Takagi-Sugeno Models and Linear Matrix Inequalities for Active Power Filter Applications

What is it about?

Thanks to active power filters, improving the quality at the mains is possible, however, this ability strongly depends on the control strategy. We use Takagi-Sugeno models and the Lyapunov stability criteria as design tools for establishing Linear Matrix Inequalities (LMI) conditions; solving these LMI conditions a parallel-distributed compensation (PDC) control law was obtained. With this control law, the shunt active power filter (SAPF) shows a good performance for reducing the total harmonic distortion (THD) and achieving the power factor (PF) correction during load changes. We could corroborate a satisfactory performance for simulation and experimental tests, even better than several other popular SAPF controllers.

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Photo by Emmanuel Ikwuegbu on Unsplash

Photo by Emmanuel Ikwuegbu on Unsplash

Why is it important?

Since the tasks of SAPF are very challenging, the design of their controllers is of great interest nowadays, so we decided to explore alternatives to traditional SAPF controllers. TS models allow an exact representation of the nonlinear system dynamics, where the result is a model with linear matrices which are useful for establishing LMI conditions. Likewise, the nonlinear character of the original system is encapsulated in nonlinear scalar functions that can be included in the control law. A PDC type control law is obtained once LMI conditions are solved by means of efficient computational algorithms. The independence of the system parameters during the SAPF operation is one of the advantages of this control strategy and allows to obtain a better performance in comparison with other controllers.

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