SYSTEM AND METHOD FOR LOCATING TURN FAULTS IN AN ELECTRICAL MACHINE

BACKGROUND

[0001] The disclosure relates generally to electrical machines and more particularly, to a system and method for locating turn faults in a stator winding of an electrical machine, for example an induction motor.

[0002] Machines such as induction motors, generators, and transformers are used in a wide array of applications and processes. For example, the induction motor typically includes a stator, and a rotor. In a typical 3-phase induction motor, power is supplied to the stator to induce a magnetic field, causing the rotor to rotate and generate mechanical energy. The stator may include any number of "windings" or "wound poles" that transmit the current required to induce the magnetic field. These windings may also be characterized by the "turns" in the windings.

[0003] The stator windings may include a number of coils provided to a plurality of phases of the induction motor, depending on requirement of an electrical application or process. In certain environments, the coils in the stator windings are more susceptible to "shorts" between the turns of the coils, commonly referred to as "turn fault". In large induction motors, once the turn fault is detected, the turn fault is usually located by manual inspection of the motor or using on-line techniques. The manual inspection method of locating turn faults takes considerable effort and time. Similarly, the conventional on-line turn fault techniques for identification and location of turn fault, typically requires complex flux sensors disposed at different locations in the winding structure. These conventional techniques tend to be tedious or complex resulting in undesirable downtime to the electrical application or process when the motor is taken offline for repair.

[0004] Thus, there is a need for an improved system and method for efficiently locating the turn fault in the electrical machine.

BRIEF DESCRIPTION

[0005] In accordance with one embodiment, a computer-implemented method is disclosed. The method includes determining a plurality of symmetrical components based on a plurality of measured phasor currents and phasor voltages of an electrical machine. The method further includes determining a negative sequence impedance of the electrical machine based on a plurality of parameters of the electrical machine. Further, the method includes generating a look-up table based on the determined negative sequence impedance and a structure of a stator winding in the electrical machine. The look-up table includes data including classification of phases, number of coil groups of the stator winding in each phase, classification of each coil group, and range of location angle of each coil group in the electrical machine. Further, the method includes determining normalized cross-coupled impedance based on the determined plurality of symmetrical components and the negative sequence impedance. The method further includes detecting a turn fault in the stator winding by comparing a magnitude of the determined normalized cross-coupled impedance to a predefined threshold value. Further, the method includes locating a coil group having the turn fault from the classified coil groups in the corresponding phase by using the look-up table and correlating an angle of the determined normalized cross-coupled impedance to the range of location angle of the coil group having the turn fault.

[0006] In accordance with another embodiment, a system is disclosed. The system includes at least one processor-based device having computer instructions. The computer instructions instruct the at least one processor-based device to determine a plurality of symmetrical components based on a plurality of measured phasor currents and phasor voltages of an electrical machine. Further, the computer instructions instruct the at least one processor-based device to determine a negative sequence impedance of the electrical machine based on a plurality of parameters of the electrical machine. The computer instructions instruct the at least one processor-based device to generate a look¬up table based on the determined negative sequence impedance and a structure of a stator winding in the electrical machine. The look-up table includes data including classification of phases, number of coil groups of the stator winding in each phase, classification of each coil group, and range of location angle of each coil group in the electrical machine. Further, the computer instructions instruct the at least one processor-
based device to determine a normalized cross-coupled impedance based on the determined plurality of symmetrical components and the negative sequence impedance. The computer instructions instruct the at least one processor-based device to detect a turn fault in the stator winding by comparing a magnitude of the determined normalized cross-coupled impedance to a predefined threshold value. Further, the computer instructions instruct the at least one processor-based device to locate a coil group having the turn fault from the classified coil groups in the corresponding phase by using the look-up table and correlating an angle of the determined normalized cross-coupled impedance to the range of location angle of the coil group having the turn fault.

[0007] In accordance with yet another embodiment, a non-transitory computer readable medium encoded with a program for enabling a processor-based device is disclosed. The program enables the processor-based device to determine a plurality of symmetrical components based on a plurality of measured phasor currents and phasor voltages of an electrical machine. Further, the program enables the processor-based device to determine a negative sequence impedance of the electrical machine based on a plurality of parameters of the electrical machine. The program enables the processor-based device to generate a look-up table based on the determined negative sequence impedance and a structure of a stator winding in the electrical machine. The look-up table includes data including classification of phases, number of coil groups of the stator winding in each phase, classification of each coil group, and range of location angle of each coil group in the electrical machine. Further, the program enables the processor-based device to determine normalized cross-coupled impedance based on the determined plurality of symmetrical components and the negative sequence impedance. The program enables the processor-based device to detect a turn fault in the stator winding by comparing a magnitude of the determined normalized cross-coupled impedance to a predefined threshold value. Further, the program enables the processor-based device to locate a coil group having the turn fault from the classified coil groups in the corresponding phase by using the look-up table and correlating an angle of the determined normalized cross-coupled impedance to the range of location angle of the coil group having the turn fault.

