Power control of an autonomous wind energy conversion system based on a permanent magnet synchronous generator with integrated pumping storage | Scientific Reports

Scientific Reports volume 14, Article number: 29776 (2024) Cite this article

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Wind energy plays a crucial role as a renewable source for electricity generation, especially in remote or isolated regions without access to the main power grid. The intermittent characteristics of wind energy make it essential to incorporate energy storage solutions to guarantee a consistent power supply. This study introduces the design, modeling, and control mechanisms of a self-sufficient wind energy conversion system (WECS) that utilizes a Permanent magnet synchronous generator (PMSG) in conjunction with a Water pumping storage station (WPS). The system employs Optimal torque control (OTC) to maximize power extraction from the wind turbine, achieving a peak power coefficient (Cp) of 0.43. A vector control strategy is applied to the PMSG, maintaining the DC bus voltage at a regulated 465 V for stable system operation. The integrated WPS operates in both motor and generator modes, depending on the excess or shortfall of generated wind energy relative to load demand. In generator mode, the WPS supplements power when wind speeds are insufficient, while in motor mode, it stores excess energy by pumping water to an upper reservoir. Simulation results, conducted in MATLAB/Simulink, show that the system efficiently tracks maximum power points and regulates key parameters. For instance, the PMSG successfully maintains the reference quadrature current, achieving optimal torque and power output. The system’s response under varying wind speeds, with an average wind speed of 8 m/s, demonstrates that the generator speed closely follows turbine speed without a gearbox, leading to efficient power conversion. The results confirm the flexibility and robustness of the control strategies, ensuring continuous power delivery to the load. This makes the system a feasible solution for isolated, off-grid applications, contributing to advancements in renewable energy technologies and autonomous power generation systems.

Nowadays, a large proportion of the world’s energy production is based on fossil fuels. The use of these non-renewable resources contributes significantly to greenhouse gas emissions, adding to environmental pollution. Moreover, the accelerated depletion of these finite resources poses a serious threat to their availability for future generations. In light of recurring economic and oil crises, scientific efforts have increasingly turned towards renewable energy sources, which have emerged as a pivotal sector, gaining importance in both research and development initiatives1,2.

Wind energy has been used for at least 3,000 years. It was first used for navigation on the Nile at least 5,000 years ago and, at the same time, windmills were pumping water in China. Since then, wind sensor technology has continued to evolve. In 1891, the Dane Poul la Cour invented the first wind generator designed to produce electricity3,4. At the beginning of the 20th century, he designed the first vertical-axis wind turbine, with a relatively low power. It wasn’t until 1957 that the Danish manufacturer Gedser achieved an output power of 200 kW. But it was only after the first oil crisis in 1973, when oil-exporting countries reduced their exports and entered the wind energy market, that the first wind turbines were developed5,6.

By the end of 2019, the installed wind power capacity worldwide had reached 650.8GW, reflecting an annual addition of 59.667GW. This was well above the 50.252GW installed in 2018. 2019 represented the second highest growth period for the wind energy sector in terms of market size, achieving a growth rate of 10.1%, an improvement on the 9.3% growth seen in 2018, although still below the peak growth rates seen in 2016 and 2017. Collectively, wind turbines installed by the end of 2019 had the capacity to meet more than 6% of global electricity demand7,8.

Wind energy is commercially deployed in over half of the world’s nations9. In 2019, many countries saw significant penetration of wind power. China and the USA dominated the market with substantial new installations, adding 27.5GW and 9.1GW respectively10. These two countries have recorded their highest market volumes in the last five years11,12. Conversely, many european markets, particularly Germany, have slowed considerably as a result of inappropriate policies. Germany, once the world leader in wind power, has added just 2GW in 2019, down sharply from the 6.2GW added in 201713.

All stakeholders agree that the corona virus crisis will have an impact on market development in 2020, leading to a general slowdown in the wind energy industry in most markets. In 2019, global wind power capacity grew by 59 GW, an increase of 10.1%14.

A variety of renewable energy sources are currently available, including hydroelectricity, geothermal energy, biomass, photovoltaic energy and wind power. One of the main advantages of these renewable energy sources is their minimal impact on the environment, as their use does not lead to air pollution or the emission of greenhouse gases such as carbon dioxide and nitrogen oxides, which are major contributors to global warming15.

Wind power has become one of the most sought-after renewable resources for electricity generation, used both in isolated locations and as an additional source of energy for interconnected grids16,17. It is a viable alternative that is helping to reduce the world’s growing demand for electricity. The continuing progress and widespread adoption of wind energy conversion systems has led to significant investment by the industrial and scientific communities, which are focusing on improving the technical efficiency, economic viability and overall quality of electricity generation18,19.

Many remote areas of the world rely on stand-alone power generation systems, using local renewable energy sources such as solar, wind, hydro and biomass. In these independent systems, the role of energy storage is crucial in maintaining reliability20. Given the intermittent nature of renewable resources, energy storage becomes essential to ensure continuous availability of electricity. In geographically remote areas without grid connection, renewable energy systems are integrated with storage solutions to maintain constant energy production, compensating for periods when renewable energy production is insufficient12.

