Baosen Zhang

Javad Lavaei, David Tse, Baosen Zhang · stanford

We investigate the geometry of injection regions and its relationship to optimization of power flows in tree networks. The injection region is the set of all vectors of bus power injections that satisfy the network and operation constraints. The geometrical object of interest is the set of Pareto-optimal points of the injection region. If the voltage magnitudes are fixed, the injection region of a tree network can be written as a linear transformation of the product of two-bus injection regions, one for each line in the network. Using this decomposition, we show that under the practical condition that the angle difference across each line is not too large, the set of Pareto-optimal points of the injection region remains unchanged by taking the convex hull. Moreover, the resulting convexified optimal power flow problem can be efficiently solved via }{ semi-definite programming or second order cone relaxations. These results improve upon earlier works by removing the assumptions on active power lower bounds. It is also shown that our practical angle assumption guarantees two other properties: (i) the uniqueness of the solution of the power flow problem, and (ii) the non-negativity of the locational marginal prices. Partial results are presented for the case when the voltage magnitudes are not fixed but can lie within certain bounds.

Albert Y. S. Lam, Baosen Zhang, David Tse · stanford

Optimal power flow (OPF) is an important problem for power generation and it is in general non-convex. With the employment of renewable energy, it will be desirable if OPF can be solved very efficiently so its solution can be used in real time. With some special network structure, e.g. trees, the problem has been shown to have a zero duality gap and the convex dual problem yields the optimal solution. In this paper, we propose a primal and a dual algorithm to coordinate the smaller subproblems decomposed from the convexified OPF. We can arrange the subproblems to be solved sequentially and cumulatively in a central node or solved in parallel in distributed nodes. We test the algorithms on IEEE radial distribution test feeders, some random tree-structured networks, and the IEEE transmission system benchmarks. Simulation results show that the computation time can be improved dramatically with our algorithms over the centralized approach of solving the problem without decomposition, especially in tree-structured problems. The computation time grows linearly with the problem size with the cumulative approach while the distributed one can have size-independent computation time.

Baosen Zhang, David Tse · stanford

We investigate the constraints on power flow in networks and its implications to the optimal power flow problem. The constraints are described by the injection region of a network; this is the set of all vectors of power injections, one at each bus, that can be achieved while satisfying the network and operation constraints. If there are no operation constraints, we show the injection region of a network is the set of all injections satisfying the conservation of energy. If the network has a tree topology, e.g., a distribution network, we show that under voltage magnitude, line loss constraints, line flow constraints and certain bus real and reactive power constraints, the injection region and its convex hull have the same Pareto-front. The Pareto-front is of interest since these are the the optimal solutions to the minimization of increasing functions over the injection region. For non-tree networks, we obtain a weaker result by characterize the convex hull of the voltage constraint injection region for lossless cycles and certain combinations of cycles and trees.

Baosen Zhang, Albert Y. S. Lam, Alejandro Dominguez-Garcia et al. · stanford

This paper addresses the problem of voltage regulation in power distribution networks with deep-penetration of distributed energy resources, e.g., renewable-based generation, and storage-capable loads such as plug-in hybrid electric vehicles. We cast the problem as an optimization program, where the objective is to minimize the losses in the network subject to constraints on bus voltage magnitudes, limits on active and reactive power injections, transmission line thermal limits and losses. We provide sufficient conditions under which the optimization problem can be solved via its convex relaxation. Using data from existing networks, we show that these sufficient conditions are expected to be satisfied by most networks. We also provide an efficient distributed algorithm to solve the problem. The algorithm adheres to a communication topology described by a graph that is the same as the graph that describes the electrical network topology. We illustrate the operation of the algorithm, including its robustness against communication link failures, through several case studies involving 5-, 34-, and 123-bus power distribution systems.

Yashodhan Kanoria, Andrea Montanari, David Tse et al. · stanford

One of the most important challenges in the integration of renewable energy sources into the power grid lies in their `intermittent' nature. The power output of sources like wind and solar varies with time and location due to factors that cannot be controlled by the provider. Two strategies have been proposed to hedge against this variability: 1) use energy storage systems to effectively average the produced power over time; 2) exploit distributed generation to effectively average production over location. We introduce a network model to study the optimal use of storage and transmission resources in the presence of random energy sources. We propose a Linear-Quadratic based methodology to design control strategies, and we show that these strategies are asymptotically optimal for some simple network topologies. For these topologies, the dependence of optimal performance on storage and transmission capacity is explicitly quantified.

Baosen Zhang, Ram Rajagopal, David Tse · stanford

Increased uncertainty due to high penetration of renewables imposes significant costs to the system operators. The added costs depend on several factors including market design, performance of renewable generation forecasting and the specific dispatch procedure. Quantifying these costs has been limited to small sample Monte Carlo approaches applied specific dispatch algorithms. The computational complexity and accuracy of these approaches has limited the understanding of tradeoffs between different factors. {In this work we consider a two-stage stochastic economic dispatch problem. Our goal is to provide an analytical quantification and an intuitive understanding of the effects of uncertainties and network congestion on the dispatch procedure and the optimal cost.} We first consider an uncongested network and calculate the risk limiting dispatch. In addition, we derive the price of uncertainty, a number that characterizes the intrinsic impact of uncertainty on the integration cost of renewables. Then we extend the results to a network where one link can become congested. Under mild conditions, we calculate price of uncertainty even in this case. We show that risk limiting dispatch is given by a set of deterministic equilibrium equations. The dispatch solution yields an important insight: congested links do not create isolated nodes, even in a two-node network. In fact, the network can support backflows in congested links, that are useful to reduce the uncertainty by averaging supply across the network. We demonstrate the performance of our approach in standard IEEE benchmark networks.

