Page 194 - Mathematical Models and Algorithms for Power System Optimization

Discrete Optimization for Reactive Power Planning 185

X
q j ¼ q ij (6.42)
i2N inf
where N inf is the set of infeasible subproblems.

Substep 3: Each of the infeasible states is resolved until they become feasible in the
following way: Choose a node with newly installed VAR equipment, and add the number of
the VAR equipment by one unit; try to reduce the infeasibility of the problem (as its value is
the upper limit of the number of VAR sources, the feasibility of problem may be increased
by increasing Y C ). To select the most effective node for decreasing infeasibility as much as
possible and increasing cost as little as possible, the node u is selected by evaluating the
following criterion:

q u ¼ min q j r j (6.43)
j2M
where r j refers to change of investment cost, which shall be calculated by this formula:

r j ¼ C j ,if Y Cj > 0 (6.44)
r j ¼ C j + D j ,if Y Cj ¼ 0 (6.45)

Then, increase the upper limit Y Cu of node u by 1, and its infeasible state shall be resolved
with MILP.

Substep 4: Select a node with newly installed VAR equipment, and decrease the number of
VAR equipment by one unit to reduce the investment cost of the whole problem. Node u
with newly installed VAR equipment shall be selected to reduce the investment cost as
much as possible with the feasibility of each subproblem maintained. For each state in
which the number of VAR units installed is equal to the upper limit (i.e., Y ij ¼ Y Cj ), the
feasibility h ij (h ij >0, i is symbol of state, j refers to the serial number of reactive
power node) shall be calculated. Then, the following equation will be applied to the
calculation of h j :

X
h j ¼ h ij (6.46)
i2N act
where N act is the set of states in which the number of VAR units installed is equal to the
upper limit.

Substep 5: Choose the most promising node u with the following equation to improve the
solution:

(6.47)
h u ¼ max h j
j2M