Recent advancements in the field of wind energy systems, particularly those employing Permanent magnet synchronous generators (PMSG) and integrated energy storage solutions, have focused on improving efficiency, stability, and autonomy in off-grid applications21,22,23. discusses fault ride-through capabilities for grid-tied PMSG systems, which is crucial for grid stability but less applicable to off-grid systems, where voltage regulation and continuous power become key challenges. In contrast, this study introduces a control framework that integrates optimal torque control (OTC) and vector control to ensure reliable operation in autonomous, off-grid settings, addressing the fluctuating nature of wind energy24. also addresses voltage stability but in grid-connected systems using SVC and STATCOM, while this research focuses on autonomous energy management through an integrated Pumped Storage System (PSS), providing dynamic energy storage and recovery25. emphasizes Direct torque control (DTC) for DFIG systems, but the current paper builds on the simpler, more reliable PMSG-based system that operates without a gearbox, thus reducing system complexity and maintenance requirements. Similarly26, explores hybrid systems combining wind, photovoltaic, and diesel generators with batteries for autonomous power generation, yet this paper highlights the scalability and efficiency of combining PMSG with a PSS, which offers superior long-term storage compared to traditional battery-based systems27,28. present fuzzy logic and energy-based speed control approaches for optimal power extraction, aligning with this research’s focus on maximizing wind energy extraction through OTC, while emphasizing real-time stability and efficiency29. extends the discussion to hybrid systems with wind-PV-battery integration, but the integration of PSS in this work provides a more targeted solution for energy storage and load balancing in off-grid scenarios30. proposes a nonlinear generalized model predictive control (MPC) for improving the robustness of DFIG-based systems, while this paper focuses on the practical application of vector control and OTC for ensuring stable energy output in isolated locations31. discusses reactive power control using fuzzy and hysteresis-modulated methods, providing a novel control strategy for microgrids, while this work refines the PMSG-PSS integration to maintain continuous power supply, even during variable wind conditions32. examines machine learning techniques for direct power control in DFIG-based systems, offering improved control over wind energy systems, but the proposed control strategy in this paper focuses on real-time adjustments to optimize power output and maintain voltage stability in response to changing wind speeds33. explores multi-level inverters for wind systems under variable speeds, yet this study provides a more straightforward solution with PMSG and PSS, ensuring robust and efficient operation in off-grid applications28. discusses speed control in PMSG-based systems, which overlaps with the control strategies proposed here, but this research incorporates a unique focus on voltage regulation and optimal torque extraction34,35. focus on wind power forecasting and optimization techniques to predict wind speed and enhance energy planning. While these methods could enhance the predictive capabilities of the system, the emphasis in this paper is on real-time energy management through PMSG and PSS integration, ensuring a stable power supply even without detailed forecasting. Finally36,37, provide insights into voltage behavior and data-driven models for wind power prediction, respectively, which complement the PMSG-based system proposed here by suggesting future integration of predictive models with real-time control for even better energy optimization. Collectively, these studies provide valuable context for the development of an integrated PMSG-PSS system, offering a comprehensive solution for the efficient, stable, and autonomous generation and storage of wind energy in off-grid environments.

Wind power has established itself as one of the leading sources of renewable energy, offering a sustainable alternative to fossil fuels. However, its inherent intermittency and variability pose major problems and challenges, particularly in isolated or off-grid systems where there is no grid stabilization. The fluctuating nature of wind can lead to unreliable energy production, making it difficult to maintain a consistent and stable energy supply in these systems. For stand-alone wind systems, it is essential to ensure continuity of energy supply, particularly in remote areas where the energy infrastructure is minimal.

To meet these challenges, the integration of energy storage systems into wind energy conversion systems (WECS) has been proposed as a solution. Among the various storage methods, pumped storage systems (PSS) are widely recognized for their efficiency and scalability in managing energy surpluses and deficits. Combining a WECS based on a permanent magnet synchronous generator (PMSG) with a PSS can provide a robust framework for reliable power supply in stand-alone systems. However, the integration of these two systems poses significant control and optimization challenges, particularly in terms of maximizing power extraction from the wind, maintaining voltage stability and ensuring a continuous flow of energy between the PMSG, the load and the storage system.

The key research problem focuses on the need for an effective control strategy that can:

Maximize wind power extraction under fluctuating conditions using an effective maximum power point tracking (MPPT) method.

Ensure voltage stability and optimal torque control of the PMSG to provide consistent power conversion.

Facilitate energy storage and recovery in the PSS, dynamically switching between the motor (storage) and the generator (power) according to energy demand and wind conditions.

Operate autonomously in off-grid or isolated environments, making the system reliable and adaptable to varying wind speeds and load conditions.

This paper proposes a control framework that integrates optimal torque control (OTC) for efficient power extraction and vector control to maintain PMSG stability. This dual approach ensures that the system can handle varying wind speeds while maintaining a stable output. The study models the seamless interaction between the PMSG and the PSS. The storage system operates dynamically in two modes - engine mode to store excess energy and generator mode to supplement supply in the event of a wind shortage - to ensure continuity of supply. The entire system, including the control strategies, is modelled and simulated in a MATLAB/Simulink environment. Simulation results demonstrate the system’s ability to operate efficiently in fluctuating wind conditions, with the PMSG maintaining a stable DC bus voltage of 465 V and achieving a peak power coefficient (Cp) of 0.43. The research validates the robustness of the system for isolated applications. The results confirm that the proposed control strategies enable reliable power management, making the system suitable for off-grid or remote areas where a stable power supply is essential. With these contributions, this paper addresses the important challenge of managing intermittent wind energy in autonomous systems and provides a scalable solution for the integration of renewable energy and storage technologies in isolated environments.