Baosen Zhang, Ramesh Johari, Ram Rajagopal · stanford

We investigate group formations and strategic behaviors of renewable power producers in electricity markets. These producers currently bid into the day-ahead market in a conservative fashion because of the real-time risk associated with not meeting their bid amount. It has been suggested in the literature that producers would bid less conservatively if they can form large groups to take advantages of spatial diversity to reduce the uncertainty in their aggregate output. We show that large groups of renewable producers would act strategically to lower the aggregate output because of market power. To maximize renewable power production, we characterize the trade-off between market power and generation uncertainty as a function of the size of the groups. We show there is a sweet spot in the sense that there exists groups that are large enough to achieve the uncertainty reduction of the grand coalition, but are small enough such that they have no significant market power.We consider both independent and correlated forecast errors under a fixed real-time penalty. We also consider a real-time market where both selling and buying of energy are allowed. We validate our claims using PJM and NREL data.

Yuanyuan Shi, Bolun Xu, Yushi Tan et al.

A vital aspect in energy storage planning and operation is to accurately model its operational cost, which mainly comes from the battery cell degradation. Battery degradation can be viewed as a complex material fatigue process that based on stress cycles. Rainflow algorithm is a popular way for cycle identification in material fatigue process, and has been extensively used in battery degradation assessment. However, the rainflow algorithm does not have a closed form, which makes the major difficulty to include it in optimization. In this paper, we prove the rainflow cycle-based cost is convex. Convexity enables the proposed degradation model to be incorporated in different battery optimization problems and guarantees the solution quality. We provide a subgradient algorithm to solve the problem. A case study on PJM regulation market demonstrates the effectiveness of the proposed degradation model in maximizing the battery operating profits as well as extending its lifetime.

Yuanyuan Shi, Bolun Xu, Baosen Zhang et al.

Energy storage in data centers has mainly been used as devices to backup generators during power outages. Recently, there has been a growing interest in using energy storage devices to actively shape power consumption in data centers to reduce their skyrocketing electricity bills. In this paper, we consider using energy storage in data centers for two applications in a joint fashion: reducing peak demand charges and enabling data centers to participate in regulation markets. We develop an optimization framework that captures the cost of electricity, degradation of energy storage devices, as well as the benefit from regulation markets. Under this frame- work, using real data Microsoft data center traces and PJM regulation signals, we show the electricity bill of a data center can be reduced by up to 20%. Furthermore, we demonstrate that the saving from joint optimization can be even larger than the sum of individually optimizing each component. We quantify the particular aspects of data center load profiles that lead to this superlinear gain. Compared to prior works that consider using energy storage devices for each single application alone, our results suggest that energy storage in data centers can have much larger impacts than previously thought possible.

Jesus E. Contreras-Ocaña, Miguel A. Ortega-Vazquez, Baosen Zhang · uw

We study competition and cooperation among a group of storage units. We show that as the number of storages increases, the profit of storages approaches zero under Nash competition. We propose two ways in which storages can achieve non-zero profit and show that they are optimal in the sense that storages achieve the maximum possible profit. The first is a decentralized approach in which storages are exposed to artificial cost functions that incentivize them to behavior as a coalition. No private information needs to be exchanged between the storages to calculate the artificial function. The second is a centralized approach in which an aggregator coordinates and splits profits with storages in order to achieve maximum profit. We use Nash's axiomatic bargaining problem to model and predict the profit split between aggregator and storages.

Atinuke Ademola-Idowu, Baosen Zhang

Increased penetration of inverter-connected renewable energy sources (RES) in the power system has resulted in a decrease in available rotational inertia which serves as an immediate response to frequency deviation due to disturbances. The concept of virtual inertia has been proposed to combat this decrease by enabling the inverters to produce active power in response to a frequency deviation like a synchronous generator. In this paper, we present an algorithm to optimally design the inertia and damping coefficient required for an inverter-based virtual synchronous machine (VSM) to participate efficiently in the inertia response portion of primary frequency control. We design the objective function to explicitly trade-off between competing objectives such as the damping rate the the frequency nadir. Specifically, we formulate the design problem as a constrained and regularized H2 norm minimization problem, and develop an efficient gradient algorithm for this non-convex problem. This proposed algorithm is applied to a test case to demonstrate its performance against existing methods.

Andrea Britto, Thiago Spina, Weiwei Yang et al.

Access to realistic transmission grid models is essential for power systems research, yet detailed network data in the United States remains restricted under critical-infrastructure regulations. We present a pipeline that constructs complete, OPF-solvable transmission network models entirely from publicly available data. The five-stage pipeline (1) extracts power infrastructure from OpenStreetMap via a local Overpass API instance, (2) reconstructs bus-branch topology through voltage inference, line merging, and transformer detection, (3) estimates electrical parameters using voltage-class lookup tables calibrated with U.S. Energy Information Administration (EIA) plant-level data, (4) allocates hourly demand from EIA-930 to individual buses using US Census population as a spatial proxy, and (5) solves both DC and AC optimal power flow using PowerModels.jl with a progressive relaxation strategy that automatically loosens constraints on imprecise models. We validate the pipeline on all 48 contiguous US states and six multi-state regions, including the full Western (5,076 buses) and Eastern (21,697 buses) Interconnections. Of the 48 single-state models, 42 (88%) converge at the strictest relaxation level for AC-OPF at peak hour and 44 (92%) off-peak. Dispatch costs (median $22/MWh) and system losses (median 1.0%) are consistent with real wholesale-market outcomes. The pipeline relies exclusively on open data sources, enabling reproducible grid analysis without proprietary data. All 54 models (48 single-state and 6 multi-state) are publicly released at https://github.com/microsoft/GridSFM.

