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1. Towards Scalable Voltage Control in Smart Grid: A Submodular Optimization Approach

   https://doi.org/10.1109/ICCPS.2016.7479120  

   Liu, Zhipeng; Clark, Andrew; Lee, Phillip; Bushnell, Linda; Kirschen, Daniel; Poovendran, Radha (April 2016, 2016 ACM/IEEE 7th International Conference on Cyber-Physical Systems (ICCPS))

   Voltage instability occurs when a power system is unable to meet reactive power demand at one or more buses. Voltage instability events have caused several major outages and promise to become more frequent due to increasing energy demand. The future smart grid may help to ensure voltage stability by enabling rapid detection of possible voltage instability and implementation of corrective action. These corrective actions will only be effective in restoring stability if they are chosen in a timely, scalable manner. Current techniques for selecting control actions, however, rely on exhaustive search, and hence may choose an inefficient control strategy. In this paper, we propose a submodular optimization approach to designing a control strategy to prevent voltage instability at one or more buses. Our key insight is that the deviation from the desired voltage is a supermodular function of the set of reactive power injections that are employed, leading to computationally efficient control algorithms with provable optimality guarantees. Furthermore, we show that the optimality bound of our approach can be improved from 1/3 to 1/2 when the power system operates under heavy loading conditions. We demonstrate our framework through extensive simulation study on the IEEE 30 bus test case. 

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2. Multigrid for model reduction of power grid networks

   https://doi.org/10.1002/nla.2201  

   Lee, B. (June 2018, Numerical Linear Algebra with Applications)

   Summary This paper presents a method for determining the relevant buses for reduced models of power grid networks described by systems of differential‐algebraic equations and for constructing the coarse‐grain dynamical power grid systems. To determine these buses, time integration of differential equations is not needed, but rather, a stationary system is analyzed. However, unlike stationary‐system approaches that determine only coarse generator buses by approximating the coherency of the generators, the proposed method analyzes the graph Laplacian associated with the admittance matrix. The buses for the reduced model are chosen to ensure that the graph Laplacian of the reduced model is an accurate approximation to the graph Laplacian of the full system. Both load and generator buses can be selected by this procedure since the Laplacian is defined on all the buses. The basis of this proposed approach lies in the close relationship between the synchrony of the system and the spectral properties of this Laplacian, that is, conditions on the spectrum of this Laplacian that almost surely guarantee the synchrony of the system. Thus, assuming that the full system is in synchrony, our strategy is to coarsen the full‐system Laplacian such that the coarse Laplacian possesses good approximation to these spectral conditions. Accurate approximation to these conditions then can better lead to synchronous reduced models. The coarsened Laplacian is defined on coarse degrees of freedom (DOFs), which are associated with the relevant buses to include in the reduced model. To realize this coarse DOF selection, we use multigrid coarsening techniques based on compatible relaxation. Multigrid is the natural choice since it has been extensively used to coarsen Laplacians arising from discretizations of elliptic partial differential equations and is actively being extended to graph Laplacians. With the selection of the buses for the reduced model, the reduced model is completed by constructing the coarse admittance matrix values and other physical parameters using standard power grid techniques or by using the intergrid operators constructed in the coarse DOFs selection process. Unfortunately, the selection of the coarse buses and the coarsening of the admittance matrix and physical parameters are not sufficient by themselves to produce a stable reduced system. To achieve a stable system, system structures of the fine‐grain model must be preserved in the reduced model. We analyze this to develop a multigrid methodology for constructing stable reduced models of power grid systems. Numerical examples are presented to validate this methodology. 

