Innovative Approaches of Optimization Methods Used in Geothermal Power Plants: Artificial Neural Networks and Genetic Algorithms

Abstract

In this study, a general description of geothermal power plants is provided, and the optimization methods used are summarized. Following the review of these optimization methods, the advantages of heuristic methods and the success of the developed models are demonstrated. The challenges in optimizing geothermal systems, including the limitations due to their complexity and the use of multiple parameters, are discussed. Heuristic methods, particularly the widely used artificial neural networks and genetic algorithms, are explained in general terms. Recent studies highlight that the combined use of artificial neural networks and genetic algorithms can produce faster and more consistent results. This demonstrates the benefits of using advanced methods for geothermal resource utilization and power plant optimization. An innovative optimization method has been developed using the operational data of an ORC geothermal power plant in the city of Izmir. The computational method, using genetic algorithms with artificial neural networks as the fitness function, has identified the optimal operating conditions, achieving a 39.41% increase in net power output. The plant’s gross power generation has increased from 4943 kW to 6624 kW.

1. Introduction

Due to the high greenhouse gas emissions of fossil fuels, they are disadvantageous for electricity generation, as they contribute to acid rain and especially global warming [1]. The transition to renewable and low-carbon energy systems has accelerated worldwide. As a result, interest in geothermal energy is increasing [2]. Geothermal energy is a renewable and reliable energy source [3], and consists of thermal energy obtained by utilizing the Earth’s internal heat. The source temperature determines the application areas of geothermal energy. According to the literature, geothermal resources are classified as high-, medium-, and low-temperature geothermal resources. Generally, sources with temperatures of 90 °C and above are used for electricity generation [4]. Different designs and optimization studies are required to generate electricity from geothermal sources with varying temperatures. Optimization involves analyzing the efficiency, cost analysis, and environmental impact of the plants. By optimizing the use of geothermal resources for electricity generation, efficient and effective designs can be achieved [5].

One of the main challenges in the optimization of power plants is solving nonlinear problems. Moreover, numerous calculations must be performed on a large number of pieces of plant equipment and parameters. These calculations are inherently lengthy, exhausting, and may lead to human errors. To prevent this, methods such as artificial neural networks and genetic algorithms, which have been proven to possess reliable predictive capabilities in the literature, stand out. The optimization of geothermal power plants using both methods has been explained [6]. Artificial Neural Networks (ANNs) are innovative approaches that process data by using connections between multiple inputs and outputs. ANNs are developed by taking inspiration from the human brain’s data processing mechanism [7]. This method interprets data through machine learning (ML), classification by labeling, and clustering of raw inputs. By establishing relationships between inputs and outputs, ANNs reveal the features among the data, thereby creating a model that can establish relationships similar to nonlinear classification and regression analyses [8]. The computational model created for the ANN method uses three basic layers: input, hidden, and output layers. The number of neurons, or in other words, the functional computational units interconnected in the hidden layers, varies depending on the number of data points and the complexity of the calculation model. The sensitivity of the method also varies depending on the number of neurons and the number of layers. Another important aspect is determining the transfer and activation functions used in the neurons’ functional calculations. While proven functions from the literature can be used, new functions can also be developed for efficient improvements to the method. In this study, a model was developed using an ANN to predict operational data for a binary geothermal power plant. Three inputs and five outputs were defined for the ANN. The inputs were specified as dead-state temperature, brine temperature, and brine flow rate. The outputs included the simple payback period and the costs associated with exergy flow, exergy efficiency, energy efficiency, and net power output. As a result, when comparing the real power plant data with the data obtained from the ANN model, it was observed that the predictions achieved an accuracy rate of 98% [6].

Another optimization method, genetic algorithms, are mathematical models based on Darwin’s theory of evolution, built on the survival of the fittest. The philosophy of the model is designed to create a design community adapted by a certain population, and then allow the adaptation to develop. In this context, we can describe the individuals within the populations that achieve the best results for the generated data. Genetic algorithms fundamentally produce possible solutions by mathematically modeling evolutionary processes such as selection and reproduction, parent characteristics, and genetic mutation. In the literature, genetic algorithms are especially used for the optimization of thermal power systems [9].

In many optimization methods such as parametric optimization, some goals or other results may be sacrificed to achieve the desired result. One of the most important challenges in optimization problems is finding the desired data that should be simultaneously at its lowest and highest values. Genetic algorithms are an important tool in solving this optimization problem, which is particularly encountered in operational processes [10]. Genetic algorithms primarily perform operations based on the fitness function. The fitness function is a mathematical tool that determines which individuals, in other words, which data, can survive. Thanks to the fitness function, which is the most important function of the genetic algorithm model, a precise and suitable model for the design can be created. The success of genetic algorithms is significantly related to the appropriate selection of the fitness function for the problem. Therefore, in the optimization of geothermal energy systems, the selection of the fitness function in the modeling of genetic algorithms determines the performance of the model [11].

In the optimization study conducted using a genetic algorithm, the environmental temperature, brine temperature, brine mass flow rate, and solar radiation values obtained from a solar energy-integrated geothermal power plant were used to optimize net power production, as well as the cost of electricity and hydrogen production. As a result of the optimization, the net power output of the geothermal plant increased from 2900 kW to 3858 kW, while solar electricity generation increased from 1361 kW to 1706 kW. Additionally, lower production costs were calculated, demonstrating economic benefits [12]. In the Qiabuqia geothermal field, Enhanced Geothermal System (EGS) applications utilized artificial neural networks and Differential Evolution (DE) models, while the objective function was defined as the Levelized Cost of Electricity (LCOE) function. Results obtained from the ANN-based DE optimization method achieved a lower LCOE value of 0.0376 $/kWh compared to the numerical simulation method. Additionally, the use of the optimization method demonstrated a reduction in computation time by 16,590 times compared to the numerical simulation method. The obtained LCOE value corresponds to approximately 50% of the current cost of the power plant. This theoretical calculation has yielded significant insights for the operation of the field [13].

According to the reviewed literature, the optimization of geothermal power plants, which are systems influenced by a large number of variables affecting efficiency, involves nonlinear relationships. Additionally, it is understood that optimization studies involving large datasets can be lengthy, exhausting, and prone to errors. Methods such as artificial neural networks and Genetic Algorithms (GAs) not only allow for significantly faster calculations compared to traditional methods, but also yield important results in the literature. These methods are particularly useful in net power production and cost calculations, emerging as effective computational approaches. Furthermore, although the accuracy of power plant modeling appears to be quite satisfactory, the limited number of studies in the literature and the recent widespread adoption of these methods necessitate the development of alternative approaches to analysis.

