  Detecting the 21-cm signal from the Epoch of Reionisation (EoR) is
challenging due to the strong astrophysical foregrounds, ionospheric effects,
radio frequency interference and instrumental effects. Understanding and
calibrating these effects are crucial for the detection. In this work, we
introduce a newly developed direction-dependent (DD) calibration algorithm
DDECAL and compare its performance with an existing algorithm, SAGECAL, in the
context of the LOFAR-EoR 21-cm power spectrum experiment. In our data set, the
North Celestial Pole (NCP) and its flanking fields were observed
simultaneously. We analyse the NCP and one of its flanking fields. The NCP
field is calibrated by the standard pipeline, using SAGECAL with an extensive
sky model and 122 directions, and the flanking field is calibrated by DDECAL
and SAGECAL with a simpler sky model and 22 directions. Additionally, two
strategies are used for subtracting Cassiopeia A and Cygnus A. The results show
that DDECAL performs better at subtracting sources in the primary beam region
due to the application of a beam model, while SAGECAL performs better at
subtracting Cassiopeia A and Cygnus A. This indicates that including a beam
model during DD calibration significantly improves the performance. The benefit
is obvious in the primary beam region. We also compare the 21-cm power spectra
on two different fields. The results show that the flanking field produces
better upper limits compared to the NCP in this particular observation. Despite
the minor differences between DDECAL and SAGECAL due to the beam application,
we find that the two algorithms yield comparable 21-cm power spectra on the
LOFAR-EoR data after foreground removal. Hence, the current LOFAR-EoR 21-cm
power spectrum limits are not likely to depend on the DD calibration method.
