_{1}

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This paper presents a closed-loop vector control structure based on adaptive Fuzzy Logic Sliding Mode Controller (FL-SMC) for a grid-connected Wave Energy Conversion System (WECS) driven Self-Excited Induction Generator (SEIG). The aim of the developed control method is to automatically tune and optimize the scaling factors and the membership functions of the Fuzzy Logic Controllers (FLC) using Multi-Objective Genetic Algorithms (MOGA) and Multi-Objective Particle Swarm Optimization (MOPSO). Two Pulse Width Modulated voltage source PWM converters with a carrier-based Sinusoidal PWM modulation for both Generator- and Grid-side converters have been connected back to back between the generator terminals and utility grid via common DC link. The indirect vector control scheme is implemented to maintain balance between generated power and power supplied to the grid and maintain the terminal voltage of the generator and the DC bus voltage constant for variable rotor speed and load. Simulation study has been carried out using the MATLAB/Simulink environment to verify the robustness of the power electronics converters and the effectiveness of proposed control method under steady state and transient conditions and also machine parameters mismatches. The proposed control scheme has improved the voltage regulation and the transient performance of the wave energy scheme over a wide range of operating conditions.

Producing energy from renewable energy resources such as solar, wind, ocean, micro-hydro, biomass, etc. is be- coming a necessity because of the continuous increasing of world energy demand of electrical power and continuous depreciation of conventional energy resources like oil, gas and coal. Since the abundance of wave power potential and its pollution-free nature, wave energy seems to be one of the attractive and exploitable alternative energy sources in the world today [

Fuzzy Logic Control System (FLCs) is a rule-based expert system with the ability to emulate a human’s subjective decision-making model through its linguistic rules [

This paper describes the application of the MOGA and MOPSO for the automatic design of the scaling factors and the membership function parameters of a Mamadani-type fuzzy sliding mode control system in order to find the best intelligent controller associated to the flux oriented control technique for a variable speed wave turbine driven SEIG interfaced to the grid. A number of fitness functions are defined to measure the performance of the proposed controllers such as minimizing the mean square errors of the DC voltage, DC current, the Root Mean Square (RMS) of the AC line voltage and the frequency. Since these objectives are conflicting, multi-objective optimization is used to find a Pareto front from which a desired optimal operating state can be chosen. This is done using MOPSO and MOGA to determine the optimal gains for the SMC controllers of both the generator- side converter and the Grid-side converter of the SEIG. For the purpose of comparing the improvement obtained in the system dynamic performance with the application of the MOPSO and MOGA procedures to design the SMC controller gains, these results are compared with those obtained using a classical regulator SMC and a Fu- zzy Logic Controller. A complete simulation model is developed for such machine under variable speed operation using MATLAB Simulink environment. Simulation results show that the proposed design approach is efficient to find the optimal design of the SMC controller and therefore improves the transient performance of the WECS over a wide range of operating conditions. This paper is organized as follows: Section II presents the SEIG and WECS mathematical model description as the systems to be studied and controlled. Section III shows the dynamic simulations of the studied system to evaluate the performance of the proposed controllers subject to a three-phase fault and load disturbances. Finally, specific important conclusions of this paper are drawn in Section IV.

The generator-side converter was implemented so that the field-oriented current control loop controls the rotor flux and the machine torque, as shown in _{r} and the machine torque T_{e} can be represented as functions of the individual current components. Therefore, the reference values of i_{dr} and i_{qr} can be determined directly from the l_{r} and T_{e} commands. In the rotor flux control loop of the gene-

Schematic representation of wave energy converter with SEIG full-controlled induction generator

Generator-side converter control

rator side converter, the actual signal of the rotor flux (l_{r}) is compared with it’s the command _{e} and sinq_{e}) generated from flux vector signals _{abc} are then compared with their reference signals

The grid-side converter is also vector-controlled using direct vector control and synchronous current control in the inner loops. _{dc}) is compared with its command

tual signal of the line current (V_{ab}) is compared with the reference line current

error signal, which is passed through the FLC-SMC controller to generate the reference signals for the q-axis current component_{sabc} are then compared with their reference signals

Sliding mode control (SMC) is a technique derived from Variable Structure Theory. The basic idea of SMC controller is to force the tracking error e(t), after a finite time of reaching phase, to approach the sliding surface S(t) containing the system operating point and and then move along the sliding surface to the origin. SMC controllers proved their capability to handle nonlinear and time varying systems, high accuracy and robustness with respect to various internal and external disturbances.

