In the realm of renewable energy, optimizing the performance of photovoltaic (PV) systems is paramount. One of the key challenges is extracting the maximum active power efficiently, especially considering the dynamic nature of solar irradiation. In this article, we delve into the application of Extremum Seeking Control (ESC) as a method to achieve this optimization, comparing it with the commonly used Maximum Power Point Tracking (MPPT) algorithm. Our focus lies on implementing ESC using Simulink version R2019 and showcasing its effectiveness in real-time simulations.
Introduction
In this work, we explore a sophisticated approach to maximizing the active power output of PV systems. We'll cover the theoretical foundations of Extremum Seeking Control, its practical implementation in Simulink, and the compelling results obtained through simulations.
Theory of Extremum Seeking Control
The core objective of Extremum Seeking Control is to identify the system input that maximizes a predefined objective function tied to the system's output. This methodology proves particularly valuable for nonlinear systems lacking precise plant models.
The control scheme, as depicted in Figure 1, involves introducing a disturbance into the control signal to ascertain the gradient of the objective signal concerning the control signal. This technique adapts dynamically to varying system dynamics influenced by solar irradiation changes.
Implementation in Simulink
Figure 3 illustrates a practical implementation of the ESC scheme within Simulink. By introducing a sinusoidal disturbance to the control signal prediction and leveraging gradient calculations, we navigate towards local maxima of the objective function concerning the control signal.
However, certain challenges arise, such as encountering gradient stagnation for specific control signal ranges. To address this, we modify the objective function to ensure continuous optimization, enhancing the system's responsiveness and performance.
Simulation
The control signal is Iref and the variable to control is Pout. A plot is made to see their relationship.
A function with an absolute maximum is obtained. However for values of Iref < 0 or Iref > Ipo it is seen that the derivative of Iref with respect Pout is equal to 0. Then the gradient at any point of that domain will be 0 for 2 directions and the control signal will remain stagnant at that point. Therefore a modification of the objective function is made to solve this problem. We can implement this algorithm:
For Pout <0, then → Pout = Pout -sign (Iref) * Iref * 5 - Pmin
The relationship between Iref-Pout has been modified to make an objective function that maximizes the power and solve the previous problem of gradient 0. It is observed that although this objective function is not derivable, the gradient values can be obtained since the algorithm is based on directional increments to draw the gradient. Our system is implemented in Simulink.
The estimation of Iref is added to a small sinusoidal disturbance signal to obtain the new input to the plant. We obtain Pout, the value which is introduced into the objective function created above. This loop runs indefinitely. The values of the amplitude and frequency of the disturbance, as well as the gain of the integrator, are hyperparameters to modify depending on the system to control. In this case, I have chosen an amplitude of 0.05 and a frequency of 5Hz.
In Figure 7, the algorithm described above is performed.
if Pout <0, then → Pout = Pout -sign (Iref) * Iref * 5 - Pmin else Pout = Pout
Results
Simulation is performed for time-varying irradiation, and the following results are obtained.
Figure 9 shows that extremum seeking control is a very optimal control for the photovoltaic system. The results obtained with the MPPT algorithm are also obtained.
Conclusion
In conclusion, Extremum Seeking Control emerges as a highly effective methodology for extracting maximum active power from PV systems. Its ability to navigate dynamic environmental conditions and optimize system performance sets it apart from conventional MPPT techniques. The continuous refinement of ESC parameters opens doors for seamless integration into real-world PV plant operations, paving the way for enhanced efficiency and sustainability in renewable energy applications.