In this study, a novel method has been developed to enhance the accuracy of computational approaches. The proposed method utilizes artificial neural networks as the fitness function within the decision-making mechanism of genetic algorithms. By training artificial neural networks with power plant data, the study aims to achieve more realistic and consistent results, thereby contributing to the literature.

2. Cycles and Optimization Methods Used in Geothermal Power Plants

Geothermal power plants use thermal energy obtained by transporting geothermal fluid in liquid or gas phase from the Earth’s crust to the surface. This fluid is passed through a cycle to convert the thermal energy into electrical energy, and then it is reinjected underground to complete the cycle. Geothermal power plants primarily consist of turbines, pumps, evaporators, and condensers [14]. Geothermal energy systems can be classified into three main types based on their cycles: dry steam, flash steam, and binary cycle plants. Additionally, theoretical models such as the Kalina cycle, which currently have limited application, are also studied in the literature. Maximizing the efficient use of geothermal resources with new technologies is a significant area of research [15].

2.1. Dry Steam Cycle

Dry steam cycles generate electricity by directing steam obtained from steam-dominant geothermal sources directly to the turbine. This is the simplest type of geothermal power plant. The steam from the geothermal source drives the turbine to produce electricity and is then condensed and reinjected underground to complete the cycle [15]. It is one of the oldest methods used by geothermal power plants. There are two types: one without condensation, which is open to the atmosphere, and another that uses a cooling method to condense the steam. Plants without condensation are environmentally disadvantageous, as the steam is released directly into the atmosphere, and their efficiency depends on atmospheric pressure. More environmentally friendly and efficient types have been developed using different condensation technologies [16].

2.2. Single- and Double-Flash Steam Cycles

Geothermal resources are generally in liquid phase under high pressures and temperatures beneath the Earth’s crust. As the geothermal fluid (brine) is brought to the surface through production wells, its pressure decreases, and it vaporizes upon reaching the atmosphere. At this point, the fluid in a saturated liquid–vapor mixture is separated into liquid and vapor phases using a separator, and sent to the plant through different pipelines. If sufficient steam flow and temperature are available, the vapor phase fluid is passed through a turbine to generate electricity. In single-flash plants, steam is separated in one step to produce electricity. However, for fluids with suitable thermophysical properties, a second separator can be used to obtain steam at a lower pressure and temperature, which is then sent to the turbine in different stages to generate electricity. This allows for the design of plants that are approximately 20–25% more efficient than single-flash cycles. It is understood that double-flash plants will have higher initial investment costs due to the additional equipment. Therefore, cost analysis and investment return periods should be considered in plant design [15].

2.3. Binary Cycle Systems

The characteristics of geothermal resources vary regionally. Binary cycle systems have been developed for electricity generation from low- and medium-temperature geothermal resources. In these geothermal fields, due to the insufficient steam phase, the thermal energy of the geothermal fluid is transferred to a secondary fluid to generate electricity. These plants typically use organic fluids as the secondary fluid and operate in geothermal resources ranging from 85 to 170 °C. The selection of the secondary fluid and the cooling method are crucial parameters affecting the plant’s efficiency. Additionally, proper design and operation parameters significantly impact the utilization of geothermal resources [15,17]. Figure 1 presents a schematic diagram of dry steam, flash steam, and binary cycle geothermal power plants [18].

2.4. Optimization Methods Used in Geothermal Power Plants

Optimization, by definition, can be described as the process of finding the best solution under certain conditions for one or more independent variables in the examined problem [19]. Optimization can be examined under two main categories. Each method has been analyzed in the literature under subcategories. The main categories are traditional and advanced methods. In the literature, they are subcategorized: artificial intelligence, multi-objective approach, analytical method, iterative method, probabilistic approach, graphical structure method, and various computer softwares, etc. [20]. Some optimization categories are shown in Figure 2 [20,21].

Traditional optimization methods like analytical, iterative, and probabilistic approaches and graphical structure methods are not preferred, due to slow convergence rates, long and laborious computation times, and the difficulty of accounting for dynamic changes in parameters [21].

Different optimization methods can be used to overcome these problems. Recent studies have frequently employed artificial neural network and genetic algorithm optimization methods. Optimization methods, used individually or in combination, are important tools for modeling and analyzing geothermal systems. They allow for the examination and analysis of operating plants in a much shorter timeframe, and with dynamic interaction. The efficient operating parameters can be identified based on the analyses, allowing geothermal resources to be managed more consistently [22].

Advanced (innovative) optimization methods, such as the multi-objective approach, allow for comprehensive evaluation by considering multiple criteria like cost and energy efficiency. Although this enables optimization for multiple desired outcomes, it is a complex and time-consuming method, due to its computational length and complexity. Small changes in parameter adjustments can significantly impact the results [23]. Analytical methods provide quicker results through simple applications, but are generally more consistent for small-scale systems, limiting their use in complex systems like geothermal power plants [24]. Iterative methods are essential for accuracy and consistency in optimization, repeatedly calculating to find the optimal solution of the objective function. Despite their high accuracy, iterative methods require significant processing power and time for large datasets and complex models, and may necessitate additional analysis to avoid local optima, requiring more expertise and experience [25,26].

The probabilistic approach in the literature allows for comprehensive analysis by including multiple possible outcomes rather than a single scenario, effectively examining resource variability and operational uncertainties. It is crucial for analyzing changes in operating conditions and optimizing performance in geothermal plants. However, the computational model can be complex and time consuming, requiring substantial data and variations [27,28,29]. The graphical structure method is important for quick evaluations, due to its ability to present data and analysis results graphically, making it easier to visualize complex data. However, the detailed analysis of complex models on a graph can be challenging and may require more extensive work [25]. The use of computer-aided design tools or software is also a common method, but it requires significant investment and continuous funding for updates, along with technical knowledge and experience [30].

Heuristic approaches like genetic algorithms and artificial neural networks solve complex problems quickly and flexibly, by searching a wide solution space for optimal results. These methods can be combined with other optimization techniques to form hybrid methods, providing a more detailed analysis. They can quickly adapt to site variables in geothermal plants, examining specific conditions and offering various solutions. However, they require precise parameter tuning and significant datasets, which is common in most optimization methods. Recent research favors heuristic methods due to their ability to hybridize with other optimization methods, eliminating certain disadvantages and producing faster, more consistent, and accurate results [31,32,33].

