods were not enthusiastic for researchers, and a few methods has been presented for fault detection. An online diagnosis method for damper bars breakage presented in Ref. [94] uses a flux probe to measure the air-gap flux from starting to the rated speed. Another method for diagnosing the broken damper bars in Ref. [96] is the Hilbert-Huang Transform (HHT) based on Empirical Mode Decomposition (EMD) method reported in Refs. [97,98].
Temperature is a key parameter for broken damper bars fault detection, and temperature sensors are mounted on the rotor to measure the temperature rise during the fault. Resistance temperature detector (RTD) is one of the sensors used to sense the temperature [99]. Besides, the temperature sensors have been reported in Ref. [100]. Therefore, temperature monitoring can be an easy and economical method for broken damper bar fault detection, but some believe that the mounted RTD is an invasive method.

| OTHER WELL-KNOWN FAULT DETECTION METHODS
Some techniques such as artificial intelligence (AI) approach help to improve diagnosis methods and their sensitivities. The AI application in electrical machines and drives are proposed in Refs. [101,102] focusing on the stator winding fault diagnosis of induction motors [102].
In the AI-based systems, several quantities such as stator currents and voltages, magnetic fluxes, and frame vibration are utilised as input signals [39]. Generally, an expert system, an artificial neural network (ANN), a fuzzy neural network [103], and their combinations are the well-known methods in AI. ANN has been widely studied during the last 2 decades and successfully applied to dynamic system modelling [104,105] as well as fault diagnosis [106][107][108][109][110].
Vibration monitoring has a long history in condition monitoring and used in various electrical equipment. Vibration is used in Ref. [111] for stator winding fault in.
induction motors. For SGs, the vibration is employed for various mechanical faults detection [112], especially bearing F I G U R E 1 0 Various kinds of eccentricity in electrical machines 400fault [113]. Generally, vibration monitoring is an expensive method because it requires some costly vibration sensors [113].
Recently, many have focused on thermal condition monitoring using infrared thermography. This apparatus identifies temperatures and hotspots of different locations. Thermography is used in induction motors [114] and SGs [115] for condition monitoring. The high cost of an infrared device is the main disadvantage of the thermal monitoring methods.
The above-mentioned methods can be combined to present a comprehensive approach which has the advantages of the both for fault diagnosis. One of these methods uses air-gap flux, stray flux, and vibration to detect the rotor-winding fault in hydro-generator precisely [116].
There are two key advantages of the presented algorithm for realising the monitoring system. The first advantage is the integration of the two methods for the measurement of magnetic flux. The applied measuring procedure includes a comparative analysis of the results of magnetic flux measurements with the results obtained by the system for measuring mechanical vibrations to approach the fault detection comprehensively. The second advantage is the mobility of the monitoring system and its application without interrupting the generators operation (the case when the leakage stator flux is measured or when the system is connected with the previously built-in sensors in the air gap of the generator) [115].
Capacitive sensors are installed on the surface of the stator [117], while the inductive sensors are fixed in the ventilation ducts of the stator [48]. Figure 11 shows the proposed algorithm, which can detect the rotor-winding fault of hydrogenerator. As shown, mounted sensors must measure the airgap and stray flux firstly, and then the signal processing method is applied to determine the THD of stray flux. Any change in magnetic flux may be the sign of a fault in the SG. Therefore, vibration measurement can complete the fault detection process. The unbalanced magnetic flux and increased vibration show the rotor-winding fault, and the SG must be shut down immediately. Table 3 presents appropriate comparisons between the measurement methods.

| CONCLUSION
The current-and voltage-based methods are generally more useful than the flux based ones, because these parameters can be measured as easy as possible by instrumental transformers. For this purpose, analysing harmonics in various conditions and using signal-processing techniques such as Wavelet and Fourier transform. Nowadays, vibration analysis is used for various fault detection in electrical machine and this processed vibration data can present much information about the SG condition especially under mechanical faults. Apart from the mentioned parameters, frequency spectrum of SG offers invaluable data about condition monitoring. In transformers, frequency based methods are popular and it can be used in SGs.
All proposed methods can be combined by AI techniques (as a hybrid method) to increase their sensitivities. Moreover, AI can help the researchers to reduce the errors and prevent some catastrophic problems that can be occurred because of CT, VT or other sensors mal-operation.