Exploring Complex Energy Networks Florian D¨ orfler

@ETH for “Complex Systems Control” compute actuate throttle sense speed 1 / 22

@ETH for “Complex Systems Control” system control “Simple” control systems are well understood. “Complexity” can enter in many ways . . . 1 / 22

A “complex” distributed decision making system . . . physical interaction local subsystems and control sensing & comm. 2 10 30 25 8 37 29 9 38 23 7 36 22 6 35 19 4 33 20 5 34 10 3 32 6 2 31 1 8 7 5 4 3 18 17 26 27 28 24 21 16 15 14 13 12 11 1 39 9 local system local control local system local control Such distributed systems include large-scale physical systems, engineered multi-agent systems, & their interconnection in cyber-physical systems. 2 / 22

Timely applications of distributed systems control often the centralized perspective is simply not appropriate ience imaging — e.g., multispacecraft distributed interferometers ying in formation to enable imaging at microarcsecond resolution Sandia National Labs MBARI AOSN NASA Terrestrial Planet Finder J. Cort´ es MAE247 – Spring 2013 robotic networks decision making social networks science imaging — e.g., multispacecraft distributed interferom flying in formation to enable imaging at microarcsecond reso Sandia National Labs MBARI AOSN NASA Terrestrial Planet Find J. Cort´ es MAE247 – Spring 2013 sensor networks self-organization Transportation networks: users that own part of local decisions about the flow circulating over a porti Social networks: social agents and/or groups make on local consensus or trends Man-machine networks: humans make use of rem machines while interacting over networks Pervasive computing Ground traffic networks The Internet “S pervasive computing Transportation networks: users that own part of th local decisions about the flow circulating over a portion Social networks: social agents and/or groups make d on local consensus or trends Man-machine networks: humans make use of remot machines while interacting over networks Pervasive computing Ground traffic networks The Internet “Sma traffic networks smart power grids 3 / 22

My main application of interest – the power grid NASA Goddard Space Flight Center Electric energy is critical for our technological civilization Energy supply via power grid Complexities: multiple scales, nonlinear, & non-local 4 / 22

Paradigm shifts in the operation of power networks Traditional top to bottom operation: generate/transmit/distribute power hierarchical control & operation Smart & green power to the people: distributed generation & deregulation demand response & load control 5 / 22

Challenges & opportunities in tomorrow’s power grid www.offthegridnews.com 1 increasing renewables & deregulation 2 growing demand & operation at capacity ⇒ increasing volatility & complexity, decreasing robustness margins Rapid technological and scientific advances: 1 re-instrumentation: sensors & actuators 2 complex & cyber-physical systems ⇒ cyber-coordination layer for smarter grids 6 / 22

Outline Introduction Complex network dynamics Synchronization Voltage collapse Distributed decision making Microgrids Wide-area control Conclusions

Modeling: a power grid is a circuit 1 AC circuit with harmonic waveforms Ei cos(θi + ωt) 2 active and reactive power flows 3 loads demanding constant active and reactive power 4 synchronous generators & power electronic inverters 5 coupling via Kirchhoff & Ohm Gij + i Bij i j Pi + i Qi i mech. torque electr. torque injection = power flows active power: Pi = j Bij Ei Ej sin(θi − θj ) + Gij Ei Ej cos(θi − θj ) reactive power: Qi = − j Bij Ei Ej cos(θi − θj ) + Gij Ei Ej sin(θi − θj ) 7 / 22

complex network dynamics: synchronization

Synchronization in power networks sync is crucial for AC power grids – a coupled oscillator analogy sync is a trade-off ✓i (t) weak coupling & heterogeneous ✓i (t) strong coupling & homogeneous 8 / 22

Synchronization in power networks sync is crucial for AC power grids – a coupled oscillator analogy sync is a trade-off ✓i (t) weak coupling & heterogeneous Blackout India July 30/31 2012 8 / 22

Our research: quantitative sync tests in complex networks Sync cond’: (ntwk coupling) ∩ (transfer capacity) > (heterogeneity) ˙ θ(t) θ(t) 220 309 310 120 103 209 102 102 118 307 302 216 202 + 0.1% load sync cond’ violated . . . Reliability Test System 96 two loading conditions 9 / 22

