This paper proposes a novel approach for studying the stationary energy characteristics of vertical geothermal systems (VGS) using stationary two-dimensional phenomenological mathematical theory. The approach describes VGS as a single, strongly nonequilibrium thermodynamic system consisting of a soil, a borehole with secondary fluid and a ground source heat pump (GSHP). The model uses continuity conditions for temperature and local heat fluxes between VGS components. The theory includes a special class of nonequilibrium spatial scale of VGS that is independent of its geometrical parameters. It is determined by the energy characteristics of the heat pump and the thermodynamic properties of soil and secondary fluid. Spatial variables can be chosen so that the energy characteristics of the VGS depend on only one dimensionless parameter (a similarity parameter), the thermal conductivity ratio of soil to secondary fluid. This considerably simplifies interpretation of theoretical and experimental results obtained using similarity methods. We show that, under real conditions of VGS functioning, the value of this similarity parameter varies from 0.5 to 10. The approach can be used to optimise GSHP systems to obtain energy of the required amount and quality to capitalise on heat pumps as 'flexible agents' in Smart Energy Systems. (C) 2019 The Authors. Published by Elsevier Ltd.