1 Multi-Variable Self-Tuning Feedback Linearization Controller for Power Oscillation Damping Jawad Arif, Member, IEEE, Swakshar Ray, Member, IEEE, and Balarko Chaudhuri, Senior Member, IEEE Abstract—The objective of this paper is to design a mea- surement based self-tuning controller which does not rely on accurate models and deals with nonlinearities in system response. A special form of neural network (NN) model called as feedback linearizable neural network (FLNN) compatible with feedback linearization technique is proposed for representation of non- linear power systems behaviour. Levenberg-Marquardt (LM) is applied in batch mode to improve the model estimation. A time varying feedback linearization controller (FBLC) is employed in conjunction with the FLNN-LM estimator to generate the con- trol signal. Validation of the performance of proposed algorithm is done through the modeling and simulating both normal and heavy loading of transmission lines, when the nonlinearities are pronounced. Case studies on a large scale 16-machine, 5-area power system are reported for different power flow scenarios, to prove the superiority of proposed scheme against a conventional model based controller. A coefficient vector Λ for FBLC is derived and utilized online at each time instant, to enhance the damping performance of controller. Index Terms—Self-tuning Control, Power Systems, Feedback Linearizable Neural Networks, Feedback Linearization Con- troller, Online Estimation. I. I NTRODUCTION E LECTRIC power supply systems are large, complex and highly interconnected. In many parts of the world, deregulation, restructuring and continued uncertainties of what is yet to come has led utilities to make different investment choices. The process of gaining permission to construct new lines has become extremely difficult, expensive, and time- consuming [1]. Also, with the increase of power flow through the tie-lines, the damping of inter-area modes degrade, exciting low frequency oscillations [2]; range: 0.1−1.0Hz. A number of incidents have been reported in the past due to such oscillatory instabilities [3]. Traditionally these oscillations are damped with the power system stabilizer (PSS), which provide a supplementary control action through the excitation control of the generator [4]. In recent years flexible ac transmission systems (FACTSs) devices [5] have proven effective in the damping of these oscillations where the supplementary control over voltage and power flow is exerted [6]. This ensures the better utilization of transmission system [7]. Power systems behaviour is highly nonlinear in nature. Under stressed operating conditions the nonlinear effects are J. Arif is former PhD Student at Imperial College London, SW7 2AZ, UK e-mail: jawad.arif@imperial.ac.uk. S. Ray is with GE Global Research, New York, USA e-mail: rays@ge.com. B. Chaudhuri is Senior Lecturer in the Department of Electrical and Electronic Engineering, Imperial College London, SW7 2AZ, UK e-mail: b.chaudhuri@imperial.ac.uk. more prominent. Thus the key challenge is to design the non- linear damping controller for the FACTS devices which takes account of nonlinearities and changes in operating conditions. Although, linear controllers are commonly designed to provide satisfactory performance around a single operating condition, their performance can be enhanced using robust control tech- niques [8]–[10]. However, following severe contingencies, the post-contingency system can be different from its nominal operating states and even beyond the performance radius of designed robust controllers. Thus, a self-tuning controller which takes account of the nonlinearities in system and adapts to the changes in operating conditions could potentially yield better results [11]. This controller relies solely on measured signals and has been proposed for PSSs [12] and FACTS devices [13], working in linear domain. A practical problem for any adaptive/self-tuning controller is that it does not have a nominal representation and hence is difficult to include in the nominal model for system studies. However, because of their self-tuning nature, they are expected to adapt/self-tune to the situation even though they were not considered in a study. For example, a conventional PSS designed without the knowledge of another adaptive/self-tuning PSS would work together in unison as the latter would have the information about updated (due to inclusion of the conventional PSS) dynamics at each sampling instant. Nonlinear model and the correct estimation of the model parameters is vital for the representation of power system dy- namics, especially under stressed operating conditions. Mostly, various neural networks models are used by researchers [14]– [19] for the accurate representation of the nonlinear systems which has the advantage of its generalization and learning ability [18]. In recent years, use of multi-layer perceptron (MLP), radial basis function (RBF), recurrent and simulta- neous recurrent neural network (RNN and SRN) has been reported for online estimation of input−output mapping of nonlinear systems [18], [20]–[22]. These methods typically use back-propagation (BP) or back-propagation through time (BPTT) to update online the neural network parameters. How- ever, the learning process of back propagation algorithm is slow [23], and they have limitations in terms of convergence time and accuracy [18], [20], [21]. In this work, an online Levenberg−Marquardt (LM) [24]–[27] algorithm is adopted to be used with nonlinear neural networks ensuring better accuracy and convergence. In our investigation of online estimation, the classical LM is adapted to work in sliding window batch mode. Neural network based control in linear/nonlinear form have been proposed in power systems [11], [16], [18], however,