Keywords

1 Introduction

The energy of the wind has played a major role in the energy systems since time immemorial especially as a windmill in producing mechanical power [1,2,3,4]. In the last century, wind energy found application in electricity generation using wind turbines (WTs) technology [5,6,7]. The total installed wind power capacity of the world was estimated at 539 GW in 2017 where 52.6 added in 2017 as found in the 2017 world energy report of the world wind energy association. This installed capacity has the potential to produce 944 Terawatt-hours annually (TWh/year) and accounts for 5% of worldwide electricity consumption [8]. Annual growth rates of cumulative wind power capacity have averaged 10.8% since the end of 2016, and global capacity has increased eightfold over the past decade. Figure 1 shows the top 10 countries by nameplate wind power capacity at the end of 2017 [9,10,11]. For the generation of energy through the wind, WTs are used, which consist basically of blades (collectors of the kinetic energy of the wind), in addition to two axes (low and high speed), the low speed being connected to a multiplier of wind speed and the high-speed connection to the generator. The current wind systems also use a series of electronic devices aimed at controlling and acting on the energy supply of the turbines, such as power converters and “soft-starters”, thus realizing the interface between the generator and the electrical network.

Fig. 1
figure 1

Top 10 countries by nameplate wind power capacity at the end of 2017

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WTs operate at wind speed values between 5 and 25 m/s (average speed). At values below 5 m/s the turbines are unable to deliver power to the system, while for winds well above 25 m/s the turbines must not operate for safety reasons due to mechanical resistance limits. For slightly higher speed values rated, the turbines must have control systems that reduce the use of wind energy by changing the angle of the blades in relation to the winds, thus maintaining constant power.

Typical speed values or blade tips range from 60 to 100 m/s, thus generating power between 5–10 and 2–3 MW. If connected to the grid, it is necessary to generate power with the rotor operating at a typical rotation for a frequency of 60 Hz or 50 Hz. There are two basic ways of operating wind systems:

  • Turbine operating at fixed speed

Fixed speed wind turbines are relatively simple, consisting of a low-speed rotor rotating by the action of the winds on the turbine blades, speed multiplier, and high-speed rotor connected to the generator. These were, historically, the first to be commercially implemented.

Squirrel cage induction generators are typically used due to their simplicity. As in this type of turbine the operating speed varies very little, less than 1%, the slip of the generator varies very little too. Capacitors are usually connected in parallel with the supply circuit to correct the generator’s power factor since this being an induction machine, it consumes reactive energy. “Soft-starters” must also be used to obtain a smooth growth of the magnetic flux and the electric current at the initial moment of energizing the generating unit.

  • Turbine operating at variable speed

Nowadays it is more common to use it in large wind systems connected to the electric power networks, because over time, the size and power of the wind farms increased, thus leading to a migration of the technology of generators working at a fixed speed to variable speed. The main advantages of this technology are that it allows the connection of these generators to large electric power networks, in addition to being viable for the generation of high energy values, in addition to being used in certain cases that do not use the speed multiplier.

There are broadly two commercially existing WTs technologies namely the horizontal axis (HA-WT) and the vertical axis (VA-WT) [12,13,14,15,16] as detailed in the following sections. The HA-WT type has from one to three rotor blades usually directed at the wind thus the rotor has fastened tail-vanes to continuously position the blades in the path of the wind. The VA-WT type is not required to be aimed at the wind and works independently of the direction of the wind. The vertical WT however, requires more ground space because of its vertical structure [17]. WTs are often mounted on vertical structures known as towers above the ground.

1.1 Horizontal Axis WTs (HA-WTs)

This is the most renowned type of WTs. There are many designs for this type, which are shown in Fig. 2. Modern HA-WTs characteristically use two or three blades. Most European WTs are three-bladed designs [18,19,20]. Two-bladed designs of WTs have the advantage of reducing the cost of one rotor blade and its weight. However, they require a higher rotational speed to produce the same energy output. Lately, several traditional manufacturers of two-bladed machines have switched to three-bladed machines. A one-bladed wind turbine is also possible; however, it is not very widespread commercially, due to the same problems of two-bladed design applied to one-bladed machines. In addition to higher rotational speed, they produce noise in the process of rotating the counterweight of the rotor placed on the other side of the hub from the rotor blade to balance the rotor [21,22,23,24,25].

