Tool employing homotopy-based approaches in finding the controlling unstable equilibrium point in the electric power grid

An analytical tool for assessing the stability of a networked power system comprising:

• at least one data acquisition circuit electrically coupled to the power system, the acquisition circuit collecting and storing data reflective of a stability state of the power system as a data model stored in computer memory;
• a stability analysis processor coupled to said computer memory to access said data model;
• the stability analysis processor including a computer-readable medium storing instructions when executed by the processor cause the processor to:
• a) compute an exit point at which a projected fault-on trajectory reaches a first local maximum of potential energy;
• b) using the exit point as an initial point to solve a post-fault reduced-state model;
• c) determine a controlling unstable equilibrium point (CUEP) with respect to the projected fault-on trajectory of the networked power system by applying a homotopy algorithm that uses the exit point as an initial condition;
• d) solve a numerical energy function at the CUEP to determine a critical energy value;
• e) calculate a value of the numerical energy function at a time of fault clearance using an initial condition of the post-fault trajectory;
• and
• f) test if the value of the numerical energy function is less than the critical energy value:
• if so, reporting that the initial condition lies within a stability boundary, and
• if not, reporting that the initial condition may be unstable.

A non-transitory computer-readable medium storing instructions which when read and operated upon by a processor cause the processor to perform a method of analyzing stability of a networked power system, comprising:

• storing a reduced state model of the power system in memory of a computer and integrating over the model to derive a fault-on trajectory;
• storing in memory of the computer a numerical energy function for a post-fault condition of the power system;
• using the computer to compute an exit point at which a projected fault-on trajectory reaches a first local maximum of potential energy;
• using the exit point as an initial point and then using the computer to solve a post-fault reduced-state model;
• using the computer to determine a controlling unstable equilibrium point (CUEP) with respect to the projected fault-on trajectory of the networked power system by applying a homotopy algorithm that uses the exit point as an initial condition;
• solving the numerical energy function at the CUEP to determine a critical energy value;
• calculating the value of the numerical energy function at a time of fault clearance using an initial condition of the post-fault trajectory;
• and
• using the computer to test if the value of the numerical energy function is less than the critical energy value:
• (a) if so, reporting that the initial condition lies within a stability boundary;
• and
• (b) if not, reporting that the initial condition may be unstable.