Genetic Algorithm Tuned Controllers for High-Performance Indirect Field-Oriented Control in DFIG-Based WECS

Samira Heroual 1, Belkacem Belabbas 1, Kheloud Ayati 1, Rabia Haloui 1, Ahmed Tawfik Hassan 2, Alfian Ma’arif 3, Mohamed Metwally Mahmoud 4,5,6, Vojtech Blazek 6

1 Department of Electrical Engineering, L2GEGI laboratory, University of Tiaret, Tiaret, Algeria;

2 Department of Electrical Engineering, Faculty of Engineering, Aswan University, Aswan 81542, Egypt

3 Department of Electrical Engineering, Universitas Ahmad Dahlan, Yogyakarta, Indonesia

4 Department of Electrical Engineering, Faculty of Energy Engineering, Aswan University, Aswan 81528, Egypt

5 Jadara University Research Center, Jadara University, P.O Box 733, Irbid, Jordan

6 ENET Centre, CEET, VSB—Technical University of Ostrava, Ostrava, 708 00, Czech Republic

1. INTRODUCTION

Power-generation technologies have evolved to meet the 21st century's increasing need for power, which is mostly driven by fast population expansion and urbanization. The spike in demand has resulted in a global electrical shortfall [1][2]. To address these difficulties, power generation systems are typically divided into two categories: RESs, which are sustainable, and non-RESs, which are finite. This paradox mirrors the greater discussion over energy sustainability and resource management in modern society [3][4]. The development of RESs, which include geothermal, biomass, wind, solar, marine, and hydroelectric power, is the greatest way to preserve the environment and lessen pollution from fossil fuels and nuclear power [5][6]. The most sustainable, efficient, and promising of these energy sources is WE, which is one of the renewable energies that has seen a growth in use in the world due to its clean and non-polluting nature, which produces power without emitting greenhouse gases and is gradually being included in electrical networks [7]-[9].

By 2030, leading nations aim to produce over 20% of their electricity from WECS, according to recent research [10][11]. Nowadays, the most widely used WT in WFs is based on a DFIG because have special qualities, which include flexible control, low cost, high efficiency, and the potential to independently regulate the interchange of active and reactive electricity with the grid system [12]-[14]. Also, improved flexibility in the controllability of power factor by preserving the modest size of power electric devices [15]-[17].

The power output of a WECS is determined by the accuracy with which the peak power points are recorded by the MPPT controller of the WECS control system, regardless of the generator type employed at any wind speed [12],[18][19]. Due to the high degree of nonlinearity in the DFIG system, some control techniques have been considered to enhance the system's operation during disruptions. The most popular control using the FOVC method is classical control. This control strategy uses a variety of loops, heavily relies on the precision of the machine parameters, and requires strong regulation to maintain stability across the entire speed range, which is based on PI correctors [7],[20][21]. It is widely used due to its dependability and ease of implementation, but its effectiveness suffers when the internal generator parameters are changed [22][23]. Recent advances in non-linear control methods have had a significant impact on the control mechanisms of converters used in RESs, particularly solar and WT applications. These non-linear control approaches are distinguished by their high robustness in the face of disturbances and capacity to deal with the complex problems given by non-linear systems. As a result, they serve as useful instruments that not only meet the stringent standards of sustainable energy applications but also provide answers to typical problems associated with traditional linear PID control systems [21].

Several MPPT and control techniques of DFIG have been proposed in the literature to improve the performance and efficiency of WECS connected with DFIG [24]-[27]. In [28], the sliding mode regulator's decoupling control of active and reactive DFIG powers, which exhibits superiority over PI during robustness testing, unfortunately, this approach has a slow reaction time. Ref. [29] presents a comparison between PI and backstepping controllers for DFIGs used in WECSs. Its main objective was to assess the suggested controller's resilience against changes in wind speed and reference tracking. In [30], a PI gain based on a Fuzzy logic scheduler for a vector controller to regulate a DFIG utilized in a variable speed WT for wind power generation, but has the sensitivity to changes in parameters and outside disturbances. In [31], various control strategies for DFIG-WECS using RST and fuzzy logic controllers were found, where the first control is more robust than the novel control compared to the rotor resistance variation, but the oscillations remain apparent. In [32], DFIG connected to a WT controlled by a novel DTC using the rotor power factor by maintaining it equal to one, and rotor voltage vectors produced by utilizing a look-up table it has a great reduction of torque ripples but has a complex structure in control. In [33], a hybrid algorithm (PSO and GSA) was used to optimize a fuzzy sliding mode controller. The major drawback of these techniques is the complexity of the synthesis process, and it needs the full knowledge of system parameters and boundaries. In [34], using the DFIG's backstepping adaptive control for variable-speed WTs utilizes an adaptive pole placement technique.