Our research: quantitative sync tests in complex networks Sync cond’: (ntwk coupling) ∩ (transfer capacity) > (heterogeneity) ˙ θ(t) θ(t) 220 309 310 120 103 209 102 102 118 307 302 216 202 ˙ θ(t) θ(t) + 0.1% load Reliability Test System 96 two loading conditions Ongoing work & next steps: analysis: sharper results for more detailed models analysis to design: hybrid control & remedial actions 9 / 22

complex network dynamics: voltage collapse

Voltage collapse in power networks reactive power instability: loading > capacity ⇒ voltages drop recent outages: Qu´ ebec ’96, Northeast ’03, Scandinavia ’03, Athens ’04 “Voltage collapse is still the biggest single threat to the transmission sys- tem. It’s what keeps me awake at night.” – Phil Harris, CEO PJM. 10 / 22

Voltage collapse on the back of an envelope reactive power balance at load: voltage Esource Eload B Qload (fixed) (variable) Eload Esource 0 Qload * * * * reactive power Qload = B Eload ( Eload Esource ) ∃ high load voltage solution ⇔ (load) < (network)(source voltage)2/4 11 / 22

Our research: extending this intuition to complex networks IEEE 39 bus system (New England) Ongoing work & next steps: existence & collapse cond’: (load) < (network)(source voltage)2/4 analysis to design: reactive compensation & renewable integration 12 / 22

distributed decision making: plug’n’play control in microgrids

Microgrids Structure low-voltage distribution networks grid-connected or islanded autonomously managed Applications hospitals, military, campuses, large vehicles, & isolated communities Benefits naturally distributed for renewables flexible, efficient, & reliable Operational challenges volatile dynamics & low inertia plug’n’play & no central authority 13 / 22

Conventional control architecture from bulk power ntwks 3. Tertiary control (offline) Goal: optimize operation Strategy: centralized & forecast 2. Secondary control (slower) Goal: maintain operating point Strategy: centralized 1. Primary control (fast) Goal: stabilization & load sharing Strategy: decentralized Microgrids: distributed, model-free, online & without time-scale separation ⇒ break vertical & horizontal hierarchy 14 / 22

Plug’n’play architecture flat hierarchy, distributed, no time-scale separations, & model-free Microgrid … … … … … … source # 1 source # 2 source # n Secondary Primary Tertiary Secondary Primary Tertiary Secondary Primary Tertiary 15 / 22

Plug’n’play architecture flat hierarchy, distributed, no time-scale separations, & model-free Microgrid: physics & power flow Di ˙ θi =P∗ i − Pi − Ωi ki ˙ Ωi =Di ˙ θi − j ⊆ inverters aij · Ωi Di − Ωj Dj Di ∝ 1/αi τi ˙ Ei =−Ci Ei (Ei − E∗ i ) − Qi − ei κi ˙ ei =− j ⊆ inverters aij · Qi Qi − Qj Qj −εei Primary control: mimic oscillators Tertiary control: marginal costs ∝ gains Secondary control: diffusive averaging of injections Ωi /Di Qi Ei ˙ θi Pi Qi /Qi Qi /Qi . . . . . . Ωi /Di . . . . . . Ωk /Dk Qk /Qk Qj /Qj Ωj /Dj Pi = j Bij Ei Ej sin(θi − θj ) + Gij Ei Ej cos(θi − θj ) Qi = − j Bij Ei Ej cos(θi − θj ) + Gij Ei Ej sin(θi − θj ) source # i 15 / 22

Experimental validation of control & opt. algorithms in collaboration with microgrid research program @ University of Aalborg DC Source LCL filter DC Source LCL filter DC Source LCL filter 4 DG DC Source LCL filter 1 DG 2 DG 3 DG Load 1 Load 2 12 Z 23 Z 34 Z 1 Z 2 Z 0 10 20 30 40 50 300 305 310 315 320 325 330 Voltage Magnitudes Time (s) Voltage (V) 0 10 20 30 40 50 100 150 200 250 300 350 400 450 500 Reactive Power Injections Time (s) Power (VAR) 0 10 20 30 40 50 49.5 49.6 49.7 49.8 49.9 50 50.1 Voltage Frequency Time (s) Frequency (Hz) 0 10 20 30 40 50 200 400 600 800 1000 1200 A ctive Power Injection Time (s) Power (W) t = 22s: load # 2 unplugged t = 36s: load # 2 plugged back t ∈ [0s, 7s]: primary & tertiary control t = 7s: secondary control activated 16 / 22

