الگوریتم مصنوعی حداقل مربعات کلونی زنبور برای حل مشکلات برآورد هارمونیک

Solving harmonic estimation problems in power quality signals has attained significant importance in recent times. Stochastic optimization algorithms have been successfully employed to determine magnitude of this information in an unknown signal contaminated with noise or containing additive dc decaying components. The present paper shows how a recently proposed stochastic optimization algorithm, called artificial bee colony algorithm, can be hybridized with least square algorithm to solve these problems effectively. The proposed algorithm has been tested for a series of case studies employing different benchmark environment situations and our extensive simulation tests validate the usefulness of the proposed algorithm and it could largely outperform several competing simulation algorithms, proposed in the recent past. The effectiveness of the proposed algorithm is further demonstrated for those situations where the number of harmonics present in the signal is also not known, along with the magnitude and phase of each harmonic.

In recent times with significant progress in industrial scenario, the use of power electronic equipments have been increased manifold. With the increased use of converter-driven equipments (from consumer electronics to computers, adjustable speed drives etc.), these sophistications have also led to increasingly unwanted situations of significant growth in voltage waveform distortions. Due to the nonlinear characteristics of these equipments, the power system suffers from serious harmonic pollution. Besides, saturation of transformer core, generation of magnetic inrush current because of switching of transformer, etc. are the possible causes of generation of harmonics. Due to the asymmetrical nature of the magnetizing inrush current, even harmonics (in particular the second harmonic) appear to be the dominant ones in the harmonic spectrum [1]. Similarly, occurrence of faults in a power system, installation of capacitor bank in utility distribution system or in industrial power system can cause harmonic problems [2] and [3]. This harmonic pollution may cause several ill effects like worsening of power quality for end users, incurrence of greater loss in transmission lines, overheating of machines, malfunctioning of relays and breakers, etc. Harmonic studies play an important role in characterizing and understanding the extent of the harmonic problem. It includes estimation of parameters of the harmonics such as the amplitudes and phases, etc. This estimated information can be possibly advantageously used to compensate the harmonic components, by injecting suitable corresponding quantities in the power system. The content of frequency, their amplitudes and phases etc. depend on the nature of waveforms present which in turn, depend on the sources of harmonics or the causes of harmonics. So far, several research works have been reported in the literature to perform useful investigations on harmonic analysis. The most widely used computational algorithm for harmonic analysis, known so far, is the fast Fourier transform (FFT) [4], [5] and [19]. However, because of certain restrictions (aliasing, leakage, and picket fence phenomena) the FFT algorithms cannot compute the results accurately under certain undesirable conditions. In [6], [7], [20] and [21], an alternate approach was proposed utilizing a simple, linear and robust Kalman filtering approach. A frequency and phasor estimating algorithm using finite impulse response (FIR) filter and the concept of using a correction factor in this regard (called combine method or CM) was proposed in [8]. It was shown that this approach could overcome the shortcomings and eliminates the pitfalls present in FFT algorithm. In recent times, several new algorithms have been reported hybridizing a stochastic optimization algorithm, e.g. genetic algorithm (GA) inspired by the Darwinian law of survival of the fittest [9], particle swarm optimization (PSO) algorithm inspired by the social behavior of bird flocking or fish schooling [10], and fuzzy bacterial foraging (FBF) optimization algorithm inspired by Takagi–Sugeno fuzzy rule applied on intelligent foraging behavior of E. coli bacteria [11] and [22], with least square (LS) strategy to solve this problem. These algorithms essentially utilize the evolutionary optimization technique for phase estimation and the LS based approach for amplitude estimation. Such hybrid methods have shown encouraging performances in solving this category of problems essentially because the actual models of voltage and current signals are nonlinear in phase and linear in amplitude. In the present work, a new swarm intelligence computation based technique, called artificial bee colony (ABC) is used for estimating the phase of the fundamental and harmonic components, whereas the conventional LS technique is used for estimating the amplitude of these components. The ABC algorithm, which is one of the most recently introduced optimization algorithms, simulates the intelligent foraging behavior of a honey bee swarm and has been successfully employed in solving several engineering problems [13], [14], [23] and [24]. ABC broadly falls within the class of metaheuristic optimization based techniques that has been successfully employed to solve several other engineering problems which include prominent evolutionary optimization based algorithms like genetic algorithm (GA) [25], [26] and [27], evolutionary strategies (ES), genetic programming (GP), differential evolution (DE) [31] and [32], etc. swarm intelligence based techniques like particle swarm optimization (PSO) [28], [29], [30], [39] and [40], ant colony optimization (ACO), etc., foraging and social behavior based algorithms like bacterial foraging optimization (BFO) [33], [34], [35] and [36], biogeography based optimization (BBO) [37] and [38], honey bee mating optimization algorithm, etc. It has been shown as a rich, early promise, simple and robust population based optimization algorithm in solving several nonlinear optimization algorithms. The performance of the proposed algorithm is compared vis-à-vis several other competing algorithms e.g. FFT, PSO, GA and FBF based algorithms for estimating the power system harmonics, utilized for several benchmark case study problems. The competing algorithms proposed before were used to solve the harmonic estimation problem considering that the number of harmonics is known a priori and those algorithms were used to determine the amplitudes and phases of these harmonics. In addition to these, the present work has been efficiently employed to solve those harmonic estimation problems, where even the number of harmonics present in the signal is considered to be unknown. It has been used for several other case studies in those situations. The simulation results show that, overall, the performance of the proposed ABC–LS combined algorithm is significantly better than the above mentioned competing algorithms and hence it can be efficiently employed to solve such engineering problems with high dimensionality. The rest of the manuscript is organized as follows. Section 2 introduces the ABC algorithm in detail. Section 3 introduces how the harmonic estimation problem can be solved using ABC–LS combine algorithm. Section 4 presents the performance evaluations for extensive simulation case studies carried out. Section 5 presents the discussion and conclusion.

