Optimal CVSR allocation to ensure network health in static load shedding– a Bi-level optimization approach

•We introduce two inter-related optimization levels to ensure network health.•We suggest general load shedding scheme for power systems in the presence of CVSRs.•Critical lines are determined using a new index.•Optimal load shedding with and without considering CVSR allocation are studied. In this paper, a new methodology is proposed for achieving a general load shedding scheme to prevent power system cascading line outages with the help of continuously variable series reactors (CVSRs). In the proposed methodology, first, critical lines are determined using a new index. Critical lines here are those lines that, if tripped out, make the post-disturbance system operate closer to instability limits. An innovative optimization problem is then solved to find a general load shedding scheme to cover the single outage of all critical lines so that three objectives, i.e. maximizing voltage stability of the system and minimizing voltage deviations as well as overloading of lines, are obtained. In addition, since CVSR as a recently introduced compensating device has the capability of increasing the capacity of lines, which is so essential for load shedding strategies, a CVSR allocation problem is also added to the proposed optimization problem. However, as the problem of maximizing voltage stability has to be solved separately from the main optimization problem, a bi-level optimization approach has been introduced. Therefore, there will be two levels of optimization each one has its own solver and variables. The effectiveness of the proposed load shedding optimization approach has been demonstrated using 30-bus test system as a test system and 200-bus Illinois system as a real system.