This work provides a thorough comparison of classic optimization methods with a novel meta-heuristic methodology known as the GA. This study focuses on optimizing the  and   parameters of the PI regulator, which is utilized in WECS and in conjunction with DFIGUREThe primary purpose of this optimization work is to increase the system's ability to track wind speed accurately, which is critical for maximizing the power output generated by WE systems. Furthermore, the analysis emphasizes the need to improve the dynamic damping performance of the associated machines, arguing that the GA may provide more effective solutions than standard methods for achieving these goals.

The paper describes the framework of the work, which is divided into six sections. Section 2 focuses on the DFIG-based WECS, including system and inverter specifications. Section 3 describes the control technique that includes MPPT, field-oriented vector control, and PWM control methodologies. Section 4 introduces the suggested GA, while Section 5 presents simulation results and debates. Section 6 present conclusion that closes the work.

2. MODELLING OF WECS COMPONENTS

1. WT Model (WTM)

Figure 1 shows a block schematic of the turbine's dynamic model [35]-[37]. The mechanical power transmitted from the wind to the aerodynamic rotor is defined as [38]-[41]:

The input torque aerodynamic:

The gearbox model is:

The shaft model is:

Figure 1. Model of the turbine [35]

2. DFIG Model

Figure 2 shows Park's transformation and the two-phase reference model of the wound rotor induction machine in the rotating field reference frame [42]. The formulae for the stator and rotor voltages are as follows [43]-[45]:

The formulae for the stator and rotor flux are as follows:

The equation between stator and rotor pulsations and rotor speed is as outlined below:

The torque formulae of the DFIG are:

The equations for the stator and rotor powers are as follows:

Figure 2. Orientation of the park frame [42]

3. Three-Level NPC Inverter

The three-level NPC, developed by Nabae et al., consists of four switches in each leg and two diodes clamped to the capacitors' midpoints and composed of four IGBT switches. The controlled switches are unidirectional in voltage and bidirectional in current, as depicted in Figure 3 [46]-[48]. Table 1 shows the three-level NPC inverter switch states based on the output voltage. Sequence positive: The switches,  are opened, and ,  are closed. The output voltage equals . Sequence zero: The switches  ,are opened, and ,   are closed. The output voltage equals . Sequence negative: The switches,  are closed and , are opened. The output voltage equals   [43].

Table 1. Switching state of the three-level NPC inverter [24].

Figure 3. Topology of NPC inverter [47]

3. CONTROL OF WIND-DRIVEN DFIG  

1. MPPT Model

WE fluctuate’s with wind speed throughout the day. The quantity of power delivered by a WECS depends on the MPPT controller's accuracy in tracking peak power points, independent of generator type [13],[49]. The power coefficient in equation (1) depends on both the blade pitch angle β and the tip-speed ratio  This work utilizes a fixed pitch angle  indicated which is the point corresponding to the maximum of the mechanical power recovered as depicted in Figure 4. The tip-speed ratio optimal is determined by [35],[50]:

Figure 4. Cp versus

Figure 5 shows the control design that uses a classical  controller to calculate electromagnetic reference torque based on the difference between reference and rotation speeds. The coefficients and  regulators are calculated as (12) and (13):

Figure 5. Block diagram of speed controls

2. Field-Oriented Vector Control

The method of vector control is intended to achieve the decoupling between flow control and electromagnetic torque [51][52]. The modeling of the DFIG with a stator field-oriented [53]-[55]. A simplified expression of the electromagnetic torque is obtained by setting the following conditions:

Equation systems can be simplified as follows:

The voltage and flux equations of the stator windings may be streamlined in a steady state as follows, assuming that the resistance of the stator winding  is neglected.