The sliding surface S(t) is defined with the tracking error e(t) and its integral

where λ_{0}, λ_{1}, λ_{2} > 0 are positive real constants.

The overall design procedure of the combined FLC as a supervisory control with the adaptive SMC controller using the MOGA and the MOPSO is illustrated in _{0}, l_{1}, l_{2}) are generated by fuzzy inference, which provides a nonlinear mapping from the error signal e (difference between system output and reference signal and defined as e(k) = Reference (k) – Output (k)) and the first-order difference of error signal De which is defined as Δe(k) = e(k) – e(k – 1). Note that the input variables to the fuzzy controller (E and DE) are transformed by multiplying the error (e) and the first-order difference of error signal (De) by the scaling factors β_{1} and β_{2} whose role is to allow the fuzzy controller to “see” the external world to be controlled.

Grid-side converter control

Schematic of the PSO-based scaling factors-tuning of the fuzzy PID controller

In this paper, the adaptation of the adequate values for the scaling and gain factors of each SMC-type FLC structure is done the MOPSO and the MOGA to find the optimal parameters of the SMC controllers to optimize the proposed fitness functions. In the DC-side and the AC-side control loops, there are four SMC controllers and each of them has four gains (k, l_{0}, l_{1}, l_{2}) and two scaling factors β_{1} and β_{2}. The sliding hyper-plane highly depends upon dynamics of error and change in error so that we have to consider this variable as input to the fuzzy logic module for updating all gains. The designed fuzzy logic controller has two inputs and four outputs. The inputs are system error (e) and the change of the system error (de/dt) in a sample time, and outputs are the sliding mode controller gains (k, l_{0}, l_{1}, l_{2}). In the proposed FLC, the membership functions of the input variables are assumed to be the Gaussian form [

where m is the mean (or the center of the membership function) and s is the deviation (or the width of the membership function) of each MF. The set of rules which define the relation between the input and output of fuzzy controller can be found using the available knowledge in the area of designing the system. These rules are defined using the linguistic variables. The membership functions for the inputs and outputs for the fuzzy controller are shown in figures 5-7. Tables 1-4 show the control rules that used for fuzzy self-tuning of SMC controller. Where, NB: negative big, NM: negative medium, NS: negative small, ZE: zero, PS: positive small, PM: positive medium and PB: positive big. VB: very big, B: big, MB: medium big, ZE: zero, M: medium, S: small, MS: medium small.

The wave model of _{1}, a hitting gain (k) and an intercept l_{0} of sliding hyper-plane. The be-

Initial membership functions of inputs (e, Δe)

Initial membership functions of outputs (l_{0}, l_{1}, and l_{2})

