Optimization of triple-pressure combined-cycle power plants by generalized disjunctive programming and extrinsic functions

Highlights

• Dynamic-link libraries implemented in the C programming language.

• Successful application of extrinsic functions and GDP model to optimize CCPPs.

• Improved optimal solutions with respect to reference cases.

Abstract

A new mathematical framework for optimal synthesis, design, and operation of triple-pressure steam-reheat combined-cycle power plants (CCPP) is presented. A superstructure-based representation of the process, which embeds a large number of candidate configurations, is first proposed. Then, a generalized disjunctive programming (GDP) mathematical model is derived from it. Series, parallel, and combined series-parallel arrangements of heat exchangers are simultaneously embedded. Extrinsic functions executed outside GAMS from dynamic-link libraries (DLL) are used to estimate the thermodynamic properties of the working fluids. As a main result, improved process configurations with respect to two reported reference cases were found. The total heat transfer areas calculated in this work are by around 15% and 26% lower than those corresponding to the reference cases.

This paper contributes to the literature in two ways: (i) with a disjunctive optimization model of natural gas CCPP and the corresponding solution strategy, and (ii) with improved HRSG configurations.

Introduction

Combined cycle power plants (CCPPs) are widely used in industrial plants or larger distribution networks to provide both electricity and heat as energy vectors. The overall thermal efficiency of combined-cycle power plants (CCPPs) depends strongly on the gas and steam turbine technologies as well as the configuration and design of the heat recovery steam generators (HRSGs). Improved CCPPs lead to reduce fuel consumption and, consequently, the greenhouse gas emissions. The configuration, design, and operating conditions of HRSGs are critical because they couple the gas turbine-based topping cycle with the steam turbine-based bottoming cycle. The exhaust waste energy of gas turbines can be recovered in HRSGs using different reheat cycles: from a single-pressure to triple-pressure cycles. In a CCPP, the optimal configuration of the HRSG depends strongly on the desired level of electricity to be generated, and, if it is the case, on the amount of steam required as utility heating if the CCPP is integrated to an industrial plant. Therefore, it is of great interest to still study the optimization of CCPPs through detailed process models and simultaneous optimization methods (Blumberg et al., 2017; Nadir and Ghenaiet, 2015), as it is proposed in this paper.

There are many published papers addressing the mathematical modeling and optimization of combined heat and power (CHP) generation systems, which differ in the criteria used to solve the resulting mathematical models (energy, exergy, cost, exergo-economic analyses, simulation-based optimization, simultaneous optimization, or meta-heuristic approaches), the number of optimization criteria (single or multi-objective optimization), and/or the model assumptions and design specifications considered for the analysis (fixed or variable process configurations, fixed or variable number of pressure levels, fixed or variable amount of steam and/or electricity to be generated).

Exergy and exergo-economic analyses of energy conversion systems to systematically locate the most inefficient system components have been used as a valuable decision-making tool (Bracco and Siri, 2010; Boyaghchi and Molaie, 2015; Bakhshmand et al., 2015; Tsatsaronis and Park, 2002; Morosuk and Tsatsaronis, 2011; Tsatsaronis, 1999; Sahoo, 2008; Ahmadi and Dincer, 2011). For instance, the retrofit of an already existing process can be improved by switching out and/or introducing new components towards a lower value of the total irreversibility of the system. These analyses are iterative in nature and contribute to improving a thermal system as a whole or at a component level. Although the calculation of exergy is more complex than the calculation of energy, the exergy analysis allows quantifying more accurately the types, causes, and locations of inefficiencies. Bakhshmand et al. (2015) performed an exergo-economic analysis and optimization of a triple-pressure combined cycle. To do this, they implemented a simulation code in MATLAB using an evolutionary algorithm. The objective function included both product cost rate and cost rates associated with exergy destruction. The obtained results allowed to propose optimal performance criteria for the studied process. The authors highlighted that this methodology is applicable to optimize steady state operation parameters of a given combined cycle, but it is not suitable to optimize the design of new cycles. Tsatsaronis and Park (2002) and Morosuk and Tsatsaronis (2011) concluded about the advantages of dividing exergy destruction and economic costs into avoidable and unavoidable parts in cogeneration plants (Tsatsaronis and Park, 2002) and simple gas turbine systems (Morosuk and Tsatsaronis, 2011), showing the potential for improvement and the interactions among the system components. In exergy analyses, structural coefficients are used to consider how the overall irreversibility of the cycle is influenced by the local irreversibilities of each component. These structural coefficients can be calculated once the irreversibilities of the components and the whole cycle are known. Therefore, in a system with many components with a large number of discrete decisions, the calculation of these coefficients may require a high number of simulation runs resulting in a time-consuming procedure (Tsatsaronis, 1999). Most exergy and exergo-economic optimization approaches are subjective in nature as they require the designer's interpretation at each iteration to find the final configuration (Sahoo, 2008).

