Motor protection principles

Motor Protection Principles

Arijit Banerjee, Arvind Tiwari Jakov Vico, Craig Wester GE Global Research, GE Multilin Bangalore, India Markham, Ontario, Canada

Abstract – This paper discusses the fundamentals of motor protection principles. Every motor is designed for a specific operating temperature depending upon its insulation. Once this limit is exceeded its life decreases drastically. Over heating condition may arise due to several factors like supply system disturbance, electrical unbalance conditions, faults, load variation and environment. It is essential to have a proper coordination between development of protection principles and the design of motors to understand the concept of motor heating and how thermal protection for motors can be used to prevent loss of motor life. In this paper an overview of existing protection methods for motors is reviewed with a special consideration of thermal protection of motors. I. Introduction Three phase motors can be classified into two types: induction and synchronous. Induction motors are the workhorses of most industrial systems. Induction motors are used on fans, blowers, conveyors, crushers, compressors, cranes, pumps, shredders, extruders, refiners and chillers. Despite their ruggedness and simplicity in construction, the motor failure rate per year is significant [1]. Motor failure rate is conservatively estimated as 3-5% per year, but in some industries like mining, and pulp and paper, motor failure rate

can be as high as 12%. Motor failure cost contributors are, repair or replacement, removal and installation and loss of production. All failures can be divided in three groups. One third of failures are electrically related, one third are mechanically related failures and remaining one third of failures are related to environment, maintenance and the other reasons. Due to occurrence of such outages, the industry has to replace or repair the motor and incur huge downtime. This necessitates the requirement of proper protection of the machine to ensure productivity targets, personnel safety and to prevent unplanned outages. Most of the motor failure contributors and failed motor components are related to motor overheating. Thermal stress can potentially cause the failure of all the major motor parts: Stator, Rotor, Bearings, Shaft and Frame.

Fig 1: Three-phase induction motor

There are two main risks for an overheated motor: Stator windings insulation degradation (for stator limited motors) and rotor conductors deforming

215978-1-4244-1949-4/08/$25.00 ©2008 IEEE

or melting (for rotor limited motors, where motor thermal limit is defined by allowed motor stall time). Insulation lifetime decreases by half if the motor operating temperature exceeds its thermal limit by 10ºC (figure 2). Apart from overheating, there are a number of conditions that can result in damage to three-phase motors also. These damages may be due to operating conditions or internal or external faults. External faults and operating conditions include: under-voltage, asymmetrical loading, phase and ground faults on the motor feeder and overloading during starting and running operation. Internal faults include: ground faults, faults between windings and inter-turn faults. The motor protection device (MPD) must be able to prevent any damage occurring to the motor. In the following sections, the requirements of several protection methods are briefly discussed. II. Overvoltage protection When an induction motor runs in an overvoltage condition, slip (being inversely proportional to square of the voltage) decreases resulting in decrease in load current. Simultaneously,

magnetizing current increases exponentially resulting in poorer power factor. Decrease in load current results in lower copper loss while increase in magnetizing current results in higher core loss. Although old motors had robust design, new motors are designed close to saturation point for better utilization of core materials and increasing the V/Hz ratio could cause saturation of air gap flux leading motor heating. This leads to higher overall loss, less efficiency and higher operating temperature of the motor [2]. In addition, the dielectric stress on the insulation of the motor is higher. This necessitates requirement of overvoltage protection for an induction motor. The overvoltage element should be set to 110% of the motors nameplate unless otherwise stated in the motor data sheets. III. Undervoltage protection When an induction motor operating at full load is subjected to an undervoltage condition, slip increases, power factor is increased and full load current increases. Although stator core loss decreases, rotor copper loss and stator copper loss increases. This leads

Fig 2: Stator windings insulation degradation

0

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0 50 100 150 200 250

TEMPERATURE (ºC)

PER

CEN

TAG

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A-CLASS (105 ºC)

