All the relays operate in response to one or more electrical quantities either to close or to open contacts. There are really only two fundamentally different operating principles:
 Electromagnetic Attraction, and

Electromagnetic Induction.
Electromagnetic attraction relays operate by virtue of a plunger being drawn into a solenoid, or an armature being attracted to the poles of an electromagnet. Such relays may be actuated by DC or by AC quantities. Visit Induction Relay – Construction Detail to know about constructional feature of Induction Relay.
Electromagneticinduction relays use the principle of the induction motor where torque is developed by induction in a rotor; this operating principle applies only to relays actuated by Alternating Current, and called Induction Type relays.
Inductiontype relays are the most widely used for protectiverelaying purposes involving AC quantities. They are not usable with DC quantities, because of their principle of operation.
An Induction Type Relay is a splitphase induction motor with contacts. Actuating force is developed in a movable element that may be a disc or other form of rotor of nonmagnetic currentconducting material by the interaction of electromagnetic fluxes with eddy currents that are induced in the rotor by these fluxes.
Figure below shows how force is produced in a section of a rotor that faces two adjacent AC fluxes. Various quantities are shown at an instant when both fluxes are directed downward and are increasing in magnitude. Each flux induces voltage around itself in the rotor, and currents flow in the rotor under the influence of the two voltages. The current produced by one flux reacts with the other flux, and vice versa, to produce forces that act on the rotor.
The quantities involved in an Induction Type relay may be expressed as follows:
Ø_{1} = Ø_{1m}sinwt
Ø_{2} = Ø_{2m}sin (wt + Ɵ)
Where Ɵ is the phase angle by which Ø_{2} leads Ø_{1}. It may be assumed with negligible error that the paths in which the rotor currents flow have negligible selfinductance, and hence rotor currents are in phase with their voltages:
iØ_{1} ∝ d Ø_{1} / dt ∝ Ø_{1}coswt
iØ_{2} ∝ d Ø_{2} / dt ∝ Ø_{2}cos (wt+Ɵ)
As clear from the figure shown above, the two forces F1 and F2 are in opposition, and consequently we may write the equation for the net force (F) as follows:
F = (F_{2} – F_{1})
∝ (Ø_{2}i_{Ø1}– Ø_{1}i_{Ø2}) …………………..(1)
Putting the values of the quantities into equation (1), we get
F ∝ Ø_{1m}Ø_{2m}[sin (wt + Ɵ)coswt – cos (wt + Ɵ)sinwt ] ………….(2)
Therefore,
F ∝ Ø1mØ2mSinƟ
Thus the actuating force in an Induction Type Relay is directly proportional to the phase displacement between the two fluxes. For maximum actuating force, the phase displacement Ɵ must be 90°.
Thus to summarize, actuating force is produced in the presence of outofphase fluxes. One flux alone would produce no net force. There must be at least two outofphase fluxes to produce any net force, and the maximum force is produced when the two fluxes are 90° out of phase. Also, the direction of the forceand hence the direction of motion of the relay’s movable memberdepends on which flux is leading the other.
A better insight into the production of actuating force in the induction relay can be obtained by plotting the two components of the expression inside the brackets of equation (2). Figure below shows such a plot when Ɵ is assumed to be 90°. It shall be observed that each expression is a doublefrequency sinusoidal wave.
The two waves are displaced from one another by 90° in terms of fundamental frequency, or by 180° in terms of double frequency. The sum of the instantaneous values of the two waves is 1.0 at every instant. If Ɵ were assumed to be less than 90°, the effect on Figure above would be to raise the zeroforce axis, and a smaller perunit net force would result. When Ɵ is zero, the two waves are symmetrical about the zeroforce axis, and no net force is produced. If we let Ɵ be negative, which is to say that Ø_{2} is lagging Ø_{1}, the zeroforce axis is raised still higher and net force in the opposite direction is produced. However, for a given value of Ɵ, the net force is the same at each instant.
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