arXiv subjects

Andy Sun

Publications and source records attributed to Andy Sun.

14 recordsLinked to original sources

arXiv2026

On Locational Marginal Emissions in Electricity Markets: A Two-Layered Dispatch Mechanism and Its Fundamental Theorems

We propose a market design for real-time electricity markets that utilizes a two-layered dispatch mechanism to systematically incorporate carbon accounting into grid operations. In this mechanism, ``dispatch'', the centralized allocation of generation resources to meet system load, is executed via a hierarchical structure where the first layer minimizes financial costs to maintain economic efficiency, while the second layer minimizes system emissions strictly within the set of cost-optimal solutions. We define locational marginal emissions (LMEs) as the marginal rate of system emissions derived from the dual variables of the two-layered formulation. Unlike standard marginal prices which correspond to right-hand-side constraint relaxations, LMEs must account for the requirement of economic optimality which introduces demand parameters into the problem's constraint structure. Under the framework, we establish that LMEs satisfy properties analogous to the first and second fundamental theorems of welfare economics. We prove that (1) decentralized ``carbon profit'' maximization by individual grid entities guarantees a system-wide emission profile consistent with the economic dispatch, and (2) any optimal low-carbon economic dispatch is supported by a corresponding set of LME signals acting as a decentralized equilibrium. Furthermore, we establish a general carbon accounting theorem, called the Carbon Footprint Theorem, showing that these market-consistent LMEs ensure the sum of carbon accounts across all grid components (loads, generators, transmission, and storage) equals the total physical carbon emissions. This completes the theoretical foundation of the LME. Finally, we investigate and validate the empirical properties of LMEs and LME-based carbon accounting through case studies on a realistic Texas grid model.

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arXiv2026

Stochastic Optimization for Resource Adequacy in Capacity Markets with Storage and Renewables

The integration of storage and renewable resources fundamentally alters resource-adequacy analysis. Because storage couples decisions across time, it invalidates the traditional reliability models that are based on time-independent capacity demand curves. Moreover, renewables introduce temporally correlated intermittency. To address this, we formulate the capacity procurement problem as a two-stage stochastic program, where the capacity decision is made in the first stage, while the expected unserved energy is evaluated by a second-stage dispatch problem that considers uncertainties such as generator failures via Markov chains, temporally correlated renewable output, and stochastic load. We implement the resulting stochastic capacity procurement (SCP) model on a New England system with 305 generators, including conventional, renewable, and storage units. Using the stochastic decomposition (SD) algorithm, we solve the SCP with up to 20,000 Monte Carlo samples, each representing a six-month trajectory of more than 4,300 hours of uncertainty across all units. We analyze the convergence behavior of SD and show that convergence for the stochastic program happens faster than reliable estimation of the reliability metrics, which require more samples than are used in typical stochastic programs. These results show that chronologically detailed Monte Carlo sampling can be integrated into capacity procurement optimization in a computationally tractable manner, enabling reliability evaluation with controlled statistical accuracy at realistic system scales.

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arXiv2025

Locational Marginal Emissions for Carbon-Aware Data Center Operations in Large-Scale Power Grids

Carbon accounting methods for electricity consumption face challenges regarding physical deliverability, double counting, additionality, and impact magnitude. Locational Marginal Emissions (LMEs) show potential to address many of these key issues. However, their use in a large-scale power grids remains understudied. We analyze the properties of LMEs from a data center's perspective in a 1493-bus Western Interconnection over one year of hourly operation. We find that LME characteristics create three distinct regions: the hydropower-dominated Pacific Northwest, with low and stable LMEs; the coal-heavy Intermountain West, containing often high LMEs; and the Sunbelt, where mixed generation leads to variable LMEs correlated with solar output. This characterization provides analytical guidance for data center emission reduction. In particular, LME-guided emission reduction interventions through data center temporal-spatial load shifting, siting, and renewable procurement display over 85% accuracy with respect to actual emission reduction. Moreover, large-scale, nodal grid simulation is shown to be critical to accurate evaluation.

