Optimal power flow power flow

Power flow• is a numerical analysis of the flow of electric power in an interconnected system.• focuses on various of AC power parameters, such as voltages, voltage angles, real power and reactive power.• uses simplified notation such as on-line diagram or per-unit system, • It analyzes the power systems in normal steady-state operation.

P Q V δP-Q bus known known unknown unknown

P-V bus known unknown known unknown

Slack bus

unknown unknown known known

Bus type

•P-Q bus load bus

•P-V bus generation bus

•Slack bus large bus

Power flow•The goal is to obtain complete voltage angle and magnitude for each bus for specified load and generator real power and voltage conditions•Once it’s known, real and reactive power flow on each branch and generator reactive power output can be analytically determined

Power flow• In a system with N buses and R generators, there are then

Unknowns• we need

Equations

Power flow equation

Solution of the Power Flow Problem

•Gauss–Seidel method

•Newton–Raphson solution method

•Fast decoupled methods

OPTIMAL POWER FLOW

Is power flow with optimization (minimize or maximize) a predefined

objective.

OPTIMAL POWER FLOW -Objective function• fuel cost, • transmission losses • reactive source allocation

OPTIMAL POWER FLOW - fuel cost Minimization

FOR ONE UNI

F

OPTIMAL POWER FLOW - fuel cost Minimization

OPTIMAL POWER FLOW

•Objective unction is expressed as

• to satisfy Non linear Equality Constraints • to satisfy Non linear Inequality Constraints

OPTIMAL POWER FLOW- Equality Constraints represented

• Load flow equations

• Load balance equation.

OPTIMAL POWER FLOW- inequality Constraints represented

.

O P F Solution Methodologies O P F Solution Methodologies

Conventional Methods

Gradient Methods

Newton – based

Linear Programming

Intelligent Methods

Artificial Neural Networks

Evolutionary Programming

Fuzzy Logic