# Dynamic Modeling and Validation of Peak Ability of Biomass Units
## 4 Dynamic Model Validation
### Model Validation  
To verify the model's accuracy, this paper uses the historical data of a biomass unit for experiments. The collection time is from 00:00:00 to 24:00:00 on 20 March 2024. A group of data is sampled every second, and a total of 86,401 groups of data are collected. The data is divided into several sections, and the static and dynamic parameters are identified and verified. The static parameters are obtained through the calculation of the steady-state operation data of the unit, as shown in Table 2.  
Root mean square error (RMSE) and mean absolute error (MAE) are adopted to evaluate the prediction accuracy of the constructed model for main steam pressure and \begin{table}
\begin{tabular}{c c} \hline \hline
**Steady State Parameters** & **Numerical Value** \\ \hline \(K_{1}\) & 1.0000 \\ \(K_{2}\) & \(6.8143\times 10^{-6}\) \\ \(K_{3}\) & \(7.1550\times 10^{-5}\) \\ \(K_{4}\) & 1.1500 \\ \(K_{5}\) & 0.0615 \\ \(K_{6}\) & 63.6531 \\ \(K_{7}\) & 39.7832 \\ \(K_{8}\) & 0.0082 \\ \(K_{9}\) & 5.6358 \\ \(K_{10}\) & 0.8758 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Static parameter values. Figure 3: Input of feed quantity after median filtering processing. unit output power. RMSE is the square of the deviation between the model output and the real value, which can show the degree of fitting between the model output and the actual output well. MAE measures the overall deviation in a model's predictions by calculating the average absolute error between the predicted and true values. The calculation method is as follows:  
\[RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_{i}-y_{i}^{*})^{2}} \tag{27}\]  
\[MAE=\frac{1}{n}\sum_{i=1}^{n}|y_{i}-y_{i}^{*}| \tag{28}\]  
where \(y_{i}\) is the actual value of main steam pressure or turbine output power data, while \(y_{i}^{*}\) is the output value of the model main steam pressure or turbine output power. The dynamic parameters and delay time constants obtained by the empirical trial and error method are shown in Table 3.  
Based on the identified dynamic model, the comparison of model outputs with actual operation data under the same excitation can be obtained, as shown in Figure 4. The distribution of model error over time is shown in Figure 5.  
Compared with Figures 3 and 4a, it can be seen that at several key periods, such as 500 s, 2000 s and 5000 s, when the feeding amount stops input, the power output also decreases, but it is not difficult to find that there is a certain lag. The feed rate is the energy input source of the biomass unit, which directly causes the fuel supply in the combustion chamber to stop and the heat generation to reduce. Because the combustion process takes time, the heat output will not respond immediately, but there is a certain delay. The decrease in heat will reduce the steam generation in the boiler and the main steam pressure, which will lead to the weakening of steam power to drive the steam turbine and the reduction in output power. In addition, due to the existence of the combustion process, boiler thermal inertia and turbine mechanical inertia, the power reduction is not instantaneous but a gradual process. This phenomenon reflects the dynamic balance relationship between energy input and output, and conforms to the physical law of biomass units. It can be considered that the model has high mechanism rationality. Figure 4 represents that the power output change trajectory of the model established in this paper is almost consistent with the actual operation data. The prediction performance of power output shows a good follow-up ability, which accurately reflects the dynamic change trend in the actual operation. However, the prediction effect of the main steam pressure circuit is slightly inferior to that of the power output circuit, but it can still be seen from the figure that its change trend is significantly similar to the actual operation data in the key decline range. The proposed model successfully captures the dominant trends,