Jochen Stiasny, Baosen Zhang, Spyros Chatzivasileiadis

The dynamic behaviour of a power system can be described by a system of differential-algebraic equations. Time-domain simulations are used to simulate the evolution of these dynamics. They often require the use of small time step sizes and therefore become computationally expensive. To accelerate these simulations, we propose a simulator - PINNSim - that allows to take significantly larger time steps. It is based on Physics-Informed Neural Networks (PINNs) for the solution of the dynamics of single components in the power system. To resolve their interaction we employ a scalable root-finding algorithm. We demonstrate PINNSim on a 9-bus system and show the increased time step size compared to a trapezoidal integration rule. We discuss key characteristics of PINNSim and important steps for developing PINNSim into a fully fledged simulator. As such, it could offer the opportunity for significantly increasing time step sizes and thereby accelerating time-domain simulations.

Lillian J. Ratliff, Chase Dowling, Eric Mazumdar et al.

We model parking in urban centers as a set of parallel queues and overlay a game theoretic structure that allows us to compare the user-selected (Nash) equilibrium to the socially optimal equilibrium. We model arriving drivers as utility maximizers and consider the game in which observing the queue length is free as well as the game in which drivers must pay to observe the queue length. In both games, drivers must decide between balking and joining. We compare the Nash induced welfare to the socially optimal welfare. We find that gains to welfare do not require full information penetration---meaning, for social welfare to increase, not everyone needs to pay to observe. Through simulation, we explore a more complex scenario where drivers decide based the queueing game whether or not to enter a collection of queues over a network. We examine the occupancy-congestion relationship, an important relationship for determining the impact of parking resources on overall traffic congestion. Our simulated models use parameters informed by real-world data collected by the Seattle Department of Transportation.

Jesus E. Contreras-Ocaña, Uzma Siddiqi, Baosen Zhang

Distributed energy resources (DERs) can serve as non-wire alternatives to capacity expansion by managing peak load to avoid or defer traditional expansion projects. In this paper, we study a planning problem that co-optimizes DERs investment and operation (e.g., energy efficiency, energy storage, demand response, solar photovoltaic) and the timing of capacity expansion. We formulate the problem as a large scale (in the order of millions of variables because we model the operation of DERs over a period of decades) non-convex optimization problem. Despite its non-convexities, we find its optimal solution by decomposing it using the Dantzig-Wolfe Decomposition Algorithm and solving a series of small linear problems. Finally, we present a real planning problem at the University of Washington Seattle Campus.

Ling Zhang, Daniel Tabas, Baosen Zhang

In this paper, we consider the scenario-based two-stage stochastic DC optimal power flow (OPF) problem for optimal and reliable dispatch when the load is facing uncertainty. Although this problem is a linear program, it remains computationally challenging to solve due to the large number of scenarios needed to accurately represent the uncertainties. To mitigate the computational issues, many techniques have been proposed to approximate the second-stage decisions so they can be dealt more efficiently. The challenge of finding good policies to approximate the second-stage decisions is that these solutions need to be feasible, which has been difficult to achieve with existing policies. To address these challenges, this paper proposes a learning method to solve the two-stage problem in a more efficient and optimal way. A technique called the gauge map is incorporated into the learning architecture design to guarantee the learned solutions' feasibility to the network constraints. Namely, we can design policies that are feed forward functions and only output feasible solutions. Simulation results on standard IEEE systems show that, compared to iterative solvers and the widely used affine policy, our proposed method not only learns solutions of good quality but also accelerates the computation by orders of magnitude.

Yuanyuan Shi, Bolun Xu, Yushi Tan et al.

We study the optimal control of battery energy storage under a general "pay-for-performance" setup such as providing frequency regulation and renewable integration. In these settings, batteries need to carefully balance the trade-off between following the instruction signals and their degradation costs in real-time. Existing battery control strategies either do not consider the uncertainty of future signals, or cannot accurately account for battery cycle aging mechanism during operation. In this work, we take a different approach to the optimal battery control problem. Instead of attacking the complexity of battery degradation function or the lack of future information one at a time, we address these two challenges together in a joint fashion. In particular, we present an electrochemically accurate and trackable battery degradation model called the rainflow cycle-based model. We prove the degradation cost is convex. Then we propose an online control policy with a simple threshold structure and show it achieve near-optimal performance with respect to an offline controller that has complete future information. We explicitly characterize the optimality gap and show it is independent to the duration of operation. Simulation results with both synthetic and real regulation traces are conducted to illustrate the theoretical results.

Nicolo Mazzi, Baosen Zhang, Daniel S. Kirschen

Power systems are increasingly operated in corrective rather than preventive security mode, which means that appropriate control actions must be taken immediately after a contingency has occurred. This paper proposes an online algorithm for automatically alleviating contingencies such as voltage limit violations and line overloads. Unlike previously proposed approaches, the network itself serves as a natural solver of the power flow equations. This makes it possible to start the implementation immediately and avoids problems caused by modeling errors. Every time the controller receives measurements from the grid, it evaluates the presence of contingencies and computes the optimal corrective actions that can be implemented before the next sampling period, subject to ramping constraints of the generators. These corrective actions are implemented through the standard Automatic Generation Control. Finding the optimal incremental corrective actions is fast because this problem is linearized. The effectiveness of this algorithm at correcting both line overloads and voltage violations is demonstrated using the IEEE-118 Bus test system.