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to poorer efficiency and higher temperature rise for the motor [2]. The undervoltage protection element can be thought of as backup protection for the thermal overload element. In some cases, if an undervoltage condition exists it may be desirable to trip the motor faster than the overload element. The undervoltage trip should be set to 90% of nameplate unless otherwise stated on the motor data sheets. Motors that are connected to the same source may experience a temporary undervoltage, when one of motors starts. To override this temporary voltage sags, a time delay setpoint should be set greater than the motor starting time. IV. Unbalance protection A voltage imbalance in a motor implies that unequal line voltages are being applied to the motor. This can happen due to several reasons like unbalance supply, faulty operation of automatic power factor connection, uneven distribution of single phase load on the same feeder etc [2]. As per symmetrical component theory, unbalance set of phasors can be decomposed into balanced sets of positive, negative and zero sequence components (figure 3). Appearance of negative sequence component clearly indicates unbalance in the supply. The negative-sequence reactance of the three-phase motor is 5 to 7 times smaller than positive-sequence reactance, and even a small unbalance in the power supply will cause high negative sequence currents. For example, for an induction motor with a starting current six times the full load current, a negative sequence voltage component of 1% corresponds to a negative sequence current component of 6%. The negative sequence current

induces a field in the rotor, which rotates with double speed in the opposite direction to the mechanical direction and causes torque pulsations, increased mechanical stress on the motor, and additional temperature rise. It is essential to measure the voltage unbalance and if it exceeds 1% the motor must be derated. If voltage unbalance exceeds 5% the motor has to be shut down [3]. However for small and medium sized motor it is often customary to have only current transformers (CTs) and no voltage transformers (VTs). Thus instead of measuring voltage unbalance, it is better to directly measure current unbalance and protect the motor. Apart from system voltage unbalance, current unbalance can also be present due to loose connections, incorrect phase rotation connection, stator turn-to-turn faults and system voltage distortion.

Fig 3: Positive and negative sequence

rotation The unbalance settings are determined by examining the motor application and motor design. The heating effect caused by the unbalance will be protected by enabling the unbalance input to the thermal memory; described later. In addition, separate current unbalance trip and alarm settings may be applied. For example, a setting of 10% x FLA for the current unbalance alarm with a delay of 10 seconds and a trip level

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setting of 25% x FLA for the current unbalance trip with a delay of 5 seconds would be appropriate. V. Ground fault protection Ground faults in a motor generally occur when its phase conductor’s insulation is damaged for example due to voltage stress, moisture or an internal fault occur between the conductor and ground. A ground fault can be detected by a zero sequence CT approach, which has

Fig 4: Zero sequence CT connection

high sensitivity and inherent noise immunity (figure 4). All phase conductors are passed through the window of a single CT referred to as a zero sequence CT [4]. Under normal circumstances, the three phase currents will sum to zero resulting in an output of zero from the zero sequence CT’s secondary. If one of the motor’s phases were shorted to ground, the sum of the phase currents would no longer equal zero causing a current to flow in the secondary of the zero sequence CT. The motor protection device (MPD) detects this current and declares a ground fault.

Fig 5: Phase to ground fault

For large cables that cannot be fit through the zero sequence CT’s window, the residual ground fault configuration can be used (figure 6). This configuration is inherently less sensitive than that of the zero sequence configurations and has two major drawbacks.

Fig 6: Residual CT connection

During starting of a motor, the motor’s phase currents are not only very high (typically 6 times the motors full load current) but also have asymmetry. Consequently, this results in a DC offset current. As the CTs are not perfectly matched, a slight mismatch of the CTs combined with the relatively large phase current magnitudes also produce a false residual current. These offset currents as seen by the MPD can be misinterpreted

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as a ground fault unless the ground fault element’s pickup is set high enough to disregard this error during starting.

Fig 7: Phase-to-phase fault VI. Differential protection Differential protection may be considered the first line of protection for internal phase-to-phase or phase-to-ground faults. In the event of such faults, the quick response of the differential element may limit the damage that may otherwise occurred to the motor. This protection function is mostly used to protect induction and synchronous motors against phase-to-phase faults. Both ends of the phase conductor must be available to use this protection. This function can be implemented in two ways. In one configuration, two sets of CT’s, one at the beginning of the motor feeder, and the other at the neutral point can be used. Alternatively, one set of three core-balance CTs can also be used as shown in figure 8 for detection. The differential element subtracts the current coming out of each phase from the current going into each phase and compares the result or difference with the differential pickup level. If this difference is equal to or greater then the pickup level a trip will occur.

