Asymptotic Global Stability

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Lijun Chen - One of the best experts on this subject based on the ideXlab platform.

  • Signal-Anticipation in Local Voltage Control in Distribution Systems
    IEEE Transactions on Smart Grid, 2020
    Co-Authors: Zhiyuan Liu, Seungil You, Xinyang Zhou, Guohui Ding, Lijun Chen
    Abstract:

    We consider the signal-anticipating behavior in local Volt/Var control for distribution systems. Such a behavior makes interaction among the nodes a game. We characterize Nash equilibrium of the game as the optimum of a Global optimization problem and establish its Asymptotic Global Stability. We also show that the signal-anticipating voltage control has less restrictive convergence condition than the signal-taking control. We then introduce the notion of Price of Signal-Anticipation (PoSA) to characterize the impact of signal-anticipating control, and use the gap in cost between network equilibrium in the signal-taking control and Nash equilibrium in the signal-anticipating control as the metric for PoSA. We characterize how the PoSA scales with the size, topology, and heterogeneity of the distribution network for a few network settings. Our results show that the PoSA is upper bounded by a constant and the average PoSA per node will go to zero as the size of the network increases. This is desirable as it means that the PoSA will not be arbitrarily large, no matter what the size of the network is, and no mechanism is needed to mitigate the signal-anticipating behavior. We further carry out numerical experiments with a real-world distribution circuit to complement the theoretical analysis.

  • SmartGridComm - Signal-anticipating in local voltage control in distribution systems
    2014 IEEE International Conference on Smart Grid Communications (SmartGridComm), 2014
    Co-Authors: Jeries Shihadeh, Seungil You, Lijun Chen
    Abstract:

    In this paper, we consider the signal-anticipating behavior in local volt/var control in distribution systems. We define a voltage control game, and show that the signal-anticipating voltage control is the best response algorithm of the voltage control game. We further show that the voltage control game has a unique Nash equilibrium, characterize it as the optimum of a Global optimization problem, and establish its Asymptotic Global Stability. We then introduce the notion of the price of signal-anticipating (PoSA) to characterize the impact of the signal-anticipating in local voltage control, and use the gap in cost between the network equilibrium in the signal-taking voltage control and the Nash equilibrium in the signal-anticipating voltage control as the metric for PoSA. We characterize how the PoSA scales with the size, topology, and heterogeneity of the power network for a few special cases. We find that the stronger the coupling between different buses is, the larger the PoSA is; the linear network gives the largest PoSA among all possible topologies, but as the size of the network increases, the PoSA will saturate.

Seungil You - One of the best experts on this subject based on the ideXlab platform.

  • Signal-Anticipation in Local Voltage Control in Distribution Systems
    IEEE Transactions on Smart Grid, 2020
    Co-Authors: Zhiyuan Liu, Seungil You, Xinyang Zhou, Guohui Ding, Lijun Chen
    Abstract:

    We consider the signal-anticipating behavior in local Volt/Var control for distribution systems. Such a behavior makes interaction among the nodes a game. We characterize Nash equilibrium of the game as the optimum of a Global optimization problem and establish its Asymptotic Global Stability. We also show that the signal-anticipating voltage control has less restrictive convergence condition than the signal-taking control. We then introduce the notion of Price of Signal-Anticipation (PoSA) to characterize the impact of signal-anticipating control, and use the gap in cost between network equilibrium in the signal-taking control and Nash equilibrium in the signal-anticipating control as the metric for PoSA. We characterize how the PoSA scales with the size, topology, and heterogeneity of the distribution network for a few network settings. Our results show that the PoSA is upper bounded by a constant and the average PoSA per node will go to zero as the size of the network increases. This is desirable as it means that the PoSA will not be arbitrarily large, no matter what the size of the network is, and no mechanism is needed to mitigate the signal-anticipating behavior. We further carry out numerical experiments with a real-world distribution circuit to complement the theoretical analysis.

  • SmartGridComm - Signal-anticipating in local voltage control in distribution systems
    2014 IEEE International Conference on Smart Grid Communications (SmartGridComm), 2014
    Co-Authors: Jeries Shihadeh, Seungil You, Lijun Chen
    Abstract:

    In this paper, we consider the signal-anticipating behavior in local volt/var control in distribution systems. We define a voltage control game, and show that the signal-anticipating voltage control is the best response algorithm of the voltage control game. We further show that the voltage control game has a unique Nash equilibrium, characterize it as the optimum of a Global optimization problem, and establish its Asymptotic Global Stability. We then introduce the notion of the price of signal-anticipating (PoSA) to characterize the impact of the signal-anticipating in local voltage control, and use the gap in cost between the network equilibrium in the signal-taking voltage control and the Nash equilibrium in the signal-anticipating voltage control as the metric for PoSA. We characterize how the PoSA scales with the size, topology, and heterogeneity of the power network for a few special cases. We find that the stronger the coupling between different buses is, the larger the PoSA is; the linear network gives the largest PoSA among all possible topologies, but as the size of the network increases, the PoSA will saturate.

Jeries Shihadeh - One of the best experts on this subject based on the ideXlab platform.