The present work has proposed a new algorithm of harmonic estimation which hybridizes a relatively recent metaheuristic optimization technique, Artificial bee colony algorithm, with conventional least squares method. The phases of different harmonic components are estimated using the ABC algorithm which is followed by the implementation of the LS method for determination of the respective magnitudes. The research work has explored two different possibilities of hybridizing these two methods. The first proposed strategy (named as ABC(1) algorithm) determines first the phases employing ABC and, at the end, determines the amplitudes using LS algorithm in a single pass. The second proposed strategy (named as ABC(2) algorithm) employs two algorithms sequentially, in an iterative manner, where within the ABC algorithm the LS algorithm determines the amplitudes on the basis of the phases determined by the ABC algorithm in that iteration. Our extensive experimentations demonstrated that both the proposed strategies could produce comparable overall results. However, the computational time consumed by ABC(1) algorithm is significantly lesser compared to ABC(2) algorithm and hence it is suggested that ABC(1) be employed in solving similar problems. It has been shown that the estimation problems for the distorted power system signals like currents or voltages, contaminated with noise and also containing dc decaying components, can be very accurately solved employing our proposed algorithm. The strength of the proposed research is also aptly demonstrated by employing it for various situations such as for solving the same problem with variations in sampling frequency and with variable window size. A great flexibility of the proposed algorithm is also demonstrated by employing it for a more difficult estimation problem where, in addition to the magnitude and phase of harmonic components, it is also assumed that the number of harmonics present in the waveform is not known a priori. The performances of the ABC algorithm have been compared with the performances of other recently proposed algorithms for similar problems employing conventional FFT algorithm and other contemporary, popular metaheuristic optimization algorithms employing GA, PSOPC and FBF methods. It has been aptly demonstrated that ABC could outperform, overall, these competing algorithms and hence could justify its involvement in proposing effective solutions for these problems. The authors feel that competing solutions can probably be proposed using other very popular branches of metaheuristic algorithms like DE and ACO. It is intended to develop such solutions and compare their performances vis-à-vis the performances obtained with ABC algorithm as a future scope of research work.