Elsevier

Applied Energy

Volume 237, 1 March 2019, Pages 210-226
Applied Energy

A neural network approach to the combined multi-objective optimization of the thermodynamic cycle and the radial inflow turbine for Organic Rankine cycle applications

https://doi.org/10.1016/j.apenergy.2019.01.035Get rights and content

Highlights

  • A novel approach is presented for the optimization of Organic Rankine cycles.

  • A model of in-flow radial turbines for Organic Rankine cycle is described.

  • The approach proved able to reduce the time required for the optimization.

  • The combined optimization of the turbine and the thermodynamic cycle is performed.

Abstract

An optimization model based on the use of Neural Network surrogate models for the multi-objective optimization of small scale Organic Rankine Cycles is presented, which couples the optimal selection of the thermodynamic parameters of the cycle with the main design parameters of In-Flow Radial turbines. The proposed approach proved well suited in the resolution of the highly non-linear constrained optimization problems, typical of the design of energy systems. Indeed the use of a surrogate model allows to adopt gradient based methods that are computationally more efficient and accurate than conventional derivative-free optimization algorithms.

The intensive numerical experiments demonstrate that assuming a constant efficiency for the In-Flow Radial turbine leads to an error in the evaluation of the performance of the system of up to 50% and that the optimization approach proposed improves the accuracy of the solution and it reduces the computational time required to reach it by two orders of magnitude. An holistic approach in which the turbine and the thermodynamic cycle are designed simultaneously and the use of multi-objective optimization proved to be essential for the design of Organic Rankine cycles that satisfy both size and performance criteria.

Introduction

Organic Rankine Cycle (ORC) is a consolidated technology to exploit thermal energy from wasted heat in low/medium temperature (400–700K) range. Although the ORC technology has been widely installed to produce power in the MW range [1], the installation of ORC machines of power in the kW range still finds little practical application. In fact, when scaling down ORC systems, additional design issues arise which still limit the widespread availability of the technology. Particular effort has been recently expended by researchers to try to optimize the performance of ORC systems in the production of power in the kW range. Tocci et al. [2], in their techno-economic review of ORC applications, stated that particular attention needs to be taken when designing the turbine, in that its performance plays a crucial role in the definition of the overall efficiency of ORC systems; therefore, a preliminary design of the turbine needs to be considered in the process of optimization of the thermodynamic parameters of the cycle.

Even though it is usual practice to define the thermodynamic cycle as a first step and subsequently to design the turbine, recently, researchers started to consider the effect of the thermodynamic parameters of ORC cycles on the performance of the turbine at an early design stage. Uusitalo et al. [3] addressed the subject of combining the design of the ORC cycle’s thermodynamics and of the turbine for low power applications, discussing the performance of different working fluids. Ventura and Rowlands [4] proposed a tool to couple the design of radial turbines to the selection of the thermodynamic parameters of the cycle. La Seta et al. [5] derived an optimization tool to carry out the simultaneous optimization of both the cycle’s and the turbine’s design. Zhai et al. [6] developed an optimization tool for the simultaneous design of the ORC cycle and of the radial turbine using genetic algorithms. Lazzaretto and Manente [7] proposed an optimization procedure of the thermodynamic cycle of the ORC in which a specific correlation for the efficiency of the turbine is included: they derived correlations for both radial and axial turbines.

The combined optimization of the thermodynamic parameters of the cycle and of the design parameters of the turbine implies the need to solve a highly non-linear constrained optimization problem, which requires the use of thermodynamic libraries to calculate the thermo-physical properties of the fluids involved in the transformations. It is usual practice in the energy field to use derivative-free optimization methods, such as artificial bees colonies [8] and genetic algorithms [9], to solve highly nonlinear black-box optimization problems. However, derivative-free optimization algorithms have the disadvantage of being intrinsically slow, due both to the high computational cost of functions’ evaluations and to the large number of such evaluations. In addition, they are less accurate than the algorithms based on the gradient method, i.e. those that use the derivative of the objective function and of the constraints during the optimization process.