2.5. Artificial Neural Networks

Artificial neural networks (ANNs) are computational models inspired by the human brain. They can model the connections between inputs and outputs in a problem mathematically. ANNs are massively parallel distributed processors made up of simple processing units that have a natural propensity for learning and using knowledge. They acquire knowledge through a learning process and store it as synaptic weights and biases, analogous to the brain’s structure [34]. Regression and classification models with fixed basis functions have useful analytical and computational properties. However, for solving high-dimensional problems and applying complex models in practical applications, it is essential to adapt the basis functions significantly to the data. ANNs, on the other hand, provide faster and more practical results when establishing connections among large amounts of data. ANNs are one of the best applicable methods in this context [35]. Figure 3 shows the schematic model of an artificial neural network [36].

Each neuron, or mathematical processing unit, in one layer is connected to neurons in the subsequent layer, forming a network. This structure allows for the development and analysis of the ANN model [34,35]. Figure 4 schematically shows the mathematical structure of a neuron [37].

Neurons are represented using the following linear equation.

$$y=w\times x+b$$

(1)

In the equation, y is the dependent variable representing the output related to the input. The independent variable and input data are denoted by x. The weight and bias are represented by w and b, respectively. The modeling of artificial neural networks is based on determining the weight and bias parameters to produce the best possible output. In other words, the effect of neurons on other neurons and the overall artificial neural network (ANN) architecture is calculated using these parameters. ANNs continuously update their weight and bias values to achieve the best results. At this stage, the optimal ANN function is determined as the loss function approaches zero [34,38]. Parameters such as the number of neurons, the number of layers, and the selection of the activation function significantly affect the performance of the output data. The initial determination of the weight and bias values also influences model performance. In Figure 4, “f” represents an activation function, which is a mathematical function applied to the output of a neuron to introduce nonlinearity into the model. It determines the neuron’s output based on its inputs and the weights assigned during the learning process. Without activation functions, artificial neural networks would operate as simple linear models, making them incapable of solving complex tasks that involve nonlinear relationships [34,38,39].

After creating the model, ANNs start the computation process to establish connections between data based on selected functions and parameter settings. Initially, determining weights and biases is necessary. Typically, weights are initialized as small random numbers, and biases are set to zero. Then, forward propagation is initiated. Each neuron receives an input signal x, and a weighted sum is applied.

$$z={{\displaystyle \sum }}_{i}w\times x+b$$

(2)

In a neuron, the above equation is input into a selected activation function, transforming the linear equation into a nonlinear one. This enables the model to handle more complex and real-world problems. Activation functions also constrain the neuron’s output within a specific range, preventing the emergence of excessively large or small weight values. Additionally, the activation functions used in backpropagation must be differentiable. Common activation functions in the literature include Sigmoid, ReLU, and Tanh. The results obtained from the output layer are compared with the desired results, typically using the Mean Squared Error (MSE) function to measure proximity to the target outcome.

$$L={\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\times {\displaystyle \sum }{\left(y_{pred}-y_{true}\right)}^2$$

(3)

Subsequently, backpropagation begins. The gradient descent algorithm is used to update weights and biases by calculating the gradient of all functions according to the chain rule. The forward and backward propagation processes continue until the loss function, or mean squared error, reaches a certain value. In the literature, this can also be achieved through a specific number of iterations. In artificial neural networks (ANNs), the loss function is a mathematical function that measures the discrepancy between the predicted outputs of the network and the actual target outputs. It is a crucial component of the training process, guiding the optimization algorithm in adjusting the network’s weights and biases to minimize prediction errors. Functions such as mean squared error and Mean Absolute Error (MAE) can be used as loss functions [34,35,39].

2.6. Genetic Algorithm

Genetic algorithms are algorithms used for optimization and data generation, utilizing mathematical models of natural selection, mutation, and evolutionary principles. They are crucial for solving complex and multidimensional problems [40]. Instead of a single solution, genetic algorithms can create a set of potential solutions. The success of genetic algorithms largely depends on how potential solutions (individuals) are defined and the choice of the fitness function [41,42,43].

In genetic algorithms, mechanisms that ensure genetic diversity, such as crossover and mutation, must be mathematically determined. Different potential solutions are generated through crossover and mutation. The algorithm concludes once fitness values reach a certain level or after a specified number of iterations [42,43]. One significant advantage of genetic algorithms is their ability to find global optimum solutions rather than local maxima and minima [41]. The general diagram of a genetic algorithm is shown in Figure 5 [44].

There is no single standard model for genetic algorithms; they can be selected or designed to be problem-specific or used for general applications [12].

Genetic algorithms are used in the literature for optimizing geothermal power plants. Different studies show variations in the parameters of genetic algorithms based on the geothermal system being analyzed and the available dataset. Results indicate that operating conditions for geothermal power plants are determined and optimized. For example, Farjollahi et al. [45] identified the operational parameters for the lowest operating costs and high thermal efficiency using artificial neural networks and genetic algorithms. The combination of genetic algorithms and neural networks with other optimization methods is common in the literature [45].

In the optimization of geothermal plants, genetic algorithms can model the characteristics of the expected fluid from the geothermal source. This modeling aims for high energy efficiency and low entropy production as the objective function. Subsequently, the geothermal plant is analyzed based on flow rate, well depth, and well temperature as the inputs, with thermal efficiency and net power outputs being maximized [46]. Using genetic algorithms to generate potential solution sets for complex issues like geothermal resource management, power plant design, and optimization is significant for engineering studies. It is also a comprehensive method for modeling geothermal production wells, as used in the literature [47].

2.7. Optimization of Geothermal Power Plants Using Genetic Algorithms and Artificial Neural Networks

Innovative optimization approaches are modeled in the literature using artificial neural networks and genetic algorithms, either alone or in combination. This allows for faster and more reliable dynamic data analysis, particularly of operational parameters [36,48,49]. Today, artificial neural networks, genetic algorithms, deep neural networks, machine learning, and their subfields are used alone or together as alternatives to traditional methods in various fields. Deep Neural Networks (DNNs) represent a sophisticated subset of artificial neural networks (ANNs), characterized by their use of multiple interconnected layers between input and output. These additional layers enable DNNs to model complex and nonlinear relationships in data. Machine learning is a broader field of artificial intelligence (AI) that enables systems to learn and improve from data without explicit programming. ML encompasses various techniques, including supervised, unsupervised, and reinforcement learning, and relies on algorithms to identify patterns and make predictions. Neural networks, including DNNs, serve as one of the core techniques in ML [35,39]. In their study, Özkaraca et al. [50]. modeled the Sinem Geothermal Power Plant using the Artificial Bee Colony (ABC) neural network. The exergy efficiency was set as the objective function to be maximized. The artificial neural network algorithm was inspired by the foraging behavior of bee colonies. The data were modeled using nonlinear computations starting from the initial data. By conducting classical and advanced exergy analyses and comparing them with the results of the ABC method, exergy efficiencies were found to be 39.1%, 43.1%, and 42.8%, respectively. The results of the advanced exergy and ABC neural network model were very close, showing that applying the optimal operating conditions obtained from this model in the plant could yield an exergy gain of 2102 kW.