[0008] In accordance with yet another embodiment, an electrical machine is disclosed. The electrical machine includes a stator having a core and a winding wound on the core. The electrical machine further includes a rotor disposed proximate to the stator. Further, the electrical machine includes a sensing device configured to sense a phasor current and a phasor voltage applied to the winding. The electrical machine further includes a processor-based device communicatively coupled to the sensing device to receive a plurality of output signals from the sensing device. The processor-based device is further configured to determine a plurality of symmetrical components based on a plurality of measured phasor currents and phasor voltages of an electrical machine. Further, the processor-based device is configured to determine a negative sequence impedance of the electrical machine based on a plurality of parameters of the electrical machine. The processor-based device is configured to generate a look-up table based on the determined negative sequence impedance and a structure of a stator winding in the electrical machine. The look-up table includes data including classification of phases, number of coil groups of the stator winding in each phase, classification of each coil group, and range of location angle of each coil group in the electrical machine. Further, the processor-based device is configured to determine normalized cross-coupled impedance based on the determined plurality of symmetrical components and the negative sequence impedance. The processor based device is further configured to detect a turn fault in the stator winding by comparing a magnitude of the determined normalized cross-coupled impedance to a predefined threshold value. The processor-based device is configured to locate a coil group having the turn fault from the classified coil groups in the corresponding phase by using the look-up table and correlating an angle.

DRAWINGS
[0009] These and other features, aspects, and advantages of the present invention will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein:

[0010] FIG. 1 is an exploded perspective illustration of an induction motor;

[0011] FIG 2 illustrates a diagrammatical representation of a structure of a stator winding in a poly-phase arrangement of an induction motor in accordance with one embodiment;

[0012] FIG 3 is a look-up table depicting relationship between angle of normalized cross-coupled impedance, range of location angle of each phase, and range of location angle of each coil group, of the induction motor in accordance with an embodiment;

[0013] FIG 4 is a table illustrating classification of each coil group having one or more coils of the induction motor in accordance with an embodiment;

[0014] FIG. 5 is a block diagram of a system that includes the induction motor of FIG. 1 in accordance with an embodiment;

[0015] FIG. 6 is a graph depicting the relationship between magnitude of normalized cross-coupled impedance and a predefined threshold value, for detecting the turn fault in accordance with an embodiment;

[0016] FIG. 7 is a graph depicting the relationship between an angle of normalized cross-coupled impedance and a range of location angle of the coil group, for locating the turn fault in accordance with an embodiment;

[0017] FIG. 8 illustrates a flow chart showing a method for locating a coil group having a turn fault in accordance with an embodiment; and

[0018] FIG 9 illustrates a look-up table for locating a coil group having a turn fault in accordance with one specific embodiment.

DETAILED DESCRIPTION
[0019] While only certain features of the invention have been illustrated and described herein, many modifications and changes will occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the invention.

[0020] Embodiments herein disclose a method for locating a turn fault in an electrical machine. The electrical machine may include a generator, a motor, a transformer, and the like. The generator may be an alternating current (herein also referred as "AC") generator. Similarly, the motor may be AC motor, and more particularly may be an AC induction motor. In a specific embodiment, although an induction motor is disclosed to describe the inventive techniques, it should not be construed as a limitation of the present system and techniques. In one embodiment, the method includes the process of generating a look-up table based on a negative sequence impedance, and a structure of a stator winding in the induction motor. The method further includes determining a normalized cross-coupled impedance of the induction motor. Further, the method includes detecting the turn fault based on a magnitude of the normalized cross-coupled impedance. The method further includes locating a coil group having the turn fault by correlating an angle of the noramlized cross-coupled impedance to a range of location angle of each coil group, in the look-up table.

[0021] More specifically, certain embodiments of the present system disclose the look-up table and different forms of the look-up table generated for various configurations of the induction motor, for example, for locating the coil group having the turn fault based on the angle of the normalized cross-coupled impedance. In such an embodiment, the look-up table has data including parameters such as number of phases, classification of phases, range of location angle of each phase, number of coil groups of the winding in each phase, classification of each coil group, and range of location angle of each coil group in the induction motor.

[0022] FIG. 1 is a perspective illustration of an induction motor 100. It should be noted herein that the illustration provided in FIG. 1 is for descriptive purposes only, and embodiments of the present system are not limited to any specific induction motor or configuration thereof. In other words, the embodiments are applicable to any type of electrical machine including generators. In the illustrated embodiment, the induction motor 100 includes a rotor assembly 102, a stator assembly 106, and a bearing assembly 108. The rotor assembly 102 includes a rotor shaft 104 extending through a rotor core 112. The rotor assembly 102 is rotatable inside the stator assembly 106. The bearing assembly 108 that encircles the rotor shaft 104 may facilitate such rotation within the stator assembly 106. The stator assembly 106 includes a plurality of stator windings 200 and a stator core 110. The stator windings 200 extend circumferentially around and axially along the rotor shaft 104.

[0023] During operation, a rotating magnetic field induced in the stator windings 200 reacts with the induced current in the rotor assembly 102 to cause the rotor assembly 102 to rotate, thereby converting electrical energy to mechanical energy through the rotor shaft 104. In some embodiments, the motor 100 is a synchronous motor, and in some other embodiments, the motor 100 is an asynchronous motor. The synchronous motors rotate at the same frequency as the power supply source, while asynchronous motors rotate at a frequency lower than the frequency of the power supply source.

[0024] The stator windings 200 may be any suitable conducting material, such as copper wire, and may include insulation between the windings 200 and other parts of the stator assembly 106. The windings 200 may be susceptible to chemical, mechanical, or electrical degradation that affects the performance of the stator assembly 106, which in turn affects the rotor assembly 102 and the functioning and efficiency of the motor 100. Any manufacturing defects may also cause poor performance of the windings 200. The turn faults in the windings 200 may interfere with current flow and the magnetic field induced in the stator assembly 106. Though the operation of the motor 100 is explained with a simple diagram, examples of the motor 100 are not limited to this particular simple design. Other suitable designs are also applicable and may benefit from the techniques discussed in detail below.

