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The main objective of this paper is to reduce the total harmonics in a single phase voltage source inverter using Artificial Bee Colony (ABC) optimization technique for critical load applications. Single phase inverter is a non-linear load using power electronic components causing distortions in the load voltage and current wave patterns from the sinusoidal waveforms due to harmonics. The mapping state space model for a full bridge voltage source inverter was developed using output load resistance. An optimal ABC technique has been designed and optimized values are estimated using a full bridge voltage controlled inverter using Proportional Integral Algorithm. The MATLAB/SIMULINK tool and Experimental setup were implemented and their THD values were estimated. Also this ABC scheme is compared with the previous results such as PI Algorithm, Fuzzy logic controller and Neuro-fuzzy controllers. From the simulation and experimental results using ABC algorithm, it is observed that the total harmonics are mitigated considerably compared to previous results with respect to the power quality standards such as IEEE-519 and IEC 61000.

Inverter is a power electronics setup used to generate AC voltage from a DC source of desired magnitude and frequency. Single phase inverters are widely used in case of power failures to deliver power to critical loads, variable speed ac drives, induction heating, uninterruptible power supplies (UPS) for hospitals, security complexes, standby aircraft power supplies, traction, HVDC transmission lines and renewable energy applications which require pure sinusoidal waveform at the specified magnitude, frequency and low total harmonic distortion (THD). Normally, DC-AC inverters operate in pulse width modulation (PWM). During the process of inversion in a thyristorised power converter; harmonics of power frequency are produced on the converter. Reducing the harmonic content of the output voltage, current is one of the important tasks of the designers. Harmonics appear as undesirable noise. Poor power factor, Excessive temperature rise may weaken the reliability and life of the motors or equipment, sensitive electronic equipment malfunction, and increase the apparent power and over- sizing of sources, acoustical noise in AC motor drives, etc. Hence an active harmonic reduction strategy is often desirable. Conventionally three harmonic reduction strategies such as switch control, vector control, and modulation technique are generally employed for harmonic reduction.

The inverters used for critical loads generally require less than 5% total harmonic distortion (THD) and the amplitude of individual harmonics should be less than 3% of the fundamental amplitude. The low THD value improves the dynamic response of the UPS in load variations. Single phase inverters are widely used due to its compact size, flexibility in operation, faster dynamic response, low acoustic noise, etc. An inverter has become the necessity of the day during the period of load shedding or as an interim source until the backbone supply is restored. Single phase inverters of small sizes (less than 1000 W) are used in domestic installations as a source of standby electric supply. Its overall cost is less than the portable generator of the same power rating. Many conventional methods have been put forward by several researchers on mitigating harmonics in power converters. The conventional methods exhibit poor system response under line and load variations.

The Single Phase Voltage Source Inverter generates harmonic content at its output due to the non-linear characteristic of power devices. In single phase voltage source inverters, the output voltage remains more or less constant due to its low internal impedances whereas the output current varies with respect to load. Therefore the terminal voltage is determined by the inverter setup whereas the load current is determined by the load. Harmonic mitigation in an inverter is an important task for its efficient operation. Conventionally, PWM techniques are used in voltage source inverters for reducing harmonic to a certain level. Moreover, the distortions of an inverter can be reduced by using composite observers both in series and shunt of the circuitry [

In this work, Artificial Bee Colony optimization Technique is applied to estimate the optimized values of PI-controller for reducing harmonic distortions in the single phase inverters. This controller is known as ABC-PI controller. Artificial Bee Colony Algorithm is a natural inspired optimization technique simulating the foraging behaviour of honeybees. It is a very robust and population based optimization algorithm. In ABC algorithm, the colony of artificial bees contains three groups of bees namely employed bees, onlookers and scouts. A bee going to the food source is named as employed bee. A bee waiting on the dance area for making a decision to choose a food source is called onlooker. A bee that carries out random search for discovering new sources is called scout bee [

The paper is organized as follows, in the subsequent sections; Inverter circuit analysis, Artificial Bee Colony Algorithm, MATLAB implementation of ABC-PI controller, Simulation results, Experimental setup and finally the conclusion.

