Optimizing power generation in a hybrid solar wind energy system using a DFIG-based control approach

Abstract

The rising demand for renewable energy has recently spurred notable advancements in hybrid energy systems that utilize solar and wind power. The Hybrid Solar Wind Energy System (HSWES) integrates wind turbines with solar energy systems. This research project aims to develop effective modeling and control techniques for a grid-connected HSWES. The goal is to optimize power tracking efficiency in an electrically linked solar photovoltaic system combined with a wind-powered Doubly Fed Induction Generator (DFIG). The back-to-back () converters’ DC link is connected to this to integrate the solar photovoltaic (PV). The study controls the rotor and grid converters via a vector control technique. This study aims to optimize power extraction efficiency and hybrid system integration with electrical grids by applying the Maximum Power Point Tracking (MPPT) technique to solar and wind systems. Combining the control strategy with the optimization algorithm makes our work new and compelling. We utilized this technology with a focus on optimization to evaluate how our system performs when applying optimization techniques to the control strategies. We optimized the solar system using the conventional Perturb and Observe (P & O) method and the metaheuristic Particle Swarm Optimization (PSO) technique. Our primary objective was to validate the effectiveness of the optimization process in enhancing the control strategy. The paper investigates the applications of Particle Swarm Optimization (PSO) and Perturb and Observe (P & O) algorithms in solar photovoltaics under constant and real-time sunlight. The hybrid Indirect Speed Controller MPPT algorithms are utilized for step-up and step-down wind speeds. An HSWES simulation is used to confirm the effectiveness and efficiency of the recommended regulation technique. The suggested control approach is simulated using the Sim Power of the MATLAB/Simulink platform. The advantage of the established techniques lies in their capacity to swiftly and precisely monitor the ideal power output of the HSWES. The comprehensive simulations conducted provide compelling evidence for the efficacy of the proposed system in attaining optimal efficiency and stability, propelling the progress of sustainable energy solutions.

Introduction

Power-producing technologies have grown to meet the growing demand for electricity in the 21st century. The global shortage of electricity is the result of the growth of population and urbanization that is happening too quickly. Power generation systems fall into two main categories: renewable and non-renewable energy systems, depending on how exhaustible they are. Natural resources such as sunlight, bioenergy, wind, water streams, geothermal heat, and tides can be used to generate renewable energy. In contrast, non-renewable energy is derived from finite resources such as nuclear energy and petroleum products, such as natural gas, coal and crude oil¹. Utility and customer energy expenditures increase due to high maintenance costs and poor quality control. Furthermore, petroleum seriously pollutes the air^2,3. In addition to adverse environmental effects, toxic waste, and expensive operations and maintenance, fossil fuels have a limited supply and will eventually run out⁴. The increasing global energy demand and the pressing need to reduce greenhouse gas emissions are driving a trend towards the use of renewable energy sources. Due to their growing availability and rapid technological advancement, solar and wind power are driving this change. Skillfully combining various clean energy sources into the electrical system ensures a stable and environmentally friendly energy source⁵. The DFIG is a well-liked option for WECSs due to its efficiency over a wide variety of wind speeds and its ability to control active and reactive power independently. Two VSCs connected by a common DC link form the converter , allowing independent control of the grid and generator sides and bidirectional power flow⁶. An integrated energy system is produced when solar photovoltaic panels are incorporated into a wind power system based on DFIG’s DC connection of the converter. Furthermore, by directly integrating solar PV systems into the DC link, no additional inverters are required, reducing the complexity and cost of the system⁷. The production of solar and wind energy depends extensively on the surrounding environment, causing electricity production to be erratic and intermittent. MPPT is necessary for both energy sources to operate at their best^8,9. For solar PV systems to maximize energy extraction under different irradiation circumstances, an independent MPPT mechanism is needed^10,11. Hybrid MPPT techniques are required for wind energy systems to optimize wind power capture. Using these MPPT methods in a DFIG hybrid system connected to the grid, a solar photovoltaic system connected to the direct current link, and a converter presents several technical challenges and opportunities^12,13. As seen in Fig. 1, the MPPT is divided into the following categories: Solar’s MPPT is implemented using conventional and metaheuristic-based MPPT. Then, the maximized independent solar is integrated with a converter of the DFIG. Then, a hybrid MPPT for the wind turbine is developed using a HSWES. The reliability of the grid-tied hybrid energy system is higher than that of a conventional renewable energy system. Renewable energy sources are being replaced with HSWES due to their higher reliability. Power grid systems involving various energy sources are more effective than traditional utility grids¹⁵. In Fig. 2, the HSWES schematic diagram is illustrated. The following sections comprise the structure of the paper. Heading 1: Describes the introduction to the problem. Heading 2: Highlights existing literature on DFIG-based wind energy systems, solar PV integration, MPPT techniques, and hybrid power systems. This section concludes with a comparison of different control methodologies and the main contributions of this work. Heading 3: Describe how each element of the hybrid power system is designed, how they work, and how their mathematical modeling works. Heading 4: Provides a detailed explanation of the use of control systems for the synchronized operation of wind and solar energy sources. Heading 5: Describes the MPPT algorithms for wind and solar power. Heading 6: Describe the simulation findings, results, and discussion. Heading 7: Summarize the main conclusions and contributions.

Fig. 1.

MPPT Classification¹⁴.

Fig. 2.

Schematic diagram of the HES, influenced by¹⁶.

