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Case study - Optimizing Hydro Scheduling in the Power
Industry
Problem
In the Power Industry, two areas in which optimization is
becoming increasingly popular are thermal and hydro scheduling.
Currently Dash Optimization's Xpress-MP modeling and optimization
software is being used to solve hydro scheduling problems.
The hydro scheduling problems appears fairly easy when planning
for a single hydro station, but planning often requires modeling
multiple stations on one or more river systems, which makes
the problem much more complicated. The problem must take into
account hydraulic coupling between stations, minimum and maximum
reservoir levels, hydro turbine prohibited zones due to cavitation,
flow time delays, and environmental constraints. To create
an optimal hydro schedule that takes all of these constraints
into consideration and outputs a solution as quickly as possible,
many independent power producers turn to Dash Optimization.
Solution
Using Xpress-MP, many independent power producers can solve
this problem using two different approaches depending on their
operating environment. The first approach is to create an
objective function that meets an hourly generation profile
while minimizing the total amount of water used. The second
approach requires an opportunity cost to be supplied for water
drawn from a storage lake, and utilizes an objective function
that maximizes revenue given a set of hourly prices. These
problems are typically solved using one-hour increments and
are solved for either one day or one week with an extra day
for end effects.
The different constraints that Xpress-MP accounts
for in this type of problem are:
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Max/min generation |
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Max/min reservoir levels |
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Max/min flows on some parts
of system |
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Max rate of change of flow
in certain river sections |
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Max rate of change of level
in reservoirs (in certain cases) |
| • |
Minimum flows for fish, recreation,
and other environmental constraints |
| • |
Piecewise linear, non-convex
water to electricity conversion factor for generators |
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Water balance (for each reservoir,
flow in - flow out = change in contents) |
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Time delays on some river reaches |
Integer variables are often used to represent
discontinuous features of the problem. These include turbine-prohibited
zones, the water to power conversion function for each turbine,
and the flow over spill weirs (i.e. a spillway not controlled
by gates, where spill occurs when water level exceeds the
height of the weir)
Why Use Xpress-MP?
The hydro scheduling problem was recently discussed at Dash
Optimization's 2001 User's Meeting, Tom
Halliburton, a well-respected Energy Consultant, gave a presentation
explaining his implementation of Xpress-MP to solve the problem.
One of the more recent river systems where Mr. Halliburton
has used Xpress-MP is California's Feather River system. This
river system has approximately 700 MW of installed capacity,
which generates over 2,000 Gwh of energy per year and revenues
of USD $100 million. Mr. Halliburton solves the hydro scheduling
problem using a spreadsheet interface to Xpress-MP. The Xpress-MP
commands are executed using a callable library.
Using a spreadsheet interface gives him the
ability to create menu bar commands that makes further analysis
easy. Many independent power producers use Xpress-MP because
of its speed and reliability. When asked why he uses Xpress-MP,
Tom stated "I tried Xpress and [other competitors' products]
and found Xpress faster. Not like 20% faster but several times
faster than using the standard Excel solver for mixed integer
problems."
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