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# GA Tuned PI Controller for Two Area System Using MATLAB

GA Tuned PI Controller for Two Area System Using MATLAB

Understanding the Two-Area Power System

A two-area power system consists of two interconnected regions (Area 1 and Area 2) that exchange power through a tie line. This setup helps balance load demands between the two areas.

#### Components of the System:

1. Areas: Each area includes a governor, generator, and load model.

2. Tie Line: Connects the two areas and facilitates power exchange based on load demands.

### System Modeling

The basic model of the two-area system includes transfer functions for each area's governor, generator, and load. Initially, we analyze the system without any controllers to understand its baseline behavior.

#### Simulation without Controller:

• Results: The system's frequency deviations (omega1 and omega2) show significant oscillations, indicating poor performance.

### Implementing PI Controllers

Next, we introduce PI controllers to each area. These controllers aim to reduce frequency deviations and improve the system's stability.

#### PI Controller Structure:

• Integral Controller: Implemented with a gain of 0.3 in both areas.

#### Simulation with PI Controller:

• Results: The inclusion of the PI controller reduces frequency deviations, but the performance is still not optimal. We observe an undershoot around -14 and an overshoot around 28 x 10^-3.

### Optimizing PI Controllers with GA

To further improve the system's performance, we use a Genetic Algorithm to tune the PI controller parameters (Kp and Ki) optimally.

#### Genetic Algorithm Basics:

• Operators: Selection, Crossover, Mutation, and Reproduction.

• Objective: Minimize the fitness function representing the system's performance.

### GA Implementation in MATLAB

We set up a MATLAB script to implement the GA. The script includes:

• Objective Function: Measures the performance of both areas.

• GA Configuration: Defines population size, iterations, and fitness evaluation criteria.

#### GA Simulation:

• Iterations: The GA runs for multiple iterations, adjusting the Kp and Ki values.

• Results: Over successive iterations, the fitness function improves, indicating better system performance.

### Final Results

After optimizing with GA, we observe:

• Improved Performance: Reduction in undershoot and overshoot, and improved settling time for frequency deviations (omega1 and omega2).

• Optimized Parameters: The GA provides optimal Kp and Ki values for both areas.

#### Comparison of Responses:

• Without Controller: Significant oscillations and instability.

• With PI Controller: Reduced oscillations but suboptimal performance.

• With GA-Optimized PI Controller: Minimal oscillations, improved stability, and faster settling time.

### Conclusion

This simulation demonstrates the effectiveness of using Genetic Algorithms to tune PI controllers in a two-area power system. By optimizing the controller parameters, we achieve a more stable and efficient system. This approach is beneficial for maintaining system reliability and performance.

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