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Discrete optimal quadratic AGC based cost functional minimization for interconnected power systems.

M Esmail1, S Krishnamurthy2

  • 1Department of Electrical, Electronic and Computer Engineering, Cape Peninsula University of Technology, Symphony Way, Bellville, Cape Town, 7535, South Africa. esmailmoh19@gmail.com.

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This study introduces Discrete Optimal Quadratic Automatic Generation Control (OQAGC) to address complex power system challenges. The new method enhances stability and robustness in interconnected power grids.

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Area of Science:

  • Electrical Engineering
  • Control Systems
  • Power Systems

Background:

  • The Automatic Generation Control (AGC) problem is increasingly complex due to larger interconnected power networks and fluctuating demand.
  • AGC aims to maintain nominal frequency and planned tie-line power flow, crucial for grid stability.
  • Existing AGC methods face challenges in managing these complexities effectively.

Purpose of the Study:

  • To introduce a novel Discrete Optimal Quadratic Automatic Generation Control (OQAGC) method.
  • To simplify AGC control laws for both linear and nonlinear systems.
  • To optimize controller performance using established control theorems and functional minimization techniques.

Main Methods:

  • Developed a Discrete Optimal Quadratic Automatic Generation Control (OQAGC) method.
  • Utilized optimum control theorem with Lagrangian multipliers for controller optimization.
  • Employed functional minimization for systematic selection of discrete state and control weighting matrices.
  • Derived discrete cost function based on area control errors, integral area control errors, and control energy.

Main Results:

  • The OQAGC method simplifies quadratic cost function results into linear terms, minimizing control actions and state deviations.
  • Simulations on four interconnected power systems and a two-area system with renewable energy demonstrated improved performance.
  • The controller showed enhanced stability, steady-state performance, and robustness to load disturbances, even with Generation Rate Constraints (GRCs).

Conclusions:

  • The proposed Discrete Optimal Quadratic Automatic Generation Control (OQAGC) offers a simple and effective discrete control law.
  • The functional minimization technique simplifies the selection of weighting matrices.
  • The OQAGC approach proves significant for discrete Linear Quadratic Regulator (LQR) controllers in multi-area power systems.