Optimization, Dynamics, and Layering in Complex Networked Systems: From the Internet to the Smart Grid

Transcription

1 Optimization, Dynamics, and Layering in Complex Networked Systems: From the Internet to the Smart Grid Lijun Chen Computer Science & Telecommunications University of Colorado at Boulder May 6, 2014

2 Networked systems Complexity is ever increasing Large in size and scope Enormous heterogeneity Incomplete information Uncertain environments Emerging technologies New applications New design dimensions Design (& understanding) is increasingly dominated by Efficiency (optimality) Manageability Reliability & Security Economic viability Scalability Evolvability emerging, collective properties 2

3 Systems requirements: functional, efficient, robust, secure, evolvable, architecture Components Organizational principles, including abstractions and interfaces Highly conserved core resource allocation, control, and management mechanisms 3

4 Systems requirements: functional, efficient, robust, secure, evolvable, architecture Components Constraints that deconstrain Certain fixed points and structure under which the network can expand/evolve Can be constraining for the issues that the network was originally not designed for Good architecture enables innovation, bad one freezes it 4

5 Systems requirements: functional, efficient, robust, secure, evolvable, architecture Components Architectural design Remains an art, primarily empirical, reasoning-based Good architecture easy to recognize in retrospect but elusive to forward-engineer No formal theory nor systematic design method 5

6 Systems requirements: functional, efficient, robust, secure, evolvable, Goal Mathematical underpinning of network architecture architecture Components Systematic methods to develop and evaluate design choices and algorithms 6

7 Systems requirements: functional, efficient, robust, secure, evolvable, Goal Understand architecture and main mechanisms of existing networks (reverse engineering) architecture Components Design architecture and main mechanisms for emerging networks (forward engineering) 7

8 Internet Application Diverse Highly conserved core mechanisms Physical TCP/AQM IP MAC Diverse Layered architecture 8

9 Internet architecture Application TCP/AQM IP Little quantitative understanding Optimal? In what sense? Lots of problems Efficiency, security, mobility, accountability, MAC Physical fixes (middle boxes & overlays & underlays) 9

10 Emerging networked systems future internet energy-efficient data center smart grid architectures are being designed now 10

11 Future Internet architecture Clean slate Internet design that aims to build in security mobility new communication paradigms not clear what the right architecture is and how to best design different components and their interactions 11

12 Energy-efficient data center How to decompose & coordinate energy management decisions spatially and temporally How to interact with other resource allocation algorithms How to interconnect servers to balance performance and energy usage 3-5% of total US energy use theories and models are needed to guide architecture and algorithm design 12

13 Smart grid Power network will go through similar architectural transformation in the next few decades that telephone network has gone through Tesla: multi-phase AC deregulation started Both started as regulated monopolies s Both provided a single commodity Both were vertically integrated Both grew rapidly through two WWs s? Enron, blackouts 2000s Bell: telephone q infrastructure (completely?) re-engineered q industry landscape drastically reshaped deregulation started 1969: DARPAnet convergence to Internet 13

14 Smart grid... to become more interactive, more distributed, more open, more autonomous, and with greater user participation what is an architecture theory to help guide the transformation?... while maintaining security & reliability 14

15 Research Systems requirements: functional, efficient, robust, secure, evolvable, architecture Components Rigorous foundations and new methodologies for understanding & designing architecture and various mechanisms Employ and develop techniques in optimization theory/algorithm distributed control game theory systems theory 15

16 Approach Architecture theory (principles and design methodologies) wireless networks network coding EE networks smart grids must be foundational and practical must be abstract and concrete 16

17 Outline q Layering and constrained optimization q Network dynamics as optimization algorithms q Look into future 17

18 Layered Internet protocol stack Each layer q controls a subset of decision variables q hides the complexity of the layer below q provides a service to the layer above q designed separately and evolves asynchronously Application TCP/AQM IP Link/MAC Physical select user criteria, web layout, utility, select source transmission rates select paths from sources to destinations select topology, medium access select coding, power,. 18

19 Optimization and layering Each layer is abstracted as an optimization problem Operation of a layer is a distributed solution Results of one problem (layer) are parameters of others Operate at different timescales Application TCP/AQM IP Link/MAC Physical minimize response time, maximize utility minimize path cost maximize throughput, minimize SINR, maximize capacities, 19

