# Evolutionary Maximization of Energy Amount Harvested by Means of Panel of Thermoelectric Modules
## 4 Simulation Experiment  
The proposed algorithm of evolutionary MPPT as well as standard, widely known, called perturbation and observation (P&O) and incremental conductance (INC) methods [13; 14; 23; 24] were implemented in a Matlab environment. These three techniques were used to search for the optimal duty cycles of boost converter (Figure 4a) signals which control MOSFET transistor switching (Figure 4b) in \(N\) = 10 boost converter sections with MPP defined by different matching curves from Figure 4c. This example normalized functions of load resistance \(R_{o}\) = 100 \(\Omega\) power dissipated vs. duty cycle of switching signal were established for internal resistances \(R_{i}\) selected from the range \((10,100)\Omega\). As it may be noticed, the maximal point strongly depends on sourcing circuits parameters and it is possible to track this optimum by means of duty cycle of switching signal regulation.  
The three completely different starting points were assumed for tests and are cross denoted in Figure 4c (sets of start points 1, 2 and 3). The initial duty cycles assumed for MPPT methods competing during tests are the same and are placed at: minimum, medium and maximum for all the optimized control signals of boost converters (i.e., at 0.2%, 50% and 99% of duty cycles, respectively). The proposed locations of coefficients of duty cycles start vector \(\mathbf{D}\) allow to test the competitive algorithms convergence speed from the initial points differently far from global optimum. Optimization was started for \(D_{MX}\) = 10,000 discrete levels that means resolution \(\Delta d\) = 0.01% of duty cycle adjusting preciseness, identical for all tested methods. Initial parameters assumed for evolutionary system were: size of population \(K\) = 20 chromosomes; allowed maximal correction for one iteration \(C_{MX}\) = 1000; minimal chance for reproduction \(P_{mn}\) = 0.2; crossover and mutation probabilities \(P_{cr}\) = 0.9 and \(P_{mn}\) = 0.2, respectively.  
The computational effectiveness for the described tests is shown in Figure 5, where the time quality progresses of the proposed evolutionary and classical approaches are presented (time vs. the best phenotype normalized fitness values). For each considered case, the proposed MPPT algorithm found the best solution up to \(t_{mx1}\approx 30\) ms, however the P&O algorithm needs \(t_{mx1}\approx 430\) ms maximally and very similar time cost in the case of INC approach (for the same tasks, on the same PC machine). This means about 14 times faster convergence of the proposed evolutionary MPPT method.  
Figure 4: Simulation verification: (**a**) analyzed boost topology, (**b**) example signal controlling output voltage, (**c**) normalized load power vs. transistor gate signal duty cycle matching curves.  
Besides, Figure 6 illustrates a normalized level of average fitness value spreading among generations. As may be seen, the initial, poor levels of the phenotypes qualities grow rapidly and stabilize after about 50 ms. This tendency proves high convergence speed of the proposed algorithm that probes solution space in many points defined by chromosome codes. It is worth noticing that when the best solution is found (i.e., after \(t_{m\text{x1}}\approx 30\) ms), average quality of population varies a little, too. This means that MPP is tracked (tested) still and in case of operational point of the TE system changes, the newly located optimum will be searched and found again. This is the effect of generations successing made in a specific way explained in Section 3.2 as well as genes mutations run during the main infinite loop of the evolutionary algorithm. Finally, thanks to a very high mean measure of electric power transferred to the system load, this system will assure very good total effectiveness of thermal- to electric-energy conversion.