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1 The Value of State Awareness in A Changing World: Tackling Dynamics in Wireless Networks and Smart Grids Junshan Zhang School of ECEE, Arizona State University

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A Growing Mobile World “ Broadband's take-up has repeatedly been jumpstarted by must-have applications. Napster drove the shift from dialup to wired broadband. Now Apple's iPhone is playing the same role in triggering explosive growth in the wireless Web. Unless we miss our guess, this dynamic is about to rudely change the subject from net neutrality to a shortage of wireless capacity to meet enthusiastic consumer demand …” [ “The Coming Mobile Meltdown,” Wall Street Journal, 10/14/2009] 2

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State-of the-Art of Power Grid “ If Alexander Graham Bell were somehow transported to the 21st century, he would not begin to recognize the components of modern telephony – cell phones, texting, cell towers, PDAs, etc; while Thomas Edison, one of the grid’s key early architects, would be totally familiar with the grid. '' [ “Final report on smart grid," Dept of Energy Report, Dec. 2008] 3

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Smart Grid in the Making The many meanings of “smart”: Generation: renewable energy integration … Transmission: enhanced situational awareness … Distribution: demand response, automatic control… End-user: smart metering, smart appliances…

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Multi-scale dynamics in mobile communications and in mega-scale power grids. 5

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Mobile Commuications Many signs of explosive growth of wireless traffic: voice/ , web browsing, audio/video streaming Unique challenges in wireless communications: Channel fading occurs on multi-timescales; Time-varying topology due to mobility; Interference varies on multi-timescales; …… 6

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7 Multi-scale Information Dynamics Multi-scale network dynamics: channel-level, link-level, path- level, user-level …

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Multi-scale Power System Dynamics and Operation Functions 8

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Multi-scale Nature of Wind Uncertainty 9

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Part I: The Value of State Awareness for Tackling Dynamics in Wireless Networks Q) How can we design state-aware transmissions in multi-scale dynamics? o Network/channel states are changing continuously; o Sensing/probing is needed to estimate/track states for state-aware network management. DOS under noiseless probing [Mobihoc 2007, IT 2009] DOS under noisy probing: reactive vs. proactive [ToN 2010] DOS for cooperative networking [JSAC 2011] DOS under delay constraint [Infocom 2010] 10 State-aware scheduling: DOS (Distributed opportunistic scheduling) Opportunistic state-aware

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System Model Model: contention-based ad-hoc network Two stages of probing: I) contention; II) channel estimation Challenges: Links have no knowledge of others’ states; even their own states are unknown before probing. Q) Which link to schedule based on local information, and how? Approach: distributed exploitation and exploration Focus: fundamental tradeoffs between probing and throughput gain. A B C D E F

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Distributed Opportunistic scheduling under noiseless probing (i.e., CSMA-type contention in Stage I and perfect channel estimation in Stage II) 12

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13 I) Noiseless Probing Suppose after contention, the successful link has poor channel, and has two options: Continue data transmission; Or, alternatively, let this link give up this opportunity, and all links re-contend. Intuition: At additional cost, further probing can lead to data transmission with better channel conditions. In this way, multiuser diversity and time diversity can be exploited in a distributed and opportunistic manner. A B C D E F

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14 Tradeoff between Probing and Throughput Gain s(n) denote the successful link in n-th round of probing. Clearly, there is a tradeoff between throughput gain from better channel conditions and the cost for further probing. Using optimal stopping theory, we characterize this tradeoff for distributed scheduling. Probing time Channel coherence time

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Technical Conditions

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Throughout Maximization via Maximizing Rate of Return

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17 Threshold Structure of Optimal Scheduling Policy

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Distributed Opportunistic scheduling under noisy probing: Reactive versus Proactive Scheduling 18

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19 II) Noisy Probing: Probing with Imperfect Rate Estimation In the above, channel state information (CSI) is assumed to be perfectly known after probing. In practical scenarios, channel conditions are often estimated using noisy observations, and CSI is imperfect. Consider channel-aware distributed scheduling with noisy rate estimation. MMSE Estimation of the channel rate:

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20 Noisy Probing Major differences between noisy/perfect probing: The rate, after probing, is not perfectly known. The stopping rule in noisy case is defined over filtration generated by noisy observations Can show that structure of optimal scheduling remains same, except that the rate is replaced with its conditional expectation. Reactive strategy: (linear) rate backoff Proactive strategy: next

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21 Proactive Strategy with Noisy Probing Further probing may be helpful to improve the quality of rate estimation and hence the throughput. Particularly interested in the wideband low SNR regime, i.e., and Potential significant improvement of rate estimation due to further probing in wideband regime. [Verdu’ IT2002] Trade-off between enhanced rate gain due to improved estimate and further probing cost. Proactive approach: DOS with two-level probing; Underlying theory: optimal stopping theory with incomplete information [Stadje’ 97].