In this work, Neural Networks are used to derive surrogate models and to overcome the limitation of derivative-free optimization algorithms. Artificial Neural Networks (ANNs) allow to derive approximated mathematical models of the nonlinear system based on samples. The resulting model can be conveniently applied to the combined optimization of the thermodynamic parameters of the ORC cycle and of the design parameters of the turbine. The use of Neural Networks to improve optimization processes has been discussed in previous works [10]. ANN models provide an intrinsically continuous and differentiable correlation function that allows for the use of analytical gradient methods for its optimization [11]. The use of gradient methods, as opposed to derivative-free methods commonly used in ORC optimization problems, allows to reach more accurate results in an amount of time that is one order of magnitude smaller with respect to that of derivative-free optimization algorithms [12]. To the authors’ knowledge, no one has ever applied the proposed methodology to the combined optimization of the thermodynamic cycle and of the design of the turbine of ORC systems. This paper aims at presenting an optimization tool specifically derived for the multi-objective optimization of small scale ORC systems, in which a novel model of radial in-flow turbines coupled to a model of the thermodynamic cycle is converted into a set of ANNs to improve the optimization performance of the highly non linear model of the system.

The paper is organized as follows. Section 2 describes the architecture of the neural network implemented, which has been developed using the platform TensorFlow [13]. Section 3 presents the thermodynamic model of the ORC cycle, the analytical model to derive the performance of IFR turbines, the model to preliminary estimate the size of the heat exchangers and the formulation of the optimization problem to be solved. Section 4 investigates the influence of the thermodynamic parameters of the ORC cycle on the performance of IFR turbines. Section 5 applies the ANN based optimization model to the combined optimization of the thermodynamic parameters of the cycle and of the design parameters of the IFR turbine of a small scale ORC system. Section 6 summarizes the results of the study.

Section snippets

Neural networks

A learning machine can be described as a regression tool capable of deriving a mathematical model by means of a set of samples representing the process and available in the form (xp,y¯p), for p=1,,P, where xpRn represents the features of the input and y¯pRmthe corresponding outputs. These samples can be derived as measures of experiments or using numerical thermodynamic tools. Among learning machines, Artificial Neural networks (ANN) are often selected, since they proved reliable in many

The mathematical models

Section 3 reports the description of the mathematical models considered in this work for the design of small scale ORC systems. The models have been coded using MATLAB [15] whereas the thermodynamic properties of the fluids have been calculated using the thermodynamic library REFPROP [16]. Fig. 2 shows the thermodynamic transformations of a regenerated ORC system on the specific entropy - Temperature diagram. Table 1 provides a brief description of the processes that take place in each of the

Effect of the thermodynamic parameters of the cycle on the performance of the turbine

Section 4 provides an investigation of the effect of the thermodynamic parameters of the ORC cycle on the efficiency of the IFR turbine, to quantify the advantages of the model proposed in this paper over a simplified model that considers a constant value for the isentropic efficiency of the IFR turbine. The objective of this section is twofold. First, the impact of the parameters listed in Table 3 on the isentropic efficiency of the turbine is investigated. Second, the discrepancy in

Optimization of the performance of an organic Rankine cycle system using the neural network approach

Section 5 presents the application of the optimization model described in Section 3 to the optimization of an ORC system for waste heat recovery applications.

The ORC system to be designed is conceived to recover the thermal energy released in the exhaust gasses of a 206kWYC6A280-30 Yuchai engine. A thermal oil loop extracts the thermal energy discharged by the engine in the exhaust gasses via a shell and tube heat exchanger. At steady state conditions, the thermal oil in input to the ORC

Conclusions

This work proposes a novel methodology based on machine learning techniques for the combined optimization of the thermodynamic cycle and of the radial in-flow turbine for small scale Organic Rankine cycle applications. The machine learning approach consists in converting the physical model of the thermodynamic cycle and of the components of the plant into a set of continuous and differentiable functions. This approach allows for the use of gradient based methods for the optimization, as opposed

Acknowledgments

Entropea Labs is acknowledged for the economic and technical support provided during the completion of this study.

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