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Author Spotlight: Optimization of Airflow Velocities in Battery Cooling Systems for Enhanced Thermal Performance and Reduced Energy Consumption
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Partial differential equation methods for stochastic dynamic optimization: an application to wind power generation

Paul Johnson1, Sydney Howell2, Peter Duck3

  • 1School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK paul.johnson-2@manchester.ac.uk.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|October 21, 2017
PubMed
Summary

Optimizing wind power generation involves a partial differential equation (PDE) to balance earnings from wind power generators (WPG) and energy storage devices (ESD). This method maximizes profits by managing physical constraints and financial penalties.

Keywords:
arbitragebattery storagedynamic optimal controlinvestmentwind energy

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Area of Science:

  • Energy Systems Engineering
  • Financial Mathematics
  • Operations Research

Background:

  • Wind power generators (WPG) face stochastic output and market price volatility.
  • Energy storage devices (ESD) offer flexibility but have physical limitations (capacity, charge/discharge rates, efficiency).
  • Electricity markets impose financial penalties for deviations from committed energy delivery rates.

Purpose of the Study:

  • To develop a mixed financial/physical partial differential equation (PDE) model.
  • To optimize the joint earnings of a WPG and an ESD.
  • To jointly optimize the design and operating rules for WPG-ESD systems in a finite market.

Main Methods:

  • Formulation of a partial differential equation (PDE) incorporating physical constraints (capacity, efficiency, charge/discharge rates) and financial factors (spot price, system balancing penalties).
  • Modeling of stochastic processes for WPG output and electricity spot prices (mean-reverting cycles with daily and evening peak patterns).
  • Optimization of expected net present value (NPV) considering arbitrage opportunities and system balancing penalties.

Main Results:

  • The PDE model successfully optimizes joint earnings for a WPG and ESD.
  • The model accounts for crucial physical limitations and financial risks.
  • Joint optimization of design and operational strategies for WPG-ESD systems is demonstrated as feasible.

Conclusions:

  • A mixed financial/physical PDE framework provides a robust method for optimizing WPG-ESD systems.
  • Effective management of physical constraints and financial penalties is key to maximizing profitability.
  • The study highlights the potential for integrated design and operational optimization in energy management.