The document discusses optimal power flow analysis which is power flow analysis with an optimization objective such as minimizing fuel costs or transmission losses. It describes power flow analysis as determining the voltage magnitude and angle for each bus given load and generator conditions. Optimal power flow aims to satisfy nonlinear equality constraints from load flow equations and inequality constraints while optimizing an objective function such as fuel costs. Common solution methods include gradient, Newton-based, and linear programming approaches as well as intelligent methods like artificial neural networks.

1. Optimal power flowpower flow

2. Power flow
• is a of the flow of electric
power in an 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

3. P Q V δ
P-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

4. 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

5. Power flow
• In a system with N buses and R generators, there are then
Unknowns
• we need
Equations

6. Power flow equation

7. Solution of the Power Flow Problem
•Gauss–Seidel method
•Newton–Raphson solution method
•Fast decoupled methods

8. OPTIMAL POWER FLOW
Is power flow with
optimization (minimize or
maximize) a predefined
objective.

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

10. OPTIMAL POWER FLOW - fuel cost Minimization
FOR ONE UNI
F= 𝛼 + 𝛽 ∗ 𝑃 + 𝛾 ∗ 𝑃2

11. OPTIMAL POWER FLOW - fuel cost Minimization

12. OPTIMAL POWER FLOW
•Objective unction is expressed as
• 𝑚𝑖𝑛𝑓 𝑝 𝑔 = 𝑓 𝑥, 𝑢
•to satisfy Non linear Equality Constraints
𝑔 𝑥, 𝑢 = 0
•to satisfy Non linear Inequality Constraints
h 𝑥, 𝑢 ≤ 0

13. OPTIMAL POWER FLOW- Equality Constraints represented
• Load flow equations
• Load balance equation.

14. OPTIMAL POWER FLOW- inequality Constraints represented
.

15. 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