I would suggest that you try ode15s or ode23t instead.
While ode15i, being an implict solver, may work well with stiff system of equations, it doesn't allow a "mass" matrix in the input set to indicate a certain equation is an algebraic equation. See https://www.mathworks.com/help/matlab/math/summary-of-ode-options.html and look for the "mass" option in the table. It's still possible to rewrite your equations with multiplier to trick ode15i into solving it, but I find it easier to use ode15s or ode23t with a mass matrix so the equations are more human-understandable.
I've seen ode15s and ode23t picked automatically in some Simscape models, which usually is a DAE system, although daessc solver is much more likely (but it's not available in MATLAB solvers).
Hope this helps.
