SM angular characteristic

It is known that SM mechanical characteristic is absolutely rigid and that`s why its angular velocity ω is constant (), but instantaneous value of this velocity may some differ from. This occur when under SM load the rotor begin to lag from synchronous speed and the more the load the more rotor lagging (at its rotation with synchronous speed) from synchronous speed of stator field. It is oppositely in synchronous generators; with load increasing the rotor leads the stator field rotating with speed of stator field.

The angle between geometrical rotor axis and imaginary axis of stator field (between vector of rotor emf and stator voltage vector) is called rotor exit angle , which can be changed at shot-time parameters changing. In this case dependence of SM moment from rotor exit angle is important.

This dependence is called angular characteristic. Analytical expression of angular characteristic is considered in course of electrical machines and has such a view

,

where - phase number;

- mains voltage;

- SM emf;

, - synchronous inductive SM resistances, respectively by longitudinal d and cross q axis.

From given formula it is seen that electromagnetic moment has two components.

The 1^st component, moment is proportional to motor emf and voltage (active moment is stipulated by basic processes of SM operating principle) and sinus of rotor exit angle.

The 2^nd component, reactive moment which arises as a result of explicit-pole system and changes with double frequency, comparatively to change frequency of active moment independently of excitation presence on SM (at the expense of difference in resistance valuesand).

Figure 3.51 – SM angle characteristic.

There are such designations on a figure:

1 –the first component characteristic (active moment);

2 – the second component characteristic (reactive moment);

3 – resulting characteristic ;

4 – mechanical characteristic of actuating mechanism (Ist class mechanism).

As it is known from the course of electric machines SM stable operation will be at , it is a condition of SM static stability, if rotor exit angle will be - the motor will fall out of step. It is desirable ti have a rated rotor exit angle , then at rated static resistance moment overload capacity will be

.

If SM is implicit-pole then reactive moment doesn`t arise in it, and its angular characteristic (as opposed to explicit-pole) is sinusoidal.

As it seen from overload capacity writing, the formula is for SM with implicit poles (), for SM with explicit poles the maximum of electromagnet moment (at the expense of reactive moment) occur at angle less than, .

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