Dynamic Ancillary Services & Virtual Power Plant Control 3rd Champéry Power Conference, 2024 Verena Häberle & Florian Dörfler

Acknowledgements Xiuqiang He (ETH Zurich) Linbin Huang (ETH Zurich) Eduardo Prieto (UPC Barcelona) Further: M. W. Fisher, A. Tayyebi, J. Björk, K.H. Johansson, & POSYTYF Partners 1/21

Dynamic ancillary services provided by Dynamic Virtual Power Plant (DVPP) Dynamic ancillary services • specified as desired dynamic behavior / responses • ever faster responses for weaker (low-inertia) grids • location of service provision & grid perception matter DVPP: coordinate a heterogeneous ensemble of DERs to collectively provide dynamic ancillary services • sufficiently heterogeneous collection of DERs – reliably provide services consistently across all power & energy levels & all time scales – none of the DERs itself is able to do so • coordination aspect – disaggregation of DVPP specifications – decentralized control implementation |∆p| t tfcr a |∆pfcr| tfcr i 8 4 1 hydro BESS su cap 8 9 3 6 4 1 hydro BESS super- capacitor SG 3 (thermal-based) DVPP 1 ⇡ 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 2/21

Problem abstraction in a simple setting • DVPP setup (simplified) consisting of – DERs connected at a common bus – PMU frequency measurement at PCC broadcasted to all DERs • ancillary service = aggregate DVPP specification: – desired grid-following fast frequency response power = H s + D = Tdes(s) · frequency • task: coordinated model matching – design decentralized DER controls so that DVPP behavior matches the aggregate specification i power i ! = H s + D · PMU-frequency – while taking device-level constraints into account broadcast + aggregate DER 1 …. DER n output signal + comm input signal (PMU frequency signal at PCC) (active power injection at PCC) DVPP ⇡ 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 desired aggregate behavior 3/21

Nordic case study aggregated 5-bus Nordic model • desired ancillary service: FCR-D power frequency = 3100 · (6.5s + 1) (2s + 1)(17s + 1) • well-known issue: actuation of hydro via governor is non-minimum phase → initial power surge opposes control → highly unsatisfactory response • discussed solution: augment hydro with batteries for fast response → works but not very economic • better DVPP solution: coordinate hydro & wind to cover all time scales remainder of the talk: how to do it ? Björk, Johansson, & Dörfler (2022). Dynamic virtual power plant design for fast frequency reserves: Coordinating hydro and wind. IEEE Transactions on Control of Network Systems. 4/21

Outline transmission grid DER 1 DER 2 DER n DVPP PCC transmission grid Tdes(s) ≈ PCC Part I: DVPP control • disaggregation of desired ancillary service • decentralized device-level model matching control • case study, experiments, & sketch of extensions Part II: grid codes & optimal services • grid codes & translation into desired I/O behavior • perceive local grid model via system identification • optimize DER response subject to grid-code flexibility 5/21

Decentralized DVPP control setup • global broadcast signal ∆f ∆v • global aggregated power output ∆pagg ∆qagg = i ∆pi ∆qi • DERs with controllable closed-loop behaviors Ti(s) • overall/global/aggregate DVPP behavior ∆pagg(s) ∆qagg(s) = i Ti(s) ∆f(s) ∆v(s) • desired DVPP specification ∆pdes(s) ∆qdes(s) = Tfp des (s) 0 0 Tvq des (s) Tdes(s) ∆f(s) ∆v(s) → aggregation condition: i Ti(s) = Tdes(s) DVPP: collection of heterogeneous DERs grid-follow. DER n grid-follow. DER 1 . . . ∆f ∆v ∆pagg ∆qagg ∆p1 ∆q1 ∆pn ∆qn plant 1 control 1 T1(s) plant n control n Tn(s) ≈ Tdes(s) ∆pdes ∆qdes ∆f ∆v Task: Find local controllers such that the aggregation condition & the local DER constraints are satisfied. 6/21

Divide & conquer strategy 1) Disaggregation & pooling desired behavior of unit i ... ... Disaggregate Tdes(s) into local desired behaviors via dynamic participation factors (DPFs) Tdes(s) Mi(s) = mfp i (s) 0 0 mvq i (s) Mi(s) · Tdes(s) such that i Ti(s) = Tdes(s) = i Mi(s) · Tdes(s) participation condition i Mi(s) = I2 2) Local matching control plant i matching control i ≈ desired behavior i Mi(s) · Tdes(s) For each unit i, design local matching control to match desired behavior i Ti(s) Ti(s) = Mi(s) · Tdes(s) Häberle, V., Fisher, M., Prieto, E. & Dörfler, F. (2021). Control design of dynamic virtual power plants: an adaptive divide-&-conquer approach. IEEE Transactions on Power Systems . 7/21