Fig 8: Core balance method

Fig 9: Summation method with six CTs

If six CTs are used in a summing configuration as shown in figure 9, during motor starting, the values from the two CTs on each phase may not be equal as the CTs are not perfectly identical and asymmetrical currents may cause the CTs on each phase to have different outputs. To prevent nuisance tripping in this configuration, the differential level may have to be set less sensitive, or the differential time delay may have to be extended to ride through the problem period during motor starting. The running differential delay can then be fine tuned to an application such that it responds very fast and is

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sensitive to low differential current levels. A biased differential protection method (figure 10 & 11) allows for different ratios for system/line and the neutral CT’s. This method has a dual slope characteristic. The main purpose of the percent-slope characteristic is to prevent a misoperation caused by unbalances between CTs during external faults. CT unbalances arise as a result of CT accuracy errors or CT saturation.

Fig 10: Biased differential protection

with six CTs

Fig 11: Biased differential protection percent-slope characteristic

This characteristic allows for very sensitive settings when the fault current is low and less sensitive settings when the fault current is high and CT

performance may produce incorrect operating signals. VII. Short circuit protection The short circuit element provides protection for excessively high over-current faults. When a motor starts, the starting current (which is typically 6 times the Full Load Current) has asymmetrical components as shown in figure 12. These asymmetrical currents may cause one phase to see as much as 1.7 times the RMS starting current.

Fig 12: Asymmetrical starting currents The rule of thumb is to set the short circuit protection pickup to a value, which is at least 1.7 times the maximum expected symmetrical starting current of the motor. This allows the motor to start without nuisance tripping. The short circuit trip should be set above the maximum locked rotor current, but below the short circuit current of the fuses. For example motor data sheets indicate a maximum locked rotor current of 540% FLC or 5.4 x FLC. A setting of 6 x FLC with a instantaneous time delay will be ideal, but nuisance tripping may result due to the asymmetrical starting currents and DC offset. If asymmetrical starting currents limits the starting capability, it is recommended to set the short circuit trip level higher to a

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maximum of 9.2 x FLC to override this condition (1.7 x 5.4 = 9.2) where 1.7 is the maximum DC offset for an asymmetrical current). With 300:5 CT and FLC of 297A, 9.2 x FLC = 9.2 x 297/300 = 9.10 CT. It is very important to note that, when an MPD detects a short circuit it gives a trip signal to the breaker or contactor of the motor. The breaker or contactor must have an interrupting capacity equal to or greater then the maximum available fault current otherwise it may cause potential damage to the equipment or personnel. If the breaker or contactor does not have an interrupting capacity equal to or greater then the maximum available fault current, it is recommended that you turn off short circuit protection and let an upstream device that is rated to interrupt the fault to open the circuit. VIII. Stator RTD Protection A simple method to determine the heating within the motor is to monitor the stator with RTDs. Stator RTD trip level should be set at or below the maximum temperature rating of the insulation. For example, a motor with class F insulation that has a temperature rating of 155°C could have the Stator RTD Trip level be set between 140°C to 150°C, with 150° C being the maximum. The stator RTD alarm level could be set to a level to provide a warning that the motor temperature is rising. IX. Overload protection The protection philosophy so far dealt with faults in the motor or fault in the supply. However cases may arise in which no such fault occur but the motor runs continuously in overload condition. The temperature rise of the motor dictates its safe operation. A motor can

run on overload for short periods of time provided its temperature limit is not reached. Direct monitoring of the temperature rise of the motor can provide thermal protection, however it has its own inherent drawbacks. Firstly, the temperature sensors itself has some time constant and response time. Further its is not always possible to fit temperature sensors in stator of squirrel cage induction motor. Hence there is a need for incorporating thermal protection based on efficient prediction of motor temperature in MPD. Temperature rise in a motor is caused due to power losses in the motor. Total power dissipated and thermal impedances of the motors are needed for proper estimation of temperature rise. Power losses in an induction motor can be broadly classified into following categories:

1) Stator copper loss 2) Stator core loss 3) Rotor copper loss 4) Rotor core loss 5) Friction loss 6) Windage loss 7) Stray load loss

