This research presents a new radio-selected sample of compact Galactic PNe from the CORNISH survey, a radio continuum survey of the inner Galactic plane. The northern counterpart of the CORNISH survey covers the 10° < l < 65°; |b| ≤ 1° region with a resolution of 1.5'' and a sensitivity that is better than 0.4 mJy/beam at 5 GHz, using the VLA. The southern counterpart observed the 295° < l < 350°; |b| ≤ 1° region of the southern Galactic plane, using the ATCA array. It achieved a resolution of 2.5'' and sensitivity better than 0.2 mJy/beam at 5.5 GHz. Candidate PNe, above a 7σ detection limit, were selected through visual inspection of multi-wavelength images. A detailed multi-wavelength investigation using properties such as radio spectral indices, MIR-to-radio ratio, and infrared colours, including near-infrared, mid-infrared and far-infrared colours, were used to confirm the PNe nature of the selected candidates. Some of the detected PNe were found to be compact and dense, having physical diameters < 0.06 pc and closer than 6 kpc, with brightness temperature > 1000 K. In the northern Galactic plane, 169 candidate PNe were analysed. 90 were classified as new PNe, out of which 12 PNe were newly detected and 78 were newly classified as PNe. A further 47 objects, previously classified as probable PNe were confirmed as such from the analysis and 24 known PNe were recovered. Eight sources were classified as possible PNe or other source types based on insufficient data. In the southern Galactic plane, 184 sources were classified as PNe. Four previously classified as probable PNe were confirmed and 29 previously known PNe were recovered. 151 were classified as new PNe, out of which 97 were newly classified as PNe and 54 have no astronomical records in the SIMBAD database, hence are classified as being detected for the first time. At 5 - 5.5 GHz, the CORNISH PNe are evenly distributed in Galactic latitude and have significantly increased (~ 200%) the number of PNe within the |b| ≤ 1° region, compared to the distribution of known PNe. Based on Galactic PNe population synthesis, the number of PNe within the CORNISH survey region was synthesized to test Moe & De Marco's binary and single stellar model. Comparison of the Galactic latitude distribution of the CORNISH PNe sample with the distribution of the synthesized population gave a best-fit scale height of 550 pc and 600 pc for the northern and southern PNe, respectively. Within the limits of the assumptions made in building the model and the predictions from population synthesis models, the modelled parameters that fit the angular size, flux density distributions and observed number of the CORNISH PNe support the formation of observable PNe through binary interactions. This model is the first of its kind and forms a basis for in depth future investigations that compare observed radio properties with predictions from population synthesis models.