Experimental validation of control & opt. algorithms in collaboration with microgrid research program @ University of Aalborg DC Source LCL filter DC Source LCL filter DC Source LCL filter 4 DG DC Source LCL filter 1 DG 2 DG 3 DG Load 1 Load 2 12 Z 23 Z 34 Z 1 Z 2 Z 0 10 20 30 40 50 300 305 310 315 320 325 330 Voltage Magnitudes Time (s) Voltage (V) 0 10 20 30 40 50 100 150 200 250 300 350 400 450 500 Reactive Power Injections Time (s) Power (VAR) 0 10 20 30 40 50 49.5 49.6 49.7 49.8 49.9 50 50.1 Voltage Frequency Time (s) Frequency (Hz) 0 10 20 30 40 50 200 400 600 800 1000 1200 A ctive Power Injection Time (s) Power (W) t = 22s: load # 2 unplugged t = 36s: load # 2 plugged back t ∈ [0s, 7s]: primary & tertiary control t = 7s: secondary control activated Ongoing work & next steps: time-domain modeling & control design integrate market/load dynamics & control 16 / 22

distributed decision making: wide-area control

Inter-area oscillations in power networks Blackout of August 10, 1996, resulted from instability of the 0.25 Hz mode 10 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 South Arizona SoCal NoCal PacNW Canada North Montana Utah Source: http://certs.lbl.gov 0.25 Hz 17 / 22

Remedies against inter-area oscillations conventional control Physical layer: interconnected generators Fully decentralized control: effective against local oscillations ineffective against inter-area oscillations 18 / 22

Remedies against inter-area oscillations wide-area control Physical layer Fully decentralized control Distributed wide-area control identification of architecture? sparse control design? optimality? 18 / 22

Trade-off: control performance vs sparsity of architecture K(γ) = arg min K J(K) + γ · card(K) optimal control = closed-loop performance + γ · sparse architecture performance 19 / 22

Case Study: IEEE 39 New England Power Grid single wide-area control link =⇒ nearly centralized performance 15 5 12 11 10 7 8 9 4 3 1 2 17 18 14 16 19 20 21 24 26 27 28 31 32 34 33 36 38 39 22 35 6 13 30 37 25 29 23 1 10 8 2 3 6 9 4 7 5 F Fig. 9. The New England test system [10], [11]. The system includes 10 synchronous generators and 39 buses. Most of the buses have constant active and reactive power loads. Coupled swing dynamics of 10 generators are studied in the case that a line-to-ground fault occurs at point F near bus 16. 0 -5 0 5 10 15 δ i / rad 0 -5 0 5 10 15 δ i / rad Fig. 10. Couple The fault duration by numerical inte !"#$%&'''%()(*%(+,-.,*%/012-3*%)0-4%5677*%899: 1 10 Ongoing work & next steps: cyber-physical security: corruption of wide-area signals data-driven & learning: what if we don’t have a model? 20 / 22

wrapping up

Summary & conclusions Complex systems control distributed, networks, & cyber-physical Apps in power networks complex network dynamics distributed decision making Surprisingly related apps coordination of multi-robot networks learning & agreement in social networks and many others . . . . . . physical interaction local subsystems and control sensing & comm. 2 10 30 25 8 37 29 9 38 23 7 36 22 6 35 19 4 33 20 5 34 10 3 32 6 2 31 1 8 7 5 4 3 18 17 26 27 28 24 21 16 15 14 13 12 11 1 39 9 local system local control local system local control 21 / 22

Acknowledgements Synchronization John Simpson-Porco Misha Chertkov Francesco Bullo Enrique Mallada Changhong Zhao Matthias Rungger Voltage dynamics Marco Todescato Basilio Gentile Sandro Zampieri Wide-area control Diego Romeres Mihailo Jovanovic Xiaofan Wu Microgrids Quobad Shafiee Josep Guerrero Sairaj Dhople Abdullah Hamadeh Brian Johnson Jinxin Zhao Hedi Boattour Robotic coordination Bruce Francis Cyber-physical security Fabio Pasqualetti Port-Hamiltonian Frank Allg¨ ower Jorgen Johnsen Social networks Mihaela van der Schaar Yuanzhang Xiao . . . Group @ ETH Bala Kameshwar Poolla plus some students on other prof’s payrolls . . . more people to join . . . 22 / 22

thank you