The remainder of this paper is structured as follows. Section “Description of the proposed studied system” presents a detailed literature review, highlighting the main advances in wind energy conversion systems (WECS), the role of permanent magnet synchronous generators (PMSGs) and the integration of pumped storage stations (PSSs) as an energy storage solution. Section “System modeling” describes the system architecture and mathematical modelling of the proposed WECS, based on a PMSG with an integrated PSS, including the equations governing the wind turbine, the PMSG and the power converters. Section “Pumping storage station (PSS)” details the control strategies implemented in the system, focusing on the optimal torque control (OTC) and vector control methodologies used for efficient power management and voltage regulation. Section “Control of the whole system” discusses the simulation setup and results obtained in MATLAB/Simulink environment, focusing on the system’s response to varying wind profiles and its ability to maintain stable energy production. Section “Results and discussions” provides a full analysis of the results, including assessments of the performance of the energy storage system and the robustness of the control strategy. Finally, Sect. 7 concludes the paper by summarizing the main results, implications for future research and potential real-world applications of the proposed system.

The process of converting wind energy into electrical energy involves several stages. As shown in Fig. 1, the wind energy conversion system under study includes a pumped water storage station, which plays a key role in managing the flow and storage of energy within the system.

Firstly, the horizontal wind turbine converts the kinetic energy of the wind into mechanical energy available on the generator shaft. The generator consists of a PMSG with a high number of pole pairs. This structure makes it possible to operate at low speeds without a gearbox, and offers another advantage as less volume (space), less maintenance and less weight.

Wind energy conversion structure studied including water pumping storage station.

The analyzed system includes three distinct power electronic converters. The first converter, known as the Generator Side Converter (GSC), is connected to the stator of the Permanent magnet synchronous generator (PMSG). It operates as a rectifier, controlling the generator by maintaining a stable DC-voltage on the DC bus. The second converter, referred as the Load Side Converter (LSC), is connected to the load and operates as an inverter. It supplies the required active and reactive power of the load, ensuring a fixed frequency and sinusoidal current through the implemented control strategy38. These two converters are interconnected via a DC bus. The third converter operates in bidirectional mode, facilitating control of another Permanent Magnet Synchronous Machine (PMSM), which operates as a pump, capable of rotating in two directions.

When available energy exceeds the load requirements, a hydraulic storage mode stores the excess energy in as a potential energy form, by pumping water from the lower basin to the upper basin. In this case, the pump is driven by a PMSM which operates in motor mode.

When there is a shortage of wind energy, PMSM operates in generator mode by transforming the potential energy of the stored water gravity into mechanical energy available on the PMSG shaft, then into electrical energy.

The wind turbine considered is a horizontal axis type with three blades of R length, fixed on the rotor shaft which is directly and mechanically connected to the PMSG rotor shaft (without gearbox). Figure 2 shows the wind turbine connected directly to the PMSG rotor.

Wind turbine connected directly to PMSG.

The power supplied by the wind is given by the following expression39:

Since the wind turbine can only recover a fraction of the wind’s power, the turbine’s power can be written as follows39:

Where: \(\:{C}_{p}\left(\lambda\:,\beta\:\right)\): is the power coefficient of the turbine.

The speed ratio is defined as the ratio between the linear speed of the blades and the wind speed39:

The aerodynamic torque expression is given as39:

Where: \(\:S=\pi\:.{R}^{2}\:\): Surface swift by the wind turbine; \(\:R\:\): Blade length; \(\:\rho\:\:\): Density of air (1.225 kg/\(\:{m}^{3}\)); \(\:{V}_{w}\):Wind speed; \(\:{\varOmega\:}_{t}\): Turbine speed.

The masses of the various turbine components are represented in the form of an inertia Jt, comprising the blades and the turbine rotor masses.

The proposed mechanical model considers that the total inertia made up of the turbine inertia transferred to the generator rotor and the generator inertia.

It should be noted that the generator rotor inertia is very low compared to the turbine inertia transferred by the same axis.

The fundamental equation of dynamics can be used to determine the mechanical speed variation from the total mechanical torque \(\:{T}_{mec}\) applied to the rotor39:

Where: \(\:J\): Total inertia on the generator rotor; \(\:{T}_{r}\:\): Mechanical torque; \(\:{T}_{em}\:\): Electromagnetic generator torque; \(\:{T}_{vis}\:\): Viscous friction torque.

The resistive torque due to friction is modelled by a viscous friction coefficient f:

The differential equation which characterizes the mechanical behavior of the turbine and the generator is given as:

PMSG with winding rotor contain three identical phase winding at the stator, however, the rotor contains a winding excitation for the synchronous machine with winding rotor or a two-phase damper winding for PMSM (direct and quadratic) in the inductor circuit39.

We consider a synchronous machine with two pair poles without dampers with smooth-pole rotor which allows to get a PMSG model40,41. A small modification of the obtained equations, we can get a PMSG model with salient pole machine42.

The mathematical model of PMSG is necessary to study and control in different operating regimes (dynamic and steady states).

Before establish the mathematical model, some simplification hypotheses are imposed.

Voltage Eq.

