# Asffsa Essay

6883 words - 28 pages

Electric Power Systems Research 95 (2013) 302- 308
Contents lists available at SciVerse ScienceDirect
Electric Power Systems Research
jou rn al h om epa ge: www.elsev ier .co
Mathem non electric
Lingjian ∗∗
a Centre for Pro don, L b School of Ene
a r t i c l
Article history: Received 20 Fe Received in re Accepted 30 S Available onlin
Keywords: Mathematical Optimisation Economic disp Power generat
isatio in th rings atica oblem for th case s ood a
1. Introdu
Economic dispatch of power generation is an important issue in power supply system. Dispatch refers to seeking the optimal power schedule giving the minimum fuel cost for a set of online thermal units while meeting the system power demands and constraints [1]. Much resea of power di power for r identiﬁed a into accoun loading effe
In the cl a quadratic power-cost
Fi(Pi) = aiP2i where Fi(Pi bi, ci are co multiple va which mean in the throt produces ri
∗ Correspon ∗∗ Correspon
in lit function term [3] to Eq. (2) above:
Fi(Pi) = aiP2i + biPi + ci + ei ∣∣sin[fi(Pi − Pmini )]∣∣ (2)
where ei and fi are coefﬁcients used to deﬁne valve loading effects and Pmin is the minimum power generation limit for unit i. It has
0378-7796/\$ - http://dx.doi.o
rch, for example [1-4], has addressed the optimisation spatch systems, aiming at minimising the cost to deliver eal and complex dispatch systems. Researchers have
number of key practical problems that need to be taken t when modelling the dispatch system, including valve cts, transmission losses, multiple fuels etc. [2]. assic economic dispatch of power generation problem,
function of power output is used to approximate the relation [3]:
+ biPi + ci (1)
) denotes fuel cost in unit i at power output Pi and ai, st coefﬁcients. However, real thermal generators with lve steam turbines experience the wire drawing effect, s the initial opening of a steam admission valve results tling of the steam ahead of the turbine nozzles [5]. It pples in the cost function curve, known as valve loading
ding author. Tel.: +44 2076793817; fax: +44 2073832348. ding author. Tel.: +44 2076792563; fax: +44 2073832348. resses: lingjian.yang.10@ucl.ac.uk (L. Yang), e.fraga@ucl.ac.uk apageorgiou@ucl.ac.uk (L.G. Papageorgiou).
i recently been noted that the modiﬁed cost curve exhibits non- monotonic incremental cost [4]. In any case, the cost function introduces mathematical difﬁculties thanks to non-smoothness, non-convexity and higher order non-linearity, which present chal- lenges for optimisation.
The capability of some power generators to consume more than one fuel gives rise to the multiple fuel options problem [6]. The cost function of thermal generators with multiple fuels is made up of a number of quadratic segments, and the piece-wise quadratic cost functions are non-convex over the entire domain. Sometimes, power loss that incurs in the...

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