Energy systems generate a lot of waste heat that thermoelectric generators can help recover. ©fhm/ Moment/ Getty Images

Game thinking boosts energy recovery 


A Sudoku-inspired method optimizes thermoelectric generators, improving performance and reducing the cost of recovering wasted energy.

Almost every machine, device, living organism or chemical reaction leaks some of its energy as heat due to inefficiencies such as friction and electrical resistance. For industry, vehicles and power plants, this wasted energy is a missed opportunity. What if we could turn it into electricity and reduce carbon emissions at the same time?  

That’s what thermoelectric generators (TEGs) promise. “TEGs offer a promising pathway to improve overall energy efficiency and reduce greenhouse gas emissions by recovering and converting otherwise wasted thermal energy into useful electricity,” says Ehab El-Saadany from Khalifa University’s Advanced Power and Energy Center. “They have no moving parts and are highly reliable.” 

“Thermoelectric generators offer a promising pathway to improve overall energy efficiency and reduce greenhouse gas emissions by recovering and converting otherwise wasted thermal energy into useful electricity.” 

Ehab El-Saadany 

But there’s a catch: TEGs themselves need to get more efficient. To tackle that problem, El-Saadany, working with colleagues from Egypt, Canada and India, used Sudoku-inspired rules to optimize the configuration of TEG arrays, improving power output without the need for complicated dynamic control systems. 

Thermoelectric generators rely on the Seebeck effect—where an electrical potential difference exists between two points on a conductor when they are at different temperatures. The challenge is to harness this effect over large areas. One approach is to electrically connect many individual TEGs in an array. But the performance of the array is limited by uneven temperature gradients, causing some modules to produce more electricity than others and reducing the efficiency of the whole array. 

“Non-uniform temperature fields lead to uneven voltage and current outputs from individual TEGs,” El-Saadany explains. “When these are connected in a fixed electrical configuration, mismatches among modules can cause current bottlenecks, reduce the total power output, and increase internal dissipation.” One approach to solving the problem is to use switches to change connections to balance the power output, but this makes the system more complex and expensive.  

As an alternative, El-Saadany and his colleagues have developed an Optimized Static Configuration (OSC) method that identifies electrical connections that optimize performance for the whole array, without the need for extra switches and sensors. The OSC method treats TEG modules like numbers in a Sudoku game, arranging them so that the temperature differences are spread out evenly.

Testing their approach in simulations and experiments, the team found the power output of six-by-six and nine-by-nine TEG arrays improved by more than 6.5% compared with a standard configuration. The OSC also saves on the costs of the arrays by reducing the need for switches and sensors.

“Our next steps will include extending the optimization framework to larger and more complex array topologies, and testing the approach in real-world industrial, renewable and vehicular environments,” says El-Saadany. 

Reference

Yousri, D., Farag, H.E.Z., Sukanya, V, Bijukumar, B. & El-Saadany, E. Optimized static configuration for output power maximization of thermoelectric generator arrays with hardware validation. Appl. Energy, 377, 124598, 2025. | Article 

Related articles