# Optimal load scheduling of hydroelectric power stations.

Mantera, I Gusti Made 1972 , 'Optimal load scheduling of hydroelectric power stations.', PhD thesis, University of Tasmania.

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## Abstract

The work presented in this thesis concerns the optimisation
of the hour-to-hour generation schedule (over a scheduling interval
of 24 hours) of the generating stations in an all-hydro electric -
system. The day-to-day system storage policy is assumed known
from the long-term schedule. System load demand is first treated
as deterministic. Later, attempts are made to treat it as
stochastic. Throughout the text, system transmission losses are
represented by means of the B-coefficient loss formula.
Chapter 1 presents brief discussions on various topics
which may play - a part in the optimization process. In particular,
the concept of frequency control and the distinction between
long-term and daily scheduling are outlined. The optimization
objective is then formulated and some of the known methods of
obtaining the solution are briefly discussed. In chapter 2, the optimization problem is first formulated .
as that of minimizing the instantaneous total power drawn from
the system subject to satisfying a . predetermined time-varying
load demand.This is analogous to the minimization of the
instantaneous total cost rate in thermal systems. Station
characteristic curves are approximated by straight line segments
and head variations are assumed negligible. The optimising -
conditions are derived using the Lagrange multiplier technique.
A small system consisting of 4 stations is studied, where
optimisation is achieved by means of an analogue computer.
By introducing weighting factors in the objective
function, the storage policy can be satisfied. (Analysis carried
out in chapter 3 later reveals that this is the correct measure
which must be taken to meet the storage policy). Problems do
arise, however, when - there are multi-unit stations present in
the system. Due to the non-monotonic nature . of the incremental
Output curves' of such stations, a. number of solutions would satisfy the optimising conditions. The optimum solution can only
be established after testing each possible solution, a prohibitive
task for large systems. Approximating the incremental output
curves of such stations may create undesirable errors. Another
weakness of the method is that it cannot readily take into account
The application of Pontryagin's Maximum Principle is
attempted in chapter 3. It is shown that, for systems with fixed—
head stations, the optimising conditions are exactly identical to
that derived using the Lagrange multiplier technique with weightings
being introduced in the objective function. Unfortunately, those
problems associated with the presence of multi—unit stations are
still unsolved.
Under ideal system conditions, it is shown that optimum
generation schedule would result if all stations; except the
is defined as an operating mode where the instantaneous station
discharge rate is only allowed to take one of two discrete values
with stepwise transitions. The analysis indicates that the
switching instants do not play any part, except they must be so
chosen that the output of the frequency control station is kept
within its limits.
systems, the optimisation. becomes that of searching for the
optimum switching instants of the step loaded stations. This is
discussed in chapter 4. For practical reasons, only two step
stations is studied. Experimental results indicate that the
short computation time.
that it can handle the optimal scheduling problem where the load demand is treated as being stochastic. The effects of head variations
can be estimated fairly accurately.
The application of the principle of dynamic programming
is discussed in chapter 5. Due to the multi-dimensional nature of
the problem, this principle must be combined with the relaxation
principle to minimise the computation time and computer storage
requirements. A good initial guess for the optimum schedule may
are then modified by applying the combination of dynamic programming
and relaxaxtion principles.
Finally, chapter 6 outlines the general conclusions drawn
from the work presented in the preceeding chapters. The possibility.
of applying Pontryagin's Maximum Principle to obtain the long-term
storage policy is also studied. Related future research areas are
suggested.
To the author's best knowledge, the materials presented
in chapters 3, 4 and 5 are original. Chapter 2 is based on the work
of Chandler Jr. and Gabrielle, where the mathematical error found
in their text has been corrected and the weighting procedure, among
other materials has been included.

Item Type: Thesis - PhD Mantera, I Gusti Made Hydroelectric power plants, Electric power-plants The Author Copyright 1972 the Author - The University is continuing to endeavour to trace the copyrightowner(s) and in the meantime this item has been reproduced here in good faith. Wewould be pleased to hear from the copyright owner(s). Thesis (Ph.D.) - University of Tasmania, 1972. Bibliography: l. 105-109 View statistics for this item