Controllability of the Electrical State via Nodal Power Injections

Contact: Cong Wang

Project Description:

In smart grids, various feedback controllers are deployed for controlling the nodal power injections. By managing the nodal power injections, people typically expect to have a full control of the electrical states. More specifically, they would like to ensure that the electrical states always fulfil security and non-singularity constraints. However, due to the nonlinear relation between electrical states and nodal power injections, controllability of the latter does not imply controllability of the former in general. In a recent research, it has been shown that, under certain conditions, full controllability of the electrical states via nodal power injections can be possible. Moreover, given a set S of nodal power injections and an initial electrical state that is secured and non-singular, an algorithm has been developed and is able to determine whether there exists a set V of electrical states such that (i) all elements in V satisfy the security and non-singularity constraints; (ii) every nodal power injection in S has exactly one corresponding electrical state in V; (iii) the initial electrical state belongs to V; (iv) by keeping the future continuous trajectory of nodal power injection in S, the future continuous trajectory of electrical state is automatically ensured to reside in V.


[1] Cong Wang, et al. “Controlling the electrical state via uncertain power injections in three-phase distribution networks” (2017)

Project Goals:

  • Understand the theories that are given in [1] as well as its references;
  • Implement the proposed patching algorithm in [1] using C++.

Required Skills:

  • Power system load-flow solvability and quasi-stationary analysis;
  • Basic knowledge of real, complex, and numerical analysis;
  • Solid skills in C++ programming.

Supervisors: Cong Wang