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22 Proactive Strategy: DOS with Two-Level Probing Q: Is it worthwhile for the successful link to “refine” rate estimation, with an additional cost? How much can we bargain? Channel condition is bad refinement is not helpful, defer and re-contend Channel condition is good refinement is relatively meager, transmit immediately at the current rate ? The answer is yes or no; there is a grey area where additional probing will help. - Gain: more accurate rate estimate;- Cost: time overhead

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23 DOS with Two-Level Probing: Structural results Optimality Conditions:

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24 Possibilities R (2) Give up and re-contend Transmit at R (2) 1st level probing Rate R (1) CI Give up and re-contend ?CI S(n) Possibilities R (1) Transmit at R (1) T 2nd Level Probing Refined rate R (2) ? DOS with Two-Level Probing: Strategy A

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25 DOS with Two-Level Probing: Strategy B 1-st level probing Rate R (1) ?CI S(n) Possibilities Give up and re-contend Transmit at R (1) T Details: [Infocom’09]

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26 Numerical Example - performance gap is significant in the low-SNR regime. - As increases, the performance gap narrows down -The overhead due to extra probing offsets its gain in mitigating estimation errors - The “gray area” collapses. As a result, Strategy A degenerates to Strategy B

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Distributed scheduling for cooperative networking 27

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State Awareness & Cooperative Networking Our initial steps started in 2001/2002 and studied 1) Capacity bounds of MIMO relay channel; 2) Power allocation in wireless relay networks; 3) Scaling laws of Wideband sensory relay networks Two of our IT papers received about 800 citations: B. Wang, JZ & Host Madsen (IT 05); Host-Madsen & JZ (IT 05). [Google scholar] High traffic volume Need cooperative networking

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III) Distributed Scheduling for Cooperative Networking: To Relay or Not to Relay? collision! re-contend no collision and ‘good’ channel: transmit no collision but ‘bad’ channel : re-contend no collision : to relay ? 29

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DOS with Dedicated Relay Node trade-off: higher rate vs. overhead for probing relay and establishing coopertive relaying re-contend 30

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DOS without Dedicated Relay Node... tradeoff: (node diversity + higher rate) vs. (probing overhead + cost of relay) re-contend 31

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Distributed scheduling under delay constraints 32

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DOS under Network-wide Delay Constraint 33

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Relaxation and Duality 34

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From Primal to Dual to Dual’s Dual 35 Details: [Infocom’10] “Hidden convexity” (Lyapunov Theorem)

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Part II: The Value of Situation Awareness: Tackling Dynamics in Smart Grid Transmission: PMU data processing for dynamic contingency analysis [He-JZ-Vittal (preprint)] CPS inter-networking architecture: robustness vs. allocation of interconnecting edges [Yagan-Qian-JZ-Cochran 2011] Wind generation integration: modeling and fortcast of wind generation; multi-scale scheduling and dispatch 36

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Situation Awareness in Smart Grid Multi-scale dynamics of power grid: Supply uncertainty: deep penetration of renewable energy (wind, solar …) Demand uncertainty: load variation, distributed generations … Traditional SCADA systems Measurements taken every few seconds; state estimation every few mins. Lack “real-time” situational awareness; may fail to prevent large-scale blackouts (e.g., 2003 northeast blackout) Emerging wide-area monitoring system (WAMS) PMU sampling frequency (30~60/s), synchronized by GPS time-stamps Useful for state estimation, fault diagnosis, and contingency analysis 37

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Synchronized Measurements of Phasor Measurement Units Location 1 Location 2 Synchronizing pulses obtained from GPS satellites. Phase angular difference between the two can be determined.

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Normal Phase angle 30 ⁰ Frequency “spikes” as Phase Angle jumps to 76 ⁰ Example: June 2005 Houston Blackout Phasor Angle Jumping and Frequency Spikes

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Frequency Collapse (T-0 min) Frequency becomes Unstable and Phase Angle difference Exceeds 120 ⁰ 5:10 PM 5:16 PM 120 ⁰ Diff

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Contingency Analysis Contingency analysis: “What-if” a hypothetical accidental event occurs, e.g., outage of lines or generators; determines if state trajectories are in insecure regions, and if yes, take preventive/corrective actions. Two important approaches (both assuming a given set of contingencies) Nonlinear system analysis [Chiang’95, Chiang’99] Decision tree [Sun-Vittal’07,Diao-Vittal’09] Dynamic contingency analysis: Goal: Incorporate new contingencies and adapt to new measurements; distributed implementation. Challenges: Large contingency list; thousands of states and many more data; Exact analysis is non-attainable since large-scale power systems are highly nonlinear; numerical study is challenging due to computational burden.

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Decision tree: a tree structure that maps observation to a predicted value is binary for classification (continuous for regression tree ) At each internal node, compare an attribute to a threshold, and generate two branches Each binary string points to a region and a predicted value per leaf Decision tree learning: Select the attribute and its threshold for each internal node, so as to minimize prediction error, e.g., for classification tree using Gini Index, For regression tree: Decision Tree for Contingency Analysis where, is the region corresponding to left branch of A, is number of samples in, and.

