Optimal design study of thermoacoustic regenerator with lexicographic optimization method

Abstract: Purpose – This paper aims to illustrate the use of the augmented epsilon-constraint method implemented in general algebraic modelling system (GAMS), aimed at optimizing the geometry of a thermoacoustic regenerator. Thermoacoustic heat engines provide a practical solution to the problem of heat management where heat can be pumped or spot cooling can be produced. However, the most inhibiting characteristic of thermoacoustic cooling is their current lack of efficiencies. Design/methodology/approach – Lexicographic optimization is presented as an alternative optimization technique to the common used weighting methods. This approach establishes a hierarchical order among all the optimization objectives instead of giving them a specific (and most of the time, arbitrary) weight. Findings – A practical example is given, in a hypothetical scenario, showing how the proposed optimization technique may help thermoacoustic regenerator designers to identify Pareto optimal solutions when dealing with geometric parameters. This study highlights the fact that the geometrical parameters are interdependent, which support the use of a multi-objective approach for optimization in thermoacoustic. Originality/value – The research output from this paper can be a valuable resource to support designers in building efficient thermoacoustic device. The research illustrates the use of a lexicographic optimization to provide more meaningful results describing the geometry of thermoacoustic regenerator. It applies the epsilon-constraint method (AUGMENCON) to solve a five-criteria mixed integer non-linear problem implemented in GAMS (GAM software)

Multiobjective optimization of a thermoacoustic regenerator

Abstract: This paper presents a new mathematical approach for optimizing the geometry of a thermoacoustic regenerator, aimed at producing efficient thermoacoustic engines. Optimal set of parameters describing the device are computed for a chosen thermoacoustic couple to illustrate this approach. Hence, a non-linear multiobjective problem is formulated in GAMS and solved using Lindoglobal solver. Lexicographic optimization is presented as an alternative optimization technique to the common used weighting methods. This approach establishes a hierarchical order among all the optimization objectives instead of giving them a specific (and most of the time, arbitrary) weight. In this work, the optimization criteria are chosen as work output, viscous resistance as well as thermal losses that are typically disregarded when modeling the device. A practical example is given, in a hypothetical scenario, showing how the proposed optimization technique may help thermoacoustic regenerator designers to identify Pareto optimal solutions when dealing with geometric parameters

Modelling of thermo-acoustic refrigerators using general algebraic modelling system

Abstract: While thermo-acoustic refrigeration is new among emerging technology, it shows strong potential towards the development of sustainable and renewable energy systems by utilising a sound wave to remove the heat. This work discusses a new mathematical programming approach that provides fast initial engineering estimates to initial design calculations, describing the optimal geometry of thermo-acoustic refrigerators. Three different criteria describing their performances were taken into account: maximum cooling, best coefficient of performance and acoustic power loss. As the stack has been identified as the heart of the device where heat transfer takes place, this new approach aims to optimise its geometrical parameters: namely, the stack position, the stack length, the blockage ratio and the stack pore sizes. Hence, the optimisation task is formulated as a three-criterion nonlinear programming problem with discontinuous derivatives. This approach was implemented in the General Algebraic Modelling Systems. The unique characteristic of this research is the computation of all efficient optimal solutions, allowing the decision maker to identify the most efficient solution. The proposed modelling approach was investigated experimentally to evaluate its ability to predict the best parameters describing the geometry of the stack. Similar trends were obtained to support the use of the proposed approach in the design of thermo-acoustic refrigerators

Lexicographic multi-objective optimization of thermoacoustic refrigerator’s stack

Abstract: This work develops a novel mathematical programming model to optimize the performance of a simple thermoacoustic refrigerator (TAR). This study aims to optimize the geometric parameters namely the stack position, the stack length, the blockage ratio and the plate spacing involved in designing TARs. System parameters and constraints that capture the underlying thermoacoustic dynamics have been used to define the models. The cooling load, the coefficient of performance and the acoustic power loss have been used to measure the performance of the device. The optimization task is formulated as a three-criterion nonlinear programming problem with discontinuous derivatives (DNLP). Since we optimize multiple objectives simultaneously, each objective component has been given a weighting factor to provide appropriate user-defined emphasis. A practical example is given to illustrate the approach. We have determined a design statement of a stack describing how the geometrical parameters describing would change if emphasis is given to one objective in particular. We also considered optimization of multiple objectives components simultaneously and identify global optimal solutions describing the stack geometry using a lexicographic multiobjective optimization scheme. Additionally, this approach illustrates the difference between a design for maximum cooling and best coefficient of performance of a simple TAR

Thermal losses considerations in thermo-acoustic engine design

Abstract: Thermo-acoustic cooling as an environmentally friendly refrigeration system is one of the research areas being pursued. Although not commercially available and simple to fabricate, the designing of thermo-acoustic coolers involves significant technical challenges. Many fundamental issues related to the thermo-acoustic effects and the associated heat transfer must be addressed. The most inhibiting characteristic of current thermo-acoustic cooling devices is the lack of efficiency. The stack has been identified as the heart of the device where the heat transfer takes place. Improving its performance will make thermo-acoustic technology more attractive. Most of the existing efforts have not taken thermal losses to the surroundings into account in the derivation of the models. Five different parameters describing the stack geometry and the angular frequency of the standing wave are considered. This work explores the use of a multi-objective optimization approach to model and to optimize the performance of a simple thermo-acoustic engine. The present study highlights the importance of thermal losses in the modelling of small-scale thermo-acoustic engines using a multi-objective approach. The unique characteristic of this research is the computing of all efficient optimal solutions describing the best geometrical configuration of thermo-acoustic engines

