Fast simultaneous feasibility test with electrical power grid perturbations over states and contingencies

A system comprising:

• one or more hardware processors with memory coupled thereto;
• and
• computer-readable storage media with instructions which, when executed by the one or more hardware processors, cause the system to perform operations comprising:
• obtaining one or more first factors of a reference bus admittance matrix of an electrical power grid;
• computing right and left power flow perturbation factor arrays for each of a plurality T of states of the electrical power grid based on:
• the one or more first factors;
• and
• one or more perturbation definition arrays characterizing perturbations of the electrical power grid for the respective state;
• and
• combining the right and left power flow perturbation factor arrays with a plurality of candidate solutions, (i) to determine violations of one or more component limits in the electrical power grid, and (ii) to cause a list of the violations to be outputted, wherein each of the candidate solutions comprises a vector of power injections at transactional nodes of the electrical power grid.

A computer-implemented method for an electrical power grid subject to perturbations characterized by respective states and/or contingencies, the method comprising:

• in a precompute phase:
• decomposing a reference bus admittance matrix A0 of the electrical power grid to obtain at least one factor of A0;
• computing a first intermediate array having slices of size J×sp and a second intermediate array having slices of size sp×sp, the slices of each intermediate array comprising:
• first slices indexed by state;
• and
• second slices indexed by both state and contingency;
• wherein:
• each slice of the first and second slices pertains to a respective perturbation;
• J is a number of buses in the electrical power grid;
• and
• sp is a branch rank of the respective perturbation;
• computing, based on the at least one factor and the intermediate arrays, right and left power flow perturbation factor arrays comprising third slices indexed by state and fourth slices indexed by both state and contingency;
• and
• storing the right and left power flow perturbation factor arrays;
• wherein the right and left power flow perturbation factor arrays are combinable with candidate solutions for the electrical power grid in the respective states (i) to determine violations in the electrical power grid for the candidate solutions, each candidate solution comprising a vector of power injections at transactional nodes of the electrical power grid, (ii) to determine feasible solutions among the candidate solutions, and (iii) to control magnitudes of power injection at the transactional nodes according to the feasible solutions in the respective states.