Arpita Sinha

Analytical structure and stability analysis of a fuzzy PID controller

Analytical structure for a fuzzy PID controller is introduced by employing two fuzzy sets for each of the three input variables and four fuzzy sets for the output variable. This structure is derived via left and right trapezoidal membership functions for inputs, trapezoidal membership functions for output, algebraic product triangular norm, bounded sum triangular co-norm, Mamdani minimum inference method, and center of sums (COS) defuzzification method. Conditions for bounded-input bounded-output (BIBO) stability are derived using the Small Gain Theorem. Finally, two numerical examples along with their simulation results are included to demonstrate the effectiveness of the simplest fuzzy PID controller.

Mathematical models of the simplest fuzzy PI/PD controllers with skewed input and output fuzzy sets

This paper unveils mathematical models for fuzzy PI/PD controllers which employ two skewed fuzzy sets for each of the two-input variables and three skewed fuzzy sets for the output variable. The basic constituents of these models are Gamma-type and L-type membership functions for each input, trapezoidal/triangular membership functions for output, intersection/algebraic product triangular norm, maximum/drastic sum triangular conorm, Mamdani minimum/Larsen product/drastic product inference method, and center of sums defuzzification method. The existing simplest fuzzy PI/PD controller structures derived via symmetrical fuzzy sets become special cases of the mathematical models revealed in this paper. Finally, a numerical example along with its simulation results are included to demonstrate the effectiveness of the simplest fuzzy PI controllers.

Analytical Structures for Fuzzy PID Controllers

In this paper, analytical structures for fuzzy proportional-integral-derivative (PID) controllers are derived by using triangular membership functions for inputs, singletons, or triangular membership functions for output, minimum triangular norm, maximum or drastic sum triangular conorm, Mamdani minimum, drastic or Larsen product inference, nonlinear control rules, and center-of-sum defuzzification. It is shown that these analytical structures are not suitable for control purpose. In this context, it is extremely important to note that the analytical structures reported by Carvajal et al. are also not valid for control.

A study on real and reactive power optimization using Particle Swarm Optimization

This paper presents a method of optimizing real and reactive power in Power Systems. A comparative study is made on simultaneous and sequential optimization of real and reactive power subproblems. For active power optimization generator real power outputs are taken as control variables and cost minimization is the objective. For reactive power optimization generator bus voltages, shunt capacitors/reactors, and transformer tap positions are taken as control variables while cost minimization/loss minimization is taken as objective. For simultaneous optimization of both the subproblems are formulated as cost minimization problem. Particle Swarm Optimization method is used for solving this complex, non-linear, non-convex optimization problem. Simulations are carried out on standard IEEE 30 bus system and results are presented.

The simplest fuzzy two-term controllers: mathematical models and stability analysis

This paper reveals mathematical models for some simplest fuzzy two-term (PI/PD) controllers which employ two symmetric fuzzy sets for each of the two input variables and three symmetric fuzzy sets for the output variable. The basic constituents of these models are Γ-function type and L-function type membership functions for the input variables and triangular membership functions for the output variable, minimum triangular norm, algebraic sum triangular conorm, different inference methods and Centre of Sums (COS) defuzzification method. The properties of these models are studied to examine their suitability for control application. Using the well-known small-gain theorem, sufficient condition for Bounded-Input Bounded-Output (BIBO) stability of a feedback system, containing any fuzzy controller as a subsystem, is established. Finally, some numerical examples along with their simulation results are included to demonstrate the effectiveness of the simplest fuzzy PI/PD controllers.

Identification and Localization of Multi-source Partial Discharges by Acoustic Measurements in Oil-pressboard Insulation System

Partial discharges (PD) deteriorate insulation of power apparatus and lead to final failure. Early detection and localization of PD can avoid unwanted failure of power apparatus. There are different techniques for PD detection. Acoustic emission technique for partial discharge detection is advantageous for online detection and source location. Normally, acoustic PD detection and location is based on the assumption of a single PD source. But in practice, more than one source of PD is present and they may be active simultaneously in a power apparatus. This paper addresses the identification and localization of two simultaneous PD sources employing acoustic emission technique in oil pressboard insulation system. The PDAE signals from two simultaneous PD sources are analyzed using wavelet analysis with time frequency resolution and Independent Component Analysis for identification and localization.