Kishan Prudhvi Guddanti, Yang Weng, Baosen Zhang

The power flow (PF) problem is a fundamental problem in power system engineering. Many popular solvers face challenges, such as convergence issues. One can try to rewrite the PF problem into a fixed point equation, which can be solved exponentially fast. But, existing methods have their own restrictions, such as the required AC network structure or bus types. To remove these restrictions, we employ the circle geometry per-bus via rectangular coordinate representation to embed our physical knowledge of operation point selection in PV curves. Each iteration of the algorithm consists of finding intersections of circles, which can be computed efficiently with high numerical accuracy. Such analysis also helps in visualizing PV curve to always select the high voltage solution. We compare the performance of our fixed point algorithm with existing state-of-the-art methods, showing that the proposed method can correctly find the solutions when other methods cannot. In addition, we empirically show that the fixed point algorithm is much more robust to bad initialization points than the existing methods.

Wenqi Cui, Linbin Huang, Weiwei Yang et al.

A key barrier to using reinforcement learning (RL) in many real-world applications is the requirement of a large number of system interactions to learn a good control policy. Off-policy and Offline RL methods have been proposed to reduce the number of interactions with the physical environment by learning control policies from historical data. However, their performances suffer from the lack of exploration and the distributional shifts in trajectories once controllers are updated. Moreover, most RL methods require that all states are directly observed, which is difficult to be attained in many settings. To overcome these challenges, we propose a trajectory generation algorithm, which adaptively generates new trajectories as if the system is being operated and explored under the updated control policies. Motivated by the fundamental lemma for linear systems, assuming sufficient excitation, we generate trajectories from linear combinations of historical trajectories. For linear feedback control, we prove that the algorithm generates trajectories with the exact distribution as if they are sampled from the real system using the updated control policy. In particular, the algorithm extends to systems where the states are not directly observed. Experiments show that the proposed method significantly reduces the number of sampled data needed for RL algorithms.

Daniel Tabas, Ahmed S. Zamzam, Baosen Zhang

Constrained multiagent reinforcement learning (C-MARL) is gaining importance as MARL algorithms find new applications in real-world systems ranging from energy systems to drone swarms. Most C-MARL algorithms use a primal-dual approach to enforce constraints through a penalty function added to the reward. In this paper, we study the structural effects of this penalty term on the MARL problem. First, we show that the standard practice of using the constraint function as the penalty leads to a weak notion of safety. However, by making simple modifications to the penalty term, we can enforce meaningful probabilistic (chance and conditional value at risk) constraints. Second, we quantify the effect of the penalty term on the value function, uncovering an improved value estimation procedure. We use these insights to propose a constrained multiagent advantage actor critic (C-MAA2C) algorithm. Simulations in a simple constrained multiagent environment affirm that our reinterpretation of the primal-dual method in terms of probabilistic constraints is effective, and that our proposed value estimate accelerates convergence to a safe joint policy.

Mingyuan Yan, Trager Joswig-Jones, Baosen Zhang et al.

Large-scale AI training workloads in modern data centers exhibit rapid and periodic power fluctuations, which may induce significant voltage deviations in power distribution systems. Existing voltage regulation methods, such as droop control, are primarily designed for slowly varying loads and may therefore be ineffective in mitigating these fast fluctuations. In addition, repeated control actions can incur substantial cost. To address this challenge, this paper proposes a decentralized switching-reference voltage control framework that exploits the structured behavior of AI training workloads. We establish conditions for voltage convergence and characterize an effective reference design that aligns with the two dominant operating levels of the AI training workload. The switching rule for voltage references is implemented solely using local voltage measurements, enabling simple local implementation while significantly reducing control effort. Simulation studies demonstrate that the proposed method substantially reduces both voltage deviations and reactive control effort, while remaining compatible with internal data center control strategies without requiring extensive coordination.

Jerry Anunrojwong, Baosen Zhang

Residential batteries increasingly serve two roles: they can earn money by arbitraging wholesale prices and providing grid services, and they provide backup power during outages. This dual use creates a basic tradeoff between earning market value and preserving outage readiness. Coordination across many batteries can help, but a provider cannot treat the fleet as a single virtual battery when each household is promised its own backup protection. We compare standalone control, in which each home is dispatched independently, with pooling, in which homes are coordinated while each battery retains its own state of charge and household-specific backup requirement. Both regimes are implemented as model predictive control problems with 15-minute decision intervals and evaluated using household telemetry together with ERCOT market inputs. The empirical design focuses on the 543 homes in our sample that can support at least one backup product in standalone operation and studies backup caps ranging from 2 to 24 hours. Lower caps relax backup obligations, while the 24-hour cap coincides with assigning each home its own longest feasible backup tier. Pooling remains beneficial in this service-constrained setting, but its value declines smoothly as backup obligations tighten. Standalone firm margin ranges from \$11.06 per home per week at the 2-hour cap to \$10.79 at the 24-hour cap, while pooling benefit falls from \$1.49 to \$1.27 per home per week. Relative to standalone firm margin, pooling is worth about 13.5% at the 2-hour cap and about 11.8% at the 24-hour cap. Coordination therefore still helps after preserving household-level backup guarantees, but its value declines as backup obligations tighten.

Jiayi Yao, Cong Chen, Baosen Zhang

Large language model (LLM) agents are increasingly deployed in competitive multi-agent settings, raising fundamental questions about whether they converge to equilibria and how their strategic behavior can be characterized. In this paper, we study LLM agent interactions in two standard games: a network resource allocation game and a Cournot competition game. Rather than converging to Nash equilibria, we find that LLM agents tend to cooperate when given multi-round prompts and non-zero-sum context. Chain-of-thought analysis reveals that fairness reasoning is central to this behavior. We propose an analytical framework that captures the dynamics of LLM agent reasoning across rounds and explains these experimental findings.