Thermal modeling ranges from thermal analysis of the machine using FEM [6] [7], lumped parameter model [8], [9] and using software like Motor-CAD [10]. These detailed modeling tools are definitely valuable for the motor design engineers, but for a protection engineer the protection philosophy should be simple yet effective. The primary motor protective element of the MPD is the thermal overload element and this is accomplished through motor thermal image modeling. This model

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must account for thermal heating in the motor while the motor is starting, running at normal load, running overloaded and stopped. An algorithm of the thermal model integrates both stator and rotor heating into a single model. The motor thermal limit is generally presented in the form of a time current curve [5] for three possible motor overload conditions: locked rotor or stall condition, acceleration and running overload as shown in figure 13. The curve represents the maximum allowable safe time at a stator current above normal load for which the motor can operate. A, B and C represents the thermal limit curves at different voltage levels. These are necessary for motors that are designed for low voltage starting. Ideally, time-current curves have been provided for both a hot and cold motor. A hot motor is defined as one that has been running for a period of time at full load such that the stator and rotor temperatures have settled at their rated temperature. Conversely, a cold motor is defined as a motor that has been stopped for a period of time such that the rotor and stator temperatures have settled at ambient temperature. For most motors, the motor thermal limits are formed into one smooth homogeneous curve. The acceleration curves are an indication of the amount of current and associated time for the motor to accelerate from a stop condition to a normal running condition. In this particular example (figure 13), there are three acceleration curves shown: The curve A is the acceleration curve at 100% rated voltage while the curve C is the acceleration at 80% of rated voltage. A soft starter is commonly used to

reduce the amount of inrush current during starting. As can be seen on the curve shown, since the voltage and current are lower, it takes longer for the motor to start. Therefore starting the motor on a weak system can result in voltage depression, providing the same effect as a soft-start. The thermal model developed in a MPD must correlate to the thermal curves obtained from the motor manufacturer to ensure proper thermal overload protection under all circumstances. In the following section, a thermal model that effectively correlates with standard overload curves is reviewed. Standard overload curves imply running overload curves for the motors that have starting time well within the safe stall time. The thermal model has flexibility so that it can incorporate protection for different motors including motors with high inertia load or motors with cyclic load.

Fig 13: Typical thermal limit curves per

IEEE 620-1996 [5]

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X. Single time constant thermal model The total heat generated in the motor equals the summation of total heat stored in the motor and total heat dissipated. Mathematically,

'''2 HTdtdTCRI (1)

Where C = thermal capacitance of the motor, T’(t) = temperature rise above ambient, I’(t) = motor current, R = electrical resistance and H = running heat dissipation factor. If current and temperature are expressed in per unit with respect to rated condition namely, Irated (rated current for the motor) and Tmax (motor temperature at thermal limit trip condition) respectively, (1) reduces to

THTdtdTCTRII rated maxmax

22 (2)

The maximum temperature related to the rated current by the following

HTRI rated max2 (3)

Equation (2) is rewritten with the help of (3) as

TdtdT

I CM2 (4)

Where HC

CM is defined as motor

thermal time constant. The above differential can be analyzed for steady overload condition. Solution of the above differential equation at steady overload condition is given by

CM

t

eItT 1)( 2 (5)

When for a motor its thermal limit is reached T(t) = 1 and (5) can be used to obtain the maximum time, denoted as tmax(I), for which the motor can operate at the given current level before the motor reaches thermal limit.

1ln)( 2

2

max IIIt CM (6)

Equation (6) can further be simplified with a Taylor’s series approximation particularly for large values of current, as shown in (7) and represents standard overload curve.

1)( 2max IIt CM (7)

When (6) and (7) is plotted they are in almost exact match at higher currents as in figure 14. The deviation at lower current value is not important, as change in temperature is slow. However in practice, both the curves are an approximation to the actual system where in a complex multiple time constant motor has been modeled as single time constant model. Either curve can be shifted horizontally or vertically and can be matched to manufacturer’s published curve.