On the other hand, the degree of development of the optimization methods and software, and the availability of powerful computational systems have motivated a renewed interest in applying evolutionary algorithms, mathematical programming techniques in industry, including utility plants and CHP systems.

Applications of evolutionary algorithms – such as simulated annealing (SA) and genetic algorithms (GA) – can be found in Ahmadi and Dincer, 2011; Ahmadi et al., 2012; Kaviri et al., 2012; Mehrpanahi et al., 2019; Ameri et al., 2018; Mehrgoo and Amidpour, 2017; Naserabad et al., 2018; Rezaie et al., 2019). These algorithms have been successfully applied for optimization of power plants with known (fixed) configurations. GAs and derivative-free algorithms are well suitable when no information is available about the gradient of the function at the evaluated points. As GAs can be parallelized with little effort, a lot of paths to the optimum are considered in parallel, which is important in high-complexity problems with many solutions. However, GAs require many parameters, such as the number of generations, population, crossover and mutation rates, and tournament size (number of individuals needed to fill a tournament during selection) that can significantly affect the obtained solutions.

The use of advanced optimization methods and the development of rigorous mathematical models made possible to find new HRSG configurations with the corresponding optimal operating conditions. In this context, there are several articles addressing the study of energy systems, including power and heat plants, which employ gradient-based optimization algorithms and deterministic mixed-integer nonlinear programming techniques (MINLP). The use of MINLP techniques for some representative applications can be found in Kim and Edgar (2014) and particularly in Gopalakrishnan and Kosanovic (2015) for optimal scheduling of CHP plants, in Santos and Urtubey (2018) for optimal energy dispatch in cogeneration plants, in Elsido et al. (2017) for optimal design of organic Rankine cycles (ORC), and in Perez-Uresti et al. (2019) for optimal design of renewable-based utility plants. Other applications include the design of supercritical coal-fired power plants (Wang et al., 2014), short-term planning of cogeneration power plants (Taccari et al., 2015; Bruno et al., 1998), optimal synthesis and design of single and/or dual-purpose seawater desalination plants (Tanvir and Mujtaba, 2008; Mussati et al., 2001; Mussati et al., 2003a; Mussati et al., 2003b; Mussati et al., 2004; Mussati et al., 2005), as well as optimal integration of natural gas combined cycle (NGCC) power plants and CO₂ capture plants (Manassaldi et al., 2014; Mores et al., 2018). Also, MINLP models were successfully applied in other areas such as design of water and wastewater treatment processes (Lu et al., 2017; Faria and Bagajewicz, 2012; Ahmetovic and Grossmann, 2011), heat exchanger network in fuel processing systems for PEM fuel cells (Oliva et al., 2011), design and dispatch of SOFC-based CCHP system (Jing et al., (2017), scheduling and retrofit of refinery preheat trains (Izyan et al., 2014), among other applications. Leon and Martin (2016) addressed the optimization of a combined cycle power plant by considering biogas as fuel. To this end, the authors implemented a mixed integer nonlinear programming (MINLP) model in GAMS and investigated two alternative schemes for the steam production. The calculation of the thermodynamics for the steam was included in the model via surrogate models. Although MINLP formulations are in general hard to solve (especially when the feasible regions are non-convex), they are the most suitable alternative for highly nonlinear and combinatorial optimization problems and large-size mathematical models (problems involving many discrete and continuous decisions and nonlinear equality constraints). In this work, due to the characteristics of the proposed optimization models, the MINLP technique is used.

