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Solving large-scale capacity expansion problems (CEPs) is central to cost-effective decarbonization of regional-scale energy systems. To ensure the intended outcomes of CEPs, modeling uncertainty due to weather-dependent variable renewable energy (VRE) supply and energy demand becomes crucially important. However, the resulting stochastic optimization models are often less computationally tractable than their deterministic counterparts. Here, we propose a learning-assisted approximate solution method to tractably solve two-stage stochastic CEPs. Our method identifies low-cost planning decisions by constructing and solving a sequence of tractable temporally aggregated surrogate problems. We adopt a Bayesian optimization approach to searching the space of time series aggregation hyperparameters and compute approximate solutions that minimize costs on a validation set of supply-demand projections. Importantly, we evaluate solved planning outcomes on a held-out set of test projections. We apply our approach to generation and transmission expansion planning for a joint power-gas system spanning New England. We show that our approach yields an estimated cost savings of up to 3.8% in comparison to benchmark time series aggregation approaches.

Building heat electrification is central to economy-wide decarbonization efforts and directly affects energy infrastructure planning through increasing electricity demand and reducing the building sector's use of gas infrastructure that also serves the power sector. Here, we develop a modeling framework to quantify end-use demand for electricity and gas in the buildings sector under various electrification pathways and evaluate their impact on co-optimized bulk power-gas infrastructure investments and operations under deep decarbonization scenarios. Applying the framework to study the U.S. New England region in 2050 across 20 weather scenarios, we find high electrification of the residential sector can increase sectoral peak and total electricity demands by up to 56-158% and 41-59% respectively relative to business-as-usual projections. Employing demand-side measures like building envelope improvements under high electrification, however, can reduce the magnitude and weather sensitivity of peak load as well as induce overall efficiency gains, reducing the combined residential sector energy demand for power and gas by 28-30% relative to the present day. Notably, a combination of high electrification and envelope improvements yields the lowest bulk power-gas system cost outcomes. We also find that inter-annual weather-driven variations in demand result in up to 33% variation in optimal power sector investments, which highlights the importance of capturing weather sensitivity of demand for planning purposes.

We focus on the problem of uncertainty informed allocation of medical resources (vaccines) to heterogeneous populations for managing epidemic spread. We tackle two related questions: (1) For a compartmental ordinary differential equation (ODE) model of epidemic spread, how can we estimate and integrate parameter uncertainty into resource allocation decisions? (2) How can we computationally handle both nonlinear ODE constraints and parameter uncertainties for a generic stochastic optimization problem for resource allocation? To the best of our knowledge current literature does not fully resolve these questions. Here, we develop a data-driven approach to represent parameter uncertainty accurately and tractably in a novel stochastic optimization problem formulation. We first generate a tractable scenario set by estimating the distribution on ODE model parameters using Bayesian inference with Gaussian processes. Next, we develop a parallelized solution algorithm that accounts for scenario-dependent nonlinear ODE constraints. Our scenario-set generation procedure and solution approach are flexible in that they can handle any compartmental epidemiological ODE model. Our computational experiments on two different non-linear ODE models (SEIR and SEPIHR) indicate that accounting for uncertainty in key epidemiological parameters can improve the efficacy of time-critical allocation decisions by 4-8%. This improvement can be attributed to data-driven and optimal (strategic) nature of vaccine allocations, especially in the early stages of the epidemic when the allocation strategy can crucially impact the long-term trajectory of the disease.

Effective investment planning decisions are crucial to ensure cyber-physical infrastructures satisfy performance requirements over an extended time horizon. Computing these decisions often requires solving Capacity Expansion Problems (CEPs). In the context of regional-scale energy systems, these problems are prohibitively expensive to solve due to large network sizes, heterogeneous node characteristics, and a large number of operational periods. To maintain tractability, traditional approaches aggregate network nodes and/or select a set of representative time periods. Often, these reductions do not capture supply-demand variations that crucially impact CEP costs and constraints, leading to suboptimal decisions. Here, we propose a novel graph convolutional autoencoder approach for spatio-temporal aggregation of a generic CEP with heterogeneous nodes (CEPHN). Our architecture leverages graph pooling to identify nodes with similar characteristics and minimizes a multi-objective loss function. This loss function is tailored to induce desirable spatial and temporal aggregations with regard to tractability and optimality. In particular, the output of the graph pooling provides a spatial aggregation while clustering the low-dimensional encoded representations yields a temporal aggregation. We apply our approach to generation expansion planning of a coupled 88-node power and natural gas system in New England. The resulting aggregation leads to a simpler CEPHN with 6 nodes and a small set of representative days selected from one year. We evaluate aggregation outcomes over a range of hyperparameters governing the loss function and compare resulting upper bounds on the original problem with those obtained using benchmark methods. We show that our approach provides upper bounds that are 33% (resp. 10%) lower those than obtained from benchmark spatial (resp. temporal) aggregation approaches.

