### Optimization and Systems Theory Seminar

March 14, 1997, 11.00-12.00

** Stefan
Feltenmark**,

Division of Optimization and Systems Theory,

Department of Mathematics,

KTH

####
Optimization of power production

In this talk, I will summarize my thesis, titled "On optimization
of power production".
It treats some large-scale, non-convex optimization problems
that appear in short-term production planning of power.
For systems with thermal generation (oil, coal, gas, nuclear),
a basic problem is when to start and stop units to minimize
operational costs, the unit commitment problem.
It contains the convex problem of optimally allocate an electric
load among units, optimal dispatch, as a subproblem.
We describe algorithms for these problems which are based
on Lagrangian relaxation and solution of the corresponding
dual problem.
For hydro power systems we study a model which explicitly
includes the dependency of dam elevation on power output.
The resulting optimization problem has bilinear objective
and structured network constraints.
We use a certain concavity property to show that any local
optimum is an extreme point of the feasible set.
This property motivates a simplex-type algorithm for computing
local optima.
Explicit convexification of the terms in the objective function
gives a family of convex problems, which underestimate the
original problem, and provides feasible solutions.
A branch-and-bound strategy is then employed to compute global
optima.
Finally, the problem of cogeneration is treated. Some power
systems has the capability to use exhaust heat from the
electricity production for district heating or for distillation
of water. Since heat or water may be stored, an inventory balance now
couples the production between time periods.
The approach for this problem is again Lagrangian relaxation, coupled
with a certain restrification to cope with the complexity of
the subproblems.
For all problems considered, computational results for real
or realistic problems will be presented.

Calendar of seminars

*Last update: March 10, 1997 by
Anders Forsgren,
andersf@math.kth.se.
*