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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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