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Procedia Technology 21 (2015) 651 - 657
SMART GRID Technologies, August 6-8, 2015
Selective Harmonic Elimination of Cascaded Multilevel Inverter
using BAT algorithm
K.Ganesana, K.Barathia, P.Chandrasekara*, D.Balajia
aVel Tech University, Avadi, Chennai-600062, India
Abstract
There are several procedures to solve the selective harmonic elimination (SHE) problem. In this paper, the elimination of undesired harmonics in a multilevel inverter with equal DC sources by using bat evolutionary optimization method is presented. SHE is an efficient method for achieving the desired fundamental component and eliminating selection harmonics. The recently developed evolutionary optimization method named BAT algorithm is used to solve the nonlinear transcendental equations of SHE problem. To verify the presented method accuracy, simulation and experimental results are provided for a 7-level cascaded multi-level inverter. The feasibility and effectiveness of the proposed algorithm is evaluated with intensive simulation. The obtained results show that the BAT algorithm is more efficient than Bee algorithm (BA) and Genetic algorithm (GA) in eliminating the selective harmonics which cause the lower total harmonic distortion (THD) in the output voltage.
© 2015Publishedby ElsevierLtd.Thisis anopenaccess article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of Amrita School of Engineering, Amrita Vishwa Vidyapeetham University Keywords: Selective harmonic elimination,; multilevel inverter; Bat optimization algorithm (BOA).
1. Introduction
Integrating multilevel inverters into medium and high voltage industrial applications, such as motor drives [1], flexible ac transmission system (FACTS) equipment [2], HVDC [3, 4] and renewable energy systems [5], is the issue of many ongoing researches. The most advantages of multilevel inverters are derived due to stepwise waveform of output voltage. The main advantages of multilevel inverters include: High power and voltage ratings and quality, more electromagnetic compatibility, lower switching losses, higher efficiency, higher voltage capability,
Corresponding author. Tel.: 919042991723 E-mail address: drchandrasekar@veltechuniv.edu.in
2212-0173 © 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of Amrita School of Engineering, Amrita Vishwa Vidyapeetham University doi: 10. 1016/j. protcy.2015.10.078
lower total harmonic distortion [6, 7]. Basically, there are three conventional topologies for multilevel inverters: flying capacitor [8], diode-clamped [9] and cascaded multilevel inverter with separate dc sources [10]. Among them, the cascaded multilevel inverter has received special attention due to its modularity and simplicity of control method [11, 12]. The principle operation of this inverter is usually based on synthesizing the desired output voltage waveform from several steps of voltage, which is typically obtained from DC voltage sources. There are different power circuit topologies for multilevel converters.
The most familiar power circuit topology for multilevel converters is based on the cascade connection of s number of single-phase full bridge inverters to generate (2s + 1) number of levels in the output voltage. However, from the practical point of view, it is difficult to keep equal the magnitude of separated dc sources (SDCSs) of different levels. This can be caused by the different charging and discharging time intervals of DC-side voltage sources [13]. One of the major topics in multilevel inverters is to eliminate the harmonics of output voltage. Output voltage of inverters must meet maximum THD limitations as specified in [14]. Basically, to control the output voltage and to eliminate the undesired harmonics in multilevel converters with equal DC voltage sources, there are four methods [15]. They are the fundamental frequency switching method, space vector control method [16], traditional pulse width modulation (PWM) control method and space vector PWM method [15, 17]. A large number of these methods which minimize the computational intricacy and obtaining good results have been proposed in the last 25 years [18]. Selective harmonic elimination method and THD minimization approach are other approaches which choose proper switching angles to eliminate low-order harmonics and minimize the THD of output voltage. In both cases low switching frequency and stepwise waveform of output voltage are considered. In THD minimization approach the objective is to specify the switching angles to achieve desired fundamental component with possible minimum THD [19, 20]. The objective of SHE method is to determine the switching angles so that specific lower order harmonics such as the 5th, 7th, 11th, and 13th are suppressed in the output voltage of the inverter. This method is known as selective harmonic elimination (SHE) or programmed PWM techniques in technical literature [21, 22]. SHE method utilizes a set of non-linear transcendental equations as the fitness or objective function that involves many local optimal [23]. There are three procedures to solve the SHE problem, analytical approach based on resultant theory method [24], numerical iterative techniques, such as Newton Raphson method [25] and evolutionary algorithms [26] such as genetic algorithm (GA) or particle swarm optimization (PSO) and etc. As illustrated before, SHE employs a fitness function aims to achieve the desired fundamental component and remove selective harmonics in the waveform of output voltage waveform. Various fitness functions can be defined for SHE problem [27, 28], which the purpose of all is the same. In this paper, the BOA approach is developed to deal SHE problem and determination of optimal switching angles subject to reduce THD further. Simulation and experimental results are provided for a 7- level cascaded multilevel inverter to show the validity of the proposed BOA method. This paper is organized as follows. Section 2 describes the configuration of multilevel inverters, output voltage and SHEPWM method. Section 3 describes the BOA method. Section 4 defines the fitness function of SHE problem. In Sections 5 and 6, the simulation and experimental results are illustrated. Finally in Section 7 a brief conclusion is presented.