Initial membership functions of output gain k

. Initial rule bases for tuning l_{0}

Δe/e | NB | NM | NS | ZE | PS | PM | PB |
---|---|---|---|---|---|---|---|

NB | B | B | B | B | B | B | B |

NM | B | B | M | MB | MB | B | B |

NS | MB | MB | S | M | MB | MB | B |

ZE | ZE | S | ZE | MS | S | S | S |

PS | MB | M | S | M | MB | MB | B |

PM | B | MB | MB | MB | MB | B | B |

PB | B | B | B | B | B | B | B |

. Initial rule bases for tuning l_{1}

Δe/e | NB | NM | NS | ZE | PS | PM | PB |
---|---|---|---|---|---|---|---|

NB | M | M | M | M | M | M | M |

NM | MS | MS | MS | MS | MS | MS | MS |

NS | S | S | S | S | S | S | S |

ZE | MS | MS | MS | ZE | MS | MS | MS |

PS | S | S | S | S | S | S | S |

PM | MS | MS | MS | MS | MS | MS | MS |

PB | M | M | M | M | M | M | M |

. Initial rule bases for tuning l_{2}

Δe/e | NB | NM | NS | ZE | PS | PM | PB |
---|---|---|---|---|---|---|---|

NB | ZE | MS | S | M | MB | VB | VB |

NM | MS | MS | MB | MB | MB | VB | VB |

NS | S | MB | B | MB | VB | VB | VB |

ZE | M | MB | MB | MB | VB | VB | VB |

PS | B | MB | VB | VB | VB | VB | VB |

PM | MB | VB | VB | VB | VB | VB | VB |

PB | VB | VB | VB | VB | VB | VB | VB |

. Initial rule bases for tuning k

Δe/e | NB | NM | NS | ZE | PS | PM | PB |
---|---|---|---|---|---|---|---|

NB | VB | VB | VB | VB | VB | VB | VB |

NM | VB | VB | MB | MB | MB | VB | VB |

NS | B | B | B | B | MB | MB | VB |

ZE | ZE | S | ZE | MS | S | S | S |

PS | B | B | B | B | MB | MB | VB |

PM | VB | VB | MB | MB | MB | VB | VB |

PB | VB | VB | VB | VB | VB | VB | VB |

The wave model

havior of the converters depends on these parameters of the SMC control system. If the controllers are tuned properly, it is possible to improve the gride-side and generator-side converter’s performance during the transient disturbances. For the same operation condition, the MOGA and MOPSO were used to adapt the scaling factors and the membership functions of the FLC to obtain the optimal gains for the SMC controller of the generator-side and the grid-side converters. To compare the improvement obtained in the system dynamic performance with the application of the MOPSO and MOGA procedures to design the FLC-SMC controller gains, these results are compared with those obtained using the traditional SMC and FLC-SMC.

The quality of the gains adjustment is measured by an index that represents the weighted sum of the Normalised Mean Square Error (NMSE) deviations between output plant variables and desired values. This way the objective to improve the system performance during the transient disturbances will be obtained by specifying optimal values for the controller gains. The NMSE deviations between output plant variables and desired values are defined as:

The SOPSO and the SOGA obtain a single global or near optimal solution based on a single weighted objective function. The weighted single objective function (J_{o}) combines several objective functions using specified or selected weighting factors as follows:

where α_{1} = 0.25, α_{2} = 0.25, α_{3} = 0.25, α_{4} = 0.25 are selected weighting factors. J_{1}, J_{2}, J_{3}, J_{4} are the selected objective functions. The weighting factors in the objective function (J_{o}) are used to satisfy different design requirements. If a large value of α_{1} is used, then the objective is to minimize the error of the DC link voltage. On the other hand, the MOPSO and the MOGA finds the set of acceptable (trade-off) Optimal Solutions. This set of accepted solutions is called Pareto front. These acceptable trade-off multi-level solutions give more ability to the user to make an informed decision by seeing a wide range of near optimal selected solutions.

In the calculation of the optimal gains by the MOGA and the MOPSO procedures, the objective is to improve the overall dynamic performance of the proposed wave energy system using the SEIG when it is subjected to severe electrical disturbances and faults in the electrical network. The dynamic simulations were carried out for two cases. In the first case, a step load change was carried out from 0.5 pu to 1 pu at time 6 s and lasting 8 s. in the second simulation case, a phase to phase short circuit was carried out next to the generator bus at time t = 10 s, lasting for 0.1 s. The RMS of the AC line voltage voltage dynamic behavior with load disturbance is shown in

. System dynamic behavior comparison with constant load

Traditional SMC | FLC-SMC | SOGA- FLC-SMC | SOPSO- FLC-SMC | MOGA- FLC-SMC | MOPSO- FLC-SMC | |
---|---|---|---|---|---|---|

RMS Grid-Side Voltage (PU) | 0.9847 | 0.9972 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |

RMS DC-Side Voltage (PU) | 0.9858 | 0.9954 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |

RMS Grid-Side Current (PU) | 0.8271 | 0.8003 | 0.7432 | 0.7502 | 0.6761 | 0.6060 |

RMS DC-Side Current (PU) | 0.9134 | 0.8420 | 0.7523 | 0.7545 | 0.6997 | 0.6591 |

Maximum Transient Grid-Side Voltage Over/Under Shoot (PU) | 0.06324 | 0.04218 | 0.006555 | 0.004388 | 0.004551 | 0.001909 |

Maximum Transient Grid-Side Current-Over/Under Shoot (PU) | 0.0976 | 0.09157 | 0.007713 | 0.006816 | 0.005627 | 0.003593 |

Maximum Transient DC-Side Voltage Over/Under Shoot (PU) | 0.04786 | 0.04922 | 0.003061 | 0.003655 | 0.001191 | 0.001473 |

Maximum Transient DC-Side Current-Over/Under Shoot (PU) | 0.05469 | 0.05595 | 0.00319 | 0.003952 | 0.002984 | 0.001387 |

NMSE_{VDC} × 10^{−3} | 0.9575 | 0.6558 | 0.2770 | 0.2870 | 0.1597 | 0.1494 |

NMSE_{Vab} × 10^{−3} | 0.9649 | 0.7358 | 0.3463 | 0.2898 | 0.2405 | 0.2176 |

NMSE_{IDC} × 10^{−3} | 0.9577 | 0.8491 | 0.5972 | 0.4456 | 0.3853 | 0.2407 |

NMSE_{fs} × 10^{−3} | 0.09706 | 0.09340 | 0.08235 | 0.08463 | 0.02239 | 0.02544 |