Literature Survey

It has been challenging for world leaders, educators, and researchers to fulfill the rising energy demand from secure, eco-friendly, and safe sources. Governments switched from traditional fossil fuel-based energy sources to non-traditional and renewable ones to meet the stated goal and reduce greenhouse gas emissions. Furthermore, RER may enhance the world economy and energy security. Thus, RER-based energy creation has quickly extended, and the world hopes to see this pattern continue in the next few decades. Various investigations and studies are available on the generation and utilization of energy from RER means; some new notable exploration is referenced as¹⁷. Solar and wind power are two essential alternative energy sources to help with the current energy crisis¹⁸. Even for independent applications in isolated places where extending the grid is difficult, employing hybrid energy systems is a more financially sensible course of action¹⁹. The purpose of this study is to conduct a quantitative analysis of the integration of wind and solar energy economics from demand and supply perspectives. This study²⁰ developed a model of the economic power dispatch. Research on the economic, social, and environmental implications and novel energy solutions, including micro-hydro power, wind energy, solar PV, and others, is needed to reduce fuel usage. This research aims to produce electricity using solar PV and WT²¹. The operational conditions of the power system have been significantly impacted by the gradual growth in the percentage of RES during the last ten years. Romania is the nation in Southeast Europe with the greatest capability for RES generation. A unique approach for evaluating the effect of integrating large fractions of RES on the functioning of national electricity networks is proposed in the study¹⁹. In particular, the approach starts with a variability study of RES output using historical data for the Romanian electricity system spanning ten years. This study examines the feasibility of incorporating diesel generator systems with photovoltaic and wind energy sources into the unstable grid. The study²² aimed to offer a consistent stream of reasonably priced, ecologically friendly supplies. Four scenarios that considered unanticipated outages were evaluated to simulate and perform a techno-economic analysis of grid-connected PV, wind, and diesel systems. These scenarios were developed using demand variation, grid disturbances, and weather data from the research domains. This work developed models for the optimal size of an IRE system. By applying a GA-based methodology, the study seeks to lower both the cost of energy and the overall cost of generation. While considering OPF and EENS, the optimal viability of the system has been examined²³. Many technical problems arise when distributed power generation is incorporated into power systems. The most important ones are related to system stability, precisely voltage at the location of the point of common coupling (PCC) and system. To make the power grid “advanced,” particularly in strength and flexibility, a controller with the ability to control the issue is needed after integrating hybrid distribution-producing systems into the utility grid. The evolving modeling of crucial system components, namely electrical power devices, the WECS, the PVECS, and the regulating mechanisms for the PVECS, is the subject of this work. A comprehensive control strategy for a grid-tied combination of decentralized solar and wind electrical systems is also provided. The DC bus connects several energy sources to the power grid²⁴. This study suggests the best way to size a hybrid system that combines solar cells, hydropower-pumped storage, and wind turbines²⁵. The grid wind-solar cogeneration system should be arranged with fully VSC and DC to DC boost converters²⁶. and INC-based algorithms for MPPT with different perturbation stages are recommended to increase energy extraction efficiency. Power converter controllers are designed to maintain consistent grid power when operating with solar and wind MPPTs. A time-domain study is carried out to confirm the efficacy of the adapted MPPT methods. The hybrid energy system’s robustness is evaluated under multiple climate scenarios. This article’s discussion of coordinated MPC approaches is intended to be applied to a DC-coupled hybrid microgrid system consisting of photovoltaic systems from solar and wind energy sources. To maximize electricity production in the microgrid, the FCS-MPC uses a controlled rectification and a DC-DC converter to handle solar and wind-produced electricity. Additionally, the results are contrasted with existing approaches. Additionally, the connection between demand in general and the electricity generated by WDG and solar power sources forms the basis of the recommended power management strategy²⁷. The suggested approach builds a PV-augmented RPMS for a DFIG with a stator linked to the grid. The RPMS architecture is designed to operate independently of the electrical grid throughout the DFIG. The recommended plan ensures the system gets a higher output power when wind speeds are low. The suggested technique calculates the rotor position and speed without overly depending on machine features²⁸. This²⁹ uses a variable structure, the SMC theory of control, to describe and control the stator reactive and active power for the DFIG in wind turbine systems. The system may suffer from the detrimental chattering effect of the standard sliding mode method. Using the second-order sliding mode method is essential to ending this chattering. The control of the DFIG structure’s controllers will be fine-tuned to enhance transient performance during electric failures, augmenting LVRT’s capacity³⁰. In solar PV systems and wind energy translation schemes that rely on doubly fed induction generators, it integrates a nonlinear MPPT controlling technique. The DC link of the DFIG converter is linked to the PV system’s DC/DC converter output through the hybrid model. Additionally, the stator-voltage-oriented control system guarantees the steady operation of the DFIG by managing the RSC on the stator end for reactive and power that is active regulation. Using a DC/DC converter, the SPVS can continue producing its maximum amount of electricity. The solar PV system’s maximum power is tracked using the approach³¹. An approach to MPPT for wind turbines determined by double-fed induction generators is presented³². This work presents the mathematical modeling techniques for the solar power system and DC-to-DC boost converters. The process is perturbed and observed step-by-step, and the outcomes are modeled and analyzed. Two kinds of solar systems were simulated and assessed using various climate factors: one with and one without the algorithm. The essay emphasizes how the suggested approach performs better and responds faster in steady and variable weather circumstances¹. This MPO technique divides the power-voltage curve into four working regions based on the expected open-circuit voltage³³. This study has considered steady-state power oscillations, temporal response, and output power efficiency. The revised algorithms’ simulation results show that they perform better than standard algorithms for PV modules in several areas, such as tracking time, converter efficiency, and steady-state circumstances. Moreover, an increase in the dynamic responsiveness for tracking the MPP is noted throughout various climate conditions³⁴. Table 1 below provides previously applied control methodologies.