Lauren Streitmatter, Trager Joswig-Jones, Baosen Zhang

Converter-based generators and loads are growing in prevalence on power grids across the globe. The rise of these resources necessitates controllers that handle the power electronic devices' strict current limits without jeopardizing stability or overly constraining behavior. Existing controllers often employ complex, cascaded control loop architecture to saturate currents, but these controllers are challenging to tune properly and can destabilize following large disturbances. In this paper, we extend previous analysis to prove the feasible output region of a grid-connected converter is convex regardless of filter topology. We then formulate a convex optimal control problem from which we derive a projected gradient descent-based controller with convergence guarantees. This approach drives the converter toward optimality in real-time and differs from conventional control strategies that regulate converter outputs around predefined references regardless of surrounding grid conditions. Simulation results demonstrate safe and stabilizing behavior of the proposed controller, in both the single-converter-infinite-bus systems and multi-converter networks.

Guangwen Wang, Jiaqi Wu, Yang Weng et al.

The growing number of individual generating units, hybrid resources, and security constraints has significantly increased the computational burden of network-constrained unit commitment (UC), where most solution time is spent exploring branch-and-bound trees over unit-hour binary variables. To reduce this combinatorial burden, recent approaches have explored learning-based guidance to assist commitment decisions. However, directly using tools such as large language models (LLMs) to predict full commitment schedules is unreliable, as infeasible or inconsistent binary decisions can violate inter-temporal constraints and degrade economic optimality. This paper proposes a solver-compatible dimensionality reduction framework for UC that exploits structural regularities in commitment decisions. Instead of generating complete schedules, the framework identifies a sparse subset of structurally stable commitment binaries to fix prior to optimization. One implementation uses an LLM to select these variables. The LLM does not replace the optimization process but provides partial variable restriction, while all constraints and remaining decisions are handled by the original MILP solver, which continues to enforce network, ramping, reserve, and security constraints. We formally show that the masked problem defines a reduced feasible region of the original UC model, thereby preserving feasibility and enabling solver-certified optimality within the restricted space. Experiments on IEEE 57-bus, RTS 73-bus, IEEE 118-bus, and augmented large-scale cases, including security-constrained variants, demonstrate consistent reductions in branch-and-bound nodes and solution time, achieving order-of-magnitude speedups on high-complexity instances while maintaining near-optimal objective values.

Aritra Roy, Kevin Shen, Andrew MacBride et al.

Large language models (LLMs) are rapidly changing how researchers in materials science and chemistry discover, organize, and act on scientific knowledge. This paper analyzes a broad set of community-developed LLM applications in an effort to identify emerging patterns in how these systems can be used across the scientific research lifecycle. We organize the projects into two complementary categories: Knowledge Infrastructure, systems that structure, retrieve, synthesize, and validate scientific information; and Action Systems, systems that execute, coordinate, or automate scientific work across computational and experimental environments. The submissions reveal a shift from single-purpose LLM tools toward integrated, multi-agent workflows that combine retrieval, reasoning, tool use, and domain-specific validation. Prominent themes include retrieval-augmented generation as grounding infrastructure, persistent structured knowledge representations, multimodal and multilingual scientific inputs, and early progress toward laboratory-integrated closed-loop systems. Together, these results suggest that LLMs are evolving from general-purpose assistants into composable infrastructure for scientific reasoning and action. This work provides a community snapshot of that transition and a practical taxonomy for understanding emerging LLM-enabled workflows in materials science and chemistry.

Lila Perkins, Baosen Zhang

In electricity markets, customers are increasingly constrained by their budgets. A budget constraint for a user is an upper bound on the price multiplied by the quantity. However, since prices are determined by the market equilibrium, the budget constrained welfare maximization problem is difficult to define rigorously and to work with. In this letter, we show that a natural dual-ascent algorithm converges to a unique competitive equilibrium under budget constraints. Further, this budget-constrained equilibrium is exactly the solution of a convex welfare maximization problem in which each user's utility is replaced by a modified utility that splices the original utility with a logarithmic function where the budget binds. We also provide an explicit piecewise construction of this modified utility and demonstrate the results on examples with quadratic and square root utility functions.

Haoxuan Li, Chenxu Wei, Haodong Wang et al.

Change detection typically involves identifying regions with changes between bitemporal images taken at the same location. Besides significant changes, slow changes in bitemporal images are also important in real-life scenarios. For instance, weak changes often serve as precursors to major hazards in scenarios like slopes, dams, and tailings ponds. Therefore, designing a change detection network that simultaneously detects slow and fast changes presents a novel challenge. In this paper, to address this challenge, we propose a change detection network named Flow-CDNet, consisting of two branches: optical flow branch and binary change detection branch. The first branch utilizes a pyramid structure to extract displacement changes at multiple scales. The second one combines a ResNet-based network with the optical flow branch's output to generate fast change outputs. Subsequently, to supervise and evaluate this new change detection framework, a self-built change detection dataset Flow-Change, a loss function combining binary tversky loss and L2 norm loss, along with a new evaluation metric called FEPE are designed. Quantitative experiments conducted on Flow-Change dataset demonstrated that our approach outperforms the existing methods. Furthermore, ablation experiments verified that the two branches can promote each other to enhance the detection performance.

Ling Zhang, Baosen Zhang

Using deep neural networks to predict the solutions of AC optimal power flow (ACOPF) problems has been an active direction of research. However, because the ACOPF is nonconvex, it is difficult to construct a good data set that contains mostly globally optimal solutions. To overcome the challenge that the training data may contain suboptimal solutions, we propose a Lagrangian-based approach. First, we use a neural network to learn the dual variables of the ACOPF problem. Then we use a second neural network to predict solutions of the partial Lagrangian from the predicted dual variables. Since the partial Lagrangian has a much better optimization landscape, we use the predicted solutions from the neural network as a warm start for the ACOPF problem. Using standard and modified IEEE 22-bus, 39-bus, and 118-bus networks, we show that our approach is able to obtain the globally optimal cost even when the training data is mostly comprised of suboptimal solutions.

