A Stability Analysis of Thermostatically Controlled Loads for Power System Frequency Control

Figure 5

Solutions for (see (61)) (solid lines) for different values of . Dashed lines show reflection in to show the effect of reversing the switching order of the groups. Blue: , yellow: , green: , and red: . Black line shows the boundary of stability (stable below, unstable above). The results are identical when is replaced by . (b) shows an enlargement centred at , showing that either switching order of the groups leads to on a small interval of . In this case the groups never merge and in all other cases they will.

(a) Full interval

(b) Enlargement