Table 2 Control system parameters.

First gain

β ₁

80

Second gain

β ₂

1600

Dynamic scaling parameter

k ₁

0.018

Steady state scaling parameter

k ₂

0.235

Boundary-layer

f

190

PI controller for DC microgrid voltage

Proportional gain

k _pv

0.43

Integral gain

k _iv

42.0366

PI controller for DDBC-based supercapacitor input current

Proportional gain

k _psc

37.7588

Integral gain

k _isc

838,920

PI controller for DDBC-based battery input current

Proportional gain

k _pb

11.9381

Integral gain

k _ib

19,739

Cut-off frequancy of LPF

f _c

10 kH

Integral backstepping for DC-based PV

First backstepping parameter

k _bs1

250

Second backstepping parameter

k _bs 2

2800

Integral gain weighting factor

k

1980