Fig. 2
figure 2

HA-WT configurations

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Figure 3 shows the influence of the number of blades on the rotor power coefficient [26]. It is obvious from this figure that three-bladed HA-WTs have the maximum obtainable power coefficient and it works at optimal tip speed ratio. The tip speed ratio is the ratio between the tangential speed of the tip of a blade and the actual velocity of the wind [27, 28]. The noise produced by a WT is proportional to the tip speed ratio. So, the three-bladed design has lower noise which makes it the most attractive option. Also, higher tip speed ratio WTs need stronger blades to compensate for the higher centrifugal forces [29, 30].

Fig. 3
figure 3

Influence of the number of blades on the rotor power coefficient (envelope) and the optimum tip speed ratio [31]

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As shown in Fig. 3, the power coefficient increases slightly with the increasing number of blades. As a result, a compromising between the increases in the power generated and the cost of extra blades should be done [32]. Most of the European manufacturers prefer three-bladed design for more stability and lesser noise while most of the USA manufacturers prefer the two-bladed design to save the cost of one extra blade with the argument that the increase in the generation from two to three-bladed design will not compensate for the cost of the extra blade [33]. Due to the high noise associated with two-bladed design, the requirement for stronger blades, the need for high wind speed sites, and the lower power coefficient make the two-bladed design less attractive. However, the two-bladed design may be attractive also in high wind speed sites and offshore applications. The main advantages of HA-WTs are self-starting, a large variety of the rated output power (Suitable for small WTs as well as very large WTs), and comparatively low cost [34,35,36,37].

There are two main disadvantages to this type. The first is the requirement that the complete components (such as generator, gearbox, and control system) of the HA-WT be located at the top of the WT which makes maintenance difficult at such heights [38]. Secondly, when the wind changes direction, the HA-WT should be reoriented to be aligned with the change in direction [39, 40].

  1. 1.

    Upwind and Downwind Horizontal Axis WTs

Upwind WTs have the rotor facing the wind to make the wind hit the blades before the tower as shown in Fig. 4a [41,42,43,44,45]. This technique has the following features:

Fig. 4
figure 4

Wind direction facing the wind turbine generator

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  • Remedy the problem of spikes on the WT’s output voltage due to the wind shade that the tower causes when the blades move in front of the tower especially in constant speed systems.

  • It decreases the power fluctuations.

  • Because the blades can hit the tower it requires a rigid hub with rigid blades away from the tower to avoid touching the tower.

  • This design is prominent in very large scale WTs.

Downwind WTs have the rotor on the flow-side as shown in Fig. 4b. This configuration is paramount in small and medium-size WTs. This configuration may not need a yaw mechanism if it is equipped with the streamlined body in the nacelle that will make it follow the wind [46,47,48,49]. It has the following features:

  • The rotor blades are more flexible as they can bend away from the tower.

  • It does not require a rigid tower as in the case of upwind.

  • It suffers from the variation in output voltage and power due to the effect of the wind shadow caused by the tower.

1.2 Vertical Axis WTs (VA-WTs)

VA-WTs type is less available as compared to the HA-WTs as a result of some design constraints. In addition to the VA-WTs having a narrow range of rated output power, it also requires a starting motor and has a high comparative cost [50,51,52]. The main advantages of VA-WTs, are that; no additional cost is required to change the VA-WTs direction when the wind direction changes and the gearbox, generator, and control system are at the ground level thus making maintenance is very simple. Figure 5 shows different VA-WTs configurations.

Fig. 5
figure 5

VA-WTs configurations [51]

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1.3 Wind Resource

Wind resources are categorized into wind regimes according to the mean speeds of the sites. To install small wind turbines of less than 100 kW, annual mean wind speeds of 4.0–4.5 m/s (14.4–16.2 km/h; 9.0–10.2 mph) are required to make the system cost-effective [53]. The wind energy conversion system (WECS) most often referred to as the WT for short should be decided upon only after assessing the site wind resources. The most important data is hourly mean wind speed taken over for at least twelve months. Many years’ data will provide a more accurate estimation of the annual mean wind speed of the site [54].