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Example: DT Learning for Contingency Analysis A classification tree trained with given historic data to find secure (insecure) regions in attribute space Learned DT applied to real-time PMU data for contingency analysis

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Pre-processing and Post-processing for DT-based Dynamic Contingency Analysis In existing approaches: DT is rebuilt to incorporate new contingencies; high complexity for updating a DT; centralized. DT with a large number of correlated attributes is prone to overfitting. Treelets based preprocessing [Lee08]: Data mining & learning tools are used for dimension reduction to transform attributes into a lower dimensional space; new attributes as linear combinations of original ones Multi-classifier boosting (MCBoost) as post-processing [Kim08]: Each classifier corresponds to a subset of contingencies. Each classifier is obtained by boosting a few simple DTs, easy to update in online applications. Combine multiple classifiers to obtain final decision.

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Use the SRP database Single DT: 35 internal nodes, largest simple DT: 7 internal nodes; complexity is much lower Examples: Boosting simple DTs

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Examples: Incorporation of New Contingency Convergence performance: the 6th contingency (CT183) is incorporated into a 5-classifier analyzer, via updates with incremental observations for CT183

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. Robust CPS inter-networking architecture: Allocating Interconnecting Links against Cascading Failures 47

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48 Networked systems: modern world consists of an intricate web of Interconnected infrastructure systems. Interdependence: Operation of one network depends heavily on the functioning of the other network Vulnerability to cascading failures: node failures in one network may trigger a cascade of failures in both networks, and overall damage on cyber-physical systems can be catastrophic since the affected area is much greater than that affected in a single network alone. CPS - Two Interacting Networks

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49 Robust Inter-networking Architecture: An Interconnecting Edge Allocation View Q) How to improve robustness against cascading failures, under constraint of average inter-edges per node Allocation without intra-degree information Random vs. Uniform allocation Unidirectional edges vs. bi-directional edges Allocation with intra-degree information Preferential allocation Ranking based allocation Approach: compute ultimate fractions of functioning giant components, and critical threshold p c; the lower p c the more robust

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50 Analysis of Cascading Failures Approach: compute the ultimate fractions of the giant components, and critical threshold p c Notation: p Ai ; p Bi : the fraction of functioning giant components in A (resp. B) at stage i p’ Ai ; p’ Bi : the remaining fraction in A (or B) which are equivalent to node removals due to cascading failures up to stage i P A (p); P B (p): After a fraction 1-p of A-nodes (B-nodes) failed, the giant component size in the remaining fraction [Newman 2002]

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51 Uniform Allocation of Bi-directional Edges Stage 1: Node failures in Network A inter-edge can be disconnected w.p. 1-p A1 The remaining fraction of nodes with inter-edges: p’ B2 = 1-(1-p A1 ) k Random failures of 1-p of nodes Removal of inter-edges functioning giant component A 1 p A1 =pP A (p) Stage 2: Cascading effect of A-node failures on network B functioning giant component B 2 p B2 =p’ B2 P B (p’ B2 )

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52 Stage 3: Network A’s further fragmentation due to B-node failures inter-edge can be disconnected w.p. 1-P B ( p ’ B2 ) The remaining fraction of A 1 : 1-(1-P B (p’ B2 )) k For A, the joint effect of Stage 1&3 on A equals the node failures in A with fraction 1-p’ A3 =1- p+p(1-P B (p’ B 2 )) k Key step: further node failures in A 1 at Stage 3 has the same effect as taking out equivalent fraction of nodes in A functioning giant component A3 p A3 =p’ A3 P A (p’ A3 ) Uniform Allocation of B-directional Edges (Cont’d)

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network A network B p A1 =pP A (p) p B2 =p’ B 2 P B (p’ B2 ) p A3 =p’ A3 P A (p’ A3 ) p B4 =p’ B2 P A (p’ B2 ) …. …. 53 The recursive process reaches an equilibrium point By calculating the equilibrium point, we can get the ultimate giant component size and critical threshold functioning giant component size in the dynamics of cascading failures Stage 1 Stage 3 Stage 2 Stage 4 Uniform Allocation of Bi-directional Edges (Cont’d)

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Robustness of Different Allocation Strategies Two Erdos-Renyi networks with average intra-degree fixed at 4 The p c varies over different average inter-degree k As expected, the uniform & bi-directional allocation leads to the lowest p c under various conditions Lower p c indicates the higher robustness

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Allocation with Intra-degree Information Preferential allocation Intuition: Important nodes have more support Probabilistically allocate the inter-degree proportional to intra- degree Ranking based allocation Rank nodes based on their intra-degrees; and partition nodes into groups Deterministically allocate more inter-edges to groups with higher intra- degrees Analysis is fairly difficult; evaluate the performance by simulations. By exploiting intra-degree information, both strategies outperform the allocations without topology information

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56 Conclusions Multi-scale dynamics is ubiquitous in complex networks, e.g., in mobile communications and in mega-scale power grids. Tackling dynamics in mobile communications: distributed opportunistic scheduling for a variety of models. Tackling dynamics in smart grids: PMU data processing for contingency analysis, and robust CPS architecture design. (We have also looked into fault diagnosis based on Markov random field model of PMU data; multi-scale scheduling and control for wind generation integration.) Many open research problems need “marriage” of expertise in power system, renewable energy, communication, control, computing, … Need multi-disciplinary research!

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