The Afyonkarahisar geothermal district heating system was modeled using artificial neural network tools available in MATLAB by Keçebaş et al. [7]. Thermodynamic analysis results were compared with the neural network results, and energy efficiencies were found to be 35.38% and 35.39%, respectively. The analysis results indicate that artificial neural networks (ANNs) can also be used to monitor system performance. Figure 6 compares findings from ANNs with actual data, demonstrating the consistency of ANN models in system modeling. In addition to ANNs, genetic algorithms (GAs) are preferred for their ability to generate potential solution sets for complex problems. He et al. used a GA in their study where the fitness function, determining the survival of individuals (solution sets), was selected as the ratio of input heat to the work obtained. This function aimed to ensure the survival of individuals that enhanced efficiency, resulting in a 16.18% increase in energy efficiency. GAs offer a different approach to geothermal plant optimization compared to traditional methods [51].

The fitness function is a crucial detail in GA modeling and can be defined using thermodynamic relations, various functions from the literature, or a newly developed function. It can also be written in vector form if one or more parameters are used [52]. GAs operate for a specified number of iterations to produce solution sets, which can vary by problem. Rudiyanto et al. found that general exergy efficiencies stabilized at 20, 50, and 100 iterations, allowing for shorter computation times without needing further iterations [31]. Yılmaz et al. [12] analyzed a complex hybrid geothermal and solar energy system using both GAs and ANNs. Figure 7 shows the net power output from actual data compared to the computation model.

The hybrid computational model developed using artificial neural networks (ANNs) and genetic algorithms (GAs) demonstrates applicability by accurately predicting real data. GAs can test various operational parameters in geothermal power plant optimization, identifying the best one. Traditional methods like analytical and iterative approaches have slow convergence rates and struggle with dynamic parameter changes, leading researchers to prefer heuristic methods for their speed and consistency. ANNs and GAs, either together or separately, are crucial tools for optimizing geothermal power plants [21].

The methods are introduced individually, their significant applications in the literature are discussed, and the originality of the developed method is emphasized. In the subsequent sections, the method will be explained with detailed technical descriptions.

3. Materials and Methods

A calculation method has been developed using real-time data obtained from a geothermal power plant located in the Seferihisar region of Izmir, Turkey. Initially, a thermodynamic analysis of the plant’s design and operational parameters was conducted. Subsequently, the operational parameters obtained from the developed method were compared with the actual plant data to investigate the consistency of the method. In this section, the computational approach utilizing artificial neural networks as the fitness function in genetic algorithms, along with the applied analysis methods, are explained in detail with technical specifications. Finally, the potential optimal operating parameters were derived from the calculation method and presented. Certain assumptions were made regarding the thermodynamic analyses, which are listed below:

• All processes are in thermodynamic equilibrium;
• Differences in kinetic and potential energy are negligible;
• Heat transfer to the environment from all equipment is negligible;
• Air is assumed to be an ideal gas;
• Cycles are considered to have balanced and steady flows;
• The amount of NCG (non-condensable gasses) is negligible;
• It is assumed that all steam entering the plant condenses upon exit;
• For exergy analyses, the annual average temperature of the region is taken as the dead state. According to meteorological data, this value is 17 °C. Additionally, the dead state pressure is taken as the ambient pressure, which is 1 bar;
• Brine values are taken as water values;
• The mechanical efficiency of the turbine is assumed to be 99%;
• The mechanical efficiencies of the pump and fan are assumed to be 95%;
• The turbine exit pressure is assumed to be 0.2 bar higher than the condenser pressure.

The efficiencies of the turbine, pump, and fans were obtained from the data sheets provided by the manufacturer. The Refprop program was used for the properties of the geothermal fluid and the secondary fluid in the thermodynamic analyses. The following thermodynamic formulas were used for the energy and exergy analyses:

$$Q-Ẇ=\left({\displaystyle \sum }{ṁ}_{out}\times h_{out}\right)-\left({\displaystyle \sum }{ṁ}_{in}\times h_{in}\right)$$

(4)

$${\displaystyle \sum }{ṁ}_{in}={\displaystyle \sum }{ṁ}_{out}$$

(5)

$${ƞ}_{sys,energy,eff}={Ẇ}_{net}/Q_{total}$$

(6)

$$Q_{brine}={ṁ}_{brine}\times \left(h_{brine,in}-h_{reinjection}\right)$$

(7)

$$Q_{steam}={ṁ}_{steam}\times \left(h_{steam,in}-h_{condens,out}\right)$$

(8)

$$Q_{total}=Q_{brine}-Q_{steam}$$

(9)

$${Ẇ}_{net}={Ẇ}_{gross}-{Ẇ}_{consumption}$$

(10)

$${Ė}_i={ṁ}_i\times {ᴪ}_i$$

(11)

$${ᴪ}_i=\left(h_i-h_0\right)-T_0\times \left(s_i-s_0\right)$$

(12)

$${ƞ}_{sys,exergy,eff}={Ẇ}_{net}/{\displaystyle \sum }{Ė}_{in}$$

(13)

A computational model within the scope of this research was developed using the Python programming language, version 2.14.0, via Google Colab. The aim was to create an innovative analysis method using a genetic algorithm optimization method that employs deep artificial neural networks as the fitness function. Numerous libraries were utilized within the Python program. Particularly, the TensorFlow and Keras libraries, which are frequently used in the literature for artificial neural networks and genetic algorithms, were also employed in this study. Additionally, the Pandas, NumPy, and Matplotlib libraries were preferred to facilitate mathematical operations and data analyses within the model. The method developed for the optimization of the geothermal power plant requires data recorded by the plant’s SCADA system. The inputs and outputs of the method were generated using data obtained from this source. By optimizing the wells and the turbine, where power generation occurs, the operational conditions can be determined based on the available data. Consequently, a comparative thermodynamic analysis can be conducted with the obtained values, allowing for a reorganization of the plant’s operations to achieve efficient performance.

In March 2022, a confidentiality agreement was signed by the management of an operational geothermal power plant located in the Izmir province for use within the scope of this research. According to this agreement, it was agreed that the plant data were to be used for the development of the calculation method and for the publication of analyses academically, while keeping the company name confidential. The geothermal power plant is designed to produce a gross power output of 12.24 MWe. N-butane was chosen as the secondary fluid. The plant uses Exergy brand turbines and has a dual-pressure staged heat exchanger and turbine design. The condensation system is designed to be air-cooled.