The torque formulae of the flux:

The electromagnetic torque expression is:

The active and reactive stator powers are as outlined (19):

The equations related between the stator and the rotor currents are calculated (20):

By replacing the direct and quadrature stator currents with their expressions in the equations of active and reactive powers:

To ensure appropriate machine management, it's necessary to determine the relation between the rotor voltages and currents supplied to the machine [51].

The equation of the voltage rotor:

In a steady regime, the equation will be as follows:

The field vector indirect control without and with power control is presented in Figure 6 and Figure 7, respectively [54]. The design of a conventional PI regulator for controlling currentsand  is seen in Figure 8.

Figure 6. Block diagram of FOPI without power control [54]

Figure 7. Block diagram of FOPI with power control [54]

Figure 8. Block diagram of current controls

The coefficients and  regulators are calculated as (25) and (26):

The design of the PI for controlling currents is depicted in Figure 9. The coefficients and  regulators are calculated as (27) and (28):

Figure 9. Block diagram of power controls

3. Three-Level Sinusoidal Pulse Width Modulation Strategy

The three-level sine-based  inverter works on the same principles as a two-level inverter. The key mechanism in its operation is producing sine carrier PWM by comparing two triangular carrier waves to three unique reference control signals. This method provides for greater control and modification of the output voltage, resulting in higher performance in a variety of situations where inverters are used. The inverter gate devices are to receive the matching pulses that are created. The three reference control signals are phase shifts by an angle of  and  with the same amplitude. With a DC voltage offset, two carrier waves are in phase with one another. For three-phase  [56][57]:

4. Genetic Algorithm

GA falls within the category of evolutionary algorithms. Holland first laid out the basic ideas of GA [58]. They aim to find an approximate solution to an optimization issue. GA employs probabilistic transition rules to handle a population of possible solutions, called individuals or chromosomes, which evolve repeatedly [59] [60]. Each iteration of the algorithm is called a generation. Solution evolution is simulated using a fitness function and genetic operators, including reproduction, crossover, and mutation [61]. The GA steps are as follows:

1. Initial Population

The algorithm starts by creating arbitrary primary inhabitants. In MATLAB, the main population typically consists of  entities, indicating an evasion rate of the population range [62]. One of the most common initialization techniques is the use of random binary characters, as depicted in Figure 10.

Figure 10. Initialization strategy

2. Function fitness

        This alludes to an individual's capacity to compete against others. Individuals are scored on their fitness function in each iteration. Each person obtains a fitness score from the fitness function. This score also affects your chances of getting picked for reproduction. The greater the fitness score, the more probable that the individual will be chosen for reproduction [63]. The GA uses present residents to generate children for future generations. The algorithm selects parents from the present population to pass on their genes to their children. The GA often chooses entities with high vigor rates, such as parents [60][61]. The GA creates three sorts of children for the following generation:

3. Selection

        During the selection stage, individuals are chosen for progeny reproduction. Every one of the chosen individuals is placed in pairs of two to improve reproduction. The following generation subsequently inherits these people's DNA [61].

4. Crossover

Crossover offspring are created by combining the vectors of a pair of parents from the current population. The evasion intersect task randomly selects a gene from one of the two parents and assigns it to the kid vector at each iteration [60].

5. Mutation

To maintain population diversity, the mutation operator transfers random genes into the offspring (new child). This can be accomplished by shifting a few chromosomal bits. Thus, mutation solves the problem of early convergence and increases diversity [61][62]. In this work, the GA is used to optimize the parameters of the conventional PI regulator in DFIG and WECS.

The following are the Genetic algorithm steps for tuning the parameters of the PI regulator, followed with flowchart depicted in Figure 11:

• The transfer function should be introduced.
• Create a random Nchromosome population 
• Fitness: Assess each population's chromosome X's objective function ITAE.
• New population:  create a new population, repeat the steps below until it is complete:
• Select two parent chromosomes,  and  from a population based on their ITAE fitness.
• Crossover: With a crossover chance, the parents will cross to produce new offspring. If no crossover were conducted, the offspring would be a replica of the parents.
• Mutation: With a mutation chance, create new offspring at each locus.
• Accepting: Add new offspring to the new populations  and
• Replace: Rerun the algorithm using the freshly created population.
• To stop the process, obtain the optimal parameters gain  
• Check if the end condition is met. Go back to step 3.

