Challenges of renewable power generation Virtual energy storage from flexible loads Workshop EDF Lab’ gestion centralis´ ee/d´ ecentralis´ ee des syst` emes ´ electriques September 16, 2016 Ana Buˇ si´ c Dyogene team, Inria & DI ENS In collaboration with Prabir Barooah, Yue Chen, Jordan Ehren, Joel Mathias, Sean Meyn University of Florida
Challenges Challenges of Renewables: ducks & ramps 27 March 8th 2014: Impact of wind Load and Net-load 25 and solar on net-load at CAISO 23 GW 21 19 $/MWh 17 1200 Price spike due to high net-load ramping 15 Toal Load Net-load: Toal Load, less Wind and Solar 1000 need when solar production ramped out Wind and Solar 4 GW 800 2 Negative prices due to high 0 600 Peak ramp Peak 24 hrs mid-day solar production Toal Wind Toal Solar 400 200 0 Ramp limitations cause price-spikes -200 Peak ramp Peak 24 hrs
Challenges Challenges of Renewables: ducks & ramps 27 March 8th 2014: Impact of wind Load and Net-load 25 and solar on net-load at CAISO 23 GW 21 19 $/MWh 17 1200 Price spike due to high net-load ramping 15 Toal Load Net-load: Toal Load, less Wind and Solar 1000 need when solar production ramped out Wind and Solar 4 GW 800 2 Negative prices due to high 0 600 Peak ramp Peak 24 hrs mid-day solar production Toal Wind Toal Solar 400 200 0 Ramp limitations cause price-spikes -200 Peak ramp Peak 24 hrs
Challenges Challenges of Renewables: ducks & ramps 27 March 8th 2014: Impact of wind Load and Net-load 25 and solar on net-load at CAISO 23 GW 21 19 $/MWh 17 1200 Price spike due to high net-load ramping 15 Toal Load Net-load: Toal Load, less Wind and Solar 1000 need when solar production ramped out Wind and Solar 4 GW 800 2 Negative prices due to high 0 600 Peak ramp Peak 24 hrs mid-day solar production Toal Wind Toal Solar 400 200 0 Ramp limitations cause price-spikes -200 Peak ramp Peak 24 hrs 4 G W ( t ) = Wind generation in BPA, Jan 2015 3 GW 2 Ramps 1 0 Jan 01 Jan 02 Jan 03 Jan 04 Jan 05 Jan 06
Challenges Challenges: regulation Lack of large-scale storage with fast charging/discharging rates
Challenges Comparison: Flight control How do we fly a plane through a storm? Brains Brawn
Challenges Comparison: Flight control How do we fly a plane through a storm? What Good Are These? Brains Brawn
Challenges Comparison: Flight control How do we operate the grid in a storm? Balancing Authority Ancillary Services Grid Σ Measurements: − Voltage Frequency Phase Brains Brawn What Good Are These?
Demand Dispatch Demand Dispatch Frequency Decomposition Demand Dispatch: Power consumption from loads varies automatically and continuously to provide service to the grid , without impacting QoS to the consumer One Day at CAISO 2020 Approach: Frequency decomposition 25 Net Load Curve Each class of flexible loads allocated to its own bandwidth of service , based on 20 Low pass QoS constraints and costs 15 GW Gas Turbine BP Coal Batteries BP 10 Water Pump Control Power Grid Σ BP The duck is a sum of a smooth energy signal, C LOAD H Voltage − BP Frequency and two zero-energy services BP C Phase A 5 Actuator feedback loop Mid pass 0 High pass Today: PJM regulation signal: -5 R = RegA + RegD 12am 3am 6am 9am 12pm 3pm 6pm 9pm 12am
Demand Dispatch Demand Dispatch Responsive Regulation and desired QoS – A partial list of the needs of the grid operator, and the consumer High quality Ancillary Service? Customer QoS constraints satisfied? Cost effective? Includes installation cost, communication cost, maintenance, and environmental. Reliable? Will AS be available each day? (may vary with time, but capacity must be predictable) Is the incentive to the consumer reliable? If a consumer receives a $50 payment for one month, and only $1 the next, will there be an explanation that is clear to the consumer?
Demand Dispatch Control Goals and Architecture Local Control: decision rules designed to respect needs of load and grid Power deviation Local decision Grid signal U i Y i ζ t Local t t Load i Control X i t Local feedback loop Min. communication: each load monitors its state and a regulation signal from the grid. Aggregate must be controllable: randomized policies for finite-state loads. Questions • How to analyze aggregate of similar loads? • Local control design?