It can also be written in matrix form, as follows:

With:

\(\:{\left[v\right]}_{abc}=\) \(\:\left[\begin{array}{c}{v}_{a}\\\:{v}_{b}\\\:{v}_{c}\end{array}\right]:\) Statoric voltage vector; \(\:{\left[i\right]}_{abc}=\) \(\:\left[\begin{array}{c}{i}_{a}\\\:{i}_{b}\\\:{i}_{c}\end{array}\right]=:\) Statoric current vector; \(\:\left[{R}_{S}\right]=\) \(\:\left[\begin{array}{ccc}{R}_{a}&\:0&\:0\\\:0&\:{R}_{b}&\:0\\\:0&\:0&\:{R}_{c}\end{array}\right]=\left[\begin{array}{ccc}{R}_{s}&\:0&\:0\\\:0&\:{R}_{s}&\:0\\\:0&\:0&\:{R}_{s}\end{array}\right]:\) Statoric resistance vector;

\(\:{\left[\phi\:\right]}_{abc}=\) \(\:\left[\begin{array}{c}{\phi\:}_{a}\\\:{\phi\:}_{b}\\\:{\phi\:}_{c}\end{array}\right]:\) Statoric phase flux vector.

By using Park transformation, we get39:

With: \(\:\left[P\left(\theta\:\right)\right]\) is the Park matrix transformation which keeps the amplitudes.

With: \(\:{\left[P\left(\theta\:\right)\right]}^{-1}\)is the Park inverse matrix transformation.

This Park inverse matrix form allows the inverse passage from (dq) referential to (abc) referential.

After simplification:

The statoric equations in Park referential are:

Flux equations.

The flux equations can be written as:

\(\:\left[{L}_{ss}\right]\:\): Inductance matrix (stator own and mutual);

\(\:\left[{\phi\:}_{f}\right]\) : Flux vector created by the permanent magnets.

Since the rotor is assumed to be smooth, the inductances do not depend on its position because the air gap is constant during rotation, which means that the matrix \(\:\left[{L}_{s1}\left(\theta\:\right)\right]\) must be neglected.

The matrix \(\:\left[{L}_{ss}\right]\) becomes:

With:\(\left\{\begin{array}{c}{L}_{sa}={L}_{sb}={L}_{sc}={L}_{s}\\\:{M}_{ab}={M}_{ac}={M}_{bc}={M}_{s}\end{array}\right.\)

So, the system (20) becomes:

The expression for the total flux in the three phases ‘a, b, c’ is given by:

By replacing the expressions for total flux (22) in the system (10), we obtain:

Ou sous la forme matricielle suivante :

\(\:{\left[{\phi\:}_{f}\right]}_{abc}\:\): Represents the flux vector created by the permanent magnets through the stator windings18.

And

With: \(\:{e}_{fa}\:\): Electromotive force produced in the stator phase;

\(\:{\omega\:}_{r}\:\): Electrical rotor speed.

By applying Park transformation, the flux equations in Park referential are:

Electromagnetic torque.

The electrical power absorbed by the machine can be expressed as:

The development of the expression (27) gives the various terms corresponding to Joule effect losses, the electromagnetic power stored in the winding and the converted mechanical power39.

Replacing the Eq. (25) in the expression (27), we get:

The mechanical power equation is given by:

The electromagnetic torque equation is therefore:

The machine has smooth poles, which means that \(\:{L}_{q}={L}_{d}\)

State model of the permanent magnet synchronous machine.

The PMSM model can be written as follows42:

The choice of \(\:{i}_{d}\)and \(\:{i}_{q}\)and \(\:{\varOmega\:}_{r}\)as state variables in equation system (33), allows us to write:

The voltages obtained by the generator are transmitted to the power electronic converter (rectifier or GSC) to obtain an average DC-voltage which is used to supply the inverter. A three-phase rectifier makes allows to control the power captured by the turbine by controlling the generator, thus improving the quality of the currents43,44.

The rectifier consists of three independent arms, each carrying two switches. A switch consists of an IGBT and a diode in antiparallel, as shown in Fig. 3.

Principle scheme of GSC (Rectifier).

The rectifier is controlled using the logic quantities Si:(i = a, b,c). We call Ti and Ti’ the transistors (assumed ideal switches), we have:

If \(\:{S}_{i}=+1\), then \(\:{T}_{i}\) is closed and \(\:{T}_{i}^{{\prime\:}}\)is open;

If \(\:{S}_{i}=0\), then \(\:{T}_{i}\) is open and \(\:{T}_{i}^{{\prime\:}}\)is closed.

Under these conditions, we can write the currents \(\:{i}_{S(a,b,c)}^{{\prime\:}}\)as a function of the control signals\(\:{S}_{i}=\left(i=a,\:b,\:c\right)\).

According to Kirchhoff’s law (law of knots), the rectified current can be obtained according to the following equation:

By expressing the above currents as a function of the delivered voltages and the points (a, b and c), we get:

By replacing (38) by (36), we obtain the rectified current as a function of the instantaneous equations of the simple voltages and control quantities Si:(i = a, b,c), and we get the mathematical converter model:

The electrical schematic of the DC bus, as depicted in Fig. 4, illustrates that the DC bus serves as an energy storage component. It is represented by a capacitor positioned between the Generator Side Converter (GSC, operating as a rectifier) and the Load Side Converter (LSC, operates as an inverter). The capacitor current originates from a junction where two modulated currents intersect, necessitating the development of a mathematical model to accurately describe the behavior of this circuit44.

DC-bus scheme.

The electrical equations of the circuit shown in Fig. 4 are given by:

With: \(\:{i}_{c}={i}_{red}-{i}_{ond}\)

In the wind energy conversion system, the inverter is located between the load and the DC-bus, so the inverter’s output signal is closer to a sinusoid45,46. Figure 5 illustrates the LSC scheme (inverter).

LSC scheme (inverter).