Fig 14: Comparison of single time constant thermal model and approximate overload curve

In order to incorporate the complex behavior of the motor, flexibility in the model must be provided such that

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various factors are accounted in the model. The thermal overload pickup has to be set to the maximum value allowed by the service factor of the motor. It is common practice to set the thermal overload pickup to no more than the rated motor full load current plus no more than 8-10% of the service factor unless there is another independent measure of motor temperature such as stator RTD's. When stator RTDs are monitored and used within the thermal model, the thermal overload pickup can be set as high as 1.25 for motors with 1.15 SF (1.15 for motors with 1.0 SF). If the motor’s winding temperature is also being directly monitored by stator RTD biasing function to the thermal model, the thermal overload pickup can be safely increased to the maximum allowable value for that motor. The motor feeder cables are normally sized at 1.25 times the motor’s full load current rating, which would limit the motor thermal overload pickup setting to a maximum of 125%. A parameter called Thermal Capacity Used (TCU) that is expressed as percentage of the thermal limit used during motor operation is used for defining the thermal content of the motor. TCU is incrementally updated every 100 milliseconds and the integrated value of TCU specifies the thermal state of the machine

100)(

100

max1@@ It

msTCUTCU TT % (8)

When TCU reaches unity or 100%, the motor reaches the thermal limit and it has to be tripped or shutdown. In order to provide a complete thermal mapping of the motor in service, the cooling process must also be taken into account in the above-mentioned model. When the motor runs in overload condition, the temperature rises above nominal operating temperature and TCU follows it as can be observed from (7) and (8). Similarly, when the motor runs with low load, the temperature decreases below nominal value and TCU must be able to track it. Motor cooling is characterized by cooling time-constants (stopped and running) depending on operating conditions. The equations to calculate TCU decay of the cooling motor are as follows:

endt

endstart TCUeTCUTCUTCU col ))(( (9) Where:

%100)1)(_

( xcoldhot

pickupoverloadI

TCUend

(10)

TCU = Thermal capacity used TCUstart = TCU value caused when motor current is operating above pick up TCUend = TCU value dictated by the hot/cold curve ratio when the motor is running (= 0 when the motor is stopped) t = Time in minutes

cool = Cool Time Constant in minutes (running or stopped) I = Motor heating current Overload_pickup = overload pickup set point as a multiple of FLA Hot/cold = hot/cold safe stall ratio Hot/cold safe stall ratio dictates the level at which TCU will settle when the motor runs in light load condition. It is

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calculated by simply dividing the hot safe stall time (locked rotor hot) by the cold safe stall time (locked rotor cold) or use the motor thermal limits curves. Another method to determine hot/cold ratio is to use the thermal limits curves as shown in figure 15. Hot/Cold ratio can be determined as follows: from the thermal limits curves: run a line perpendicular to the current axis that intersects the hot and cold curves at the stall point, draw lines from each points of intersection to the time axis, record the corresponding times.

Fig 15: Method to determine hot/cold ratio using the thermal limits curves

If hot and cold times are not provided and only one curve is given verify with the manufacturer that it is the hot curve (which is the worst case), then the Hot/ Cold ratio should be set to 1.0. The significance of two cooling time constant lies in the fact that natural cooling of the rotating motor or forced cooling by means of special fans installed on the machine shaft cause a

much higher cooling rate of the running machine compared to the motor at standstill. It takes the motor typically 5 time constants to cool. Typically, a motor takes twice as long to cool when stopped versus when running. If the motor data sheet says it takes 150 minutes to cool when stopped, use a stopped cooling time constant of 30 minutes (30 minutes is a typical stopped cooling time constant). If the motor data sheet says it takes 75 minutes to cool when running, use a running time constant of 15 minutes (15 minutes is a typical running time constant). If RTD’s are present and are wired to the motor relay, biasing of the thermal model will be used and it is not critical to have these running and stopped cooling times from the manufacturer.

Fig 16: Typical TCU v/s time curve when motor current reduces to rated

value from overload

Equation (7) and (10) holds true when there is no negative sequence current. However an unbalanced supply will give rise to negative sequence currents, which will cause additional rotor heating due to substantial increase in rotor

COLD

HOT

LRTLRTHCR

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resistance because of skin effect in the rotor bars. To incorporate the effect of negative sequence current, an equivalent current consisting of both positive and negative sequence current replaces the current used in the thermal model. The idea is that the current input into the thermal model is biased to reflect the additional heating caused by the negative sequence component of the load current. This equivalent motor heating current is reflected as:

2

1

21II

KII meq (11)

Where: Ieq - equivalent motor heating current Im - real motor current I1 - positive sequence component of real motor current I2 - negative sequence component of real motor current K - unbalance bias factor The Unbalance Bias K factor reflects the degree of extra heating caused by the negative sequence component of the load current and can be defined as the ratio of Positive Sequence Rotor Resistance to Negative Sequence Rotor Resistance. It is practical and quite accurate to use the estimate method to define the K factor. Equations for typical and conservative estimates [3] are presented below.