The transition to a deeply decarbonized energy system requires coordinated planning of infrastructure investments and operations serving multiple end-uses while considering technology and policy-enabled interactions across sectors. Electricity and natural gas (NG), which are vital vectors of today's energy system, are likely to be coupled in different ways in the future, resulting from increasing electrification, adoption of variable renewable energy (VRE) generation in the power sector and policy factors such as cross-sectoral emissions trading. This paper develops a least-cost investment and operations model for joint planning of electricity and NG infrastructures that considers a wide range of available and emerging technology options across the two vectors, including carbon capture and storage (CCS) equipped power generation, low-carbon drop-in fuels (LCDF) as well as long-duration energy storage (LDES). The model incorporates the main operational constraints of both systems and allows each system to operate under different temporal resolutions consistent with their typical scheduling timescales. We apply the modeling framework to evaluate power-NG system outcomes for the U.S. New England region under different technology, decarbonization goals, and demand scenarios. Under a global emissions constraint, ranging between 80-95\% emissions reduction compared to 1990 levels, the least-cost solution disproportionately relies on using the available emissions budget to serve non-power NG demand and results in the power sector using only 15-43\% of the emissions budget.

A rapid transformation of current electric power and natural gas (NG) infrastructure is imperative to meet the mid-century goal of CO2 emissions reduction requires. This necessitates a long-term planning of the joint power-NG system under representative demand and supply patterns, operational constraints, and policy considerations. Our work is motivated by the computational and practical challenges associated with solving the generation and transmission expansion problem (GTEP) for joint planning of power-NG systems. Specifically, we focus on efficiently extracting a set of representative days from power and NG data in respective networks and using this set to reduce the computational burden required to solve the GTEP. We propose a Graph Autoencoder for Multiple time resolution Energy Systems (GAMES) to capture the spatio-temporal demand patterns in interdependent networks and account for differences in the temporal resolution of available data. The resulting embeddings are used in a clustering algorithm to select representative days. We evaluate the effectiveness of our approach in solving a GTEP formulation calibrated for the joint power-NG system in New England. This formulation accounts for the physical interdependencies between power and NG systems, including the joint emissions constraint. Our results show that the set of representative days obtained from GAMES not only allows us to tractably solve the GTEP formulation, but also achieves a lower cost of implementing the joint planning decisions.

We consider the security-by-design of a signal-free intersection for connected and autonomous vehicles in the face of strategic jamming attacks. We use a fluid model to characterize macroscopic traffic flow through the intersection, where the saturation rate is derived from a vehicle coordination algorithm. We model jamming attacks as sudden increase in communication latency induced on vehicle-to-infrastructure connectivity; such latency triggers the safety mode for vehicle coordination and thus reduces the intersection saturation rate. A strategic attacker selects the attacking rate, while a system operator selects key design parameters, either the saturation rate or the recovery rate. Both players' actions induce technological costs and jointly determine the mean travel delay. By analyzing the equilibrium of the security game, we study the preferable level of investment in the intersection's nominal discharging capability or recovery capability., Comment: Accepted by 2022 IEEE Conference on Decision and Control(CDC)

This paper introduces a "green" routing game between multiple logistic operators (players), each owning a mixed fleet of internal combustion engine vehicle (ICEV) and electric vehicle (EV) trucks. Each player faces the cost of delayed delivery (due to charging requirements of EVs) and a pollution cost levied on the ICEVs. This cost structure models: 1) limited battery capacity of EVs and their charging requirement; 2) shared nature of charging facilities; 3) pollution cost levied by regulatory agency on the use of ICEVs. We characterize Nash equilibria of this game and derive a condition for its uniqueness. We also use the gradient projection method to compute this equilibrium in a distributed manner. Our equilibrium analysis is useful to analyze the trade-off faced by players in incurring higher delay due to congestion at charging locations when the share of EVs increases versus a higher pollution cost when the share of ICEVs increases. A numerical example suggests that to increase marginal pollution cost can dramatically reduce inefficiency of equilibria., Comment: 8 pages

Highway capacity is often subject to stochastic perturbations due to the combined effects of weather, traffic mixture, driver behavior, etc. This paper is motivated by the need of a systematic approach to traffic control with performance guarantees in the face of such perturbations. We develop a novel control-theoretic method for designing perturbation-resilient ramp metering. We consider a cell-transmission model with 1) Markovian cell capacities and 2) buffers representing on-ramps and upstream mainline. Using this model, we analyze the stability of on-ramp queues by constructing piecewise Lyapunov functions that consider the nature of nonlinear traffic dynamics. Then, we design ramp controllers that guarantee bounds for throughput and queue sizes. We also formulate the problem of coordinated ramp metering as a bi-level optimization with non-convex inner sub-problems. To address the computational issue in solving this problem, we also consider localized and partially coordinated reformulations. A case study of a 18.1-km highway in Los Angeles, USA indicates a 8.3\% (resp. 9.9\%) reduction of vehicle-hours-traveled obtained by the localized (resp. partially coordinated) control, both outperforming the classical ALINEA and METALINE controllers.

