Particle swarm optimization

Chapter - 1INTRODUCTION1.1 PREAMBLEMultilevel voltage-source inverters are suitable configuration to reach high power ratings and high quality output waveforms besides reasonable dynamic responses. Among the different topologies for multilevel converters, the Cascaded Multilevel Inverter (CMLI) has received special attention due to its modularity and simplicity of control. The principle of 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 an s number of single-phase full-bridge inverters to generate (2s + 1) number of levels. However, from the practical point of view, it is somehow difficult to keep equal the magnitude of Separated DC Sources (SDCSs) of different levels. This is because of the different charging and discharging time intervals of DC-side voltage sources.To control the output voltage and to eliminate the undesired harmonics in multilevel converters with equal DC voltages, various modulation methods such as sinusoidal Pulse Width Modulation (PWM) and space-vector PWM techniques are suggested. However, PWM techniques are not able to eliminate lower order harmonics completely. Another approach is to choose the switching angles so that specific higher 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. A fundamental issue associated with such method is to obtain the arithmetic solution of nonlinear transcendental equations which contain trigonometric terms and naturally present multiple solutions. This set of nonlinear equations can be solved by iterative techniques such as the NewtonRaphson method. However, such techniques need a good initial guess which should be very close to the exact solution patterns. Furthermore, this method finds only one set of solutions depending on the initial guess. Therefore, the NewtonRaphson method is not feasible to solve the SHE problem for a large number of switching angles if good initial guesses are not available.A systematic approach to solve the SHE problem based on the mathematical theory of resultant, where transcendental equations that describe the SHE problem is converted into an equivalent set of polynomial equations and then the mathematical theory of resultant is utilized to find all possible sets of solutions for this equivalent problem.This method is also applied to Multilevel Inverters with unequal DC sources. However, applying the inequality of DC sources results to the asymmetry of the transcendental equation set to be solved and requires the solution of a set of high-degree equations, which is beyond the capability of contemporary computer algebra software tools. In fact, the resultant theory is limited to find up to six switching angles for equal DC voltages and up to three switching angles for non-equal DC voltage cases.More recently, the real-time calculation of switching angles with analytical proof is presented to minimize the Total Harmonic Distortion (THD) of the output voltage of multilevel converters. However, the presented analytical proofs only validate to minimize all harmonics including triples and cannot be extended to minimize only non-triple harmonics that are suitable for three-phase applications.The harmonic elimination for multilevel converters by Genetic Algorithm (GA) approach is only applied to equal DC sources and needs considerable computational time. Moreover, this method has not succeeded to find switching angles for some modulation indices which have solutions. This thesis presents a modern stochastic search technique based on Firefly Algorithm (FFA) to deal with the problem for equal DC sources.In this thesis, the FFA approach is developed to deal with the SHE problem with unequal DC sources while the number of switching angles is increased and the determination of these angles using conventional iterative methods as well as the resultant theory is not possible. In addition, for a low number of switching angles, the proposed FFA approach reduces the computational burden to find the optimal solution compared with iterative methods and the resultant theory approach. The proposed method is used to solve the asymmetric transcendental equation set of the harmonic minimization problem of the Cascaded Multilevel Inverter.

