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Enhancing Energy Arbitrage with Micro-Storage Solutions

This presentation by Antonio De Paola at Imperial College London explores the concept of energy arbitrage utilizing domestic micro-storage devices. As renewable energy sources proliferate, the need for effective management of electric networks grows, particularly with increased load from electric vehicles and heat pumps. The study models energy charging and discharging behaviors using differential game theory and coupled partial differential equations (PDEs). The findings suggest optimized strategies for energy management, improving both user profits and overall system efficiency while addressing peak demand challenges.

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Enhancing Energy Arbitrage with Micro-Storage Solutions

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

  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

  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

  4. Modelling SINGLE DEVICE: DEMAND:Original profile D0 Charge of the device Rate of charge Storage modifies demand: • The stored energy and the rate of charge are limited: To model efficiency, quadratic losses are introduced: PRICE:Monotonic increasing function of demand UKACC PhD Presentation Showcase

  5. Coupled PDEs TRANSPORT EQUATION: evolution in time of distribution m of devices • Distribution of devices • Transport equation • HJB equation HJB EQUATION: returns cost-to-go function V and optimal control u* • Optimal charge profile The coupled PDEs are solved numerically until converge to a fixed point • The two equations are interdependent • They must be integrated in different directions UKACC PhD Presentation Showcase

  6. Energy arbitrage • LATEST DEVELOPMENTS: • Multiple populations of devices, each of them with different parameters • Consider uncertainties, for example on wind generation. • Arbitrage + reserve services: devices can be asked to provide reserve in the 24h interval and are penalized if they are unable to do so • Multi-area systems: take into account transmission constraints between connected systems SIMULATIONS: • - Typical UK demand profile- Total storage capacity: 25GWh- Each device can fully charge/discharge in 10 hours UKACC PhD Presentation Showcase

  7. Future work • SO FAR: equations are solved iteratively until convergence • Theoretic analysis on the existence of a fixed point • - Schauderfixed point theorem - existence of solution for MFG • NUMERICAL METHODS: • - Numerical methods specifically tailored for MFG- Planning problem: explicitly set a desired final charge for all devices • In the resolution of the MFG, the equations are considered separately:- HJB equation: upwind method- Transport equation: Friedrich-Lax method UKACC PhD Presentation Showcase

  8. THANK YOU UKACC PhD Presentation Showcase

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