Page 177 - Mathematical Models and Algorithms for Power System Optimization

168 Chapter 6
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Substep 4: When LP is not resolved for the new (Y , W ), check whether the cost stated in
Eq. (6.1) can be decreased. If the cost decreases, then go to Substep 5. Otherwise, move to
Step 7. Simplex tableau is used to check whether the infeasibility of the problem
is smaller than 0 (infeasibility calculation formula is shown in Appendix A).
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Substep 5: Check whether the new (Y , W ) makes continuous variable vector X violate
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operating constraints, that is, check whether (Y , W ) results in an insufficient or excessive
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VAR supply. With integer variable vector (Y, W) fixed to (Y , W ), the checking is finished
in two ways. The first way is to calculate the violations without resolving problem LP; if the
violations do not happen, then go to Substep 6. Otherwise, readjust continuous variable
vector X, that is, resolve the LP problem. If resolving problem LP is feasible, then go to
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Substep 6, otherwise proceed to Substep 7, that is, abandon (Y , W ).
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Substep 6: Accept the new integer solution (Y , W ). It is better than (Y*, W*), because the
installation cost decreases, and insufficient or excessive VAR supply does not occur.
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Replace (Y*, W*) with (Y , W ) and return to Substep 2 to decrease the cost further.
Substep 7: Readjustment of these two integer variable values makes it impossible to decrease
the installation cost or supply appropriate quantity of VAR resources. Abandon this new
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integer solution (Y , W ), and return to Substep 2 to check another pair of integers in Y*.
Please refer to Fig. 6.2 for the improved integer algorithm.
Set the integer solution obtained
Substep 1 from Step 4 as (Y*,W*)
Yes
No
Whether it is possible to choose Further improvement impossible,
Substep 2 one pair of nonzero integers quit

Establish a new integer solution
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Substep 3 (Y ,W ); add up with 1or2,
deduct by 1
Yes
No
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Substep 4 (Y ,W ) cost <(Y*,W*) cost
Yes
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Whether (Y ,W ) leads to
Substep 5 infeasible solution?
No
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Substep 6 (Y*,W*) (Y ,W )

n
Substep 7 Give up (Y ,W ) n
Fig. 6.2
Flow chart of integer improved algorithm of Step 5 in algorithm flow.