1.2 LITERATURE REVIEWMLIs have been drawing growing attention in the recent years especially in the distributed energy resources area because several batteries, fuel cells, solar cells or rectified wind turbines or micro turbines can be connected through a MLI to feed a load or interconnect to the AC grid without voltage balancing problems. In addition, MLIs have a lower switching frequency than standard PWM inverters and thus have reduced switching losses [1]. The development of MLI began in the early 1980s when Nabae et al proposed the NPC pulse width modulated inverter [2]. Since then several multilevel topologies, namely the diode clamped MLI, the flying capacitors MLI and cascaded MLI have evolved and are applied in adjustable speed drives, electric utilities and renewable energy systems [3-8]. Among the three MLI topologies, cascaded MLIs have more advantages than the other two. Cascaded MLIs require less component count in producing the same output voltage levels. They do not require a large number of clamping diodes and flying capacitors. They are easier to be modularized and soft switched and they do not have the problem of neutral point voltage unbalancing [9].Cascaded MLIs have been the subject of research in the last several years [10], where the DC sources were considered to be identical in that all of them were batteries, solar cells, fuel cells etc. In [11], a MLI was presented in which the two SDCS were the secondaries of two transformers coupled to the utility AC power. Corzine et al [28] have proposed a MLI using a single DC power source and capacitors for the other DC sources. A method was developed to transfer power from the DC power source to the capacitor in order to regulate the capacitor voltage. A similar approach was later proposed in [12] by Du et al. These approaches required a DC power source for each phase. The scope of this thesis has been restricted to the cascaded MLIs with SDCS for each H-bridge cell which are typically produced by using transformer/rectifier combination. The hot point in MLI research is its control strategies based on PWM.During the past two decades, variety of multilevel PWM methods have been proposed and researched which have significantly promoted the development of the field. Three multilevel PWM methods most discussed in the literature are Multilevel SVPWM, carrier based PWM and SHE [13-15].Carrara et al have successfully extended the basic two level sinusoidal PWM techniques to MLI and have shown three different ways to position the carrier waves. Calais et al analyzed the multicarrier PWM methods for a single phase five level inverter. Most of the modulation methods developed for MLIs are based on multiple carrier arrangements with PWM. The carrier can be arranged with vertical shifts (phase disposition, phase opposition disposition and alternative phase disposition PWM) [16].SHE is also extended for MLIs [17]. A different approach to the problem of harmonic elimination for PWM waveform generation was used in [18]. This approach is based on the use of Walsh series expansion of PWM waveforms rather than Fourier series. Walsh series were also applied for optimum PWM pattern in induction motor [19]. It is shown that the Walsh coefficients [19] of a PWM waveform are not only a function of PWM waveform angle but also of Walsh subinterval within which the angle lies. It is pointed out that the algorithm has the restriction that within a given interval, only one angle is allowed to vary and if there exists a solution that requires two or more angles to vary in the same selected interval, then such a solution cannot be detected by the method shown. Chiasson et al [20-22] used the mathematical theory of resultants to compute the optimum switching angles. The expressions involved were high order polynomials that could not be solved when the number of levels in the MLI became large. The switching times (angles) are chosen appropriately such that a desired fundamental output is generated and specifically chosen harmonics of the fundamental are suppressed [23-26]. In particular, the harmonic elimination approach in [24] produces a system of non-linear transcendental equations that requires the Newton-Raphson matrix method for its solutions.SHE methods such as Newton-Raphson method [24] and elimination by the theory of resultant [20] are complicated and time consuming. There are a few examples of applications of GA for power electronics in the literature [27-29] but only recently has GA been applied to Multilevel Inverters. FFA a global search technique for optimizing problem in [30, 31] is applied for optimizing the switching angles of MLIs in this work.

1.3 SCOPE AND OBJECTIVEIn this thesis, Firefly Algorithm is proposed for the solution of selective harmonic elimination problem. In this thesis work, Firefly Algorithm is used to find the switching angles of the Multilevel Inverter to minimize particular order harmonics. The proposed method is tested on an 11-level cascaded Inverter. The results of the proposed Firefly Algorithm technique show the elimination of selected harmonics in the output voltage of the Multilevel Inverter.

1.4 CHAPTER ORGANISATIONChapter 1Describes the Literature Survey, Scope and Objective.Chapter 2Deals the different types of Multilevel Inverter and development of harmonic optimization strategy.Chapter 3 Describes Firefly algorithm.Chapter 4 Presents the simulation results.Chapter 5Conclusion.

Chapter - 2DEVELOPMENT OF HARMONIC OPTIMIZATION STRATEGY FOR SINGLE PHASE CASCADED ELEVEN LEVEL INVERTER2.1 INTRODUCTIONThe problem of eliminating harmonics in inverter has been focus of research for many years. If the switching losses in an inverter are not a concern (i.e. switching on the order of a few kHz is acceptable) then the sine-triangle PWM method and its variants are very effective in controlling the inverter. This is because the generated harmonics are beyond the bandwidth of the system being actuated and therefore these harmonics do not dissipate power. Multilevel inversion is a control strategy in which the output voltage is obtained in steps thus bringing the output closer to a sine wave and reducing the THD [34]. The multilevel VSI is popularly used in high power industrial applications such as AC power supplies, static VAR compensators, drive systems etc. [33]. The outputs of MLIs are in stepped form, resulting in reduced harmonics compared to a square-wave inverter. To reduce the harmonics further, different multilevel SPWM and SVPWM schemes are suggested in the literature [35-36]; however these PWM techniques increase the control complexity and switching frequency. On the other hand, for systems where high switching efficiency is of utmost importance, it is desirable to keep the switching frequency much lower. In this case, another approach is to choose the switching times (angles) such that a desired fundamental output is generated and specifically chosen harmonics of the fundamental are suppressed [22-25]. This is referred to as selective harmonic elimination or programmed harmonic elimination as the switching angles are chosen or programmed to eliminate specific harmonics.SHEPWM has been intensively studied in order to achieve low THD [20]. The common characteristic of the SHEPWM method is that the waveform analysis is performed using Fourier theory. The selective harmonic elimination problem is formulated as a set of transcendental equations that must be solved to determine the time (angles) in an electrical cycle for turning the switching devices on and off in a full H-bridge inverter so as to produce a desired fundamental amplitude while eliminating particular order harmonics. These transcendental equations are mostly solved using iterative numerical techniques like Newton-Raphson method to compute the switching angles [24, 25]. This method is derivative dependent and may end in local optima, however a judicious choice of the initial values alone guarantees convergence [35, 36]. As an alternative solution to the harmonic optimization problem, Firefly Algorithm (FFA) technique is presented in this work. FFA solves the same problem with a simpler formulation and with any number of levels without extensive derivation of analytical expressions.

