Introduction

Here we will introduce an exciting algorithm called TPWL to model dynamic power system units like DFIG, SG, and HVDC. In fact, this algorithm can be applied to any dynamic system if you want.

The TPWL algorithm was proposed by Imperial College London in 2000, and the idea of it is pretty easy. Let's see the figure below:

This figure (left) shows a fixed point K1 on the nonlinear curve whose slope could be obtained by linearization. As for point K3, we also could get its slope by the same method. However, for point K2 between K1 and K3, we could also obtain its slope using K1 and k2 instead of directly linearizing. The slope of a point is just like the state derivative of our dynamic system. However, the slope for a 2-D curve has only one dimensions, but the dynamic system may have tons of dimension, just like the right figure.

Work we did

In this paper, we use the algorithm to model some power system components to obtain their dynamic behaviors using data. And we compare the result with the original linearized system model. And the procedure of TPWL is depicted below.

Specific Procedures

Well, model in m-files. Classic DFIG.

And SG model.

Model linearization based on key operation point.

And generate some operation trajectories.

Model Reduction (with easy line coding in Matlab)

Weight Calculation for Subsystem

Conclusion

We can see TPWL model can capture the dynamic behavior in a large scope. (To be frank, heavy calculation burden here)

Reference

[1] M. Rewienski and J. White, “A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices,” IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 22, no. 2, pp. 155–170, Feb. 2003.

[2] "A Data-model-driven Modeling Approach for Grid Connected Doubly Fed Induction Generator System Using Trajectory Piecewise Linearization," ICPET Conference, 2023.

Main Code in Matlab

*Paper Authors from MuFeng: GDG and WYX