Sanjeeb Kumar Kar

Orthogonal functions approach to optimal control of delay systems with reverse time terms

Using block-pulse functions (BPFs)/shifted Legendre polynomials (SLPs) a unified approach for computing optimal control law of linear time-varying time-delay systems with reverse time terms and quadratic performance index is discussed in this paper. The governing delay-differential equations of dynamical systems are converted into linear algebraic equations by using operational matrices of orthogonal functions (BPFs and SLPs). The problem of finding optimal control law is thus reduced to the problem of solving algebraic equations. One example is included to demonstrate the applicability of the proposed approach.

Comments on "Optimal control via Fourier series of operational matrix of integration"

In the last four decades, the orthogonal functions approach has been extensively applied to study problems like analysis, identification, and control of continuous-time dynamical systems. The success of this approach lies in the fact that it converts calculus into algebra approximately in the sense of least squares. Sine-cosine functions are a class of orthogonal functions, and they were applied to study the optimal control problem with some success. In order to have a computationally attractive method for solving the optimal control problem via sine-cosine functions, an attempt was made. In this note, we show that the Fourier series approach to the optimal control problem in a paper by Endow (Optimal control via Fourier series of operational matrix of integration, IEEE Trans. Autom. Control, vol. 34, no. 7, p. 770-3, Jul. 1989) is incorrect.

Optimal control of multi-delay systems via shifted Legendre polynomials

Based on using shifted Legendre polynomials (SLPs) a new approach for computing optimal control law of linear time-invariant/time-varying, time-delay free/time-delay dynamic systems with quadratic performance index is discussed in this paper. The governing delay-differential equations of dynamic systems are converted into linear algebraic equations by using the operational matrices of differentiation, integration, delay and product of SLPs. Thus, the problem of finding optimal control law is reduced to the problem of solving algebraic equations obtained via the operational matrices. Numerical examples are included to demonstrate the applicability of the proposed approach.

Voltage and frequency control of a micro-grid using a fuzzy logic controller based STATCOM equiped with battery energy storage system

It has become now a big challenging task to generate electricity in remote locations without the help of any external energy sources. One of the most effective solution to encounter this problem is the use of self excited induction generator producing electricity even in the absence of external energy source. Though self excited induction generator can act as a good isolated source of electricity, one of its greatest disadvantage is its fluctuating nature of voltage and frequency under varying load condition. Here in this paper we have considered a self excited induction generator along with a doubly fed induction generator with the former connected to the latter by a transmission line to form the proposed micro-grid system. The problems associated with the system are the varying nature of voltage and frequency which can be observed under different loading conditions such as linear load, nonlinear load, and dynamic load. The system also comprises of also a STATCOM with battery energy storage system which acts in order to balance the deviation resulted in the reactive and active power thereby maintaining the voltage and frequency. The controller used in this work is a fuzzy logic controller which carries out the controlling action through the STATCOM. The simulation for the above model is done in MATLAB / SIMULINK.

Voltage profile improvement of a two generator based micro grid system using STATCOM

Power shortage has become a very serious problem for the power distribution and consumers. Along with it, power demand at remote locations and providing uninterrupted power have created more challenges which have to be dealt with. The most feasible solution for these problems is distributed generation or formation of micro-grids involving renewable energy sources. But micro-grids suffer from voltage fluctuations and power oscillations, which increase the instability of the system. Use of FACTS devices can be effective for improvement of the stability of the micro-grid system. This paper presents a micro-grid system comprising of two diesel generating units using alternators and a load. A STATCOM is connected to the load bus for the voltage profile improvement of the system. Dynamic modeling of the micro-grid system is done and the system is simulated with and without STATCOM. The results are analyzed. The system is simulated using MATLAB/SIMULINK environment.