Understanding the design operation of the geothermal power plant allows the researcher to comparatively interpret the analysis results. In this plant, the liquid phase (brine) and the vapor phase of the geothermal fluid enter the high-pressure (HP) evaporator, which has different pipelines and heat exchanger surfaces. The steam separates from the HP evaporator and is transferred to a condensation tank before being sent to reinjection wells.

Subsequently, the brine exiting the HP evaporator enters the HP preheater. In the dual-pressure staged plant, the brine transfers some thermal energy to the low-pressure (LP) evaporator after exiting the HP evaporator. The LPHP preheater is a single preheater where heat transfer to the organic fluid occurs without splitting into two pressure stages. At the point where the organic fluid section of the plant has not yet split into HP or LP, the brine proceeds to LPHP preheater exchangers and finally exits the plant to be pumped underground via reinjection wells. In the Organic Rankine Cycle (ORC), the N-butane working fluid pressurized by feed pumps first receives some thermal energy from the recuperator and then enters two preheaters. Then, using an actuator-controlled valve, it is divided into HP and LP stages, and a portion enters the LP evaporator and expands as superheated vapor in the LP section of the turbine. The working fluid going to the HP section passes through the HP preheater and evaporator before expanding in the HP section of the turbine. The fluids from both pressure stages exit the turbine at the same temperature and pressure and transition to the liquid phase in the air-cooled condenser, completing the cycle.

The specially designed turbine integrates high- and low-pressure stages into a single turbine, aiming to produce more energy with lower investment and operating costs. The heat and mass diagram using the design values of the plant is shown in Figure 8. In the diagram, the states represented by J, S, and numbers correspond to the states of brine, steam, and butane working fluid, respectively. Thermodynamic analyses were performed using SCADA screen images taken from the plant on 11 June 2024at 15:30, along with all data obtained from manual indicators installed during the plant’s setup, which could not be obtained electronically.

A deep artificial neural network model was developed using data obtained from the plant in operation, and a fitness function to be used in the genetic algorithm was generated. Forty data points obtained from the geothermal power plant, consisting of 38 inputs and 2 outputs, were used to construct a function in the deep artificial neural network. Furthermore, Figure 9 explains the architecture of the developed innovative computational method by illustrating the data usage scheme of the artificial neural network and the genetic algorithm.

The artificial neural network model used in the calculation method is a multilayer deep artificial neural network. The architecture of the model comprises a total of 8 layers: 1 input layer, 6 hidden layers, and 1 output layer. The input layer consists of 38 neurons, which correspond to the number of input data. Similarly, the output layer contains a total of 2 neurons representing the objective functions of the deep artificial neural network: gross power generation and internal consumption. The hidden layers collectively contain 2464 neurons. Each layer in the artificial neural network model has defined functions and properties, including activation functions, regularizers, and dropout codes. The activation function allows the multilayer deep artificial neural network to form meaningful correlations from the data and produce the desired function. In this study, the ReLU (rectified linear unit) function was used. The sigmoid function was used in the output layer to allow negative values as output. In the model, the coefficients in the smallest unit of the neural cell, referred to as weights, are readjusted after a certain calculation cycle to ensure that the model predicts the outputs in the best possible way. The mechanism for rechecking during these specific calculation cycles is defined by the ‘batch_size’ command in the model. In this study, the batch_size value was set to 32.

In general, the basis of learning is performed using predetermined numbers and formulas through an algorithm. The deep artificial neural network model is automatically implemented using the TensorFlow coding available within the Python programming language’s library. To facilitate the learning and testing of learned values with the specified parameters and algorithms, it is necessary to determine what portion of the plant data will be used separately for learning and testing. In the literature, it is typically common to use 80% of the data for learning and 20% for testing. Researchers can determine different ratios specific to their studies.

By modeling the deep artificial neural network, a function that can establish correlations between inputs and outputs using the data obtained from the plant is obtained. This function can then be used as the fitness function in the genetic algorithm. Through this method, the aim is to develop a more consistent and innovative calculation method by using the plant’s own operational data for the fitness function, which is the most important function of the genetic algorithm.

In the genetic algorithm, each piece of data is referred to as a gene, and the rows are referred to as individuals. These individuals or data rows represent the operating conditions. By using the generated data, a mathematical algorithm model is created to predict the plant’s working conditions and optimal operating parameters. In the genetic algorithm, which is the fundamental working method of the calculation model, the generated individuals are evaluated through the fitness function to obtain a fitness value. As mentioned earlier, these fitness values are determined using the function created by the deep artificial neural network trained with actual data. The fitness function is critically important for the consistent formation of individuals. The higher the fitness value an individual obtains, the greater its chance of survival and passing on to subsequent generations. This process is repeated until the data to be optimized reach the best possible outcome.

Another important aspect to determine is the mathematical modeling of the survival threshold, mutation probability threshold, and crossing over tools used in the genetic algorithm, due to its inherent nature. Each tool is modeled by adding factors with Gaussian distribution to increase randomness. The aim here is to reach data that can create different conditions and to develop a model that can analyze the best possible outcome. In the literature, different values are found for these tools. Although there is no optimal value, the coding language within the Python program is used for crossing over.

Subsequently, a random multiplier is assigned to each value within the obtained individuals, i.e., rows, by examining them one by one. This randomness is determined using the Gaussian distribution method. If the new value obtained with the assigned multiplier is greater than the mutation probability, it is modified by multiplying it with another mutation multiplier determined by the Gaussian distribution, meaning the genes undergo mutation. There is no optimal value for determining mutation probability in the literature. Therefore, through empirical methods, the best results in this study were achieved with a value of 0.95. In other words, if the number obtained from the above process is greater than 0.95, gene mutation will occur. In the genetic algorithm, physical limits are applied to mutation and survival thresholds to prevent outcomes that are impossible to implement but thermodynamically feasible.

Different values for the survival threshold are used in the literature. Since there is no optimal value, the researcher determined this value through empirical methods. In this study, a value of 0.85 was found to be optimal. A very high survival threshold prevents the formation of new variations by causing most individuals to die. Conversely, a very low threshold results in the production of individuals that are very similar to previous ones, reducing diversity and hindering optimization. All values were determined empirically based on the data obtained from the plant and the duration of the research. It should be noted that these values may vary depending on the data and fieldwork conducted by the researchers.