20 Optimization and layering Networks as optimizers q integrate various protocol layers, by regarding them as carrying out distributed computation over the network to implicitly solve a certain global optimization problem q different layers iterate on different subsets of the decision variables using local information to achieve individual optimality q taken together, these local algorithms achieve a global optimality 20

21 Protocol decomposition: TCP/AQM 21 Duality model: TCP/AQM as distributed primal-dual algorithm over network to maximize aggregate utility (Kelly 98, Low 99, 03) c Rx x U s s s x s.t. ) ( max 0 + l l l s l l ls s s s x p p c p R x x U s ) ( max min 0 0 Primal: Dual c x x c x x + = c c x x x Rx x 1 x 3 x 2 c 2 c 1

22 Protocol decomposition: TCP/AQM Duality model: TCP/AQM as distributed primal-dual algorithm over the network to maximize aggregate utility (Kelly 98, Low 99, 03) Primal: max x 0 s.t. s U s Rx c ( x s ) Dual min p 0 s max U xs 0 s ( x s ) x s l R ls p l + l p c l l ' 1 xs () t = U ( s Rls pl ) l pl ( t+ 1) = [ pl ( t) + γ ( Rlsxs( t) cl )] s horizontal decomposition + 22

23 Optimization and layering Application max x 0 s U s ( x s ) s.t. Rx c Transport Network Link/MAC Physical Extend to include decision variables and constraints of other layers Derive layering from decomposition of extended utility maximization 23

24 Generalized utility maximization Objective function: user application needs and network cost Constraints: restrictions on resource allocation (could be physical or economic) Variables: Under the control of this design Constants: Beyond the control of this design Application utility Network cost max x, R, c, p subj to IP: routing i U ( x Rx c c X ( p) i i ) λ T Rx Phy: power Link: scheduling 24

25 Layering as optimization decomposition Network generalized NUM Layers sub-problems Interface functions of primal/dual variables Layering decomposition methods Application TCP/AQM IP Link/MAC Physical Vertical decomposition: into functional modules of different layers Horizontal decomposition: into distributed computation and control over geographically disparate network elements 25

26 Layering as optimization decomposition Network generalized NUM Layers sub-problems Interface functions of primal/dual variables Layering decomposition methods Application TCP/AQM IP Link/MAC Physical Provides a top-down approach to design protocol stack q explicitly tradeoff design objective q explicitly model constraints and effects of, e.g., new technologies q provide guidance on how to structure and modularize different functions q make transparent the interactions among different components and their global behaviors 26

27 Cross-layer design in ad hoc wireless networks Application TCP/AQM IP MAC Physical Network performance can be improved if network layers are jointly designed Most works design based on intuition, evaluated by simulations unintended consequences 27

28 Cross-layer design in ad hoc wireless networks Application TCP/AQM IP MAC Physical A principled/holistic approach Capture global structure of the problem design objective constraints Derive the design from the distributed decomposition of certain optimization problem 28

29 Cross-layer design/optimization each source s: sending rate x s and utility U s x ) s ( s c f l N l N, Π ; f Π d Network model routing of service requirement H(x) allocation of service capacity A( f ) H ( x) A( f ) 29

30 Problem formulation Network resource allocation: max x, f s. t. s U ( x H ( x) A( f Π s s ) f ) constraint for routing constraint from wireless interference 30

31 Protocol decomposition 31 )} ( max )) ( ) ( ( min{max ), ( ) (.. ) ( max 0, Dual: Primal: f A p x H p x U f f A x H s t x U T f T s s s x p s s s f x Π + Π Rate control Scheduling Routing rate constraint schedulability constraint

32 Cross-layer implementation Dual: T T min{max ( U ( x ) p H( x)) + max p A( f)} s s p 0 x f Π s Application Rate control Routing Scheduling Transport Network Link/MAC Physical q q q q Rate control: T x( t) = x( p( t)) = argmax U s ( xs ) p ( t) H( x) Routing: solved with rate control or scheduling Scheduling: T f ( t) = f ( p( t)) = arg max p ( t) A( f ) x s f Π Congestion update: vertical decomposition 1) = [ p( t) γ { A( f ( p( t))) H ( p( t + x( p( t)))}] t + 32

33 Extension to time-varying channel Application Transport Network Link/MAC Physical q q q q channel state h : i.i.d. finite state process with distribution Rate control: T x( t) = x( p( t)) = argmax U s ( xs ) p ( t) H( x) Routing: solved with rate control or scheduling Scheduling: f ( t) = f ( p( t)) = arg Congestion update x s max f Π ( h( t)) p T q(h) ( t) A( f ) random p( t + 1) = [ p( t) γ { A( f ( p( t))) H ( x( p( t)))}] t + 33

