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In this two-part paper, we consider the problem of profit-seeking distributed energy resource aggregators (DERAs) participating in the wholesale electricity market operated by an independent system operator (ISO). Part I proposes a market-based coordination mechanism in the form of a forward auction to allocate network access limits to DERAs. The proposed coordination mechanism results in decoupled DSO-DERA-ISO operations in the real-time electricity market, ensuring the distribution system reliability independent of DERAs' aggregation actions and wholesale market conditions. Welfare-maximizing market clearing problems under robust and risk-sensitive formulations are derived. Properties of the proposed auction, such as nonnegative surpluses of DSO and DERAs, along with empirical performance studies, are presented. Part II of the paper develops competitive profit-maximizing aggregation strategies for DERAs and their bidding strategies as virtual storage participants in the wholesale market., Comment: 12 page, 8 figure

We consider the control of a Markov decision process (MDP) that undergoes an abrupt change in its transition kernel (mode). We formulate the problem of minimizing regret under control-switching based on mode change detection, compared to a mode-observing controller, as an optimal stopping problem. Using a sequence of approximations, we reduce it to a quickest change detection (QCD) problem with Markovian data, for which we characterize a state-dependent threshold-type optimal change detection policy. Numerical experiments illustrate various properties of our control-switching policy.

Solar hosting capacity analysis (HCA) assesses the ability of a distribution network to host distributed solar generation without seriously violating distribution network constraints. In this paper, we consider risk-sensitive HCA that limits the risk of network constraint violations with a collection of scenarios of solar irradiance and nodal power demands, where risk is modeled via the conditional value at risk (CVaR) measure. First, we consider the question of maximizing aggregate installed solar capacities, subject to risk constraints and solve it as a second-order cone program (SOCP) with a standard conic relaxation of the feasible set with power flow equations. Second, we design an incremental algorithm to decide whether a configuration of solar installations has acceptable risk of constraint violations, modeled via CVaR. The algorithm circumvents explicit risk computation by incrementally constructing inner and outer polyhedral approximations of the set of acceptable solar installation configurations from prior such tests conducted. Our numerical examples study the impact of risk parameters, the number of scenarios and the scalability of our framework., Comment: 10 pages, 7 figures, 2 tables

We study finite-time performance of a recently proposed distributed dual subgradient (DDSG) method for convex constrained multi-agent optimization problems. The algorithm enjoys performance guarantees on the last primal iterate, as opposed to those derived for ergodic means for vanilla DDSG algorithms. Our work improves the recently published convergence rate of $\Ocal(\log T/\sqrt{T})$ with decaying step-sizes to $\Ocal(1/\sqrt{T})$ with constant step-size on a metric that combines suboptimality and constraint violation. We then numerically evaluate the algorithm on three grid optimization problems. Namely, these are tie-line scheduling in multi-area power systems, coordination of distributed energy resources in radial distribution networks, and joint dispatch of transmission and distribution assets. The DDSG algorithm applies to each problem with various relaxations and linearizations of the power flow equations. The numerical experiments illustrate various properties of the DDSG algorithm--comparison with vanilla DDSG, impact of the number of agents, and why Nesterov-style acceleration fails in DDSG settings.

We consider a market in which both suppliers and consumers compete for a product via scalar-parameterized supply offers and demand bids. Scalar-parameterized offers/bids are appealing due to their modeling simplicity and desirable mathematical properties with the most prominent being bounded efficiency loss and price markup under strategic interactions. Our model incorporates production capacity constraints and minimum inelastic demand requirements. Under perfect competition, the market mechanism yields allocations that maximize social welfare. When market participants are price-anticipating, we show that there exists a unique Nash equilibrium, and provide an efficient way to compute the resulting market allocation. Moreover, we explicitly characterize the bounds on the welfare loss and prices observed at the Nash equilibrium., Comment: 8 pages, 4 figures

We consider the problem of characterizing the locational marginal value of energy storage capacity in electric power networks with stochastic renewable supply and demand. The perspective taken is that of a system operator, whose objective is to minimize the expected cost of firm supply required to balance a stochastic net demand process over a finite horizon, subject to transmission and energy storage constraints. The value of energy storage capacity is defined in terms of the optimal value of the corresponding constrained stochastic control problem. It is shown to be concave and non decreasing in the vector of location-dependent storage capacities -- implying that the greatest marginal value of storage is derived from initial investments in storage capacities. We also provide a characterization of said marginal value, which reveals its explicit dependency on a specific measure of nodal price variation. And, more generally, we derive an upper bound on the locational marginal value of energy storage capacity in terms of the total variation of the corresponding nodal price process, and provide conditions under which this bound is tight.

In this paper we quantify the total economic impact of an epidemic over a complex network using tools from random matrix theory. Incorporating the direct and indirect costs of infection, we calculate the disease cost in the large graph limit for an SIS (Susceptible - Infected - Susceptible) infection process. We also give an upper bound on this cost for arbitrary finite graphs and illustrate both calculated costs using extensive simulations on random and real-world networks. We extend these calculations by considering the total social cost of an epidemic, accounting for both the immunization and disease costs for various immunization strategies and determining the optimal immunization. Our work focuses on the transient behavior of the epidemic, in contrast to previous research, which typically focuses on determining the steady-state system equilibrium., Comment: 25 pages, 12 figures. Submitted to Informs Journal of Mathematics of Operations Research

A branch flow model has recently been proposed for the analysis and optimization of power flows. In this paper we show that the model is equivalent to the more popular bus injection model. Moreover, we prove the equivalence of various relaxations of these two models.