At the end of all these processes, the best individuals, or in other words, the data in the rows, are printed and organized. The optimal results from the selected rows are then evaluated by the researcher. All the results analyzed by the model are exported as an Excel file. Subsequently, the researcher will examine the data with the best net power outputs to find the optimal result, and verify the accuracy of the results using thermodynamic calculation methods.

A genetic algorithm optimization method using deep artificial neural networks as the fitness function has been developed as an innovative calculation method. This method aims to identify the optimal operating conditions for geothermal power plants in operation. Additionally, it allows for the rapid and accurate calculation of the plant’s optimal working parameters, taking into account changes in external conditions and geothermal fluids throughout the year, thus significantly reducing the time and effort required for extensive and exhaustive engineering studies.

4. Results and Discussion

Analyses were conducted using a genetic algorithm that employs deep artificial neural networks as the fitness function to model an operational geothermal power plant and determine its optimal operating conditions. The purpose of this study is to investigate whether geothermal power plants can be modeled and their optimal operating conditions predicted using a genetic algorithm with deep artificial neural networks as the fitness function. According to the analysis results, data generated that are very close to the plant’s actual data could be repeatedly obtained. Figure 10 presents a comparative graph of the data obtained from the plant and the data derived from the calculation method. This graph demonstrates that the plant calculation method was modeled with minimal error, closely matching the operational data. The mean absolute error (MAE) and mean squared error (MSE) used to evaluate the error magnitude of the artificial neural network (ANN) model were found to be 0.3426 and 0.2115, respectively. These values were obtained from the model intended for optimization. A comparatively worse result for the same metrics was found to be 0.5728 for MAE and 0.5309 for MSE. If the ANN model does not exhibit a significant improvement in MAE and MSE values after 15 iterations, it is programmed to select the ANN model with the lowest MAE and MSE values for further computations.

A large number of models representing the operational periods of the plant, similar to Figure 10, could be produced from the data obtained through the calculation method. It is understood that the innovative calculation method can dynamically model the plant’s different operating conditions and produce results with very low error rates. In this context, analyses can be performed using data from different geothermal plants with the applied method.

The results obtained from the developed method were analyzed to evaluate its predictive capability in modeling the power plant. The computational method demonstrated its most significant finding by predicting the net power output with a margin of error of 1.55%. Additionally, operational data obtained from the power plant were modeled within the computational method with an average error margin of 4.9%. These findings validate the accuracy of the computational method.

By adjusting the number of inputs and outputs in the data definition section of the developed method, geothermal power plants can be modeled and optimization studies can be conducted. The thermodynamic properties of the design parameters of the examined plant are shown in

Table 1. The thermodynamic properties of the plant’s design parameters.

State	Phase	Mass Flow Rate (kg/s)	Temperature (°C)	Pressure (bara)	Enthalpy (kJ/kg)	Entropy (kJ/kg)	Exergy (kW)
0geo	-	-	17	1	71.45	0.2534	-
0orc	-		17	1	239.9	1.1412	-
J1	Liquid	228.8	144.2	11	607.64	1.7818	21,236.01
J2	Liquid	228.8	127.64	10.5	536.88	1.6089	16,524.32
S1	Steam	6.97	152		2748.3	6.8192	5379.96
S2	Liquid	6.97	139	4.9	584.96	1.7287	596.23
6	Liquid	150	123	24.6	536.88	1.9927	7484.89
7	Gas	150	125	24	744.29	2.5139	15,915.16
J3	Liquid	228.8	115.24	10	484.23	1.4755	13,313.34
5	Liquid	150	98	25	455.46	1.7804	4514.42
J4	Liquid	228.8	102.94	9.5	432.23	1.3396	10,437.64
10	Liquid	46.94	98	15.7	456.37	1.7881	1350.56
11	Gas	46.94	100	15	720.89	2.4973	4108.08
J5	Liquid	228.8	70	8.5	293.73	0.9546	4307.58
3	Liquid	196.94	41.11	27.6	300.57	1.327	1331.34
4	Liquid	196.94	98	27	455.3	1.7788	5987.05
8	Gas	196.94	58.21	4	675.93	2.5293	6552.74
9	Gas	196.94	53.81	3.8	668.12	2.5123	5986.06
2	Liquid	196.94	38	27.8	292.82	1.3021	1227.89
1	Liquid	196.94	36.7	3.8	288.17	1.3010	374.98

.

The design parameters are important for indicating the physical limits of the plant. In this context,

Table 2. Thermodynamic analysis results based on the plant’s design parameters.

Equipment	Total Heat Transfer/Work (kW)	Total Exergy Destruction (kW)	Total Net Exergy Efficiency (%)	Total Net Energy Efficiency (%)
HP Evaporator	31,269	1049.62	88	-
HP Preheater	12,041.7	215.34	93.24	-
LP Evaporator	11,897.6	118.18	95.89	-
LPHP Preheater	31,688.8	1474.35	75.95	-
Recuperator	1538.1	456.2	17.91	-
HP Turbine	10,254	661.26	93.86	-
LP Turbine	2110	1561.82	82.86	-
ORC Pump	915.77	62.86	93.14	-
AC Condenser	74,636	3928.09	29.75	-
Plant Gross Power	12,240	-	-	-
ORC Consumption	1920	-	-	-
Plant Net Power	10,320	-	-	-
Overall	86,901.09	-	47.53	11.88

presents the energy and exergy analyses of all equipment based on the plant’s design parameters.

To interpret the thermodynamic analyses of the operational parameters and optimal conditions, the results of the analyses conducted of the plant’s design parameters should be compared. This comparison allows for the investigation of whether the theoretically obtained optimization results are feasible. According to the results of the thermodynamic analysis conducted based on the design parameters, the net exergy and energy efficiencies of the power plant were determined to be 47.53% and 11.88%, respectively. Additionally, the exergy efficiencies of the AC condenser and the recuperator, which exhibited the highest exergy destruction, were determined to be 29.75% and 17.91%, respectively.

Table 3. Thermodynamic properties of operational parameters.

