Page 204 - Mathematical Models and Algorithms for Power System Optimization

Discrete Optimization for Reactive Power Planning 195

used to judge the gearing direction in case of integer truncation. According to a simple tail-off
method, 0.49 is 0, and 0.51 is 1. However, real projects are not that simple. Such a simple tail-
off method may lead to a result where the number of reactive power compensation equipment
installed or the direction of adjustment of transformer tap position may be different from
expectation, which may further lead to voltage violation, increasing calculation time, and
reducing the possibility of obtaining integer solution. Expert rules may help judge truncation
direction, and it is possible to obtain an integer-feasible solution faster.

6.5.3 Algorithm based on Expert Rules for Discrete VAR Optimization

6.5.3.1 Basic procedure of the algorithm

As described in Section 6.6.1, selecting a different objective function does not affect the
structure of the algorithm but has different expression and leads to different solutions.
However, sometimes two objective functions are contradictory: to minimize the investment
cost may increase the operating cost (such as network loss), but minimizing network loss may
increase the investment cost. Practical engineering calculations are restricted by many
conditions, which have to consider multiple aspects. Thus, practical engineering calculation
requires VAR optimization with at least two different objective functions, so that planning
engineers may make comparisons. Discrete VAR optimization in this section takes into account
two objective functions: investment cost and active power grid loss.
Objective function of discrete VAR optimization:

(1) Minimization of VAR investment costs investment planning for VAR sources; the
objective function expression is the same as that in Section 6.3.
(2) Minimization of network power loss optimization of VAR unit operation; the objective
function expression is:

ð
min ΣP S Þ (6.48)
P S is active power variable at balancing node. Because grid loss is calculated based on the sum
of active power output minus the sum of active power load, to minimize active power output at
the balancing node is equivalent to minimizing total active power grid loss.

In addition, different weight coefficients are taken for the previous objective functions to form
discrete VAR optimization objective functions, which can take both the grid loss and
investment cost into consideration. One of the objectives can be treated as constraint in
optimization calculation, and a multiobjective problem may as well be transformed into a single
objective problem. Weight coefficient and transformation method are involved in another
research field. This section focuses on discrete optimization with a single objective.