This paper introduces a novel DC power flow model that incorporates network loss and voltage magnitudes, aiming to achieve comparable calculation results to AC power flow while mitigating convergence issues. The proposed model addresses network loss by formulating a fixed-point equation for voltage angles, effectively accounting for the impact of network losses through the introduction of a virtual load. Furthermore, an inverse function of the complex power equation is derived to calculate voltage magnitudes, with the voltage angles serving as input. To evaluate the performance of the proposed model, extensive case studies are conducted on various test systems, ranging from small-scale to large-scale networks, including a real-world power grid. The results demonstrate the high accuracy of the proposed DC power model regarding voltage angles and magnitudes, active and reactive power. Importantly, the model showcases its ability to overcome power flow convergence issues, providing reliable and precise solutions in situations where the traditional Newton-Raphson algorithm fails to converge. The findings of this research offer a promising alternative for power flow calculations and adjustments in real-world applications.

Approaches to apply graph computing to power grid analysis are systematically explained using real-world application examples. Through exploring the nature of the power grid and the characteristics of power grid analysis, the guidelines for selecting appropriate graph computing techniques for the application to power grid analysis are outlined. A custom graph model for representing the power grid for the analysis and simulation purpose and an in-memory computing (IMC) based graph-centric approach with a shared-everything architecture are introduced. Graph algorithms, including network topology processing and subgraph processing, and graph computing application scenarios, including in-memory computing, contingency analysis, and Common Information Model (CIM) model merge, are presented.