Dynamic participation factor (DPF) selection Define DPFs mfp i (s) and mvq i (s) of the DVPP units as transfer functions, among others characterized by • a time constant τi for the roll-off frequency • a DC gain mi(0) = µi to account for power capacity limitations → divide DVPP units into three categories, i.e., we envision low-pass filter participation units that can provide regulation on longer time scales including steady-state contributions mi(s) = µi τis+1 frequency amplitude high-pass filter participation units that can provide regulation on very short time scales (fast response capability) mi(s) = τis τis+1 frequency amplitude band-pass filter participation units able to cover the intermediate regime mi(s) = (τi−τj )s (τis+1)(τj s+1) frequency amplitude 8/21

Local matching control Control objective: for each DVPP unit, find local matching controllers such that the local closed-loop behavior matches the local desired specification Ti(s) = Mi(s) · Tdes(s) General setup for matching control of unit i • incorporate local desired behavior Mi(s) · Tdes(s) as reference model into conventional converter control architecture • different matching control implementations, e.g., classical PI-based control, robust & optimal H∞ methods, etc. ˙ x = Ax + Bu + ˆ Bw y = Cx + Du + ˆ Dw Ti(s) K(s) plant i matching control controller local reference model w = ∆f ∆v y = ∆pi ∆qi Mi(s) · Tdes(s) Goal: minimize local matching error! 9/21

Case study Nonlinear & detailed simulation model 2 7 8 9 3 5 6 4 1 SG 2 SG 3 SG 1 wind PV STATCOM DVPP DVPP specification: frequency & voltage control ∆pdes(s) ∆qdes(s) = Dp+Ms τps+1 0 0 Dq τqs+1 = Tdes(s) ∆f(s) ∆v(s) Participation factor selection 10-1 100 101 10-2 100 102 10-2 10-1 100 10-2 100 102 wind pv statcom sum wind pv statcom sum mfp i (s) mvq i (s) System response during load increase at bus 6 -0.1 -0.05 0 -4 -2 0 2 4 -0.05 0 0.05 -2 0 2 4 6 active power deviation (MW) reactive power deviation (Mvar) voltage deviation (pu) frequency deviation (Hz) 5 25 5 25 wind pv statcom sum wind pv statcom wind pv statcom sum wind pv statcom 10/21

Experimental validation: Multi-converter PHIL testbed SG resisitve load unit grid acquisition module MC220 CPU FC 1 ASM SG PLC FC 2 FC 3 main power supply ASM PCC pconv p pconv s p pconv w fref grid pv statcom wind 49.8 50 50.2 0.45 0.5 0.55 0.26 0.28 0.3 0.32 0.34 -0.05 0 0.05 0 5 10 15 20 25 30 0.18 0.2 0.22 wind desired desired desired statcom pv sum desired with DVPP without DVPP • DVPP (wind, PV, STATCOM) for frequency regulation • DVPP response during a ± 1kW load jump • response characteristics according to selected DPFs Andrejewski, M., Häberle, V., Goldschmidt, N., Dörfler, F. & Schulte, H. (2023). Experimental validation of a dynamic virtual power plant control concept based on multi-converter power hardware-in-the-loop test bench, 22nd Wind and Solar Integration Workshop . 11/21

DVPP extensions coupled Tdes(s) Tdes(s) = Tfp des (s) Tvp des (s) Tfq des (s) Tvq des (s) noncontrollable units 4 1 hydro BESS super- capacitor DVPP 10-2 100 102 10-3 10-2 10-1 100 101 grid-forming DVPP ∆fdes(s) ∆vdes(s) = Tdes(s) ∆p ∆q adaptive DPF active power before cloud during cloud spatially distributed POC 1 POC r remaining power system DVPP area ≈ Tdes(s) DVPP POC 1 POC r remaining power system DVPP area others • complex-frequency DVPP • DC DVPP • ... Häberle, V., Fisher, M., Prieto, E. & Dörfler, F. (2021). Control design of dynamic virtual power plants: an adaptive divide-&-conquer approach. IEEE Transactions on Power Systems. Häberle, V., Tayyebi, A., He, X., Prieto, E. & Dörfler, F. (2023). Grid-forming & spatially distributed control design of dynamic virtual power plants. IEEE Transactions on Smart Grid. Domingo-Enrich, R., Häberle, V., He, X., Prieto-Araujo, E. & Dörfler, F. (2023). Complex frequency control of dynamic virtual power plants. Master Thesis. 12/21

