Improving Stability Margin

This is a consequence of the improvement in the power angle characteristics and is one of the major benefits of using midpoint shunt compensation. As mentioned before, the stability margin of the system pertains to the regions of acceleration and deceleration in the power-angle curve. We shall use this concept to delineate the advantage of mid point shunt compensation.

Consider the power angle curves shown in Fig. 10.6.

The curve of Fig. 10.6 (a) is for an uncompensated system, while that of Fig. 10.6 (b) for the compensated system. Both these curves are drawn assuming that the base power is V²/X . Let us assume that the uncompensated system is operating on steady state delivering an electrical power equal to P_m with a load angle of δ_⁰ when a three-phase fault occurs that forces the real power to zero. To obtain the critical clearing angle for the uncompensated system is δ_cr , we equate the accelerating area A₁ with the decelerating area A₂ , where

with δ_max = π - δ₀ . Equating the areas we obtain the value of δ_cr as

(10.11)

Let us now consider that the midpoint shunt compensated system is working with the same mechanical power input P_m. The operating angle in this case is δ₁ and the maximum power that can be transferred in this case is 2 per unit. Let the fault be cleared at the same clearing angle δ_cr as before. Then equating areas A₃ and A₄ in Fig. 10.6 (b) we get δ₂, where

Example 10.1