2.2 MULTILEVEL INVERTERSMLIs easily produce high-power, high-voltage output with the multilevel structure because of the way the device voltage stresses are controlled in the structure. Increasing the number of voltage levels in the inverter without requiring higher ratings on individual devices can increase the power rating. The unique structure of multilevel VSI allows them to reach high voltages with low harmonics without the use of transformers or series connected synchronized switching devices. As the number of voltage levels increases, the harmonic content of the output voltage decreases significantly[37].The MLIs synthesize a near sinusoidal voltage from several DC voltage sources. As the number of levels increases, the synthesized output has more steps, resembling a staircase wave that approaches a desired sinusoidal waveform. As the number of levels increases, the output voltage that can be spanned by summing multiple voltage levels also increases.MLIs have many attractive features like high voltage capability, reduced common mode voltages, near sinusoidal outputs, low dv/dt and smaller or even no output filter, making the inverters suitable for high power applications.

Fig. 2.1 MLI topologies (a) Diode clamped MLI (b) Flying capacitor MLI (c) Cascaded MLIThe MLIs can be classified into three types as shown in Fig. 2.1: i) Diode Clamped Multilevel Inverterii) Flying Capacitors Multilevel Inverter iii) Cascaded Multilevel Inverter Table 2.1 Comparison of power component requirements among three types of MLIsInverter ConfigurationDiode clampedMLIFlying capacitors MLICascaded MLI

Main switchingDevices2(m-1) 2(m-1) 2(m-1)

Main diodes2(m-1) 2(m-1) 2(m-1)

Clamping diodes(m-1)(m-2) 0 0

DC bus capacitors(m-1) (m-1) (m-1)/2

Balancing capacitors0 (m-1)(m-2)/2 0

Table 2.1 compares the power component requirements among three types of MLIs having m levels in the output. This table shows that the same number of main switches and main diodes are needed by the inverters to achieve the same number of m voltage levels in the output. Clamping diodes are not needed in flying capacitor and cascaded inverter configurations while balancing capacitors are not needed in diode clamped and cascaded inverter configurations. Implicitly, the cascaded MLI requires the least number of components to achieve given number of voltage levels and hence a sample cascaded seven level inverter is taken for study in this work.

2.3 CASCADED MULTILEVEL INVERTERThe power circuit (Fig.2.2 (a)) consists of a cascade of N independent single-phase inverters. These are of full-bridge configuration with SDCS, which may be batteries, fuel cells or solar cells and are connected in series. Each FBI unit can generate a three level output: +VDC, 0 or VDC by connecting the DC source to the AC load by different combinations of the four switches of each FBI. Using the top FBI as the example, turning on S11 and S41 yields +VDC output. Turning on S21 and S31 yields -VDC output. Turning off all switches yields 0 volts output. The AC output voltage at other FBIs can be obtained in the same manner. The number of voltage levels at the load generally defines the number of FBIs in cascade. The number of FBI units or DC sources N is (m-1)/2 where m is the sum of zero level and the number of positive and negative levels in MLI output. Each switching component turns ON and OFF only once per cycle i.e. at the line frequency.

Fig.2.2 (a) Cascaded Multilevel Inverter

The main features of cascaded Multilevel Inverters are: For real power conversions from DC to AC, the cascaded inverters need separate DC sources. The structure of SDCS is well suited for various renewable energy sources such as fuel cell, photovoltaic cell and biomass. It can generate almost sinusoidal output voltage while switching only one time per fundamental cycle. It can eliminate transformers of multi-pulse inverters used in conventional utility interfaces and static VAR compensators. Least number of components is required to achieve the same number of voltage levels. Optimized circuit layout and packaging are possible Soft-switching techniques can be used to reduce switching losses and device stresses.

Fig. 2.2 (b) Cyclic switching sequence of a sample seven level inverterFig. 2.2 (b) shows the cyclic switching sequence for a sample MLI. The switching strategies to generate +3VDC ,-3 VDC ,+2 VDC, -2 VDC ,+ VDC,- VDC ,0 at load are displayed in Fig. 2.2 (c) Fig. 2.2 (i). The Multilevel Inverters load voltage Va0 (Fig. 2.22(a)) is equal to the sum of the output voltages (Va1,Va2,.VaN) of the individual FBI units.

