1. A computer system for modeling a topology of an electrical power system, the topology comprising a plurality of power system components, the computer system comprising: a processor; a component database; a component control engine that receives a selection of one of a plurality of power system components stored in the component database as a selected component, receives a position of the selected component within a framework, and interfaces the selected component with other selected components within the framework, wherein the selected components comprise representations of one or more of a generator, motor, governor, relay, transformer, breaker, fuse, and transmission line; a power system topology modeling engine that renders each of the selected components, which represent physical devices that are not shaped like jigsaw puzzle pieces, as drag-and-drop virtual jigsaw puzzle pieces with virtual male or virtual female connectors, wherein the virtual male connectors comprise rounded jigsaw tabs, and wherein the virtual female connectors comprise rounded jigsaw cuts to receive the rounded jigsaw tabs, renders the topology of the electrical power system, the topology comprising the selected components, and generates a virtual system model of the electrical power system, wherein the virtual system model comprises virtual component data corresponding to the selected components; a virtual modeling engine that generates predicted output using the virtual system model; and an analytics engine that monitors the predicted output and real-time output from at least one sensor of the electrical power system, and synchronizes the virtual system model with the electrical power system based on the real-time output when a difference between the predicted output and the real-time output falls between a set value and an alarm condition value.