34 Stability and optimality Theorem (Chen-Low-Chiang-Doyle 06, 11): The Markov chain is stable. Moreover, the cross-layer algorithm solve the following optimization problem max x, f s. t. H ( x) f s U s Π ( x s ) A( Π = { r : r = q( h) r( h), r( h) Π( h)} q Applicable to any queueing network with interdependent, time-varying, parallel servers optimality holds even with time-varying topologies throughput-optimal when flow-level dynamics is considered A Wi-Fi implementation by Rhee s group at NCSU shows significantly better performance than existing system h f ) 34

35 Outline q Layering and constrained optimization q Network dynamics as optimization algorithms q Look into future 35

36 Smart grid Power network will go through a similar architectural transformation in the next few decades that telephone network has gone through Tesla: multi-phase AC deregulation started Both started as regulated monopolies s Both provided a single commodity Both were vertically integrated Both grew rapidly through two WWs s? Enron, blackouts 2000s Bell: telephone q infrastructure dramatically reengineered q industry landscape drastically reshaped deregulation started 1969: DARPAnet convergence to Internet 36

37 Emerging trends Proliferation of renewable and distributed generation Electrification of transportation Participation of end users drivers Advances in power electronics Deployment of sensing, communication, computation infrastructure enablers 37

38 Proliferation of renewables (GW) 400 Global renewable power capacities, excluding hydro Wind q driven by sustainability q enabled by government policy and investment Regional growth (US) in non-hydro renewable generation (billion KWH), Biomass Solar PV Geothermal real opportunity for sustainability Sources: REN21, Renewables global status report ( ); DOE/EIA-0383 (2013) 38

39 Random/rapid fluctuations Source: Rosa Yang, EPRI 39

40 Migration to distributed architecture Small CHP (combined heat & power) Large CHP (combined heat & power) Wind q 2-3x generation efficiency q relieve demand on grid capacity q also in control and management Denmark s experience 40

41 Large-scale network of DERs Distributed energy resources (DERs): PVs, wind turbines, smart loads, inverters, storages, EVs offices solar panels smart appliances wind farms small generators houses millions of ac.ve endpoints that may generate, sense, compute, communicate, and control Sensors demand management industrial plant Transmission: from generator to substa.on, long distance, microgrid high voltage storage Distribu/on: from substa.on to customer, shorter distance, lower voltage central power plant Source: ITERES 41

42 Large-scale network of DERs Challenge: an interconnected system of millions of DERs introducing rapid, large, and random fluctuations in supply, demand, voltage, and frequency Opportunity: increased capability to coordinate and optimize their operation for unprecedented efficiency and robustness 42

43 Current control paradigm Hierarchical control structure spanning multiple timescales from subseconds to hours and up primary freq control secondary freq control economic dispatch unit commitment sec min 5 min 60 min day year dynamic model e.g. swing eqn power flow model e.g. DC/AC power flow Frequency control as an example 43

44 Current control paradigm Centralized, open-loop, worst-case preventive, and often human-in-the-loop at slow timescales q cope with slow/predictable but often large variations q economic efficiency and system security are the key (optimization model) Local and automatic at fast timescales q cope with fast but relatively small variations q (local) stability is the key (dynamical model) q oblivious of system-wide properties or global perspective Sufficient for today s power system q relatively low uncertainties, few active assets, mainly to match controllable supply to passive load q the lack of ubiquitous sensing, control and communication

45 Current control paradigm Centralized, open-loop, worst-case preventive, and often human-in-the-loop at slow timescales q cope with slow/predictable but often large variations q economic efficiency and system security are the key (optimization model) Local and automatic at fast timescales q cope with fast but relatively small variations q (local) stability is the key (dynamical model) q oblivious of system-wide properties or global perspective Sufficient for today s power system q relatively low uncertainties, few active assets, mainly to match controllable supply and passive load q the lack of ubiquitous sensing, control and communication

46 Future control needs Real-time and close-loop q with rapid, large, and random fluctuations, feedback control based on real-time information is needed Distributed to ensure scalability q with large number of control points, information must be decentralized and decisions must be made locally Fast/local controls actively and globally coordinated q local controls must be bridged with the global situation, to ensure system-wide efficiency and robustness Enabled by the deployment of sensing, control, and communication infrastructure and the advances in power electronics 46

47 New control paradigm Autonomous DERs for distributed real-time control q Each DER made autonomous through local sensing, computing, communication, and control q intelligence embedded everywhere Local algorithms with global perspective q algorithm design starts with global objectives, which will be decomposed into local algorithms Layered architecture q control as a service: the network should provide a set of common control services to various applications q applications call and synthesize the control services to meet performance specifications

48 New control paradigm Autonomous DERs for distributed real-time control Local algorithms with global perspective Layered architecture What are fundamental challenges motivated?

