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The power system is complex multi‐component dynamic system with many operational levels made up of a wide range of energy sources with many interaction points. Low frequency oscillations are observed when large power systems are interconnected by relatively weak tie lines. These oscillations may sustain and grow to cause system separation if no adequate damping is available. The present paper aims to propose an on‐line self‐learning PID (OLSL‐PID) controller in order to damp the low frequency power system oscillations in a single‐machine system.

The proposed OLSL‐PID is used as a controller in order to damp the low frequency power system oscillations. It has a local nature because of its powerful adaption process based on back‐propagation (BP) algorithm that is implemented through an adaptive self‐recurrent wavelet neural network identifier (ASRWNNI). In fact PID controller parameters are updated in on‐line mode, using BP algorithm based on the information provided by the ASRWNNI which is a powerful fast‐acting identifier because of its local nature, self‐recurrent structure and stable training algorithm with ALRs based on discrete lyapunov stability theorem.

The proposed control scheme is applied to a single machine infinite bus power system under different operating conditions and disturbances. The nonlinear time‐domain simulation results are promising and show the effectiveness and robustness of the proposed controller and also reveal that: because of the high adaptability, the local behavior and high flexibility of the OLSL‐PID controller, it can be damp the low frequency oscillations in the best possible manner and significantly improves the stability performance of the system.

The proposed controller adaption process is done in each sampling period using a powerful adaption law based on BP algorithm. Also during the process the system sensitivity is provided by a powerful fast‐acting identifier. As an alternative to multi‐layer perceptron neural network, self‐recurrent wavelet neural networks (SRWNNs) which combine the properties such as attractor dynamics of recurrent neural network and the fast convergence of the wavelet neural network were proposed to identify synchronous generator. Also to help the OLSL‐PID stability first, PID parameters tuning problem under a wide range of operating conditions is converted to an optimization problem which solved by a chaotic optimization algorithm (COA), and afterwards PID controller is hooked up in the system and on‐line tuning is done in each sampling period.

Subsynchronous resonance (SSR) problem is often created in generator rotor systems with long shafts (non‐rigid shaft) and large inertias constituting a weakly damped mechanical system. When the electrical network resonance frequency (in which the transmission line is compensated by series capacitors) approaches shaft natural frequencies, the electrical system increases torsional torques amplitude on the shaft. The purpose of this paper is to propose a self‐tuning proportional, integral, derivative (PID) controller to damp the SSR oscillations in the power system with series compensated transmission lines.

To accommodate the PID controller in all power system loading conditions, the gradient descent (GD) method and a wavelet neural network (WNN) are used to update the PID gains on‐line. All parameters of the WNN are trained by the gradient descent method using adaptive learning rates (ALRs). The ALRs are derived from discrete Lyapunov stability theorem, which are applied to guarantee the convergence of the proposed control system. Also, the suggested controller is designed based on a non‐linear model.

The proposed self‐tuning PID controller is applied to a power system non‐linear model. Simulation results are used to demonstrate the effectiveness and performance of the proposed controller. It has been shown that self‐tuning PID is able to damp the SSR under any circumstances, because the WNN ensures the robustness of the controller. Simplicity and practicality of the proposed controller with its excellent performance make it ideal to be implemented in real excitation systems.

The proposed self‐tuning PID approach is interesting for the design of an intelligent control scheme based on non‐linear model to damp the torsional oscillations. In this suggested controller, the system conditions and requirements adjust on‐line the PID gains. On other words, to damp the SSR, PID gains are intelligently computed by the controlled system. The main contributions of this paper are: the overall control system is globally stable and hence, the SSR is controlled; the control error can be reduced to zero by appropriate chosen parameters and learning rates; and the self‐tuning PID can achieve favorable controlling performance.