) (230

) (175

2

2

veconservatiI

K

typicalI

K

LRC

LRC (12)

where ILRC is locked rotor current. When K equals 8, it is almost identical to NEMA derating curve [3].

It may happen due to unforeseen condition, that the motor cooling ventilation is blocked or motor ambient temperature changes. In such case, the TCU calculated by the MPD will not be able to track the thermal content of the motor due to lack of this temperature information. It is, therefore, practical to have a feedback of the actual temperature of the motor and bias the TCU as calculated from the motor current information. The temperature can be measured through RTDs placed in the stator. As RTDs are slow in response this effectively accounts for slow motor heating. The thermal model with this varied flexibility can effectively map the thermal image of a motor and can replicate the running overload curves obtained from motor manufacturer as shown in figure 13. The MPD’s standard overload curve has to be just below the cold thermal limit and above the hot thermal limit to give maximum process uptime, without compromising protection as shown in figure 17.

Fig 17: Thermal limit plot includes hot and cold running overload limit curves

and MPD standard overload curve

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Additional enhancement is required for the motors which are used for starting high inertia load for which starting time exceeds safe motor stall time. Acceleration condition is different from locked rotor condition. Even when acceleration time is same as stall time, the temperature rise during acceleration will be less as compared to the motor when stalled [11]. If a standard overload curve is used, the MPD will calculate incorrectly that the thermal limit has been reached and will trip the motor. In order to avoid this, the MPD must be able to distinguish between locked rotor, accelerating and running condition. Generally for such motors, custom overload curves have to be applied. For custom overload curves, the cooling and overload time constants can be matched using a graphical procedure. The goal is to match the explicit cooling time constant to the time constant that is implied by the overload curve in the vicinity of rated current. Moreover for these starts, thermal model must account for the current change during acceleration and also use the acceleration thermal limits for TCU calculations. Motor thermal limit is growing along with motor rotation speed during acceleration. As starting current is proportional to system voltage during motor acceleration, voltage could be a good indication of the current level corresponding to the locked rotor conditions. Voltage dependant dynamic thermal limit curve is employed to enhance the thermal model algorithm for long starts. For voltages in between 100% and 80% nominal voltage, the MPD will shift the acceleration thermal limit curve linearly and constantly based

on measured line voltage during a motor start as shown in figure 18. Thus, the single time constant thermal model developed with all its flexibility can effectively protect the motor in different conditions. It has taken into account different conditions of motor operation like start, acceleration and run but also field variability like unbalance current, environmental change. It is thereby possible to exactly replicate the motor thermal limit curve as provided by the motor manufacturer.

Fig 18: Voltage dependant protection

curves within thermal model A case study follows where the behavior of the thermal model for a motor subjected to a cyclic loading is analyzed.

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XI. CASE STUDY: Cyclic loading When a motor is operated under cyclic loading on a motor, the motor heating is proportional to the square of the current, so the effective current for heating over the cycle is:

highlow

lowlowhighhigheffectiveeffective tt

ItItIH

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(13)

where: Ieffective = effective value of the load current Heffective = effective heating value of the load ILOW = Current during no load condition IHIGH = Current during overload condition TLOW = Time duration of no load condition THIGH = Time duration for over load condition Equation (13) can also be expressed in terms of a duty cycle ratio:

22 )1( lowhigheffective IDDIH (14) where:

lowhigh

high

ttt

D = Duty Cycle ratio

When the low cycle current is zero and the heating and current are expressed in per unit values (14) becomes,

21 highID (15) This provides the ideal overload detection boundary. Extension of the previous analysis for single time constant model to values of current below pickup, the motor thermal model is defined by the following differential equation:

