1. Energy arbitrage with micro-storage UKACC PhD Presentation Showcase Antonio De Paola Supervisors: Dr. David Angeli / Prof. Goran Strbac Imperial College London

2. 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

3. 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

4. UKACC PhD Presentation Showcase Slide 4 Modelling SINGLE DEVICE: Charge of the device Rate of charge  The stored energy and the rate of charge are limited: To model efficiency, quadratic losses are introduced: DEMAND: Original profile D 0 PRICE: Monotonic increasing function of demand Storage modifies demand:

5. 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 Optimal charge profile 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

6. 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

7. 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

8. THANK YOU UKACC PhD Presentation Showcase Slide 8