Page 179 - Mathematical Models and Algorithms for Power System Optimization

170 Chapter 6

Because Cases 1–5 adopt an infeasible power flow solution as the initial value, infeasible power
flow means voltage or reactive of some nodes may violate the limits.

“Fixed cost” refers to construction cost coefficients of Cases 1–5, which are relative values. The
range of fixed cost for Case 1 is 2.6–3.8, and for Cases 2–5 is 0.5–0.9.

“Variable cost” is the single bank cost coefficient of capacitors in Cases 1–5. The variable cost
of all single bank capacitors in Cases 1–5is1.

“The number of existing capacitor nodes” refers to the number of existing capacitor nodes.
“The number of new capacitor nodes” refers to the number of candidate nodes to be installed
with new capacitors.

“The number of new nodes” refers to the number of nodes to be installed with new capacitors
based on the algorithm in this section.

The convergence tolerance for continuous variables is 0.0001.

In Table 6.2, Cases 2 and 3 have the same voltage bound and the same candidate nodes installed
with capacitors. The difference is that Case 3 increases the upper limit of existing capacitor
bank number, yet decreases the upper limit of new capacitor bank number. Except for the
difference in voltage bound, Cases 4 and 5 have the same calculation conditions as that of Cases
2 and 3 in Table 6.2.
All over limits of nodes may be eliminated in the first iteration with the algorithm to find the
integer-feasible solution. Generally, nonlinear convergence solution can be obtained in eight
iterations, and an average over six LPs will be calculated in one iteration, the second and third
stage will be calculated in each iteration, and each stage has to calculate more than three LPs.
When changing each integer to recalculate LP, the algorithm utilizes the use of the function
provided by MPS-II to calculate LP from the original base. Thus, the calculation time is
acceptable.
In Cases 1–5 where the number of newly installed reactive compensation equipment is zero,
then zero is used as the initial power flow value. The calculation results show that, although the
number of newly installed capacitor nodes is decreased from 6 to 5 after the upper limit of
existing capacitor bank number is increased, the fixed investment cost can be largely reduced.
Cases 2 and 3 have almost the same calculation time. Different voltage bounds lead to more
initial voltage values crossing the threshold. Moreover, more violation volume means higher
investment in newly installed capacitor nodes and more calculation time. The total sum of
existing capacitor node number and newly installed capacitor node number can be up to 49 (see
Table 6.2). The capacity of the capacitor provided for each node shall be expressed with an
integer variable. Whether it is necessary to provide capacitors for the newly installed capacitor
nodes is also expressed with the integer variable. As for this, the number of integer variables to