All nations have national meteorological administrations that record and distribute climate-related information, including wind paces and headings. The strategies are settled and composed inside the World Meteorological Association in Geneva, with the principle point of giving constant runs of information for a long time. Information have a tendency to be recorded at a moderately few for all time staffed official stations utilizing strong and confided in gear. Sadly, for wind control forecast, official estimations of wind speed tend to be estimated just at the one standard stature of 10 m, also, at stations close to airplane terminals or towns where protection from the breeze might be a characteristic component of the site. Such information are, in any case, critical as fundamental “stays” for automated breeze displaying, yet are not appropriate to apply straightforwardly to foresee wind control conditions at a particular site. Standard meteorological breeze information from the closest authority station are just valuable as first-arrange gauges; they are not adequate for definite arranging, particularly in sloping (complex) landscape. Estimations at the designated site at a few statures are expected to foresee the power created by specific turbines. Such estimations, notwithstanding for a couple of months yet best for a year, are contrasted and standard meteorological information so that the fleeting correlation might be utilized for longer term expectation; the strategy is called “measure-connect foresee”. Also, data is held at expert breeze control information banks that are gotten from air ship estimations, wind control establishments and scientific demonstrating, and so forth. Such composed and open data is progressively accessible on the Internet. Wind control forecast models empower point by point wind control forecast for forthcoming breeze turbine destinations from moderately meager nearby information, even in uneven territory [54, 55].

2 Wind Energy Conversion Systems (WECS)

WT can be one of the renewable energy components of the HRES. WTs are classified from several viewpoints as discussed before. From the rotational speed perspective, there is fixed speed (FS), limited variable speed (LVS), and variable speed (VS) WTs. From the power regulation perspective WTs are classified into stall and pitch control. From the side of drive train WT is grouped into direct drive (DD) and gear drive (GD). The FS type uses a gearbox, squirrel cage induction generator (SCIG), and classified as stall, active stall, and pitch control WT. Most of the HRES are using a small WT size lower than 250 kW that may use PMSG with DC or AC output power [55, 56]. The integration configuration of the WTs depends on the output voltage type (AC or DC) as will be discussed below.

WTs can be classified according to the rotational speed concept, variable, and constant rotational speed. The variable speed operation has many advantages over constant speed operation such as increased energy capture, operation at MPPT over a wide range of wind speeds, high power quality, reduced mechanical stresses, aerodynamic noise improved system reliability, and it can provide (10–15%) higher output power and has less mechanical stresses in comparison with the operation at a fixed speed [57]. Also, WTs can be classified according to the type of drive train into direct drive (DD) and gear drive (GD). The DD operation WTs have no gearbox and have been used with small and medium-size WTs employing permanent magnet synchronous generator (PMSG) with higher numbers of poles to eliminate the need for gearbox which can be translated to higher efficiency. The GD type uses a gearbox, squirrel cage induction generator (SCIG), and classified as stall, active stall, and pitch control WT and work in constant speed applications. The variable speed WT uses doubly-fed induction generator, (DFIG) especially in high rating WTs. PMSG appears more and more attractive, because of the advantages of permanent magnet, (PM) machines over electrically excited machines such as its higher efficiency, higher energy yield, no additional power supply for the magnet field excitation, and higher reliability due to the absence of mechanical components such as slip rings. Besides, the performance of PM materials is improving, and the cost is decreasing in recent years. Therefore, these advantages make direct drive PM WT systems more attractive in the application of small and medium-scale WTs [57].