Fig.2.2 (c) Switching strategies to Fig.2.2 (d) Switching strategies to generate +3VDCat load generate -3VDC at load

Fig.2.2 (e) Switching strategies to Fig.2.2 (f) Switching strategies togenerate +2VDCat load generate -2VDC at load

Fig.2.2 (g) Switching strategies to Fig.2.2 (h) Switching strategies togenerate +VDCat load generate -VDC at load

Fig. 2.2 (i) Switching strategies to generate 0 volts at load

Fig. 2.3 Output of a 11 level Cascaded Multilevel Inverter

The use of transformers presents advantages particularly in terms of voltage matching, protection and insulation. The transformer increases the cost and reduces the overall efficiency of the compensator. These transformers 1) are the most expensive equipment in the system2) will produce about 50% of the total losses of the system3) will occupy a large area of real estate, about 40% of the total system4) will cause difficulties in control due to DC magnetizing and surge over voltage problems resulting from saturation of transformers and5) are unreliable.MLIs are an attractive option for a transformer-less series voltage sag/swell compensator. The number of possible voltage levels at the output generally defines the Multilevel Inverter topologies. The relatively low harmonic content of the unfiltered output voltage, compared to conventional inverters, is also an attractive feature. The voltage levels needed for compensation are provided in this work by a sample single phase seven level inverter structure consisting of three H-bridge inverters connected in series. The individual bridges are switched at line frequency when voltage step control is employed. Hence switching losses are reduced resulting in high efficiency and therefore operating costs of the compensator are low.

Fig. 2.4 sample Cascaded seven level topologyThe cascaded Multilevel Inverter has a separate DC source (VDC) for each individual FBI. Each FBI unit can generate a three-level output +VDC or -VDC. The Multilevel Inverter output voltage Va0 in Fig. 3.2 is equal to the sum of the output voltages of the individual FBI units (Va1, Va2,Va3) and can be controlled to produce a staircase waveform similar to that in Fig. 2.3.

The cascaded inverter structure is simple since no real power needs to be supplied other than the losses. The DC sources are floating and no transformer is required for coupling to the transmission system. For each FBI unit, the current rating is the nominal current of the transmission system. The AC output rating and therefore the DC source rating depend upon the total compensation voltage required, the number of converters and the sharing of the load voltage among individual units. One of the main advantages of this topology, compared to other multilevel topologies, is the fact that the maximum number of levels is only limited by isolation constraints. Its robustness and ease of control are also advantages.

Fig. 2.5 Four possible switching states for each FBI of MLI

2.4 HARMONICS IN POWER SYSTEMSOne of the biggest problems in power quality aspects is the harmonic contents in the electrical system. Harmonic in power circuits is created by non-sinusoidal loads which are integer multiples of the supply frequency. The rapid growth of power electronics has greatly increased the number and size of these loads, with the utility and their control. Harmonics are unnecessary high frequency voltages or currents flowing in a power system. Generally, harmonics may be divided into two types: 1) Voltage harmonics 2) Current harmonics Current harmonics are usually generated by harmonics contained in supply voltage and depend on the type of load such as resistive load, capacitive load and inductive load. Both harmonics can be generated by either the source or the load. Harmonics generated by load are caused by non-linear operation of devices including power converters, arc-furnaces, gas discharge lighting devices etc. Load harmonics can cause the overheating of the magnetic cores of transformer and motors. On the other hand, source harmonics are mainly generated by power supply with non-sinusoidal voltage. Voltage and current harmonics imply power losses, EMI and pulsating torque in AC motor drives. There are several methods to indicate the quantity of harmonic contents of a periodic wave. One among them is THD which is mathematically given by

and defined in terms of the amplitudes of the harmonics Hn at frequency n0 where 0is frequency of the fundamental component whose amplitude is H1and n is an integer. Since any periodic waveform can be shown to be the superposition of a fundamental and a set of harmonic components, by applying Fourier transformation, these components can be extracted. The frequency of each harmonic component is an integral multiple of its fundamental.2.4.1 EFFECTS OF HARMONICS(i)Sudden increase in demand reduced capacity utilization and increased energy losses.(ii)Increase in neutral current, overheating of motor windings, overloading of diesel generator sets, fire hazards due to burning of over-heated cables.(iii)Saturation of transformers, frequent damage to switchgears and controls.(iv)Amplification of harmonic currents in capacitor banks and frequent failure of capacitors.(v)Inaccurate and excess recording by power/energy meters.(vi)Interference with communication equipment.(vii)Nuisance, tripping of circuits and interruption in production flow.2.4.2 SOURCES OF HARMONICS Non-linear loads like thyristors/IGBT based drives/Variable Frequency drives Induction heating furnaces Arc furnaces Battery Charging Rectifiers UPSs SMPSs PCs Electronic chokes in lights.2.4.3 SYMPTOMS OF HARMONICS Blinking of incandescent bulbs Capacitor failure Circuit breaker tripping Computer malfunction or lock-up Conductor failure Failure of electronic equipment Flickering of fluorescent tubes Fuses blowing for no apparent reason Motor failures due to overheating Excessive neutral current. Neutral conductor and terminal failures Failure of electromagnetic loads Overheating of metal enclosures Power interference on voice communication

