Mathematical Models for Optimal Distribution of Power Shortage in Calculating the Electric Power System Adequacy Indicators

Existing approaches for calculating electric power system (EPS) adequacy indicators are more focused on determining the undersupply of electricity to consumers associated with random emergency disturbances in the power system. The main technique for calculating adequacy indicators is the statistical test method with a built-in procedure for selecting optimal control actions, which include partial limitation of generation and (or) load (the problem of optimal distribution of power shortage). To speed up calculations, a set of assumptions and constraints is adopted. It is noted that failure to take Kirchhoff’s second law into account leads to ambiguity and large errors in load flow estimates, which depreciates the identification of the most frequently overloaded electrical network elements. The article places emphasis on selecting a set of control variables that ensure the maximum speed of the computation procedure while ensuring acceptable accuracy of the EPS adequacy indicators of interest. It is shown that mathematical models based on defining a special slack node yield a significantly limited range of feasible solutions, which affects the resulting adequacy indicators.