The following article details a model predictive control (MPC) to improve grid resilience when faced with variable generation resources. This topic is of significant interest to utility power systems where distributed intermittent energy sources will increase significantly and be relied on for electric grid ancillary services. Previous work on MPCs has focused on narrowly targeted control applications such as improving electric vehicle (EV) charging infrastructure or reducing the cost of integrating Energy Storage Systems (ESSs) into the grid. In contrast, this article develops a comprehensive treatment of the construction of an MPC tailored to electric grids and then applies it integration of intermittent energy resources. To accomplish this, the following article includes a description of a reduced order model (ROM) of an electric power grid based on a circuit model, an optimization formulation that describes the MPC, a collocation method for solving linear time-dependent differential algebraic equations (DAEs) that result from the ROM, and an overall strategy for iteratively refining the behavior of the MPC. Next, the algorithm is validated using two separate numerical experiments. First, the algorithm is compared to an existing MPC code and the results are verified by a numerically precise simulation. It is shown that this algorithm produces a control comparable to existing algorithms and the behavior of the control carefully respects the bounds specified. Second, the MPC is applied to a small nine bus system that contains a mix of turbine-spinning-machine-based and intermittent generation in order to demonstrate the algorithm’s utility for resource planning and control of intermittent resources. This study demonstrates how the MPC can be tuned to change the behavior of the control, which can then assist with the integration of intermittent resources into the grid. The emphasis throughout the paper is to provide systematic treatment of the topic and produce a novel nonlinear control compatible design framework applicable to electric grids and the control of variable resources. This differs from the more targeted application-based focus in most presentations.

This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

This paper demonstrates that a power grid may be fully protected from E₃ high-altitude magnetic pulses (HEMP) using E₃ arrestor devices placed at substations that represent any vertex cover of the grid. This serves as a simple linear time check to see if pre-existing E₃ arrestor-type assets are sufficient for the mitigation of E₃ HEMP waveforms. The algorithm to determine where to place new arrestor devices is computationally inexpensive, with a runtime of 8 ms for an 18-bus test case and a runtime of 486 ms for a 150-bus test case in MATLAB to determine the bounding case approximation. The algorithm accomplishes this by finding the minimum vertex cover of the grid and placing E₃ arrestor devices in those locations. Since computing the minimum vertex cover is NP-Hard, the algorithm approximates this by computing the solution of a linear program combined with a heuristic based on the four color theorem and knowledge of the permissible substations to upgrade (i.e. substations with E₃ arrestors). If the solution exists, it guarantees the near zeroing out of flux across all transformers. If some flux can be tolerated, there may exist an even smaller set of substations to protect that allow system specifications to be met. Additionally, if there already exist devices that make up a vertex cover on the grid, then it is guaranteed that the grid is already protected from E₃ disturbances. The check for this distribution of devices is linear in time. The vertex cover solution may be used with other optimization techniques as a homotopy to find the minimum number of required E₃ arrestors. The minimum vertex cover is the bounding case solution for the E₃ arrestor device.