A quadratic convex approximation for optimal operation of battery energy storage systems in DC distribution networks

This paper proposes a quadratic convex model for optimal operation of battery energy storage systems in a direct current (DC) network that approximates the original nonlinear non-convex one. The proposed quadratic convex model uses Taylor’s series expansion to transform the product between voltage variables in the power balance equations into a linear combination of them. Numerical simulations in the general algebraic modeling system (GAMS) for both models show small diferences in the daily energy losses, which are lower than 3.00%. The main advantage of the proposed quadratic model is that its optimal solution is achievable with interior point methods guaranteeing its uniqueness (convexity properties of the solution space and objective function), which is not possible to guarantee with the exact nonlinear non-convex model. The 30-bus DC test feeder with four distributed generators (with power generation forecast via artifcial neural networks with errors lower than 1% between real and predicted generation curves) and three batteries is used to validate the proposed convex and exact models. Numerical results obtained by GAMS show the efectiveness of the proposed quadratic convex model for diferent simulation scenarios tested, which was confrmed by the CVX tool for convex optimization in MATLA

Optimal Placement and Sizing of Wind Generators in AC Grids Considering Reactive Power Capability and Wind Speed Curves

This paper presents an optimization model for the optimal placement and sizing of wind turbines, considering their reactive power capacity, wind speed, and demand curves. The optimization model is nonlinear and is focused on minimizing power losses in AC distribution networks. Also, paired wind turbine and power conversion systems are treated via chargeability factor η at the peak hour. This factor represents the percentage of usage of the power conversion system in the nominal wind speed conditions, and allows to support reactive power dynamically during all periods of the day as a function of the distribution system requirements. In addition, an artificial neural network is used for short-term forecasting to deal with uncertainties in wind power generation. We assume that the number of wind power distributed generators could be from zero to three generators integrated into the system, considering unit power factors and reactive power injections to follow up the effect of reactive power compensation in the daily operation. The General Algebraic Modeling System (GAMS) is employed to solve the proposed optimization model

A mixed-integer nonlinear programming model for optimal reconfiguration of DC distribution feeders

This paper deals with the optimal reconfiguration problem of DC distribution networks by proposing a new mixed-integer nonlinear programming (MINLP) formulation. This MINLP model focuses on minimising the power losses in the distribution lines by reformulating the classical power balance equations through a branch-to-node incidence matrix. The general algebraic modelling system (GAMS) is chosen as a solution tool, showing in tutorial form the implementation of the proposed MINLP model in a 6-nodes test feeder with 10 candidate lines. The validation of the MINLP formulation is performed in two classical 10-nodes DC test feeders. These are typically used for power flow and optimal power flow analyses. Numerical results demonstrate that power losses are reduced by about 16% when the optimal reconfiguration plan is found. The numerical validations are made in the GAMS software licensed by Universidad Tecnológica de Bolívar

On the mathematical modeling for optimal selecting of calibers of conductors in DC radial distribution networks: An MINLP approach

This paper addresses the problem of optimal conductor selection in direct current (DC) distribution networks with radial topology. A nonlinear mixed-integer programming model (MINLP) is developed through a branch-to-node incidence matrix. An important contribution is that the proposed MINLP model integrates a set of constraints related to the telescopic structure of the network, which allows reducing installation costs. The proposed model also includes a time-domain dependency that helps analyze the DC network under different load conditions, including renewable generation and battery energy storage systems, and different voltage regulation operative consigns. The objective function of the proposed model is made up of the total investment in conductors and the total cost of energy losses in one year of operation. These components of the objective function show multi-objective behavior. For this reason, different simulation scenarios are performed to identify their effects on the final grid configuration. An illustrative 10-nodes medium-voltage DC grid with 9 lines is used to carry out all the simulations through the General Algebraic Modeling System known as GAMS

Optimal Location-Reallocation of Battery Energy Storage Systems in DC Microgrids

This paper deals with the problem of optimal location and reallocation of battery energy storage systems (BESS) in direct current (dc) microgrids with constant power loads. The optimization model that represents this problem is formulated with two objective functions. The first model corresponds to the minimization of the total daily cost of buying energy in the spot market by conventional generators and the second to the minimization of the costs of the daily energy losses in all branches of the network. Both the models are constrained by classical nonlinear power flow equations, distributed generation capabilities, and voltage regulation, among others. These formulations generate a nonlinear mixed-integer programming (MINLP) model that requires special methods to be solved. A dc microgrid composed of 21-nodes with existing BESS is used for validating the proposed mathematical formula. This system allows to identify the optimal location or reallocation points for these batteries by improving the daily operative costs regarding the base cases. All the simulations are conducted via the general algebraic modeling system, widely known as the General Algebraic Modeling System (GAMS)