Page 185 - Mathematical Models and Algorithms for Power System Optimization

176 Chapter 6

considered in this program only include the static outages, such as transmission lines,
transformers, or generator outages, not including some severe dynamic faults in the power
system. This research discusses development of a computer algorithm, a multiple state
algorithm, that can select one overall reactive power installation pattern that will satisfy system
performance for both base state and contingency states. Most importantly, this algorithm needs
only a little more computer storage than that of a single-state algorithm.
As previously mentioned, VAR planning should provide a system with VAR equipment, which
can experience the most severe state along with each possible state. The consideration of
several contingency states of various load conditions (light, medium, and peak load) creates an
enormous nonlinear mixed-integer optimization problem. For example, there are more than
900 continuous variables and 120 integer variables for a 135 node system VAR planning
problem under three contingencies.
The goal of the reactive power planning problem is to find the minimum cost installation plan of
new reactive power sources so that the system voltage is maintained within an acceptable range.
The formulation of the multistate VAR planning problem must take into account the following
two aspects:
(1) The number of installed VAR sources takes an integer value.
(2) The installed VAR sources must be sufficient even in contingency states or in anticipated
operating states.
A consideration of multiple states, together with the discrete nature of VAR facilities, creates a
large-scale nonlinear MIP problem. Because no general mathematical programming
technique for solving such a problem exists, a new algorithm should be developed that can
handle both the discrete nature of capacitor units and multiple states in power systems.
In previous researches, the consideration of both the multiple states in power systems and the
discrete nature of VAR facilities has not been well treated. In this section, based on the previous
study, an approximate solution method for MIP problems is employed. Because the
method is LP-based, it is efficient for large-scale problems.

To take multiple states into account, a resource directive decomposition approach is used in the
proposed algorithm. To apply the approach to the multistate VAR planning problem, the
number of installed VAR sources is treated as “resources,” which are assigned to each state. If
the value of a resource (installed VAR source) is fixed, the overall problem can be decomposed
into mutually independent subproblems. This is because the multistate VAR planning problem
has a special form of a block diagonal structure. Then subproblems are coordinated to
give a minimum cost VAR installation pattern for the overall problem. This method takes into
consideration the “cooperative” effect of a VAR source installation for multiple operating
states. The states considered in this section include not only normal operating states but also
such outages as transmission line outages, transformer outages, and generator outages.