Abstract
This paper presents an algorithm for finding the optimal control for a current controller that operates as a part of a control system of a shunt active power filter. The algorithm is based upon the Karush–Kuhn–Tucker conditions for finding an optimal value where control signal is limited and constraints create a cube. The explicit solution of the Karush–Kuhn–Tucker problem is presented and simplified calculations are given to lower calculation complexity. The presented Karush–Kuhn–Tucker algorithm is compared with a classical PI controller. It is given the algorithm for finding the optimal parameters of the PI controller and the behavior of the PI controller is compared with the presented algorithm. Attention has been paid to the saturation of controllers in commutation states of load currents, which has a negative impact on the final performance of the controllers and the controlled shunt active power filter. The paper also presents the software and hardware platforms applied to run the presented algorithms in real-time. For both controllers, the shunt active power filter response is shown using real experimental results. The results of the experiments prove better behavior regarding the presented algorithm, especially in the case of commutative load currents, where the output signals from other controllers become saturated.
Highlights
In modern electrical engineering, it is important to ensure good power quality
Besides the execution of the algorithm for finding the optimal control vector, the real-time application performs other functions related to S-Active power filters (APFs) control, e.g., the reading of voltages and currents from ADC converters, implementation of the PLL algorithm synchronizing the shunt (parallel) APF (S-APF) to the grid, calculation of the reference currents in the control algorithm module, and communication with output PWM blocks and functions monitoring safe S-APF operation
Saturation is an important state because it allows an object to be controlled by the extreme power value; at the same time, it breaks the feedback loop because the output signal of the controller does not depend on the value of the input signals
Summary
It is important to ensure good power quality. It contributes to improved efficiency and functioning of a power system and connected consumers. In order to achieve the elimination of adverse current components, the applied S-APF control algorithm must appropriately determine the current components corresponding to higher harmonics, reactive power (defined for 50 Hz), and the load currents negative sequence component. Other controller design methodologies and operating principles have been tested, such as harmonic component compensation by a deadbeat controller to guarantee a low steady-state error and fast dynamic response [17,18], a second-order sliding-mode control applied to a hybrid active power filter [19], and the global current control method where a controller consists of a linear proportional resonant controller and a non-linear sliding mode controller [20]. The S-APF equipped with the presented KKT algorithm shows an advantage over the PI controller in both reference current tracking and THD currents’ reduction at the grid side
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