[0025] FIG 2 represents an example of the stator winding 200 in a poly-phase arrangement of the induction motor 100 in accordance with one embodiment of the present system. The structure of the stator winding 200 includes a number of poles, a number of phases, a number of coils, a type of stator winding, and a number of slots in the induction motor 100. In the illustrated embodiment, the stator winding 200 is a double layered winding having an outer layer 234 and an inner layer 236. Each coil of the induction motor 100 has a supply end and a return end. In the illustrated embodiment, the supply ends 210, 212, 214, 216, 218, 220, 222, 224, 226, 228, 230, 232 of the coils 211, 213, 215, 217, 219, 221, 223, 225, 227, 229, 231, 233 are located within the outer layer 234 of the stator winding 200, and the return ends 210', 212', 214', 216', 218', 220', 222', 224', 226', 228', 230', 232' of the coils 211, 213, 215, 217, 219, 221, 223, 225, 227, 229, 231, 233 are located in the inner layer 236 of the stator winding 200.

[0026] In this embodiment, the induction motor 100 has three phases and is classified as "R", "Y", and "B". In the illustrated embodiment, the induction motor 100 has four poles at phase-R represented by reference numerals 202, 204, 206, 208. In each phase, two poles are paired and perpendicular to each other i.e. placed orthogonal at approximately 90 degrees to each other. In the illustrated embodiment, the phase of the pole 202 that has been paired with the pole 204 in the phase-R, is represented as R'. Similarly, the phases of the poles that has been paired with the poles in the phase-Y and phase-B, are represented as Y' and B'. In this example, there are twelve coils 211,213, 215, 217, 219, 221, 223, 225, 227, 229, 231, 233 in each phase, where three coils are disposed at each pole of the stator winding 200. In the illustrated embodiment, the supply ends 210, 212, 214 are provided at the pole 202 of phase-R, and the supply ends 216, 218, 220 are provided at the pole 204 of phase-R'. Similarly, the return ends 228', 230', 232' are provided to the pole 202 of phase-R, and the return ends 210', 212', 214' are provided to the pole 204 of phase-R'. In this example, the coil 211 wounds from the supply end 210 at pole 202 in phase-R to the return end 210' at pole 204, in phase-R'. Similarly, the other coils 213, 215 wounds around from the supply ends 212, 214 at pole 202 in phase-R to the return ends 212', 214' at pole 204 in phase-R'. For the simplicity of the illustration, the coils 217, 219, 221, 223, 225, 227, 229, 231, 233 belonging to the phase-R are not illustrated and should not be construed as limitation of the invention.

[0027] In this example, the phases-Y and phases-B also have coils, supply ends and return ends of the coils as discussed herein. The coils, supply ends, and return ends in the phases-Y and phases-B are not illustrated in FIG. 2, to keep the description of the structure of the stator winding 200 simple, and should not be considered as a limitation of the stator winding 200. Additionally, for the phases "Y" and "B", the coils, supply ends and the return ends of the coils may be numbered with same referral numerals used for explaining the coils, supply ends and return ends of the coils in the phase-R.

[0028] The induction motor 100 may have three types of slots, which may be classified as open slots, semi-closed slots, and tapered slots. The slots 238, 240, 242, 244 are typically open ended slots provided both on the stator core 110 and the rotor core 112 (refer to FIG 1), and may be made of a laminated compressed sheet steel. The slots 238, 240, 242, 244 may be laminated to reduce Eddy current and Hysteresis losses. The number of slots 238, 240, 242, 244 may be varied based on the design of the induction motor 100 and also based on operating characteristics of the induction motor 100. Generally, the slots 238, 240, 242, 244 provide mechanical support as the coil pass through the slots 238, 240, 242, 244. The number of slots 238, 240, 242, 244 may also depend on the number of poles in the induction motor 100. In the illustrated embodiment, there are thirty six slots.

[0029] FIG 3 is a look-up table 300 generated based on negative sequence impedance (herein also referred as " Znn"), and the structure of the stator winding 200 discussed herein with reference to FIG 2. The determination of the negative sequence impedance Znn based on a plurality of parameters of the induction motor is explained below with reference to subsequent figures. Similarly, the determination of the normalized cross-coupled impedance based on a plurality of symmetrical components and the negative sequence impedance Znn is explained below with reference to subsequent figures. The look-up table 300 illustrates the relationship between an angle 302 of the normalized cross-coupled impedance, range of location angle 304, 306, 308 of each phase and range of location angle 310, 312, 314, 316, 318, 320, 322, 324, 326, of each coil group, of the induction motor in accordance with an embodiment of the present system. The data representative of the structure of the stator winding 200 of the induction motor, includes features such as number of poles, the number of phases, number of slots, number of coils, and coil type of the stator winding. The angle 302 of the normalized cross-coupled impedance is determined based on a plurality of symmetrical components and the negative sequence impedance Znn.

[0030] The symmetrical components are determined based on a plurality of measured phasor currents and phasor voltages of the motor. The plurality of symmetrical components typically includes a positive sequence voltage, a negative sequence voltage, a positive sequence current, and a negative sequence current. The determined normalized cross-coupled impedance includes a complex number component
represented by and an angle component represented by tan" {y/ x), where "y " is an imaginary component of the complex number and "x" is a real component of the complex number. The range of location angle 304, 306, 308 of each phase are determined based on the structure of the stator winding 200 and the negative sequence impedance Znn. In this embodiment, the range of location angle of phase-R is Znn +35 to Znn-35, where (+) 35, (-85) denotes degrees and Znn denotes negative sequence impedance, more particularly angle of the negative sequence impedance.