The inverter is controlled using the logic quantities Si:(i = a, b, c). We call Ti and Ti’ the transistors (assumed ideal switches), we have44:

If \(\:{S}_{i}=+1\), then \(\:{T}_{i}\) is closed and \(\:{T}_{i}^{{\prime\:}}\)is open;

If \(\:{S}_{i}=0\), then \(\:{T}_{i}\) is open and \(\:{T}_{i}^{{\prime\:}}\)is closed.

Under these conditions, we can write the voltages \(\:{V}_{{in}_{0}}\)as a function of the control signals \(\:{S}_{i}=\left(i=a,\:b,\:c\right)\)and taking into account the fictitious point 0 shown in Fig. 5.

If “n” is the neutral point on the AC side (PMSG), three composite voltages \({U}_{ab},{U}_{bc},{U}_{ca}\)are defined by the following relationships:

By expressing the above voltages with respect to the midpoint0, we obtain:

Considering a balanced three-phase system\(\:\left({V}_{an}+{V}_{bn}+{V}_{cn}=0\right)\), we have:

Or in the following matrix form:

By replacing (41) in (46), we obtain the instantaneous equations of the simple voltages as a function of the control quantities Si:(i = a,b,c), and we get the mathematical model of the converter:

Storing electrical energy by converting it into the potential energy of water, usually by pumping it to a higher altitude, is currently the most efficient way of meeting the large-scale demands of modern power systems. This method is the main reason why dams and Pumped Storage Stations (PSS) account for the vast majority of the world’s installed stationary energy storage capacity47.

Pumped storage stations are a unique form of hydroelectric installation, designed with two reservoirs located at different altitudes. These stations store energy by pumping water from the lower reservoir to the upper reservoir when energy demand is low or electricity costs are low. Conversely, during periods of high energy demand or high electricity prices, the stored water is released from the upper reservoir to generate electricity, which is either supplied to the grid or directly to the load, as shown in Fig. 6.

Pumping storage station (PSS) scheme.

E is the energy exchanged between the hydraulic machine and the fluid per unit mass.

We pose E > 0: if the machine is powered (pump) and E < 0 If the machine is a receiver (turbine).

The energy balance applied is48:

With: \(\:{\varDelta\:H}_{1;2}\:\)is the load losses.

Bernoulli’s theorem can then be written as:

The power exchanged between the hydraulic machine and the fluid is hydraulic power.

With: \(\:{Q}_{m}\:\)is the fluid mass flow rate.

Energy losses in machines are reflected by their efficiency; which is the ratio of hydraulic power to mechanical power:

In the case of a pump:

In the case of a turbine:

The geometric height \(\:{H}_{G}\) is the vertical difference between the suction level and the upper level where it is proposed to discharge the fluid.

The length of the pipe and its changes of direction (bends, tees, etc.) cause head losses\(\:{\varDelta\:H}_{1;2}\).

In the circuit, the pump must overcome48:

Height variation \(Z_{2} - Z_{1} = H_{G}\);

Pressure variation \(p_{2} - p_{1} = \Delta p\);

Pressure losses in the pipework \(\Delta H_{{1;2}}\).

The first two factors are generally constant. If: \(\:{p}_{2}=\:{p}_{1}=\:{P}_{atm}\), therefore, the pump must overcome geometric pressure and load losses.

We define the manometric height \(\:{H}_{m}\)as:

The whole system consists of different subsystems, such as: wind turbine, PMSG, DC-bus, load and pump storage station. Each subsystem must be controlled according to the operating goals.

The curve of aerodynamic power as a function of wind turbine speed is in the form of a bell for each value of wind speed. The mechanical load must therefore be adapted to ensure good energy extraction, by constantly adjusting the speed of the wind turbine to that of the wind. This is done using the maximum power extraction technique (MPPT), which is applied in different ways depending on whether or not the wind turbine is equipped with an anemometer to determine the wind speed, and whether or not the characteristics of the wind turbine’s power curves are known. As long as the wind speed is variable, there are two problems; protecting the machine and obtaining optimum power. Four operating zones can be distinguished as a function of wind speed49,50.

The MPPT algorithm designed for a low-power wind turbine must respect the constraints of simplicity and cost without altering the efficiency. Given these constraints, generator torque control is applied by knowing the characteristic curve Cp(λ) of the wind turbine to be controlled for a zero-stall angle β = 0.

With:\(\:\frac{1}{{\lambda\:}^{{\prime\:}}}=\frac{1}{\lambda\:+0.08\beta\:}-\frac{0.035}{{\beta\:}^{3}+1}\)

This approach enables the optimum operating point to be reached efficiently by means of basic internal measurements in the mechanical-electrical converter. As a result, the system does not require a wind speed sensor; the machine is controlled by directly applying the optimum rotational speed.

The torque control algorithm approximates the optimum torque by measuring the rotational speed, which is then used to establish the reference torque. This reference torque is applied to the mechanical shaft by adjusting the electromechanical torque of the generator, ensuring efficient power conversion. Using the power calculation formula found above, it is easy to determine the corresponding wind torque49:

Where: \(\:K=\:\frac{1}{2}.\frac{{C}_{p}\left(\lambda\:,\beta\:\right).\rho\:.\pi\:.{R}^{5}}{{\lambda\:}^{3}}\)

In maximum power extraction scenarios, where the system operates at optimum torque, the corresponding maximum power can be expressed mathematically using the following equation:

With: \(\:{K}_{opt}=\:\frac{1}{2}.\frac{{C}_{p}\left({\lambda\:}_{opt},\beta\:\right).\rho\:.\pi\:.{R}^{5}}{{\lambda\:}_{opt}^{3}}\)

After a few iterations, the optimal pair of coordinates at [ΩT−opt; TT−opt] is reached and the maximum power Pmax is extracted at this point. This search mode allows each calculation step to converge towards the optimal point, as shown in Fig. 7.

