A Matrix State-to-Responsibility Mapping Model for Post-Contingency Corrective Dispatch in Power Systems

Post-contingency corrective dispatch restores a feasible AC voltage–current state, but the corrected state is usually not carried forward to responsibility allocation. This paper proposes a matrix state-to-responsibility mapping (MSRM) model that maps the corrected AC state to network use, loss allocation, regional marginal cost, and line-level carbon responsibility indices. The model treats the corrected post-contingency state as a common attribution basis, so feasibility recovery and responsibility assessment are linked within the same state-dependent mapping. Corrective dispatch is formulated in rectangular coordinates as a constrained optimization problem that minimizes generation cost and controllable redispatch amount under current balance, generator output, voltage, and line capacity constraints. The resulting voltage–current solution is used to build generator-side and load-side contribution matrices, from which settlement quantities and line-level responsibility are obtained through a unified matrix sequence. Carbon responsibility is calculated after redispatch from the generator-side traced flow matrix and generator carbon intensity matrix; it is not imposed as a dispatch objective. A feasibility-guided adaptive particle swarm optimization method is adopted to obtain the corrected state. Reported data from a practical 58-bus Taipower 345 kV transmission system are used for validation. In the line outage and generator outage cases, maximum line loading is reduced from 110% to 98.973% and from 103.99% to 98.99%, respectively. The positive carbon responsibility of Line 36 decreases from 91.72 to 88.80 tCO2/h, whereas that of Line 80 remains nearly unchanged despite wider redispatch. In the two tested contingency cases, feasibility recovery, settlement quantities, total emissions, and line-level responsibility change in different directions after corrective redispatch, indicating that these indices should be evaluated separately under stressed post-contingency operation.