Solar Adaptive Optics (AO) shares many issues with night-time AO, but it also has its own particularities. The wavefront sensing is performed using correlations to efficiently work on the solar granulation as a reference. The field of view for that measurement usually is around 10". A sensor collecting such a wide field of view averages wavefront information from different sky directions, and the anisoplanatism thus has a peculiar impact on the performance of solar AO and MCAO systems. Since we are entering the era of large solar telescopes (European Solar Telescope, Advanced Technology Solar Telescope) understanding this issue is crucial to evaluate its impact on the performance of future AO systems. In this paper we model the correlating wide field sensor and the way it senses the high altitude turbulence. Thanks to this improved modelling, we present an analysis of the influence of this sensing on the performance of each AO configuration, conventional AO and MCAO. In addition to the analytical study, simulations similar to the case of the EST AO systems with FRiM-3D (the Fractal Iterative Method for Atmospheric tomography) are used in order to highlight the relative influence of design parameters. In particular, results show the performance evolution when increasing the telescope diameter. We analyse the effect of high altitude turbulence correlation showing that increasing the diameter of the telescope does not degrade the performance when correcting on the same spatial and temporal scales.