Convergence to the optimum point with torque control.

The main objective of vector control is to assimilate the behavior of the PMSG to that of a DC machine, i.e., a linear and decoupled model, which improves its dynamic behavior.

In our case, we impose \(\:{i}_{sdref}=0\) for a synchronous machine with smooth poles to ensure that we are working at maximum torque and \(\:Cos\phi\:=1\).

The Eq. (32) gives the electromagnetic torque. As the flux \(\:{\phi\:}_{f}\) is constant, the electromagnetic is directly proportional to \(\:{i}_{q}\:\):

With: \(\:K=\frac{3}{2}.p.{\phi\:}_{f}\)

Vector control consists of two main loops, i.e., the speed loop and the internal current loops \(\:{i}_{d},{i}_{q}\), as shown by the Fig. 8.

Global scheme of the PMSG vector control.

The direct current reference \(\:{i}_{d\_ref}\) is set to zero. The system is equipped with a speed control loop, which generates the \(\:{\:i}_{q\_ref}\)reference current. The measured current \(\:{i}_{d}\)and \(\:{i}_{q}\)are compared separately to their reference currents \(\:{i}_{d\_ref}\) and \(\:{\:i}_{q\_ref}\), respectively43,51.

The PMSG model in Park’s frame of reference leads to a system of differential equations where the currents are not independent.

PMSG statoric equations can be written as:

The axis coupling between d and q can be eliminated using a compensation method. This decoupling makes it possible to simplify the equations of the PMSG with its control and to easily calculate the parameters, as shown in Fig. 9.

In the first equation, we separate the voltages according to the axes in two parts:

With:

And

According to the Eq. (61), the currents \(\:{i}_{d}\) and \(\:{\:i}_{q}\) can be written as:

Decoupling by compensation.

To control the DC-voltage, we need to choose a controller capable of obtaining a reference power from the DC bus power, which is expressed as follows44:

The power in the capacitor: \(\:{P}_{dc}={U}_{dc}.{I}_{dc}\:\);

Load power: \(\:{P}_{l}={U}_{dc}.{I}_{l}\:\);

Exchanged power with the pump: \(\:{\:P}_{p}={U}_{dc}.{I}_{p}\).

By neglecting all the converter losses, the provided power is the resultant power of the DC-bus powers.

The objective of the DC-bus control is to fix the DC-voltage. The reference current of the capacitor in the DC-bus is issued from the controller, it can be expressed as:

And

The main objective of LSC control is to obtain a good quality signal for currents and voltages, on the one hand, and power regulation with a unitary power factor, on the other. In this way, active and reactive power regulation corresponds to the power supplied by the wind turbine. Figure 10 illustrates the principle of LSC control.

The differential equations defining the filter are given as follows44:

Applying Park’s transformation to Eq. (67), we find:

LSC control principle.

We consider the following coupling voltages:

The current equations at the output filter are given as follows:

For operation with a unitary power factor on the load side, the current references are obtained from the following power expression:

The current references will be as the following:

Figure 11 illustrates the currents control principle.

Currents control principle.

To ensure the continuity and availability of energy on the load side and to satisfy the customer, it is necessary to connect a storage system to the wind turbine. The storage system consists of a water pumping station, based on a PMSM, which operates in engine mode as a storage system and in generator mode when electricity production is required. In this case, the PMSM is controlled by a bi-directional converter enabling it to operate in both modes51. Figure 12 shows the control principle of the storage station.

Storage station control principale.

In order to validate the models and control strategies detailed above, the entire wind energy conversion system, including the pumped storage station, is implemented and simulated in the Matlab/Simulink environment, which allows the various variables characteristic of the overall system describing the wind energy production chain to be visualized.

In order to approximate real wind conditions, the wind profile is assumed to be variable and slightly fluctuating. Figures 13 and 14 show the simulation results obtained at the turbines, such as the wind speed in Fig. 13 and the turbine and generator speeds in Fig. 14. The average speed of the assumed profile is 8 m/s.

Wind profile velocity.

We can see that the speed of the turbine (Fig. 14) is variable and undergoes the same variations as the wind profile. The speed of the generator is exactly the same as that of the turbine, because there is no speed multiplier (no gear), so it also undergoes the same variations.

Turbine and generator speed.

Figure 15 shows the reference torque and the electromagnetic generator torque. It can be seen that they are both similar, with the same values and the same variations, but with opposite signs at the rotation speed.

Turbine and generator torque.

PMSG quadrature currents.

As indicated in section V.2, the PMSG quadrature current follows its reference value perfectly, as shown in Fig. 16. It undergoes the same variations as the generator torque shown in Fig. 15. Figure 17 shows the PMSG direct current, which follows its reference value, kept equal to 0.

PMSG direct currents.

In order to present and examine the different powers, three load cases are considered according to the possible situations. Figure 18 shows the different powers, such as the generator power, which depends on the wind speed or power, the power required by the load and the power exchanged with the storage system, which depends on whether the PMSG is operating in engine mode to store excess energy or in generator mode to supply the power required by the load.

PMSG power, stored power and load power.