The inverter load voltage is defined as,

Instantaneous inverter output voltage,

If the load of the inverter is purely resistive, then the load current is given by,

Instantaneous inverter output current,

The power absorbed by the load is given by

Total Harmonic Distortion (THD) is a measure of harmonic content in a signal, which is the ratio of all the harmonic components together to the rms amplitude of the fundamental. It is given by,

In full bridge inverter, the switching frequency, f_{s} must be above the audible range of 20 KHz. It is given by, switching frequency,

Supply frequency

where, f_{o} is the output frequency and “P” is the pulses per half period. The source voltage and output voltages are related as,

where, V_{on} is the output voltage including on-state voltages of the switching device.

The switching scheme determines the frequency of the output ac waveform. The output voltage amplitude is controlled by varying the amplitude of the source voltage. The steady-state inverter operation can be explained by assuming two circuit modes with control variable u ?{0, 1}. The mathematical model for the voltage controlled single phase full bridge inverter based on bipolar voltage switching with sinusoidal pulse width modulation is presented. It is assumed that all components are ideal. The alternating voltage is produced when switches S_{A} and S_{D} are closed for half the switching period while S_{B} and S_{C} are open. In the second half-period S_{A} and S_{D} are open while S_{B} and S_{C} are closed. The control variable “u” is defined as,

If switches S_{A} and S_{D} are on, then u = 1. If switches S_{B} and S_{C} are on, then u = 0, where u is a control variable.

Topology (1): When switches S_{A} and S_{D} are on, then u = 1 and the system can generate a positive half sine wave.

According to the circuit topology, the state-space equation can be written as follows.

Applying KVL,

Also,

Topology (2): S_{B} and S_{C} are on, then u = 0 and the system can generate a negative half sine wave.

Applying KVL,

Applying KCL,

Equations (11) and (14) are merged with controlled variable u ∈ {0, 1} into following state space equation (15):

where,

U = Control variable;

L_{f} = Filter inductance;

C_{f} = Filter capacitance;

R = Load resistance;

V_{in} = DC input voltage.

The LC low pass filter at the inverter terminals act as parallel resonance and blocks the harmonics into a lower level and passes almost sinusoidal output. In inverters, the LC elements are used for building up the oscillations and are called resonant elements. It should be under damped in nature such that,

Filter inductance,

Filter capacitance,

Filter cut-off frequency,

Artificial Bee Colony (ABC) algorithm, proposed [

In ABC algorithm the colony of artificial bees contains three groups of bees: employed bees, onlookers and scouts. First half of the colony consists of the employed artificial bees and the second half includes the onlookers. For every food there is only one employed bee. In other words, the number of employed bees is equal to the number of food sources. The employed bee of an abandoned food source becomes a scout. The search carried out by the artificial bees can be summarized as follows:

Employed bees determine a food source within the neighborhood of the food source in their memory. Employed bees share their information with onlookers within the hive and then the onlookers select one of the food sources. Onlookers select a food source within the neighborhood of the food sources chosen by them. An employed bee of which the source has been abandoned becomes a scout and starts to search a new food source randomly.

1. Load samples of Controller parameters.

2. Initialize the population of solutions,

X_{i}, I = 1............ SN (size of population).

3. Evaluate the fitness (f_{i}t_{i}) of the population.

4. Set Cycle = 1.

5. Repeat.

6. Produce new solutions for the employed bee,

X_{new} by using Equation (25) and evaluate their fitness using Equation (22).

7. Apply the greedy selection process for the employed bees.

8. Calculate the probability values for the solutions

Using Equation (24).

9. Produce the new solutions for the onlookers from the solutions X_{i} selected depending on probability and evaluate them.

10. Apply greedy selection process for the onlookers.

11. Determine the abandoned solution for the scout

if exists and replace it with a new randomly

Produced solution X_{i} by (26).

12. Memorize the best solution so far.

13. Cycle = cycle + 1 Until Cycle = MCN (Maximum Cycle Number).

The objective function of the VSI comprises reducing total harmonic distortion (THD), which largely depends on the controller parameters.

where,

V_{ref} = Reference d.c voltage.

V_{con} = Controller d.c voltage.

Minimise THD subject to the constraint

where φ represents K_{p} and K_{i}.

