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This paper presents a thorough design and comparative study of two popular control techniques,
*i.e*., classical Proportional Integral (PI) and RST, for Matrix Converters (MCs) in terms of tracking the reference and robustness. The output signal of MCs is directly affected by unbalanced grid voltage. Some research works have attempted to overcome this problem with PI control. However, this technique is known to offer lower performance when it is used in complex and nonlinear systems. On the other hand, RST control offers better performance, even in case of highly nonlinear systems. Therefore, the RST can achieve better performance to overcome the limitation of PI control of nonlinear systems. In this paper, a RST control method is proposed as output current controller to improve the performance of the MC powered by unbalanced grid voltage. The overall operating principle, Venturini modulation strategy of MC, PI control and characteristics of RST are presented.

Recent advances in power electronics have enabled the emergence of Matrix Converter (MC) for direct AC/AC conversion [

This part consists of a brief description and modeling of each element of the matrix converter. We start with modeling the MC, then the input filter and it ends with the load RL. Ideal bidirectional switches are represented by

The basic diagram of a MC is represented in

With these restrictions, a

where,

The transfer matrix of the converter is defined by [

The input voltage and current of the matrix converter are given by [

Assuming the relationship between the output and the input signal of the matrix converter [

The matrix converter will be designed and controlled to provide desired output voltage and output current [

The neutral to phase output voltages

The input current

The LC input filter [

The filter output voltage and input current are obtained as Equation (12) and Equation (13) [

Generally, the neutral at the load (n) is isolated from that of the source (N) as shown in

The potential difference between the two neutral is given by [

As the transfer function of the load current is given by [

This method can produce the sinusoidal input current with unity power factor independently of load [

According to the optimal amplitude in expression of Venturini, the modulation function is [

The

Therefore, only six duty cycles are sufficient to calculate the gate signals of the power switches [

The carrier signal is expressed by [

This section deals with the design and synthesis of the PI and RST controllers. Both controllers are designed to achieve current reference tracking with constant and varying current reference signals. This also has to be achieved under both balanced and unbalanced grid voltage conditions.

Current measurements of the load RL using a PI controller is illustrated by

The transfer function of the system is:

The values of A and B are:

The transfer function of the open-loop including the regulator is:

To cancel the pole, a zero was added at the same location as the pole [

The transfer function of the open-loop becomes:

The transfer function of the closed loop is expressed by:

Which:

For a response time

The closed-loop system of the RST controller for MC is given by the following block diagram in

The goal of this section to determinate the RST controller’s current. This type of controller is a structure with two freedom degrees and compared to a one degree of freedom structure, it has the main advantage that it allows the designer to specify performances independently with reference trajectory tracking (reference variation) and with regulation [

With:

For our model, we obtain [

The terms A and B are expressed by Equation (22). According to the robust pole placement strategy [

To accelerate the system, the following conditions were adopted:

With

By identifying Equation (31) and Equation (34), coefficients of polynomial D were found and are linked to the coefficients of R and S by the Sylvester Matrix [

The reference current is calculated as shown in

The measured load’s current and the reference load’s current are given by Equation (36) [

The PI and RST are used to control a matrix converter and a set of simulation runs is performed using SimPowerSystems toolbox of Matlab/Simulink software. The input filter parameters are calculated as given in [

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

Input voltage phase to neuter RMS | |

Input frequency | |

Switching frequency | |

Input filter resistance^{ } | |

Input filter inductance | |

Input filter capacitor | |

Load resistance | |

Load inductance | |

Input voltage phase to neuter RMS | |

Input frequency |

・ Constant reference current

・ Time-varying reference current

・ Constant reference current

・ Time-varying reference current

In this case, the amplitude of the input voltage of phase b is reduced to 20% relative to the phases a and c (

・ Constant reference current

・ Time-varying reference current

・ Constant reference current

・ Time-varying reference current

In

The THD increases for the unbalanced grid unlike in the balanced case (

Case with balanced grid | Values THD | IMP% |
---|---|---|

Constant | 1.94% | 10.82% |

Constant | 1.73% | |

Time-varying | 1.86% | 3.220% |

Time-varying of | 1.80% |

Case with unbalanced grid | Values THD | IMP% |
---|---|---|

Constant | 6.10% | 7.700% |

Constant | 5.63% | |

Time-varying | 6.49% | 23.11% |

Time-varying of | 4.99% |

Case with balanced grid | Values SSE |
---|---|

Constant | |

Constant | |

Time-varying | |

Time-varying of |

Case with unbalanced grid | Values SSE |
---|---|

Constant | |

Constant | |

Time-varying | |

Time-varying of |

In terms of the response of the system and the static error, the PI controller gives little better results than RST controller as it can be seen the

In this paper, a thorough theoretical modeling, analysis and comparison are presented for PI and RST control of MCs. A comprehensive control compensation method is used to find the PI gains. Moreover, the use of the pole placement technique is also shown to determine the RST’s polynomial coefficients. Results for a balanced grid show lower load current THD as opposed to the unbalanced grid case, which is expected. However, RST control shows better performance. Nonlinear controllers tend to outperform these techniques at the expense of added complexity and computation. However, it is noteworthy that compared controllers are known for similar design complexity, which has been driving their use in the industry.

BekhadaHamane,Mamadou LamineDoumbia,HichamChaoui,MohamedBouhamida,AhmedChériti,MustaphaBenghanem, (2015) PI and RST Control Design and Comparison for Matrix Converters Using Venturini Modulation Strategy. Journal of Power and Energy Engineering,03,36-54. doi: 10.4236/jpee.2015.38005