Mean Field Model Load Model Controlled Markovian Dynamics & Mean Field Model of the Aggregate Load 1 Power Consumption (MW) BA Load 2 + Reference (MW) ζ G c r ... Load N Discrete time: i th load X i ( t ) evolves on finite state space X Each load is subject to common controlled Markovian dynamics. Signal ζ = { ζ t } is broadcast to all loads Controlled transition matrix { P ζ : ζ ∈ R } : t +1 = x ′ | X i P { X i t = x, ζ t = ζ } = P ζ ( x, x ′ ) Mean-field analysis for the aggregate of loads (R. Malhame et. al. 1984 –)
Mean Field Model Example: pool pumps How Pools Can Help Regulate The Grid 1,5KW 400V Needs of a single pool ⊲ Filtration system circulates and cleans: Average pool pump uses 1.3kW and runs 6-12 hours per day, 7 days per week ⊲ Pool owners are oblivious, until they see frogs and algae ⊲ Pool owners do not trust anyone: Privacy is a big concern Single pool dynamics: 1 2 I − 1 I On . . . Off . . . I − 1 I 2 1
Mean Field Model Pools in Florida Supply G 2 – BPA regulation signal ∗ Stochastic simulation using N = 10 6 pools 300 Reference Output deviation (MW) 200 100 0 −100 −200 −300 0 0 20 20 40 40 60 60 80 80 100 100 120 120 140 140 160 160 t/hour t = � t PI control: ζ t = 19 e t + 1 . 4 e I e t = r t − y t and e I t , k =0 e k Each pool pump turns on/off with probability depending on 1) its internal state, and 2) the BPA reg signal ∗ transmission.bpa.gov/Business/Operations/Wind/reserves.aspx
Local Control Design
Local Control Design Local Design Goal: Construct a family of transition matrices { P ζ : ζ ∈ R } Individual Perspective Design Local welfare function: W ζ ( x, P ) = ζ U ( x ) − D ( P � P 0 ) , � P ( x,x ′ ) where D denotes relative entropy: D ( P � P 0 ) = � x ′ P ( x, x ′ ) log � . P 0 ( x,x ′ )
Local Control Design Local Design Goal: Construct a family of transition matrices { P ζ : ζ ∈ R } Individual Perspective Design Local welfare function: W ζ ( x, P ) = ζ U ( x ) − D ( P � P 0 ) , � P ( x,x ′ ) where D denotes relative entropy: D ( P � P 0 ) = � x ′ P ( x, x ′ ) log � . P 0 ( x,x ′ ) � T 1 Markov Decision Process: lim sup T →∞ t =1 E [ W ζ ( X t , P )] T Local control is a solution of AROE: � � � max W ζ ( x, P ) + P ( x, x ′ ) h ∗ ζ ( x ′ ) = h ∗ ζ ( x ) + η ∗ ζ P x ′
Local Control Design Local Design Goal: Construct a family of transition matrices { P ζ : ζ ∈ R } Individual Perspective Design Local welfare function: W ζ ( x, P ) = ζ U ( x ) − D ( P � P 0 ) , � P ( x,x ′ ) where D denotes relative entropy: D ( P � P 0 ) = � x ′ P ( x, x ′ ) log � . P 0 ( x,x ′ ) � T 1 Markov Decision Process: lim sup T →∞ t =1 E [ W ζ ( X t , P )] T Local control is a solution of AROE: � � � max W ζ ( x, P ) + P ( x, x ′ ) h ∗ ζ ( x ′ ) = h ∗ ζ ( x ) + η ∗ ζ P x ′ Explicit construction via eigenvector problem: P ζ ( x, y ) = 1 v ( y ) ˆ P ζ ( x, y ) , x, y ∈ X , λ v ( x ) ˆ ˆ where P ζ v = λv, P ζ ( x, y ) = exp( ζ U ( x )) P 0 ( x, y ) Extension/reinterpretation of [Todorov 2007] + [Kontoyiannis & Meyn 200X]
Local Control Design Local Design Goal: Construct a family of transition matrices { P ζ : ζ ∈ R } Myopic Design (one step optimization) P ζ ( x, x ′ ) := P 0 ( x, x ′ ) exp � ζ U ( x ′ ) − Λ ζ ( x ) � �� �� � with Λ ζ ( x ) := log x ′ P 0 ( x, x ′ ) exp ζ U ( x ′ ) the normalizing constant.
Local Control Design Local Design Goal: Construct a family of transition matrices { P ζ : ζ ∈ R } Myopic Design (one step optimization) P ζ ( x, x ′ ) := P 0 ( x, x ′ ) exp � ζ U ( x ′ ) − Λ ζ ( x ) � �� �� � with Λ ζ ( x ) := log x ′ P 0 ( x, x ′ ) exp ζ U ( x ′ ) the normalizing constant. System Perspective Design Linearized aggregate model is passive: � ∞ t =0 u t y t +1 ≥ 0 , ∀{ u t } .
Local Control Design Tracking performance and the controlled dynamics for an individual load Heterogeneous setting: 40 000 loads per experiment; 20 different load types in each case Air Conditioners Fast Electric Water Heaters Slow Electric Water Heaters 6 6 15 4 4 10 Power (MW) 2 5 2 0 0 0 -5 -2 -2 -10 -4 -15 -4 -6 BPA balancing reserves (filtered/scaled) Mean-field Model Stochastic Output 1 m t 0 6 hrs 24 hrs 24 hrs Nominal Demand Dispatch
Local Control Design Unmodeled dynamics Setting: 0 . 1 % sampling, and Heterogeneous population of loads 1 Load i overrides when QoS is out of bounds 2 Output deviation Reference N = 30,000 N = 300,000 10 100 5 50 MW 0 0 −5 −50 0.5 opt out % 0.5 −10 −100 0 0 100 110 120 130 100 110 120 130 t/hour t/hour Closed-loop tracking
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