Page 143 - Modern Control of DC-Based Power Systems

Generation Side Control 107

MVDC bus and therefore the output of this system can be considered
constant during the period of observation;
• The generic generating system has been represented by DC ideal
voltage DC sources E n (representing the buck converter output) with
the duty cycle d connected to a second-order RLC filter, whose
parameters are R fn ,L fn and C fn ;
• The zonal loads and single component loads and their characteristics
can be lumped into an equivalent load which exhibits CPL
characteristic;
• The generic load has been represented by a load branch resistor R Lm
and a controlled current source I Lm 5 P m /V m ; these two branches
represent the linear and the nonlinear (assumed as infinite bandwidth
CPL) parts of the load;
• The generic lines which connect the loads to the MVDC bus
are characterized by the lumped cable parameters R cm , L cm and by a
possible input filtering capacitor C cm of the load converter.
Based on Fig. 4.3 it is possible to derive a state-space average model
of a multimachine MVDC system. The Kirchhoff current and voltage
laws enable us to express the mathematical model by n 1 2m 1 1nonlinear
differential equations with the following state variables:
• MVDC bus voltage, V (1 equation);
• Generators currents, I n (n equations);
• Line currents, I ch (m equations);
• Load voltages, V m (m equations).
The state-space model of the system presented in Fig. 4.3 is therefore
defined in (4.1) by the n 1 2m 1 1 equations of the system, where a total
capacitor C eq has been defined as the sum of all filter capacitors C fn :
8 !
n m
dV 1 X X
5 I k 2
>
>
> I ch
dt
>
>
k51 h51
> C eq
>
>
>
>
dI k
> 1
> 5 2 R fk I k 1 V 1 E k ’k 5 1; 2; .. . ; n
>
dt
>
< L fk
(4.1)
1
dI ch
5
>
> 2 R ch I ch 1 V 2 V h Þ’h 5 1; 2; .. . ; m
> ð
> dt L ch
>
>
>
!
>
>
> 1
dV h P h
>
> 5 I ch 2
> ’h 5 1; 2; .. . ; m
dt
>
: C ch V h