Wenqi Cui, Baosen Zhang

Transient stability of power systems is becoming increasingly important because of the growing integration of renewable resources. These resources lead to a reduction in mechanical inertia but also provide increased flexibility in frequency responses. Namely, their power electronic interfaces can implement almost arbitrary control laws. To design these controllers, reinforcement learning (RL) has emerged as a powerful method in searching for optimal non-linear control policy parameterized by neural networks. A key challenge is to enforce that a learned controller must be stabilizing. This paper proposes a Lyapunov regularized RL approach for optimal frequency control for transient stability in lossy networks. Because the lack of an analytical Lyapunov function, we learn a Lyapunov function parameterized by a neural network. The losses are specially designed with respect to the physical power system. The learned neural Lyapunov function is then utilized as a regularization to train the neural network controller by penalizing actions that violate the Lyapunov conditions. Case study shows that introducing the Lyapunov regularization enables the controller to be stabilizing and achieve smaller losses.

Yuanyuan Shi, Baosen Zhang

In this work, we study the interaction of strategic agents in continuous action Cournot games with limited information feedback. Cournot game is the essential market model for many socio-economic systems where agents learn and compete without the full knowledge of the system or each other. We consider the dynamics of the policy gradient algorithm, which is a widely adopted continuous control reinforcement learning algorithm, in concave Cournot games. We prove the convergence of policy gradient dynamics to the Nash equilibrium when the price function is linear or the number of agents is two. This is the first result (to the best of our knowledge) on the convergence property of learning algorithms with continuous action spaces that do not fall in the no-regret class.

Liyuan Zheng, Yuanyuan Shi, Lillian J. Ratliff et al.

This paper focuses on finding reinforcement learning policies for control systems with hard state and action constraints. Despite its success in many domains, reinforcement learning is challenging to apply to problems with hard constraints, especially if both the state variables and actions are constrained. Previous works seeking to ensure constraint satisfaction, or safety, have focused on adding a projection step to a learned policy. Yet, this approach requires solving an optimization problem at every policy execution step, which can lead to significant computational costs. To tackle this problem, this paper proposes a new approach, termed Vertex Networks (VNs), with guarantees on safety during exploration and on learned control policies by incorporating the safety constraints into the policy network architecture. Leveraging the geometric property that all points within a convex set can be represented as the convex combination of its vertices, the proposed algorithm first learns the convex combination weights and then uses these weights along with the pre-calculated vertices to output an action. The output action is guaranteed to be safe by construction. Numerical examples illustrate that the proposed VN algorithm outperforms vanilla reinforcement learning in a variety of benchmark control tasks.

Chase P. Dowling, Baosen Zhang

Faults in HVAC systems degrade thermal comfort and energy efficiency in buildings and have received significant attention from the research community, with data driven methods gaining in popularity. Yet the lack of labeled data, such as normal versus faulty operational status, has slowed the application of machine learning to HVAC systems. In addition, for any particular building, there may be an insufficient number of observed faults over a reasonable amount of time for training. To overcome these challenges, we present a transfer methodology for a novel Bayesian classifier designed to distinguish between normal operations and faulty operations. The key is to train this classifier on a building with a large amount of sensor and fault data (for example, via simulation or standard test data) then transfer the classifier to a new building using a small amount of normal operations data from the new building. We demonstrate a proof-of-concept for transferring a classifier between architecturally similar buildings in different climates and show few samples are required to maintain classification precision and recall.

Yan Yang, Zhifang Yang, Juan Yu et al.

Probabilistic power flow (PPF) plays a critical role in power system analysis. However, the high computational burden makes it challenging for the practical implementation of PPF. This paper proposes a model-based deep learning approach to overcome the computational challenge. A deep neural network (DNN) is used to approximate the power flow calculation and is trained according to the physical power flow equations to improve its learning ability. The training process consists of several steps: 1) the branch flows are added into the objective function of the DNN as a penalty term, which improves the approximation accuracy of the DNN; 2) the gradients used in the back propagation process are simplified according to the physical characteristics of the transmission grid, which accelerates the training speed while maintaining effective guidance of the physical model; and 3) an improved initialization method for the DNN parameters is proposed to improve the convergence speed. The simulation results demonstrate the accuracy and efficiency of the proposed method in standard IEEE and utility benchmark systems.

Pan Li, Baihong Jin, Ruoxuan Xiong et al.

We present a machine learning approach to the solution of chance constrained optimizations in the context of voltage regulation problems in power system operation. The novelty of our approach resides in approximating the feasible region of uncertainty with an ellipsoid. We formulate this problem using a learning model similar to Support Vector Machines (SVM) and propose a sampling algorithm that efficiently trains the model. We demonstrate our approach on a voltage regulation problem using standard IEEE distribution test feeders.

Yize Chen, Yushi Tan, Baosen Zhang

Load forecasting plays a critical role in the operation and planning of power systems. By using input features such as historical loads and weather forecasts, system operators and utilities build forecast models to guide decision making in commitment and dispatch. As the forecasting techniques becomes more sophisticated, however, they also become more vulnerable to cybersecurity threats. In this paper, we study the vulnerability of a class of load forecasting algorithms and analyze the potential impact on the power system operations, such as load shedding and increased dispatch costs. Specifically, we propose data injection attack algorithms that require minimal assumptions on the ability of the adversary. The attacker does not need to have knowledge about the load forecasting model or the underlying power system. Surprisingly, our results indicate that standard load forecasting algorithms are quite vulnerable to the designed black-box attacks. By only injecting malicious data in temperature from online weather forecast APIs, an attacker could manipulate load forecasts in arbitrary directions and cause significant and targeted damages to system operations.