State	Phase	Mass Flow Rate (kg/s)	Temperature (°C)	Pressure (Bara)	Enthalpy (kJ/kg)	Entropy (kJ/kg)	Exergy (kW)
0geo	-	-	17	1	71.45	0.2534	-
0orc	-		17	1	239.9	1.1412	-
J1	Liquid	160.75	149.6	11	630.45	1.8371	15,992.93
J2	Liquid	160.75	124	9	521.29	1.5702	10,894.1
S1	Steam	2.69	167.4	6.63	2771.9	6.7517	2192.26
S2	Liquid	2.69	66	6.2	276.8	0.90567	43.3
6	Liquid–Gas	78.61–22.17	110.5	19.1	495.48–732.15	1.8898–2.5070	3016.56–952.49
7	Gas	100.78	112	18.71	736.02	2.5166	9780.47
J3	Liquid	160.75	103	8.9	432.41	1.3404	7324.88
5	Liquid	100.78	81	19.2	406.21	1.6479	1924.88
J4	Liquid	160.75	88	8.36	369.2	1.1691	5153.59
10	Liquid	34.21	81	11.2	406.43	1.653	616.85
11	Gas	34.21	85	11.12	703.41	2.4838	2529.99
J5	Liquid	160.75	72.6	8	304.59	0.9863	3293.62
3	Liquid	135	58	20	343.55	1.4645	1329
4	Liquid–Gas	129.6–5.4	81	19.1	406.22–697.62	1.6479–2.4757	2882.19
8	Gas	135	69	5.4	692.18	2.5388	6313.18
9	Gas	135	60	5.38	673.89	2.4851	5947.75
2	Liquid	135	52.5	20.5	329.22	1.4206	1114.03
1	Liquid	135	52	5.35	327.33	1.4234	749.2

and

Table 4. Thermodynamic analysis results based on operational parameters.

Equipment	Total Heat Transfer/Work (kW)	Total Exergy Destruction (kW)	Total Net Exergy Efficiency (%)	Total Net Energy Efficiency (%)
HP Evaporator	24,259.29	1436.37	80.18	-
HP Preheater	14,287.46	1544.32	57.85	-
LP Evaporator	10,161	258.15	88.11	-
LPHP Preheater	10,386.05	306.78	83.51	-
Recuperator	1937.25	150.74	58.78	-
HP Turbine	4418.2	649.15	87.19	-
LP Turbine	384.18	545.84	41.31	-
ORC Pump	688	-	-	-
AC Condenser	46,785.6	3773.37	27.41	-
Plant Gross Power	4943	-	-	-
ORC Consumption	1195	-	-	-
Plant Net Power	3748	-	-	-
Overall	59,093.82	-	25.24	6.34

present the thermodynamic properties and analysis results of the operational parameters. According to the thermodynamic analysis of the operational parameters, the net exergy and energy efficiencies of the plant are significantly lower than the design values. It is observed that the operational conditions differ from the design parameters, particularly with the flow rates of brine and steam being significantly lower than the design values. Therefore, a loss of efficiency in the plant is expected. However, when the ORC equipment is analyzed in more detail according to the operational parameters, it is found that the exergy efficiency of the high-pressure preheater is particularly low.

Moreover, it is observed that approximately 22% of the butane fluid evaporates before entering the high-pressure evaporator according to the operational parameters. As a result, the heat transfer is not distributed as desired, leading to exergy losses.

According to the analysis results, the exergy efficiency of the HP preheater was found to be 57.58%, while the efficiency of the LP turbine was determined to be 41.31%. Both results are significantly lower than the design parameters, indicating that the plant operates differently from its design conditions and requires an optimization study. The discrepancies in other equipment appear to result from differences in the thermodynamic properties of the brine and steam in the operating plant compared to the design specifications. However, the significant decrease in the efficiencies of the HP preheater and LP turbine should be further investigated.

While the plant operates under similar conditions, more optimal operating parameters can be established by making changes in the flow rate, pressure, and temperature on the butane side. At this stage, the optimal data obtained from the calculation method using deep artificial neural networks as the fitness function were selected by the researcher and analyzed by establishing thermodynamic equilibrium under the same external and geothermal fluid conditions. In this way, significant increases in exergy and energy efficiency were achieved in the plant. The thermodynamic properties and analysis results of the obtained optimal operating conditions are shown in

Table 5. Thermodynamic properties of optimal operating parameters.

State	Phase	Mass Flow Rate (kg/s)	Temperature (°C)	Pressure (Bara)	Enthalpy (kJ/kg)	Entropy (kJ/kg)	Exergy (kW)
0geo	-	-	17	1	71.45	0.2534	-
0orc	-		17	1	239.9	1.1412	-
J1	Liquid	160.75	149.6	11	630.45	1.8387	15,992.93
J2	Liquid	160.75	123	9.5	517.07	1.5595	10,714.81
S1	Steam	2.69	167.4	6.63	2771.9	6.7517	2192.26
S2	Liquid	2.69	66	6.2	276.8	0.90567	43.3
6	Liquid	115	119.7	22.5	525.9	1.9661	5365.36
7	Gas	115	120.4	22	742.79	2.5185	11,875.64
J3	Liquid	160.75	102.76	9	431.39	1.3376	7291.52
5	Liquid	115	81	23	406.14	1.6455	2290.49
J4	Liquid	160.75	84.68	8.5	355.27	1.1302	4728.7
10	Liquid	40	81	13.5	406.37	1.6518	732.78
11	Gas	40	92.3	13	712.28	2.4911	3228.26
J5	Liquid	160.75	70.33	8	295.05	0.95862	3051.1
3	Liquid	155	58	23.5	343.69	1.4627	1628.55
4	Liquid	155	81	23.1	406.14	1.6455	3087.19
8	Gas	155	69	5.4	692.18	2.5388	6313.18
9	Gas	155	60	5.38	673.89	2.4851	5947.75
2	Liquid	155	52.5	23.8	329.22	1.4206	1114.03
1	Liquid	155	52	5.35	327.33	1.4234	749.2

and

Table 6. Thermodynamic analysis results based on optimal operating parameters.

Equipment	Total Heat Transfer/Work (kW)	Total Exergy Destruction (kW)	Total Net Exergy Efficiency (%)	Total Net Energy Efficiency (%)
HP Evaporator	24,937.65	916.99	87.65	-
HP Preheater	13,773.06	348.42	89.82	-
LP Evaporator	12,236.29	67.34	97.37	-
LPHP Preheater	9680.36	21.96	86.95	-
Recuperator	2224.25	150.74	58.78	-
HP Turbine	5820.15	677.36	89.58	-
LP Turbine	804	553.61	59.22	-
ORC Pump	-	-	-	-
AC Condenser	53,716.8	4332.39	-	-
Plant Gross Power	6624	-	-	-
ORC Consumption	1399	-	-	-
Plant Net Power	5225	-	-	-
Overall	60,627.37	-	34.62	8.62

.

Additionally, the critical results derived from the analyses are presented through graphical representations. In particular, optimal conditions were achieved by modifying the N-butane fluid flow rate and increasing the inlet pressures at both stages of the turbine. The optimal values obtained from thermodynamic calculations have been compared with the design and operational values, and are illustrated in Figure 11.

