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Resilience of power systems is already a key issue that is getting frequent attention all over the world. It is useful to analyze resilience issues not only for bulk supply, but at all levels including at a customer level. This is because distributed energy resources can play a prominent role in enhancing resilience. Although the literature on planning models, tools and data for bulk supply and distribution systems have expanded in recent years, customer-centric planning, e.g., for an individual household, is yet to receive adequate attention. Although solar PV and battery storage at a household level have been analyzed, how these resources can be optimally combined, together with grid supply, from a resilience perspective is the focus of this study. The study demonstrates how a conceptual framework can be developed to show the trade-off between system costs and resilience including its dimensions such as duration, depth and frequency of service outages. A planning model is developed that incorporates multiple facets of resilience and individual customer preferences. The model considers power system resilience explicitly as a constraint. The model is implemented for a household level case study in Miami, Florida. The results show there are complex trade-offs among different dimensions of resilience. The study demonstrates how combined resilience metrics can be formulated and evaluated using the proposed least-cost planning model at a household level to optimize grid supply together with solar, battery storage and diesel generators. The model allows a planner to directly embed a resilience standard to drive the optimal supply mix. These concepts and the modeling construct can also be applied at other levels of planning, including community level and bulk supply system planning.

This paper presents the design and results of a model that uses household smart meter data, electric vehicle (EV) travel load and charging options, and multiple solar resource profiles, to make decisions on optimal combinations of photovoltaics (PV), battery energy storage systems (BESS) and EV charging strategies. The least-cost planning model is formulated as a stochastic mixed integer programming (MIP) problem that makes first stage decisions on PV/BESS investments, and recourse decisions on purchase/sell from/to the grid to minimize expected household electricity costs. The model undertakes a customer-centric optimization taking into consideration net metering policy, time-of-use grid pricing, and uncertainties around inter-annual variability of solar irradiance. The model adds to the existing literature in terms of stochastic representation of inter-annual variability of solar irradiance, together with BESS capacity optimization, and EV charging mode selection. Three case studies are presented: two for a residential house with and without EV load, and a third for a larger community facility. Results from the model for the first residential house case study are compared with commercially available software to show the impacts of an accurate load profile and different policy parameters. The stochastic feature of the model proves useful in understanding the impact of variability in solar resource profiles on PV sizing. Finally, simulations of alternative EV travel patterns and tariff policies that discourage charging during the evening peak show the efficacy of `super off-peak' pricing being introduced in the state of Maryland.

Small-scale battery energy storage systems (BESS), especially for behind-the-meter applications, are still relatively expensive, but we show that it can be a potent solution to render homes resilient to storm related power outages. We present a stochastic programming model formulation to optimize PV/BESS explicitly accounting for resilience benefits these investments entail, over and above their ability to reduce cost of supply. The stochastic optimization considers uncertainties around storm related grid supply failures as well as variability of solar PV. The model includes an embedded Monte Carlo simulation module that considers storm related outage risks using climate model reanalysis data. It is a least-cost planning framework that optimizes selection of BESS, solar PV, grid supply, and diesel generator, from a home-owner's perspective. We present two case studies with low and high storm risks that demonstrate how different risk exposures can impact on the selection of alternative options to build resilience. Duals, or shadow prices, of demand-supply constraints from the model for both normal days and for storm related contingencies, provide interesting insights into the marginal cost of supply that can inform innovative pricing schemes to promote customer level resilience measures. The case study results reveal significant merits of BESS, in combination with PV, to enhance resilience. We find that in low-risk areas like Bethesda, MD, incremental PV and BESS required for a more resilient system can add $79 (4%) to annual electricity costs for a typical household, and a considerably higher $208 (10.6%) in Miami, FL which is at a much greater risk. These options are, however, 27% (in Bethesda) and 20% (in Florida) less expensive than the conventional solution of installing a diesel generator. These results provide insights into the value of BESS as part of a resilient and clean energy solution for households.