Aaron Jaech, Baosen Zhang, Mari Ostendorf et al.

This paper addresses the problem of predicting duration of unplanned power outages, using historical outage records to train a series of neural network predictors. The initial duration prediction is made based on environmental factors, and it is updated based on incoming field reports using natural language processing to automatically analyze the text. Experiments using 15 years of outage records show good initial results and improved performance leveraging text. Case studies show that the language processing identifies phrases that point to outage causes and repair steps.

Yize Chen, Pan Li, Baosen Zhang

We present a method to generate renewable scenarios using Bayesian probabilities by implementing the Bayesian generative adversarial network~(Bayesian GAN), which is a variant of generative adversarial networks based on two interconnected deep neural networks. By using a Bayesian formulation, generators can be constructed and trained to produce scenarios that capture different salient modes in the data, allowing for better diversity and more accurate representation of the underlying physical process. Compared to conventional statistical models that are often hard to scale or sample from, this method is model-free and can generate samples extremely efficiently. For validation, we use wind and solar times-series data from NREL integration data sets to train the Bayesian GAN. We demonstrate that proposed method is able to generate clusters of wind scenarios with different variance and mean value, and is able to distinguish and generate wind and solar scenarios simultaneously even if the historical data are intentionally mixed.

Hao Wang, Baosen Zhang

In this paper, we derive a temporal arbitrage policy for storage via reinforcement learning. Real-time price arbitrage is an important source of revenue for storage units, but designing good strategies have proven to be difficult because of the highly uncertain nature of the prices. Instead of current model predictive or dynamic programming approaches, we use reinforcement learning to design an optimal arbitrage policy. This policy is learned through repeated charge and discharge actions performed by the storage unit through updating a value matrix. We design a reward function that does not only reflect the instant profit of charge/discharge decisions but also incorporate the history information. Simulation results demonstrate that our designed reward function leads to significant performance improvement compared with existing algorithms.

Yize Chen, Yishen Wang, Daniel Kirschen et al.

Scenario generation is an important step in the operation and planning of power systems with high renewable penetrations. In this work, we proposed a data-driven approach for scenario generation using generative adversarial networks, which is based on two interconnected deep neural networks. Compared with existing methods based on probabilistic models that are often hard to scale or sample from, our method is data-driven, and captures renewable energy production patterns in both temporal and spatial dimensions for a large number of correlated resources. For validation, we use wind and solar times-series data from NREL integration data sets. We demonstrate that the proposed method is able to generate realistic wind and photovoltaic power profiles with full diversity of behaviors. We also illustrate how to generate scenarios based on different conditions of interest by using labeled data during training. For example, scenarios can be conditioned on weather events~(e.g. high wind day) or time of the year~(e,g. solar generation for a day in July). Because of the feedforward nature of the neural networks, scenarios can be generated extremely efficiently without sophisticated sampling techniques.

Yuanyuan Shi, Bolun Xu, Di Wang et al.

We consider using a battery storage system simultaneously for peak shaving and frequency regulation through a joint optimization framework which captures battery degradation, operational constraints and uncertainties in customer load and regulation signals. Under this framework, using real data we show the electricity bill of users can be reduced by up to 15\%. Furthermore, we demonstrate that the saving from joint optimization is often larger than the sum of the optimal savings when the battery is used for the two individual applications. A simple threshold real-time algorithm is proposed and achieves this super-linear gain. Compared to prior works that focused on using battery storage systems for single applications, our results suggest that batteries can achieve much larger economic benefits than previously thought if they jointly provide multiple services.

Baosen Zhang, Ramesh Johari, Ram Rajagopal

We investigate the impact of coalition formation on the efficiency of Cournot games where producers face uncertainties. In particular, we study a market model where firms must determine their output before an uncertain production capacity is realized. In contrast to standard Cournot models, we show that the game is not efficient when there are many small firms. Instead, producers tend to act conservatively to hedge against their risks. We show that in the presence of uncertainty, the game becomes efficient when firms are allowed to take advantage of diversity to form groups of certain sizes. We characterize the tradeoff between market power and uncertainty reduction as a function of group size. In particular, we compare the welfare and output obtained with coalitional competition, with the same benchmarks when output is controlled by a single system operator. We show when there are $N$ firms present, competition between groups of size $Ω(\sqrt{N})$ results in equilibria that are socially optimal in terms of welfare and groups of size $Ω(N^{2/3})$ are socially optimal in terms of production. We also extend our results to the case of uncertain demand by establishing an equivalency between Cournot oligopoly and Cournot Oligopsony. We demonstrate our results with real data from electricity markets with significant wind power penetration.

Pan Li, Hao Wang, Baosen Zhang

We study a demand response problem from utility (also referred to as operator)'s perspective with realistic settings, in which the utility faces uncertainty and limited communication. Specifically, the utility does not know the cost function of consumers and cannot have multiple rounds of information exchange with consumers. We formulate an optimization problem for the utility to minimize its operational cost considering time-varying demand response targets and responses of consumers. We develop a joint online learning and pricing algorithm. In each time slot, the utility sends out a price signal to all consumers and estimates the cost functions of consumers based on their noisy responses. We measure the performance of our algorithm using regret analysis and show that our online algorithm achieves logarithmic regret with respect to the operating horizon. In addition, our algorithm employs linear regression to estimate the aggregate response of consumers, making it easy to implement in practice. Simulation experiments validate the theoretic results and show that the performance gap between our algorithm and the offline optimality decays quickly.

Siddharth Patel, Raffi Sevlian, Baosen Zhang et al.

