Page 168 - Mathematical Models and Algorithms for Power System Optimization

Discrete Optimization for Reactive Power Planning 159

6.3.2 Single-State Model for Discrete VAR Optimization

6.3.2.1 Description of the problem
The reactive power planning problem in this section focuses on capacitor allocation. All VAR
sources mentioned in the following text are capacitors. The objective function is to
minimize investment on newly installed capacitor banks with constraints, including investment
cost and operating constraint. The number of capacitor banks installed at each node is
taken as an integer variable. The objective and constraint for single-state reactive power
planning problems are stated as follows.

(1) Objective: to minimize total investment on capacitors by deciding the location and
capacity of newly installed capacitors. The key to this section is a discrete optimization
algorithm. Here, for the objective function, only the investment cost of capacitors is
considered, whereas its operating cost will be ignored.
(2) Investment cost constraint: investment cost of capacitor is comprised of two aspects:
1. Capital cost of investment location is a fixed cost, which has a complicated
calculation procedure. The more investment locations, the higher total capital cost.
Different investment locations also lead to different construction costs. Thus, the
fixed cost will be used to differentiate costs of different locations. This is a relative
value, which may lead to significant influence toward selection of location for newly
installed reactive power compensation equipment. For existing reactive power
compensation equipment locations, the algorithm in this chapter will take their
fixed costs as 0, because they may be considered in an optimization calculation
formula and so they are differentiated from new locations. As it is a problem related to
investment minimization, it is natural that the equipment with a fixed cost of 0 will
be installed first if it meets the operation constraint conditions.
2. Unit capacity cost of a capacitor is a variable cost, which is calculated based on the
investment cost needed for capacitors. The more capacitor banks to be installed, the
higher the cost, so it shall be expressed as a variable cost. Like the fixed cost, the
variable cost of reactive power compensation equipment is assumed as 0.
This method can easily handle the situation of adding new reactive power compensation
equipment to an existing reactive node. The test system in this section is not involved in
such a situation, but in Section 6.5, a similar situation is involved.
(3) Power system operation constraint: power system operation constraint consists of several
aspects:
1. The power generation and load balancing constraint under the given load conditions,
namely the power flow constraint. In reactive power optimization, except for active
power output of the balancing node, the active power outputs of the generators
are given.
2. Generator node and load node bound constraint: location and capacity of capacitors
are closely related to local voltage distribution.