[0031 ] For example, if the negative sequence impedance Znn is 20 degrees, then the range of location angle for phase-R is (+)55 degrees to (-)65 degrees. Similarly, for phase-Y, the range of location angle is (+)175 degrees to (+)55 degrees, and for phase-B, the range of location angle is (+)295 degrees to (—)175 degrees.

[0032] In this embodiment, the coil groups are classified as "X", "Y" and "Z", and the coil groups "X", "Y", "Z" are classified accordingly for each phase "R", "Y", "B". The range of location angle 310 of "coil group-X" of phase-R is Z„„+35 to Znn - 5. The values discussed herein are in accordance with the illustrated look-up table 300. For example, if the negative sequence impedance Znn is 20 degrees, then the range of location angle 310 for coil group-X in phase-R, is 55 degrees to 15 degrees. Similarly, for phase-R, the location angle 312 for the "coil group-Y" is (+)15 degrees to (-)25 degrees, and the location angle 314 for "coil group-Z" is (-)25 degrees to (-)65 degrees. In other embodiments, the look-up 300 table may vary depending on the structure of the stator winding. In another embodiment, the machine may include more than four coil groups. Similarly, the number of coils in each group may vary depending on the number of poles in the induction motor.

[0033] In one example, the process used for generating the look-up table 300 is described. A standard "steady state model" may be coded in a computer to create a simulation model. The created simulation model may be executed in the computer, for "N" number of application by using one or more parameters corresponding to different types of machines. The one or more parameters used for executing the simulation model may include Rs i.e. a stator resistance, Lj.e. is an inductance of the stator winding,
M i.e. is a mutual inductance between the stator and the rotor, and the structure of the stator winding. The structure of the stator winding may include the number of poles, the number of phases, the number of slots, the number of coils, and type of the stator winding. .The "N" number of applications may relate to different type of machines simulated to have certain percentage of turn faults at one or more locations of the coil groups. The output from the simulation model may be the normalized cross-coupled impedance for "N" number of machines. The location of the fault for "N" number of cases are associated with an angle of the normalized cross-coupled impedance to generate a range of location angle for each phase and a range of location angle for each coil group.

[0034] In another embodiment, the process used for generating the look-up table 300 may include using a finite element analysis model. The created finite element analysis model may be executed in the computer, for "N" number of applications by using one or more parameters corresponding to the different types of machines. The one or parameters used for executing the FE model, may include geometry, and composition of the stator and rotor. In one specific embodiment of the present invention, equations used in the steady state model for coding in the computer to create the simulation model are provided below:

where, coe is supply angular frequency of the electrical machine, V, V are positive and negative phasor voltages of the stator winding, I, I are positive and negative phasor currents of the stator winding, If fault in current phasor, s is rotor slip, Rs is stator resistance, Rr is rotor resistance, β is percentage of turn faults, Lr is inductance of the rotor winding, is a complex operator, M is mutual inductance between the stator and the rotor, Ls is inductance of the stator winding, Lh is the stator leakage inductance, Llr is the rotor leakage inductance, Lm is the magnetizing inductance, / is a positive sequence current of the rotor, I is a negative sequence current of the rotor, I is a negative sequence current of the stator, I is a positive sequence current of the stator, L f is a quadrature-axis mutual inductance between faulted coil and other phases of the stator, Lfcj is a direct-axis mutual inductance between faulted coil and other phases of the stator, Lqrf is a quadrature-axis mutual inductance between faulted coil and other phases of the rotor, Ldrf is a direct-axis mutual inductance between faulted coil and other phases of the rotor, Lff is a self-inductance of the faulted coil, A and B are Fourier co¬efficient constants of winding function, Nx is a total number of turns in the electrical machine.

[0035] The A and B Fourier co-efficient constants may be mapped to Am,Bm values based on the stator winding function approach.

where Am .and Bm are constants of fault related inductances in the stator windings.

[0036] Based on the constants Am .and Bm, the location of the turn fault in the stator windings may be expressed as explained below:

where S is width of the slots, which in one embodiment, may be — for the stator windings and j3 is percentage of turn faults.

[0037] The expression of the constants Am .and Bm for each fault locations are derived using the following equations:

where Nasl( is an angular position of the winding.

[0038] In this specific embodiment, based on the steady state model, and the stator winding function approach, explained from equations (1) to (21), the simulation model may be executed in the computer to determine the angle of the normalized cross-coupled impedance for various electrical machines as explained below:

[0039] The Am .and Bm constants of fault related inductances in the stator windings are determined using the expression as described in above table for fault location-1, for example. The Am .and Bm values are used for determining Lqsf ,Ldsf,Lqsf,and,Ldlf as described in equations (6) to (9). The Lqs f ,Ldsf ,L qsf ,and,Ldrf values and the parameters of the stator winding structure are
used to calculate the positive and negative sequence components i.e. of voltage and current for the electrical machine, as described in equations (1) to (5). The determined positive and negative sequence components may be used to determine the normalized cross-coupled impedance. The determination of the normalized cross-coupled impedance is explained below with reference to subsequent figures.

[0040] In this specific embodiment, once the normalized cross-coupled impedance is determined for "N" number of machines, the angle of the normalized cross-coupled impedance is associated to generate the look-up table 300.