2.5 PROBLEM FORMULATION AND ANALYSIS FOR HARMONIC OPTIMIZATIONThe output voltage for a sample cascaded seven level Inverter is shown in Fig.2.4 for m=7 where m=number of steps in the positive and negative side after including the zero levels also. Switching angles to eliminate 5th,7th,11th and higher order are designed usually assuming that the peak fundamental output voltage is a desired fraction of its maximum value. For any Cascaded Multilevel Inverter, the output voltage isva0= va1+va2+.+vaN.(1)Where Due to the quarter wave symmetry along the x-axis in load voltage of Fig.2.3, both Fourier coefficients A0 and An are zero. Bn is defined as

Bn [k1sin(nt)d(t) +k2sin(nt)d(t) +. +kNsin(nt)d(t)]

.(2)which gives the instantaneous output voltage va0 as

.(3) Where Equation (3) provides the generalized Fourier series expansion of the output voltage. If the peak output voltage va0(peak) must equal to the carrier peak voltage vcr(peak), vcr(peak) = (m-1) VDC. Thus the modulation index M is

. (4)

Fig. 2.6 Inverter outputs and load voltage in a sample seven level inverterTwo predominating techniques in choosing the switching angles 1, 2 ,.. N are to:1) eliminate the lower frequency dominant harmonics or2) minimize the THD.The more popular and straight forward of the two techniques is the first, that is to eliminate the lower dominant harmonics and filter the output to remove the higher residual frequencies. Here the choice is also to eliminate the lower frequency harmonics. The goal here is to choose the switching angles 01< 2 itermaxIter=Iter+1BPrint the first firefly as the best solution.STOPbeta = beta0 * exp( - gamma * r2 )For all j=1 to nsij = [ij(1-beta)]+[nkjbeta]+[alpha(rand -0.5)]is k > ik=k+1i=i+1Ak = 1Find distance between fireflies i and kr = is i > nfYES3.3 FLOW CHART FOR SOLVING SHE PROBLEM USING FIREFLY ALGORITHM

Chapter-4SIMULATION RESULTS4.1 INTRODUCTIONThe nonlinear transcendental equation considering the non-equality of the DC sources are solved by using Firefly Algorithm (FFA) technique. The proposed algorithm is coded in MATLAB platform. The proposed algorithm gives the global optimum switching angles for the 11 level Cascaded Inverter. The 11 level Cascaded Multi Level Inverter used in this work was simulated in a MATLAB/SIMULINK platform. Fast Fourier Transform (FFT) of the output phase voltage and line voltage are plotted and given.4.2 MATLAB/SIMULINKMATLAB/SIMULINK is one of the most successful software packages currently available. It is a powerful, comprehensive and user friendly software package for simulation studies. A very nice feature of SIMULINK is that it visually represents the simulation process by using simulation block diagram. Especially, functions are then interconnected to form a SIMULINK block diagram that defines the system structure. Once the system structure is defined, Parameters are entered in the individual subsystem blocks that correspond to the given system data. Some additional simulation parameter must also be set to govern how the computation is carried out and the output data will be displayed. The block diagram of a sample five level Cascaded Multilevel Inverter is shown in the figure.4.3 MATLAB PLATFORMThe MATLAB platforms consist of five main parts. They are,a) Development Environment It incorporates a set of tools and facilities, which allows the use of MATLAB function and files. Most of these tools are of graphical user interface in nature. It includes the MATLAB desktop, a command window a command history, editor, debugger and browsers for viewing help, the workspace, files and the search path.

b) The MATLAB Mathematical function library This is a vast collection of computational algorithms ranging from elementary functions, like sum, sine, cosine, and complex arithmetic to more sophisticated functions such as matrix inverse, eigen values, basset functions, and Fast Fourier Transforms (FFT).c) The MATLAB languageThis is a high level matrix/ array language with control flow statement that serves to process functions, data structure, input/output, besides it includes object oriented programming.d) GraphicsMATLAB has extensive facilities for displaying vectors and matrix as graphs, besides annotating and printing the graphs. It includes high level function for two-dimensional and three dimensional data visualization, image processing, animation and presenting graphics.7.4 SIMULINK SIMULINK is an interactive tool for modeling, simulating and analyzing dynamic, multi domain systems. It lets the user to accurately describe, simulate, evaluate and refine a systems behavior through standard and custom block libraries. SIMULINK models serve to access MATLAB, providing flexible operation and an extensive range of analysis.7.4.1 Simpower system and physical modelingSimpower system models serves to simulate electrical power systems and drives in a SIMULINK environment. It facilitates to build circuits, develop algorithms, and incorporate controllers in the feedback path and enables to predict the performance of the modeled systems.7.5 SIMULATION RESULTSTo obtain an insight on the proposed optimization technique, a MATLAB simulation is carried out. The eleven level Cascaded Multi-level Inverter is simulated using MATLAB/SIMULINK block sets. The harmonic elimination problem of the Multi-Level Inverter was solved considering the non-equality of the DC sources. The magnitudes of the DC voltage levels in the experiment are considered as follows,

