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...ent Stability Power system transient stability describes the ability of a smart grid to remain in synchronism when subjected to large disturbances, such as transmission line faults and generator loss =-=[4]-=-. For smart grids, achieving transient stability consists of maintaining both exponential frequency synchronization and phase angle cohesiveness of its synchronous generators through application of di...

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...ation delay. We also investigate the situation of random communication delay where the random delay τ is modeled using packet service time statistics in a M/M/1 queueing system and defined as follows =-=[23]-=-: p(τ ) = (1/κ)e−(τ/κ), where κ denotes the average service time, which is equivalent to average communication delay in our framework. Fig. 21. Phase angles with hierarchical control for fixed communi...

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... informed-adaptation. Members of a flock are referred to as flockmates or agents. The behavior within a flock has been described by a following set of heuristic agent-interaction rules that we employ =-=[9]-=-. 1) Flock Centering: Agents attempt to stay close to nearby flockmates. 2) Collision Avoidance: Agents avoid collisions with nearby flockmates. 3) Velocity Matching: Agents attempt to match velocity ...

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...kmates. 2) Collision Avoidance: Agents avoid collisions with nearby flockmates. 3) Velocity Matching: Agents attempt to match velocity with nearby flockmates. Based on these three rules, Olfati-Saber =-=[10]-=- provided a framework for design and analysis of scalable distributed flocking algorithms using a double integrator model: q̇ = p and ṗ = u, where q ∈ RN is the position vector of the flockmates, p ∈...

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...plication of singular perturbation techniques to in (9) to study the dynamics of the lead agents over a longer time scale. Specifically, applying singular perturbation analysis and letting Mi = Di+Bi =-=[12]-=-, where the index i = 1, . . . , C, gives the form of a double integrator model as follows: { θ̇i = ωi Miω̇i = ũi. (10) Here, the simplification has allowed the physical notion of generator “jerk” re...

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... phase angles of Generators i and j should be below a predefined threshold γ ∣ ∣θi − θj ∣ ∣ ≤ γ (2) where γ is normally set to 5π/9 as discussed in [6]. The reader should note that other formulations =-=[7]-=-, [8] have set the upper bound as π/2. The discrepancy is due to the fact that in our model, we consider transfer conductances and thus are able to relax the upper bound from 90◦ to 100◦ as supported ...

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...es the physical coherency between the agents by applying flocking-based control only to lead agents. Specifically, we show in the Appendix that given an accurate identification of generator coherency =-=[13]-=-, the following control law guarantees transient stability: ũl = −s− L̃ωl − c1 ( ωl − ω∗ ) (17) where c1 is a positive parameter for the linear navigational feedback, ω∗ = 0 is the desired normalized...

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...l framework with dynamics in (15) and (16) collectively also described by (5) in achieving transient stability for two case studies on the New England 39 Bus system as shown in Fig. 2 and detailed in =-=[15]-=- consisting of C = 10 generators. MATLAB/Simulink is employed for simulations. In each case, we illustrate the efficiency of our 2692 IEEE TRANSACTIONS ON SMART GRID, VOL. 5, NO. 6, NOVEMBER 2014 Fig....

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...e angles of Generators i and j should be below a predefined threshold γ ∣ ∣θi − θj ∣ ∣ ≤ γ (2) where γ is normally set to 5π/9 as discussed in [6]. The reader should note that other formulations [7], =-=[8]-=- have set the upper bound as π/2. The discrepancy is due to the fact that in our model, we consider transfer conductances and thus are able to relax the upper bound from 90◦ to 100◦ as supported in [5...

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...tler@tamu.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSG.2014.2341211 problem. Ilić et al. =-=[1]-=- propose a dynamic framework to represent the interactions amongst generators and loads. Here a module with linear closed-loop dynamics is used to represent each generator and load that are interconne...

