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At least 127 records · Page 7

Multi-Game Modeling for Counter-Smuggling

International trade provides an avenue for terrorists to smuggle illicit materials into a target country. Policymakers need models and decision support tools that are both reliable and germane to inform their responses to this. Game theoretic approaches have been used in the analysis of counterterrorism strategies, but the models involved have often been small and abstracted. To address this need, we have developed a multi-game model to account for both security-related and economic aspects of counter-smuggling interdiction efforts. Additionally, we use different games to represent different types of interactions, and these games are then coupled to each other to form an integrated model. In this paper, we demonstrate the model's capabilities on a representative system of ports (both foreign and domestic), trade routes, and commodities. We specifically investigate the impacts of changes in screening policies at domestic ports, detection device capabilities, shipping subsidies, and worldwide corruption levels. In these studies, we find that economic factors play a large role in the interdiction task and provide correspondingly important tools for deterrence.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

Game Theoretic Orchestration for Cooperation among Power Distribution System Applications

The evolving transformation with the proliferation of distributed energy resources and advanced metering, necessitates advanced distribution systems to integrate and orchestrate a large number of grid-edge devices while also serving multiple system-level objectives such as resilience, decarbonization, equity and other system mandates. The parallel deployment and control of resources towards achieving diverse objectives may lead to conflicts between applications that want to control overlapping sets of device setpoints, potentially leading to oscillatory behavior and suboptimal performance. This work aims at leveraging game theoretic framework to drive cooperative behavior among competitive applications. The work proposes a weighted-consensus based game design to facilitate conflict resolution through consensus-building iterations for modular platform. Simulation-based evaluation on a sample test system demonstrates the performance the proposed deconfliction strategy in resolving operational conflicts and achieving close-to-optimal trade off among the applications. Results also compare the proposed strategy with a distribution optimization approach and illustrate it effectiveness in diverse apps regardless of their design while also incentivizing apps with flexible design.

Advanced distribution operations, cooperation, app↗

A Non-cooperative Game-based Approach to Distributed Beam Scheduling in Millimeter-Wave Networks

We consider the distributed beam scheduling problem in mm-Wave networks where the base stations may belong to different operators and there is no centralized coordination among them. Our goal is to design distributed beam scheduling algorithms such that the network utility, which is defined as a logarithm function of the average throughput of the user equipment, can be maximized. We propose a non-cooperative game-based scheduling approach where the base stations are modeled as players that greedily maximize their own utilities. The Nash Equilibrium (NE) then provides a distributed solution to the network utility maximization problem. By employing the Lyapunov optimization, the asymptotic optimality of the proposed scheduling can be guaranteed. We prove the existence and provide sufficient conditions which guarantee the uniqueness of the NE by establishing an equivalence to the Variational Inequality (VI) problem. We also propose a parallel power adaptation algorithm which is proved to converge to the NE. Numerical results show the superiority of the proposed scheduling over several distributed baseline schemes.

99 GENERAL AND MISCELLANEOUS↗

Allocating Reserves in Active Distribution Systems for Tertiary Frequency Regulation

This paper proposes a cooperative game theory-based approach for reserve optimization to enable distributed energy resources (DERs) participate in tertiary frequency regulation. Tertiary frequency regulation schemes ensure that reserve requirements of primary and secondary frequency regulation are fulfilled with a minimum cost. While the available reserve from a single distribution system may not suffice tertiary frequency regulation, stacked reserve from several distribution systems can enable them participate in tertiary frequency regulation at scale. In this paper, a two-stage strategy is proposed to effectively and precisely allocate spinning reserve requirement from each DER in distribution systems. In the first stage, two types of characteristic functions are computed: worthiness index (WI) and power loss reduction (PLR). In the second stage, the equivalent Shapley values are computed based on the characteristic functions, which are used to determine distribution factors for reserve allocation among DERs. The effectiveness of the proposed method for allocating reserves among DERs is demonstrated through several case studies on modified versions of the IEEE 13-node and 33-node distribution systems.

Gautam, Mukesh↗

Multi-Stage Modeling With Recourse Decisions for Solving Stochastic Complementarity Problems With an Application in Energy

This paper presents a multi-stage model with recourse decisions for solving complementarity problems in a competitive electricity market under uncertainty, while also considering renewable energy technologies and battery storage utilization. The model is based on a Nash-Cournot formulation of imperfect competition among power producers. We analyze the value of variable renewable energy (VRE) and battery storage under different uncertainties, such as demand level and VRE availability. To illustrate the proposed model, we apply it to three- bus five-player model and analyze different cases varying costs, including a user-optimal perspective (with market power) and a system-optimal perspective (with central planning). We also consider the potential for congestion in the system by restricting the transmission capacity between a single interface that connects two buses. Our findings show that increasing the battery storage capacity results in a decrease in the need for perfect information about future uncertainties. Additionally, as the model allows for more uncertainty, it becomes more apparent that the stochastic mixed complementarity problem (MCP) has an advantage over a deterministic equivalent. We propose the use of the Value of the Stochastic Equilibrium Solution (VSES) as a quality metric to compare the stochastic MCP with its deterministic equivalent. Overall, expanding battery storage capacity can lower the maximum, mean, and variance values of delivered prices, but there are diminishing returns to this approach.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Game-Theoretic Strategies for Cyber-Physical Infrastructures Under Component Disruptions