Table-4.1, DC voltage levels used in this thesis work.VDC1VDC2VDC3VDC4VDC5

120 94858276

Table: 4.2, output switching angles obtained using FFA and PSO.Modulation index (M)SWITCHING ANGLESTHD%

12345

0.6FFA36.8110 48.960859.618070.869883.98406.82

PSO36.9310 49.4483 60.232672.0874 85.34848.10

1FFA7.6400 15.341426.058236.920957.17454.79

PSO12.1793 23.0990 37.0486 58.6290 59.39606.60

1.062FFA4.8004 11.920821.932329.054443.19424.14

PSO6.8672 18.2654 25.9392 40.4031 59.19405.09

The above results are given with the following parameters of FFA and PSO.

FFANo. of fireflies: 100Itermax: 300Attractiveness coefficient () = 0.005 PSONo. of particles: 100Itermax: 300Cogitative parameter (C1) = 2Social parameter (C2) = 3

The calculated switching angles by the FFA method and the corresponding resulted objective function values are plotted with respect to the modulation index (M) in Fig. 4.1 and 4.2. The number of generations that evolve depends on whether an acceptable solution is reached or a set number of iteration is exceeded. In this paper, the maximum-number-of-iteration criterion is used to stop the algorithm. Moreover, the threshold of the cost to accept a solution is chosen to be 10-5. However, most of the time, the resulted cost values reached by the algorithm is below 210-6, which is many times better than the reported results for the GA method applied to the equal-dc-source case in [15]. By changing the dc-side voltage, the switching pattern has to be recalculated but, if not, there will be considerable harmonics in the output voltage waveform. Fig 4.3 shows the plot between modulation index (M) and the amplitude of the fundamental component.

Fig-4.1 (a)modulation index (M) Vs objective function

Fig-4.2 modulation index (M) Vs switching angles

Fig-4.3 modulation index (M) Vs fundamental voltage

The output voltage waveform for different modulation indices and the corresponding Fast Fourier transform (FFT) analysis are shown in fig(4.4 to 4.9). The output phase voltage of the eleven level Cascaded Multi Level Inverter for the optimum switching angle is given below.

Fig-4.4 (a)output phase voltage (M=0.6) (b)FFT analysis for phase voltage (M=0.6)

From the FFT plot of the phase voltage, it is observed that the 5th, 7th, 11th, 13th order harmonics are effectively minimized. THD is 43.92% with 3rd order harmonic dominating more than 40% of fundamental.

Fig-4.5 (a)output line voltage (M=0.6) (b)FFT analysis for line voltage (M=0.6)

From the FFT plot of the line voltage, the triplen harmonics are eliminated. Thus the total harmonic distortion further reduces. THD is 6.82%.

Fig-4.6 (a)output phase voltage (M=1) (b)FFT analysis for phase voltage (M=1)

From the FFT plot of the phase voltage, it is observed that the 5th, 7th, 11th, 13th order harmonics are effectively minimized. THD is 10.24%.

Fig-4.7 (a)output line voltage (M=1) (b)FFT analysis for line voltage (M=1)

From the FFT plot of the line voltage, the triplen harmonics are eliminated. Thus the total harmonic distortion further reduces. THD is 4.79%.

Fig-4.8 (a)output phase voltage (M=1.062) (b)FFT analysis for phase voltage (M=1.062)

From the FFT plot of the phase voltage, it is observed that the 5th, 7th, 11th, 13th order harmonics are effectively minimized. THD is 10.24%.

Fig-4.9 (a)output line voltage (M=1.062) (b)FFT analysis for phase voltage (M=1.062)

From the FFT plot of the line voltage, the triplen harmonics are eliminated. Thus the total harmonic distortion further reduces. THD is 4.14%.

