Small Signal Stability Analysis

I am attempting to perform small signal stability analysis on a DC power system. More specifically, I want to evaluate the source impedance and load impedance at a given interface and look at the ratio of Z(S) / Z(L). Essentially, I am trying to apply the Middlebrook stability criteria.

See Section C from this paper https://ntrs.nasa.gov/api/citations/20210018276/downloads/12%20-%20AIAA%20NASA%20Revolutionary%20Vertical%20Lift%20Technology%20Aircrafts%20Power%20Quality%20Analysis%207_9_21%20NF.pdf for what I am attempting to do.

Are there any resources or examples I can look at for doing this in simulink?

Answer 1

[Antonino Riccobono]

Dear Basil,

I studied small-signal stability of DC Power Distribution Systems during my PhD at University of South Carolina. My dissertation is free for download - here's the link Stabilizing Controller Design for a DC Power Distribution System Using A Passivity-Based Stability Criterion.

In that work, I extended the Middelbrook's stability criterion by proposing a passivity-based stability criterion that is looking, instead of ZS / ZL (ratio), at ZS // ZL (parallel combination) or in other words at the bus impedance. An impedance estimation method based on injection of Pesud-Random Binary Sequence (PRBS) was deployed both in simulation and experimentally.

Eleven years have passed by since I graduated, and now in MathWorks I provide support to the Simulink Control Design development team in the area of Frequency Response Estimation (FRE). I contributed to put together an example on how FRE can be applied to measure converter input and output impedances. An example is of your potential interest:

Frequency Response Estimation to Measure Input Admittance and Output Impedance of Boost Converter

FRE is also used to estimate battery impedance - you can use a very similar approaches to estimate ZS and ZL for your stablity study.

Analyze Battery Impedance Using Exact Linearization (since R24b!)

Estimate Battery Impedance Using Signal Generator Blocks (since R24b!)

The final piece of information I would like to share with you is about a training course I designed: Power Electronics Control Design with Simulink and Simscape. In that course you can learn about FRE in great detail for digital control design purposes.

Hope this helps.

Cheers,

Antonino

[Basil]

Thanks a lot! This is a great information. I will take a look.