Hi 依娃柯,
I understand that you want to identify a suitable solver for a power convertor project that contains switches which change directions across time. The behaviour of switches which can change direction or state rapidly can often introduce discontinuities and stiffness, thus making the choice of solver a critical decision.
Here are some possible points to consider understanding the mechanisms provided by solvers and your project system:
Multistep Solvers and Switching States
- Solvers like “ode15s” handle the discontinuities introduced by the switching states by considering the states before and after. They may not automatically detect the exact amount of the switch since standard ODE solvers work effectively with smooth, continuous models and are not inherently designed for discrete events.
- The solver should be able to handle the states correctly to avoid errors or an inefficient simulation. Hence the handling of states dictated by the switch should be backed by some correctly implemented system equations and logic.
Handling Discontinuities
- An event detect mechanism can be incorporated for a more accurate simulation of the switches and its behaviour. The “Events” option in MATLAB can allow the solver to find where the function for the solution is zero (to identify discontinuities). This detection can then be extended into a trigger for the solver to change its configuration accordingly. Please refer to the below documentation to know more about the “events” options in MATLAB: https://www.mathworks.com/help/matlab/events-sending-and-responding-to-messages.html
- Another way to handle discontinuities is to restart the solver with the new initial conditions post-switching, thus avoiding the potential errors that might arise from using states before the switch changed.
Stiffness in Power Electronics Systems
- The stiffness in Power Electronics Systems is majorly due to the presence of fast-switching behaviour working alongside dynamic elements like capacitors etc.
- This stiffness can also be seen significant in transitional stages when the switches are changing states or rapid changing in voltages.
- A stiff solver like `ode15s` is generally recommended for such systems because it can handle the wide range of time constants without taking excessively small time steps, which would be necessary for a non-stiff solver to maintain stability.
Choosing a Suitable Solver
- When choosing a solver for your power converter project, consider the following:
- Does the solver handle stiff systems effectively?
- Can the solver detect and handle events (switching actions)?
- Is the solver robust enough to handle the discontinuities introduced by the switches?
- Does the solver allow for variable step sizes to efficiently simulate periods of fast and slow dynamics?
Given that you've already gathered information on ODEs, comparisons of solvers, and guidance on selecting a solver, you're on the right track. Make sure to incorporate event handling in your solver choice to manage the switch actions accurately. If you're using MATLAB, `ode15s` with the 'Events' option could be a suitable choice for your power converter project, provided you set up the event detection correctly to handle the switching behavior.
Hope it helps,
Regards,
Ayush Misra
