Advanced grid-forming control for low-inertia systems Florian D¨ orfler ETH Z¨ urich Emerging Topics in Control of Power Systems
Acknowledgements ! ! ! ! Marcello Colombino Ali Tayyebi-Khameneh Dominic Groß Irina Subotic Further: T. Jouini, C. Arghir, A. Anta, B. Johnson, M. Sinha, & S. Dhople 1
Replacing the power system foundation fuel & synchronous machines renewables & power electronics – not sustainable + sustainable + central & dispatchable generation – distributed & variable generation + large rotational inertia as buffer – almost no energy storage + self-synchronize through the grid – no inherent self-synchronization + resilient voltage / frequency control – fragile voltage / frequency control – slow actuation & control + fast / flexible / modular control 2
Critically re-visit modeling / analysis / control Foundations and Challenges of Low-Inertia Systems (Invited Paper) David J. Hill ∗ and Gregor Verbiˇ Federico Milano Florian D¨ orfler and Gabriela Hug c ETH Z¨ University College Dublin, Ireland urich, Switzerland University of Sydney, Australia ∗ also University of Hong Kong email: federico.milano@ucd.ie emails: dorfler@ethz.ch, ghug@ethz.ch emails: dhill@eee.hku.hk, gregor.verbic@sydney.edu.au The later sections contain many suggestions for further New control methodologies, e.g. new controller to work, which can be summarized as follows: • mitigate the high rate of change of frequency in low New models are needed which balance the need to • inertia systems; include key features without burdening the model A power converter is a fully actuated, modular, and (whether for analytical or computational work) with • very fast control system, which are nearly antipodal uneven and excessive detail; characteristics to those of a synchronous machine. New stability theory which properly reflects the new • Thus, one should critically reflect the control of a devices and time-scales associated with CIG, new converter as a virtual synchronous machine; and loads and use of storage; The lack of inertia in a power system does not need to • Further computational work to achieve sensitivity • (and cannot) be fixed by simply “adding inertia back” guidelines including data-based approaches; in the systems. key unresolved challenge: resilient control of grid-forming power converters → industry & academia willing to explore green-field approach (see MIGRATE) 3
Outline Introduction: Low-Inertia Power Systems Problem Setup: Modeling and Specifications State of the Art Grid-Forming Control Comparison & Discussion
Modeling: synchronous generator i r 1. energy supply τ m from governor M L θ i s ω v g 2. mechanical ( θ, ω ) swing dynamics τ m of rotor (flywheel) with inertia M 3. i s stator flux dynamics (rotor/damper flux dynamics neglected) d θ d t = ω 4. electro-mechanical energy M d ω � − sin θ � ⊤ i s conversion through rotating magnetic d t = − Dω + τ m + L m i r cos θ field with inductance matrix d i s � − sin θ � L s d t = − R s i s + v g − L m i r ω L s 0 L m cos θ cos θ L θ = 0 L s L m sin θ L m cos θ L m sin θ L r 4
Modeling: voltage source converter 1. energy supply i dc from i dc i x upstream DC boost converter m αβ L f i f v dc v g 2. DC link dynamics v dc with capacitance C dc C dc v x 3. i f AC filter dynamics (sometimes also LC or LCL) 4. power electronics modulation d v dc = − G dc v dc + i dc + m ⊤ i f C dc d t i x = − m ⊤ i f and v x = m v dc , d i f L f d t = − R f i f + v g − m v dc with averaged & normalized duty cycle ratios m ∈ [ − 1 2 , 1 2 ] × [ − 1 2 , 1 2 ] 5
Comparison: conversion mechanisms M i r i dc L θ i s m ω v g L f τ m i f v dc v g C dc d θ d t = ω d v dc M d ω � − sin θ � ⊤ i s = − G dc v dc + i dc + m ⊤ i f d t = − Dω + τ m + L m i r C dc cos θ d t d i s d i f � − sin θ � L s d t = − R s i s + v g − L m i r ω L f d t = − R f i f + v g − m v dc cos θ controllable controllable energy AC power physical & robust energy energy storage system supply conversion vs. controlled & agile resilient τ m (slow) M (large) L θ (physical) signal / energy vs. vs. vs. vs. transformer fragile i dc (fast) C dc (small) m (control) 6 (over-currents)