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arXiv2025

Dispatch-Aware Deep Neural Network for Optimal Transmission Switching

Optimal transmission switching (OTS) improves optimal power flow (OPF) by selectively opening transmission lines, but its mixed-integer formulation increases computational complexity, especially on large grids. To address this, we propose a dispatch-aware deep neural network (DA-DNN) that accelerates DC-OTS without relying on pre-solved labels, eliminating costly OTS label generation that becomes impractical at scale. DA-DNN predicts line states and passes them through an embedded differentiable DC-OPF layer, using the resulting generation cost as the loss function so that physical network constraints are enforced throughout training and inference. To stabilize training, we adopt a customized weight and bias initialization that keeps the embedded DC-OPF feasible from the first epoch. To improve inference robustness, we incorporate a binary regularization term that reduces ambiguity in the relaxed line-status outputs prior to thresholding. Once trained, DA-DNN produces a feasible topology and dispatch pair with highly predictable computation time comparable to a single DC-OPF solve, while conventional MIP solvers can become intractable. Moreover, the embedded OPF layer enables DA-DNN to generalize to untrained system configurations, such as changes in line flow limits, and to support post-contingency corrective operation. As a result, the proposed method captures the economic advantages of OTS while maintaining scalability and generalization ability.

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arXiv2025

GPU-Accelerated Dynamic Programming for Multistage Stochastic Energy Storage Arbitrage

We develop a GPU-accelerated dynamic programming (DP) method for valuing, operating, and bidding energy storage under multistage stochastic electricity prices. Motivated by computational limitations in existing models, we formulate DP backward induction entirely in tensor-based algebraic operations that map naturally onto massively parallel GPU hardware. Our method accommodates general, potentially non-concave payoff structures, by combining a discretized DP formulation with a convexification procedure that produces market-feasible, monotonic price-quantity bid curves. Numerical experiments using ISO-NE real-time prices demonstrate up to a 100x speedup by the proposed GPU-based DP method relative to CPU computation, and an 8,000x speedup compared to a commercial MILP solver, while retaining sub-0.3% optimality gaps compared to exact benchmarks.

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arXiv2025

Dynamic Line Ratings in AC Optimal Power Flow: Transient Temperature, Decomposition, and Large-scale Evaluation

As power grids experience increasing renewable penetration and rapid load growth from AI data centers and electrification, alleviating line congestion becomes critical to unlocking additional grid capacity. This work investigates Dynamic Line Rating (DLR), a congestion mitigation method that adjusts power line current limits in response to meteorological conditions. Unlike traditional approaches that impose predefined time-varying limits, we propose a novel optimization framework that embeds the transient-state heat equation governing conductor temperature dynamics, enabling direct constraints on conductor temperature rather than simplified steady-state approximations. We derive a closed-form solution to the heat equation, enabling a finite-dimensional reformulation of the dynamics. We then leverage a distributed decomposition method, a bi-level Alternating Direction Method of Multipliers (ADMM) algorithm with provable convergence, aided by regularity properties of the heat equation solution. These modeling and algorithmic innovations allow us to conduct the first large-scale evaluation of DLR using multi-period AC optimal power flow. Numerical experiments on the 2000-bus Texas grid demonstrate that DLR allows significant reduction in generation cost in congested systems over Static Line Rating (SLR) and Ambient Adjusted Ratings (AAR). The transient temperature formulation provides additional grid flexibility and headroom benefits with minimal computational overhead.

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arXiv2025

Storage Participation in Electricity Markets: Time Discretization through Robust Optimization

Electricity storage is used for intertemporal price arbitrage and for ancillary services that balance unforeseen supply and demand fluctuations via frequency regulation. We present an optimization model that computes bids for both arbitrage and frequency regulation and ensures that storage operators can honor their market commitments at all times for all fluctuation signals in an uncertainty set inspired by market rules. This requirement, initially expressed by an infinite number of nonconvex functional constraints, is shown to be equivalent to a finite number of deterministic constraints. The resulting formulation is a mixed-integer bilinear program that admits mixed-integer linear relaxations and restrictions. Empirical tests on European electricity markets show a negligible optimality gap between the relaxation and the restriction. The model can account for intraday trading and, with a solution time of under 5 seconds, may serve as a building block for more complex trading strategies. Such strategies become necessary as battery capacity exceeds the demand for ancillary services. In a backtest from 1 July 2020 through 30 June 2024 joint market participation more than doubles profits and almost halves energy output compared to no FCR participation.