2. Multilevel inverters
2.1. configuration of the cascaded seven-level inverter
Fig. 1 shows the structure of a single-phase cascaded 7-level converter topology with separate DC sources. A cascaded multilevel inverter consists of several single-phase full bridge inverters connected in series. The function of this multilevel inverter is to synthesize desired ac output voltage from several DC voltage sources connected to the individual inverter units. A cascaded multilevel inverter has advantages that have been offered in [29]. It should be pointed out that, unlike the flying-capacitor topologies and diode-clamped, isolated DC voltage sources are essential for each cell in each phase. The number of output-phase-voltage levels in a cascade multilevel inverter is 2s + 1, where s is the number of DC voltage sources. This topology recently becomes very popular in ac power supply and adjustable speed drive applications. This inverter can avoid extra clamping diodes or voltage balancing capacitors [30]. To obtain the three-phase structure, the outputs of three single-phase cascaded inverters can be connected in A or Y connection.
Fig. 1 Configuration of a single-phase cascaded seven-level inverter.
Fig. 2 The half cycle of the phase voltage of 7-level inverter.
2.2. Output Voltage Of Seven-Level Inverter
A half cycle of phase voltage of 7-level inverter that synthesized by several DC voltage sources is presented in Fig. 2. In this figure a1-a2 and a3 are switching angles.
2.3. Selective Harmonic Elimination PWM
A 7-level inverter waveform shown in Fig.2 has three variables a1-a2 and a3, and voltage levels are assumed to be equal. Switching angles are limited between zero and n/2 (0 < ai < n/2). Because of the phase voltage waveform is an odd function, so utilizing the Bat Optimization Algorithm for Selective Harmonic Elimination Strategy in the Cascaded Multilevel Inverter 9 the even order harmonics become zero. Therefore its Fourier expansion will be contained only odd harmonic components. Considering equal amplitude of all DC voltage sources, the Fourier series expansion of the output voltage waveform, shown in Fig. 2, will be written as:
V (rot) = X® n=1 Vnsin (nrot) (1)
Where Vn is the amplitude of the nth harmonic component.
