Page 112 - Mathematical Models and Algorithms for Power System Optimization

102 Chapter 4

(1) Objective function is to minimize the system loss, which is equal to the total generator
output minus the total load. Because the load is fixed, to minimize the generator output
means to minimize loss. The objective function is a nonlinear expression.
(2) Constraints: The constraint functions include nonlinear functions.
1. Constraint of reactive devices: constrained by upper limit of number of reactive
device banks.
2. Operational constraints of the power system.
a. Constrained by balance between generation and load under given load condition,
that is, power flow balance constraint.
b. Constrained by the upper and lower voltage limits at generator buses and
load buses.
c. Constrained by the upper and lower limits of reactive output of generator. Here, the
reactive output of generator is a continuously adjustable variable.
d. Constrained by variation range of transformer tap. Here, the tap is a discrete
adjustable variable.
e. Constrained by variation range of number of capacitor banks. This number is a
discrete adjustable variable.
(3) Number of continuous variables.
Unlike reactive power optimization, OPF needs to consider not only reactive power
optimization but also active power optimization. In active power optimization, the active
output of the generator is treated as a continuous variable.
Number of continuous variables ¼ 2 number of system buses +
number of reactive output variables of generator + number of active output variables of generator:
(4) Number of discrete variables.
Number of discrete variables ¼ number of variables of reactive devices +
number of variables of tapratio
1. Number of problem constraint functions¼number of system buses N 2.
2. There are two types of variables: continuous variable and discrete variable; each
variable has its upper and lower limits, and the number of integer variables
is very large.

An actual power system usually has more than 100 buses, so both the number of constraints and
number of variables are more than a few hundred. The experimental system studied in this
chapter has 135 buses, 36 generators, 17 transformers, 10 capacitors, and 4 reactors.
Therefore, the number of continuous variables is 2 135+36 2¼342, the number of discrete
variables is 17+10+4¼31, and the number of constraint functions is 2 135¼270.
The previous analysis indicates that the discrete power flow optimization problem is a large-
scale MIP problem. The process for solving this complex problem is explained here.