Browsing by Author "Bhela, Siddharth"

Now showing 1 - 6 of 6
  • Thumbnail Image
    Efficient Topology Design Algorithms for Power Grid Stability
    Bhela, Siddharth; Nagarajan, Harsha; Deka, Deepjyoti; Kekatos, Vassilis (IEEE, 2022-01-01)
    The dynamic response of power grids to small disturbances influences their overall stability. This letter examines the effect of network topology on the linearized time-invariant dynamics of electric power systems. The proposed framework utilizes ${\mathcal{ H}}_{2}$ -norm based stability metrics to study the optimal placement of lines on existing networks as well as the topology design of new networks. The design task is first posed as an NP-hard mixed-integer nonlinear program (MINLP) that is exactly reformulated as a mixed-integer linear program (MILP) using McCormick linearization. To improve computation time, graph-theoretic properties are exploited to derive valid inequalities (cuts) and tighten bounds on the continuous optimization variables. Moreover, a cutting plane generation procedure is put forth that is able to interject the MILP solver and augment additional constraints to the problem on-the-fly. The efficacy of our approach in designing optimal grid topologies is demonstrated through numerical tests on the IEEE 39-bus network.
  • Thumbnail Image
    A Game-theoretic Framework to Investigate Conditions for Cooperation between Wind Power Producers and Energy Storage Operators
    Bhela, Siddharth (Virginia Tech, 2015-05-05)
    Game theory has its applications in various domains, but has only recently been applied to study open problems in smart microgrids. A simple microgrid system with a small wind farm, a storage facility and an aggregate load entity is studied here using a non-cooperative game-theoretic framework. The framework developed is used to study the behavior of rational market participants (players), namely wind power producer and energy storage. The framework is implemented to find the existence of any Nash equilibria and see if cooperation is a natural outcome of the game. If cooperation is not self-enforcing then usefulness of the framework to find the conditions for cooperation is presented. It must be noted that cooperation is not automatically guaranteed as the payoff of the energy storage operator is dependent on the strategy employed by the wind power producer. Similarly, the payoff for the wind power producer is highly intertwined with the strategy employed by the energy storage operator. Historical weather and market data is used to calculate expected payoffs for each possible combination of strategies. The results are presented in the form of payoff matrices and the best response algorithm and/or elimination of dominated strategies is used to find the Nash equilibrium. Sensitivity of the Nash equilibrium to various storage parameters like storage size, charging/discharging limits, charging/discharging efficiency, and other market parameters like energy imbalance penalties, efficiency of up/down regulation, and electricity market prices is studied and necessary conditions for cooperation are presented.
  • Thumbnail Image
    A game-theoretic framework to investigate the conditions for cooperation between energy storage operators and wind power producers
    Bhela, Siddharth; Tam, Kwa-sur (Virginia Tech, 2015-06)
    Energy storage, has widely been accepted as a means to provide capacity firming service to renewable sources of energy due to its capability to quickly start and shut down and its ability to have flexible ramping rates. Lithium Ion batteries in particular are of interest as their production cost is expected to significantly decrease over the next few years. In addition, Li-Ion batteries have high efficiency, high energy density and high cycling tolerance. These batteries are also used in electric vehicles whose penetration is expected to grow rapidly in the coming years. The social benefit of energy storage to provide energy balancing service to renewable producers is evident, especially in the context of a micro-grid where deviations from distributed generation sources can be handled locally. However, co-operation with renewable producers may not be automatically guaranteed and would depend on the amount of revenue generated by balancing such deviations. Storage may derive more benefit from choosing to operate independently. Balancing wind deviations would take capacity away from providing other high value services to the micro-grid community such as arbitrage and regulation service. The decision to enter the market and balance deviations for the wind producer is highly intertwined with the strategy adopted by the wind producer. Interactive problems in which the outcome of a rational agent's action depends on the actions of other rational players are best studied through the setup of a game-theoretic framework. A case-study is presented here using wind and electricity market data for a site in west Texas. Historical data is used to calculate expected pay-offs for the month of January. The columns in the following table are the available strategies for the wind producer and the rows are the available strategies for the energy storage. There are four possible combination of strategies, which are discussed next: The pay-off table provides the net revenues of the wind producer in the upper right corner and the net revenues of the energy storage in the lower left corner of each cell. Note that revenue from Production Tax Credits (PTC) is not included for the wind producer.
