A New Index of Power System Flexibility: Response Delay ($\theta$) of Distributed Devices

Power system flexibility consists of three indices: ramping capability limit ( ρ), power capacity ( π), and energy capacity ( ε). The existing research body neglects the effect of demand response (DR) units' action delay time, and its effect on the system's contingency response. This paper proposes a fourth flexibility index, the Response Time Delay, denoted as ( θ), and investigates the isolated effect of this factor on the system. A novel extension on the security constrained optimal power flow formulation is presented in this paper, to explicitly model DR unit's response delay time. The value of the response delay ( θ) on the system's operation cost is determined. Making this information available to Virtual Power Plants (VPP) and aggregators empowers management of demand & distributed generation profiles, market design for ancillary services, and policy making for aggregators. It also supports making better investments decisions for all stakeholders. The proposed formulation is tested on a modified version of the IEEE14-bus system with DR units having different response characteristics. DR units yield a decrease in secure energy price, total system operation cost and up-reserve. On the other hand, DR units raise the price of down-reserve.