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In this paper, a novel decoupling control method based on generalized inverse system is presented to solve the problem of SHAPF (Shunt Hybrid Active Power Filter) possessing the characteristics of 2-input-2-output nonlinearity and strong coupling. Based on the analysis of operation principle, the mathematical model of SHAPF is firstly built, which is verified to be invertible using interactor algorithm; then the generalized inverse system of SHAPF is obtained to connect in series with the original system so that the composite system is decoupled under the generalized inverse system theory. The PI additional controller is finally designed to control the decoupled 1-order pseudolinear system to make it possible to adjust the performance of the subsystem. The simulation results demonstrated by MATLAB show that the presented generalized inverse system strategy can realise the dynamic decoupling of SHAPF. And the control system has fine dynamic and static performance.

In recent years, many nonlinear electrical components are widely used in our life; harmonics produced by Power System electronic devices have a serious impact on power quality. So it is important to find equipment to suppress harmonics and compensate reactive power for the grid.

The traditional compensation equipment is passive filter (PPF); it is inexpensive, but it cannot solve the impedance deviation caused by the mutation of the system, and it can only compensate fixed harmonics. Active power filter (APF) can be used to compensate each of the order harmonics of the grid, but it is not so feasible in large-capacity situation [

As a new compensation device, HAPF combines the advantages of PPF and APF; it can solve almost all the matters that PPF and APF have. Harmonics and reactive power are compensated by PPF. The main function of APF is to improve the filtering characteristics of passive filters and overcome the shortcomings that the PPF has which can easily resonate with the grid impedance. The capacity of APF occupies only about 2%–5% of the capacity of the harmonic source load, and most harmonics are compensated by PPT. So SHAPF can be used in large-capacity situations with relatively small-capacity, and it can improve the cost effectiveness of the system. So the use of SHAPF is becoming a significant practical direction for grid harmonic governance.

The design of the controllers seriously affects the harmonics compensation. Many controllers have been designed to make the APF decoupling. Reference [

SHAPF consists of command current arithmetic circuit, current tracking control circuit, driving circuit, and the main circuit (PWM converter). The structure of SHAPF is shown in Figure

Mathematical model of SHAPF [

The mathematical model of SHAPF is shown as Figure

From [

Providing that

Here, we use inverse system to analyze the invertibility of SHAPF. We first calculate the derivative of the output (

The Jacobi matrix is nonsingularity; relative degree vector of the system is

As is proved in the previous Section

It is obvious that, compared with the inverse system, generalized inverse system increases some parameters, so the pseudolinear system can configure the poles to anywhere by adjusting parameters. It cannot be resolved by inverse system. So the decoupling effect by generalized inverse system is better than the traditional inverse system.

In this paper, ordering the input vector

Feedback linearization and decoupling of SHAPF with generalized inverse system method.

With generalized inverse system method, the controller is designed to achieve the desired effect. In this paper, generalized inverse PI composite controller is designed to achieve the decoupling control; two PI additional controllers are used to control the two decoupled 1-order pseudolinear systems which can reduce steady-state error of the system and configure the poles reasonably. The capacitor in DC side is controlled by PI control. Simulation flow chart of generalized inverse system is shown in Figure

Simulation flow chart of generalized inverse system.

The composite system is a second-order system, structure diagram of SHAPF control system is shown in Figure

Structure diagram of SHAPF control system.

In order to verify the effectiveness of the generalized inverse control policy, we use the MATLAB simulation platform to build a simulation study. And we do the comparison with feedforward PI control and inverse control. System parameters for simulation are shown in Table

SHAPF and controller parameter.

System parameters | value |
---|---|

Virtual value of grid voltage ( |
220 V/50 Hz |

Equivalent inductance on grid ( |
0.01 mH |

Passive filter parameters |
10^{−4} F/1 mH/0.1 Ω |

DC side capacitor ( |
0.01 F/480 V |

PWM frequency | 10000 Hz |

PI parameter of generalized inverse system ( |
10000/2000, 10000/2000 |

Generalized inverse parameter ( |
0.01, 1.41, 0.01, 1.41 |

PI controller parameter in DC side ( |
0.01/0.002 |

Three-phase bridge load | 10 Ω/5 mH |

The SHAPF model is built as Figure

Load current waveform comparison. (a) Load current waveform without decoupling method. (b) Load current waveform with feedforward decoupling method. (c) Load current waveform with inverse system decoupling method. (d) Load current waveform with generalized inverse system decoupling method.

It is obvious that the load compensated waveform with generalized inverse system method is most close to ideal sine wave. The spectrum analysis is shown in Figure

Spectrum analysis comparison. (a) Spectrum analysis of load current without decoupling method. (b) Spectrum analysis of load current with feedforward decoupling method. (c) Spectrum analysis of load current with inverse system decoupling method. (d) Spectrum analysis of load current with generalized inverse system decoupling method.

In Figure

Voltage of DC side capacitor (

In Figure

Compensated current in

It is easy to see that

In this paper, a novel method is presented to achieve the decoupling control of SHAPF; generalized inverse theory is applied to the system so that we can configure the pole parameters to adjust the dynamic performance of the system. The generalized inverse system is connected in series with SHAPF and the pseudolinear system can be decoupled into two linear systems to achieve the decoupling control. Decoupled subsystems can be easily bridled by PI controller. The simulation research proves that the system is completely decoupled and the compensation effect is better than the traditional PI control system and inverse system. This method can be used in reality for further research.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China under Project 61165006, the Science Foundation of Gansu Province of China under Project 145RJZA182, the Large Electric Drive System and State Key Laboratory of Equipment Technology Openness Foundation of China under Project SKLLDJ022016015, and a Project Funded by the Colleges Fundamental Research under Project 214144.