Multi-Objective Optimization of Two-Stage Thermo-Electric Cooler Using Differential Evolution: MO Optimization of TEC Using DE

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Introduction

TEC is solid state cooling devices. The operational principle of TEC is not similar to vapor-cycle based refrigerator, they use the Peltier effect through p-type and n-type semiconductor elements (Zhang, Mui, & Tarin, 2010). TEC is used to convert electrical energy into a temperature gradient. TEC uses no refrigerant and have no dynamic parts which make these devices highly reliable and require low maintenance. TEC generates no electrical or acoustical noise and are ecologically clean. TEC is compact in terms of size, light weight and have high precision in temperature control.

TEC can be a single-stage or multi-stages type. The commercially available single-stage TEC (STEC) (Figure 1) can yield a maximum temperature difference of about 60-70^oK when the hot side remains at room temperature (Huang, Wang, Cheng, & Lin, 2013). However, when a large temperature difference is required for some special applications, STEC will not be qualified. To enlarge the maximum temperature difference of TEC two-stage TEC (TTEC) (Figure 1) or multistage TEC can be used. Additional stage increases achievable but also leads to more power consumption and the reduction of efficiency of thermo-electric system (Wang, Wang, & Xu, 2014).

Figure 1.

Single-stage TEC (left) and two-stage TEC (right) (Ferrotec)

The application of TEC has been partitioned by their relatively low energy conversion efficiency and ability to dissipate only a limited amount of heat flux (Enescu & Virjoghe, 2014). Two parameters play a crucial role in characterization of TEC, one is cooling rate defined as the heat absorbed by the cold end of the TEC, the other one is coefficient of performance (COP) defined as the ratio of cooling capacity to electrical power consumed by the TEC. TEC operate at about 5-10% of Carnot cycle COP whereas compressor based refrigerators normally operates at more than 30% (Rowe, 2005). In TTEC, the cooling capacity, COP are related to the material properties of semiconductor, ratio number of semiconductor elements between the two stages and the applied current of each stage.

The main drawback of TEC is the poor COP and low cooling rate. They can be improved personally or simultaneously. From the parameters of the equation of TEC performance, we can group them into three categories which are specifications, material properties and design parameter (Rowe, 2005). The specification for TEC is the required temperature different and electric power consumption, the required value of cooling rate with or without satisfying respective COP. The specifications are usually provided by customers depending on the requirement of a particular application. The material parameters are restricted by currently materials and module fabricating technologies. Consequently, the main objective of the TEC design to determine a set of design parameters which meet the required specifications or create the best performance at minimum cost.

In optimization the design parameters of TTEC, (Cheng & Shih, 2006) used GA to maximize separately the cooling rate and COP of TTEC. The author had considered the effect of thermal resistance and determined the optimum value of input current and number of legs for two different design configurations of TTEC. The optimal search in this GA converges so rapidly with over 30 runs. The optimal results showed reliability when checking with obtained from Xuan’s work (Xuan, Ng, Yap, & Chua, 2002) and showed that GA had a robust behavior and effective search ability. (Venkata Rao & Patel, 2013) used modified teaching-learning-based optimization (TLBO) in MOO the dimensional structure of two different design configuration of TTEC. TLBO based on the effect of the influence of a teacher on the output learners in a class. The algorithm mimics the teaching-learning ability of teacher and learners in a classroom, the teacher and learners are the two vital components of the algorithm. TLBO was modified and applied successfully to the MOO of TTEC and find the Pareto front of maximum cooling and maximum COP. The determination of the number of semiconductor elements in hot stage and cold stage as well as the supply current to the hot stage and the cold stage were considered as search variables.

Key Terms in this Chapter

Meta-Heuristic: Is a higher-level procedure or heuristic designed to find, generate, or select a lower-level procedure or heuristic (partial search algorithm) that may provide a sufficiently good solution to an optimization problem, especially with incomplete or imperfect information or limited computation capacity. Meta-heuristic may make few assumptions about the optimization problem being solved, and so they may be usable for a variety of problems.

Thermo-Electrics Coolers: Uses the Peltier effect to create a heat flux between the junctions of two different types of materials. A Peltier cooler, heater, or thermoelectric heat pump is a solid-state active heat pump which transfers heat from one side of the device to the other, with consumption of electrical energy, depending on the direction of the current. Such an instrument is also called a Peltier device, Peltier heat pump, solid state refrigerator, or thermoelectric cooler (TEC). They can be used either for heating or for cooling (refrigeration), although in practice the main application is cooling. It can also be used as a temperature controller that either heats or cools.

Computational Effort: While meta-heuristic produce superior solutions are important, the speed of computation is a key factor. There are many portions of the process should be time, including time to best-found solution, total running time and time per phase. In this research, total running time is focused more than the rest. This is the algorithm’s execution time prior to termination by its stopping condition.

Genetic Algorithm: Is a search meta-heuristic that mimics the process of natural selection. This meta-heuristic routinely used to generate useful solutions to optimization and search problems. Genetic algorithms belong to the larger class of evolutionary algorithms which generate solutions to optimization problems using techniques inspired by natural evolution, such as inheritance, mutation, selection and crossover.

Thermodynamics: Is a branch of physics concerned with heat and temperature and their relation to energy and work. It defines macroscopic variables, such as internal energy, entropy, and pressure that partly describe a body of matter or radiation. It states that the behavior of those variables is subject to general constraints that are common to all materials, not the peculiar properties of particular materials. These general constraints are expressed in the four laws of thermodynamics. Thermodynamics describes the bulk behavior of the body, not the microscopic behaviors of the very large numbers of its microscopic constituents, such as molecules. Its laws are explained by statistical mechanics, in terms of the microscopic constituents. Thermodynamics applies to a wide variety of topics in science and engineering.

Robust Optimization: Is a field of optimization theory that deals with optimization problems in which a certain measure of robustness is sought against uncertainty that can be represented as deterministic variability in the value of the parameters of the problem itself and/or its solution. There are a number of classification criteria for robust optimization problems/models. In particular, one can distinguish between problems dealing with local and global models of robustness; and between probabilistic and non-probabilistic models of robustness. Modern robust optimization deals primarily with non-probabilistic models of robustness that are worst case oriented and as such usually deploy Wald's maximum models.

Hybrid Algorithm: Is an algorithm that combines two or more other algorithms that solve the same problem, either choosing one (depending on the data), or switching between them over the course of the algorithm. This is generally done to combine desired features of each, so that the overall algorithm is better than the individual components. “Hybrid algorithm” does not refer to simply combining multiple algorithms to solve a different problem – many algorithms can be considered as combinations of simpler pieces – but only to combining algorithms that solve the same problem, but differ in other characteristics, notably performance.

Coefficient of Performance: Or COP of a heat pump is a ratio of heating or cooling provided to electrical energy consumed. Higher COPs equate to lower operating costs. The COP may exceed 1, because it is a ratio of output – loss, unlike the thermal efficiency ratio of output – Input energy. For complete systems, COP should include energy consumption of all auxiliaries. COP is highly dependent on operating conditions, especially absolute temperature and relative temperature between sink and system, and is often graphed or averaged against expected conditions.