[0041] FIG. 4 is a table 400 representative of classification of each coil group having one or more coils, in the induction motor in accordance with an embodiment of the present system. In this example, the coil groups are classified as "X", "Y", "Z". The number of coil group in the stator winding is determined based on factors such as the number of coils, number of phases, and number of poles in the induction motor. In the illustrated embodiment of FIG. 2, there are thirty six coils, thirty six slots, four poles, and three phases. The number of coil groups is determined based on the number of coils in each phase per number of poles i.e. (36/3)/4 = 3. Each coil group may have one or more coils. In the illustrated embodiment, "coil group-X" includes the coils 210, 216, 222, 228, "coil group-Y" includes coils 212, 218, 224, 230, and "coil group-Z" includes coils 214, 220, 226, 232. The coil numbers denote the particular coils in the group (Refer to FIG. 2). In this example, the number of coils in each coil group is determined based on the number of poles in the induction motor.

[0042] FIG. 5 is a block diagram of a system 500 that includes the induction motor 100 in accordance with an exemplary embodiment of the present system. The induction motor 100 may be coupled to a three-phase power supply source 502, for example, an AC power supply source. The power supply source 502 delivers three-phase AC power 504 to the induction motor 100. The system 500 includes a processor-based device 506, such as a relay, meter, or any other suitable device, having computer instructions for monitoring and controlling operation of the motor 100. The processor-based device 506 may include components such as at least one processor 508, a memory 510, and the like. The memory 510 may be a volatile memory, non-volatile memory, or combination thereof. The memory 510 may store any parameters, algorithms, or instructions, or other data for controlling and monitoring the motor 100, and permit access to the stored data.

[0043] In the illustrated embodiment, a plurality of sensors 512 are used to detect a three-phase current of the motor 100 and outputs signals 516 representative of phasor currents to the processor-based device 506. A plurality of sensors 514 are used to detect three-phase voltage of the motor 100 and outputs signal 518 representative of the phasor voltages to the processor-based device 506. The system 500 may include various signal processing components such as signal conditioners, amplifiers, filters, and the like in the processor-based device 506 or these components may be disposed between the motor 100 and the processor-based device 506. The system 500 may also include a switch 520 to turn the motor 100 on and off. The processor-based device 506 in one example shuts down the motor 100 via the switch 520, based on a detection of a turn fault in a coil of the stator winding of the motor 100. In the illustrated embodiment, the processor-based device 506 also includes a graphical user interface 522 to display, for example, a stator coil group having the turn fault. In another embodiment, the processor-based device 506 may include an alerting means, such as a visual and/or audio display capability to locate the stator coil group having the turn fault and indicate or communicate the stator coil group for servicing.

[0044] In one embodiment, the processor-based device 506 is used to obtain the symmetrical components based on a plurality of measured phasor currents Ia,Ib,Ic, and phasor voltages Va,Vb,Vc of the motor 100. The plurality of symmetrical components includes a positive sequence voltage V , a negative sequence voltage Vn, a positive sequence current Ip, and a negative sequence current In .

[0045] The relationship between the voltages, currents, and impedances of a three-phase winding is represented by:

Va,Vb, and Vc are the voltages for phases a, b, and c;
Ia, Ib, and Ic are the currents for phases a, b, and c;
Zaa, Zbb, and Zcc are the impedance for phases a, b, and c, and
Zab,Zba,Zac,Zca,Zbc and Zbc are the mutual impedances between phases a, and b, phases a, and c, and phases b and c.

[0046] Applying symmetrical component theory to Equations (22), (23), (24), the relationship between symmetrical components of voltages, currents, and impedances, is represented by:

where Vp is the positive sequence voltage, Vn is the negative sequence voltage, Ip is the positive sequence current, In is the negative sequence voltage, Zpp is the positive sequence impedance, Znn is the negative sequence impedance, Znp is the negative-to-positive differential impedance, Zpn is the positive-to-negative differential impedance.

[0047] For an ideal induction motor, the off-diagonal elements of Equation (25) are zero, signifying decoupled positive and negative sequence components of the motor 100. Based on Equation (25), the negative sequence voltage may be determined as follows:

[0048] The negative sequence impedance Znn may be determined using various techniques. In some embodiments, the negative sequence impedance Znn may be determined using any one of, or a combination of, the following techniques: 1) computation using machine parameters; 2) measurement of the negative sequence impedance Znn directly by deliberate creation of unbalance; 3) heuristic determination of the negative sequence impedance of the parameters of the motor 100.

[0049] In one embodiment, the heuristic determination involves a regression analysis to determine the relationship between the negative sequence impedance Znn and the parameters of the motor 100. In one such embodiment, Znn is determined as a standstill impedance having a relationship that may be expressed as follows:

where HP is the rated horsepower of the motor 100, Pole is the number of poles of the motor 100, Voltage is the line-to-line voltage of the motor 100, frequency is the frequency of the motor 100, /is the function of transformation, and size is the size of the motor 100.

[0050] In one embodiment, the regression analysis may be divided into a first analysis for low HP machines (less or equal to 500HP) and a second analysis for high HP machines (greater than 500HP). In such an embodiment, the negative sequence impedance Znn may be expressed as a non-linear higher order function of the parameters mentioned above. For example, the magnitude of Znn may be expressed as follows:

where A, B, C, D, E, F, G, H, I, and J are constants determined by the regression analysis; HP is the rated horsepower of the motor; VLL is the line-to-line voltage of the motor, and P is the number of poles.

[0051 ] Similarly, the phase of Znn may be determined as follows:

where Au Bh Ct, D,, E,, Ft, Gi, Hi, I,, and J/ are constants determined by the regression analysis.