Chapter-5CONCLUSIONInverters are used to convert DC input voltage to AC output voltage of desired magnitude and frequency. MLI structures have been developed to overcome short comings in solid-state switching device ratings, so that they can be applied to high voltage electrical systems. Cascaded type MLIs are taken for study in this work since they have been the subject of research in the last several years, where the DC sources are batteries, solar cells etc., SHE is implemented in chosen cascaded MLI by pre-calculating the switching angles of devices such that particular orders of harmonics are minimized. By employing Firefly Algorithm technique and by using MATLAB, the formulated non-linear asymmetric transcendental equations are solved to find the switching angles for minimizing the harmonics. The simulation results for output voltage and THD for the proposed technique is evaluated. The principle of operation of a sample seven level inverter non-carrier PWM technique for one phase is explained. Thus the harmonics in the output voltage of the Cascade Multilevel Inverter by considering the non-equality of separated DC sources is eliminated by using firefly algorithm. The simulation results are provided for an under modulation (M=0.6), critical modulation (M=1) and over modulation (M=1.062) an 11-level cascaded H-bridge inverter to validate the accuracy of the computational results.

REFERENCE[1] Nabae , I. Takahashi and H.Ahagi, A new neutral-point clamped PWM inverter, IEEE Trans. on Industry Applications, Vol.IA-17, pp. 518-523, Sep./Oct. 98.[2] B.Ozpineci, L.M.Tolbert and J.N.Chiasson, Harmonic optimization of multilevel converters using Genetic Algorithms, in Proceedings of IEEE Power Electronics Specialists Conference, 2004, pp. 3911-3916.[3] P.M.Bhagwat and U.R.Stefanovic, Generalized structure of multilevel PWM inverter, IEEE Trans. on Industry Applications, Vol. 1A-19, No.6, pp.1057-1069, Nov./Dec. 1983.[4] FeiWanmin, Lu Zhengu, YaWenni and Qian Zhaoming, Research on composite cascaded Multilevel converters and its control strategies, Transactions of China Electrochemical Society, Vol.19, pp.61-66, Aug. 2004.[5] T.A.Meynard and H.Foch, Multilevel chopper for high voltage applications, Journal of European Power Electronic Drives, Vol.2, No.1, March 1992.[6] M.Ohsato, G.Kimura and M.Shiya, Five stepped PWM inverter used in photovoltaic systems, IEEE Trans. on Industrial Electronics, Vol.38,pp.393-397, Oct. 1991.[7] R.W.Menzies et al, Five-level GTO inverter for large induction motor drives, IEEE Trans. on Industry Applications, Vol.30, No.4, pp.938-943, 1994.[8] E.Cengelci, S.V.Sulistijo, B.O.Woom, P.Enjeti, R.Teodorescu and F.Blaabjerge,A new medium voltage PWM inverter topology for adjustable speed drives, in Conference Rec., IEEE IAS Annual Meeting, St.Louis, MO, Oct. 1998,pp.1416-1423.[9] F.Z.Peng and J.S.Lai, Multilevel cascaded voltage source inverter with separate DC sources, U.S.Patent 5 642 275, June 24, 1997.[10] J.K.Steinke, Control strategy for a three phase AC traction drive with three level GTO PWM inverter, in Proceedings of IEEE Power Electronic Specialist Conference (PESC), 1998, pp.431-448.[11] M.Manjrekar, P.K.Steimer and T.A.Lipo, Hybrid multilevel power conversion system: A competitive solution for high power applications, IEEE Trans. on Industry Applications, Vol.36, pp.834-841, May/June 2000.[12] Z.Du, L.M.Tolbert, J.N.Chiasson and B.Ozpineci, Cascaded Multilevel Inverter using a single DC source, in Proceedings of the Applied Power Electronics Conference (APEC), 2006, Dallas TX, pp.426-430.[13] R.Luna, M.D.Manjrekar, P.Steimer and T.A.Lipo, Control strategies for a hybrid seven-level inverter, in Proceedings of EPE99, CDROM.[14] J.Vassallo, J.C.Clare and P.W.Wheeler, Power equalized harmonic-elimination scheme for utility-connected cascaded H-bridge multilevel converters, in Proceedings of the 29th Annual Conference of the IEEE Industrial Electronics Society, IECON03, 2003 ,Vol.2, pp.1185-1190.[15] M.Fracchia, T.Ghiara, M.Marchesoni and M.Mazzucchelli, Optimized modulation techniques for the generalized N-level converter, in Proceedings of IEEE PESC, 1992, pp.1205-1213.[16] B.P.McGrath and D.G.Holmes, Multi-carrier PWM strategies for multilevel inverters, IEEE Trans. on Industrial Electronics, Vol.49, No.4, pp.858-867, Aug. 2002.[17] L.Li, D.Czarkowski, Y.Liu and P.Pillay , Multilevel selective harmonic elimination PWM technique in series connected voltage inverters, in Proceedings of 33rd IAS Annual Meeting, Oct.1998, pp.1454-1461.[18] J.A.Aumadu and R.G.Hoft, Microprocessor based sinusoidal waveform synthesis using Walsh and related orthogonal functions, IEEE Trans. on Power Electronics, Vol.4, pp.234-241, 1989.[19] M.Razzaghi and J.Nazarzadeh, Optimum pulse-width modulated pattern in induction motor using Walsh functions, Electrical Power System Research, Vol.35, pp.87-91, 1995.[20] J.Chiasson, L.M.Tolbert, K.McKennzie and Z.Du, Eliminating harmonics in multilevel converter using resultant theory, in Proceedings of IEEE Power Electronics Specialists Conference, 2002, pp.503-508.[21] J.Chiasson, L.M.Tolbert, K.McKennzie and Z.Du, A complete solution to the harmonic elimination problem, IEEE Trans. on Power Electronics, Vol.19, No.2, pp.491-499, Mar. 2004.[22] J.Chiasson, L.M.Tolbert, K.McKennzie and Z.Du, A unified approach to solving the harmonic elimination equations in multilevel converters, IEEE Trans. on Power Electronics, Vol.19, No.2, pp.478-490, March 2004.[23] P.N.Enjeti, P.D.Ziogas and J.F.Lindsay, Programmed PWM techniques to eliminate harmonics: a critical evaluation, IEEE Trans. on Industry Applications, Vol.26, pp.302-316, Mar./Apr. 1990.[24] H.S.Patel and R.G.Hoft, Generalized harmonic elimination and voltage control in thyristors inverters: part-I-harmonic elimination, IEEE Trans. on Industry Applications, Vol.9, pp.310-317, May/June 1973.[25] H.S.Patel and R.G.Hoft, Generalized harmonic elimination and voltage control in thyristors inverters: part II-voltage control technique, IEEE Trans. on Industry Applications, Vol.10, pp.666-673, Sep./Oct. 1974.[26] J.Sun and I.Grotstollen, Pulsewidth modulation based on real time solution of algebraic harmonic elimination equations, in Proceedings of 20th Conference on Industrial Electronics and Control Instrumentation, IECON, 1994,Vol.1, pp.79-84.[27] A.I.Maswood, S.Wei and M.A.Rahman, A flexible way to generate PWM-SHE switching patterns using genetic algorithms, in Proceedings of IEEE Applied Power Electronics Conference Expo, 2001, pp.1130-1134.[28] M.J.Schutten and D.A.Torrey, Genetic algorithm for control of power converters, in Proceedings of IEEE Power Electronics Specialist Conference, 1995, pp.1321-1326.[29] K.Sundareswaran and A.P.Kumar, Voltage harmonic elimination in PWM AC chopper using genetic algorithm, IEE Proceedings-Electronic Power Applications, Vol.151, No.1, pp.26-31, 2004.[30] X.-S. Yang, Firefly algorithms for multimodal optimization, in: Stochastic Algorithms: Foundations and Applications, SAGA 2009, Lecture Notes in Computer Sciences, Vol.5792, pp. 169-178 (2009).[31] B. Rampriya, K. Mahadevan, S. Kannan, Unit commitment in deregulated power system using Lagrangian firefly algorithm, IEEE International Conference on Communication Control and Computing Technologies, pp389 393, 2010.[32] J.Rodriguez, J.S.Lai and F.Z.Peng, Multilevel Inverters: A survey of topologies, controls and applications, IEEE Trans. on Industrial Electronics, Vol. 49, No.4, pp.724-738, Aug. 2002.

