# Application of the Residue Method in Steam Superheater Fault Detection
## 1 Introduction  
Power plants are likely to experience energy-related issues such as equipment failures and fault detection due to the ever-increasing demand for energy. Detailed monitoring of the process's parameters is necessary to comprehend these failures fully. Sensors are installed in power plants to monitor different processes and trigger alarms when operating parameters exceed their typical values or limits. Each power plant requires individual monitoring of measurements based on fixed set points or statistical limits that consider the relationships between parameters. Abnormal measurements outside the acceptable range indicate that a system component is not functioning correctly, which can decrease efficiency. Power generation involves converting various forms of primary energy into electricity through specialized power plants, but technological, economic, environmental, and safety considerations limit their capacity. A power plant is a complex system that allows for the conversion of primary energy into electrical energy. To ensure the safety and efficiency of modern manufacturing processes, plants must be equipped with advanced control systems and reliable online fault detection and diagnosis tools. Component failures, device malfunctions, and human errors can lead to substantial material or human losses, making fault detection and identification crucial. Although an automatic fault detection system working in tandem with process control is the ideal solution, many industrial processes rely on semi-automatic instruments that alert process operators to the presence of faults. In the design and implementation of the fault detection system, the ability to detect fault symptoms as early as possible is critical to provide personnel with ample time to alter the control policy, repair the faulty device, or safely halt the process. Power plant systems are complex and require a systematicapproach for examination. This investigation focuses on the superheater subsystem, which plays a crucial role in ensuring efficient operation. The objective is to provide a thorough understanding and detect faults in the subsystem to improve performance. According to a study by [PERSON], [PERSON] et al., published in [1], achieving optimum energy conversion in thermodynamic systems, such as in thermal power plants (TPPs), is a complex task due to the involvement of several factors. One of the effective ways of determining the quantity and quality of energy systems is via energy and exergy analysis. This study is a comparative evaluation of the energy and exergy analyses of coal and gas-fired TPPs. Details of different studies on TPPs over the years were critically reviewed, followed by an independent thermodynamics analysis of each component of the TPPs system. Improvements in the performance of power plants were also highlighted. From the outcome of the comparative analysis, combustion chambers were identified as the main contributors to exergy destruction owing to their associated high irreversibility. The results show that the exergy efficiency of the entire system is about 20%. The main exergy loss occurred in the boiler and the steam turbine in the system. For further improvements, this review highlighted some of the areas for further research and made recommendations for improvement in some aspects of the existing TPPs. The paper authored by [PERSON] and [PERSON] [2], presents a comprehensive amount of fault diagnosis methods. The authors classify these methods into three main approaches. The first approach involves the use of various signal processing techniques, such as spectral analysis, principal component analysis (PCA), wavelet transforms, and fast Fourier transforms (FFT), to carefully analyze the system and identify faults. This approach is particularly useful when dealing with complex systems that have multiple variables and dependencies.