Page 282 - Power Electronic Control in Electrical Systems

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270 Harmonic studies of power compensating plant

i
ψ ψ

δ
t i

t
Fig. 7.4 Afull cycle of the TCR current and flux excitation.

Fig. 7.5 Afamily of instantaneous c i characteristics of a single-phase TCR.

However, this relationship does not hold at conduction angles s smaller than 180 .

In such a situation, the current will exhibit dead-band zones and becomes non-sinusoi-
dal. This effect is clearly shown in Figure 7.4, where the c±i characteristic relates a
full cycle of the excitation flux to a full cycle of the TCR current.
More generally, the characteristics exhibited by a single-phase TCR, acting under a
sinusoidal AC excitation flux, are a family of straight lines which are a function of the
flux-based firing angle d c , as shown in Figure 7.5.
Furthermore, numeric differentiation can be used to obtain a full cycle of the
derivative of the TCR current with respect to the flux with respect to time.
It is noted from Figure 7.6 that when the TCRs are conducting the magnitude of
the derivative is inversely proportional to the reactor's inductance L R and it is zero if
no conduction takes place. Also, the conduction angles s 1 and s 2 may differ.