In this work, networked infrastructures of recursively defined systems composed of discrete cyber and physical components are considered. The components of basic systems at the finest levels can be disrupted by cyber or physical means, and can be reinforced to survive at certain costs. A problem of ensuring the infrastructure performance is formulated as a game between a provider and an attacker, who probabilistically choose components to reinforce and attack, respectively. The disruptions of this infrastructure are characterized using the aggregate failure correlation function that specifies the conditional failure probability of the infrastructure given the failure of an individual system at that level. The survival probabilities of basic systems satisfy simple product-form, first-order differential equations expressed in terms of the multiplier functions. The utility functions of the provider and attacker are composed of the reward and cost terms, both expressed in terms of the component reinforcement and attack probabilities. The Nash equilibrium of this game is characterized, along with the sensitivity functions of the survival probabilities of basic systems that highlight their dependence individually on the cost-benefit terms, the correlation functions, and the multiplier functions. These results are illustrated using simplified models of a distributed cloud servers infrastructure, a 5G data network infrastructure, a high performance computing federation, and a smart energy grid infrastructure.

42 ENGINEERING↗

Multi-scale, Multi-disciplinary, and Multi-agent Explainable AI with Koopman-Undergirded Learning, Prediction, and Analysis (M3EA KULPA) (Project Closeout Report)

The goal of this project was to develop and use domain-aware machine learning formulations, based on the Koopman Operator (KO), for modelling multi-scale, multi-disciplinary (e.g., multi-physics), and/or multi-agent systems. The project developed these formulations for the following cases: • Systems with dynamics at two separate time scales, • Systems with a bi-level hierarchical control structure, • Systems with bi-level hierarchical control and dynamics at two separate time scales (the lower level controls operating at the faster time scale), and • Systems with n separate but interacting agents/disciplines (with/without control, respectively); the controls for each agent could include bi-level hierarchical control and dynamics at two separate time scales as described above. The project then defined a set of dynamical systems consisting of different nonlinear oscillators that could be used to test these different formulations and then subsequently learned the KO models for those systems. With the KO models, we were able to do the following: • Quantify system stability, including both long-term and transient behavior, • Quantify the effects of feedbacks between the different time scales and agents/disciplines in terms of those feedbacks’ effects on system stability, • Replace a standard Proportional-Integral (PI) control in the hierarchical control structure with a KO-based Linear-Quadratic Regular (LQR), a form of optimal control, • Calculate optimal supervisory control policies a) with and without time scale separated dynamics at the lower level control levels and b) with both PI and KO-based LQR lower level control policies, and • Calculate dynamic Nash equilibria for multi-agent systems where each agent makes its own control decisions.

97 MATHEMATICS AND COMPUTING↗

Evolutionary Game Dynamics between Distributed Energy Resources and Microgrid Operator: Balancing Act for Power Factor Improvement

This article investigates the intricate dynamics between Distributed Energy Resources (DERs) and the Microgrid Operator (MGO) within a microgrid interconnected with the main grid. Employing an evolutionary game framework, the study scrutinizes the strategic evolution of DERs’ decision-making processes in their interactions with the MGO. Modeled as an evolutionary game, these interactions encapsulate the strategies adopted by DERs, resulting in stable equilibrium strategies over time. Motivated by direct benefits linked to increased active power production, DERs strive to sell all available power, while the MGO focuses on optimizing the microgrid’s overall performance. The study assesses the microgrid’s performance in terms of its power factor, emphasizing the strategic balance DERs must achieve in their active power generation to avoid penalization. This penalization results in decreased individual utility for DERs due to the overall power factor decrease resulting from their prioritization of active power generation. Additionally, the diminished overall power factor implies a decrease in MGO utility. The individual utility of each DER is further influenced by the strategies adopted by other DERs, impacting the penalization factor. Leveraging a modified IEEE 13-node distribution microgrid consisting of three DERs, the study presents case studies encompassing both cooperative and non-cooperative evolutionary game scenarios. These case studies illuminate the intricacies of interactions and the resulting equilibrium outcomes.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Modeling arson - An exercise in qualitative model building

A detailed example is given of the role of von Neumann and Morgenstern's 1944 'expected utility theorem' (in the theory of games and economic behavior) in qualitative model building. Specifically, an arsonist's decision as to the amount of time to allocate to arson and related activities is modeled, and the responsiveness of this time allocation to changes in various policy parameters is examined. Both the activity modeled and the method of presentation are intended to provide an introduction to the scope and power of the expected utility theorem in modeling situations of 'choice under uncertainty'. The robustness of such a model is shown to vary inversely with the number of preference restrictions used in the analysis. The fewer the restrictions, the wider is the class of agents to which the model is applicable, and accordingly more confidence is put in the derived results. A methodological discussion on modeling human behavior is included.

Heineke, J. M.↗