EMTP simul(17)
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198 Power systems electromagnetic transients simulation u y + – e G 1 G s Fi gur e 8.3 First- or der lag written in FORTRAN, C, C++, MATLAB or BASIC, and l ink this with EMTDC. Interpolat ion of controls is also an important issue for accurate results [6] . 8.3.1 Ex ampl e The first-order lag control system, dep icted in Figure 8.3, is used to demonstrat e the use of the z-domain for the prediction of instabilities. The corresponding transfer function is: y u = 1 1 + f g = G 1 + sτ (8.1) where f = feedback path = 1/ G g = forward path = G/(sτ) τ = time lag. The equations for the two blocks are : e = u − 1 G y (8.2) y = Ge s τ (8.3) Substitution of the trapezoidal rule to form difference equations gi ves: e k = u k − 1 G y k (8.4) y k = t(e k + e k−1 )G 2τ (8.5) Thedifference in dat a pat hsbec omes app are nt. Ifsolvedas twose pa ra te difference equations, then e k must be calculated from y at the previous time step as y k is not available and this introduces one time-step delay in the y data path. Swapping the orde r of equa tionswill res ult in th e same pr oble m for th e e dat a pat h. Substituting on e equation into the other and rearranging, results in a difference equation w ith no delay
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