Objectives for grid-forming converter control ( αβ frame) stationary control objectives ◮ voltage amplitude � v k � = v ⋆ k ◮ synchronous frequency ◮ active & reactive power injections � 0 � d − ω 0 dt v k = v k � 0 � v ⊤ k i f,k = p ⋆ k , v ⊤ − 1 i f,k = q ⋆ ω 0 0 k k +1 0 ω 0 unique ⇐ ⇒ relative voltage angles ω 0 conversion v k � cos( θ ⋆ � − sin( θ ⋆ jk ) jk ) θ ⋆ v k = v j jk sin( θ ⋆ cos( θ ⋆ v ⋆ v j jk ) jk ) k dynamic control objectives ◮ droop at perturbed operation: ω − ω 0 = k · ( p − p ⋆ ) with specified power/frequency sensitivity k = ∂p ∂ω droop (similar for � v � and q ) ◮ disturbance (fault) rejection: passively via physics (inertia) or via control ◮ grid-forming: intrinsic synchronization rather than tracking of exogenous ω 0 7
Naive baseline solution: emulation of virtual inertia !""" #$%&'%(#!)&' )& *)+"$ ','#"-'. /)01 23. &)1 2. -%, 2456 5676 !"#$%&'"'() %* +$,(-.'() /'-#%(-' !89:;8;<=><? />@=AB: !<;@=>B >< CD!EFGBH;I .( 0.1$%2$.3- 4-.(2 5.$)6,7 !('$)., +><I *JK;@ E;<;@B=>J< 8.".-9 :%(. ! "#$%&'# (&)*&+! ,--- ; :6$<,(,$,<,(, =%%77, ! (&)*&+! ,--- ; ,(3 06>67 ?@ ?9,(3%$>,$ ! (&)*&+! ,--- -JLB88BI@;MB DBNLB@> -J?LBIIB8 %@B<> ! "#$%&'# (&)*&+! ,--- . B<I "LBO D1 ":F'BBIB<P ! "&'./+ (&)*&+! ,--- !"#$%&'()*+,-+#'"(./#0*/1(2-33/*04($(5&*0-$1(( Virtual synchronous generators: A survey and new perspectives 6#+*0&$(7*/8&9+9(:"(!&;0*&:-0+9(<#+*="(20/*$=+( Hassan Bevrani a,b, ⇑ , Toshifumi Ise b , Yushi Miura b a Dept. of Electrical and Computer Eng., University of Kurdistan, PO Box 416, Sanandaj, Iran 0/(6;/1$0+9(7/>+*(2";0+%;(( b Dept. of Electrical, Electronic and Information Eng., Osaka University, Osaka, Japan !""" #$%&'%(#!)&' )& *)+"$ ','#"-'. /)01 23. &)1 2. -%, 2456 ?$-0@&+*(!+1&11+A( !"#$"%&'())) A(B*-#/()*$#C/&;A( *"+,-%'!"#$"%&'())) A($#9(?&11+;(D$1$*$#=+( !789:;< "=>?<:;@7 (@7:9@? ':9<:8AB C@9 !"#$%&#'$%()*+'",'"%-#,.%/#",012%3#*',#4% /'(DE/F( #9<7G=;GG;@7 'BG:8=G 5,)"16'% H;8I8; JK>. (<=LI8?? F1 M@@:K. N9<;7 *1 %O<=. %7O98P H1 $@GQ@8. <7O (K9;G N1 M9;AK: 7898:%+1*%;'<'*=''4> ? %@%58;8A8%$'%A11* ? @% !"#$%&'("()"&*'+,,, @%98%/1"'21 B %1*$%38%/#<<4.'" C @% !"#$%&'("()"&'+,,, % 8
Virtual synchronous machine ≡ flywheel emulation • reference model for converter voltage i dc m loop : detailed model of synchronous L f i f generator + controls (of order 3,...,12) v dc C dc → most commonly accepted solution in ? industry ( backward compatibility ?) • robust implementation needs tricks : M i r L θ i s low-pass filters for dissipation, virtual ω τ m impedances for saturation, limiters,... → performs well in small-signal regime but performs very poorly post-fault → poor fit : converter � = flywheel very different actuation & energy storage → over-parametrized & ignores limits controllable controllable energy AC power energy energy storage system supply conversion slow vs. fast large vs. small physics vs. control resilient vs. fragile 9
Droop as simplest reference model [Chandorkar, Divan, Adapa, ’93] ! ◮ frequency control by mimicking p − ω ω droop property of synchronous machine: ! * ω 0 ω − ω 0 ∝ p − p ⋆ ! sync ω sync ◮ voltage control via q − � v � droop control: dt � v � = − c 1 ( � v � − v ⋆ ) − c 2 ( q − q ⋆ ) P d P 1 P 2 p ( t ) − p ∗ • reference are generator controls → good small-signal but poor large signal behavior (rather → direct control of ( p, ω ) and ( q, � v � ) narrow region of attraction) assuming they are independent (approx. true only near steady state) → main reason for poor performance: two linear SISO loops for MIMO → requires tricks in implementation : nonlinear system (SISO & linear similar to virtual synchronous machine only near steady state) 10
Duality & matching of synchronous machines [Arghir & D¨ orfler,’19] M i r i dc L θ i s m ω L f v g i f v dc τ m v g C dc d θ d θ d t = ω d t = η · v dc M d ω � − sin θ d v dc � − sin θ � ⊤ i s � ⊤ i f d t = − Dω + τ m + L m i r C dc d t = − G dc v dc + i dc + m ampl cos θ cos θ d i s � − sin θ d i f � − sin θ � � L s d t = − R s i s + v g − L m i r ω L f d t = − R f i f + v g − m ampl v dc cos θ cos θ ( a ) ( b ) 10 ms/ div 1. modulation in polar coordinates: P ∗ P g 200 W/ div g � − sin θ � & ˙ 0 m = m ampl θ = m freq cos θ ω ref 2. matching : m freq = ηv dc with η = i s 1 ,a i s 2 ,a v dc,ref 2 A/ div theory & practice: robust duality ω ∼ v dc 11 → duality : C dc ∼ M is equivalent inertia
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