From Swift monitoring of a sample of active galactic nuclei (AGN) we found a transient X-ray obscuration event in Seyfert-1 galaxy NGC 3227, and thus triggered our joint XMM-Newton, NuSTAR, and Hubble Space Telescope (HST) observations to study this event. Here in the first paper of our series we present the broadband continuum modelling of the spectral energy distribution (SED) for NGC 3227, extending from near infrared (NIR) to hard X-rays. We use our new spectra taken with XMM-Newton, NuSTAR, and HST/COS in 2019, together with archival unobscured XMM-Newton, NuSTAR, and HST/STIS data, in order to disentangle various spectral components of NGC 3227 and recover the underlying continuum. We find the observed NIR-optical-UV continuum is explained well by an accretion disk blackbody component (Tmax = 10 eV), which is internally reddened by E(B-V) = 0.45 with a Small Magellanic Cloud (SMC) extinction law. We derive the inner radius (12 Rg) and the accretion rate (0.1 solar mass per year) of the disk by modelling the thermal disk emission. The internal reddening in NGC 3227 is most likely associated with outflows from the dusty AGN torus. In addition, an unreddened continuum component is also evident, which likely arises from scattered radiation, associated with the extended narrow-line region (NLR) of NGC 3227. The extreme ultraviolet (EUV) continuum, and the soft X-ray excess, can be explained with a warm Comptonisation component. The hard X-rays are consistent with a power-law and a neutral reflection component. The intrinsic bolometric luminosity of the AGN in NGC 3227 is about 2.2e+43 erg/s in 2019, corresponding to 3% Eddington luminosity. Our continuum modelling of the new triggered data of NGC 3227 requires the presence of a new obscuring gas with column density NH = 5e+22 cm^-2, partially covering the X-ray source (Cf = 0.6).
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