On the use of cyber-physical hierarchy for - IEEE Xplore

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1 G 1 Agent 1 Agent 2 Agent 1 Agent 2 G 2 12 13 G 1 G 3 G 1 2 23 3 G 2 G 3 G 2 G 3 (a) (b) (c) (d) Fig. 2. WECC 9-bus power system representations. Solid (dashed) lines represent physical (cyber) couplings. (a) Dynamical-graph representation of Kron-reduced system, (b) Cyber-physical couplings without hierarchy, (c) Hierarchical cyber-physical couplings for 3-phase short at Bus 6, (d) Possible two-tier hierarchy. Normalized Frequency 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 G1 G2 G3 1 0 2 4 6 8 10 Time (s) (a) Normalized frequencies versus time. Phase Angle (Degree) 104 G1 8 G2 G3 6 4 2 0 −2 0 2 4 6 8 10 10 x Time (s) (b) Phase angles versus time. Phase Angle Difference (Degree) 104 G1 and G2 6 G1 and G3 G2 and G3 4 2 0 −2 −4 −6 −8 0 2 4 6 8 10 8 x Time (s) (c) Phase angle differences versus time. Fig. 3. Results for 3-phase short at Bus 6 when line is removed at t =0.3 s without application of flocking-based control; G 1 and G 2 form a coherent group distinct from G 3. value is unity not zero as for the relative normalized frequency ω ∗ ) and phase when the two-tier flocking-based cyber-physical control is activated at t =0.45 s. The injected power is shown in Fig. 6(a) and demonstrates clipping for G 1 and G 3; the injected power at bus G 2 is zero given the tiered architecture and its physical coherence to G 1. In contrast, Fig. 2(b) illustrates the flocking-based cyber-physical control framework without the hierarchy [1]. All generators have the same priority and the cyber links exist connecting each generator pair; this full connectivity comes at the cost of communication overhead. Figure 6(b) shows the associated P u,i with clipping as discussed above. Thus, every generator pair is coupled through both cyber and physical means. This is in contrast to Fig. 2(c) in which all generators are coupled physically, but cyber coupling only exists between G 1 and G 3. Assuming that the control is activated at t = 0.4 s, Fig. 5 presents the results. Comparing Figs. 4 and 5 we observe that our two-tier framework does not cause noticeable reduction in maintenance of transient stability. Figure 6(c) compares the total power transmission between the fast-reacting power grid and the WECC 9-bus power system by using the cyber-physical control framework with and without the two-tier hierarchical structure. The area under each power transmission curve determines the total energy exchanged between the fast acting grid and the WECC 9-bus system to enable transient stability in the face of the fault. Thus, the results validate the energy efficiency of our proposed two-tier hierarchical control framework. In order to evaluate the robustness of our approach to delays in cyber information possibly stemming from denial-of-service cyber attacks, we study the performance of our control strategy in the face of information delay. Figs. 7 and 8 evaluate the performances of our hierarchical and non-hierarchical control strategies, respectively, under a communication delay of τ =0.05 s; here, the information from neighboring generators used for computation of u i is assumed to be delayed by τ. We observe that our hierarchical structure is more robust to communication delay as transient stability is facilitated whereas for the non-hierarchical case instability results. We believe that the reason for this stems from the greater dependence on physical couplings within the hierarchical approach which makes the approach less susceptible to cyber attacks applied to the information used to compute the control laws. We emphasize that our two-tier approach requires that generator groupings within agents must exhibit physical coherence for correct identification of lead generators. For example, if for the case of the 3-phase short circuit at Bus 6 the generator groupings do not follow the results of the coherence identification method but instead the lead generators are selected to be G 1 and G 2 the hierarchical flockingbased control does not enable transient stability. 5. FINAL REMARKS Overall, we have investigated the application of hierarchy for cyberphysical control and security of smart grid systems. The generators within a smart grid are grouped into coherent clusters such that each cluster is embodied by an agent. The first layer in the two-tier framework reflects cyber-physical interactions amongst lead genera-
Normalized Frequency 1.06 1.04 1.02 1 0.98 0.96 G1 G2 G3 Phase Angle (Degree) 500 400 300 200 100 0 G1 G2 G3 Phase Angle Difference (Degree) 150 100 50 0 −50 −100 G1 and G2 G1 and G3 G2 and G3 0.94 0 2 4 6 8 10 Time (s) (a) Normalized frequencies. −100 0 2 4 6 8 10 Time (s) (b) Phase angles. −150 0 2 4 6 8 10 Time (s) (c) Phase angle differences. Fig. 4. Results for 3-phase short at Bus 6 when line is removed at t =0.3 s with proposed two-tier hierarchical cyber-physical control at t =0.45 s; no information delay. Normalized Frequency 1.04 1.02 1 0.98 0.96 G1 G2 G3 Phase Angle (Degree) 500 400 300 200 100 0 G1 G2 G3 Phase Angle Difference (Degree) 150 100 50 0 −50 −100 −150 G1 and G2 G1 and G3 G2 and G3 0.94 0 2 4 6 8 10 Time (s) (a) Normalized frequencies. −100 0 2 4 6 8 10 Time (s) (b) Phase angles. −200 0 2 4 6 8 10 Time (s) (c) Phase angle differences. Fig. 5. Results for 3-phase short at Bus 6 when line is removed at t =0.3 s with non-hierarchical cyber-physical flocking control at t =0.4 s; no information delay. Pu 3 2 1 0 −1 −2 G1 G2 G3 Pu 3 2 1 0 −1 −2 G1 G2 G3 Total Power Transmission 6 5 4 3 2 1 With Hierarchical Structure Without Hierarchical Structure −3 0 2 4 6 8 10 Time (s) (a) Power transmission P u with hierarchy. −3 0 2 4 6 8 10 Time (s) (b) Power transmission P u without hierarchy. 0 0 2 4 6 8 10 Time (s) (c) Total power transmission P u. Fig. 6. Power transmission between the fast-reacting power grid and the WECC 9-bus power system for 3-phase short at Bus 6.
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