Page 57 - Mechanical Engineers' Handbook (Volume 2)

46 Input and Output Characteristics

Figure 5 Common dissipative load characteristics.

4.2 Operating Points in an Exchange of Power or Energy
When resistive source and load characteristics are plotted on the same coordinates, they
intersect at least once. The coordinate values at that point, or at those points if there are
several, are the values of the power variables at which that combination of source and load
must operate if they are connected. This is called an operating point. From a computational
point of view, the source causes one of the power variables given the other and the load
causes the other given the source. They must operate at the same point in the power plane
to satisfy continuity (common flows) and compatibility (common efforts) conditions.
When there are multiple intersections, all are possible operating points, but not all will
be stable operating points; for example, any disturbance from equilibrium might result in a
transition to another operating point. The condition for a stable intersection is best seen
graphically in Fig. 7. For a stable intersection, as shown on the left, it is required that a
small perturbation of the load, which increases its demand for power, be countered by a
shortage of power from the supply side of the system and a small perturbation of the load,
which decreases its demand for power, be met with an excess from the source. In either
case, the load will be driven back to the intersection by the excess or deficit in the source
capability. A reversal of these conditions is an unstable operating point because disturbances
will be driven further in the direction of their initial departure.
At the unstable intersection in Fig. 7 (2, on the right-hand side), a slight increase in the
flow demand of the load will result in an overwhelming increase in the supply flow available
to drive the load, which will then cause a traversal to point 1 in the figure. Similarly, if the