Table 1.

Comparison of different control methodologies.

Methodology	Pros	Cons	Novelty	Citation
Second-order sliding Mode Control	Reduced chattering compared to SMC and increased system stability.	Complex and requires fine-tuning.	STA-based second-order sliding mode control.	35
Proportional-Integral Sliding Mode Control	Improves transient response and reduces chattering.	Complex tuning of the PI controller.	PSO-based proportional-integral sliding mode control.	36
Integrated Solar and Wind using DFIG	Enhances overall system efficiency.	High initial cost and grid synchronization challenges.	DFIG-based hybrid integration.	37
ROMI Control for Solar-Wind-Battery Integration	Enhances stability in grid-connected renewable energy systems.	Requires complex tuning and control strategies.	ROMI control for hybrid renewable systems.	38
Effect of Distributed Energy Sources on System Dynamics	Increases power stability with renewables.	Load-supply mismatch may cause instability.	Analysis-based observation.	39
Vector Control with MPPT	Ensures optimal power extraction with precise control.	Grid synchronization and complexity.	MPPT-based vector control.	40
Speed Estimation Using an Anemometer	Reduces steady-state error.	Requires anemometer and complex initialization.	SSM-PSO speed estimation.	41

The combination of the control strategy with the optimization algorithm makes this work novel and effective. The combination is used with a focus on optimization to evaluate how the hybrid system performs while applying optimization techniques to control strategies. The solar system was optimized using both the conventional P & O method and the metaheuristic PSO technique. The primary objective of this work was to validate the effectiveness of the optimization process in enhancing the control strategy. The following advantages have been achieved by combining the optimization algorithms and the controller:

• It is cost-effective, as one inverter is reduced.

• Real-time data was applied for solar irradiance.

• The DC link voltage remains stable for the wide range of fluctuations for the solar-side irradiance.

• For a single-objective function in a hybrid configuration, conventional algorithms perform better.

System Modeling and Design

As seen in Fig. 3, this research creates HSWES using DFIG, a photovoltaic system, a DC to DC converter, and wind turbines. The aim is to generate 2 MW of power at the rated wind speed. The system consists of a turbine that produces electricity by DC linking a capacitor, a DFIG, a gird-side converter (GSC), a rotor-side converter (RSC), and a PV system. The rotor winding of the DFIG is coupled to the RSC. The VSC is connected to the PCC, whereas the GSC stator winding is directly connected to the grid. The RSC and the GSC work together to achieve the varied operational conditions of the DFIG. Figure 4 displays the block scheme for the described system. A WECS that integrates isolated solar power with a grid-connected DFIG. The system converts wind energy into electrical energy by combining a solar PV system and connecting it to the DC connection of the capacitor via a DFIG.

Fig. 3.

Configuration of an HSWES.

Fig. 4.

Block diagram of the electrically linked HSWES.

Modeling of Solar PV System

This model includes two resistive elements, one in parallel and one in series, to simulate a single-diode solar energy system and to consider supply loss. The relationship between parallel resistance, sometimes called shunt resistance, and current leakage in a cell is caused by impact on the surface and cell thickness. In Fig. 5(a), a solar PV cell is depicted, and in Fig. 5(b), a circuit diagram of the boost converter is depicted.

Fig. 5.

Solar PV cell and boost converter circuit diagram.

When a photovoltaic cell is subjected to continuous illumination, the current density produced in a particular cell volume is represented by the symbol . If the area of the cell is , the current of the PV cell is determined in equation (1), and the output current is given in equation (2).

1

2

denotes the diode current flowing through the parallel diode, and denotes the shunt current flowing through the parallel resistor¹⁵. Equation (3) shows the current that flows across the diode according to the Shockley diode calculation.

3

The symbols for the reverse saturation current (A) are , the ideality diode factor (n), the diode temperature (T), the fundamental charge (q), the constant Boltzmann (k), and the elementary charge (q). kT/q is about equal to 0.0259 volts at 25 , where “1” denotes an ideal diode. Equation (4) provides the voltage at the diode.

4

Here, the voltage across the shunt resistor and diode is . The output voltage across the ports is V. The resistance in the series is , after changing every equation to the one representing the output current, the shunt current and the output current are illustrated in equations (5) and (6), respectively.

5

6

Boost Converter

Step-up DC-to-DC converters are utilized to match the DC link voltage and increase the DC-to-DC converters of the solar PV module. The unit placed between the solar PV panels and the connection between the DC and the converters is the boost converter, a basic switch-mode step-up converter. The boost converter consists of an inductor, a diode, a capacitor, and a switch device. The most crucial piece needed for voltage conversion is a switch. The output voltage of IGBT switching is determined by its duty cycle D, represented in equation (7).

7

The MPPT algorithm describes a duty cycle D that works as a pulse that gates to the IGBT.

Table 2 below provides the design specifications of the proposed model for the photovoltaic system. Figure 6 displays the PV system block diagram.

Table 2.

Design specification of the PV systems.

Parameters	Parameter values
Input Voltage	600 V
Output Voltage	1200 V
Rated Power	50 kW
Switching Frequency	5 kHz
Current Ripple	5%
Voltage Ripple	1%

Fig. 6.