We study learning dynamics induced by strategic agents who repeatedly play a game with an unknown payoff-relevant parameter. In each step, an information system estimates a belief distribution of the parameter based on the players' strategies and realized payoffs using Bayes' rule. Players adjust their strategies by accounting for an equilibrium strategy or a best response strategy based on the updated belief. We prove that beliefs and strategies converge to a fixed point with probability 1. We also provide conditions that guarantee local and global stability of fixed points. Any fixed point belief consistently estimates the payoff distribution given the fixed point strategy profile. However, convergence to a complete information Nash equilibrium is not always guaranteed. We provide a sufficient and necessary condition under which fixed point belief recovers the unknown parameter. We also provide a sufficient condition for convergence to complete information equilibrium even when parameter learning is incomplete.

In recent years, it has become crucial to improve the resilience of electricity distribution networks (DNs) against storm-induced failures. Microgrids enabled by Distributed Energy Resources (DERs) can significantly help speed up re-energization of loads, particularly in the complete absence of bulk power supply. We describe an integrated approach which considers a pre-storm DER allocation problem under the uncertainty of failure scenarios as well as a post-storm dispatch problem in microgrids during the multi-period repair of the failed components. This problem is computationally challenging because the number of scenarios (resp. binary variables) increases exponentially (resp. quadratically) in the network size. Our overall solution approach for solving the resulting two-stage mixed-integer linear program (MILP) involves implementing the sample average approximation (SAA) method and Benders Decomposition. Additionally, we implement a greedy approach to reduce the computational time requirements of the post-storm repair scheduling and dispatch problem. The optimality of the resulting solution is evaluated on a modified IEEE 36-node network., Comment: 6 pages, 5 figures, accepted to 2020 American Control Conference

Traffic navigation services have gained widespread adoption in recent years. The route recommendations generated by these services often leads to severe congestion on urban streets, raising concerns from neighboring residents and city authorities. This paper is motivated by the question: How can a transportation authority design an information structure to induce a preferred equilibrium traffic flow pattern in uncertain network state conditions? We approach this question from a Bayesian persuasion viewpoint. We consider a basic routing game with two parallel routes and an uncertain state that affects the travel cost on one of the routes. The authority sends a noisy signal of the state to a given fraction of travelers. The information structure (i.e., distribution of signals in each state) chosen by the authority creates a heterogeneous information environment for the routing game. The solution concept governing the travelers' route choices is Bayesian Wardrop Equilibrium. We design an information structure to minimize the average traffic spillover -- the amount of equilibrium route flow exceeding a certain threshold -- on one of the routes. We provide an analytical characterization of the optimal information structure for any fraction of travelers receiving the signal. We find that it can achieve the minimum spillover so long as the fraction of travelers receiving the signal is larger than a threshold (smaller than 1).

In this paper, we study the problem of traffic management in highways facing stochastic perturbations. To model the macroscopic traffic flow under perturbations, we use cell-transmission model with Markovian capacities. The decision variables are: (i) the admissible flow through each on-ramp, and (ii) whether individual on-ramps are metered to prioritize the mainline traffic or not. The objective is to maximize the throughput while ensuring that on-ramp queues remain bounded on average. We develop a computational approach to solving this stability-constrained, throughput-maximization problem. We establish a mixed-integer linear program for throughput maximization and construct an algorithm that gives the optimal solution in particular settings. We illustrate the performance benefits of the proposed approach through a computational study on a segment of Interstate 210 in California, USA., Comment: 27 pages

This article studies a problem of strategic network inspection, in which a defender (agency) is tasked with detecting the presence of multiple attacks in the network. An inspection strategy entails monitoring the network components, possibly in a randomized manner, using a given number of detectors. We formulate the network inspection problem $(\mathcal{P})$ as a large-scale bilevel optimization problem, in which the defender seeks to determine an inspection strategy with minimum number of detectors that ensures a target expected detection rate under worst-case attacks. We show that optimal solutions of $(\mathcal{P})$ can be obtained from the equilibria of a large-scale zero-sum game. Our equilibrium analysis involves both game-theoretic and combinatorial arguments, and leads to a computationally tractable approach to solve $(\mathcal{P})$. Firstly, we construct an approximate solution by utilizing solutions of minimum set cover (MSC) and maximum set packing (MSP) problems, and evaluate its detection performance. In fact, this construction generalizes some of the known results in network security games. Secondly, we leverage properties of the optimal detection rate to iteratively refine our MSC/MSP-based solution through a column generation procedure. Computational results on benchmark water networks demonstrate the scalability, performance, and operational feasibility of our approach. The results indicate that utilities can achieve a high level of protection in large-scale networks by strategically positioning a small number of detectors.