The robust controller has been developed in many literature [58,59,60] to track the MP available in the wind. They include tip speed ratio (TSR) [61], power signal feedback (PSF) [62], and the hill-climb searching (HCS) [59] methods. The TSR control method regulates the rotational speed of the generator to maintain an optimal TSR at which power extracted is maximum [61]. For TSR calculation, both the wind speed and turbine speed need to be measured, and the optimal TSR must be given to the controller. The first barrier to implement TSR control is the wind speed measurement, which adds to system cost and presents difficulties in practical implementations. The second barrier is the need to obtain the optimal value of TSR, this value is different from one system to another. This depends on the turbine generator characteristics results in custom-designed control software tailored for individual WTs. In PSF control [62], it is required to have the knowledge of the wind turbine’s MP curve, and track this curve through its control mechanisms. The power curves need to be obtained via simulations or offline experiments on individual WTs or from the datasheet of WT which makes it difficult to implement with accuracy in practical applications [63]. The HCS technique does not require the data of wind, generator speeds, and turbine characteristics. But, this method works well only for very small WT inertia. For large inertia WTs, the system output power is interlaced with the turbine mechanical power and rate of change in the mechanically stored energy, which often renders the HCS method ineffective [59]. On the other hand, different algorithms have been used for MP extraction from WT in addition to the three methods mentioned above. For example, reference [55] presents an algorithm for MP extraction and reactive power control of an inverter through the power angle, δ of the inverter terminal voltage, and the modulation index, ma based variable speed WT without a wind speed sensor. Reference [64] presents an algorithm for MPPT via controlling the generator torque through q-axis current and hence controlling the generator speed with a variation of the wind speed. These techniques are used for a decoupled control of the active and reactive power from the WT through q-axis and d-axis current individually. Also, reference [65] presents a decoupled control of the active and reactive power from the WT, independently through q-axis and d-axis current but MPP operation of turbine system has been produced through regulating the input dc current of the dc/dc boost converter to follow the optimized current reference [65]. Reference [66] presents an algorithm for MPPT through directly adjusting DR of the dc/dc boost converter and modulation index of the PWM–VSC. Reference [67] presents the MPPT control algorithm based on measuring the dc-link voltage and current of the uncontrolled rectifier to attain the maximum available power from wind. Finally, references [68, 69] present MPPT control based on a fuzzy logic control (FLC). The function of FLC is to track the generator speed with the reference speed for MP extraction at variable speeds. The MPPT algorithms can be divided into two categories, the first one is MPPT algorithms for WT with wind speed sensor and the second one is MPPT algorithms without a wind speed sensor (sensorless MPPT controller). The wind speed sensor is normally used in conventional wind energy conversion systems, WECS for implementing the MPPT control algorithm. This algorithm increases cost and reduces the reliability of the WECS in addition to inaccuracies in measuring the wind speed. Therefore, some MPPT control methods estimate the wind speed; however, many of them require the knowledge of air density and mechanical parameters of the WECS [57]. Such methods require turbine generator characteristics that result in custom-design software tailored for individual WTs. Air density, on the other hand, depends upon climatic conditions and may vary considerably over various seasons. Therefore, this technique is not favorite in the modern design of WT and a lot of research efforts are focused on developing wind speed sensorless MPPT controller which does not require the knowledge of air density and turbine mechanical parameters. Therefore, the cost and maintenance of the power control system are decreased and implementation of the power control system is not difficult compared to the sensor MPPT controller [70].

According to [71], only a portion of the kinetic energy of the wind that reaches the area of the turbine blades is converted into the rotational energy of the rotor. This conversion of part of the kinetic energy of the winds causes a reduction in its speed right after it passes through the blades of the wind turbine. If we try to extract all the kinetic energy from the incident wind, the air would end at zero speed, that is, the air could not leave the turbine. In this case, we would not be able to extract energy, since obviously all the air would also be prevented from entering the turbine rotor. In the other extreme case, the wind speed after passing through the blades would remain the same as the speed before passing. With that, we would not have extracted energy from the wind either.

It is possible to assume that there must be some form of a reduction in the speed of the wind that is between these two extremes and is the most efficient situation to convert the kinetic energy of the winds into rotational energy in the rotor. According to [71], the answer is to reduce the wind at the turbine output to 2/3 of its original speed. This ideal operating point is known as Betz’s Law, whose main result says that the maximum portion of the kinetic energy of the wind that can be converted into mechanical energy by a wind turbine is 59% [72].

The portion of the wind power converted into rotational energy of the rotor and which will be transmitted to the electric generator through the gear system is then defined by multiplying the power coefficient by the total wind power:

$$P_{m} \, = \frac{1}{2}C_{P} \left( {\lambda ,\beta } \right)\,\rho \,A\,u^{3}$$
(1)

where,

\(C_{p}\):

Turbine power coefficient.

\(\rho\):

Air density (kg/m3).

\(A\):

Turbine sweeping area (m2).

\(u\):

wind speed (m/s).

\(\lambda\):

tip speed ratio of the WT which is given by the following equation [57];

$$\lambda \, = \frac{{r_{m} \,\omega_{r} }}{u}$$
(2)

where, \(r_{m}\) is the turbine rotor radius, \(\omega_{r}\) is the angular velocity of the turbine (rad/s).

The turbine power coefficient, Cp, describes the power extraction efficiency of the WT. It is a nonlinear function of both tip speed ratio, λ, and the blade pitch angle, β. While its maximum theoretical value is approximately 0.59, it is practically between 0.4 and 0.45. There are many different versions of fitted equations for Cp made in the literature. A generic equation has been used to model Cp(λ, β) and based on the modeling turbine characteristics as appeared in the following equation [57]:

$$C_{P} \left( {\lambda ,\beta } \right)\, = 0.5176\left( {116*\frac{1}{{\lambda_{i} }} - 0.4\beta - 5} \right)e^{{ - \frac{21}{{\lambda_{i} }}}} + 0.0068\lambda$$
(3)
$${\text{With}}\,\frac{1}{{\lambda_{i} }} = \frac{1}{\lambda + 0.08\beta } - \frac{0.035}{{1 + \beta^{3} }}$$
(4)

The Cp-λ characteristics, for different values of the pitch angle β, are illustrated in Fig. 6. The maximum value of Cp is achieved for β = 0°. The particular value of λ is defined as the optimal value (λopt). Continuous operation of WT at this point guarantees the maximum available power which can be harvested from the available wind at any speed.