Outline transmission grid DER 1 DER 2 DER n DVPP PCC transmission grid Tdes(s) ≈ PCC Part I: DVPP control • disaggregation of desired ancillary service • decentralized device-level model matching control • case study, experiments, & sketch of extensions Part II: grid codes & optimal services • grid codes & translation into desired I/O behavior • perceive local grid model via system identification • optimize DER response subject to grid-code flexibility 13/21

From grid codes to feasible transfer functions • translate piece-wise linear time-domain grid code curves into parametric transfer functions ∆p(s) ∆q(s) = Tfp des (s, αfp) 0 0 Tvq des (s, αvq) = Tdes(s,α) ∆f(s) ∆v(s) −→ parameters α need to satisfy grid code requirements & device-level constraints • superposition of different ancillary services Tfp des (s, αfp) = Tfcr des (s, αfcr) FCR + Tffr des (s, αffr) FFR + ... |∆p| t tfcr a |∆pfcr| tfcr i exact Tfcr des (s, αfcr) minimum grid code Example: FCR Capability Curve (EU 2016/631) • active power capability curve after frequency drop • parameterized by time constants αfcr := [tfcr i , tfcr a ] • grid code requirements on FCR capacity |∆pfcr| 0 ≤ tfcr i ≤ tfcr i,max & tfcr i ≤ tfcr a ≤ tfcr a,max • device-level ramping rate constraint |∆pfcr| ≤ tfcr a − tfcr i · rp max Goal: optimize response over α & grid perception Häberle, V., Huang, L., He, X., Prieto-Araujo, E., & Dörfler, F. (2023). Dynamic ancillary services: From grid codes to transfer function-based converter control. arXiv:2310.01552 . 14/21

Optimal dynamic ancillary services provision: Perceive & Optimize (P&O) reserve unit control PCC utility grid G(s) ≈ Tdes(s, α) “Perceive” unknown & local grid dynamics → identify grid dynamic equivalent G(s) ∆f(s) ∆v(s) = G11(s) G12(s) G21(s) G22(s) =:G(s) ∆p(s) ∆q(s) → takes into account local grid characteristics: sensitivity, short circuit & R/L ratios, etc. G(s) Tdes(s, α⋆) grid equivalent ancillary services specification input disturbance performance output to be minimized optimization problem α⋆ ∆p ∆q ∆f ∆v “Optimize” device response subject to constraints • ensure grid code & device-level requirements • stable closed-loop interconnection of grid equivalent G(s) & parametric service Tdes(s, α) → optimize for feasible α⋆ which results in best closed-loop & system-level performance Häberle, V., He, X, Huang, L, Prieto-Araujo, E. & Dörfler, F. (2024). Optimal dynamic ancillary services provision based on local power grid perception. arXiv:2401.17793. 15/21

Perceive: dynamic grid equivalent identification “Perceive” unknown & local grid dynamics → identify G(s) ∆f(s) ∆v(s) = G11(s) G12(s) G21(s) G22(s) =:G(s) ∆p(s) ∆q(s) Dynamic grid equivalent identification • inject uncorrelated wideband excitation signals in converter’s control loop • measure & collect f, v, p, q responses at PCC • apply parametric system identification techniques (e.g., PEM methods, subspace methods, etc.) to compute G(s) Practical power converter control setup vdc = ≈ power converter PI PI q⋆ p⋆ Lf Rf PLL & power computation grid equivalent identification p, q fpll, v vabc iabc modulation abc dq θpll θpll wideband excitation signal injection inner loop: current θpll i⋆ d i⋆ q G(s) grid PCC control iabc vabc + + − + Closed-loop identification problem G(s) controlled reserve unit excitation grid ∆p ∆q ∆f ∆v equivalent Häberle, V., Huang, L., He, X., Prieto-Araujo, E., Smith, R. S. & Dörfler, F. (2023). MIMO grid impedance identification of three-phase power systems: parametric vs. nonparametric approaches. IEEE Conference on Decision and Control. 16/21