  • Thumbnail Image
    Inferring Power System Dynamics from Synchrophasor Data using Gaussian Processes
    Jalali, Mana; Kekatos, Vassilis; Bhela, Siddharth; Zhu, Hao; Centeno, Virgilio A. (2022-01-01)
    Synchrophasor data provide unprecedented opportunities for inferring power system dynamics, such as estimating voltage angles, frequencies, and accelerations along with power injection at all buses. Aligned to this goal, this work puts forth a novel framework for learning dynamics after small-signal disturbances by leveraging Gaussian processes (GPs). We extend results on learning of a linear time-invariant system using GPs to the multi-input multi-output setup. This is accomplished by decomposing power system swing dynamics into a set of single-input single-output linear systems with narrow frequency pass bands. The proposed learning technique captures time derivatives in continuous time, accommodates data streams sampled at different rates, and can cope with missing data and heterogeneous levels of accuracy. While Kalman filter-based approaches require knowing all system inputs, the proposed framework handles readings of system inputs, outputs, their derivatives, and combinations thereof collected from an arbitrary subset of buses. Relying on minimal system information, it further provides uncertainty quantification in addition to point estimates of system dynamics. Numerical tests verify that this technique can infer dynamics at non-metered buses, impute and predict synchrophasors, and locate faults under linear and non-linear system models under ambient and fault disturbances.
  • Thumbnail Image
    Inferring Power System Frequency Oscillations using Gaussian Processes
    Jalali, Mana; Kekatos, Vassilis; Bhela, Siddharth; Zhu, Hao (IEEE, 2021-12-14)
    Synchronized data provide unprecedented opportunities for inferring voltage frequencies and rates of change of frequencies (ROCOFs) across the buses of a power system. Aligned to this goal, this work puts forth a novel framework for learning dynamics after small-signal disturbances by leveraging the tool of Gaussian processes (GPs). We extend results on inferring the input and output of a linear time-invariant system using GPs to the multi-input multi-output setup by exploiting power system swing dynamics. This physics-aware learning technique captures time derivatives in continuous time, accommodates data streams sampled potentially at different rates, and can cope with missing data and heterogeneous levels of accuracy. While Kalman filter-based approaches require knowing all system inputs, the proposed framework handles readings of system inputs, outputs, their derivatives, and combinations thereof on an arbitrary subset of buses. Relying on minimal system information, it further provides uncertainty quantification in addition to point estimates for dynamic grid signals. The required spatiotemporal covariances are obtained by exploring the statistical properties of approximate swing dynamics driven by ambient disturbances. Numerical tests verify that this technique can infer frequencies and ROCOFs at non-metered buses under (non)-ambient disturbances for a linearized dynamic model of the IEEE 300-bus benchmark.
  • Thumbnail Image
    Load Learning and Topology Optimization for Power Networks
    Bhela, Siddharth (Virginia Tech, 2019-06-21)
    With the advent of distributed energy resources (DERs), electric vehicles, and demand-response programs, grid operators are in dire need of new monitoring and design tools that help improve efficiency, reliability, and stability of modern power networks. To this end, the work in this thesis explores a generalized modeling and analysis framework for two pertinent tasks: i) learning loads via grid probing, and; ii) optimizing power grid topologies for stability. Distribution grids currently lack comprehensive real-time metering. Nevertheless, grid operators require precise knowledge of loads and renewable generation to accomplish any feeder optimization task. At the same time, new grid technologies, such as solar panels and energy storage units are interfaced via inverters with advanced sensing and actuation capabilities. In this context, we first put forth the idea of engaging power electronics to probe an electric grid and record its voltage response at actuated and metered buses to infer non-metered loads. Probing can be accomplished by commanding inverters to momentarily perturb their power injections. Multiple probing actions can be induced within a few tens of seconds. Load inference via grid probing is formulated as an implicit nonlinear system identification task, which is shown to be topologically observable under certain conditions. The analysis holds for single- and multi-phase grids, radial or meshed, and applies to phasor or magnitude-only voltage data. Using probing to learn non-constant-power loads is also analyzed as a special case. Once a probing setup is deemed topologically observable, a methodology for designing probing injections abiding by inverter and network constraints to improve load estimates is provided. The probing task under noisy phasor and non-phasor data is tackled using a semidefinite-program relaxation. As a second contribution, we also study the effect of topology on the linear time-invariant dynamics of power networks. For a variety of stability metrics, a unified framework based on the H2-norm of the system is presented. The proposed framework assesses the robustness of power grids to small disturbances and is used to study the optimal placement of new lines on existing networks as well as the design of radial topologies for new networks.