Despite the existence of many articles concerning with the study of NGCC power plants under different assumptions and using different computational tools, only a few papers considering the simultaneous optimization of the HRSG configuration, process-unit sizes, and operating conditions can be found in literature (Ahadi-Oskui et al., 2010, Martelli et al., 2017; Zhang et al., 2014; Manassaldi et al., 2016; Franco and Giannini, 2006). Ahadi-Oskui et al. (2010) applied mathematical programming methods to simultaneously optimize the configuration and operating conditions of a combined-cycle-based cogeneration plant. To this end, the authors formulated a nonconvex mixed-integer nonlinear problem (MINLP). The resulting model was successfully solved by using their own MINLP solver called LaGO which generates a convex relaxation of the MINLP and applies a Branch and Cut algorithm to the relaxation. Martelli et al. (2017) proposed a two-stage methodology to optimize HRSGs of simple CHP cycles considering external heat/steam sources/users with the possibility of multiple supplementary firing. The proposed methodology was clearly described through an integrated gasification combined cycle (IGCC) plant with CO₂ capture. Zhang et al. (2014) proposed a superstructure-based MINLP model to optimize the configuration of a HRSG embedding several candidate matches between the HRSG and external heat flows. The resulting model is non-convex because of the presence of bilinear terms. The solver BARON (Branch-And-Reduce Optimization Navigator) (Sahinidis, 2000), which is supported in GAMS (General Algebraic Modeling System) (Brooke et al., 1992), was used as a global optimizer. Several case studies considering different pressure levels, with and without steam reheating, were successfully solved. Franco and Giannini (2006) proposed a two-level optimization framework of HRSGs. The former level consists on obtaining the main operating conditions, and the second one the detailed design of each section (sizes and geometric variables). The framework uses the optimal output of the first level as the input to the second level. The authors successfully verified the proposed framework using already existing HRSG structures. Also, simultaneous optimization has been successfully applied to other integrated systems such as biomass Fischer-Tropsch liquids plants. Manassaldi et al. (2016) proposed a discrete and continuous mathematical model to optimize the synthesis and design of dual-pressure HRSGs coupled to two steam turbines. The optimization problem consisted in determining how the heat exchangers (economizers, evaporators, and superheaters) should be connected in the HRSG to maximize the total net power keeping fixed the total heat transfer area, or either to minimize the total heat transfer area keeping fixed the total net power. Also, the optimal operating conditions and size of each process unit were determined simultaneously. The resulting MINLP problem was solved using SBB (Standard Branch and Bound) (Bussieck and Drud, 2001) and the solver CONOPT for the nonlinear problems (NLP) (Drud, 1992). The authors found a novel HRSG configuration not previously reported in the literature. Recently, Bongartz et al. (2020) discussed three bottoming cycles for combined cycle power plants of increasing complexity. The authors employed their open-source deterministic global solver MAiNGO and developed a novel method for constructing relaxations of the functions reported in IAPWS-IF97 to calculate the thermodynamic properties of water and steam. The relaxations were implemented in the MC++ library (https://omega-icl.github.io/mcpp/index.html). The authors concluded that the proposed relaxations considerably reduce the computational time required to find the global optimal solution with respect to McCormick relaxations.

Generalized disjunctive programming (GDP) is an alternative modeling framework to represent optimization problems with discrete and continuous decisions (Chen and Grossmann, 2019). In GDP formulations, discrete decisions are represented in a natural way through the use of disjunctions in the continuous space and logic propositions in the discrete space which are then relaxed, obtaining a MINLP problem (Lee and Grossmann, 2000). GDPs can be reformulated via the convex hull (Grossmann and Lee, 2003) or via Big-M formulations (Grossmann and Ruiz, 2012). Vecchietti et al. (2003) developed the computer code LogMIP to solve discrete/continuous nonlinear optimization problems that are modeled with either algebraic, disjunctive, or hybrid formulations.

This paper is a natural continuation of the work presented by Manassaldi et al. (2016). Here, the superstructure-based model developed by Manassaldi et al. (2016) is used as a basis and it is properly extended to include three pressure levels as well as more candidate process configurations, thus highly increasing the combinatorial nature of the resulting superstructure-based optimization model. From a qualitative point of view, the main differences between this work and that of Manassaldi et al. (2016) are: (a) the type of the combined cycle to be studied (the inclusion of a third pressure level significantly increases the degrees of freedom for the optimization problems), (b) the mathematical modeling strategy (a generalized disjunctive programming (GDP) model is formulated instead of a pure MINLP model), and (c) the solution strategy includes a dynamic-link library (DLL) to estimate the thermodynamic properties of both circulating fluids (flue gas and water) at different conditions (in the case of water as subcooled and saturated liquid, saturated and superheated steam). On the other hand, the main difference between this work and papers published by other authors is the obtaining of improved configurations for a triple-pressure HRSG. Thus, to the best of our knowledge, this paper contributes to the literature of this field in two ways: (i) with a mathematical optimization model of NGCC power plants operated at three pressure levels and the corresponding solution strategy, and (ii) with improved HRSG configurations with respect to reference configurations taken from the literature.

The paper is organized as follows. Section 2 describes the process superstructure representation. Section 3 defines the problem statement. Section 4 presents the mathematical model. Section 5 discusses the obtained results. Finally, Section 6 provides the conclusions of the investigation.