PV system block diagram.

Wind Turbine Modeling

The wind turbine converts the wind’s kinetic energy into rotational energy or torque. The following formula shown in equation (8) provides the amount of power available in the wind.

8

A: The area swept by the turbines , : Air density , : Wind speed (m/s). Equation (9) provides the power of the turbine.

9

R:It is the turbine rotor’s radius (in meters), : The power coefficient is determined by its angle of pitch () with tips speed ratio (). (,) can be written as in equations (10) and (11).

10

11

Equation (12) expresses the TSR, while equation (13) expresses the turbine’s torque.

12

13

: The wind turbine rotor’s angular rotational speed (rad/sec).

Modeling of the DFIG

We employ both direct and inverse transformations to demonstrate the DFIG’s operation. Using space-vector theory, we may divide the rotor and stator’s three windings into two windings. Equations (14), (15), and (16), (17), respectively, express the voltage vector between the stator and the rotor.

14

15

16

17

Where , the stator voltages and , are the rotor voltages in the DQ frame. The DQ-equivalent circuit of the DFIG is shown in Fig. 7a,b. Equations (18), (19), and (20), (21) express the flux of the stator and rotor;

18

19

20

21

The DQ axis fluxes along the stator and rotor frame are represented by and . and respectively. and indicate the phase of leaking the inductances for the rotor and stator, respectively. represents the mutual inductance between the stator and rotor¹³.

Fig. 7.

DFIG DQ equivalent circuit.

The electromagnetic torque is denoted as , as shown in equation (22). The fundamental torque expression is given in equation (23).

22

23

, the load torque supplied to the shafts and J, the inertia of the rotor, are used to calculate the rotor speed, .

Development of the Control Strategy

The DFIG’s stator winding receives three-phase grid power at a constant frequency and amount. In contrast, to achieve different DFIG working conditions, RSC provides the rotor at various frequencies and magnitudes. The operating point of the machine determines the power flow through the rotor and the grid. Equations (24) and (25) give the speed at which each of the three DFIG function modes depends.

24

25

In the DQ frame, DFIG is used in a vector control technique as visible from Fig. 9. The d-axis is where the stator flux vector is oriented, as shown in Fig. 8¹³.

Fig. 9.

Control Strategy for the RSC.

Fig. 8.

D-axis component that is aligned with the stator flux.

However, the combination of the control strategy with the optimization algorithm makes this work novel and effective. The combination is used with a focus on optimization to evaluate how the hybrid system performs while applying optimization techniques to control strategies. The solar system was optimized using both the conventional P & O method and the metaheuristic PSO technique. The primary objective of this work was to validate the effectiveness of the optimization process in enhancing the control strategy. The main advantages achieved by combining optimization algorithms and the controller include cost-effectiveness as one inverter is reduced, real-time data utilization for solar irradiance, stability of the DC-link voltage for the wider range of fluctuations on the solar-side irradiance, and the conventional algorithms’ better performance for a single objective function in hybrid configuration.

Control of the Rotor Side

Equations from (18)-(21) are substituted in (16)-(17) by the RSC, which applies the voltage to the rotor winding, generating the voltage shown in equations (26) and (27).

26

27

Where is given by the equation (28).

28

Because the fixed grid values are close to zero.

As seen in Fig. 9, the primary objectives of the RSC are to regulate the percentage of stator power, apply a three-phase voltage to the rotors at a slip frequency, and increase the DFIG energy using the MPPT algorithm. Consequently, these converters control the system’s bidirectional power flow. The control strategy must be applied to the DQ elements to use the ABC-DQ transform to convert the rotor voltage and current to DQ elements. The stator voltage vector estimate is subtracted by angle . PLLs minimize minor interuptions while synchronizing the grid. The 1/3 letter denotes the stator-rotor turn ratio¹².

Power and Speed Control Loops

Equation (29) expresses the torque in the DQ frame because the d-axis aligns with the stator flux and is close to zero. The resulting torque is given in the equation (30).

29

30

Where .

Equation (30) illustrates that the torque generated by the electromagnetic field is linear in direction to the rotor’s q-axis current. The reactive power equations for the DQ frame can be found using the formula in (31). Equation (32) shows that the d-axis component of the rotor current is precisely proportional to the stator’s reactive power.

31

32

So, the power and speed control loops provide the reference of and ²⁸.

Control of the Grid Side

The GSC control approach controls the DFIG power flow. Two crucial elements to consider while maintaining the power flow are the reactive power transfer with the grid and the voltage of the DC link. Figures 10(a) and 10(b) display the DQ model of the grid-side system in a stationary frame. Equations (33) and (34) can define the DQ component of filter voltage, and Equations (35) and (36) express the transfer of active and reactive power from the grid.

33

34

35

36

Fig. 10.

DQ model representation of the grid-side system.

After taking into account equations (37), (38), and (39), Fig. 11 shows the actual component of the voltage vector oriented along .

37

38

39

Fig. 11.

The voltage vector of the grid aligned with .

Equations (35) - (36) show that the current component governs the value of , while the current element governs the value of . In Fig. 12, the GSC controller block diagram is shown. The RSC-Capacitor-GSC pathway is used to send active power to the grid. A capacitor serves as the DC link. As a result, they keep constant to guarantee proper operation of the RSC and GSC under active power flow. The reactive power flow to the electrical system is preserved in a similar way. By reference and , this configuration provides pulses about GSC switching , , and . Figure 13 shows the GSC’s vector control methodology¹³.