Fig. 6
figure 6

Aerodynamic power coefficient variation against λ and β

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2.1 Electric Generators—Variable Speed Turbines

  1. 1.

    Doubly-Fed Induction Generator (DFIG)

DFIG generators are of the induction type with a coiled rotor and use brushes to feed the rotor windings. The brushes receive energy through a power converter, which can decouple the operating frequency from the grid from the operating frequency of the turbine rotor. The stator is supplied directly by connecting to the grid. Usually, a circuit element called a “crowbar” is used to protect the converter. It has the function of providing a path for the overcurrent arising from electrical transients in the system when they exceed a certain level of design.

The main advantages of this type of machine are the operation with maximum efficiency, the control of active and reactive power, in addition to using lower capacity converters when compared to the FRC configuration. The main disadvantage is the need for slip rings with brushes, thus requiring constant maintenance [73,74,75]. A typical composition of this wind turbine configuration is shown in Fig. 7 [76].

Fig. 7
figure 7

Typical configuration of DFIG turbines

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  1. 2.

    Fully Rated Converter Wind Turbine (FRC)—Wind Turbine with Full Converter

This type of configuration is quite versatile, as it may or may not need a speed multiplier and, besides, a range of electric generators can be used: squirrel cage and synchronous generators. As all of the turbine energy flows through converters, the dynamic operation of the generator is isolated from the grid [76].

This isolation is essential for operating at variable speed, as the operating speed of the turbine and, consequently, the operating frequency varies with the wind speed, while the network frequency is stable and varies very little under normal operating conditions. Thus, it is noticed that the power converter is the fundamental device to obtain harmonic integration between variable speed turbines with electrical networks. A typical configuration for this type of system is shown in Fig. 8 [77].

Fig. 8
figure 8

Typical configuration of FRC turbines [77]

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As can be seen in Fig. 8, converters associated with a dc bus can be used interconnecting the turbine with the network output transformer.

A typical operating configuration is to use the grid side converter to keep the voltage level constant, while the converter next to the generator acts to control the generator torque. An alternative way of working is to control the torque of the turbine through the converter next to the grid, while active power is transmitted from the generator to the converters [78].

This system has a disadvantage with the cost of the power converter, since now as all the energy flows through it, it will be necessary to increase the rated power of the converter and thus increase the system.

2.2 Wind Generators—Impacts on the Electrical Network

Wind turbines have their peculiarities of operation and integration with the electricity grid when compared to traditional means of power generation (hydroelectric, thermoelectric, and nuclear). Some differences in basic information can be cited [79, 80]:

  • The control system for wind turbines is different, with the use of power converters being quite common;

  • The driving force that generates energy, the wind, is typically a phenomenon subject to occasional variations and is therefore not controllable;

  • The dimensions of the wind generator are much smaller when compared to those of conventional generators and, therefore, a large number of units make up the plant.

Thus, the behavior of the wind turbine in relation to the electrical networks is different, requiring detailed treatment.

  1. 1.

    Impact on Local Networks

  2. –

    Voltage control

The influence of wind turbines on local energy networks depends on the type of operation chosen, that is, operation at fixed or variable speed.

For fixed speed, the generator used is the squirrel cage induction generator, which has advantages such as being more economical and easier maintenance compared to other models. However, it is not able to control the grid voltage alone. Thus, the voltage control is done by inserting reactive power through the use of elements external to the system, as in the case of capacitor banks in parallel.

Variable speed turbines are able, in principle, to vary the reactive power exchanged with the grid and, thus, influence the stabilization of the voltage level in the local power grid. This characteristic will depend on the type of converter used specifically for each turbine [81,82,83,84].

  • Protection Coordination

As wind turbines that operate at fixed speed use induction generators, in the event of balanced faults, these only contribute to sub-transitory currents. For unbalanced faults, the contribution of wind turbines to the fault current value is integral.