49 Comparison with the Internet Motivated by the Internet q power flow versus information flow q how it is managed and controlled q theories for architecture and protocol design the precedence on the Internet lends hope to a much bigger scale and more dynamic and distributed control architecture The physics of electricity cuts through all power system functionalities and operation q nonconvexity of power flow q dynamics cannot be designed

50 Fundamental Challenges Convexification of power flow q for fast computation for real-time optimization q for distributed algorithm Distributed decomposition under dynamics constraints q for distributed real-time control with global perspective q exploit or implemented as power system dynamics Integrating sensing, communication, and control q fundamental limits on control performance arising form sensing constraints and communication constraints q communication/networking for distributed control Architecture and layering q mathematical underpinning of smart grid architecture q systematic methods to develop/evaluate design choices 50

51 Fundamental Challenges Convexification of power flow q convex relaxation Distributed decomposition under dynamics constraints q reverse and forward engineering q network dynamics as optimization algorithms Integrating sensing, communication, and control q fundamental limits on control performance arising form sensing constraints and communication constraints q communication/networking for distributed control Architecture and layering q mathematical underpinning of smart grid architecture q systematic methods to develop/evaluate design choices 51

52 Convexification of OPF Optimal power flow (OPF) problem q a fundamental problem underlying power system controls and operations q huge literature since first formulated in 1962, focusing on approximate algorithms and solutions Convexity critical to the development of efficient, distributed, and robust algorithms q for real-time computation at scale q for distributed algorithms q for efficient market, as foundation for pricing schemes such as LMP q for global optimality, critical for new/enhanced application 52

53 Branch flow model bus voltage z ij real/reactive branch power flow and current Power flow constraints V i V j = z ij I ij S ij = V i I ij * ( p, q ) j j real/reactive bus power flow Kirchhoff law power definition ( 2 S ij z ij I ) ij S jk i j j k = s j power balance 53

54 Optimal power flow z ij OPF: max i (0, j) over x: = ( P, Q, I, V, p, q) ( p, q ) 2 Ui( pi) C P0 j ri, j Ii, j social welfare s. t. x PFC( x) ( v, p, q ) OC( x) i i i power flow constraints j j operation constraints, e.g., in safe range 54

55 Convexity structure z ij OPF: max Ui pi C P0 j ri, j Ii, j i (0, j) over x: = ( P, Q, I, V, p, q) s. t. x PFC( x) 2 ( ) ( v, p, q ) OC( x) i i i ( p, q ) j j Convex? 55

56 Convexity structure z ij OPF: max Ui pi C P0 j ri, j Ii, j i (0, j) over x: = ( P, Q, I, V, p, q) s. t. x PFC( x) 2 ( ) ( v, p, q ) OC( x) i i i nonconvex ( p, q ) j j Convex? A 56

57 Convexity relaxation z ij OPF: max Ui pi C P0 j ri, j Ii, j i (0, j) over x: = ( P, Q, I, V, p, q) s. t. x PFC( x) 2 ( ) ( v, p, q ) OC( x) i i i A SOCP relaxa.on ( p, q ) j j ROPF: " % max U i ( p i ) C $ P 0 j ' r I i, j i, j 2 i #(0, j) & over x := (P,Q, I,V, p,q) s. t. x RPFC(x) (v i, p i,q i ) OC(x) A 57

58 Exact relaxation Theorem (Li-Chen-Low 12a): Convex relaxation is exact provided that for any i, and for any link (k,l) in the network and (i,j) on the path from 0 to k, q if only load buses, relaxation is always exact relaxation is always exact for real systems where IEEE distribution test systems Southern California Edison circuits many decomposition approaches (thus distributed algorithms) apply (Li-Chen-Low 12b, 12c) 58

