# Application of the Residue Method in Steam Superheater Fault Detection
## 3 A Mathematical Modelling Method of the Proposed System
### Testing Equivalent Models of Steam Superheaters for Actuator Faults  
#### 3.1.1 Steam Superheaters Model  
The thermal scheme of the steam superheater assembly is shown in Figure 3. Saturated steam taken from the reboiler system passes successively through 3 or 4 superheaters located in the flue gas path taking the heat required to reach the required final value Ta = 545 \({}^{\circ}\)C.  
In the case of superheaters in steam boilers, the thermal agent (flue gas) and the product (steam) are dictated by other processes, independent of the exchanger, and cannot be changed at will. To regulate the temperature of the live steam, the superheater is divided into two or more parts, and devices are installed at the connection points to cool the steam by condensate injection (Figure 3). In modern steam boilers with high steam flow rates, three superheating stages with two water injections are generally provided as shown in Figure 3. A single superheat step with a single injection device would be insufficient to control the temperature within narrow limits, given the character of a distributed process with large time constants and strongly acting disturbances on the controlled process. Based on the analysis of the heat transfer process in steam superheaters, the block diagram shown in Figure 4 corresponds to the superheated steam temperature T\({}_{\rm a}\). Figure 3: Structure of condensate injection superheaters. Steam superheaters can be regarded as a set of autoclave-type heat exchangers with a coil. The steam flow temperature \(T_{a}\) at the output of the last superheater (representing the output size) depends on the boiler inlet sizes (steam flow rate \(\mathrm{F_{ac}}\), exhaust gas flow rate \(F_{ge}\)), which can be changed externally, and on the boiler internal size (gas temperature \(T_{g}\)) which will be defined by the block \(M_{Tg}\), depending on the combustion process, thus on the air flow rate A and the fuel flow rate B. For the control of the live steam temperature, the injection water flow rate \(\mathrm{Winj}\) is chosen from the input sizes, the rest of the input sizes are used to control other parameters. The automatic control system has the task of ensuring constant output temperatures of superheaters \(SA_{2}\) (\(T_{3}\) by \(W_{inj1}\) control) and \(SA_{3}\) (\(T_{a}\) by \(W_{inj2}\) control)--see Figure 5. Simple structures of automatic control systems will not meet the requirements due to the speed of the steam transfer process (low inertias due to high flow rates, high inertias in the heat transfer channels) and the high performance required of the system. The boiler's superheater increases the temperature of live steam at the boiler's outlet as the load increases due to its convection characteristic. \(W_{inj1}\), \(W_{inj2}\) water injections are used to cool the superheater and maintain a constant temperature. The superheater outlet temperature is controlled, while the superheater inlet temperature serves as an auxiliary control. To regulate the temperature, a cascade control system is used. This system has a P-type intermediate controller for local compensation of disturbance effects and a PI central controller for maintaining the steam temperature at the superheater outlet. During load changes, a pre-pulse is given by the diverter element D on the injection water flow when there is a difference between the fuel and live steam flow. This helps to reduce temperature oscillations caused by load changes. The control structure currently being used for further experiments is in place at two of Romania's thermal power plants. This structure utilizes three identical temperature sensors placed in equivalent positions. While it has its downsides, such as increased mass loading,  
Figure 4: Block diagram corresponding to temperature \(\mathrm{T_{a}}\). Figure 5: Thermomechanical diagram of superheaters. power consumption, and practical volume, the majority vote method is still widely used due to its fault tolerance.