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CATEGORIES:Land Economy Seminar Series
SUMMARY:Large wind farms: Output and maximising Value from
trading with the power system - Prof. S Howell\,
Manchester Business School\, University of Manches
ter
DTSTART;TZID=Europe/London:20100310T160000
DTEND;TZID=Europe/London:20100310T170000
UID:TALK23279AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/23279
DESCRIPTION:About the speaker:\n\nProf Sydney Howell read Engl
ish at Cambridge and gained industrial experience
with Alcan\, Ranks Hovis McDougall and Philips Ele
ctronic Components before completing his PhD at MB
S on forecasting for inventory control. He joined
MBS to teach Management Accounting and Control\, i
ncluding applied multivariate statistics. He spent
a two year secondment to IBM's school of Internat
ional Finance\, Planning and Administration in Bru
ssels in the 1980s\, and has continued to teach fo
r IBM at intervals since\, in a total of 12 countr
ies. At MBS in recent years he has developed the M
BA design to include two compulsory in-company con
sultancy projects\, respectively in the first and
second years\, and presently restricts his degree
course teaching (other than PhD supervision and ex
amination) to the direction of both these parts of
the MBA. For MBS's executive and corporate teachi
ng he has been closely involved in designing\, neg
otiating and/or delivering multi-million pound ven
tures with Arthur Andersen\, IBM\, Tesco and BP. H
e has also worked with Banking\, Insurance and Leg
al companies. Two of his practitioner books have b
een translated\, respectively into into Italian an
d Chinese. In recent years he has been drawn into
energy research\, chiefly the modelling of wind an
d other renewables\, using the mathematics of fina
nce as a fast way to model the dynamics of physica
l storage systems. For this work he collaborates w
ith the School of Mathematics\, and with engineers
at Imperial College and BP Alternative Energy.\n\
nAbout the seminar:\n\nOptimal electric heating or
cooling\, for a building which is intermittently
occupied\, has not previously been solved in conti
nuous time. Outside temperature has both stochasti
c and deterministic dynamics (e.g. Geometric Brown
ian Motion\, mean-reverting towards the current po
int of a daily temperature cycle)\; the space’s in
side temperature changes continuously\, in respons
e to the outside temperature and its own determini
stic thermal dynamics\, and to forcing by its heat
ing or cooling system. Electricity prices change o
n a daily cycle\, often in steps. The minimum prob
lem-space dimensions are three: outside temperatur
e\, inside temperature and time of day\, and we fi
nd 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 eco
nomic dynamics within a single partial differentia
l 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 v
alue of all future costs (the sum of electricity c
osts and discomfort costs) from any and every star
ting point in the problem space\, conditional on u
sing the prescribed control action at every state
point. An optimal control policy therefore optimiz
es the control action at every state point\, and i
t resembles an economically-weighted Hamiltonian s
urface\, here in four dimensions. In financial lan
guage\, the optimal hyper-surface solves the Hamil
ton-Jacobi Bellman equation. We have found a rapid
numerical solution method (in minutes on a PC) wh
ich is robust to step discontinuities in electrici
ty price\, in user occupation and in the optimal c
ontrol policy itself (which for this problem has a
“bang-bang” form). Our solution finds the economi
cally optimal control policy itself\, without expl
icitly calculating the required means and variance
s of the system’s physical behaviors (all of their
physics is present within the PDE\, and under opt
imization the means and variances of the physical
parameters vary across the problem space). Given t
he optimal policy\, it is possible in seconds to r
ecover any desired physical and/or economic statis
tical moments\, across any chosen region of the pr
oblem space. This includes the expected time to fi
rst exit from a region\, the total expected time s
pent outside the region etc.\nThis approach can mo
del many stochastic/deterministic systems in which
one state variable is the integral of another (pa
rtly) stochastic variable (e.g. when a stock of fl
uid\, heat or money is fed and/or depleted at a st
ochastic flow rate\; or when the cumulative rotati
on speed of a high-inertia generator is subject to
stochastic accelerations by a control system). In
tegration relationships can be defined successivel
y between several variables in the PDE\, so as to
model systems with arbitrarily high order linear d
ynamics. Any level of integrated variable can be e
ither 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-shari
ng agreements between oil companies and their host
governments.
LOCATION:Mill Lane Lecture Rooms\, Room 1
CONTACT:Dr A. Zabala
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