In the ongoing power system reform in Japan, the division of transmission and distribution is separated from the former general electric utility and became a general power transmission and distribution business operator. After the reform, the power transmission and distribution business operators will procure reserve power from the reserve market. We have formulated the clearing problem in the reserve market as a 0-1 integer programming problem. This problem can be viewed as a Min-Max set multi-cover problem. Since the set covering problem belongs NP-hard, it is not easy to solve large-scale problems in practical time. In this paper, we propose a greedy solution and local search solution to the Min-Max set multi-cover problem and evaluate its performance by numerical experiments.

This paper provides a distributed event-triggered controller with aperiodic event detection for finite-time consensus of multi-agent systems. In previous research, event-triggered control for finite-time consensus of multi-agent systems still needs continuous communication to update the trigger function. Therefore, we introduce a trigger function based on broadcast state which only updates at each event along with the controller. It is proved that such event-triggered controller satisfies the requirements of finite-time consensus. And the system does not exhibit Zeno behavior if and only if the precision of state error is lower bounded. Simulation results show that although aperiodic event detection has greater estimation error in consensus time, it saves more computation and communication resource compared with continuous event detection.