System Modeling with BOTH Differential and Algebraic Equations

Hello everyone,

I am trying to model an Inverter based microgrid in MATLAB which has several sub components with BOTH differential and algebraic equations. I have attached a block diagram with this post.

Does anyone know the best way to do this? Are there any examples out there with both differential equations and algebraic equations? I tried doing a google search and didn't find anything.

1) I could solve the differential equations for a particular time instant, feed those values to the algebraic equations, and simply loop for the duration for the simulation. See the block diagram for the Power and Current Controllers.

2) I could discretize the differential equations and do the same kind of thing as #1.

Please let me know your thoughts.