Two time scales stochastic dynamic optimization Managing energy storage investment, aging and operation in microgrids P. Carpentier, J.-Ph. Chancelier, M. De Lara and T. Rigaut EFFICACITY CERMICS, ENPC UMA, ENSTA LISIS, IFSTTAR August 29, 2017 Two time scales SDP August 29, 2017 1 / 39
Optimization for microgrids with storage Microgrids control architecture is often constituted of multiple levels handling multiple time scales Energy storage management requires to deal with uncertainty and information dynamic We use two time scales stochastic dynamic optimization to model two control levels and their interaction Two time scales SDP August 29, 2017 2 / 39
Outline Introduction: Electrical storage management in microgrids 1 Storage control in a microgrid Hierarchical control architecture of microgrids Modeling: Managing intraday arbitrage, aging and renewal 2 Two time scales management: investment/arbitrage Intraday arbitrage problem statement Long term aging/investment problem statement Two time scales stochastic optimization problem Solving: Decomposition method and numerical results 3 Decomposition method Numerical results Two time scales SDP August 29, 2017 3 / 39
Outline Introduction: Electrical storage management in microgrids 1 Storage control in a microgrid Hierarchical control architecture of microgrids Modeling: Managing intraday arbitrage, aging and renewal 2 Two time scales management: investment/arbitrage Intraday arbitrage problem statement Long term aging/investment problem statement Two time scales stochastic optimization problem Solving: Decomposition method and numerical results 3 Decomposition method Numerical results Two time scales SDP August 29, 2017 3 / 39
Storage control in a microgrid Two time scales SDP August 29, 2017 3 / 39
Why storage in a microgrid? Ensure supply demand balance without wastes or curtailment: Two time scales SDP August 29, 2017 4 / 39
Why storage in a microgrid? Energy tariff arbitrage and ancillary services Two time scales SDP August 29, 2017 5 / 39
Why stochastic dynamic optimization? Price of electricity might be Demand and production are uncertain uncertain Two time scales SDP August 29, 2017 6 / 39
Subway station microgrid example S ⊖ ⊕ D B E s E l Two time scales SDP August 29, 2017 7 / 39
Hierarchical control architecture of microgrids Two time scales SDP August 29, 2017 7 / 39
A way to deal with multiple time scales To handle multiple time scales Multiple control levels Tertiary level ∆ T Tertiary . . . ∆ T 2∆ T 1 min Target Info Info Secondary ∆ t 2∆ t ∆ t ∆ t ∆ t ∆ T . . . 2∆ T Primary 1 s 1 s 1 s Secondary level Two time scales SDP August 29, 2017 8 / 39
Small time scale: voltage stability of the grid Objective: voltage stability of the grid Time step: 1s Horizon: 1 min Input from superior level: storage input/output energy target every minute Output: effective command for storage every second Two time scales SDP August 29, 2017 9 / 39
Medium time scale: intraday energy tariff arbitrage Objective: energy intraday arbitrage Time step: 1 min Horizon: 24h Input from superior level: storage aging target everyday Output to inferior level: storage input/output energy target every minute Two time scales SDP August 29, 2017 10 / 39
Large time scale: long term aging and investments strategy Objective: storage long term economic profitability Time step: 1 day Horizon: 10 years Output to inferior level: storage aging target every day SAFT intensium max technical sheet Two time scales SDP August 29, 2017 11 / 39
Structure of the talk We focus on medium and large levels interaction to optimize storage: Long term aging Intraday energy arbitrage SAFT intensium max technical sheet Two time scales SDP August 29, 2017 12 / 39
Outline Introduction: Electrical storage management in microgrids 1 Storage control in a microgrid Hierarchical control architecture of microgrids Modeling: Managing intraday arbitrage, aging and renewal 2 Two time scales management: investment/arbitrage Intraday arbitrage problem statement Long term aging/investment problem statement Two time scales stochastic optimization problem Solving: Decomposition method and numerical results 3 Decomposition method Numerical results Two time scales SDP August 29, 2017 12 / 39
Two time scales management: investment/arbitrage Two time scales SDP August 29, 2017 12 / 39
Two time scales Long term aging and renewal ∆ T ∆ T . . . ∆ T 2∆ T D ∆ T 0 24h 24h ∆ t 2∆ t M − 1 ∆ t ∆ t ∆ t . . . ∆ T 2∆ T 1 min 1 min 1 min Intraday arbitrage Two time scales SDP August 29, 2017 13 / 39