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arXiv2025

Contingency-Aware Nodal Optimal Power Investments with High Temporal Resolution

We present CANOPI, a novel algorithmic framework, for solving the Contingency-Aware Nodal Power Investments problem, a large-scale nonlinear optimization problem that jointly optimizes investments in generation, storage, and transmission upgrades, including representations of unit commitment and long-duration storage. The problem's scale arises from the confluence of spatial and temporal resolutions, along with the large number of contingency constraints. Further, the underlying problem is nonlinear due to transmission upgrades' impact on impedances. We propose algorithmic approaches to address these computational challenges. We pose a linear approximation and develop a fixed-point algorithm to adjust for nonlinear impedance feedback. We solve the large-scale linear expansion model with a specialized level-bundle method leveraging a novel interleaved approach to contingency constraint generation. We introduce a minimum cycle basis algorithm that improves numerical sparsity and solve times of cycle-based DC power flow. CANOPI is demonstrated on a 1493-bus Western Interconnection test system built from realistic-geography network data, with hourly operations spanning 52 week-long scenarios and a total possible set of 20 billion individual transmission contingency constraints. Numerical experiments quantify reliability and economic benefits of incorporating transmission contingencies in integrated planning models and highlight the computational advantages of the proposed methods.

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arXiv2023

Carbon-Aware Optimal Power Flow

To facilitate effective decarbonization of the electric power sector, this paper introduces the generic Carbon-aware Optimal Power Flow (C-OPF) method for power system decision-making that considers demand-side carbon accounting and emission management. Built upon the classic optimal power flow (OPF) model, the C-OPF method incorporates carbon emission flow equations and constraints, as well as carbon-related objectives, to jointly optimize power flow and carbon flow. In particular, this paper establishes the feasibility and solution uniqueness of the carbon emission flow equations, and proposes modeling and linearization techniques to address the issues of undetermined power flow directions and bilinear terms in the C-OPF model. Additionally, two novel carbon emission models, together with the carbon accounting schemes, for energy storage systems are developed and integrated into the C-OPF model. Numerical simulations demonstrate the characteristics and effectiveness of the C-OPF method, in comparison with OPF solutions.

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arXiv2022

Impacts of Dynamic Line Ratings on the ERCOT Transmission System

Grid regulators and participants are paying increasing attention to Dynamic Line Ratings (DLR) as a new approach to address transmission system bottlenecks. In this paper, a thorough comparison of DLR, Ambient Adjusted Ratings (AAR), and the traditional Static Line Ratings (SLR) are conducted on a synthetic ERCOT grid. Estimates of DLR and AAR are calculated using an equation based on heat balance physics, along with high-resolution weather data of temperature and wind velocities. A constraint generation method for contingency screening is developed for solving security-constrained optimal power flow. Numerical results suggest that employing DLR could double the benefits compared to those of AAR relative to SLR, in terms of system costs, renewable curtailment, and emissions.

