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THERMAL MODEL BASED DIGITAL RELAYING ALGORITHM FOR INDUCTION MOTOR PROTECTION

M.S. Abou-El-Ela A.I. Megahed Dept. of Electric Engg. Alexandria University Alexandria, Egypt.

Abstract - Thermal models can be used to protect induction motors from excessive overheating resulting from overloading, failure to start, unbalance and frequent starting. Such a model is adopted for use in a relaying algorithm. The developed algorithm accurately calculates the change in motor temperature and hence, protects the motor from excessive overheating. The lab results, included in this paper, of motor temperature during a loading cycle show high correspondence with the established thermal model.

1. INTRODUCTION Adequate protection of induction motors is routinely achieved

via locked-rotor, phase unbalance and overload protection. However, conditions of changing load torque, frequent starts, temporary phase unbalance and high inertia loading must often be tolerated. Design of protective schemes for these conditions using conventional relays is difficult and sometimes impossible. The on- line computational capability of microprocessor based relays can bring within the realm of feasibility the design of adequate protection schemes for induction motors.

Motor protection is primarily a temperature estimation problem. Recognizing that good thermal models exist leads to their adoption for motor protection so that the heating and cooling process is well represented for virtually all loading and terminal conditions.

In this paper, the method by which temperature rise in induction motors is calculated is first reviewed and then adopted for use in a digital relay. The methods by which the relaying algorithm can detect overload, failure of starting, unbalance and successive starting are explained. Finally, a comparison between lab temperature measurements taken for an induction motor during its loading cycle and temperature calculations for the same motor during its loading cycle done by the proposed algorithm i s presented.

2. OVERLOAD National Electrical Code (NEC) requirements for motor

protective devices [I] state that the device(s) selected for "motor running overcurrent (overload) protection", must, "protect the motor against excessive heating due to motor overload and failure to start." By NEC definition, "overload in electrical apparatus is an operating overcurrent which, when it persists for a sufficient length of time, would cause damage or dangerous overheating of the apparatus".

Before overload problem is discussed, it is necessary to review how temperature rise is calculated in a motor. Motor heating has been analyzed in several references [2,3,4] on the basis of the theory of heating an ideal solid body i.e. a homogeneous mass possessing the property of uniform dissipation of heat from its entire surface and of infinitely large heat conduction.

Consider a body in which Q heat units are liberated in a unit of time. The heat energy generated in the body during an infinitely small time dt will then be equal to (Qdt). If during this period the temperature of the body rises by dT degrees, the heat energy absorbed by the body will then equal (GcdT) where G is the mass

O.P. Malik

The University of Calgary Calgary. Canada.

Dept. of Electrical & Computer Engg.

of the body and c its specific heat. if in the process of heating of the body its temperature rises by z"C with respect to the surrounding medium, the heat energy dissipated by the body into the surroundings by radiation, convection and heat conduction during the time dt will equal (Akdt), where A is the surface area of the body and h is the surface heat transfer coefficient.. The difference between the heat energy generated in the body (Qdt) and the heat energy dissipated by the body into ambient space (Ahzdt) is responsible for raising the temperature of the body. Hence, the fundamental difference equation of heating can be written as:

Qit -Akdt = G c d ~ (1)

At s,teady state, the temperature rise with respect to the surrounding medium attains a final value, z,,, and the body temperature will cease to rise, i.e. dz=O"C. Hence, (1) becomes:

(2) Qit -A1.~p, dt = 0 whence:

Solution of (1) by integration yields:

t - =-In ( Tfin -7) + & =I

(3)

(4)

where, TI= heating time constant = (Gc/Ah) and k: = integration constant.

If at the initial moment, t = 0, the body has an initial temperature rise zo above the ambient medium, then from (4):

k = E n ( ~ ~ -7,) (5 )

Substituting for k in (4). and solving for z, gives: I I -_ - _

TI 7 ' T f i , ( l - e 9 + 7 , e

If there is no heat dissipation from the surface of the body, all generated heat will cause a rise of temperature. Eliminating (Ahzdt)l from (l), the temperature rise equation will then be:

Integrating (7) and substituting with, TI= Gc/Ah, T,~ = Q/Ah and the initial temperature rise 5, the temperature rise T becomes:

QJt =Gail (7)

7 =rfi x+7 ,

where, in this case, T,, is defined as the temperature rise achieved by a motor developing Q heat units in time t equal to T,, provided that the initial temperature rise T" = 0°C.