Sliding mode controller based decoupled control of STATCOM for voltage profile improvement in a micro grid system

Micro grids have become ultimate solution to the energy crisis in the world. But the micro grid are most vulnerable while working in the isolated mode. Because due to the small generation capacity and highly fluctuating loads the voltage profile of the micro grid system deteriorates, which undesirable voltage dips and even causes instability. To get rid of these problems many FACTS devices have been developed which can compensate reactive power of the system rapidly. In this work micro grid system is considered which constitutes of an alternator feeding a concentrated load through a transmission line. A STATCOM is connected at the load bus to improve the voltage profile of the system. The STATCOM is controlled by a control scheme which enables fast and decoupled control of active and reactive power. Sliding mode controllers, which are considered to be fast and robust are designed and implemented for the power control purpose of the STATCOM. The performance of the micro grid is simulated and analyzed with and without STATCOM, and the results are presented. The simulation is done in Matlab/Simulink platform.

Automatic generation control of multi-area thermal power system using TLBO algorithm optimized fuzzy-PID controller

This paper deals with design and performance scrutiny of automatic generation control (AGC) of a multi area interconnected power system. Here three thermal systems with equal ratings have been considered. Single input Fuzzy proportional integral-derivative (FPID) controller is used to study the transient response of the proposed system. In order to get realistic approach turbine time constant along with the governor dead band are used in all the three areas. The gains of FPID controller is optimized by using Teaching Learning Based Optimization (TLBO) technique & Particle Swarm Optimization (PSO). Step load perturbation (SLP) of 1 % is applied in area 1 to study the performance of the proposed controller. Finally it is observed that TLBO algorithm yields better dynamic performance.

Fuzzy-PID controller optimized TLBO algorithm on automatic generation control of a two-area interconnected power system

Design and performance analysis of load flow frequency of a two area four unit interconnected non-reheat thermal power system is depicted in this paper. Two different controllers that are fuzzy proportional integral-derivative (FPID) controller & proportional integral-derivative (PID) are used to study transient response of the proposed system. Area1 consists of two thermal generating units with non-reheat turbines as well as area2 also. The gains of FPID & PID controllers are optimized by using a novel Teaching Learning Based Optimization (TLBO) technique. Step load of 10 % is applied to area1 to study dynamic performance of different proposed controller. Finally it is observed that the FPID controller of single input configuration performs better than the other.

Performance improvement of a STATCOM using fuzzy controller for isolated generator

Purpose This paper aims to demonstrate the efficacy of fuzzy logic controller (FLC) over proportional integral (PI) and sliding mode controller (SMC) for maintaining flat voltage profile at the load bus of a single-generator-based micro-grid system using STATCOM. Design/methodology/approach A STATCOM is used to improve the voltage profile of the load bus. The performance of the STATCOM is evaluated by using three different controllers: PI controllers, FLCs and SMCs. The performance comparison of the controllers is done with different dc bus voltages, different load bus voltage references, various loads such as R-L loads and dynamic loads. Findings A comparative analysis is done between the performances of the three different controllers. The comparative study culminates that FLC is found to be superior than the other proposed controllers. SMC is a close competitor of fuzzy controller. Originality/value Design of fuzzy logic and SMCs for a STATCOM implemented in a single-generator-based micro-grid system is applied.

A sliding mode controller-based STATCOM for voltage profile improvement of micro-grids

Purpose The purpose of this paper is to evaluate the suitability and robustness of sliding mode controller (SMC) for maintaining flat voltage profile at the load bus of two different micro-grid systems using STATCOM. Design/methodology/approach Two micro-grid systems are dynamically modelled and simulated using MATLAB/Simulink. The first micro-grid has a single diesel engine-driven synchronous generator. The second micro-grid has one diesel engine-driven synchronous generator and a doubly fed induction generator-based wind energy conversion system. The STATCOM is connected to the load bus in both the micro-grids. SMC is used for the control of STATCOM for voltage profile improvement of micro-grid. The performance of SMC-based STATCOM is analysed and compared with the performance of conventional PI controller-based STATCOM. Findings The SMCs are more suited for STATCOM control as these are more immune to load disturbances even with the presence of wind energy generators. The voltage deviations and the steady state errors in voltage are less with SMC. Although SMC introduces a bit of steady state error in the dc link voltage of the STATCOM, it is much less than the settling limit of 2 per cent, which is quite acceptable. SMC proves to be better than conventional PI controllers in both the proposed models of micro-grid. Originality/value Design of a robust first-order SMC for a STATCOM is used for voltage profile improvement in two different micro-grid systems.