University of Cambridge > Talks.cam > Land Economy Seminar Series > Large wind farms: Output and maximising Value from trading with the power system

Large wind farms: Output and maximising Value from trading with the power system

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About the speaker:

Prof Sydney Howell read English at Cambridge and gained industrial experience with Alcan, Ranks Hovis McDougall and Philips Electronic Components before completing his PhD at MBS on forecasting for inventory control. He joined MBS to teach Management Accounting and Control, including applied multivariate statistics. He spent a two year secondment to IBM ’s school of International Finance, Planning and Administration in Brussels in the 1980s, and has continued to teach for IBM at intervals since, in a total of 12 countries. At MBS in recent years he has developed the MBA design to include two compulsory in-company consultancy projects, respectively in the first and second years, and presently restricts his degree course teaching (other than PhD supervision and examination) to the direction of both these parts of the MBA . For MBS ’s executive and corporate teaching he has been closely involved in designing, negotiating and/or delivering multi-million pound ventures with Arthur Andersen, IBM , Tesco and BP. He has also worked with Banking, Insurance and Legal companies. Two of his practitioner books have been translated, respectively into into Italian and Chinese. In recent years he has been drawn into energy research, chiefly the modelling of wind and other renewables, using the mathematics of finance as a fast way to model the dynamics of physical storage systems. For this work he collaborates with the School of Mathematics, and with engineers at Imperial College and BP Alternative Energy.

About the seminar:

Optimal electric heating or cooling, for a building which is intermittently occupied, has not previously been solved in continuous time. Outside temperature has both stochastic and deterministic dynamics (e.g. Geometric Brownian Motion, mean-reverting towards the current point of a daily temperature cycle); the space’s inside temperature changes continuously, in response to the outside temperature and its own deterministic thermal dynamics, and to forcing by its heating or cooling system. Electricity prices change on a daily cycle, often in steps. The minimum problem-space dimensions are three: outside temperature, inside temperature and time of day, and we find it is necessary to model these at more than 106 state points. Using tools derived from financial mathematics we unite the system’s physical and economic dynamics within a single partial differential equation, which can be solved numerically (in seconds on a PC) for any prescribed control policy. The PDE solution gives the expected net present value of all future costs (the sum of electricity costs and discomfort costs) from any and every starting point in the problem space, conditional on using the prescribed control action at every state point. An optimal control policy therefore optimizes the control action at every state point, and it resembles an economically-weighted Hamiltonian surface, here in four dimensions. In financial language, the optimal hyper-surface solves the Hamilton-Jacobi Bellman equation. We have found a rapid numerical solution method (in minutes on a PC) which is robust to step discontinuities in electricity price, in user occupation and in the optimal control policy itself (which for this problem has a “bang-bang” form). Our solution finds the economically optimal control policy itself, without explicitly calculating the required means and variances of the system’s physical behaviors (all of their physics is present within the PDE , and under optimization the means and variances of the physical parameters vary across the problem space). Given the optimal policy, it is possible in seconds to recover any desired physical and/or economic statistical moments, across any chosen region of the problem space. This includes the expected time to first exit from a region, the total expected time spent outside the region etc. This approach can model many stochastic/deterministic systems in which one state variable is the integral of another (partly) stochastic variable (e.g. when a stock of fluid, heat or money is fed and/or depleted at a stochastic flow rate; or when the cumulative rotation speed of a high-inertia generator is subject to stochastic accelerations by a control system). Integration relationships can be defined successively between several variables in the PDE , so as to model systems with arbitrarily high order linear dynamics. Any level of integrated variable can be either heavily constrained or discontinuous in its behavior over the problem space (e.g. constraints on rates of inflow and outflow). Applications seem numerous in engineering, economics and finance. Examples in energy (alone) include the optimal use, trading and storage of wind power, the optimal heating and cooling of large thermal electricity generators, and the valuation of production-sharing agreements between oil companies and their host governments.

This talk is part of the Land Economy Seminar Series series.

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