[33] B.Shanthi and S.P.Natarajan, Carrier overlapping PWM methods for single phase cascaded five level inverter, International Journal of Science and Techniques of Automatic Control and Computer Engineering, (IJ-STA, Tunisia), Special issue on Control of Electrical Machines, pp.590-601, Dec.2008.[34] S.Siriroj, J.S.Lai and T.H.Liu, Optimum harmonic reduction with wide range of modulation indicies for Multilevel Inverters, in Conference Rec. IEEE-IAS Annual Meeting, Rome, Italy, Oct. 2000, pp.2094-2099.[35] T.J.Liang, R.M.OConnell and R.G.Hoff, Inverter harmonic reduction using Walsh function harmonic elimination method, IEEE Trans. on Industrial Electronics, Vol.12, No.6, pp.971-982, Nov.1997.[36] V.G. Agelidis, A.Balouktsis and L.Balouktsis, On applying a minimization technique to the harmonic elimination PWM control: the bipolar waveforms, IEEE Power Electronics Letters, Vol.2, pp.1-4, June 2004.[37] K.Gopakumar, J.Rodriguez, M.A.Perez, "A Survey on Cascaded Multilevel Inverters", IEEE Transactions on Industrial Electronics, July 2010, Vol. 57, No.7, pp2197 - 2206.41