## 3 Frequency Coordination Control Strategy at LCC Terminal
### Auxiliary Frequency Controller Design Based on VFF-RLS Algorithm
The basic idea is to transform the system model, minimizing the sum of squared errors and performing recursive operations on the instantaneous input data to find the optimal parameters. This overcomes the limitations of offline identification and enables the online identification of parameters. The forgetting factor \(\lambda\) is one of the key parameters in RLS algorithm, and the convergence speed, tracking speed, and correction effect of the algorithm are all affected by the forgetting factor. VFF-RLS algorithm is adopted to make the forgetting factor dynamically adjusted according to the changes of the estimated parameters so as to realize a faster tracking speed, have a small parameter estimation error, and improve the online recognition accuracy. The defining expression is as follows:  
\[\lambda(k)=\lambda_{\mathrm{max}}-(\lambda_{\mathrm{max}}-\lambda_{\mathrm{min} })\times\tan\mathrm{h}\Bigg{(}\mu\times\sum_{j=0}^{M}\parallel\mathrm{e}(k-j) \parallel^{2}\Bigg{)}, \tag{3}\]  
where \(\lambda_{\mathrm{max}}\) and \(\lambda_{\mathrm{min}}\) is the range of the forgetting factor adjustment to ensure that RLS algorithm does not diverge during iteration. The error \(e\) comes from the error between the calculated value and the real measured value, reflecting the dynamic changes in parameters by calculating the error. The approach to realize the identification of the open-loop transfer function of the system is as follows:  
Utilizing the low-amplitude step disturbance at the control signal of the rectifier-side main controller as the input \(I\), the inter-generator speed difference is used as output \(y\). Assuming the sensor sampling error at time k is \(e(k)\), then  
\[y(k)=\Phi^{T}(k)\theta+e(k). \tag{4}\]  
To minimize the sum of squares of the errors between the estimate of \(\hat{y}_{k}=\Phi_{k}\hat{\theta}\) and the actual value of \(y_{k}=\Phi_{k}\hat{\theta}\), minimize \(J\big{(}\hat{\theta}\big{)}=(y-\Phi\hat{\theta}\big{)}^{T}\big{(}y-\Phi\hat{ \theta}\big{)}\). Let  
\[\frac{\partial J}{\partial\theta}\bigg{|}_{\theta=\hat{\theta}}=-2\Phi^{T} \big{(}y-\Phi\hat{\theta}\big{)}=0, \tag{5}\]  
resulting in  
\[\hat{\theta}=\Big{(}\Phi^{T}\Phi\Big{)}^{-1}\Phi^{T}y. \tag{6}\]  
Each time the system updates the measurement data each time, it will update the matrix \(\Phi\) and the \(I_{\mathrm{k}}\) matrix, thereby further correcting the existing estimated values. Consequently, as the system continually updates the measurement data, the identified parameters also continuously evolve. The steps of the VFF-RLS algorithm are as shown in Table 1.  
In order to realize the precise control of the system frequency, the root locus method is used to design the AFC controller. The root locus method is a graphical method which is easy to implement, and it has been widely used in engineering practice. The position of the closed-loop pole determines the stability and dynamic characteristics of the system. By adjusting the position of the closed-loop pole, the dynamic performance of the system can be regulated. The basic principle is to use the open-loop transfer function obtained by using the VFF-RLS algorithm to identify an open-loop system. Based on the root locus of the open-loop system, the dominant poles of the system are determined for the desired dynamic characteristics. Negative feedback correction is applied by adding zeros and poles to the open-loop transfer function through the correction loop \(G_{c}(s)\). This adjustment positions the closed-loop dominant poles of the system at the desired ideal dominant poles, making the closed-loop system's root locus pass through these characteristic roots for improved system stability and dynamic response characteristics.