A bilevel modeling methodology to optimize the value of distributed energy resources in electric transmission and distribution systems

The transition of electricity generation from a centralized structure to a more distributed framework in grids across the globe calls for new methods to appropriately value the services that distributed energy resources (DER) can provide. Current methods for valuing DER services account for the grid operator perspective but typically ignore DER owner objectives and constraints. The goal of this dissertation is to develop new methods for valuing distributed energy resources in electricity transmission and distribution systems, with a particular focus on accounting for multiple perspectives. This goal is achieved by developing a new linearization technique for bilevel optimization problems that allows modeling energy system optimization problems at scales that matter. The linearization technique is leveraged to develop a new framework for valuing distributed energy resources in transmission and distribution systems. The proposed framework allows for competing perspectives to be modeled. Furthermore, a new method for creating synthetic electricity price scenarios is developed and its value demonstrated in a stochastic optimization framework. The current model for valuing electricity generation in deregulated energy markets determines prices from an optimal power flow problem whose objective is to maximize the social welfare. This work develops a general framework for determining the spatiotemporal value of DER that includes DER owner objectives in concert with maximizing the social welfare. The framework is built in a bilevel program that allows for incorporation of any optimal power flow model as well as replacing the social welfare objective with any value function, such as the objective of a profit-oriented DER aggregator. Special attention is placed on linearizing bilinear products of dispatch and price variables such that the framework can scale to large network models. The general framework is leveraged to develop a method to assess the techno-economic potential of DER for distribution system upgrade deferrals. The state-of-the-art for valuing DER for distribution system upgrade deferrals is advanced by accounting for DER owner objectives and constraints in concert with system operator goals and constraints. A use-case shows how the framework can be leveraged to value DER for non-wires alternatives. Comparing life cycle costs over 20 years for the system planner, the results show that by valuing DER for non-wires alternatives the DSO can avoid upgrading most of the overloaded components as well as achieve a net present value of nearly $3M relative to the cost of the traditional upgrades. The results also show that the DSO can achieve an additional $1M in net present value when valuing privately owned DER relative to a scenario with utility owned batteries. Finally, recognizing the need for better representation of the uncertainty in electricity market prices in energy system models, a novel method for generating realistic, synthetic electricity prices is developed. Several weaknesses in the state-of-the-art for stochastic price generation methods are addressed: (1) better characterization of daily and weekly trends is achieved by replacing the mean-reversion component of the stochastic differential equation with an autoregressive integrated moving average process; (2) the conditional probability of consecutive price-spikes, or “jumps”, is captured for the first time by replacing the traditional Poisson process with a generalized point process inspired by brain neuron models; and (3) a more realistic model variance is achieved by replacing the static empirical variance with a Markov process. The new methodology allows researchers and practitioners to evaluate bidding strategies for DER in electricity markets. In addition to accurately modeling historical trends, market behavior that has not been observed can be created by tuning model parameters. The method is exercised with electricity prices from the US ERCOT market and a use-case example is provided for bidding an energy storage unit into the ERCOT market. The results show that accounting for price uncertainty via the synthetic time-series can increase market profits by as much as 47% over a bidding strategy that relies on a deterministic price forecast.