###### Abstract  
The uncertainty in the new power system has increased, leading to limitations in traditional stability analysis methods. Therefore, considering the perspective of the three-dimensional static security region (SSR), we propose a novel approach for system static stability analysis. To address the slow training speed of traditional deep learning algorithms using batch gradient descent (BGD), we introduce an improved stochastic-batch gradient descent (S-BGD) search method that combines the advantages of stochastic gradient descent (SGD) in fast training. This method ensures both speed and precision in parameter training. Moreover, to tackle the problem of getting trapped in local optima and saddle points during parameter training, we draw inspiration from kinematic theory and propose a gradient pile (GP) training method. By utilizing accumulated gradients as parameter corrections, this method effectively avoids getting stuck in local optima and saddle points, thereby enhancing precision. Finally, we apply the proposed methods to construct the static security region for the IEEE-118 new power system using its data as samples, demonstrating the effectiveness of our approach. static security region of power systems; wind power penetration rate; improved stochastic-batch gradient pile descent; hyperplane +
Footnote †: journal: Applied  
0000-0001-9993-3227-3327-3327-327  
static security region [6]. In the literature [7], the method based on the Lagrange multiplier is proposed to trace the Security Region Boundary (SRB) to construct the SSR. In the literature [8], the efficiency of constructing the SSR is improved by optimizing the search model based on the properties of the power grid boundary. The literature [9] approximates the SSR through the relationship between the spatial angles of the critical point's space static security domain mathematical model tangent vector and the maximum spatial angle threshold. The literature [10] solves the security region using the Taylor series trajectory sensitivity method. The literature [11] uses based least absolute shrinkage and selection operator (Lasso) for optimal power flow calculation. All of the above studies aim to improve the efficiency and accuracy of constructing the security domain, but they do not consider the construction of the security domain under the scenario of new energy integration into the system. In addition, intelligent optimization algorithms are commonly utilized in power system analysis. The gradient descent algorithm is a type of iterative optimization algorithm that can be applied to solve linear or nonlinear problems. Depending on the different data usage approaches, such as data size, time complexity, and algorithm accuracy, the gradient descent algorithm can be categorized into the following distinct forms: (1) the batch gradient descent (BGD) algorithm; (2) the stochastic gradient descent (SGD) algorithm; and (3) the Mini-Batch Gradient Descent (MBGD) algorithm. The literature [12] proposes the BGD algorithm, which computes the gradient of the cost function using the entire dataset during each iteration. However, with the growth of massive datasets and memory limitations, loading all the data at once becomes increasingly impractical, leading to slow training processes. Addressing the low efficiency of gradient descent in handling large-scale samples, the literature [13] introduces the SGD algorithm, which calculates the gradient using only a single sample during each iteration to update the parameters, eliminating computational redundancy. However, the process introduces more noise, causing not every iteration to converge towards the global optimum and reducing training accuracy. To overcome the shortcomings of the two methods mentioned above, the literature [14] presents the Mini-Batch Gradient Descent algorithm, which uses a fixed number of training samples to form a small sample set during each parameter update.