It can be seen that the load powers are constant, but that the generated power is variable depending on the primary source, the wind, which is variable and fluctuates from the outset. This variability makes the stored power variable. The power generated by the PMSG is always negative, however, the power involved in the storage system is negative when the PMSM is operating in engine mode, and positive in generator mode.

Power coefficient Cp.

Figure 19 shows the evolution of the power coefficient (Cp). We note that after 0.1s (transient), the power coefficient reaches its maximum value (0.43), which confirms that the maximum power is extracted using the maximum power point tracking (MPPT) algorithm described in section (V. 1).

PMSG voltage and current phase and their zoom.

The single-phase voltage, the phase of the current of the PMSG driven by the wind turbine and their zoom are shown in Fig. 20. We note that the amplitude of both is variable and that the current is in π phase with the voltage, implying that the PMSG is operating in generator mode.

DC-voltage.

The regulated DC-voltage is shown in Fig. 21. After a slight overshoot, the DC-voltage follows its reference value of 465 V perfectly, confirming the effectiveness of the closed-loop regulation. The DC-voltage is used to supply the inverter, which controls the power of the load.

The load voltage and load current of one phase are illustrated in Fig. 22 and their zoom are illustrated in Fig. 23. a, b, & c. We note that the current amplitude is variable according to the load and it is in 0 phase with the voltage which has a constant amplitude. Three resistive load level are imposed. We note that the current amplitude varies according to the load variations. However, the voltage amplitude is almost kept at its constant value. Really, current value is low. In these figures, it is multiplied by 30. From 0s to 20s, the load Rl= 75Ω, the current value is 9.66 A. From 20s to 40s, the load Rl= 55Ω, the current value is 6.66 A. From 40s to 60s, the load Rl= 35Ω, the current value is almost 5 A.

Load voltage and load current.

Zoom of load voltage and load current.

The following figures relate to the storage system (pumping machine). Figure 24 shows the reference and measured speeds of the PMSM used in the storage system. We note that the reference speed is variable depending on the required situation. It depends on the generated power available and the power required by the load.

Reference and measured PMSM speeds.

When the generated power is greater than the power of the load, the excess power feeds the PMSM, which operates in motor mode and pumps water from the lower basin to the upper basin, and the speed of the PMSM is positive. When the generated power is insufficient to meet the load demand, the PMSM generates the lack of power and therefore operates in generator mode (negative speed). It can also be seen that the measured speed follows the reference speed perfectly, confirming the effectiveness of the vector control method and the closed-loop control.

Quadrature currents (reference and measured).

Figure 25 shows the reference and quadrature currents measured. They are similar, the measured current follows its reference and undergoes the same variations.

Figure 26 shows the measured reference and quadrature currents. The measured current follows its reference and undergoes the same variations.

Direct currents (reference and measured).

The reference electromagnetic torque and the measured electromagnetic torque are shown in Fig. 27. It is variable and undergoes the same variations as the quadrature currents. It can be seen that the measured electromagnetic current follows its reference perfectly, which confirms the effectiveness and robustness of the control method used.

Electromagnetic torques (reference & measured).

Figure 28 shows a phase of the voltage and current of the PMSM used in the storage system and Fig. 29 shows them zoomed in. We can see that this is a variable operating mode where the amplitudes of the voltage and current are variable and fluctuating. The PMSM operates in motor mode (the voltage is in phase 0 with the current) when there is enough wind and the wind turbine is producing enough energy to meet demand. The excess power will power the pumping motor to pump water from the lower basin to the upper basin.

Voltage and current phase of pumping PMSM.

Zoom of voltage and current phase of pumping PMSM.

The PMSM operates in generator mode (the voltage is in π phase with the current) when there is insufficient wind and the turbine produces less power and cannot meet the load demand. The pumping machine turns in the opposite direction to generate the missing power, then the water flows from the upper basin to the lower basin.

This paper presents the design, modeling, and control of an autonomous wind energy conversion system (WECS) based on a Permanent magnet synchronous generator (PMSG), integrated with a Pumped Storage Station (PSS) to attenuate the inherent variability of wind energy. Research is successfully meeting the challenge of ensuring a continuous and reliable power supply in isolated or off-grid areas. The fluctuating nature of wind energy and the absence of a grid require effective energy management solutions.

The proposed system integrates a PMSG with a PSS, enabling it to operate efficiently in both energy production and storage mode. Applying Optimum torque control (OTC) to the wind turbine enables maximum power extraction, with a peak power coefficient (Cp) of 0.43. In addition, the use of vector control for the PMSG ensures voltage stability by maintaining the DC bus voltage at a constant value of 465 V, allowing the system to adapt dynamically to varying wind conditions.

Simulations carried out in MATLAB/Simulink environment demonstrate the effectiveness of control strategies for balancing electricity generation, energy storage and load demand. The system’s ability to switch seamlessly between motor mode (for energy storage) and generator mode (for power supply) in the PSS ensures that excess energy is stored when wind power surplus demand and recovered when wind resources are insufficient. The simulation results, based on a fluctuating wind profile with an average speed of 8 m/s, show that turbine and generator speeds are well coordinated, and the PMSG delivers optimum torque while maintaining stable performance.

This research is making several key contributions to the renewable energy field, particularly in terms of control strategies for autonomous wind energy systems. The proposed control system effectively manages the power flow between the PMSG, the load and the storage system, ensuring reliable system operation in variable wind conditions. In addition, the integration of a pumping station and water storage improves the flexibility and robustness of the system, making it a viable solution for off-grid renewable energy production.