)(11)( tTcoldhotI

dttdT

cool

(16)

where: cool = cooling time constant

The (1 - hot/cold) factor is included to match the hot and cold stall times specified by the motor manufacturer. By including the factor in the cooling computation, the hot overload curve is effectively shifted down by the correct amount relative to the cold overload curve to account for the difference in ‘time to trip’ of hot and cold motor conditions. For the load cycle under consideration, the current during the unloaded part of the cycle is approximately equal to zero, so the differential equation given by equation (16) reduces to:

cool

tTdttdT )()(

(17)

Equations (4) and (17) describe the behavior of the thermal model during the assumed load cycle. Whether or not the temperature reaches a tripping condition depends on the severity of the duty cycle. For a severe overload, the temperature ratchets up past the maximum value. For a load just below the threshold of tripping, the temperature reaches a steady state cycle just below the maximum value and the MPD allows the motor to continue to operate. The approximate boundary between overload and normal operation can be determined by analyzing the steady state limit cycle, as the temperature approaches 1 per unit. The approximate temperature rise during the overload portion of the load cycle estimated by the overload curve is computed by multiplying (4) by the overload time:

highhighCM

high tIT )1(1 2 (18)

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The approximate temperature drop estimated by the cooling model during the unloaded portion of the duty cycle is computed by multiplying (18) by the appropriate time, with per unit temperature equal to 1, because that is what it will be approximately during a limit cycle that approaches tripping:

lowcool

low tT 1 (19)

The overload detection boundary is determined by setting the net temperature change equal to zero. This implies that the total of the right hand sides of (18) and (19) is equal to zero:

01)1(1 2low

coolhighhigh

CM

ttI (20)

So for proper setting of this thermal model with respect to a cyclic load

21 highCM

cool DI (21)

Equation (21) expresses the actual overload detection boundary terms of its settings, the duty cycle, and the amount of overload. Except for the factor of

cool/ CM, (21) is the same as ideal overload detection boundary specified by (15). Equations (18) and (15) will be identical, provided that cool/ CM is set equal to one. This makes sense from a physical point of view. The cooling time constant as well as the overload curve time constant arise from the same physical parameters, so they should come out to be the same. In other words, in order for the model to provide appropriate thermal protection during load cycling applications, it is necessary to satisfy the following constraint:

CMcool (22) Equation (22) represents a consistency constraint relating the cooling time constant and the overload curve. For

most applications, it is not necessary to satisfy the constraint. However, in the case of a load that cycles above and below pickup, equation (22) should be approximately satisfied. Otherwise, the computed motor temperature will tend to ratchet up or down. Figure 19 illustrates three cases for a cycling load with an approximate per unit heating value of one. In the first case, the cooling time constant is set too long resulting in over-protection and early motor tripping. In the second case, the cooling time constant is set to match the implied time constant of curve multiplier, and the protection is correct. In the third case, the cooling time constant is set too short, resulting in under-protection and possible motor overheating.

Fig 19: Thermal model response to cyclic load for different settings

XII. Phase CT and Ground CT Selection The phase CT should be chosen such that the FLA is 50% to 100% of CT primary. For example, for a FLA of 297 a 300:5 CT may be chosen. For high resistive grounded systems, sensitive ground detection is possible with the 50:0.025 CT. On solidly grounded or low resistive grounded systems where the fault current is much higher, a 1A or 5A secondary CT should

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be used. If residual ground fault connection is to be used, the ground fault CT ratio must equal the phase CT ratio. If residual connection is used, pickup levels and timers must be set with respect to the motor acceleration time. The zero sequence CT chosen need to be able to handle all potential fault levels without saturating. XIII. Conclusions The temperature rise for an electrical motor ultimately dictates its life. This necessitates the requirement of an accurate monitoring of the thermal content of the motor. The thermal model described here is based on equivalent single time constant thermal model but with the flexibilities incorporated into the model it can effectively create an accurate image of the thermal condition of the motor. The model when subjected to a cyclic loading case study behaved exactly the way it should as physical understanding of the system predicts. If the implied thermal constant of the overload curve matches the explicit cooling constant of the running motor, the MPD algorithm computes the correct thermal image of the motor during a cyclic load. Additional protection elements such as overvoltage, undervoltage, unbalance, ground fault, differential, short circuit and stator RTD supplement the thermal model protection and provide complete motor protection. XIV. Biographies Arijit Banerjee received the M.Tech degree in Electrical Engineering from Indian Institute of Technology, Kharagpur, India in 2007 where he specialized in machine drives and power electronics. He was awarded with DAAD