 Figure 11.  Flowchart of GA

4. SIMULATED RESULTS AND DISCUSSIONS

The suggested methodology was validated by thorough testing of a DFIG-based WECS in Simulink/MATLAB. This validation carefully investigates the system's performance under changing wind speeds, particularly between 7.6 and 8.4, as shown in Figure 12. Several simulations were carried out to better understand the differences between the various suggested controllers used in MPPT for maximizing power extraction from WECS. The simulation results shown in Figure 13 show a clear link between mechanical speed and reference speed. The results support the usefulness of the genetic algorithm used, demonstrating its capacity to provide a quick reaction while reducing overshoot. This high performance is critical since it helps to maximize power production.

Figure 12. Wind input

Figure 13.  Turbine wind speed obtained by PI and GA

The graphic depicted in Figure 14 and Figure 15 compares the d-q rotor current responses of a DFIG under two control strategies: the Pole Placement controller and the GA controller. During a , the d-axis rotor current demonstrates that both controllers are in operation, the PP controller exhibits greater variations, whilst the GA controller has a smoother, better-damped response. The q-axis rotor current has a transient. At  and a step change at 1 s, with the PI controller providing a gentle transition, reacting lower with more fluctuations. The PI controller thus provides better dampening and smoother dynamics, whereas the AG controller allows for faster response at the expense of harsher transients. According to the analysis, the GA approach outperforms the PP method in terms of response characteristics and dynamics. Figure 16 and Figure 17 exhibit the machine's effective decoupling, emphasizing the relevance of the FOCI in power regulation. The research shows that the pole placement method generates gain values that result in inferior performance, particularly when system gains fluctuate, highlighting its shortcomings. In contrast, the GA optimization method produces superior outcomes, demonstrating excellent stability and dynamic performance in the face of change. The data strongly show that GA optimization outperforms pole placement in terms of delivering stable and efficient power regulation while avoiding the introduction of major dynamic faults.

Figure 14. DFIG rotor current direct

Figure 15. DFIG rotor current quadrature

Figure 16. Active power

Figure 17. Reactive power

Table 2 and Table 3 compare the PI controller gains obtained by two different methods: pole placement and genetic algorithm optimization. The Table 1 shows that the pole placement method gives much larger gains  compared to the genetic algorithm method which indicates a stronger control action but makes the control system less sensitive to disturbances. Table 3 emphasizes the current and power control loops, where the same conclusion is drawn, indicating that the pole placement method always gives larger gains in both cases. This indicates that the pole placement method favors fast response and accuracy in tracking, while the genetic algorithm method favors a stable and moderate control action.

Table 2. PI controller gains speed controls.

Table 3. PI gains currents and powers controls.

5. CONCLUSIONS

This paper introduces a WECS using a DFIG, with emphasis on the construction of a global model and a vector control scheme aimed at controlling the active and reactive power outputs of the DFIGUREThe control scheme uses PI control with the addition of a genetic algorithm for optimization, particularly in MPPT and FOC. Among the major findings of this research work is that the use of PI control with variable parameters (PI-PP) results in better performance with lower settling times and over-peak overshoots, culminating in a faster stabilization process. On the other hand, the use of genetic algorithm-optimized PI control shows greatly improved convergence speeds to the gain values and better transient response characteristics compared to traditional PI control schemes. This improvement is critical in ensuring that the DFIG system performs well even at high power levels, ultimately providing better performance and stability. The paper recognizes some limitations, which open avenues for future research, especially in the area of adaptive methodologies. It is postulated that hybrid approaches may be used to improve dynamic behavior. Such advances may help to improve the efficiency and scalability of GA and extend its applications to different areas, such as real-time control systems and machine learning. The paper also stresses the need to validate the present findings by comparing them with the results of virtual simulations and real-time experimental results.

Appendix

Table 4. DFIG Parameters

Table 5. Wind Turbine Parameters

List of Abbreviations

Declaration

Author Contribution

All authors contributed equally to the main contributor to this paper. All authors read and approved the final paper.

Acknowledgment

This article has been produced with the financial support of the European Union under the REFRESH-Research Excellence for REgion Sustainability and High-tech Industries project number CZ.10.03.01/00/22_003/0000048 via the Operational Programme Just Transition.

Conflicts of Interest

The authors declare no conflict of interest.

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