energy arbitrage with micro-storage ukacc phd presentation showcase antonio de paola supervisors:...
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Energy arbitrage with micro-storage
UKACC PhD Presentation Showcase
Antonio De Paola
Supervisors: Dr. David Angeli / Prof. Goran Strbac
Imperial College London
UKACC PhD Presentation Showcase Slide 2
Introduction
Increasing penetration of renewable energy:- greater variability in availability of generation- reduced system inertia
Growth of loads such as electric vehicles and heat pumps
Increasing participation of customers to system operations
The electric network is undergoing significant changes:
- Interactions between high numbers of agents- Traditional structure of the power system may not be adequate
- Increase in the amount of available data- Improved controllability of the system
UKACC PhD Presentation Showcase Slide 3
Energy arbitrage
Domestic micro-storage devices are considered: they charge/discharge energy from the network during a 24h interval trying to maximize profit
ADVANTAGES:- Profit for the users- Benefits for the system (reduction in peak demand)
MAIN PROBLEM: management of the devices (i.e: if they all charge at low prices → shifting of peak demand)
PROPOSED APPROACH:- model the problem as a differential game with infinite players- solve the resulting coupled PDEs and find a fixed point
UKACC PhD Presentation Showcase Slide 4
Modelling
SINGLE DEVICE:
)()( tutE
MAXEE 0 MAXMIN uuu
:E
:uCharge of the device
Rate of charge
The stored energy and the rate of charge are
limited:
To model efficiency,
quadratic losses
are introduced:
)()()( 2 tututy
DEMAND:
Original profile D0
PRICE:
Monotonic
increasing function
of demand
Storage modifies demand:
dEEtyEtmtD ),(),()(0
))(( tDp
UKACC PhD Presentation Showcase Slide 5
Coupled PDEs
TRANSPORT EQUATION: evolution in
time of distribution m of devices
HJB EQUATION: returns cost-to-go
function V and optimal control u*
Distribution of devices
),( Etm
Optimal charge profile
),(* Etu
HJB
equation
Transport
equation
The two equations are interdependent
They must be integrated in different directions
The coupled PDEs are
solved numerically
until converge to a
fixed point
UKACC PhD Presentation Showcase Slide 6
Energy arbitrage
SIMULATIONS:
- Typical UK demand profile
- Total storage capacity: 25GWh
- Each device can fully
charge/discharge in 10 hours
LATEST DEVELOPMENTS:
1. Multiple populations of devices, each
of them with different parameters
2. Consider uncertainties, for example
on wind generation.
3. Arbitrage + reserve services: devices
can be asked to provide reserve in the
24h interval and are penalized if they
are unable to do so
4. Multi-area systems: take into account
transmission constraints between
connected systems
UKACC PhD Presentation Showcase Slide 7
Future work
- Schauder fixed point theorem
- existence of solution for MFG
SO FAR:
equations are
solved iteratively
until convergence
NUMERICAL METHODS:
In the resolution of the MFG, the
equations are considered separately:
- HJB equation: upwind method
- Transport equation: Friedrich-Lax method
- Numerical methods
specifically tailored for MFG
- Planning problem: explicitly
set a desired final charge for
all devices
Theoretic analysis on the
existence of a fixed point
THANK YOU
UKACC PhD Presentation Showcase Slide 8