Fig. 12.

Grid side system block diagram.

Fig. 13.

Control strategy for the GSC.

MPPT Review

This chapter describes the MPPT techniques for independent solar and hybrid MPPT systems.

Solar MPPT

Along with sun irradiation and other meteorological parameters, temperature impacts the nonlinear I-V properties of a PV solar cell. Therefore, MPPT algorithms optimize power output to extract the highest amount of electricity from the sun. One such technique that continuously monitors the output voltage and power of the solar photovoltaic method is the “perturb and observe” method²⁹.

To formulate the objective function for solar MPPT using the given expression, we first need to understand its role in solar PV systems. In solar photovoltaic systems, the MPPT technique maximizes the electricity output of solar panels. These feature a distinct power-voltage (P-V) characteristic curve compared with the MPP, or single peak point. The MPPT algorithms constantly monitor the solar panels’ point of operation to guarantee that they work at or close to the MPP and harvest the maximum amount of power. The given objective function for MPPT is given by an equation (40).

40

represents the desired power output in the MPP, represents the power output previously measured or estimated. This function measures the absolute difference between the desired and previous power output. The objective of the MPP algorithm is to minimize the difference. A lower value of the fitness function indicates that the system operates closer to the MPP, thus maximizing the power extraction from the solar panels. By minimizing the absolute difference between and , the MPPT algorithm ensures efficient use of solar energy. This approach helps to adapt to changing environmental situations, such as variations in sunlight intensity and temperature, which affect the MPP.

Perturb and Observe Algorithm

The optimal point of a given function can be found using the arithmetic modeling technique known as P & O. This approach emphasizes utilizing a control variable adjusted in tiny steps and figuring out the target function’s result before the slope goes to zero. This method continuously checks the output power of the solar photovoltaic system. If the operating point is to the left of the highest point of the curve, as shown in Fig. 14, the controller proceeds to the right to reach the highest point. If the operational point is to the right of the maximum value, the controller moves to the left to maximize the output. One way to determine this process is to calculate the slope of the control variable to the target variable³⁰. This technique uses the voltage and power of the PV array as input. When there is a disturbance in the voltage that operates and a rise in power, the position changes, approaching the maximum power point. This technique is repeated until the power goes off. The operational position will be diverted from the MPP if the power is interrupted. Subsequently, the operating voltage on the other path should be interrupted. The mobility of the point of operation can also be computed using the curve of the voltage variation in voltage and power. The program thus ensures that the system approaches the maximum power operational point, as shown in Fig. 15. There is a compromise to be made when setting the duty cycle’s step count because a greater step size indicates a faster response and more oscillations during the peak point, which means lesser efficiency. Substantially smaller step sizes increase efficiency but significantly slow convergence.

Fig. 14.

Voltage and power curve for a solar cell.

Fig. 15.

Perturbs and observe flow chart.

Particle Swarm Optimization

A random population of particles whose coordinates correspond to potential optimization issue solutions in the search space is used as the starting point for the PSO method. Velocity is a variable that controls how these particles move to share information with the swarm. The objective function that needs to be optimized assesses the fitness of each particle’s position that is formulated above in equation (40).

The PSO technique has already been applied to solar and wind systems, but only independently. Through an extensive literature review, we found no evidence that PSO is being implemented in a combined, integrated solar wind system. This gap in research makes our work innovative. The initialization of the PSO is given in Table 3;

Table 3.

Particle Swarm Optimization Parameters.

Parameter	Value
Number of particles	20
Number of dimensions	1
Maximum iterations	200
(Cognitive coefficient)	2
(Social coefficient)	2
W (Inertia weight)	0.4

Its single-dimensional problem can be resolved in five iterations, but we performed 200 iterations.

Each particle in the search area is updated in each iteration according to the best position it has found on its own thus far, known as particle best (), and the best position the population has seen, known as global best ()¹⁰. The maximum output power of the solar panel and the ideal duty cycle are shown, respectively, by the particle’s position and fitness, which may be solved in the PSO-based MPPT algorithm. Equations (41) and (42) determine the updated velocities and the new location (duty cycle) of particle i at each time step t.

41

42

Where and are weighting variables related to cognition and society, respectively; and are random values between 0 and 1, where the weight of inertia (w), which regulates the amount of old velocity v(t) in computing of the new velocity v(t+1). The effects of and are determined by the coefficients , and , . Based on the formula (, ) = (, ), the lower limit (), and the upper limit () for velocity are set to be the lower limit () and upper () limits of . A velocity is limited to or , respectively, if any updated velocity is in equations (41) and (42) or . The update of the velocity and the corresponding duty cycle will continue until t reaches the highest number of iterations. For every irradiance, the procedure for determining the ideal duty cycle and matching MPP will be repeated. Figure 16 displays the flow chart of the PSO algorithm.

Fig. 16.

PSO Algorithm’s flow chart.

MPPT for the Wind Turbine

Wind turbines are divided into FSWT and VSWT according to their operating speeds. FSWTs work at a fixed angular velocity to provide rated power, usually 1.0 percent of the nominal wind speed. As a result, power production varies as wind speed varies. On the other hand, VSWTs function in a wide variety of wind speeds, modifying the rotor speed to achieve optimal efficiency. VSWTs use power converter devices to maintain power output at rated levels despite variations in wind speed. Effective speed control in wind turbines is crucial for safe operation and for reducing mechanical strain on the drive train. This speed control system operates in three distinct regions, as in Fig. 17.

