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Flexible loads are a resource for the Balancing Authority (BA) of the future to aid in the balance of power supply and demand. In order to be used as a resource, the BA must know the capacity of the flexible loads to vary their power demand over a baseline without violating consumers' quality of service (QoS). Existing work on capacity characterization is model-based: They need models relating power consumption to variables that dictate QoS, such as temperature in the case of an air conditioning system. However, in many cases the model parameters are not known or are difficult to obtain. In this work, we pose a data driven capacity characterization method that does not require model information, it only needs access to a simulator. The capacity is characterized as the set of feasible spectral densities (SDs) of the demand deviation. The proposed method is an extension of our recent work on SD-based capacity characterization that was limited to the case where the loads dynamic model is completely known. Numerical evaluation of the method is provided, which compares our approach to the model-based solution of our past work. 

With increase in the frequency of natural disasters such as hurricanes that disrupt the supply from the grid, there is a greater need for resiliency in electric supply. Rooftop solar photovoltaic (PV) panels along with batteries can provide resiliency to a house in a blackout due to a natural disaster. Our previous work showed that intelligence can reduce the size of a PV+battery system for the same level of post-blackout service compared to a conventional system that does not employ intelligent control. The intelligent controller proposed is based on model predictive control (MPC), which has two main challenges. One, it requires simple yet accurate models as it involves real-time optimization. Two, the discrete actuation for residential loads (on/off) makes the underlying optimization problem a mixed-integer program (MIP) which is challenging to solve. An attractive alternative to MPC is reinforcement learning (RL) as the real-time control computation is both model-free and simple. These points of interest accompany certain trade-offs; RL requires computationally expensive offline learning, and its performance is sensitive to various design choices. In this work, we propose an RL-based controller. We compare its performance with the MPC controller proposed in our prior work and a non-intelligent baseline controller. The RL controller is found to provide a resiliency performance — by commanding critical loads and batteries—similar to MPC with a significant reduction in computational effort. 

The high penetration of renewable sources of energy in electrical power systems implies an increase in the uncertainty variables of the economic dispatch (ED). Uncertainty costs are a metric to quantify the variability introduced from renewable energy generation, that is to say: wind energy generation (WEG), run-of-the-river hydro generators (RHG), and solar photovoltaic generation (PVG). On other side, there are associated uncertainties to the charge/uncharge of plug-in electric vehicles (PEV). Thus, in this paper, the uncertainty cost functions (UCF) and their marginal expressions as a way of modeling and assessment of stochasticity in power systems with high penetration of smart grids elements is presented. In this work, a mathematical analysis is presented using the first and second derivatives of the UCF, where the marginal uncertainty cost functions (MUCF) and the UCF’s minimums for PVG, WEG, PEV, and RHG are derived. Further, a model validation is presented, considering comparative test results from the state of the art of the UCF minimum, developed in a previous study, to the minimum reached with the presented (MUCF) solution.