Optimization of Hybrid Geothermal–Solar Power Plant Based on Advanced Exergy Analysis Using Genetic and Water Cycle Algorithm

Since the use of solar energy is inherently intermittent, geothermal energy can provide basic power. However, geothermal sources decrease over time by temperature or flow velocity. By combining solar and geothermal power plants, the benefits of both technologies can be used. There are several methods for hybridizing solar and geothermal technologies, and their efficiency depends on factors such as location, the relative quality of geothermal and solar resources (MC Tigio et al., 2018).
Exergy, such as enthalpy, is a thermodynamic characteristic that measures the ability of materials to work and includes chemical and physical components. Exergy is mainly used in the early stages of development to achieve better structures, chemical processes, engines, and others. Exergy is defined as the maximum theoretical work that a system can achieve when logging in (Alibaba et al., 2020a).
Conventional analysis of exergy examines the system thermodynamically and describes the level of exergy degradation (ED) in each piece of equipment and its thermodynamic causes (James et al, 2015). While advanced analysis evaluates the effects between components of the entire system and measures the real potential for improving one component in the system. In fact, the exergy degradation of each piece of equipment is divided into endogenous and exogenous components as well as avoidable and avoidable components (Alibaba et al., 2020 b).
Boyagchi and Heidarnejad (2015) studied a hybrid solar-geothermal cycle. According to the results, thermal efficiency, exergy efficiency, and product cost rates are 23.66%, 9.51%, and 5114.5 $/s, respectively in the summer season. But in the winter, the values were 48.45%, 13.76%, and 5688.1 $/s, respectively. The results of optimization showed that improvement for thermal efficiency, exergy efficiency, and overall cost rate of products were by 28%, 27%, and 17%, respectively in summer while they were by 4%, 13%, and 4% in winter. Rashidi and Khorshidi (2018) investigated the system of simultaneous production of power by exergo-economic analysis. They performed the optimization on the cycle using the differential evolution (DE) algorithm and the results were verified by (Vazini, 2019). Herberle et al. (2017) technologically and economically analyzed a solar-geothermal power plant of the Rankin cycle. Islam et al. (2017) evaluated an integrated multi-power system based on a hybrid solar-geothermal energy. Ramos et al. (2017) investigated a hybrid solar heat collector with photovoltaic heating systems to generate renewable heat. Anetor et al. (2020) used conventional and advanced analysis to investigate the factors for improving the 750 MW supercritical steam power plant of refined coal. The results showed that the condenser had the most exergy degradation, followed by the boiler.
The basic limitations of advanced analysis of exergy can be overcome by optimization. In engineering, many optimizations and decision-making issues are instinctively multi-objective. In most cases, engineers and decision-makers seek to achieve different and sometimes conflicting goals e.g. the subject of quality and cost of production (Yazdanpanah and Barakati, 2016). The main problem in solving multi-objective optimization problems arises from the fact that there is rarely a single point that optimizes all objectives simultaneously and as much as possible. Instead, one should look for a satisfactory balance between these answers and identify a set of optimal answers. Then, according to the decision-maker, one of those points is selected as the optimal point. Evolutionary algorithms have the ability to generate several potential answers to problems, and the choice of the final answer is up to the user. Therefore, they are known to be very efficient in solving problems such as multi-objective optimization (Alavi et al., 2018). Gorbani and Khoshgoftar Manesh (2020) presented a modified hybrid system including solid oxide fuel cell, gas turbine with organic Rankine cycle (ORC), and then thermodynamically modeled and simulated to evaluate its performance. The thermodynamic results of the simulation showed that the net power and overall efficiency of the proposed cycle were increased by 1.1 MW and 7.7%, respectively, compared to the original system.
In the present paper, genetic and water cycle algorithms were used for optimization. Genetic algorithms (GA) are part of evolutionary algorithms in which chromosomes (candidate solution for an optimization problem) result in a more appropriate solution. Using a genetic algorithm, a design is created. Data is then specified for several different variables, for example around 20 variables. Then the genetic algorithm is implemented and examines the best function and variables. The water cycle algorithm (WSA) is used to estimate the parameters of the cycles. This nature-inspired algorithm works based on how streams and rivers flow downhill to the sea and vice versa. In this method, the population matrix, called raindrops, is made up of seas, rivers, and streams. In each repetition, these streams flow into each other and lead to great discoveries in the space of exploration (Alexander and Lange., 2011; Shirin Zaban et al., 2019).
In general, in previous research, a system is evaluated only from an economic or environmental point of view. Exergo-conomic and exergo-environmental analyses were evaluated. Optimizations were also performed for both systems by genetic and water cycle algorithms.

2. Materials and Methods
2.1. Explanation of proposed hybrid solar-geothermal power plant
The cycles of the proposed hybrid system include the solar cycle, the upstream steam cycle, the middle coupling cycle, the downstream Rankin cycle, and the geothermal cycle coupled by an intermediate system. The heat of saltwater with a temperature of 150°C and a pressure of 1bar is transferred to the downstream working fluid R114 of the ORC and supports the hybrid system at night. The heat transfer fluid (HTF) in the upstream steam cycle receives thermal energy from the lubricant oil flowing at the center of the linear parabolic collector (LPC) solar collectors at 395°C. In the upstream cycle, the temperature of HTF fluid is 395°C when exits the super-heater. Then enters the steam turbine and left there at 170°C. During the day, all the heating power is transferred to the upstream cycle through the solar section and provides the healing power of the hybrid system, and then it transfers and stores some of the heat energy to the geothermal cycle by passing through the middle cycle. At night, when there is no solar thermal energy, the energy stored in the geothermal section is used for heating.