  • SmartGridComm - Signal-anticipating in local voltage control in distribution systems
    2014 IEEE International Conference on Smart Grid Communications (SmartGridComm), 2014
    Co-Authors: Jeries Shihadeh, Seungil You, Lijun Chen
    Abstract:

    In this paper, we consider the signal-anticipating behavior in local volt/var control in distribution systems. We define a voltage control game, and show that the signal-anticipating voltage control is the best response algorithm of the voltage control game. We further show that the voltage control game has a unique Nash equilibrium, characterize it as the optimum of a Global optimization problem, and establish its Asymptotic Global Stability. We then introduce the notion of the price of signal-anticipating (PoSA) to characterize the impact of the signal-anticipating in local voltage control, and use the gap in cost between the network equilibrium in the signal-taking voltage control and the Nash equilibrium in the signal-anticipating voltage control as the metric for PoSA. We characterize how the PoSA scales with the size, topology, and heterogeneity of the power network for a few special cases. We find that the stronger the coupling between different buses is, the larger the PoSA is; the linear network gives the largest PoSA among all possible topologies, but as the size of the network increases, the PoSA will saturate.

Ibrahim Sefa - One of the best experts on this subject based on the ideXlab platform.

  • Lyapunov-Function-Based Control Options for Grid-Connected Inverters
    2019 11th International Conference on Electronics Computers and Artificial Intelligence (ECAI), 2019
    Co-Authors: Ibrahim Sefa
    Abstract:

    Control methods of grid-interactive inverters are an interesting research topic in power electronics. Various control methods are investigated to control the output current of the inverter and both steady-state and transient response performances are studied. L filters are used to reduce the switching harmonics in inverter output current in initial studies. However, the LCL filter which is third order becomes popular recently because of its advantages such as smaller inductive component sizes, reduced power loses, better attenuation, and lower inverter output current ripple. in inverter output current. Nevertheless, LCL-type filters have the risk of closed-loop inStability due to two additional complex-conjugate poles and require resonant damping. Therefore, the design of an appropriate control strategy for an LCL filter-based gridconnected inverter becomes more complex than L-filter-based ones. Although different active and passive damping methods applied to solve the damping issue, these methods either in introduce some additional power loss or increase the control complexity. Therefore, developing a control algorithm which removes the additional active or passive damping requirement is more effective. The Lyapunov's direct control scheme which employs Lyapunov function was successfully applied to the control of dc-dc converters, three-phase ac-dc converters, single-phase power factor pre-regulators, single- and threephase shunt active power filters, L-filter-based single-phase grid-connected photovoltaic inverters, switched reluctance motor drive system, and single-phase uninterrupted power supply inverters accomplishing excellent dynamic response and assuring Global Stability under large signal transients. In this study, various Lyapunov-function-based control (LFBC) schemes proposed for a single-phase grid connected voltage source inverter with LCL filter is introduced. Since the use of LCL filter causes resonance, the conventional (CLFBC) scheme employing the inverter-side current guarantees the Asymptotic Global Stability, but it is not able to damp the resonance. In order to damp the resonant, the Lyapunov-function based control scheme can be extended with capacitor voltage or second current feedback. The analytical equations of the closed-loop poles for each control scheme, the effect of changing controller gains on the loci of closed-loop poles is also discussed. These methods are validated with simulation and experimental studies.

  • Comparative study on Lyapunov-function-based control schemes for single-phase grid-connected voltage-source inverter with LCL filter
    IET Renewable Power Generation, 2017
    Co-Authors: Ibrahim Sefa, Saban Ozdemir, Hasan Komurcugil, Necmi Altin
    Abstract:

    This study deals with various Lyapunov-function-based control (LFBC) schemes proposed for a single-phase grid-connected voltage source inverter with LCL filter. Use of LCL filter causes resonance which may adversely affect the controller's Stability. The conventional (CLFBC) scheme employing the inverter-side current guarantees the Asymptotic Global Stability, but it is not able to damp the resonance. As a remedy to the poor resonance damping, the adoption of grid-current and capacitor-voltage feedback schemes have been investigated. Although the former offers a Globally Asymptotically stable system, it cannot improve the poor resonance damping. However, the CLFBC with capacitor-voltage feedback scheme not only preserves the Global Stability, but also improves the resonance damping substantially. The analytical equations of the closed-loop poles for each control scheme are provided which can be used to compute the pole positions and the damping ratio needed for a desired response. Furthermore, the effect of changing controller gains on the loci of closed-loop poles is also studied. Simulation and experimental results obtained from 3.3 kW system demonstrate that the CLFBC with capacitor-voltage feedback scheme not only offers a Global Stability, but also leads to good quality sinusoidal grid current with reasonable total harmonic distortion and fast dynamic response.

Zhiyuan Liu - One of the best experts on this subject based on the ideXlab platform.

  • Signal-Anticipation in Local Voltage Control in Distribution Systems
    IEEE Transactions on Smart Grid, 2020
    Co-Authors: Zhiyuan Liu, Seungil You, Xinyang Zhou, Guohui Ding, Lijun Chen
    Abstract:

    We consider the signal-anticipating behavior in local Volt/Var control for distribution systems. Such a behavior makes interaction among the nodes a game. We characterize Nash equilibrium of the game as the optimum of a Global optimization problem and establish its Asymptotic Global Stability. We also show that the signal-anticipating voltage control has less restrictive convergence condition than the signal-taking control. We then introduce the notion of Price of Signal-Anticipation (PoSA) to characterize the impact of signal-anticipating control, and use the gap in cost between network equilibrium in the signal-taking control and Nash equilibrium in the signal-anticipating control as the metric for PoSA. We characterize how the PoSA scales with the size, topology, and heterogeneity of the distribution network for a few network settings. Our results show that the PoSA is upper bounded by a constant and the average PoSA per node will go to zero as the size of the network increases. This is desirable as it means that the PoSA will not be arbitrarily large, no matter what the size of the network is, and no mechanism is needed to mitigate the signal-anticipating behavior. We further carry out numerical experiments with a real-world distribution circuit to complement the theoretical analysis.