###### Abstract
The learning rate of the parameter is affected not only by the learning rate parameter \(\eta\) but also by the value of the mini-batch size \(\mathrm{m}\). However, when the value of \(\mathrm{m}\) is too large, the parameter update becomes slower, and achieving the same accuracy requires a significantly increased cost. To further accelerate the parameter update rate of the gradient descent algorithm and escape from the attraction basin of local minima, the literature [15] proposes the Momentum Learning Rate as a supplementary term in the parameter update formula of the gradient descent algorithm. It accumulates the historical gradients throughout the parameter update process to influence the current direction of gradient descent. Furthermore, the literature [16] introduces a pipelined stochastic gradient descent with Taylor expansion. The proposed method generates multiple model replicas to solve the weight inconsistency problem and adopts a Taylor expansion-based gradient prediction algorithm to mitigate the delayed gradient problem. The literature [17] designs a projection sub-gradient method based on the Nesterov accelerated gradient algorithm, which can achieve stable learning accuracy while maintaining convergence speed. The literature [18] builds on the idea of variance reduction and designs the distributed implementation algorithm Dis-SAGD, which employs an adaptive sampling strategy and momentum acceleration to achieve near-linear acceleration in distributed clusters. Lastly, the literature [19] utilizes mini-batch samples instead of all samples during the training process and performs batch subtraction updates while computing average gradients, resulting in the variance-reduced BSUG algorithm. The batch gradient descent method targets the entire dataset and has the ability to search for global optimal solutions, but it comes with a high computational cost and slow training speed. On the other hand, the Mini-Batch Gradient Descent method divides the large dataset into several small subsets and computes the gradient only for a specific small subset during each iteration. This effectively reduces the computational workload per iteration and improves computational efficiency. The stochastic gradient descent method treats each sample as a small subset, and both Mini-Batch Gradient Descent and stochastic gradient descent methods can be considered as types of it. While the stochastic gradient descent method efficiently searches for the optimal parameter region, it may fall short in finding the global optimal solution. Current research has delved deeply into improving the efficiency and accuracy of constructing safety domains, but there has been less consideration of the impact of large-scale new energy integration and penetration rates on the boundaries of power system safety domains. Addressing the shortcomings of fitting accuracy in stochastic gradient descent and the insufficient training efficiency of batch gradient descent, this study utilizes the fast training speed of stochastic gradient descent and the high fitting accuracy of batch gradient descent to improve traditional gradient descent algorithms. We propose an improved stochastic-batch gradient descent method and a gradient accumulation strategy, applying them to the construction of the static safety domain in power systems incorporating new energy. The method is used to track critical stable operating points within the safety domain, forming the SSR and conducting static stability analysis of the system. Through this method, this paper aims to achieve the following contributions. First, it aims to enhance the accuracy and efficiency of static safety domain analysis in new energy power systems. Second, it aims to explore the characteristics of changes in the static safety domain boundaries of power systems under different wind power penetration rates. Finally, through case study analysis, it aims to validate the practical utility of the proposed methods and provide new insights for power system stability research.