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...ommunication delay caused by DoS attack [19]. Hence, various researches have been focused on the study of communication delay impacts caused by network congestion or DoS attack on the power grid [20]–=-=[22]-=-. We investigate both fixed and random communication delay for the cases addressed in the previous section. In each case, we consider the situation of unexpected communication delay for t = 0.2 s to t...

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...ion to 1. Letting ωi be the normalized relative frequency of Generator i with respective to f0, we can describe exponential frequency synchronization as follows: ωi(t) → 0, as t → ∞. (1) As stated in =-=[5]-=-, the loss of synchronism of generators results if the rotor angle difference between two generators is beyond a certain limit, which causes a rapid drop in bus voltages. Therefore, as shown in (2), p...

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...(cyber) communication network. A greedy search algorithm is proposed to identify a communication topology that can enable synchronism for a given smart grid topology. Existing research by Wei. et al. =-=[3]-=- has studied the analogy between the dynamics of generator synchronization and that of flocking theory. A distributed cyber-physical control approach is developed such that in the face of disturbances...

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...stem equation to model the cyberphysical interactions. To describe the physical system, we make use of the well-known interconnected swing equations to describe rotor dynamics [4] of the Kron-reduced =-=[11]-=- power system as detailed in [7] and [8] to give the following dynamical representation for each agent: Miω̇i = −Diωi + Pm,i − |Ei|2Gii − N ∑ j=1,js=i Pij sin ( θi − θj + ϕij ) (3) where i ∈ {1, 2, . ...

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...ohesiveness necessitates that the difference between phase angles of Generators i and j should be below a predefined threshold γ ∣ ∣θi − θj ∣ ∣ ≤ γ (2) where γ is normally set to 5π/9 as discussed in =-=[6]-=-. The reader should note that other formulations [7], [8] have set the upper bound as π/2. The discrepancy is due to the fact that in our model, we consider transfer conductances and thus are able to ...

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...ous communication delay caused by DoS attack [19]. Hence, various researches have been focused on the study of communication delay impacts caused by network congestion or DoS attack on the power grid =-=[20]-=-–[22]. We investigate both fixed and random communication delay for the cases addressed in the previous section. In each case, we consider the situation of unexpected communication delay for t = 0.2 s...

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...sults applicable to some forms of DoS, the emphasis of the paper is on the introduction of a modeling and distributed control framework and not on cyber security. The interested reader is referred to =-=[24]-=- for a more comprehensive understanding of the effects of more general cyber attacks such as false data injection. Ongoing research focuses on theoretically analyzing the impact of the initial value o...

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...mongst generators and loads. Here a module with linear closed-loop dynamics is used to represent each generator and load that are interconnected using a linear network model of the system. Li and Han =-=[2]-=- study how the addition of communication links can effectively restabilize a faulted power grid. They employ a linearized swing equation-based model relating the overall generator synchronization to s...

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...ude that by using the information of ωi and θi of each lead agent, which are both available, the value of ul can be calculated. IV. TIMELY DYNAMIC AGENT COHERENCY IDENTIFICATION In our previous paper =-=[14]-=-, we propose a timely dynamic agent coherency identification scheme which requires very short observation window. Our scheme transforms the data of agents’ state from the observation space to an infor...

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...vironment With Communication Delay We evaluate the performance of our hierarchical framework by studying unexpected communication delay of the PMU data associated with the “lead" agents. As stated in =-=[16]-=-–[18] smart grid communication delay is a significant problem and is typically a result of high network congestion or cyber attack 2696 IEEE TRANSACTIONS ON SMART GRID, VOL. 5, NO. 6, NOVEMBER 2014 Fi...

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...ment With Communication Delay We evaluate the performance of our hierarchical framework by studying unexpected communication delay of the PMU data associated with the “lead" agents. As stated in [16]–=-=[18]-=- smart grid communication delay is a significant problem and is typically a result of high network congestion or cyber attack 2696 IEEE TRANSACTIONS ON SMART GRID, VOL. 5, NO. 6, NOVEMBER 2014 Fig. 20...