Stochastic multi-objective security-constrained market-clearing considering static frequency of power system

• Post-contingency intervals are formulated in detail.
• System frequency following the occurrence of a contingency is modelled.
• Rocof of the system and Rocof for single generators are considered and controlled.
• Two objective functions have been proposed to control the frequency and the Rocof.

This paper deals with frequency control following the occurrence of a contingency. The frequency is considered by modelling the generators’ governor performance during pre- and post-contingency intervals, load frequency dependency, rate of change of frequency (Rocof) of generators and Rocof of the system and frequency-based reserve scheduling. The time intervals following the occurrence of a contingency are formulated in detail to analyze the influential factors in static frequency. A novel index besides the frequency dependent social welfare function and frequency excursion index has been proposed to control the frequency and the Rocof during post-contingency intervals. The proposed stochastic multi-objective model incorporates the precise scheduling of reference power setting of generators based on participants’ bids for energy and reserve services. The eventual goal of the proposed approach is to help the ISOs to make a trade-off concurrently between system frequency profile, Rocof and total operating cost to operate the power system securely in an economically efficient manner. This multi-objective programming formulation is simulated through two case studies; a three-bus system scheduled over 1 h and the IEEE Reliability Test System over 24 h, solved by means of lexicographic optimization and ε-constraint method.