The results of this study highlight the potential of combining PMSG-based WECS with PSS to provide stable and sustainable energy solutions for remote areas. Future work should focus on experimental validation of the system under real-conditions, refining the control algorithms and exploring additional energy storage options to improve the system’s performance.

The scalability of the proposed system and its adaptability to larger-scale applications should also be investigated, which could contribute to the wider deployment of autonomous wind energy systems in regions where grid access is limited or unreliable.

In conclusion, this paper proposes a global solution that addresses both the power variability and energy storage needs of wind energy systems. By guaranteeing a stable energy supply thanks to efficient control strategies and the integration of energy storage, the proposed system represents a significant advance in the development of autonomous wind energy conversion systems for the sustainable production of off-grid electricity.

Although this research provides a robust framework for the integration of a permanent magnet synchronous generator (PMSG)-based wind energy conversion system (WECS) with a pumped storage station (PSS), further advances can be explored to improve the performance and applicability of the system. Future work should focus on experimental validation of the proposed system under real conditions to assess its performance in a variety of environments, including extreme wind profiles and varying load demands. In addition, optimizing control algorithms, such as Optimum torque control (OTC) and vector control, can further improve the efficiency of the overall system and its ability to adapt quickly to wind fluctuations.

The integration of machine learning techniques for predictive energy management and adaptive control could enable more dynamic responses to wind fluctuations and load requirements.

In addition, research should explore other energy storage technologies, such as Battery Energy Storage Systems (BESS), to assess hybrid storage configurations and their benefits in terms of energy availability and system flexibility. The evolution of the proposed system should be explored, with a focus on larger-scale applications, such as microgrids and large-scale wind farms, to broaden its impact in isolated areas and grid-connected locations.

Finally, economic feasibility studies, including cost-benefit analyses, should be carried out to assess the financial viability of deploying these integrated systems in isolated or developing regions where access to energy is essential.

Parameters.

Turbine parameters.

Vw_nom = 9.6544.

λopt = 2.1213.

Cp_max = 0.4308.

c1 = 0.5176.

c2 = 116.

Cf = 12e− 2.

PMSG parameters.

Rs = 5.

Ld = 7.5e− 2.

Lq = Ld.

Ls = 8e− 3.

p = 24.

Qf = 0.88.

J = 0.07.

f = 0.001.

Ωnom = 12.9777.

DC-capacitor.

C = 10e− 3.

Load side filter.

Rfc = 0.01.

Lfc = 0.164.

Cfc = 3e− 5.

Load.

Rl−1 = 75Ω, Rl−2 = 55Ω, Rl−3 = 35Ω.

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Permanent Magnet Synchronous Machine

Permanent magnet synchronous generator

Pulse width modulation

Proportional-integral

Maximum power point tracking

Pumping storage station

Optimal torque control

Wind power

Turbine power

Power coefficient

Pitch angle

Air mass density

Shaft length

Swept surface by turbine

Speed tip ratio

Optimal speed tip ratio

Turbine speed

Wind speed

Turbine torque

Optimal torque

Electromagnetic torque

Rotoric speed

Angular speed

Pair pole numbers

Resistant torque

Friction coefficient

Turbine inertia

Generator inertia

Wind total inertia

Statoric voltages

Statoric currents

Statoric resistance

Statoric flux

Phase inductance

Mutual inductance

Magnetic flux

Flux vector

Electromotive forces

Statoric d and q voltages

Rotoric angle

Park transformation matrix

Statoric cyclic inductance

Statoric d and q currents

Electrical power

DC-power

Statoric d and q flux

Laplace operator

DC-voltage.

DC-capacitor

Electrical constant time

Response time

Proportional-integral coefficients

Decoupling terms

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Automatic Laboratory of Setif, Electrical Engineering Department, University Ferhat Abbas Setif-1, Maabouda city, Algeria

Farid Merahi & Abd Essalam Badoud

Industrial and Information Techology Laboratory, Faculty of technology, University of Bejaia, Béjaïa, 06000, Algeria

Hamza Mernache

Renewable Energies Mastering Laboratory, Faculty of technology, University of Bejaia, Béjaïa, 06000, Algeria

Djamal Aouzelag

Department of Electrical Engineering, Graphic Era (Deemed to be University), Dehradun, 248002, India

Mohit Bajaj

Hourani Center for Applied Scientific Research, Al-Ahliyya Amman University, Amman, Jordan

Mohit Bajaj

College of Engineering, University of Business and Technology, Jeddah, 21448, Saudi Arabia

Mohit Bajaj

Department of Theoretical Electrical Engineering and Diagnostics of Electrical Equipment, Institute of Electrodynamics, National Academy of Sciences of Ukraine, Beresteyskiy, 56, Kyiv-57, Kyiv, 03680, Ukraine

Ievgen Zaitsev

Center for Information-Analytical and Technical Support of Nuclear Power Facilities Monitoring, National Academy of Sciences of Ukraine, Akademika Palladina Avenue, 34-A, Kyiv, Ukraine

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F. M., H. M., D. A.: Conceptualization, Methodology, Software, Visualization, Investigation, Writing—Original draft preparation. A. E. B., M. B., I. Z.: Project administration, Supervision, Resources, Writing—Review & Editing.

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Merahi, F., Mernache, H., Aouzelag, D. et al. Power control of an autonomous wind energy conversion system based on a permanent magnet synchronous generator with integrated pumping storage. Sci Rep 14, 29776 (2024). https://doi.org/10.1038/s41598-024-81522-8

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