The .formula for the cooling of a motor can be obtained from (1) by substituting with Q = 0, hence:

0-7803-3143-5 /96/$4.00 0 1996 IEEE ___- CCECE'96

1,017

where, T,= cooling time constant. (17) t x -X 100 + A q l 4) %. I * p AV( I ) %=

I 2p,.d TI It is, of-course, an over-simplification to regard a machine as a

homogeneous body. It actually comprises several parts, each with a characteristic surface area, mass, heat capacity, thermal conductivity and rate of heat production so that each part in the motor may have a different temperature rise. However the exponential equations give a fair approximation of motor heating and cooling characteristics.

3. THERMAL OVERLOAD PROTECTION 3.1. Current-Temperature-Time Relation In section 2, the rise of temperature in a motor is discussed. In

the operation of an induction motor, the most likely phenomenon to occur is overloading due to overcurrent. The function of a digital relay is to translate the current drawn by an induction motor into rise of temperature (T), and detect whether this rise of temperature has reached the maximum permissible temperature rise or not. If it reaches that maximum, then the relay should directly initiate a trip signal to disconnect the motor.

It is clear that in order to adequately protect the motor against overload, the variation of current with time must be correlated with the motor temperature. The relation between the final temperature rise in a motor and current drawn is driven from (3). In that equation; Q = heat generated in unit time = k,$z, where k, is a constant and I, peak value of fundamental component of current drawn by motor. Hence (3) can be written as:

rfm = k 2 I P 2 where,

k, = constant

If I = Ipnlcdr peak value of the rated motor current, then T~~ = T~~~ = rated temperature rise above coolant temperature, as indicated in (1 1).

'rated = k 2 1 'pnared

If (6,8) are divided respectively by (1 l), then:

where, T/T=,~ = relative temperature rise in motor and T , , / T ~ , ~ = relative initial temperature rise in motor.

TIT^^,, = AV(t) and T,,IT~~& = AV(,*,. let:

hence:

If AV(t) is expressed as a percentage, then: I I 2

Now, if AV%=lOO% this means that the motor is at its rated temperature and if AV%>IOO% this means that it is overloadcd.

Similarly the cooling of a motor is expressed by: -I -

A V ( t ) % = A ~ , , , ) % e *,

3.2. Motor Thermal Capaciry The permissible limit temperature of the winding, and hence

the thermal capacity of the motor, is dctermincd by thc insulation. The IEC recommendations for electric machines [5] differentiate between various insulating material classes to which specific limits are assigned, Fig. 1. The rated operational temperature data of a standard motor always refers to the coolant temperature of 4OOC. At rated operational temperature the motor can deliver its rated power without becoming unacceptably hot. The winding temperature is the sum of the coolant temperature and the temperature rise due to loading. The sum of the maximum tcmperature rise in a motor and the coolant temperature should be less than the limit temperature of winding.

~ m . x > 1 8 0 ' 180 $*I n 185 155 14 0 13 0 12 0 110

40

0 E B F H C

Fig. 1. Permissible temperature rise for various insulation classes. m Coolant temperature "rn Limit temperature &., Maximum permissible temperature rise

3.3. Use of Temperature Rise Equations in Rehying Algorithm

Equations (16.17) are used in the relaying algorithm to:

operating conditions except in case of short circuit.

of overload. maximum temperature rise (AV,%) is not exceeded.

1) Calculate temperature rise of the motor during all its

2) Calculate the thermal tripping characteristics at the detection The relay permits overloading as long as the

The relay has two thermal tripping characteristics, one without prior loading (cold curve, AVo,% = 0), and the other with prior rated load (hot curve, AV,,,% = 100%) [5 ] . The inverse characteristics are calculated using (16.17) by substituting with AV,% as AV(t)% and inverting the equations such that, VT, = F (I~,,,, AV,,%). It should be noted that (16) is used when there is proper ventilation in the motor. However, during overload, the motor current increases, and accordingly its speed decreases [2]. The substantial decrease in speed prevents heat dissipation to the atmosphere and hence the temperature rise is calculated using (17). As the use of either one of these equations, (16,17), depends on motor characteristics, the value of current, above which (17) is used, is lcft as a sct paramctcr. In this rclaying algorithm a sctting of twice the rated motor current is used. Hence, for current less than twice rated current the cold curve equation is

