Date of Award


Publication Type


Degree Name



Mechanical, Automotive, and Materials Engineering


Dynamic study, Epsilon constraint method, Multi-objective optimization, Particle swarm optimization, Thermoelectric generator, TOPSIS analysis


P. Henshaw


D. S-K. Ting



Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Waste heat recovery plays an important role for alleviating the energy crisis and mitigating climate change. The thermoelectrical generator (TEG), a solid energy convertor, is a promising technology. However, the performance of a TEG is sensitive to its geometric structure and working conditions. An improved geometric structure and matching to the working conditions can make a TEG fully utilize its thermoelectrical conversion potential.

The TEG optimization is a kind of combinatorial problem. An effective algorithm is needed to optimize a TEG’s performance. The particle swarm optimization (PSO) algorithm is introduced in this study to optimize a TEG’s output power, efficiency, and even some economic indices (exergy efficiency and levelized cost of energy (LOCE)). In order to address the premature convergence (which is one of the main challenges for algorithms), a mutation program is used to improve the traditional PSO method. Meanwhile, many parameter combinations related to the algorithm (such as mutation factor (mu), cognitive parameter (C1), and social parameter (C2)) were tried. The mutation particle swarm optimization (M-PSO) is an effective algorithm to optimize the performance for the TEG. The results indicate that it is difficult to reach the optimal state in different performance indices simultaneously, necessitating a multi-objective optimization. Although the multi-objective optimization can be solved by the M-PSO using a weighted approach, there are biases introduced when selecting a weighting factor. In order to improve the multi-objective optimization further, the ε-constraint method is introduced into the M-PSO algorithm. Through optimizing of the TEG by this method, a series of acceptable solutions are acquired, which are named Pareto solutions. After that, the technique for order preference by similarity ideal solution (TOPSIS) method was used to analyze these Pareto solutions to search for a TOPSIS ideal solution.

Additionally, a hyperbolic-shaped variable cross-section TEG was simulated. Based on a comprehensive thermodynamic model, it appears that the hyperbolic TEG is equipped with higher output power and efficiency compared to the constant cross-section one. The study also indicates that the four non-dimensional parameters (shape parameter (β), area ratio (μ), temperature ratio (θ), and resistance ratio (rx)) have considerable influences on the hyperbolic TEG performance. In this way, it is necessary to optimize the TEG power generation and efficiency in the variable searching space of these parameters. However, differing from the traditional optimization, it is necessary to solve the control equations in every iteration when searching for an optimal configuration based on the comprehensive model. In order to do this, the Dual-MPSO algorithm was used in the optimizing research.

Finally, a transient TEG model is established using the SIMULINK. Under a periodic source temperature varied with a sinusoidal function, it is verified that the hyperbolic TEG has a higher mean power output and overall efficiency compared to that of the traditional one. Moreover, the results indicate that the shape parameter (β) and the period of the source temperature have considerable influences on the mean power output and overall efficiency of the hyperbolic TEG.