The N-butane flow rate in the plant was increased from 135 kg/s to 155 kg/s, enhancing the amount of heat transfer. Additionally, by increasing the HP and LP turbine inlet pressures, the formation of wet steam before the evaporator heat exchanger was prevented, thereby improving efficiency. Simultaneously, the HP and LP N-butane distributions were adjusted to maintain thermodynamic equilibrium. During these optimizations, the reinjection temperature decreased by 2.67 °C, remaining relatively unchanged. It has been demonstrated that, through the optimization of operational parameters in binary-type geothermal power plants, more efficient operating conditions can be achieved under nearly identical circumstances.

Moreover, Figure 12 presents the efficiency improvements achieved through the optimization process, compared specifically with the exergy variations in equipment operating at low exergy efficiency within the plant. Finally, Figure 13 comparatively illustrates the changes in the plant’s gross and net power production, along with the variations in exergy and net energy efficiencies.

One of the most significant findings obtained after the optimization process was the critical reduction in exergy destruction within the HP preheater exchanger. The exergy destruction was reduced from 1544.32 kW to 348.42 kW by modifying the operating conditions, to prevent the formation of wet steam in this equipment and achieve a more balanced heat transfer. Consequently, the exergy efficiency of the HP preheater also increased. Another significant improvement occurred in the LP turbine. Under the optimized operating conditions, the power output from the LP turbine increased by 419.82 kW.

The developed calculation method optimized the operating conditions under the same environmental conditions. As a result of the analyses, the net power produced by the plant increased from 3748 kW to 5225 kW. Under optimal operating conditions, the reinjection temperature was reduced from 72.6 °C to 70.33 °C, allowing for greater energy and exergy input. Additionally, the flow rate and pressure of butane were increased to make the system more efficient. Due to these increases, the internal consumption of the ORC also increased. However, the amount of increase in gross energy obtained was much greater than the increase in internal consumption. This resulted in a net power increase of 1477 kW. Under optimal operating conditions, the temperatures and pressures at the equipment’s inlet and outlet were balanced, reducing thermal stresses during operation. Simultaneously, the exergy destruction in the equipment was significantly reduced. Specifically, the exergy efficiency of the high-pressure preheater increased from 57.85% to 89.82%. The exergy efficiencies of all equipment improved after optimization. Consequently, the overall plant exergy and energy efficiencies became 34.62% and 8.62%, respectively. The gross power increase was 34%, while the increase in internal consumption was 17%. When comparing the design parameters with the optimal operating conditions, the equipment’s exergy efficiencies were found to be close to the design values.

This ensured that the operation was optimized within the design limits. The optimal operating conditions were established using the data obtained from the developed calculation method. A thermodynamic balance was established, and a comparison with the design parameters showed a net power increase of 39.41%. By integrating the calculation method with the SCADA algorithm controlling the plant’s operation, continuous thermodynamic monitoring of the plant can be achieved. This enables the creation of more efficient operating conditions that can quickly adapt to changes in environmental conditions and geothermal fluid. In addition to modeling renewable energy sources, the developed calculation method identified more optimal operating conditions under the same environmental conditions.

The calculated optimal operating conditions are practically applicable, as they remain within the design parameter limits of the power plant. Additionally, it is possible to operate a more efficient and profitable power plant by achieving increased power output without requiring any modifications to the equipment. However, more advanced software and algorithms may be needed to enable the automatic control software of the SCADA system to adjust pump and valve controls simultaneously based on the obtained results.

For the current approach used in this study, a large amount of power plant data is required. This is because the learning and validation capabilities of the ANNs, which reveal the relationships among plant data, depend on the quantity of the data. Furthermore, in addition to the quantity of the data, the patterns of data variation are also important. Modeling a power plant with constant operating conditions presents significant challenges. However, geothermal power plants are inherently dynamic systems due to both seasonal variations and changes in production wells over time. Therefore, if there are no limitations on the amount of data, the current approach can yield excellent results in optimizing geothermal power plants.

The computational method can be further developed by integrating it with various optimization and statistical methods from the literature to minimize human intervention in the analysis. Additionally, data obtained from different geothermal power plants can be introduced to the method as inputs and outputs for testing purposes. In other words, it is possible to utilize the method with data from different power plants without making any modifications to the method itself. This allows the method to learn from a larger dataset of geothermal fields and power plants, thereby expanding its optimization range.

Furthermore, the data obtained from the method can be integrated into automatic control systems through the development of a dedicated program. This integration would enable simultaneous monitoring of power plant efficiency and identification of optimal operating conditions.

5. Conclusions

In this study, methods used in optimizing geothermal power plants were examined. The use of heuristic approaches in optimization methods was discussed with examples from the literature. The challenges of optimizing geothermal power plants and the application of artificial neural networks (ANNs) and genetic algorithms (GAs) were explained. The modeling, structure, and process steps of ANNs and GAs were described. Optimizing geothermal power plants is a complex, multidimensional problem requiring extensive computations and analysis of the dynamic variables encountered during operation. The advantages and disadvantages of traditional methods were discussed, and the reasons for using heuristic methods were explored. An innovative optimization method has been developed using a genetic algorithm with deep artificial neural networks as the fitness function. The modeling and optimization of an ORC geothermal power plant, from which operational data were obtained, have been conducted and the findings have been presented. Some findings from the research are summarized below:

• Geothermal power plants and wells can be modeled using heuristic methods to develop operational strategies for power plants. Hybrid models developed using heuristic methods can produce fast, reliable, and consistent results for geothermal power plant optimization. An innovative optimization method using a genetic algorithm with deep artificial neural networks as the fitness function has been developed;
• HP preheater exchanger exergy destruction was reduced from 1544.32 kW to 348.42 kW. Under the optimized operating conditions, LP turbine power output was increased by 419.82 kW;
• With the optimal operating conditions obtained through the developed innovative calculation method, a net power increase of 1477 kW was achieved. This resulted in a net power increase of 39.41% for the examined geothermal plant. The exergy efficiencies of the equipment operating with low exergy efficiency under operational conditions were increased after optimization, resulting in overall plant exergy and energy efficiencies of 34.62% and 8.62%, respectively. By optimizing the operating conditions with the calculation method, the reinjection temperature was reduced to 70.33 °C, close to the design value, allowing for greater energy and exergy inputs to the plant.

Advanced methods can model and optimize geothermal energy systems based on operational parameters. Using hybrid analysis methods created with a more innovative approach in future research can provide faster and more reliable engineering solutions for the design and operation of geothermal plants. The use of heuristic methods is likely to increase in the optimization of geothermal power plants, as in many other fields. Combining different methods can yield better and more consistent optimal analysis results.