Based on the performance index in (12), the objective function to search for optimal parameters for the PI controllers (i.e., PI1, PI3, and PI7) responsible for DC bus voltage regulation is formulated.
where [x.sub.dc] represents the control parameters for the PI3 and PI7 controller gains, [T.sub.0] is the time at which the reference is changed within the entire length of the simulation time, [T.sub.F], and [T.sub.1] is suitably selected intermediate point that permits the assignment of different weighting factors, [W.sub.1] and [W.sub.2], to the initial and later portions of the response.
Rating and leakage (TR1) inductance PI1, PI2 1, 0.005, 0.2, 1 [k.sub.pdc1], [k.sub.idc1], controller [k.sub.pq2], [k.sub.iq2] gains (G-VSC voltage mode) PI3, PI4, PI5, 2, 0.001, 0.6, 0.05, [k.sub.pd3], [k.sub.id3], PI6 controller 0.1, 20, 5, 0.05 [k.sub.pq4], [k.sub.iq4], gains (G-VSC [k.sub.pd5], [k.sub.id5], current mode) [k.sub.pq6], [k.sub.iq6] PI7, PI8 1.2, 0.2, 1, 0.5 [k.sub.pb7], [k.sub.ib7], controller [k.sub.p8], [k.sub.i8] gains (BES DC/ DC converter) SOC limits Max 0.95 p.u.
The B-minor triad" (i.e., pi7, divided into pi3+4) is blurred first by accretion in the left hand (measures 92-97) and by filling in the right hand (measures 98-104).
After this chord sounds for six measures, the piece takes a new step - partitioning the octave (pi12, the sum of earlier boundary-intervals pi5 and pi7) into two equal parts.
Accretion and filling(22) then proceed until the span from [A.sub.6-Fb.sub.7] (pi7) is completely fired (measures 163-69).
Like its predecessor, Coulee begins with a single oscillating interval, here a pi7. But Coulee's opening interval turns out not to be a partition-interval (as in Continuum) but a boundary-interval, which is then partitioned.(24) The resulting trichordal signal, a perfect fifth divided into a tritone and a minor second (017, pi7 divided into 6 + 1), has two principal ramifications.
The resultant chain of open octaves in the upper part of the texture (measures 93-107) displays an expansion of the basic signal's boundary-interval from pi7 to pi12 similar to what happens in Sections III and IV of Continuum).
There do exist direct relations between the numerators (and the denominators) of the different PIs, however, like between the numerators (and denominators) of PI6 and PI1 unto PI5, and the numerator (and denominator) of PI8 and the numerator (and denominator) of the set of PI7s