Page 208 - Mathematical Models and Algorithms for Power System Optimization

Discrete Optimization for Reactive Power Planning 199

Rule 1. If the Q constraint of node i is over the upper limit, then (1) change the voltage limits
of the node, if possible; (2) change the voltage limits of the adjoining nodes; (3) install new
capacitors at this node, if possible; or (4) install new capacitors at adjoining nodes, if
possible; otherwise (5) change the tap position limit, if possible, which is equivalent to
changing transformer settings.
Rule 2. If the Q constraint of node i is below the lower limit, then (1) change the voltage
limits of the node, if possible; (2) change the voltage limits of the adjoining nodes; or (3)
check the input data; otherwise (4) change the tap position limits, if possible.
Rule 3. If the linearized P equation of node i is unbalanced, then (1) check the related node
data and line data, and (2) change the voltage limits, if possible.
Rule 4. If the linearized Q equation of node i is unbalanced, then (1) check the related node
data and line data; (2) change the voltage limits, if possible; and (3) install new capacitors or
change the new tap position, if possible.

6.5.3.5 Rules to determine integer variables for tap ratio

The basic idea of expert rules is to consider the relationship between tap ratio and voltage to
keep voltage within the limits after the gearing of tap ratio. The rule is not complicated and is
helpful in reducing voltage violation. Expert rules introduced in this section are: first, determine
whether the transformer is a step-up or a step-down transformer according to the active power
flow direction; then, determine transformer tap position according to voltage bound, which
reduces the possibility of voltage violation after transformer tap position adjustment and lays a
solid foundation for finding subsequent discrete solution.

As previously mentioned, the main basis for the rules given in this section is the relation
between the active power flow direction and the tap ratio and voltage, and the rounded-off
value is determined based on the position of the integer solution. According to fuzzy
mathematics, values around 0.5 are fuzzy, and it is hard to determine the transformer tap
gearing direction with integer initial value truncation. Simple round-off truncation leads to
the same results as that of expert rules. Thus, the following rules only determine truncation
with tap ratio number Y T within the range of fuzzy values.

Suppose that a transformer is located between node i and node j, where i is the fixed side and j is
¼1, the tap is located at the highest position;
the changeable side for this transformer. When y T k
otherwise, the tap is located at the lowest position. The following rules to set taps are formulated
after obtaining a relaxed solution:

ð
T k ¼ T k +1 y T k ÞΔT k
Rule 1. If the tap is changeable, calculate the tail setting of the continuous solution Y T and
its decimal value ΔY T .