[0052] Using the Equations (27) and (28), the negative sequence impedance Znn
may be determined for the induction motor 100. The negative sequence impedance Znn and the symmetrical components are used in the determination of the normalized cross-coupled impedances as discussed below.

[0053] Based on Equation (26), a normalized cross-coupled impedance with respect to the negative sequence impedance Znn may be determined as follows:

where Znp I Zpp is the normalized cross-coupled impedance with respect to positive sequence impedance.

[0054] It should be noted herein that the determined normalized cross-coupled impedance is a complex number. A magnitude of the normalized cross-coupled impedance is determined by, wherein "x" is a real component of the complex number, and "y" is an imaginary component of the complex number.
Similarly, an angle of the normalized cross-coupled impedance is represented by tan" (y/x), wherein "y" is the imaginary component of the complex number and "x" is the real component of the complex number.

[0055] The normalized cross-coupled impedance with respect to the positive sequence impedance Zpp may be used, in addition to the normalized cross-coupled impedance, with respect to the negative sequence impedance Znn, to further enhance detection of a turn fault in a coil group-X, Y, Z of the stator winding.

[0056] FIG. 6 shows a graph 600 illustrating the relationship between magnitude of the normalized cross-coupled impedance Znp IZpp (with respect to positive sequence impedance Zpp) and the number of turn faults of a stator winding. The y-axis of the graph 600 is represented by magnitude of the normalized cross-coupled impedance Znp I Zpp, and the x-axis is represented by the number of turn faults. A first point 602 corresponds to Znp I Zpp of about 0.02 (i.e. a predefined threshold value) and
indicates a "healthy" motor, e.g., a motor that does not have any turn faults. A second point 604 corresponds to a normalized cross-coupled impedance ZnpIZpp of about 0.025, indicating the presence of about one turn fault. A third point 606 corresponds to a normalized cross-coupled impedance Znp I Zpp of about 0.045, indicating the likely presence of about two turn faults. As illustrated in the graph 600, an increase in the normalized cross-coupled impedance Znp I Zpp from the "healthy" value at the first point 604 corresponds to an increase in the number of turn faults of the induction motor 100. By comparing the magnitude of the normalized cross-coupled impedance Znp I Zpp to these correlated values, an indication of the number and/or severity of turn faults may be determined. The predefined threshold value is determined based on experimental results and name plate data of the electrical machine. In some embodiments, the name plate data of the electrical machine includes a rated power of the machine, a rated voltage of the machine, a number of poles and a frequency of the machine. In one embodiment, the predefined threshold value is in the range of 0.01 to 0.07, wherein the predefined threshold value up to 0.02 indicates healthy condition of the machine, wherein the predefined threshold value up to 0.025 indicates presence of one turn fault, wherein the predefined threshold value up to 0.045 indicates presence of two turn faults, and 0.07 indicates presence of three turn faults.

[0057] FIG. 7 is a graph 700 depicting the relationship between an angle of the normalized cross-coupled impedance Z / Zpp and a range of location angle of the coil group-X, Y, Z, for locating the turn fault in accordance with embodiment of FIG. 2. The y-axis of the graph 700 is represented by the angle of the normalized cross-coupled impedance Znp I Zpp, and the x-axis is represented by the magnitude of the normalized cross-coupled impedance Znp IZ or slip that may exist in the induction motor 100.
The angle of the normalized cross-coupled impedance Znp I Zpp is used for locating the
turn fault in the coil groups X, Y, Z. In the illustrated embodiment, for example, when the angle of the normalized cross-coupled is at (-)100, the location of the turn fault is in phase-R, the range of location angle of phase-R is (-)200 degrees to (-)120 degrees, the range of location angle of coil group-X is (-)80 degrees to (-)120 degrees. The coil group-X representing the coils 210, 216, 222, 228 may have the turn fault.

[0058] FIG. 8 depicts a flow chart illustrating a method 800 for locating a coil group having a turn fault in accordance with an embodiment of the present invention. According to one embodiment, a processor-based device is used for determining a turn fault in the machine and subsequently location of the coil group having the turn fault. The phasor voltages Va,Vb, and Vc and the phasor currents Ia,Ib, and Ic of a machine are acquired via a plurality of sensors as represented by reference numeral 802. Symmetrical components are obtained based on the plurality of measured phasor currentsIa,Ib,Ic, and phasor voltages Va,Vb,Vc of the machine as represented by the reference numeral 804. The plurality of symmetrical components includes a positive sequence voltage Vp, a negative sequence voltage Vn, a positive sequence current / , and a negative sequence current/„ . A symmetrical sequence transformation may be used to convert phasor voltages and phasor currents from the three phases to a positive, a negative and a zero sequence components. A negative sequence impedance Znn may be determined via one of the three techniques discussed herein (computation using machine parameters, direct measurement of the negative sequence impedance Znn, or regression analysis of the negative sequence impedance Z„„) as represented by the reference numeral 806. The method 800 includes checking whether a look-up table is already generated for the machine's stator pattern and parameters, as represented by reference
numeral 807. If the look-up table is not generated then the method 800 includes generating the look-up table based on a data representative of a structure of the stator winding and the determined negative sequence impedance Znn as represented by the reference numeral 808. The normalized cross-coupled impedance with respect to the negative sequence impedance and/or the positive sequence impedance may be determined as represented by the reference numeral 810. If it is determined in step 807, the look-up table is already generated the normalized cross-coupled impedance with respect to the negative sequence impedance and/or the positive sequence impedance may be determined as represented by the reference numeral 810. A magnitude and an angle of the normalized cross-coupled impedance may be determined, as explained with reference to FIG. 4.