• Regions of minimum operating speed and maximum power extraction

• Operating speed maximum at partial and full/rated power output regions

Fig. 17.

Different operating regions of the wind turbine.

Region 1 and Region 3 Regions 1 and 3 aim to keep the wind turbine at the lowest point in the first case and its maximum value in the second. Likewise, the turbine rotates at a low frequency at a relatively low wind speed. The resonance frequencies of the tower are correlated with this lower frequency. Constant operation of the turbine at reduced speeds stimulates the resonance frequency of the tower, weakening the structures, and causing vibration-induced breakdowns. Because of this, the turbine has a defined lower limit, after which it shouldn’t be used. Turbine speeds should be restricted to the highest safe operating limits for dangerously high wind speeds, so the turbine runs only within its absolute safe operating parameters. Maintaining wind speeds within the defined lower and upper limits is the primary focus in such a situation.

Region 2 The primary goal in this field of work is to generate as much electricity as possible. To accomplish this, the turbine rotates at a speed that increases linearly with the wind speed. The use of several controllers and MPPT techniques optimizes power extraction. One method is tracking of the MPP, or ISC by using the electromagnetic torque as a reference. To use the tip speed ratio, the DSC is an alternative technique that establishes the ideal turbine rotation speed for each range of the wind speed and utilizes it as a reference for the speed of rotation.

Indirect Speed Controller

The primary goal in area 2 of the speed of the turbine properties is to maximize the extraction of wind energy through the usage of MPPT. This can be accomplished by setting the controller’s reference variable to either the torque-based ISC or the DSC based on the actual wind speed. The primary goal of the MPPT controller is to ensure that the DFIG WECS receives the best possible power delivery. The optimal torque reference for the generator is chosen using MPPT to manage the RSC. Equations (43) and (44) show that the power coefficient should be kept at its most significant value to obtain the ideal torque value. Various methods for extracting wind turbine electricity have been proposed in several studies. The following equation provides expressions for when the wind turbine operates on MPPT.

The indirect speed controller is designed based on the wind power equation, which is then transformed into torque form. Since wind power is a function of wind speed, any variation in wind speed directly affects both power and torque. As the wind speed increases, the generated power and torque also increase, while a decrease in wind speed leads to a corresponding reduction. For a step-up in wind speed, the torque is higher compared to that in a step-down scenario.

43

44

The torque is expressed by equations (45) and (46);

45

Where;

46

This suggested MPPT is shown in Fig. 18.

Fig. 18.

Indirect speed controller for the wind turbine.

Simulation, Results and Discussion

Simulink Model and Input of the System

The suggested HSWES is simulated using the MATLAB/Simulink environments. Tables 4 and 5 provide the parameters of the wind turbine system and the parameters of the solar module, respectively. A wind turbine system is modeled with a wind speed rated of 11 m/s and 2 MW of electricity. The solar system has a 50-kW rating at 1000 W/m2 rated irradiance. For the specifications of the HSWES, please refer to Table 4 For the continuous power supply, we used a constant infinite grid (grid voltage: 690 V (phase-to-phase Vrms), 50 Hz) to sink our system, which is already improved as seen in the results and also offers the following benefits in the result of the approach adopted.

Table 4.

Model parameters for wind turbine simulation.

Parameter	Parameter value
Rated wind speed	11 m/s
Frequency	50 Hz
Air density	1.225 kg/m3
Rated torque	12732 N-m
Pole pair	2
Tip speed ratio	7.2
Pitch angle	0°
Inertia	127 kg-m2
Power coefficient	0.4411
Gear ratio	100
Nominal power	2 MW
Turbine radius	42 m

Table 5.

Module specifications of the solar system.

Parameter	Parameter value
Module: Advanced solar hydro wind power	API156P-230
Maximum power	229.8 W
Cells per module	60
Open circuit voltage	37 V
Short circuit current	8.18 A
Maximum voltage	30 V
Maximum current	7.66 A
Number of series modules	20
Number of parallel modules	11

The first irradiance profile is of the real-time data taken from the NREL website on March 18, 2024, as shown in Fig. 19(a). The second irradiance profile is constant, as shown in Fig. 19(b).

Fig. 19.

Inputs used for the solar system.

Figure 20 shows a Simulink diagram of the solar system. Figure 21 shows the wind speed profile that was used in the system. Increase and decrease of inputs ranging from 9 to 11 m/s and 11 to 9 m/s are applied to the system, as depicted in Fig. 21a,b, respectively. The suggested control technique works effectively for monitoring speed.

Fig. 20.

Simulink diagram of the PV system.

Fig. 21.

Input used for Wind turbine.

Figures 22 and 23 show the Simulink diagrams for the RSC and the GSC, respectively. Figure 24 shows the simulink model of the overall hybrid diagram of the proposed system.

Fig. 22.

RSC’s Simulink diagram.

Fig. 23.

GSC’s Simulink diagram.

Fig. 24.

The hybrid system’s Simulink diagram.

Results and Discussion

The design and modeling of the electrically linked DFIG system with a standalone solar energy source combined with a converter architecture are presented in this research. A separate MPPT algorithm is utilized for the solar power system, and a hybrid MPPT method is used for the wind energy source. Step-up, step-down, and actual values were used to evaluate the wind input, while constant and actual values were used to assess the solar input. The efficacy and efficiency of the system were confirmed by analyzing its performance in various scenarios.