The conventional practice of retail electric utilities is to aggregate customers geographically. The utility purchases electricity for its customers via bulk transactions on the wholesale market, and it passes these costs along to its customers, the end consumers, through their rate plan. Typically, all residential consumers are offered the same per unit rate plan, which leads to cost sharing. Some consumers use their electricity at peak hours, when it is more expensive on the wholesale market, and others consume mostly at off peak hours, when it is cheaper, but they all enjoy the same per unit rate through their utility. This paper proposed a method for the utility to segment a population of consumers on the basis of their individual consumption patterns. An optimal recruitment algorithm was developed to aggregate consumers into groups with a relatively low per unit cost of electricity on the wholesale market. It was then proposed that the utility should group together enough consumers to ensure an adequately low forecast error, which is related to risks it faces in wholesale market transactions. Finally, it was shown that by repeated application of this process, the utility could segment the entire population into groups and offer them differentiated rate plans based on their actual consumption behavior. These groupings are stable in the sense that no one consumer can unilaterally improve her outcome.

Jesus E. Contreras-Ocana, Miguel A. Ortega-Vazquez, Baosen Zhang

An important function of aggregators is to enable the participation of small energy storage units in electricity markets. This paper studies two generally overlooked aspects related to aggregators of energy storage: i) the relationship between the aggregator and its constituent storage units and ii) the aggregator's effect on system welfare. Regarding i), we show that short-term outcomes can be Pareto-inefficient: all players could be better-off. In practice, however, aggregators and storage units are likely to engage in long rather than short-term relationships. Using Nash Bargaining Theory, we show that aggregators and storage units are likely to cooperate in the long-term. A rigorous understanding of the aggregator-storage unit relationship is fundamental to model the aggregator's participation in the market. Regarding ii), we first show that a profit-seeking energy storage aggregator is always beneficial to the system when compared to a system without storage, regardless of size or market power the aggregator may have. However, due to market power, a monopolist aggregator may act in a socially suboptimal manner. We propose a pricing scheme designed to mitigate market power abuse by the aggregator. This pricing scheme has several important characteristics: its formulation requires no private information, it incentivizes a rational aggregator to behave in a socially optimal manner, and allows for regulation of the aggregator's profit.

Pan Li, Baihong Jin, Dai Wang et al.

Voltage control plays an important role in the operation of electricity distribution networks, especially with high penetration of distributed energy resources. These resources introduce significant and fast varying uncertainties. In this paper, we focus on reactive power compensation to control voltage in the presence of uncertainties. We adopt a chance constraint approach that accounts for arbitrary correlations between renewable resources at each of the buses. We show how the problem can be solved efficiently using historical samples via a stochastic quasi gradient method. We also show that this optimization problem is convex for a wide variety of probabilistic distributions. Compared to conventional per-bus chance constraints, our formulation is more robust to uncertainty and more computationally tractable. We illustrate the results using standard IEEE distribution test feeders.

Pan Li, Baosen Zhang

Demand response aims to stimulate electricity consumers to modify their loads at critical time periods. In this paper, we consider signals in demand response programs as a binary treatment to the customers and estimate the average treatment effect, which is the average change in consumption under the demand response signals. More specifically, we propose to estimate this effect by linear regression models and derive several estimators based on the different models. From both synthetic and real data, we show that including more information about the customers does not always improve estimation accuracy: the interaction between the side information and the demand response signal must be carefully modeled. In addition, we compare the traditional linear regression model with the modified covariate method which models the interaction between treatment effect and covariates. We analyze the variances of these estimators and discuss different cases where each respective estimator works the best. The purpose of these comparisons is not to claim the superiority of the different methods, rather we aim to provide practical guidance on the most suitable estimator to use under different settings. Our results are validated using data collected by Pecan Street and EnergyPlus.

Hossein Hosseini, Yize Chen, Sreeram Kannan et al.

Advances in Machine Learning (ML) have led to its adoption as an integral component in many applications, including banking, medical diagnosis, and driverless cars. To further broaden the use of ML models, cloud-based services offered by Microsoft, Amazon, Google, and others have developed ML-as-a-service tools as black-box systems. However, ML classifiers are vulnerable to adversarial examples: inputs that are maliciously modified can cause the classifier to provide adversary-desired outputs. Moreover, it is known that adversarial examples generated on one classifier are likely to cause another classifier to make the same mistake, even if the classifiers have different architectures or are trained on disjoint datasets. This property, which is known as transferability, opens up the possibility of attacking black-box systems by generating adversarial examples on a substitute classifier and transferring the examples to the target classifier. Therefore, the key to protect black-box learning systems against the adversarial examples is to block their transferability. To this end, we propose a training method that, as the input is more perturbed, the classifier smoothly outputs lower confidence on the original label and instead predicts that the input is "invalid". In essence, we augment the output class set with a NULL label and train the classifier to reject the adversarial examples by classifying them as NULL. In experiments, we apply a wide range of attacks based on adversarial examples on the black-box systems. We show that a classifier trained with the proposed method effectively resists against the adversarial examples, while maintaining the accuracy on clean data.

Hossein Hosseini, Sreeram Kannan, Baosen Zhang et al.

Social media platforms provide an environment where people can freely engage in discussions. Unfortunately, they also enable several problems, such as online harassment. Recently, Google and Jigsaw started a project called Perspective, which uses machine learning to automatically detect toxic language. A demonstration website has been also launched, which allows anyone to type a phrase in the interface and instantaneously see the toxicity score [1]. In this paper, we propose an attack on the Perspective toxic detection system based on the adversarial examples. We show that an adversary can subtly modify a highly toxic phrase in a way that the system assigns significantly lower toxicity score to it. We apply the attack on the sample phrases provided in the Perspective website and show that we can consistently reduce the toxicity scores to the level of the non-toxic phrases. The existence of such adversarial examples is very harmful for toxic detection systems and seriously undermines their usability.