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3. Voltage Collapse Stabilization in Star DC Networks

   https://doi.org/10.23919/ACC.2019.8814708  

   Avraam, Charalampos; Rines, Jesse; Sarker, Aurik; Mallada, Enrique; Paganini, Fernando (July 2019, American Control Conference)

   Voltage collapse is a type of blackout-inducing dynamic instability that occurs when the power demand exceeds the maximum power that can be transferred through the network. The traditional (preventive) approach to avoid voltage collapse is based on ensuring that the network never reaches its maximum capacity. However, such an approach leads to inefficiencies as it prevents operators to fully utilize the network resources and does not account for unprescribed events. To overcome this limitation, this paper seeks to initiate the study of voltage collapse stabilization. More precisely, for a DC star network, we formulate the problem of voltage stability as a dynamic problem where each load seeks to achieve a constant power consumption by updating its conductance as the voltage changes. We show that such a system can be interpreted as a game, where each player (load) seeks to myopically maximize their utility using a gradient-based response. Using this framework, we show that voltage collapse is the unique Nash Equilibrium of the induced game and is caused by the lack of cooperation between loads. Finally, we propose a Voltage Collapse Stabilizer (VCS) controller that uses (flexible) loads that are willing to cooperate and provides a fair allocation of the curtailed demand. Our solution stabilizes voltage collapse even in the presence of non-cooperative loads. Numerical simulations validate several features of our controllers. 

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4. Demand response through ventilation and latent load adjustment for commercial buildings in humid climate zones

   https://doi.org/10.1016/j.apenergy.2024.123940  

   Ma, Zhihao; Cui, Shuang; Chen, Jianli (November 2024, Applied Energy)

   Space cooling constitutes >10% of worldwide electricity consumption and is anticipated to rise swiftly due to intensified heatwaves under emerging climate change. The escalating electricity demand for cooling services will challenge already stressed power grids, especially during peak times of demand. To address this, the adoption of demand response to adjust building energy use on the end-user side becomes increasingly important to adapt future smart buildings with rapidly growing renewable energy sources. However, existing demand response strategies predominantly explore sensible cooling energy as flexible building load while neglecting latent cooling energy, which constitutes significant portions of total energy use of buildings in humid climates. Hence, this paper aims to evaluate the demand response potential by adjusting latent cooling energy through ventilation control for typical medium commercial office buildings in four representative cities across different humid climate zones, i.e., Miami, Huston, Atlanta, and New York in the United States (US). As the first step, the sensible heat ratio, defined as sensible cooling load to total building load (involving both sensible and latent load), in different humid climates are calculated. Subsequently, the strategy to adjust building latent load through ventilation control (LLVC) is explored and implemented for demand response considering the balance of energy shifting, indoor air quality, and energy cost. Results reveal that adjusting building ventilation is capable of achieving 30%–40% Heating, Ventilation, and Air-conditioning (HVAC) cooling demand flexibility during HVAC operation while among this, the latent cooling energy contributes 56% ~ 66.4% to the overall demand flexibility. This work provides a feasible way to improve electricity grid flexibility in humid climates, emphasizing the significant role of adjusting latent cooling energy in building demand response. 

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5. An Unsupervised Approach to Enhance Cyber Resiliency of Power Systems Against False Data Injection Attacks on Voltage Stability

   https://doi.org/10.18178/ijeetc.14.2.88-93  

   Fahim, Shahriar Rahman (January 2025, International Journal of Electrical and Electronic Engineering & Telecommunications)

   The digital transformation of power system introduces False Data Injection Attacks (FDIAs) on voltage stability that compromises the operational integrity of power grids. Existing detection mechanisms for FDIAs often fall short as they overlook the complexities of cyberattacks targeting voltage stability and rely on outdated models that do not capture the dynamic interplay between power system operations and potential threats. In response to these gaps, this paper proposes a novel FDIA detection method designed specifically for voltage regulation vulnerabilities, aiming to enhance the voltage stability index. The proposed method utilizes an unsupervised learning framework capable of identifying cyberattacks targeting voltage regulation. A bi-level optimization approach is put forward to concurrently optimize the objectives of both attackers and defenders in the context of voltage regulation. The effectiveness of this approach is validated through comprehensive training and testing on a variety of attack scenarios, demonstrating superior generalization across different conditions. Extensive simulations on the Iberian power system topology, with 486 buses, show that the proposed model achieves more than 93% detection rate. These results highlight the robustness and efficacy of the proposed strategy in strengthening the cyber resilience of power systems against sophisticated FDIA threats on voltage stability. 

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