As illustrated before, switching angles are limited between zero and n/2 (0 < ai < n/2). Consequently, Vn becomes: f(n) = { 4 nn /Vdc Xs i=1 cos(nai) , n=odd
0 , n=even (2)
The purpose of SHE-PWM is to eliminate the lower order harmonics while remaining harmonics are removed by filter. In this paper, without loss of generality, a 7-level cascaded inverter is chosen as a case study to eliminate its low-order harmonics (fifth and seventh). It is needless to take the triple harmonics into consideration, since they will disappear for three-phase applications, in the line-to-line voltages. So, to satisfy fundamental harmonic and eliminate fifth and seventh harmonics, three nonlinear equations with three angles are provided as follows: V1 = 4 n Vdc(cos(a1) + cos(a2) + cos(a3)) V5 = 4 5n Vdc (cos (5a1) + cos (5a2) + cos(5a3))
V7 = 4 7n Vdc (cos (7a1) + cos (7a2) + cos (7a3)) (3)
In (3), V5 and V7 are set to zero in order to eliminate fifth and seventh harmonics, respectively. For obtaining various switching angles, a new index titled modulation index is determined to be a representative of V1 : M=V1/sVdc (4)
For 7-level inverter s will be equal 3. By substituting (4) into (3), the nonlinear equation (5) can be derived and for a 7-level inverter the goal is to solve these equation. M = 4 3n (cos(al) + cos(a2) + cos(a3)) 0 = (cos(5a1) + cos(5a2) + cos(5a3)) 0 = (cos(7a1) + cos(7a2) + cos(7a3)) (5) Now, three optimal switching angles, namely a1-a2 and a3, must be found with respect to the modulation index M.
3. Proposed Bat Algorithm
If we idealize some of the echolocation characteristics of microbars, we can develop various bat-inspired algorithms or bat algorithms. For simplicity, we now use the following approximate or idealized rules:
1. All bats use echolocation to sense distance, and they also 'know' the difference between food/prey and background barriers in some magical way;
2. Bats fly randomly with velocity vi at position xi with a fixed frequency fmin, varying wavelength _ and loudness A0 to search for prey. They can automatically adjust the wavelength (or frequency) of their emitted pulses and adjust the rate of pulse emission r 2 [0, 1], depending on the proximity of their target
3. Although the loudness can vary in many ways, we assume that the loudness varies from a large (positive) AO to a minimum constant value Amin.
Modulation Index
Fig. 3 Optimal switching angles (degree) versus modulation index, for fitness function (7).
0.2 M 4.4 II.« I 1.2
Modulation Index
Fig. 4 (a) The optimum value of cost function (b) Normalized amplitude of fundamental harmonic.
= u v v 'i V/^-; •
il ll_2 0.4 0.6 O.N
Modulation Index
Fig. 5 (a) Normalized amplitude of 5th harmonic (b) 7th harmonic (Vh /3Vdc).
4. Definition Of The Fitness Function For SHE Problem
Determination of switching angles to meet the Fitness function is the main goal of proposed approach. Satisfying the desired value of fundamental component with eliminating the undesired harmonics are considered as the fitness function. In this paper BOA. is utilized to solve the SHE problem. The number of harmonic components which can be eliminated from the output voltage of the 2s+1 level inverter is s- 1, where s is the number of separate DC voltage sources. Fitness function of seven-level inverter is considered combination of three nonlinear equations (5) that satisfy fundamental component and eliminate fifth and seventh harmonics. In (3), fundamental, fifth and seventh harmonics are achieved, respectively and will be used in (7). With previous descriptions, constructed fitness function and its restrictions are shown, respectively, in the fitness functions are defined as follows [24]:
100 *[ M - |V1| sVdc + (|V5| + |V7| + ■ ■ ■ + |V3s-2orV3s-1| sVdc ) ] (7)
Subject to: 0 < al < a2 < a3 < n 2 Where V1 is the desired fundamental component of phase voltage and M is modulation index.
5. Simulation Result
To validate of the simulation results for optimum switching angles, a simulation is carried out in MATLAB/SIMULINK software for a 7-level cascaded inverter.
1.99 Time It)
Fig. 6 Simulation results of a 7-level multilevel inverter for M = 1.17, (a) Output phase voltage (b) Output line voltage (c) FFT analysis for phase
voltage (d) FFT analysis for line voltage.
6. Conclusion
In this paper, the BAT evolutionary optimization method to solve the SHE problem is investigated. The simulation and experimental results are provided for a 7-level cascaded multi-level inverter to validate the accuracy and effectiveness of the proposed BOA method for convergence objective. Based on obtained results, the presented method in this paper is compared to previous works based on BA and GA which shows that suggested method satisfying the fundamental component and eliminating the undesired low order harmonics simultaneity is well done. From the experiment we found that the percentage of THD is more in BA and GA techniques than that of BOA technique.
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