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An optimization-on-manifold approach to the design of distributed feedback control in smart grids Saverio Bolognani An optimization-on-manifold approach to the design of distributed feedback control in smart grids Saverio Bolognani Future electric power distribution grids An optimization-on-manifold approach to the design of distributed feedback control in smart grids FUTURE ELECTRIC POWER DISTRIBUTION GRIDS Saverio Bolognani, Florian Dörfler Automatic Control Laboratory ETH Zürich ECC 2016 Workshop Distributed and Stochastic Optimization: Theory and Applications An optimization-on-manifold approach to the design of distributed feedback control in smart grids Saverio Bolognani An optimization-on-manifold approach to the design of distributed feedback control in smart grids Saverio Bolognani Future electric power distribution grids Future electric power distribution grids Power distribution grids New challenges I Distributed microgenerators (conventional and renewable sources) Traditional Power I Electric mobility (large flexible demand, spatio-temporal patterns). Generation Installed renewable generation I Distribution grid: the Germany 2013 Germany 17 August 2014 24 GW solar “capillary system” of wind 41GW power networks wind 15 GW 75% I It delivers power from biomass hydro + biomass 6 GW the transmission grid hydro to the consumers. solar Transmission grid Distribution grid transmission I Very little sensing, grid Switzerland Energy consumption monitoring, actuation. VISION 2020 Electric Vehicle 800k by sector Fast charging (2010) Buildings I The “easy” part of the 73.9% 40.9% 600k grid: conventionally Industry 25.9% 4KW 120KW 400k BEV 31.3% fit-and-forget design. Domestic Tesla consumer supercharger distribution Transportation 200k grid 27.8% PHEV Primary fuel Electricity consumption consumption 2015 2020

An optimization-on-manifold approach to the design of distributed feedback control in smart grids Saverio Bolognani An optimization-on-manifold approach to the design of distributed feedback control in smart grids Saverio Bolognani Future electric power distribution grids Future electric power distribution grids Distribution grid congestion control control Transmission Grid Distribution Grid Curtailment Reduced hosting capacity x x x x control control Higher renewable generation Larger hosting capacity Transmission Grid distribution CONTROL Distribution Grid LAYER grid I Virtual grid reinforcement I same infrastructure Operation of the grid close or above the physical limits , due to uncontrolled I more sensors and intelligence overvoltage simultaneous and uncoordinated power demand/generation. controlled controlled I controlled grid = larger capacity undervoltage ! lower e � ciency, blackouts uncontrolled I Transparent control layer ! curtailment of renewable generation renewable generation power demand I invisible to the users ! bottleneck to electric mobility I modular design Fit-and-forget ! unsustainable grid reinforcement An optimization-on-manifold approach to the design of distributed feedback control in smart grids Saverio Bolognani An optimization-on-manifold approach to the design of distributed feedback control in smart grids Saverio Bolognani A feedback control approach OVERVIEW A FEEDBACK CONTROL APPROACH 1. A feedback control approach 2. A tractable model for control design 3. Control design example I Reactive power control for voltage regulation 4. Next step I Optimization on the power flow manifold 5. Conclusions

An optimization-on-manifold approach to the design of distributed feedback control in smart grids Saverio Bolognani An optimization-on-manifold approach to the design of distributed feedback control in smart grids Saverio Bolognani A feedback control approach A feedback control approach Distribution grid model Distribution grid model 0 0 supply point supply point voltage magnitude v h active power p h voltage magnitude v h active power p h voltage angle θ h h voltage angle θ h h microgenerator load microgenerator load reactive power q h reactive power q h Grid equations Actuation I Tap changer / voltage regulators – supply point voltage v 0 diag ( u ) Yu = s I Reactive power compensators – reactive power q h I static compensators where I power inverters of the microgenerators (when available) I u h = v h e j θ h complex voltages I Active power management – active power p h I s h = p h + jq h complex powers I smart building control, storage and deferrable loads I generator curtailment and load shedding An optimization-on-manifold approach to the design of distributed feedback control in smart grids Saverio Bolognani An optimization-on-manifold approach to the design of distributed feedback control in smart grids Saverio Bolognani A feedback control approach A feedback control approach Distribution grid model A control framework plant power generation power demands 0 Power distribution grid sensing network grid actuation supply point state x voltage magnitude v h active power p h voltage angle θ h h microgenerator load reactive power q h Control objective Drive the system to a state x ∗ = Sensing v ∗ ✓ ∗ p ∗ q ∗ ⇤ ⇥ subject to x ∗ = argmin x J ( x ) I soft constraints I Power meters – active power p h and reactive power q h x 2 X I hard constraints I Voltage meters – nodal voltage v h P [ x 62 X ] < ✏ I Phasor measurement units (PMU) – voltage magnitude v h and angle ✓ h I chance constraints (PQube @ UC Berkeley, GridBox in Zürich/Bern, Smart Grid Campus @ EPFL) I Line currents, transformer loading, ...

An optimization-on-manifold approach to the design of distributed feedback control in smart grids Saverio Bolognani An optimization-on-manifold approach to the design of distributed feedback control in smart grids Saverio Bolognani A feedback control approach A feedback control approach Feedforward control Feedback control plant plant power generation power generation disturbance power demands power demands Power distribution grid sensing Power distribution grid sensing network network grid actuation grid actuation output OPF state x state x input FEED BACK Conventional approach: Optimal Power Flow I Similar to power transmission grid OPF Control theory answer I Motivated by encouraging results on OPF convexification (Lavaei (2012), Farivar (2013), ...) I Robustness against parametric uncertainty / unmodeled disturbance I Requires full disturbance knowledge - full communication I Time varying demand/generation becomes disturbance I Heavily model based I Model-free design I Requires co-design of grid control and users’ behavior I Explored so far only for limited cases (e.g. purely local VAR control) I Allows modular design of grid control and users’ behavior An optimization-on-manifold approach to the design of distributed feedback control in smart grids Saverio Bolognani An optimization-on-manifold approach to the design of distributed feedback control in smart grids Saverio Bolognani A feedback control approach A tractable model for control design A similar scenario: frequency control plant disturbance power demands Power frequency network power generation output state x input A TRACTABLE MODEL FOR CONTROL DESIGN FEED BACK primary control secondary control In the transmission grid , feedback is used for frequency regulation I Frequency deviation as a implicit signal for power unbalance I Purely local proportional control: primary droop control I Integral control: secondary frequency regulation