Page 15 - Mathematical Models and Algorithms for Power System Optimization

Introduction 5

(3) The way to reduce solution difficulty
One way to simplify the model is to set up the auxiliary variables in different ways, which
makes it easier for the optimization calculation to obtain the expected results. For
example, to reduce the solution’s difficulty, basic variables may be represented as
constraints by decreasing the number of variables (in this case, the model would be
more complicated). Another way to eliminate the need to develop different models for
different operating conditions is to use virtual cost coefficients. For example, in Chapter 2,
the virtual cost coefficient enables the pump storage unit to pump more water at the valley
of the load curve, generating more power at the peak of the load curve.
(4) The way to select a model type for a large-scale problem
The control objects of a large-scale power system are widely distributed, but there is a closed
coupling relationship among them. Centralized control makes it difficult to collect
information from an entire system, whereas full decentralized control (using only local
information)makesitdifficulttoachieveaglobaloptimalsolution.Inaddition,itisobviously
uneconomical and unreasonable to achieve large-scale information exchange among the
objects to be controlled in the power system. The problem could be solved by establishing a
decomposition coordination model or a decoupling control observation model, that is, using
hierarchical estimation or decoupling control methods. Under conditions where the search
space is clear and small, stochastic optimization methods can also be applied.

1.4 Ideas about the Selection of the Algorithm

Available algorithms are prerequisites for optimization modeling. If the developed model
is a standard one, then it can be solved the existing or standard algorithm, otherwise it is necessary
to develop a new calculation method. In the procedure of formulating the model, we should
especially consider to formulate whether simple or complex model. The simple model has to deal
with complex results, whereas the complex model only needs to handle simple results.
Some ideas about the selections of the algorithm, including models versus results, use of the
standard solution tools, local solutions and future expectations, are explained as follows:

(1) Considerations of compromises for models versus results
If an approximated continuous algorithm is adopted, then there are many existing
algorithms, by which the calculation complexity could be reduced. However, the
complexity of the solution in a practical application is increased because the variables are
continuous rather than discrete. Thus, the solution in this way can not satisfy the practical
needs. This example explains the relationship between a simple model and complex results.
If a discrete model is to be considered when formulating the model, then there is no
ready-made algorithm, which will significantly increase the calculation complexity.
However, the complex algorithm could derive a straightforward integer solution, and the
calculation result would not require further processing, which is the relationship between a
complex model and simple results.