59 Convexification of OPF Exact convex relaxation q tremendous progress since Lavaei and Low 11; see survey Low 14 q effectiveness depends on graph properties of underlying physical and/or communication networks q not always possible, and conditions may violate operation constraints Convex approximation? q geometry of power flow and its dependence on operation constraints and graph properties q systematic approach to construct convex approximation, to trade off tractability and optimality 59

60 Distributed decomposition under dynamics constraints Power network is a physical system q cannot be re-set arbitrarily, but has to evolve from one state to another q algorithms must be consistent with system dynamics Reverse engineering q what can we learning from current system? q can we bridge existing local control with system-wide property? Forward engineering q engineer the model from reverse engineering to guide systematic design of new algorithms 60

61 Frequency control mechanical or renewable power P i M, P i R i P ij branch power flow frequency-sensitive load P i S + P i I j uncontrolled load 61

62 Frequency control P i M, P i R i P ij focus on primary control for insight P i S + P i I q Synchronous generator: j P i M = F i (ω i ) decreasing; e.g., F i (ω i ) = S i ω i q Renewable generator: deceasing P i R = H i (ω i ) q Frequency sensitive load: increasing; e.g., G i (ω i ) = D i ω i P i S = G i (ω i ) 62

63 Dynamics Synchronous generator bus: M i ω i = F i (ω i ) G i (ω i ) P i I Renewable generator bus: 0 = H i (ω i ) G i (ω i ) P I i P ij j:i~ j Load bus (no generator): 0 = G i (ω i )+ P i I + P ij Real branch power flow: P ij = b ij ( ω i ω ) j j:i~ j j:i~ j P ij system state ( ω(t), P(t) ) 63

64 Cost/disutility functions Control functions defines relations between equilibrium frequency and equilibrium generation and load synchronous generator: C i M (P i M ) = 0 P i M F 1 i (P)dP renewable generator: C i P (P i R ) = 0 P i M H 1 i (P)dP frequency sensitive load: C i S (P i S ) = 0 P i M G 1 i (P)dP The equivalence of control and decision problem P i M = arg min P C i M (P)+ Pω i depend only on the control function but is independent of how the feedback signal is updated 64

65 Reverse engineering Theorem (You-Chen 14a): Power system dynamics is a distributed primal-dual gradient algorithm to solve min C M i (P M i ) + C R i (P R i ) + C S i (P S i ) i N M s.t. P i S + P i I + P ij j P i S + P i I + P i S + P i I + P j ij P j ij i N R and the dual variables are frequencies and equal. i N = P i M, i N M = P i R, i N R = 0, i N L DC OPF problem network dynamics as optimization algorithms 65

66 Network dynamics as optimization algorithms q A new perspective to understand collective behavior arising from interaction between local controls q structural properties of the equilibrium point q efficiency and tradeoffs, etc Suggests a Lyapunov function for global stability or convergence analysis q important both theoretically and practically Suggests a principled way to systematically design new algorithms and control schemes 66

67 Forward engineering Suggests a principled way to systematically design new algorithms and control schemes q new design goals (e.g., frequency recovery, fairness, and economic efficiency) incorporated by engineering the global objective function and the constraints q new control schemes with different dynamical properties based on various optimization algorithms q insights from reverse engineering can guide particular way to engineer the model and derive the algorithm 67

68 Nominal frequency recovery Key observation: at equilibrium ω = 0 can be ensured if G i (ω) = 0 i N I M P i = P i i N i N M R + P i i N R Impose the above indirectly by imposing decoupling constraints P I i + Q j ij = P M i, i N M P I i + Q j ij = P R i, i N R P I i + Q ij = 0, i N L Q ij = Q ji j do not have the decoupling structure 68

69 Nominal frequency recovery A new optimization problem (You-Chen 14a): max C M i (P M i ) + C R i (P R i ) + C S i (P S i ) i N M s.t. P i S + P i I + P ij j P i S + P i I + P i S + P i I + P i I + P i I + P i I + Q j ij Q j ij Q j ij P j ij P j ij i N R i N = P i M, i N M = P i R, i N R = 0, i N L = P i M, i N M = P i R, i N R = 0, i N L all are physical variables Q is not physical 69

70 Nominal frequency recovery New control scheme (You-Chen 14a): P i M = F i (ω i ), i N M P i R = H i (ω i ), i N R P M i = F i (2ω i ν i ), i N M P R i = H i (ω i + µ i ), i N R ν i = (G i (ω i )+ (P ij Q ij )) / M i, i N M j µ i = ξ i (G i (ω i )+ (P ij Q ij )), i N R N L Q ij = ε ij (µ i µ j ) j distributed control 70