Optimize: Closed-loop power grid optimization “Optimize” • closed-loop interconnection of G(s) and parametric Tdes(s, α) • optimize for α⋆ to get optimal & stable closed-loop performance G(s) Tdes(s, α⋆) grid equivalent ancillary services specification input disturbance performance output to be minimized optimization problem α⋆ ∆p ∆q ∆f ∆v parametric in α minimize α frequency deviation + RoCoF + voltage peak s.t. dynamics: identified grid equivalent ancillary services specification grid-code constraints device-level constraints Solution: smooth objective → compute explicit gradient + project on constraints + scalable first-order methods 17/21

Case studies 2-area Kundur system • two additional reserve units • detailed (nonlinear, EMT) models 1 7 6 11 3 9 8 2 SG 1 SG 4 SG 2 5 10 SG 3 4 13 reserve unit 1 12 reserve unit 2 Case studies to demonstrate the effectiveness of the P&O strategy: Cheap ancillary services: Tdes(α0, s) • encodes minimum open-loop grid-code requirements • cheap, but feasible dynamic ancillary services provision • indistinguishable for any grid location vs. Optimal ancillary services: Tdes(α⋆, s) • ensures optimal and stable closed-loop performance based on local grid perception • takes grid-codes & device-level limits into consideration • can accommodate time-varying grid conditions 18/21

Case study I • nominal grid conditions • apply P&O strategy for unit 1, keep unit 2 disconnected • initial situation: cheap ancillary services provision by reserve unit 1 1 6 2 SG 1 SG 2 5 reserve unit 1 G1(s) 12 ∆f(s) ∆v(s) = G11(s) G12(s) G21(s) G22(s) =:G(s) ∆p(s) ∆q(s) -80 -60 -40 -80 -60 -40 10 0 10 2 400 600 800 10 0 10 2 400 500 600 -30 -20 -10 0 -20 -10 0 10 0 10 2 0 200 400 10 0 10 2 300 350 400 reference identified 0 10 20 30 40 50 -0.25 -0.2 -0.15 -0.1 -0.05 0 0 10 20 30 40 50 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 2 2.1 2.2 2.3 2.4 2.5 -0.2 -0.15 -0.1 -0.05 0 2 2.1 2.2 2.3 2.4 2.5 -0.04 -0.02 0 cheap optimal cheap optimal System response during load increase at bus 7 12.6% improvement in RoCoF 11.6% improvement in frequency nadir 32.9% reduction in voltage peak -80 -60 -40 -80 -60 -40 10 0 10 2 400 600 800 10 0 10 2 400 500 600 -30 -20 -10 0 -20 -10 0 10 0 10 2 0 200 400 10 0 10 2 300 350 400 reference identified 19/21

Case study II • oscillatory grid with weakly-damped inter-area modes • sequentially apply P&O strategy for both units • initial situation: cheap ancillary services by both units 1 6 2 SG 1 SG 2 5 reserve unit 1 G1(s) 12 G2(s) 11 3 9 8 SG 4 10 SG 3 4 13 reserve unit 2 0 10 20 30 40 50 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0 10 20 30 40 50 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025 cheap 1 & cheap 2 optimal 1 & cheap 2 optimal 1 & optimal 2 cheap 1 & cheap 2 optimal 1 & cheap 2 optimal 1 & optimal 2 significant improvement of the closed-loop system behavior after first & second P&O cycle during a load increase at bus 7 -100 -50 0 -50 0 10 0 10 2 100 200 300 10 0 10 2 400 500 600 -40 -20 0 20 -20 -10 0 10 0 10 2 0 200 400 10 0 10 2 300 350 400 reference identified G1(s) inter-area mode 20/21

Conclusions Summary • Part I: DVPP control – disaggregation via dynamic participation factors – decentralized model matching control – case study, experiments & extensions • Part II: grid codes & optimal services – grid codes & translation into I/O behavior – perceive power grid via system identification – optimize DER response s.t. grid-code flexibility transmission grid DER 1 DER 2 DER n DVPP PCC transmission grid Tdes(s) ≈ PCC Future work • extension of P&O strategy to multi-agent scenarios: what if many DERs learn in parallel ? • development of next-generation grid codes: decentralized stability certificates, service criteria, ... link to related publications 21/21