Page 205 - Mathematical Models and Algorithms for Power System Optimization

196 Chapter 6

Constraints of discrete VAR optimization are:

(1) Node reactive power and active power flow equations.
(2) Generator voltage limits.
(3) Reactive generation limits.
(4) Transformer tap setting limits for all adjustable tap position.
(5) VAR limits for the new installation nodes.
(6) VAR limits for the existing installation nodes.

Except for the expression of adjustable transformer tap position, the constraint expressions are
the same as those in Section 6.3. In this section, the capacitor bank number and transformer
ratio number in real-scale distribution system are treated as discrete adjustable equipment.
Taking into consideration a planning engineer’s practical demand, the algorithm is divided into
five major steps:

Step 1: Perform power flow to provide initial value before optimization.
Step 2: Calculate continuous optimization with relaxed integer constraints.
Step 3: Obtain discrete solution based on expert rules, and fix the discrete solution.
Step 4: Perform power flow after optimization.
Step 5: If some over limits occurred in the power flow solution after optimization, then
execute the algorithm in Section 6.2;

To obtain discrete solutions, Steps 1–4 may be executed first; if the results are infeasible,
execute Step 5.

Through Steps 1–4, the power flow after optimization has been improved both in grid loss or
over limit values compared with that before optimization.

6.5.3.2 Way of processing transformer tap ratio

Themathematicalmodelfor thetap ratiointhissection is thesame asthatinprevioussections. The
only difference is the calculation method of tap position number. In the calculation, the tap ratio
number is expressed by the practical expression method corresponding to the real equipment. That
is, the upper limit of tap ratio corresponds to the highest tap position number 1, and the lower limit
correspondstothelowesttappositionnumberN.ThevariationrangeofintegertaprationumberY T
is [1, N]. The expression of tap ratio T based on tap position number shall be:

T ¼ T +1 Y T ÞΔT
ð
where Y T —optimal solution of tap position number; T—upper limit of tap ratio; ΔT—unit step
size of tap ratio.

For example, if U N (kV) in the nameplate of a certain transformer is 110 2 2.5%/11,
variation range of its tap ratio number T shall be [0.95,1.05], and variation range of tap ratio