Independent Solar System

This section presents the standalone solar system’s findings and the hybrid system’s comprehensive outcomes.

A constant solar irradiation was applied, resulting in consistent power production from the PV system. The MPPT algorithm efficiently tracked the MPP, guaranteeing maximum energy harvest. Throughout the simulation, fluctuations in the actual solar irradiance values occurred, and the MPPT algorithm effectively adjusted to these shifting conditions. The system handled the dynamic nature of the solar input well without causing a noticeable drop in performance. Three different MPPTs are used to track the maximum output power for both the constant and actual input values of the irradiance. The two MPPTs are , and PSO. Firstly, for constant irradiance, the efficiency and power graph of the solar system are observed for , and PSO is depicted in Figs. 25a,b, and 26a,b respectively. There is a possibility that the conventional algorithms can perform better in a single objective function, which can be seen from the results shown in Figs. 25 and 26.

Fig. 25.

Efficiency and power graphs for constant irradiance using P & O.

Fig. 26.

Efficiency and power graphs for constant irradiance using PSO.

For real-time irradiance, the efficiency and power graph of the solar system are observed for , and PSO as depicted in Figs. 27a,b, and 28a,b respectively.

Fig. 27.

Efficiency and power graphs for real-time irradiance using P & O.

Fig. 28.

Efficiency and power graphs for real-time irradiance using PSO.

Hybrid Energy System

The rotor speed vs the turbine power for different wind speeds is shown in Fig. 29a. Also, the power coefficient vs the tip speed ratio for different values of pitch angle are shown in Fig. 29b.

Fig. 29.

Turbine parameters for different wind speeds and pitch angles.

The converter’s DC link integration of wind and solar energy sources showed an effective strategy. The hybrid MPPT for wind and the independent MPPT for solar cooperated to maximize power extraction from both sources. Despite variations in wind speed and sun irradiation, the DC link voltage remained constant, guaranteeing a reliable grid connection and power delivery. Now, the hybrid results of the system for the increase in wind speed input are shown in Fig. 30. In this figure, Figs. 30a–d represent the WT parameters, which are power coefficient, tip speed ratio, turbine power, and turbine torque, respectively. For the rated wind speed, 2 MW is generated, which is depicted in Fig. 30c.

Fig. 30.

Turbine parameters for the step-up input.

The RSC parameters for the increased input are mentioned in Fig. 31. In this figure, Figs. 31a–c represent the reference torque, mean torque, and rotor speed, respectively. When the speed changes from 9 m/s to 11 m/s, which is the rated wind speed, the rotor speed is 1500 rpm.

Fig. 31.

Rotor side parameters for step-up input.

The GSC parameters for the increased input are shown in Fig. 32. In this figure, Figs. 32a–d represent the stator current, stator voltage, DC-Link voltage, and the grid voltage, respectively. In this, the wind increases from 9 to 11 m/s and the DC link voltage remains constant, which means that the system controls work properly.

Fig. 32.

Grid side parameters for the step-up input.

Now, the hybrid results of the system for the step-down input of the wind speed are depicted in Fig. 33. In this figure, Figs. 33a–d represent the power coefficient of the WT parameters, the tip speed ratio, the turbine power and the turbine torque, respectively. At the start the wind speed is 11 m/s, the power generated is 2MW. So, for the WT works properly.

Fig. 33.

Turbine parameters for step-down input.

The RSC parameters for the step-down input are shown in Fig. 34. In this figure, Figs. 34a–c represent the reference torque, mean torque, and rotor speed. respectively.

Fig. 34.

Rotor side parameters for step-down input.

The GSC parameters for the step-down input are shown in Fig. 35. In this figure, Figs. 35a–d represent the stator current, the stator voltage, the DC-Link voltage, and the grid voltage, respectively. In this, the wind is stepped down input is used while the dc link voltage remains constant.

Fig. 35.

Grid side parameters for the step-down input.

Discussion

The simulation results demonstrate how well the intended DFIG system works with an integrated solar energy source and converter strategy. Independent MPPT for solar and hybrid MPPT for wind maximized energy utilization from both renewable sources, allowing efficient and flexible power extraction.

The DC link voltage stability across different input conditions demonstrates the system’s robustness. The transient responses observed during step-up and step-down wind inputs were within acceptable limits, indicating a reliable performance under varying operational scenarios.

The idea of MPPT algorithms significantly influenced the system’s evaluation. The algorithm for solar MPPT provided consistent results, while the hybrid MPPT for wind, combining and FLC, enhanced adaptability to rapid changes in wind speed. This hybrid approach proved beneficial in maintaining optimal power extraction from the wind turbine.

