Pavithra Harsha

Optimal Management and Sizing of Energy Storage Under Dynamic Pricing for the Efficient Integration of Renewable Energy

We address the optimal energy storage management and sizing problem in the presence of renewable energy and dynamic pricing associated with electricity from the grid. We formulate the problem as a stochastic dynamic program that aims to minimize the long-run average cost of electricity used and investment in storage, if any, while satisfying all the demand. We model storage with ramp constraints, conversion losses, dissipation losses and an investment cost. We prove the existence of an optimal storage management policy under mild assumptions and show that it has a dual threshold structure. Under this policy, we derive structural results, which indicate that the marginal value from storage decreases with its size and that the optimal storage size can be computed efficiently. We prove a rather surprising result, as we characterize the maximum value of storage under constant prices and i.i.d. net-demand processes: if the storage is a profitable investment, then the ratio of the amortized cost of storage to the constant price is less than 1/4. We further perform sensitivity analysis on the size of optimal storage and its gain via a case study. Finally, with a computational study on real data, we demonstrate significant savings with energy storage.

Optimal sizing of energy storage for efficient integration of renewable energy

In this paper, we study the optimal storage investment problem faced by an owner of renewable generator the purpose of which is to support a portion of a local demand. The goal is to minimize the long-term average cost of electric bills in the presence of dynamic pricing as well as investment in storage, if any. Examples of this setting include homeowners, industries, hospitals or utilities that own wind turbines or solar panels and have their own demand that they prefer to support with renewable generation. We formulate the optimal storage investment problem and propose a simple balancing control for operating storage. We show that this policy is optimal for constant prices and some special cases of price structures that restrict to at most two levels. Under this policy, we provide structural results that help in evaluating the optimal storage investment uniquely and efficiently. We then characterize how the cost and efficiency of storage, dynamic pricing and parameters that characterize the uncertainty in generation and demand impact the size of optimal storage and its gain. One surprising result we prove is that for storage to be profitable under the balancing policy the ratio amortized cost of storage to the peak price of energy should be less than 1 over 4

A Framework for the Analysis of Probabilistic Demand Response Schemes

We describe the class of probabilistic demand response (PDR) schemes, which are particularly suited for dynamic load management in the residential sector. Our main contribution is a new methodology for implementing and analyzing these schemes based on an operational objective function that balances the total cost of meeting demand, which includes the costs of supply generation, and spinning reserves, with the total revenue from the met demand and the gain from storage/deferment. We derive structural results for the design of PDR schemes in terms of sufficient conditions that yield a well-posed joint optimization problem for the two decision variables: the planned supply generation level and the real-time PDR signal magnitude. These results are used to evaluate the suitability of various proposed PDR schemes in single-period and multiple-period contexts. Finally, using simulations, we illustrate the application and effectiveness of the proposed methodology for a collection of thermostatically-controlled residential loads.

DESIGNING PRICE INCENTIVES IN A NETWORK WITH SOCIAL INTERACTIONS

The recent ubiquity of social networks allows firms to collect vast amount of data on their customers and on their social interactions. We consider a setting where a monopolist sells an indivisible good to consumers who are embedded in a social network. This an important problem as sellers can use available data to design and send targeted promotions that account for social externality effects and ultimately increase their profits. We capture the interactions among consumers using a broad class of non-linear utility models. This class extends the existing models by explicitly capturing externalities from subsets of agents (communities or groups) and includes several existing models as special cases (e.g., full information version of the triggering model). Assuming complete information about the interactions, we model the optimal pricing problem as a two-stage game. First, the firm designs prices to maximize profits and then consumers choose whether or not to purchase the item. Under positive network externalities, we show the existence of a pure Nash equilibrium that is preferred by both the seller and the buyers. Using duality theory and integer programming techniques, we reformulate the problem into a linear mixed-integer program (MIP). We derive efficient ways to optimally solve the MIP using its linear programming relaxation for two pricing strategies: discriminative and uniform. Finally, we propose two intuitive heuristic algorithms to solve the problem for which we derive worst-case parametric performance bounds. We draw interesting insights on the structure of the optimal prices and the sellers profit. In particular, we quantify the effect on prices when using a non-linear utility model relative to a linear model and identify settings when it is beneficial to offer a price below cost to influential agents. Finally, we extend our model and results to the case where the seller offers incentives (in addition to prices) to solicit actions so as to ensure network externality effects.