SMALL SIGNAL STABILITY ENHANCEMENT USING POWER SYSTEM STABILIZER

Abstract

Modern power systems are large, complex and multi-component dynamic systems being prone to fluctuating characteristics with varying generation schedules and loads. These power systems suffer with small signal oscillations (SSOs) on occurrence of fault on system network and sudden changes in load changes of low magnitude and in the frequency range of 0.2 – 3.0 Hz. The power transfer capability of the system is restricted over the weak transmission lines because of the persistent oscillations. In late 1950s, the generators were equipped with high gain and fast acting automatic voltage regulators (AVRs) to improve the system voltage profile. The application of AVRs has invited the problem of small signal oscillations in the power system. The power system stabilizer (PSS) was added to AVR for modulate the excitation of the generator by improving electrical damping torque component in phase with rotor speed deviation, which in turn reduces the SSOs in the power system. The uniformly adopted type of PSS is known as conventional PSS (CPSS), which consists of the lead-lag type components. The CPSS suffers from some limitations as (a) these are designed off-line, therefore, requires re-tuning during commissioning, (b) these are tuned for one operating condition, therefore, may not perform properly for varying operating conditions and (c) because of changing conditions and configuration throughout the power system, they require retuning for good performance, regularly. The power system and control researchers have presented significant efforts to the design of CPSS after the pioneering contribution made by deMello and Concordia in 1969 [1]. The designs of PSS were followed by using modern control theory like adaptive control, optimal control and eigenvalue (pole) assignment. It is reported that the selection of PSS and design methodology is a complex iterative method around an operating point resulting to unsatisfactory operation. Lyapunov based adaptive control and self-tuning are effective methods but requires knowledge of power system dynamics. Artificial intelligence (AI) based tuning and learning processes such as fuzzy logic, adaptive fuzzy, neuro-fuzzy, artificial neural networks (ANNs) and type-2 fuzzy have been used to design effective PSS. In case of ANN, the gradient algorithm is being used to learn its parameters; either input/output parameters or online data at different operating points of a power system network. Another technological development was based on optimization methods to design PSS. The classical optimization methods were unable to converge for non-linear and non-differential engineering problems. Some of the optimization methods such as the genetic algorithm (GA), particle swarm optimization (PSO), simulated annealing (SA), and differential evolution (DE) algorithm, have been applied to large and complex power systems. ii It is worth mentioning that the designed PSS by every method (forth-coming) has been applied to three well known test power system models, such as single-machine infinite-bus (SMIB) power system, two-area four-machine ten-bus power system and New England ten-machine thirty nine-bus power system. In this thesis, Bat algorithm is used to tune the gain, pole - zero parameters of CPSS and tested with all three power system models. The designed BA-CPSS for SMIB system is compared to performance with that of CPSSs designed with different methods in [2-11]. The performance comparison of BA-CPSS over a wide range of operating conditions along with fault condition is compared with each above CPSSs. The performance comparing parameters such as integral of square of error (ISE) and integral of time weighted squares of error (ITSE) performance indices are initially introduced in [12]. In 1999 [12], Prof. Malik has used these indices to differentiate, two superimposed responses by two different PSSs. Therefore, the performance comparison is carried out using integral of time weighted absolute error (ITAE), integral of absolute error (IAE) and ISE as performance indices of speed response and found better as compared to others. The superiority of BA-CPSS is also validated for 231 plant conditions by plot of eigenvalue on s-plane and found to be within the D-shape sector which is the requirement of guaranteeing stability. In case of four-machine ten-bus power system, BA-CPSSs are compared with the controllers designed by different methods in [11, 13-19]. Again the better value of performance indices (ITAE, IAE and ISE) of speed response with proposed BA-CPSS as compared to others is able to prove its effectiveness over the others. The application of the bat algorithm to tune CPSS is also extended to New England 39-bus power system and performance are