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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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Energy arbitrage with micro storage

Energy arbitrage with micro-storage

Antonio De Paola

Supervisors: Dr. David Angeli / Prof. Goran Strbac

Imperial College London

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  • 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

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Energy arbitrage

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

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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

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Coupled pdes

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

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Energy arbitrage1

Energy arbitrage


  • 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


  • - Typical UK demand profile- Total storage capacity: 25GWh- Each device can fully charge/discharge in 10 hours

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Future work

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 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

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Thank you


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