[0059] The magnitude of the normalized cross-coupled impedance (with respect to positive impedance) Znp I Zpp is compared to a predefined threshold value as represented by the reference numeral 812. If the magnitude of the normalized cross-coupled impedanceZnp I Zpp is below the predefined threshold value, the method 800 is repeated. If the magnitude of the normalized cross-coupled impedance Znp I Zpp is above the predefined threshold value, then a turn fault is detected and in such a scenario, a processing-device may declare the turn fault condition in the induction motor, as represented by the reference numeral 814. There are a number of other embodiments if there is a detected fault condition. For example, there may be an alert for maintenance or service without a trip condition based on the measured values and the thresholds. Prognostic determinations related to remaining useful life may allow for predicting that a turn fault is growing more likely and allow for preventative maintenance. As per the alerting, there are a number of mechanisms for alerting such as audio/visual alerts both local and remote. Such notifications can be transmitted wired or wireless to operators or monitoring stations.

[0060] The angle of the normalized cross-coupled impedance Znp I Zpp may be compared to a range of location angle of each phase to determine the phase in which the turn fault is located as represented by the reference numeral 816. Based on the identification of the turn fault in a particular phase, the angle of the normalized cross-coupled impedance Znp I Zpp is correlated with the range of location angle of each coil to locate the coil group having the turn fault. The location of the coil group having the turn fault may facilitate identifying one or more coils corresponding to the coil group, having the turn fault, during repair/ maintenance of the electrical machine.

[0061] FIG. 9 depicts a look-up table 900 for locating a coil group having a turn fault in accordance with one specific embodiment of the present invention. The look-up table is generated based on a determined negative sequence impedance Znn and data representative of a structure of a stator winding in the electrical machine. In one embodiment, the machine may be a six Horse Power (HP) machine. The structure of the stator winding includes data associated with poles, phases, coils, slot and winding type of the machine. In this example, the stator winding of the machine includes four poles, thirty six coils, thirty six slots, with double layer winding. The number of coils per phase = 36/3 = 12. The number of coil group per =12/4 = 312/4. The number of coils in each coil group is equal to no. of poles i.e. four coils. Thus, based on the information discussed herein, the exemplary technique is used to detect and locate turn faults at nine locations on the stator winding, and specifically three locations on each phase of the machine. After locating the coil group having the turn fault, a user can narrow down the focus to corresponding four coils for either repair or maintenance work. The look-up table 900 generated herein using the above information includes the angle of normalized cross-coupled impedance Znp IZpp 902. Further, the look-up table 900 includes a range of location angle 904, 906, 908 of each phase and the range of location angle 910, 912, 914, 916, 918, 920, 922, 924, 926 of each coil group. The range of location angle of phase-R 904, is (-)58 degrees to (-) 178 degrees. Similarly, the range of location angle of phase-Y 906, is 62 degrees to (-)58 degrees, and for phase-B 908, is 182 degrees to 62 degrees. The range of location angle of the "coil group-X" 910 of phase-R 904, is (-58) degrees to (-)98 degrees. Similarly, for the "coil group-Y" 912 of phase-R 904, range of location angle is (-)98 degrees to (-)138 degrees and for "coil group-Z" 914 of phase-R 904, is (-)138 degrees to (-)178 degrees.

[0062] In the illustrated embodiment, the turn fault is detected by comparing the magnitude of the normalized cross-coupled impedance Znp IZpp with a predefined threshold value, and the turn fault is located by correlating the angle of normalized cross-coupled impedance Znp I Zpp with the range of location angle of the coil groups. For example, when the angle of normalized cross-coupled impedance Znp I Zpp 902 is at (-)l 19 degrees at the rated speed and with full load of the machine, then the turn fault location is at coil group-Y 912 on Phase-R 904. In another example, when the angle of normalized cross-coupled impedance Znp I Zpp is at 102 degrees at the rated speed and with no-load condition of the machine, then the turn fault location is at coil group-Y 924 on Phase-B 908.

[0063] The embodiments of the present system and techniques increase the efficiency in locating the coil group having the turn fault. Hence, repair/maintenance of electrical machines is convenient.

CLAIMS
I/We claim

1. A computer-implemented method, comprising:

determining a plurality of symmetrical components based on a plurality of measured phasor currents and phasor voltages of an electrical machine;

determining a negative sequence impedance of the electrical machine based on a plurality of parameters of the electrical machine;

generating a look-up table based on the determined negative sequence impedance and a structure of a stator winding in the electrical machine, wherein the look-up table comprises data including classification of phases, number of coil groups of the stator winding in each phase, classification of each coil group, and range of location angle of each coil group in the electrical machine;

determining a normalized cross-coupled impedance based on the determined plurality of symmetrical components and the negative sequence impedance;

detecting a turn fault in the stator winding by comparing a magnitude of the determined normalized cross-coupled impedance to a predefined threshold value; and

locating a coil group having the turn fault from the classified coil groups in the corresponding phase by using the look-up table and correlating an angle of the determined normalized cross-coupled impedance to the range of location angle of the coil group having the turn fault.

2. The method of claim 1, wherein the plurality of symmetrical components comprises a positive sequence voltage, a negative sequence voltage, a positive sequence current, and a negative sequence current.

3. The method of claim 1, wherein the plurality of parameters of the electrical machine comprises a rated horsepower, number of poles, a rated voltage, a frequency, a size, the plurality of measured phasor currents, and the phasor voltages.