1,018

-

and the hot curve equation is

t =T,h ( I p l f p r a e d . (20) (I,/ I w e d ) *-AVm,% 0. 01

while for current greater than twice rated current the cold C U N ~ equation is

AV,,%x 0.01 ( I p / ’ p t e d ) 2

=T,x

and the hot curve equation is

(AV,,%- 100 ) x O . 01 t = T1x

( I J I , m r e d IZ where,

t = the relay inverse trip time,

The thermal tripping characteristics obtained using (1 9,20,21,22) are shown in Fig. 2. The relaying algorithm uses the outlined thermal model to follow the changes in motor temperature and to trip when the thermal capacity is exceeded. The logic used by the relay is as follows: 1) Calculate the magnitudes of the three phase currents of the

induction motor. 2) Calculate the ratio of the highest current value in the three

phases relative to the rated current, i.e. I&,,. 3) According to the motor status (cold or hot) and the highest

current value (<21,, or > 2&,J select one of ( 19,20,2 1,22) to calculate the inverse trip time.

4) Start counter that has a setting corresponding to the inverse trip time.

5) When the counter reaches its setting the relay trips, provided that neither the motor highest current value nor motor status changes during this period. However, if a change occurs the following procedure is done: - If the motor status changes from cold to hot, i.e. the

motor temperature reaches loo%, then the relay calculates a new inverse time using either (20) or (22) depending on motor current. Afterwards the relay proceeds with steps 4 and 5 as mentioned above.

- If a change in current occurs, the relay also calculates a new inverse time using one of (19,20,21,22),, then the relay proceeds with steps 4 and 5.

*l t

-1 c I ti++-+ Cold curve - Hot curve

Once the motor has tripped (18) is used in order to calculate the minimum cooling time for the motor before it could be restarted. The c;alculation of the cooling time is done in the cool down section which is described later.

4. PROTECTION FUNCTIONS 4.1. Start Up Protection Starting normally causes a temperature rise of about 30 to 40 %

of motor rated temperature rise ‘tmId, if a motor is started from cold. Hence it is not possible to detect a prolonged starting case based ;purely on temperature calculation. The correct measure of the starting of a motor is given by the integral IZt [6], where; I is the root mean square value of the motor phase to neutral current. The quantity f,,,, T,,,, provides the exact amount of energy dissipated by the motor during starting, where; I- is the root mean square value of staring current and T,, is the maximum starting time of motor. Tripping takes place when calculated 12t exceeds the setting 1’- T-. The logic used by the relaying algorithm for start up protection is as follows: 1) The start setting (ST) is calculated as follows:

ST = ( I p d T,, (23) whexe,

I,, = peak value of starting current, 2) The value of t] is summed every 20ms and

3) Tripping takes place if the value of the start setting (ST) is compared to the start setting (ST).

exceeded.

4.2. Unbalance Protection Unbalance, including phase unbalance or loss of one phase,

causes excessive heating in the motor [6]. Hence, if unbalance is detected by the relaying algorithm the relay should disconnect the motor after a selected time delay, usually between 1-5 seconds, provided that unbalance continues during this period.

4.3. Protection Against Successive Starting According to the temperature rise associated with the starting

of the motor and the initial temperature rise of motor at starting, the rela.ying algorithm should be able to calculate the permissible number of consecutive starts. This part is done in the cool down section mentioned before. When the relay trips due to any fault except ,phase faults, the cool down section does the following: 1) It decides whether the motor can withstand restarting or not. 2) If motor can withstand restarting it calculates the permissible

number of consecutive starts. 3) If tht: motor can not withstand restarting it specifies a minimum

cooling time before restarting, and initiates a blocking signal. 4) If the motor is not started after the elapse of the minimum

cooling time, it keeps calculating the temperature of motor.

5. COMPARISON OF LAB TEST RESULTS AND MOTOR THERMAL MODEL RESULTS

The aim of the lab tests is to verify the established thermal model of the motor by measuring the variation of temperature of the motor with time during a complete loading cycle, and companing the measured results with those calculated using the thermal model. The machine used for these tests is the Universal Machine set [7], with a squirrel cage rotor. This machine is provided with thermocouples, embedded in different parts of the stator, tlo measure the rise in temperature.

