The optimization of controller parameters for three phases PLL tracking system

In order to improve the performance of the three phases PLL system, this paper designs an algorithm to optimize the PI controller parameters based on the integral of squared error theory. First, it analyzes the nonlinear character of the three phases PLL which uses the d-q coordinate transformation theory to lock the voltage phase, and deduces the closed loop transfer function of the PLL system with PI controller. In the second part, it analyzes the harmonic component of the voltage projected on q axis, and designs a reasonable filter to eliminate the effect of the harmonic voltage. With the linearizated closed loop transfer function, it establishes the cost function of the controller parameters optimization problem based on the ISE theory, and provides a rule that how to design the reference trajectory. For the cost function optimization, it deduces the partial derivative of the cost function and uses conjugate gradient method to solve the optimization problem. In the last part, it applies the optimized PI controller to unbalanced grid and voltage distortion conditions, the simulation results indicate that the optimized PI controller obtains robust and fast tracking ability.