compared to that of with CPSSs reported in [11, 19-26]. The application of the bat algorithm is also applied to tune a proportional-integral-derivative based PSS and compared to PID-PSSs reported in [27-33] for SMIB power system. The application is extended to four-machine system and compared to Iterative Linear Matrix Inequality [34]. The bat algorithm based PID is also designed for New England ten-machine power system and compared with CPSSs reported in [11, 24, 35]. In continuation, the small signal stability is analyzed through the application of a fuzzy logic controller. The distinct fuzzy rule bases proposed by different researchers are arranged in groups with similar entries and numbered from 1 to 21 as reported in [12, 36-71]. Total 21 different fuzzy rule matrices (FRMs) have been detected and applied to SMIB system with a nominal operating condition for small signal stability analysis. It is worth mentioning that some of the rule bases have appeared with similar performances. Therefore, these 21 rule bases are re-arranged in categories with similar performances and resulting to 6 categories in the number. Based on superior performance, category-6 rule bases show the unstable results and category-1 iii [36-45, 52-54, 61] shows the best performance. As a core work, a new rule table is designed, and the performance is compared to rule base in category-1 [36-45, 52-54, 61] and category-2 [12, 49, 50, 55-59] with SMIB, four-machine and New England power system test systems and found superior in performance. The fuzzy logic controller lacks the mathematical reasoning, and the performance is reviewed by transient response of the closed-loop system. A small-signal model of the fuzzy logic power system stabilizer (FPSS) is derived to optimize the scaling factors using Harmony Search Algorithm (HSA) and Bat algorithm (BA). The derived such a small signal model of FPSS is proven to be a Proportional Derivative controller. Since the input of a fuzzy PSS can be error and derivative of error, therefore, changes in speed and acceleration are applied to input of FPSS. The parameters of the PD controller are considered as the normalized factors of the FPSS and are tuned using HSA and BA. The optimized PD controller is placed just before the FPSS and results to optimize the scaling factors of the FPSS. Such optimized FPSS using harmony search (HS-FPSS) and bat algorithm (BA-FPSS) is connected to SMIB, four-machine and ten-machine power system and the performance are compared to FPSS as in [72, 73]. Superior performance of BA-FPSS is validated for the wide range of operating conditions along with fault application. Another way of optimization of scaling factors is introduced by El-Hawary, 1998 as a book chapter in [74]. The main aspect to this approach is to apply a change in speed and change in power as input to FPSS and correction voltage at output. The scaling factors for input as well as output signals are optimized by Zonkoly in 2009 using particle swarm optimization [65]. The same approach is applied to three power system models using harmony search and bat algorithm and performance is compared to PSO-FPSS [65] and FPSS [72, 73] for SMIB system and FPSS [40, 41] for multimachine system. In both approaches, BA-FPSS proves to be the best performer as compared to its counter parts. The next generation of type-1 fuzzy sets is the interval type-2 fuzzy sets (IT2-FS) were again introduced by Zadeh in 1975. The stronger part of an interval type-2 fuzzy set is to model imprecision and uncertainty in a better way. These IT2-FS were developed by Mendel, who characterized IT2-FS as the footprint of uncertainty (FOU). In most of the cases, IT2 FS performance is better than its type-1 counterpart. Therefore, the evaluation and performance analysis of an interval type-2 fuzzy logic controller (IT2 FLC) as a power system stabilizer (PSS) is carried out. The single machine infinite bus (SMIB) system is considered for evaluation and implementation of IT2 FLC as PSS. The input signals to the controller are considered as speed deviation and acceleration. The evaluation of the controller is considered with 20 separate types of membership functions (MFs) and treated as IT2 FPSS on SMIB system to evaluate the performance of each. The performance of these MFs is evaluated graphically as well as in terms of iv ISE, IAE and ITAE as the performance index. The better suitable MF as FPSS is decided out of considered 20 MFs. The selected MF based IT2 FPSS is tested for small signal performance analysis of an SMIB system with wide operating conditions of a power system and extended to the four-machine system and ten-machine power systems. The thesis work may be a good source of different type of PSSs with application of new techniques in the field of small signal stability enhancement.