__The Electromagnetic Torque and the Load-Angle Characteristic of a Synchronous Motor __

Similarly to Eq. (15.9) defining the electric power developed by a three-phase synchronous generator, that taken by a three-phase synchronous motor is given by

*P* = 3*VI* cos φ = 3*E*_{0}*I* cos φ_{0} = 3*E*_{0}*I* cos (φ - θ) (15.17)

where θ > 0.

Rearranging Eq. (15.17) in the same manner as Eq. (15.9) and noting that θ > 0, we derive an expression for the electromagnetic torque developed by a synchronous motor, similar to that defining the electromagnetic torque of a synchronous generator, Eq. (15.11):

*T*_{em} = (3*p*/2π*f*) *E*_{0}*V* sin θ/ (15.18)

Since the mechanical power developed by a synchronous motor is *P*_{m} = *P* = *T*_{em}ɷ_{rot}

then, subject to Eq, (15.18), we get

*P*_{m} = *P* = 3*VI* cos φ = 3*E*_{0}*V* sin θ/ (15.19)

In a large power system the system voltage *V* and the system frequency *f* are constant.

In view of this observation we may conclude that, at a constant field (excitation) current, the electromagnetic torque *T*_{em} and the power *P* developed by a synchronous motor operating as part of a large power system depend solely on the load angle θ . The relations *T*_{em} = *f *(θ) and *P* = *f* (θ) are called the torque-angle and power-angle characteristics of a synchronous motor and have the shape similar to that of the load-angle characteristics of a synchronous generator (see Fig 10) . These characteristics give insight into what happens in a synchronous motor as its load is varied. As the load (retarding) torque at the shaft of a synchronous motor increases

*T*_{ret}._{2} > *T*_{ret,l} = *T*_{em,1 }

the rotor of the motor slows down, and the load angle θ and the electromagnetic torque *T*_{em} begin to increase. The retarding and electromagnetic torques strike a balance, *T*_{ret.2 }= *T*_{ern.2}, some time later, at a new value of the load angle, θ_{2} > θ_{1} .If we wish to retain the necessary margin of stability, π/2 – θ , at an increased retarding (load) torque, we should increase the field (excitation) current.