Power System Operation and Control

1.4 LAGRANGE MULTIPLIER METHOD – AN OVERVIEW

Nonlinear function optimization problems such as ED can be solved by the Lagrange multiplier method.

1.4.1 Nonlinear Function Optimization Considering Equality Constraints

Let the problem be to minimize the function

 

f (x₁, x₂, … , x_n)                        (1.7)

Subject to k number of equality constraints

 

g_i(x₁, x₂, … , x_n) = 0 for i = 1, 2, … , k.                    (1.8)

The constrained function f can be written as an unconstrained function with the help of the Lagrange method as:

In Eq. (1.12) £ is the Lagrange function and λ is the Lagrange multiplier. The necessary condition for minimum ...