# Temperature Rise in Electrical Machine

Heat is developed in all electrical machine due to the losses in the various parts,

- copper loss(I^2R loss) in conductor,
- Hysteresis losses and eddy current losses in iron and
- mechanical losses (in rotating machine only) due to friction of the bearing,air friction or windage causing the temperature of that part to rise.

(The temperature rise continues until all the heat generated is dissipated to the surroundings by one or more of the natural modes of heat transfer i.e Conduction,Convection and radiation)

The temperature rise depends upon

- The amount of heat produced and
- The amount of heat dissipated per 1°C rise of the surface of a machine.

According to Newtons law of cooling the rate of loss of energy of a hot body is proportional to the difference in temperature between that body and its surroundings.This law is only valid for the moderate temperature difference(up to 100°C ) and for the bodies dissipating heat by radiation and natural convection.

### Note:

**The amount of heat dissipated per 1°C rise of the surface of a machine depends on the surface area of cooling.**

The size of motor for any service is governed by the maximum temperature rise when operating under the given load conditions and the maximum torque required.Electrical machine are designed for a limited temperature rise.

[Continuous rating of machine is that rating for which the final temperature rise is equal to or just below the permissible value of temperature rise for the insulating material used in protection of motor windings]

When the machine is overloaded for long time that its final temperature rise exceeds the permissible limit,it is likely to be damaged.In worst cases,it will results in thermal breakdown of the insulating material which will cause a short circuit in the motor.The short circuit may lead to fire.But in less severe cases,the quality of the insulation will deteriorate such that thermal breakdown with future overloads occur,shortening the useful life of machine.

Temperature rise is limited by the insulation and is important factor for the calculation of the size of motor.The maximum temperature rises which should not be exceeded by different types of motor are fully set out in the relevant ISS.

## Heating-Time curve:

For determination of an expression for the temperature rise of an electrical machine after time t seconds from the instant of switching it on,

Power converted into heat=P joules/s or Watts

Mass of active parts of machine=m Kg

Specific heat of material=Cp joules/kg/°C

surface area of cooling=α in watts per metre^2 of surface per °C of difference between surface and ambient cooling temperatures.

**Assumptions made**

- Losses or heat produces remains constant during the temperature rise.
- Heat dissipated is directly proportional to the difference in temperature of the motor and the cooling medium.

Suppose a machine attains a temperature rise of θ°C above ambient temperature after t seconds of switching on the machine and further rise of temperature by dθ in very small time dt.

Energy converted into heat=Pdt joules

Heat absorbed=mCpdθ joules

Heat dissipated=Sθαdt joules

since energy converted into heat=Heat absorbed+heat dissipated

:pdt=mCpdθ+Sθαdt

or,(p-Sαθ)dt=mCpdθ

When the final temperature is reached,there is no absorption of heat.The heat generated is dissipated.

[Heating time constant is defined as the time taken by the motor in attainning the final steady value if the initial rate of rise of temperature were maintained throught the operation ]

Substituting t=τ in equation iii we get,

[Heating time constant is also defined as the time duration which the machine will attain 63.2% of its final temperature rise above ambient temperature]

θF is directly proportional to the power losses and inversely proportional to the surface area S and specific heat dissipation α.

**Note:**

**Typical values of heating time constant lie between about 3/2 hour for small motors(7.5Kw to 15Kw) up to about 5 hours for motors of several hundred kW.**

## cooling-Time curve:

Let the machine be switched off after reaching final steady-temperature rise of θF.when the machine is switched off,no heat is produced,

0=Heat absorbed+heat dissipated

or 0=mCpdθ+Sθα’dt

where α’=rate of heat dissipation during cooling

Substituting t=0,θ=θF from initial conditions in above equation(iv) we get,

[Cooling time constant may be also defined as the time required to cool the machine down to 0.368 times the initial temperature rise above ambient temperature]

**Note:**

**The cooling time constant of a rotating machine is usually larger than its heating time constant.In self cooled rotating machines the cooling time constant is about 2-3 times greater than its heating time constant.**