In hybrid renewable energy systems, the solar photovoltaic system can be directly connected to the DC link of a converter, eliminating the need for an additional inverter in the solar system. A DC link capacitor connects two voltage source VSCs to form a converter. This setup enables effective power control in systems that incorporate solar, wind, and grid, among other energy sources. AC electricity from sources such as wind turbines is usually converted into the DC electricity by a front-end converter (rectifier side), and DC power is converted into AC for grid or load supply by a back-end converter (inverter side). Direct integration of solar PV into the DC link eliminates the need for a separate inverter, which reduces conversion losses, simplifies the system design, and saves money. The stable DC bus voltage is guaranteed by the current converter, and the extraction of solar energy is maximized by the MPPT mechanism. To ensure stability in the face of fluctuating solar input circumstances, this design necessitates efficient voltage regulation techniques. The system’s stability throughout a broad range of solar irradiance levels, from 0 to 1500 W/m2, indicates that variations in the amount of sunlight do not affect the system’s overall performance. The controlled power flow in the DC link, where the converter dynamically regulates power exchange between sources and loads, is what gives this stability. Alternative power sources, such as the grid, can be added to the energy supply at low irradiance levels to ensure continuous operation. The MPPT controller continuously modifies the solar panels’ operating point to maximize power extraction without generating voltage oscillations, thus improving the system stability. Compared to traditional solar systems, which frequently suffer instability as a result of irradiance fluctuations, this method offers a substantial advantage. Solar PV can be immediately integrated into the DC connection of a converter strengthening, optimizing, and lowering the cost of the hybrid system. This arrangement is perfect for applications where uninterrupted energy supply is essential as it can maintain stable performance under a variety of solar conditions, ensuring reliable power output. For smooth operation and to avoid voltage spikes, careful design considerations are required, including load-sharing techniques and DC link voltage regulation. This approach opens the door for more sustainable and financially feasible energy solutions by improving the overall efficiency and dependability of hybrid renewable energy systems.

In conclusion, this chapter’s results and discussion support the design and modelling of the grid-tied DFIG system with a combined solar energy source and converter topology. Separate and hybrid MPPT algorithms ensured stable and reliable system performance, efficiently optimizing power from the corresponding renewable sources. The results highlight how this integrated strategy could improve the resilience and efficiency of renewable energy systems.

Conclusion

This paper presents a detailed analysis of HSWES. Combining solar and wind power with their MPPT for maximum power harvesting was the primary goal of increasing the efficiency and dependability of clean energy sources and promoting sustainable energy solutions. The WECS based on DFIG was a practical choice for wind energy harvesting because it can function well in circumstances with varying wind speeds. The converter arrangement made it easier to separate grid-side and generator operations, giving users more control over power flow and improving system stability in general. Integrating an independent solar PV system with MPPT and hybrid MPPT was a significant aspect of this study. The combination of the control strategy with the optimization algorithm makes this work novel and effective. The combination is used with a focus on optimization to evaluate how the hybrid system performs while applying optimization techniques to control strategies. The solar system was optimized using both the conventional P & O method and the metaheuristic PSO technique. The primary objective of this work was to validate the effectiveness of the optimization process in enhancing the control strategy. The main advantages achieved by combining optimization algorithms and the controller includes cost-effectiveness as one inverter is reduced, real-time data utilization for solar irradiance, stability of the DC-link voltage for the wider range of fluctuations on the solar-side irradiance and the conventional algorithms’ better performance for a single objective function in hybrid configuration.

Using MPPT ensured that the solar system operated at its MPP under varying environmental conditions, maximizing the energy harvested from the solar array. The hybrid MPPT approach combined conventional techniques, improving tracking accuracy and response time. An analysis was conducted on the grid-connected design of the combined wind-solar system. The results showed that the suggested system could successfully synchronize with the grid, guaranteeing smooth power distribution and maintaining frequency and voltage stability. Furthermore, it was revealed that the hybrid approach to MPPT was advantageous in maximizing the energy output of the solar PV system, enhancing the efficiency of wind energy, and improving overall system performance. The simulation results validated the theoretical models and control strategies proposed in this thesis. The findings confirmed that the integration of wind and solar energy sources using advanced control techniques could lead to a more reliable and efficient renewable energy system. This hybrid approach offers a promising solution to address intermittency issues associated with individual renewable energy sources and contributes to a more sustainable and resilient energy infrastructure. In conclusion, the study has successfully demonstrated the feasibility and advantages of integrating a DFIG-based WECS with an independent solar PV system using MPPT and hybrid MPPT techniques for grid-connected applications.

Abbreviations

HSWES

Hybrid solar wind energy system

DFIG

Doubly fed induction generator

MPPT

Maximum power point tracking

PSO

Particle swarm optimization

Back to back

WECSs

Wind energy conversion systems

VSCs

Voltage source converters

GSC

Grid side converter

RSC

Rotor side converter

RER

Renewable energy resources

WT

Wind turbine

RES

Renewable energy sources

IRE

Integrated renewable energy

OPF

Optimization of power factor

PCC

Point of common coupling

PVECS

PV energy conversion system

MPC

Model predictive control

FCS-MPC

Finite control set MPC

RPMS

Rotor power management system

SMC

Sliding mode control

LVRT

Low voltage ride through

INC

Incremental conductance

FSWT

Fixed speed wind turbine

VSWT

Variable speed wind turbine

WDG

Wind diesel generator

DSC

Direct speed controller

STA

Super twisting algorithm

DPC

Direct power control

ISMC

Integral sliding mode control

PR

Proportional resonant

DSRF

Double synchronous reference frame

DOB

Disturbance observed based

ROMI

Reduced order multiple integral

SSM-PSO

Search space minimization particle swarm optimization

Author contributions

S.A.R.K. conceived the idea, M.S. and S.A.R.K. conducted the simulations and experiment(s), M.S., S.A.R.K., M.S.F. and A.R. analyzed the results, S.A.R.K, M.S.F. and A.R. validated the results, M.S. and A.K.S. prepared the figures and tables. All authors read and reviewed the manuscript.

Funding

The authors declare that they had no funding available to carry out this research work.

Data availability

The authors declare that they have provided the data that were generated or analyzed in the publication of this article.

Declarations

Competing interest

The authors declare that they have no competing interests in the publication of this article.