## Tuesday, April 22, 2014

### Hardware setup

Been a while since I posted about the simulator. Have been crazy busy with my day job but am happy to announce, that my microgrid setup is finally ready!

Inverter and control board with sensors and microcontroller:

Intelligent power module with dc bus capacitors:

Hopefully I will be able to work on the simulator again before my trip to Japan.

## Saturday, April 5, 2014

### Initializing new stiff equations

Another problem that arises when there are a large number of nonlinear devices is that nonstiff loops become stiff loops but their current has still not become negligible because the diode has turned off at the previous iteration. For example, current through a diode is -0.1A causing the diode to turn off and it's resistance to change to megaohms. When this stiff loops interacts with other stiff loops and the currents of those stiff loops are calculated, all other stiff loops end up having currents of close magnitudes of 0.1 A. Result: entire simulation is disrupted.

Two things need to be done:
1. Need to identify which loops have just become stiff.
2. Calculate those stiff loops before running the ode solver.

The code to identify the newly formed stiff loops is:

And running the stiff loop ode:

One other thing still needs to be done. What if the newly formed stiff loops themselves are interacting with each other through a stiff branch? Now even this ode solver would fail because they would disrupt each other. The only thing to do would be do perform an upper triangularization of the newly formed stiff loops with respect to the newly formed stiff branches and solve them backwards. Will do this later.

### Nodal analysis

There might have been a mistake in the previous current initialization of branch currents. The branches are current sources if:
1. They have inductors and are not stiff.
2. They have voltages and have zero impedance.

If the branches are stiff or are purely resistive with or without a voltage, their currents will need to be calculated by nodal analysis. The code to set the branch currents is:

The actual nodal analysis is:

Other than that, the code is quite the same as the previous case. This code was tested with a three phase diode bridge rectifier and was found to be working OK. The previously released code was breaking.

### Rewriting the loop finder algorithm

Previously, the system loops were added if they met the following criteria:

1. Did not pass through the same branch or same node more than once.
2. Last node was the same as the first node.

During the loop finder, no check was imposed on whether the loops were independent and so they were several loops which were independent.The way to deal with this was to let the simulation run and after the first run, the dependent loops would become void and be deleted. A simpler method could be used to find the independent loops:

1. Did not pass through the same branch or same node more than once.
2. Last node was the same as the first node.
3. The system branches must be contained in at least one loop.
4. As the loops are added, a loop will be added if and only if it passes through a new branch that the previously found loops have not passed through yet.

The 4th check simplifies the process and at the first iteration, the loops found are independent loops and equal to the number (Branches-Nodes+1).

Here is the code (click on "view raw" to see it in a new window):

The rest of the loop finder code is pretty much the same. The only difference is that the parallel branches are found in the main block above so they have been eliminated from the other functions. Anyway, the rest of the function code is below (click on "view raw" to see it in a new window):

### After a long break

Been a while since I updated this blog. I have been working on the project off and on but I was busy doing all sorts of other things that made documentation difficult if not impossible. I have had to extend my work permit and that means getting together all my documents. I have had to send a paper to a conference in Hiroshima, Japan which meant I had to rush to get the final paper ready. And finally, had to plan my trip to Japan which will be in the month of May and get my visa ready.

There have been some questions about how the simulator should work for nonlinear circuits and I am going to start thinking out aloud on the next few blog posts.