. System dynamic behavior comparison with 50% step load disturbance

Traditional SMC | FLC-SMC | SOGA- FLC-SMC | SOPSO- FLC-SMC | MOGA- FLC-SMC | MOPSO- FLC-SMC | |
---|---|---|---|---|---|---|

RMS Grid-Side Voltage (PU) | 0.98143 | 0.9989 | 1.000 | 1.000 | 1.000 | 1.000 |

RMS DC-Side Voltage (PU) | 0.9836 | 0.9974 | 1.000 | 1.000 | 1.000 | 1.000 |

RMS Grid-Side Current (PU) | 0.9293 | 0.9120 | 0.8506 | 0.8547 | 0.8256 | 0.8100 |

RMS DC-Side Current (PU) | 0.9500 | 0.9372 | 0.8839 | 0.8749 | 0.8362 | 0.8234 |

Maximum Transient Grid-Side Voltage Over/Under Shoot (PU) | 0.2967 | 0.1623 | 0.08291 | 0.08173 | 0.05693 | 0.04840 |

Maximum Transient Grid-Side Current-Over/Under Shoot (PU) | 0.2512 | 0.1943 | 0.09133 | 0.08687 | 0.05797 | 0.04400 |

Maximum Transient DC-Side Voltage Over/Under Shoot (PU) | 0.2161 | 0.1813 | 0.01525 | 0.0845 | 0.05499 | 0.04173 |

Maximum Transient DC-Side Current-Over/Under Shoot (PU) | 0.2733 | 0.2286 | 0.08258 | 0.0998 | 0.04450 | 0.0497 |

NMSE_{VDC} × 10^{−2} | 0.3517 | 0.1657 | 0.05384 | 0.0599 | 0.03530 | 0.03027 |

NMSE_{Vab} × 10^{−2} | 0.8308 | 0.6020 | 0.09961 | 0.08001 | 0.06221 | 0.06448 |

NMSE_{IDC} × 10^{−2} | 0.5853 | 0.2630 | 0.0783 | 0.06315 | 0.05510 | 0.04909 |

NMSE_{fs} × 10^{−3} | 0.05498 | 0.01541 | 0.00427 | 0.005107 | 0.00133 | 0.00193 |

RMS of the AC line voltage with load disturbance (a) Response with classical SMC controller, (b) Response with FLC-SMC controller, (c) Response with MOGA-FLC-SMC controller, (d) Response with MOPSO-FLC-SMC controller

DC voltage with load disturbance (a) Response with classical SMC controller, (b) Response with FLC-SMC controller, (c) Response with MOGA-FLC-SMC controller, (d) Re- sponse with MOPSO-FLC-SMC controller

RMS of the AC line voltage with phase to phase fault (a) Response with classical SMC controller, (b) Response with FLC-SMC controller, (c) Response with MOGA-FLC- SMC controller, (d) Response with MOPSO-FLC-SMC controller

DC voltage with phase to phase fault (a) Response with classical SMC controller, (b) Response with FLC-SMC controller, (c) Response with MOGA-FLC-SMC controller, (d) Response with MOPSO-FLC-SMC controller

MOPSO and MOGA algorithms controllers in spite of the presence of disturbances such as step changing of the load and short circuit fault.

This paper has presented the modeling and simulation of wave energy driven self-excited induction generator which feeds power to the utility grid. The adaptive fuzzy tuning control strategy was applied to the sliding mode controller for adopting the controller parameters according to the tracking error to both the dc-link voltage and ac line voltage regulation. The estimation of sliding slope, intercept of sliding surface and hitting gain can be solved by implementation of fuzzy logic control tuner based on the particle swarm optimization (PSO) algorithm and Genetic Algorithm (GA) to enhance the system performance which is insensitive to the parameter variations and disturbance effects. The indirect field-oriented mechanism was implemented for the control of the SEIG to regulate the dc-link voltage of the ac/dc power converter and the AC line voltage of the DC/AC power inverter with robust control performance. Simulation studies are carried out and compared the results obtained with the proposed optimal tuned FLC-SMC controller parameters design using MOPSO and MOGA with those using conventional variable structure SMC controller and fuzzy sliding mode control FLC-SMC controllers. The simulation results verified the effectiveness and robustness of the proposed tuning technique and it was comparatively superior to conventional SMC and FLC-SMC in the sense of the transient performance of the wave energy system over a wide range of operating conditions. The future work is to support the system by the PSO MPPT controller which can perform as a shunt active power filter as well as a wave energy extractor.