71 Economic dispatch Theorem (You-Chen 14a): Power system dynamics with the new control scheme solves economic dispatch problem min C M i (P M i ) + C R i (P R i ) + C S i (P S i ) i N M s.t. P i I + P ij j P i I + P i I + P j ij P j ij i N R = P i M, i N M = P i R, i N R = 0, i N L real-time frequency control recovering frequency and achieving economic efficiency at the same time different from current approach achieving these objectives at different timescales and with centralized control needed for future smart grid to cope with rapid/large fluctuations and manage a huge number of control points i N 71

72 Network dynamics as optimization algorithms q Natural system dynamics exploited for simplicity, scalability, and robustness q desired for distributed real-time control Lots of progress q automatic generation control (Li-Chen-Zhao-Low 14); local volt/var control (Farivar-Chen-Low 13); load side frequency control (Zhao et al 12, 14, Mallada et al 14); distributed frequency control in microgrids (Dorfler et al 14) More work needed q remove approximations q integrate frequency and voltage control q distributed decomposition of full-fledged AC OPF problem 72

73 Outline q Layering and constrained optimization q Network dynamics as optimization algorithms q Look into the future 73

74 Theory-based network design Architecture (principles and design methodologies) network design/control as distributed decomposition of optimization wireless networks network coding EE networks Smart grids 74

75 Theory-based network design network design/control as distributed decomposition of optimization The most important feature q not the specific algorithms proposed and analyzed q but that we can derive the layering structure and modularity of the various mechanisms the interfaces between these mechanisms the control/signaling information that must cross these interfaces to achieve a certain performance and robustness 75

76 Foundations for a theory of architecture Architecture (principles and design methodologies) network design/control as distributed decomposition of optimization and game A common analytical framework and language q handle and integrate computation, communication, control, and incentives q allow rigorous analysis and systematic design Two of the key components q explore architectural implication of complexities of network engineering q network compatible mechanism design 76

77 Approach Architecture (principles and design methodologies) future Internet EE data center smart grid must be both abstract and concrete must be both foundational and practical 77

78 Lower sub-architecture design A clean slate for the technology infrastructure q content (re)placement, content discovery, cache selection q multipath multicast routing q congestion control q inter-scope/domain issues Apply theory-based approach q how to layer various components (optimization) q inter-scope/domain design (game) information-centric networks social technical Zegura, Wroclawski, et al,

79 Energy-efficient data center A new branch of research with its own rich structures and unique challenges Aim to develop models and theories to guide the analysis and design of practical algorithms for energy efficient data centers q have taken initial step on some of these issues (Chen-Li-Low 10, Chen-Li 13, Chen-Andrew-Wierman 14) 3-5% of total US energy use 79

80 4-5& 6$0+$&!"#$%&'("$%&!..%/,0(1.0& C 1 C!.2230,-(1.0& 2 P 1 )*"+,-+& P 2 4-5& 6$0+$& Smart grid Nonconvexity of power flows q convex relaxation q convex approximation Network dynamics as optimization algorithms q reverse and forward engineering q distributed decomposition of full fledged AC OFP Integrating sensing, communication, control q fundamental limits on control performance under sensing and communication constraints (You-Chen 14b, Shihadeh-You-Chen 14) q communication/networking for distributed control )*"+,-('&'("$%& 80

81 4-5& 6$0+$&!"#$%&'("$%&!..%/,0(1.0& C 1 C!.2230,-(1.0& 2 4-5& 6$0+$& Smart grid Architecture and layering q mathematical underpinning of smart grid architecture q systematic methods to develop and evaluate design choices and algorithms q overarching framework to reason about architectural questions design goals: to allow distributed management, to support different types of energy services, to allow plug-n-play microgrids, design principles: layering, division of functionality, placement of intelligence, P 1 )*"+,-+& P 2 )*"+,-('&'("$%& 81

82 Acknowledgements Advisors and students: John Doyle and Steven Low; Tao Cui, Na Li, Seungil You, Chenyu Zheng, and Xinyang Zhou Collaborators: Lachlan Andrew, Tim Brown, Mung Chiang, Tracey Ho, Eugene Liu, Doug Sicker, and Adam Wierman Thank you! 82