Fitness value (f_{i}t_{i}) is calculated using iom

Here f(x_{i}) is the objective function (THD) in the steady state.

a possible solution to the optimization problem and the nectar amount of a food source corresponds to the quality (fitness) of the associated solution. The number of the employed bees or the onlooker bees is equal to the number of solutions in the population. At the first step, the ABC generates a randomly distributed initial population X_{i} of SN solutions (food source positions), where SN denotes the size of population. Each solution_{p} & K_{i}.

i.e.

After initialization, the population of the positions (solutions) is subjected to repeated cycles, ^{th} food source is represented as:

After all employed bees complete the search process; they share the nectar information of the food sources and their position information with the onlooker bees on the dance area. An onlooker bee evaluates the nectar information taken from all employed bees and chooses a food source with a probability related to its nectar amount. The probability P_{i} determined as,

where n is total number of food sources. Fitness value f_{i}t_{i} is calculated using (16). The onlooker finds its food source in the region of X_{i} by using the following relation,

where,

All the employed bees have completed search process, the information is shared with onlookers. The onlookers select food sources according to the above probability so that better food sources are selected. Each bee will search for a better food source for certain number of cycles (limit), and if fitness value doesn’t improve then that particular bee becomes scout. In ABC algorithm, it is simulated by producing a position of scout bees randomly and replacing it with the abandoned one. If the position cannot be improved further through a predetermined of cycles, then that food source is assumed to be abandoned. The value of predetermined number of cycles is an important control parameter of the ABC algorithm, which is called “limit” for abandoned. Assume that the abandoned source is X_{i} and_{i}. This operation can be expressed as

The Total Harmonic Distortion of Single Phase VSI using Proportional Integral Controller with ABC Optimization is simulated by using Matlab/Simulink software. In single phase full-bridge voltage fed inverter the initial and estimated values of Proportional constant (K_{p}) and Integral constant (K_{i}) values are K_{p} = 19 and K_{i} = 7.1. In the simulation using PI controller the optimized values K_{p} =19.862 and K_{i} = 9 are estimated using ABC algorithm and its THD values are computed. The switching frequency of the inverter is taken as 7.69 KHZ [_{p}_{max}}, {0, K_{i}_{max}} where,

The Specification of the 1-Phase inverter is tabulated in

The detailed closed loop simulation voltage source Inverter using Proportional Integral Controller with ABC optimization is in

Parameters | Values |
---|---|

Input DC Voltage, V_{in} | 15 V |

Load Resistance, R_{0} | 50 Ω |

Filter Inductance, L_{f} | 2 mH |

Filter Capacitance, C_{f} | 500 µF |

Reference Signal, V_{ref} | 5V Sine, 50 Hz |

ABC-PI Controller | K_{p}_{ }= 19.862, K_{i}_{ }= 9.0 |

Switching Frequency, f_{s} | 7.69 KHz |

Load Waveform | Sine wave |

and also it eliminates the steady state error. The overall controller tuning methods include both time and frequency domain methods such as Routh-Hurwitz Criterion, Root Locus method, pole placement technique, Ziegler-Nichols tuning formula, etc. Among this techniques, the Ziegler and Nichols tuning method is used to compute PI gains of the voltage source inverter. The Output of the controller is applied to Power Inverter switches. The Percentage THD Values of voltage and current Harmonics are measured and the response Curves of voltage and current Harmonics of Single Phase Inverters are plotted in

This paper demonstrates that ABC optimization for a single phase voltage source full bridge inverter reduces THD values better than PI controllers for harmonic mitigation. This technique also provides constant voltage and reduced current THD values. The single phase inverter using proportional integral algorithm controlled by PIC microcontroller was directly implemented using hardware setup and its total harmonic distortions were

estimated with ABC optimization technique. It is observed that the optimization technique provides better reduction of current THD values compared to other non-optimization methods. This system reduces switching losses and thereby improves overall efficiency. Both software and hardware implementation provides reduced total harmonics as per IEEE and IEC standards.

N. M. Spencer Prathap Singh,Kesavan Nair,T. Ajith Bosco Raj, (2016) Distorted Waveform Balancing Using an Artificial Bee Colony (ABC) Based Optimal Control for Mitigating Total Harmonics in Single Phase Inverter. Circuits and Systems,07,2154-2167. doi: 10.4236/cs.2016.79187