We make decisions every minutes m and every day d Day d , Minute m : How much energy U d , m do I charge or discharge from my current battery with capacity C d ? At the end of Day d should I buy a new battery with capacity R d ? U d , 0 U d , 1 U d , 2 U d , M − 1 R d ∆ t ∆ t ∆ t 0 . . . d , 0 d , 1 d , 2 d , N t − 1 d , N t d + 1 , 0 Two time scales SDP August 29, 2017 14 / 39
Uncertain events occur right after we made our decisions Day d , end of Minute m : we observe how much intermitent energy W d , m +1 we receive At the end of Day d we observe the batteries cost W d +1 on the market U d , 0 U d , 1 U d , 2 U d , M − 1 R d ∆ t ∆ t ∆ t 0 . . . d , 0 d , 1 d , 2 d , N t − 1 d + 1 , 0 d , N t W d , 1 W d , 2 W d , 3 W d , M W d +1 Two time scales SDP August 29, 2017 15 / 39
Decisions and uncertainty impact state variables Day d , end Minute m : decision U d , m and realization W d , m +1 change our battery state of charge S d , m to S d , m +1 and our battery state of health H d , m to H d , m +1 At the end of Day d decision R d change our battery capacity C d to C d +1 S d , 0 , H d , 0 S d , 1 , H d , 1 S d , 2 , H d , 2 S d , M − 1 , H d , M − 1 S d , M , H d , M U d , 0 U d , 1 U d , 2 U d , M − 1 C d +1 R d ∆ t ∆ t ∆ t 0 . . . d , 0 d , 1 d , 2 d , N t − 1 d , N t d + 1 , 0 W d , 1 W d , 2 W d , 3 W d , M W d +1 Two time scales SDP August 29, 2017 16 / 39
Intraday arbitrage problem statement Two time scales SDP August 29, 2017 16 / 39
Representation of the subway station problem S ⊖ ⊕ D B E s E l Station node Subways node D : Demand station B : Braking E s : From grid to station E l : From grid to battery ⊖ : Discharge battery ⊕ : Charge battery Two time scales SDP August 29, 2017 17 / 39
Battery state of charge dynamics For a given charge/discharge strategy U over a day d : S d , m +1 = S d , m − 1 U − + ρ c sat ( S d , m , U + d , m , B d , m +1 ) d , m ρ d � �� � � �� � ⊖ ⊕ with sat ( x , u , b ) = min( S max − x , max( u , b )) ρ c . . . d , 0 d , M − 1 1 min 1 min Two time scales SDP August 29, 2017 18 / 39
Battery aging dynamics For a given charge/discharge strategy U over a day d H d , m +1 = H d , m − 1 d , m − ρ c sat ( S d , m , U + U − d , m , B d , m +1 ) ρ d . . . d , 0 d , M 1 min 1 min Two time scales SDP August 29, 2017 19 / 39
Every minute we save energy and money If we have a battery on day d and minute m we save: � � p e E s d , m +1 + E l d , m +1 − D d , m +1 d , m � �� � Saved energy p e d , m is the cost of electricity on day d at minute m Two time scales SDP August 29, 2017 20 / 39
Summary of short term/Fast variables model We call, at day d and minute m , � S d , m � fast state variables: X f d , m = H d , m � � U − fast decision variables: U f d , m d , m = U + d , m � B d , m � fast random variables: W f d , m = D d , m fast cost function: L f d , m ( X f d , m , U f d , m , W f d , m +1 ) fast dynamics: X f d , m +1 = F f d , m ( X f d , m , U f d , m , W f d , m +1 ) Two time scales SDP August 29, 2017 21 / 39
Long term aging/investment problem statement Two time scales SDP August 29, 2017 21 / 39
We decide our battery purchases at the end of each day . . . ∆ T 2∆ T N T 0 24h 24h Should we replace our battery C d by buying a new one R d or not? � R d , if R d > 0 C d +1 = f ( C d , H d , M ), otherwise paying renewal cost P b d R d at uncertain market prices P b d Two time scales SDP August 29, 2017 22 / 39
Summary of long term/Slow variables model We call, at day d , slow state variables: X s d = ( C d ) slow decision variables: U s d = ( R d ) slow random variables: W s d = ( P b d ) slow cost function: L s d ( X s d , U s d , W s d +1 ) = P b d R d slow dynamics: X s d +1 = F s d ( X s d , U s d , W s d +1 ) Two time scales SDP August 29, 2017 23 / 39
A link between days The initial ”fast state” at the begining of day d deduces from: X f d , 0 = φ d ( X s d , X f d − 1 , M ) The initial ”slow state” at the begining of day d + 1 deduces from all that happened the previous day: X s d +1 = F s d ( X s d , U s d , W s d +1 , X f d , 0 , U f d , : , W f d , : ) X f d , 0 , X s X f d +1 , 0 , X s X f X f X f X f 0 d , 1 d , 2 d , M − 1 d +1 d , M U f U f U f U f U s U f d , 0 d , 1 d , 2 d , M − 1 d d +1 , 0 ∆ t ∆ t ∆ t 0 . . . d , 0 d , 1 d , 2 d , N t − 1 d , N t d + 1 , 0 W f W f W f W f W s d , 1 d , 2 d , 3 d , M d +1 Two time scales SDP August 29, 2017 24 / 39
We formulate a two time scales stochastic optimization problem Two time scales SDP August 29, 2017 24 / 39
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