BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Large wind farms: Output and maximising Value from trading with th e power system - Prof. S Howell\, Manchester Business School\, University of Manchester DTSTART:20100310T160000Z DTEND:20100310T170000Z UID:TALK23279@talks.cam.ac.uk CONTACT:Dr A. Zabala DESCRIPTION:About the speaker:\n\nProf Sydney Howell read English at Cambr idge and gained industrial experience with Alcan\, Ranks Hovis McDougall a nd Philips Electronic Components before completing his PhD at MBS on forec asting for inventory control. He joined MBS to teach Management Accounting and Control\, including applied multivariate statistics. He spent a two y ear secondment to IBM's school of International Finance\, Planning and Adm inistration 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 consult ancy projects\, respectively in the first and second years\, and presently restricts his degree course teaching (other than PhD supervision and exam ination) to the direction of both these parts of the MBA. For MBS's execut ive and corporate teaching he has been closely involved in designing\, neg otiating and/or delivering multi-million pound ventures with Arthur Anders en\, IBM\, Tesco and BP. He has also worked with Banking\, Insurance and L egal companies. Two of his practitioner books have been translated\, respe ctively into into Italian and Chinese. In recent years he has been drawn i nto energy research\, chiefly the modelling of wind and other renewables\, using the mathematics of finance as a fast way to model the dynamics of p hysical storage systems. For this work he collaborates with the School of Mathematics\, and with engineers at Imperial College and BP Alternative En ergy.\n\nAbout the seminar:\n\nOptimal electric heating or cooling\, for a building which is intermittently occupied\, has not previously been solve d in continuous time. Outside temperature has both stochastic and determin istic dynamics (e.g. Geometric Brownian Motion\, mean-reverting towards th e current point of a daily temperature cycle)\; the space’s inside tempe rature changes continuously\, in response to the outside temperature and i ts own deterministic thermal dynamics\, and to forcing by its heating or c ooling system. Electricity prices change on a daily cycle\, often in steps . The minimum problem-space dimensions are three: outside temperature\, in side temperature and time of day\, and we find it is necessary to model th ese at more than 106 state points. Using tools derived from financial math ematics we unite the system’s physical and economic dynamics within a si ngle partial differential equation\, which can be solved numerically (in s econds 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 prob lem space\, conditional on using the prescribed control action at every st ate point. An optimal control policy therefore optimizes the control actio n at every state point\, and it resembles an economically-weighted Hamilto nian surface\, here in four dimensions. In financial language\, the optima l 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 itse lf\, without explicitly calculating the required means and variances of th e system’s physical behaviors (all of their physics is present within th e PDE\, and under optimization the means and variances of the physical par ameters vary across the problem space). Given the optimal policy\, it is p ossible in seconds to recover any desired physical and/or economic statist ical moments\, across any chosen region of the problem space. This include s the expected time to first exit from a region\, the total expected time spent outside the region etc.\nThis approach can model many stochastic/det erministic systems in which one state variable is the integral of another (partly) stochastic variable (e.g. when a stock of fluid\, heat or money i s fed and/or depleted at a stochastic flow rate\; or when the cumulative r otation speed of a high-inertia generator is subject to stochastic acceler ations by a control system). Integration relationships can be defined succ essively between several variables in the PDE\, so as to model systems wit h arbitrarily high order linear dynamics. Any level of integrated variable can be either heavily constrained or discontinuous in its behavior over t he problem space (e.g. constraints on rates of inflow and outflow). Applic ations seem numerous in engineering\, economics and finance. Examples in e nergy (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. LOCATION:Mill Lane Lecture Rooms\, Room 1 END:VEVENT END:VCALENDAR