(German Academic Exchange Service) scholarship in 2006 and did his thesis work in Technical University of Darmstadt, Germany. Currently he is with GE Global Research, Bangalore, India working in power electronics, control and protection of drives. Arvind Tiwari, Ph D, is with GE Global Research, Bangalore, India. Prior to joining GE in November 2003, he was faculty with Institute of Technology, Banaras Hindu University, Varanasi, India (1998-2003) and with M/s Crompton Greaves Limited, India as Design Executive from 1997 to July 1998. Arvind is C. Engg and MIET (UK), AMIE (India). Arvind has to his credit 20 international and national publications in the area of electrical engineering. His main research interests are Electromagnetic devices, Wavelet Transform and its application in Digital Signal Processing, Power Quality and Condition monitoring. Jakov Vico received his Bachelor of Science and Master of Science Engineering degrees from University of Belgrade, Serbia, in 1986 and 1988. Jakov started his career with Hydro Power Stations on the Trebisnjica River, Yugoslavia, in the Protection and Control Section. From 1993-1998, Jakov worked for ABB South Africa as Testing and Commissioning Engineer for relay protection and control. He transferred to the ABB Canada, in 1998, where he became Senior Protection Application Engineer. In 2001, Jakov joined GE Multilin as Senior Application Engineer. He is Professional Engineer of Ontario and Senior Member of IEEE.

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Craig Wester is southeast US regional sales/application manager for GE Multilin in Norcross, Georgia. He was born in Belgium, Wisconsin, and received a B.S. in Electrical Engineering with a strong emphasis on power systems from the University of Wisconsin-Madison in 1989. Craig joined General Electric in 1989 as a utility transmission & distribution application engineer. He is a member of the IEEE. XV. References [1] W.Premerlani et al, “Fundamental of motor thermal model and its application in motor protection”, 58th Annual Conference for Protective Relay Engineers, pp 127-142, July 2005 [2] G.A.Macoy, T Litman et al, “Energy Efficient selection of Motor handbook”, pp 6, Jan 1993. [3] Information Guide for General Purpose Industrial AC Small and Medium Squirrel-Cage Induction Motor Standards, NEMA Standards Publication, 2002. [4] IEEE Guide for AC Motor Protection IEEE, Std C37.96-2000 (Revision of IEEE Std C37.96-1988) [5] IEEE Guide for the Presentation of Thermal Limit Curves for Squirrel Cage Induction Machines, Std 620-1996 (Revision of IEEE Std 620-1987) [6] D. Sarkar, P. Mukherjee, S.K. Sen, “Approximate analysis of steady state heat convection in an induction motor”, IEEE Transactions on Energy Conversion, Vol. 8, No. 1, March 1993. [7] M.Rajagopal, K.Seetharamu, P.Ashwatknarayan, ”Transient thermal analysis of induction motor”, Proceedings of the 1996 International Conference on Power Electronics, Drives and Energy Systems for Industrial Growth, vol 2, pp-932-936, 1996.

[8] A. Bousbaine, M. McCorrnick, W.F. Low, “In-Situ Determination of thermal coeffiecients for electrical machines”, IEEE Transactions on Energy Conversion, Vol. 10, No. 3, September 1995. [9] A. Boglietti, A. Cavagnino, M. Lazzari, M. Pastorelli, “A Simplified Thermal Model for Variable Speed Self-Cooled Industrial Induction Motor”, IEEE Transactions on Industry Applications, Vol. 39, No. 4, July/August 2003. [10] A. Boglietti, A. Cavagnino, D.A.Staton, “Thermal Analysis of TEFC Induction Motors”, Conference Record of 38th IAS Annual Meeting the Industry Applications Conference, vol.2, pp-849- 856, 2003. [11] James H. Dymond, “Stall Time, Acceleration Time, Frequency of Starting: The Myths and The Facts” IEEE Transactions On Industry Applications, Vol. 29, No. 1, Jan/Feb 1993. [12] GE Multilin, “Setting The 469 Motor Management Relay for A Cycling Load Application”, GE Publication GET-8478.

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