Page 184 - Mathematical Models and Algorithms for Power System Optimization

Discrete Optimization for Reactive Power Planning 175

The idea of considering a discrete variable under a multistate situation is to transform reactive
power optimization into complicated multistate discrete reactive power optimization. The key
to this section is to present a pragmatic algorithm to solve multistate discrete reactive
power optimization. Multistate as mentioned in this section includes: normal state, transmission
line failure, transformer failure, and generator failure.
To consider multistate problems, Literature [30] proposed a direct energy decomposition
method. To apply the algorithm to multistate discrete reactive power optimization, the number
of capacitor banks at the location of reactive power compensation equipment is treated as the
energy for each state. If the value of the energy is fixed, the whole multistate discrete reactive
power optimization may be decomposed into several mutually independent subproblems,
because multistate discrete reactive power optimizations have a special structure, that is,
diagonal block structure. Thus, these subproblems may be solved separately. By coordinating
results from these subproblems, the minimum reactive power investment cost of the entire
problem can be found. The coordination process is actually to comprehensively consider the
infeasibility of each state, and install the reactive power compensation equipment at nodes
where the infeasibility of all states can be minimized.
According to traditional multistate reactive power optimization, reactive power optimization
under each single state will be calculated separately. The maximum reactive power
compensation equipment number of nodes under a respective single state will be taken as the
reactive power configuration of the node. This method only considers optimization of a single
state and ignores the mutual effect of reactive power configuration under all states. This might
not be economically efficient, because it may deploy newly installed reactive power
compensation equipment at adjacent nodes or many nodes. Even if the total reactive power
compensation capacity keeps still, the method may also increase fixed capital cost of new
reactive power compensation equipment, in turn, increasing total investment.

The proposed algorithm fully takes into consideration the mutual support role of reactive power
under multiple states. The proposed integer improvement procedure for multistate conditions
can help new reactive power meet the requirements of each state to the largest extent, and
comprehensively and optimally balance under single state to achieve the overall optimum of all
states. As for this, new reactive power compensation equipment will be centrally allocated to
make the total investment less than the conservative investment results obtained by separately
calculating each single state. In addition, compared with a single-state calculation
procedure, the calculation procedure for multistate reactive power optimization developed
with the algorithm will not lead to more workload of calculation.

In the previous chapter, only the normal state in a power system is considered. VAR planning,
without considering possible changes in the system configuration, may not be realistic. There
might exist a minimum VAR equipment installation that can correct unacceptable voltage
profiles during anticipated normal and contingency states in power systems. The contingencies