4. The method of claim 1, wherein generating the look-up table based on structure of the stator winding comprises generating the look-up table based on number of poles, number of phases, number of slots, number of coils, and type of the stator winding.

5. The method of claim 4, further comprising determining the number of coil groups based on the number of coils, a number of phases, and the number of poles in the electrical machine.

6. The method of claim 1, further comprising determining the predefined threshold value based on a rated power of the machine, a rated voltage of the machine, a number of poles, and a frequency of the machine.

7. The method of claim 1, wherein the data further comprises number of phases, and range of location angle of each phase.

8. A system comprising:

at least one processor-based device having computer instructions, wherein the computer instructions instruct the at least one processor-based device to:

determine a plurality of symmetrical components based on a plurality of measured phasor currents and phasor voltages of an electrical machine;

determine a negative sequence impedance of the electrical machine based on a plurality of parameters of the electrical machine;

generate a look-up table based on the determined negative sequence impedance and a structure of a stator winding in the electrical machine, wherein the look-up table comprises data including classification of phases, number of coil groups of the stator winding in each phase, classification of each coil group, and range of location angle of each coil group in the electrical machine;

determine a normalized cross-coupled impedance based on the determined plurality of symmetrical components and the negative sequence impedance;

detect a turn fault in the stator winding by comparing a magnitude of the determined normalized cross-coupled impedance to a predefined threshold value; and

locate a coil group having the turn fault from the classified coil groups in the corresponding phase by using the look-up table and correlating an angle of the determined normalized cross-coupled impedance to the range of location angle of the coil group having the turn fault.

9. The system of claim 8, wherein the computer instructions further instruct the at least one processor-based device to determine the symmetrical components comprising a positive sequence voltage, a negative sequence voltage, a positive sequence current, and a negative sequence current.

10. The system of claim 8, wherein the computer instructions further instruct the at least one processor-based device to determine negative sequence impedance based on the plurality of parameters of the electrical machine, comprising a rated horsepower, number of poles, a frequency, a size, a rated voltage, the plurality of measured phasor currents, and the phasor voltages.

11. The system of claim 8, wherein the computer instructions further instruct the at least one processor-based device to generate the look-up table based on the structure of the stator winding comprising number of poles, a number of phases, number of slots, number of coils, and type of the stator winding.

12. The system of claim 8, wherein the computer instructions further instruct the at least one processor-based device to determine the number of coil groups based on number of coils, a number of phases, and number of poles in the electrical machine.

13. The system of claim 8, wherein the computer instructions further instruct the at least one processor-based device to determine number of coils in each coil group based on the number of poles in the electrical machine.

14. The system of claim 8, wherein the computer instructions further instruct the at least one processor-based device for determining the predefined threshold value based on a rated power of the machine, a rated voltage of the machine, a number of poles, and a frequency of the machine.

15. The system of claim 8, wherein the data further comprises number of phases, and range of location angle of each phase.

16. The system of claim 8, wherein the at least one processor-based device comprises at least one of a relay or a meter.

17. The system of claim 8, wherein the at least one processor-based device comprises a graphical user interface for displaying the coil group having the turn fault among the classified coil groups.

18. A non-transitory computer readable medium encoded with a program for enabling a processor-based device to:
determine a plurality of symmetrical components based on a plurality of measured phasor currents and phasor voltages of an electrical machine;

determine a negative sequence impedance of the electrical machine based on a plurality of parameters of the electrical machine;

generate a look-up table based on the determined negative sequence impedance and a structure of a stator winding in the electrical machine, wherein the look-up table comprises data including classification of phases, number of coil groups of the stator winding in each phase, classification of each coil group, and range of location angle of each coil group in the electrical machine;

determine a normalized cross-coupled impedance based on the determined plurality of symmetrical components and the negative sequence impedance;

detect a turn fault in the stator winding by comparing a magnitude of the determined normalized cross-coupled impedance to a predefined threshold value; and

locate a coil group having the turn fault from the classified coil groups in the corresponding phase by using the look-up table and correlating an angle of the determined normalized cross-coupled impedance to the range of location angle of the coil group having the turn fault.

19. The method of claim 18, wherein the data further comprises number of phases, and range of location angle of each phase.

20. An electrical machine, comprising:

a stator having a core and a winding wound on the core,

a rotor disposed proximate to the stator,

a sensing device configured to sense a phasor current and a phasor voltage applied to the winding; and

a processor-based device communicatively coupled to the sensing device, wherein the processor-based device receives a plurality of output signals from the sensing device and is configured to:

determine a plurality of symmetrical components based on a plurality of measured phasor currents and phasor voltages of an electrical machine;

determine a negative sequence impedance of the electrical machine based on a plurality of parameters of the electrical machine;

generate a look-up table based on the determined negative sequence impedance and a structure of a stator winding in the electrical machine, wherein the look-up table comprises data including classification of phases, number of coil groups of the stator winding in each phase, classification of each coil group, and range of location angle of each coil group in the electrical machine;

determine a normalized cross-coupled impedance based on the determined plurality of symmetrical components and the negative sequence impedance;

detect a turn fault in the stator winding by comparing a magnitude of the determined normalized cross-coupled impedance to a predefined threshold value; and

locate a coil group having the turn fault from the classified coil groups in the corresponding phase by using the look-up table and correlating an angle of the determined normalized cross-coupled impedance to the range of location angle of the coil group having the turn fault.

21. The method of claim 20, wherein the data further comprises number of phases, and range of location angle of each phase.