On the simplest fuzzy two - term controller structure derived via algebraic product t-norm - bounded sum t-conorm - Mamdani minimum inference combination

Patael and Mohan (2002, Automatica, 38, 981-993) state that the analytical structure of the simplest fuzzy PI controller, derived via algebraic product t-norm, bounded sum t-conorm and Mamdani minimum inference, is not suitable for control purpose. Here we show that the above statement is incorrect, and the above analytical structure is very much suitable for control. Moreover, using the well-known small gain theorem we establish sufficient conditions for bounded-input bounded-output (BIBO) stability of feedback systems containing the above controller as a subsystem.

Modeling and real-time simulation of an AC microgrid with solar photovoltaic system

With the increasing growth of renewable energy sources, it is important to understand and analyze its effect on the overall power system. The real-time simulation is a platform that allows virtual plant and controller to be thoroughly investigated before they can be implemented in an actual system. In a valid real-time simulation, the virtual model closely resembles its physical counterpart. It promotes flexibility of operation, faster simulation with no risk of component failure under any contingency analysis. This paper presents modeling and simulation of an AC microgrid with a solar photovoltaic system, in a real time environment using HYPERSIM from Opal-RT. The photovoltaic system is connected to a 15 node test distribution network to examine its interaction with the AC grid. Various case studies like steady state operation, step changes in irradiation, generation outage, and three-phase to the ground fault have been carried out in the real time simulator, HYPERSIM. This preliminary real-time electrical transients simulation with the modeled AC microgrid can be useful for beginners in this field, using HYPERSIM.

Behavior of Acoustic Partial Discharge Signal in Oil-Pressboard Insulation System

Online monitoring of partial discharges (PD) can reduce the risk of catastrophic failure of power apparatus. Acoustic emission technique is advantageous for online PD measurement. PDs are classified according to the origin of discharges and their effects on insulation deterioration are also different. Acoustic emission (AE) signal produced by PD are detected by sensors mounted on the experimental tank surface, stored on an oscilloscope and fed to computer for analysis. PDAE signal propagates from source to sensor through oil and pressboard insulation. This paper discusses the effects of different thicknesses of pressboard insulation barrier on the propagation path of partial discharge acoustic emission signal. PD may occur at surface of insulation having different thickness at different voltages. This paper also discusses the effect of insulation thickness on surface discharge. The behavior of PDAE signal at different voltage level is also discussed. The AE signals are analyzed using FFT and DWT. The parameters calculated are frequency at peak magnitude & median frequency from FFT data and percentage signal energy in different frequency bands from DWT data. Effect of applied voltage beyond PD inception voltage is also examined. Acoustic PD magnitude (mV) and electrical PD magnitude (pC) relation for different electrode system is investigated.

Classification of acoustic emission based partial discharge in oil pressboard insulation system using Fractal Features

Oil pressboard insulation used in transformer deteriorates due to partial discharge (PD). This paper reports experimental results and analysis for classification of PDs using acoustic emission (AE) signal of laboratory simulated PDs in oil pressboard insulation system using three different electrode systems. AE signal produced by PD are detected by sensors mounted on the experimental tank surface, stored on an oscilloscope and fed to computer for further analysis. The measured AE signals are analyzed using Fractal Features. A variety of algorithms are available for computation of Fractal Dimension. In this paper, Box counting and Higuchis algorithm for the determination of fractal dimension, Lacunarity and Approximate Entropy are used for the extraction of fractal features from the time domain PD AE signals. There are significant overlaps of few features for different types of PDs. But few features are distinct for different types of PDs. These features are used for the classification PDs.