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Energy arbitrage with micro-storage

Energy arbitrage with micro-storage. Antonio De Paola Supervisors: Dr. David Angeli / Prof. Goran Strbac Imperial College London. Introduction. Increasing penetration of renewable energy: - greater variability in availability of generation - reduced system inertia

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Energy arbitrage with micro-storage

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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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