Page 75 - Modern Control of DC-Based Power Systems

40 Modern Control of DC-Based Power Systems

ω c PICM and the phase of the loop gain of T PICM ðsÞ is equal to

2 180 1 PM PICM at the control bandwidth ω c PICM .From (2.58), the
following equations are derived.

T PICM ðjω c PICM Þ 5 1 5 G c I ðjω c PICM Þ G i L d OL ðjω c PICM Þ (2.59)

arg T PICM jω c PICM 52 180 1 PM PICM

5 arg G c I ðjω c PICM Þ 1 arg G i L d OL ðjω c PICM Þ
(2.60)
The latter equation can be rewritten as follows.

arg G c I ðjω c PICM Þ 52 180 1 PM PICM 2 arg G i L d OL ðjω c PICM Þ
(2.61)

is function of known quantities.
Notice that arg G c I ðjω c PICM Þ
Solving (2.59) and (2.60), and taking into account the current control trans-
fer function (2.62), its control coefficients (2.63) and (2.64) are calculated.
K i I
G c I sðÞ 5 K p I 1 (2.62)
s

(2.63)

K p I 5 cos arg G c I ðjω c PICM Þ = G i L d OL ðjω c PICM Þ

K i I 52 ω c PICM sin arg G c I ðjω c PICM Þ = G i L d OL ðjω c PICM Þ
(2.64)
To find the coefficients of the outer voltage controller (2.65),the
designer is required to use the proper plant transfer function, i.e., G vc ðsÞ and
substitutes to G i L d OL ðsÞ. These coefficients are calculated as in (2.66) and in
(2.67). The outer voltage control is designed so that a certain phase margin
PM PICM FB at the control bandwidth ω c PICM FB is obtained. Notice that,

again, arg G c V ðjω c I Þ is function of known quantities (2.68).
K i V
G c V sðÞ 5 K p V 1 (2.65)
s

(2.66)

K p V 5 cos arg G c V ðjω c PICM FB Þ = G vc ðjω c PICM FB Þ

(2.67)
K i I 52 ω c PICM FB sin arg G c V ðjω c I Þ = G vc ðjω c PICM FB Þ

(2.68)
arg G c V ðjω c I Þ 52 180 1 PM PICM FB 2 arg G vc ðjω c PICM FB Þ
Notice that to design the outer voltage controller G c ðsÞ of a converter
in PCMC (see Fig. 2.7), the designer can follow exactly the same
procedure.