5.1. Healing and CooZing characteristics of an Znduction Motor

51.1. Tests The inachine was operated at its rated values (380 volts, 9

ampere), and the readings of the slot (middle of winding)

thermocouple were recorded. The machine was then allowed to cool down at standstill condition and the readings of the slot thermocouple were also recorded. Comparisons of measured and calculated values of temperature in the slot during temperature rise and cooling down are shown in Figs. 3 and 4.

5.1.2. Results 1) The heating time constant at the slot is 50 minutes (T, = 50

minutes) and the cooling time constant is 105 minutes (T2= 105 minutes) as calculated from Figs. 3 and 4 (lab results).

2) Rated current corresponds to a temperature rise of 53.3 OC.

5.2. Induction Motor Loading cycle 5.2.1. Test The Universal Machine was loaded as follows:

1) Loaded at 1.08 rated current for 60 minutes. 2) Loaded at 0.48 of its rated current for 55 minutes. 3) Allowed to cool at stand still for 133 minutes. 4) Blocked for 1 minute at 3 times its rated current. 5) Loaded at 1.08 its rated current for 40 minutes. A comparison between measured and calculated values is shown in Fig. 5.

5.2.2. Results 1) The motor winding cooled with a time constant of 50 minutes

when it operated at a current of 0.48 of its rated current and cooled with a time constant of 105 minutes at standstill.

2) The algorithm is able to follow changes in motor winding temperature during all its operating conditions except during blocking.

g1 I

+++U Measured Calcu lated

_ - - - -

I]//, , , ,

0 50 100 150 200 250 300 Time (min)

Fig. 3. Comparison between measured and calculated va!ues of rise in

. , temperature in slot.

01 I I

Time (min)

colculated values of cool down temeperature in slot.

0 50 I00 150 200

Fig. 4. Comparison between measured and

$1

0 4 I I I d d0 160 150 200 250 300 Time (min)

Fig. 5. Comparison between calculated and measured temperoture in slnt r i ~ w ; ~ - -

5.3. Comments The following comments on the results can be made:

1) The motor cools during running conditions with a time constant equal to the heating time constant, i.e. T,, and during standstill condition it cools with its cooling time constant T2. This shows that the cooling characteristics differ in running conditions than at standstill condition.

2) Equation (16) can be used during motor running conditions to follow the changes in motor temperature, while (18) can be used at standstill condition to express the cooling in motor.

3) The rise in motor temperature is proportional to the square of the input current, (10).

4) Equation (17) failed to follow changes in motor temperature during a blocked rotor condition. This may be attributcd to thc change of the value of the heating time T, constant during blocking conditions, due to the changes in the surface area available for cooling and the cooling coefficient. It should be noted that (17) is used to calculate the rise in motor temperature when the motor is overloaded with a current higher than twice its rated current. At this value the motor is still running, i.e. not blocked. Hence the value of T, could remain unchanged and this permits the use of (17) in the algorithm.

6. CONCLUSIONS This paper describes a new relaying algorithm that can be used

in induction motor protection. The proposed algorithm adopts an induction motor thermal model. The relaying algorithm manages to faithfully calculate changes in motor temperature, hence adequately protecting the motor from overload, failure of starting, unbalance and successive starting.

7. REFERENCES [ I ] ANSI/IEEE, IEEE Guide for AC Motor Protection, The

Institute of Electrical and Electronics Engineers, Inc. 1976. [2] M. Kostenko and L. Piotrovsky, Electrical Machines, volume

[3] M.G. Say, The Performance and Design of Alternating Current

[4] A. Still and C.S. Siskind, Elements of Electrical Machine

[5] Sprecher -t Schuh, Contactor Selection Made Easy, Sprecher

[6] S.P. Patra, S.K. Basu and S. Choudhuri, Power System

[7] Siemens, A.C. Universal Machine and D.C. Machine, Siemens,

II, Mir. Publishers, 1969.

Machines, Sir Isaac Pitman and Sons, LTD., 1958.

Design, McGraw-Hill Inc., 1954.

+ Schuh-Group, 1985.

Protection, Oxford and IBH Publishing Co., 1980.

El , E4. 78/49.