^{1}

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^{2}

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^{3}

Multilevel inverters are used in many industrial applications because of good power quality, minimum losses and less harmonics contents. Multilevel inverters require no series connected synchronized switching devices, transformer and complex filters. In this paper 10, 18, 24 diode clamped multi-level inverters (DCMLI) are implemented using trust region dog leg optimization method to find the optimized values of switching angles ( θ). It decreases the total harmonic distortion (THD) of the output voltages and to reduce the complexity of external filter required. The multi-level inverters are implemented in MATLAB Simulation and results are compared in terms of harmonics, system complexity and efficiency.<

Different techniques like Sinusoidal pulse width modulation (SPWM), SVPWM and multilevel inverters are used for the conversion of DC into AC power [

Comparison between two diodes clamped inverter nerve point of converter (DNPC-3 l tests such as pre- employment) and (ANPC-3 l tests such as pre-employment) discussed options for switching energy volume [

H-bridge multilevel inverter flying capacitor using two different schemes of voltage balancing and equations used [

This proposed converter, diodes clamped multilevel inverters (DCMLI) for different levels of switching angles are calculated using the dog leg in order to minimize the total harmonic distortion (THD), improve the quality of the electricity voltage wave form, the overall efficiency of the inverter, as well as to study the relations of levels with THD.

Circuit diagrams of diode clamped multilevel inverters (DCMLI) 10, 18, 24 levels are shown in the Figures 1-3 respectively. DCMLI consists of two legs and each leg consists of two sub-systems connected in series. Each subsystem comprises

Switches of subsystem 1 are connected in series with subsystem 2 in one leg and similarly subsystem 3 with subsystem 4 in other leg. The output of the DCMLI is stepped stair case voltage levels as shown in ^{rd}, 5^{th}, 7^{th}, 11^{th} and 13^{th}, selective harmonic elimination technique is implemented using Trust Region Dog Leg, the flow diagram is shown in

DCMLI | Number of switches | Number of batteries | Number of diodes |
---|---|---|---|

10 level | 16 | 4 | 12 |

18 level | 32 | 8 | 56 |

24 level | 44 | 11 | 110 |

two methods ensures a fast convergence and a solution of function in the steepest descent direction. The second step involves finding the value of trust region radius to estimate length of step for the current iteration such that the following condition is obeyed. Trust region dog leg optimization technique is utilized to find out the optimized switching angles using a set of non-linear equations derived to selectively eliminate specific harmonics (Selective Harmonic Elimination). The set of non-linear equations are shown in Equations (14), (15) and (16) and trust region dog leg method determines the optimized switching angles to result a wave form with minimum Total Harmonic Distortion (THD).

For particular switching angle different switches are turned on, for 10 levels four switches and 8 for 18 levels and 11 for 24 levels are on in one leg and 4, 8 and 11 in another leg. Every switch is turned on and off only once in half cycle therefore the switching losses are low.

For positive cycle all switches of subsystem 3 are OFF and sub system 4 are ON. For negative cycle, switches

Output | Switches state of first leg for positive half cycle of 10 levels DCMLI | ||||||||
---|---|---|---|---|---|---|---|---|---|

1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | ||

0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | ||

0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | ||

0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | ||

0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | ||

of subsystem 3 and subsystem 4 are ON and OFF in the similar way and all switches of sub system 1 are OFF and subsystem’s 2 are ON. Similarly switching states of 18 and 24 levels are shown in

As shown in

From Fourier series the periodic function can be expressed as following

Here T is the fundamental period and

Multi-level inverters have odd quarter wave symmetry so they posse both odd and half wave symmetry. The Fourier coefficient for odd quarter wave symmetry simplifies to

Output | Switches state of first leg for positive half cycle of 18 level DCMLI | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||

0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||

0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | ||

0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | ||

0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | ||

0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | ||

0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | ||

0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | ||

0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

Switches state of 24 level DCMLI in both legs | ||
---|---|---|

Conducting switches | Non conducting switches | |

. . . | . . . | |

0 |

As

Integrating Equation (12) W.R.T switching angles

Equation (13) shows odd harmonics in DCMLI as switching angles. To eliminate 3^{rd}, 5^{th}, 7^{th}, 9^{th}, 11^{th} and 13^{th} harmonics and output peak voltage is controlled to v, harmonics equations results in

The values of switching angles can be calculated from these set of non-linear equations using iterative method.

Equation (14) can also be written as

where

Modulation index

s = No. of DC sources.

The total harmonic distortion is calculated from the following equation

^{nd}, 3^{rd} and n^{th} harmonics and

Computed values of switching angles in radians of 10, 18 and 24 levels DCMLI when dog leg method is applied are Tables 5-7.

Total harmonic distortion values and output voltage wave forms are observed for m = 0.9 and the variation in harmonics and the quality of output waveforms. The value of m is kept constant while total numbers of voltage levels in half cycle (0 - π) of output waveforms are increased gradually, when Voltage levels are increased the

Modulation index | ||||
---|---|---|---|---|

0.0942 | 0.3209 | 0.5219 | 0.8744 |

Modulation index | ||||||||
---|---|---|---|---|---|---|---|---|

0.1359 | 0.2103 | 0.3392 | 0.5003 | 0.6483 | 0.9308 | 1.0887 | 1.5631 |

Modulation index | ||||||
---|---|---|---|---|---|---|

0.0000 | 0.1502 | 0.2408 | 0.359 | 0.491 | ||

0.603 | 0.710 | 0.838 | 1.030 | 1.3253 | 1.5808 |

wave form gets closer to pure sinusoidal wave form and consequently the percent total harmonic distortion decreases. Total harmonic distortion (THD) depends on the 3^{rd}, 5^{th}, 7^{th}, 9^{th}, 11^{th}, and 13^{th} (in the proposed case) lower harmonics when levels are increased the harmonics results smaller peak values which decreases the THD value as shown in

Trust region dog leg method employing optimized switching angles has reduced total harmonic distortion in multilevel inverters compared to when non-optimized switching angles are considered. It is evident from the

DCMLI | % THD |
---|---|

10 Level | 9.76 |

18 Level | 5.91 |

24 Level | 3.80 |

results that an increasing number of voltage levels in the output waveforms decrease the total harmonic distortion (THD) and the output wave form gets closer to pure sinusoidal voltage plus overall efficiency of the system rises. Moreover, the number of battery sources, IGBTs and diodes required makes the system bulkier and expensive as the number of levels is increased but ensures a sooth input to the industrial load (e.g. AC Motor Drive runs with maximum torque, less noise and maximum efficiency when the higher level of multi-level inverter output is fed to it).

HaiderAli,Mohamed Z. H.Qawaqzeh,MuhammadAbbas,Takialddin AlSmadi, (2015) Implementation & Comparative Analysis of 10, 18 & 24 Level Diode Clamped Inverters Using “Trust Region Dog Leg” Method. Circuits and Systems,06,70-80. doi: 10.4236/cs.2015.63008