Exploring Complex Energy Networks Florian D¨ orfler
@ETH for “Complex Systems Control” sense actuate speed throttle compute 1 / 22
@ETH for “Complex Systems Control” system c ontrol “Simple” control systems are well understood. “Complexity” can enter in many ways . . . 1 / 22
A “complex” distributed decision making system lo cal subsystems and control lo cal s y s tem lo cal c ontrol . . . lo cal s y s tem local control physical interaction 8 37 10 9 30 25 3 8 26 2 29 1 3 27 6 1 39 28 35 18 22 4 9 17 21 8 5 24 7 12 14 15 23 36 31 6 s ens ing & comm. 2 13 16 7 11 10 19 3 20 2 33 3 34 4 5 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 robotic networks decision making social networks sensor networks self-organization pervasive computing traffic networks smart power grids 3 / 22
My main application of interest – the power grid Electric energy is critical for our technological civilization Energy supply via power grid Complexities : multiple scales, nonlinear, & non-local NASA Goddard Space Flight Center 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 1 increasing renewables & deregulation 2 growing demand & operation at capacity ⇒ increasing volatility & complexity, decreasing robustness margins www.offthegridnews.com 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 E i cos( θ i + ω t ) i j G ij + i B ij 2 active and reactive power flows 3 loads demanding constant i active and reactive power P i + i Q i 4 synchronous generators mech. electr. torque torque & power electronic inverters 5 coupling via Kirchhoff & Ohm injection = � power flows ◮ active power: P i = � j B ij E i E j sin( θ i − θ j ) + G ij E i E j cos( θ i − θ j ) ◮ reactive power: Q i = − � j B ij E i E j cos( θ i − θ j ) + G ij E i E j sin( θ i − θ j ) 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 θ i ( t ) θ i ( t ) weak coupling & heterogeneous 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 θ 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 ) 202 209 220 216 θ ( t ) + 0.1% load 102 102 120 103 s y nc cond’ 309 vi olated . . . 118 310 302 307 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 ) 202 209 220 216 θ ( t ) + 0.1% load 102 102 ˙ 120 103 θ ( t ) Ongoing work & next steps: 309 118 ◮ analysis: sharper results for more detailed models 310 θ ( t ) 302 307 ◮ analysis to design: hybrid control & remedial actions Reliability Test System 96 two loading conditions 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: Q load = B E load ( E load − E source ) E source (fixed) reactive power B E load E source 0 voltage * * E load * Q load * (variable) Q load ∃ 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 Primary Primary Primary Tertiary Tertiary Tertiary … … … S e c ond ary S ec ond ary S e c ond ary … … … s ource # 1 s ource # 2 s ource # n 15 / 22
Plug’n’play architecture flat hierarchy, distributed, no time-scale separations, & model-free � Microgrid: � P i = j B ij E i E j sin( θ i − θ j ) + G ij E i E j cos( θ i − θ j ) physics � Q i = − j B ij E i E j cos( θ i − θ j ) + G ij E i E j sin( θ i − θ j ) & p ower flow ˙ P i Q i E i θ i � D i ˙ θ i = P ∗ i − P i − Ω i Primary control: m i m i c os c i ll ators τ i ˙ E i = − C i E i ( E i − E ∗ i ) − Q i − e i Tertiary control: � D i ∝ 1 /α i m arginal costs ∝ gains � Ω i /D i Ω i /D i � Ω i − Ω j � k i ˙ Ω i = D i ˙ � θ i − a ij · . . . D i D j . . . Secondary control: j ⊆ inverters Ω j /D j Ω k /D k d i ff u s i v e aver aging Q j / Q j � � Q i / Q i Q i − Q j � of injections κ i ˙ e i = − a ij · − εe i . . . Q i Q j . . . j ⊆ inverters Q k / Q k Q i / Q i s ource # i 15 / 22
Experimental validation of control & opt. algorithms in collaboration with microgrid research program @ University of Aalborg Voltage Magnitudes Reactive Power Injections 330 500 DG DG 1 4 450 DC Source LCL filter DC Source LCL filter 325 Power (VAR) Voltage (V) 400 320 350 315 300 Load 1 Load 2 Z Z 250 1 2 310 200 Z Z 12 305 34 150 300 100 0 10 20 30 40 50 0 10 20 30 40 50 Time (s) Time (s) DG DG 2 3 DC Source Voltage Frequency A ctive Power Injection DC Source LCL filter LCL filter 50.1 1200 Z 23 Frequency (Hz) 50 1000 Power (W) 49.9 800 49.8 600 49.7 400 49.6 49.5 200 0 10 20 30 40 50 0 10 20 30 40 50 Time (s) Time (s) t = 22 s : load # 2 t ∈ [0 s, 7 s ]: primary unplugged & tertiary control t = 36 s : load # 2 t = 7 s : secondary plugged back control activated 16 / 22
Experimental validation of control & opt. algorithms in collaboration with microgrid research program @ University of Aalborg Voltage Magnitudes Reactive Power Injections 330 500 DG DG 1 4 450 DC Source LCL filter DC Source LCL filter 325 Power (VAR) Voltage (V) 400 320 350 Load 1 315 300 Load 2 Z Z 250 1 2 310 200 Z Z 305 12 34 150 300 100 0 10 20 30 40 50 0 10 20 30 40 50 Time (s) Time (s) DG DG 2 3 Voltage Frequency A ctive Power Injection DC Source DC Source LCL filter LCL filter 50.1 1200 Ongoing work & next steps: Z 23 Frequency (Hz) 50 1000 Power (W) ◮ time-domain modeling & control design 49.9 800 49.8 600 ◮ integrate market/load dynamics & control 49.7 400 49.6 49.5 200 0 10 20 30 40 50 0 10 20 30 40 50 Time (s) Time (s) t ∈ [0 s, 7 s ]: primary t = 22 s : load # 2 unplugged & tertiary control t = 7 s : secondary t = 36 s : load # 2 plugged back control activated 16 / 22
distributed decision making: wide-area control
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