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arXiv2021

Dual Descent ALM and ADMM

Classical primal-dual algorithms attempt to solve $\max_{\mu}\min_{x} \mathcal{L}(x,\mu)$ by alternatively minimizing over the primal variable $x$ through primal descent and maximizing the dual variable $\mu$ through dual ascent. However, when $\mathcal{L}(x,\mu)$ is highly nonconvex with complex constraints in $x$, the minimization over $x$ may not achieve global optimality, and hence the dual ascent step loses its valid intuition. This observation motivates us to propose a new class of primal-dual algorithms for nonconvex constrained optimization with the key feature to reverse dual ascent to a conceptually new dual descent, in a sense, elevating the dual variable to the same status as the primal variable. Surprisingly, this new dual scheme achieves some best iteration complexities for solving nonconvex optimization problems. In particular, when the dual descent step is scaled by a fractional constant, we name it scaled dual descent (SDD), otherwise, unscaled dual descent (UDD). For nonconvex multiblock optimization with nonlinear equality constraints, we propose SDD-ADMM and show that it finds an $\epsilon$-stationary solution in $\mathcal{O}(\epsilon^{-4})$ iterations. The complexity is further improved to $\mathcal{O}(\epsilon^{-3})$ and $\mathcal{O}(\epsilon^{-2})$ under proper conditions. We also propose UDD-ALM, combining UDD with ALM, for weakly convex minimization over affine constraints. We show that UDD-ALM finds an $\epsilon$-stationary solution in $\mathcal{O}(\epsilon^{-2})$ iterations. These complexity bounds for both algorithms either achieve or improve the best-known results in the ADMM and ALM literature. Moreover, SDD-ADMM addresses a long-standing limitation of existing ADMM frameworks.

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arXiv2021

Solar Radiation Ramping Events Modeling Using Spatio-temporal Point Processes

Modeling and predicting solar events, particularly the solar ramping event, is critical for improving situational awareness for solar power generation systems. It has been acknowledged that weather conditions such as temperature, humidity, and cloud density can significantly impact the emergence and position of solar ramping events. As a result, modeling these events with complex spatio-temporal correlations is highly challenging. To tackle the question, we adopt a novel spatio-temporal categorical point process model, which intuitively and effectively addresses correlation and interaction among ramping events. We demonstrate the interpretability and predictive power of our model on extensive real-data experiments.

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arXiv2014

A Cycle-Based Formulation and Valid Inequalities for DC Power Transmission Problems with Switching

It is well-known that optimizing network topology by switching on and off transmission lines improves the efficiency of power delivery in electrical networks. In fact, the USA Energy Policy Act of 2005 (Section 1223) states that the U.S. should "encourage, as appropriate, the deployment of advanced transmission technologies" including "optimized transmission line configurations". As such, many authors have studied the problem of determining an optimal set of transmission lines to switch off to minimize the cost of meeting a given power demand under the direct current (DC) model of power flow. This problem is known in the literature as the Direct-Current Optimal Transmission Switching Problem (DC-OTS). Most research on DC-OTS has focused on heuristic algorithms for generating quality solutions or on the application of DC-OTS to crucial operational and strategic problems such as contingency correction, real-time dispatch, and transmission expansion. The mathematical theory of the DC-OTS problem is less well-developed. In this work, we formally establish that DC-OTS is NP-Hard, even if the power network is a series-parallel graph with at most one load/demand pair. Inspired by Kirchoff's Voltage Law, we give a cycle-based formulation for DC-OTS, and we use the new formulation to build a cycle-induced relaxation. We characterize the convex hull of the cycle-induced relaxation, and the characterization provides strong valid inequalities that can be used in a cutting-plane approach to solve the DC-OTS. We give details of a practical implementation, and we show promising computational results on standard benchmark instances.

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arXiv2014

Adaptive Robust Optimization with Dynamic Uncertainty Sets for Multi-Period Economic Dispatch under Significant Wind

The exceptional benefits of wind power as an environmentally responsible renewable energy resource have led to an increasing penetration of wind energy in today's power systems. This trend has started to reshape the paradigms of power system operations, as dealing with uncertainty caused by the highly intermittent and uncertain wind power becomes a significant issue. Motivated by this, we present a new framework using adaptive robust optimization for the economic dispatch of power systems with high level of wind penetration. In particular, we propose an adaptive robust optimization model for multi-period economic dispatch, and introduce the concept of dynamic uncertainty sets and methods to construct such sets to model temporal and spatial correlations of uncertainty. We also develop a simulation platform which combines the proposed robust economic dispatch model with statistical prediction tools in a rolling horizon framework. We have conducted extensive computational experiments on this platform using real wind data. The results are promising and demonstrate the benefits of our approach in terms of cost and reliability over existing robust optimization models as well as recent look-ahead dispatch models.

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