As you are dealing with provinces, you could assume that these are within a specified UTM zone. You could add a UTM zone-grid, extract the UTM zone per province, and then repeat the analysis for each province separately, or calculate the values required with the required UTM zone.
If you really want to use a projection for the whole of Iran, then you would be looking for a lambertian projection. I used once the EPSG:6931 which is a projected grid system (EASE-Grid projections) developed recently in a version 2.0 by Brodzik et al. 2014. https://doi.org/10.3390/ijgi1010032
I hope this helps!