For turbines operating at variable speed, DFIG generators have at first also contributed to the fault currents in the network. However, as these generators are usually associated with power converters and these converters are quite sensitive to over-currents and have to be quickly disconnected from the grid [85, 86]. Thus, by design, these turbines are quickly disconnected from the network in the event of faults, except for some caveats that are imposed by network codes for the “Ride through Fault” capability.

  • Energy Quality

Harmonic distortions are more associated with turbines that operate at variable speed, as they use power converters that are great sources of high-frequency harmonic currents. In turbines operating at fixed speed, variations in wind speed are directly transmitted to the generator’s output power, thus causing small voltage variations. If the network to which these turbines are connected is “weak”, these small voltage variations will be able to generate the phenomenon known as voltage fluctuations and, consequently, flicker [87].

  1. 2.

    Impact on Global Networks

  2. –

    Grid stability

For turbines operating at fixed speed using an induction type generator with a squirrel cage rotor, a serious problem that can occur is the rotor’s over-speed. The trip occurs due to the occurrence of a fault in the system and the consequent voltage drop of that fault will generate a serious imbalance between the mechanical power generated by the wind and the power generated to the network. After the fault ceases, another problem occurs, which is the absorption of reactants from the generator through the network, contributing to delay in the recovery of voltage in the network. If the system voltage is not restored to nominal values quickly, the turbines tend to accelerate and absorb more reactive power. Thus, it is noticed that fixed speed turbines composed of squirrel cage generators are not able to help maintain the stability of the network, a fact that is essential for delivering quality energy to the consumer.

For variable speed turbines, a risk to the stability of the system is the high sensitivity of the power converters to variations in voltage and current. Thus, if the system has a large presence of this type of turbine (current market trend), and these disconnect for small and medium voltage variations, a large voltage drop will affect the entire energy system. To avoid this problem, the network codes in general establish the levels of voltage sags to which wind turbines must withstand without disconnecting, thus avoiding large losses of generation power [88, 89].

3 MPPT Control Strategies for the WECS

3.1 Power Signal Feedback (PSF) Control

In PSF control, it is required to have the knowledge of the wind turbine’s MP curve, and track this curve through its control mechanisms. The MP curves need to be obtained via simulations or offline experiments on individual WTs or from the datasheet of WT which makes it difficult to implement with accuracy in practical applications. In this method, reference power is generated using an MP data curve or using the mechanical power equation of the WT where wind speed or the rotational speed is used as the input. Figure 9 shows the block diagram of a WECS with the PSF controller for MP extraction. The PSF control block generates the optimal power command Popt which is then applied to the grid side converter control system for MP extraction as appeared in the following equation [72]:

$$P_{opt} \, = K_{opt} \,*\omega_{r}^{3}$$
(5)
Fig. 9
figure 9

The block diagram of power signal feedback control [72]

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The actual power output, Pt is compared to the optimal power, Popt and any mismatch is used by the fuzzy logic controller to change the modulation index of the grid side converter, PWM-VSC as appeared in Fig. 9. The PWM-VSC is used to interface the WT with the electrical utility and will be controlled through the power angle, δ, and modulation index, ma to control the active and reactive power output from the WTG [72].

3.2 Optimal Torque Control

The torque controller aims to optimize the efficiency of wind energy capture in a wide range of wind velocities, keeping the power generated by the machine equal to the optimal defined value. It can be observed from the block diagram represented in Fig. 10, that the idea of this method is to adjust the PMSG torque according to the optimal reference torque of the WT at a given wind speed. A typical WT characteristic with the optimal torque-speed curve plotted to intersect the CP-max points for each wind speed is illustrated in Fig. 11. The curve Topt defines the optimal torque of the device (i.e. maximum energy capture), and the control objective is to keep the turbine on this curve as the wind speed varies. For any wind speed, the MPPT device imposes a torque reference able to extract the MP. The curve Topt is defined by the following equation [70]:

$$T_{opt} \, = K_{opt} \,*\omega^{2}_{opt}$$
(6)
Fig. 10
figure 10

The block diagram of optimal torque control MPPT method

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Fig. 11
figure 11

Wind turbine characteristic for MP extraction [70]

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where, \(K_{opt} \, = 0.5*\rho \,A\,*\left( {\frac{{r_{m} }}{{\lambda_{opt} }}} \right)^{3} *C_{P - \max }\).

4 Decoupled Control of the Active and Reactive Power

In this study, a simple ac-dc-ac power conversion system and proposed a modular control strategy for grid-connected wind power generation systems have been implemented [65]. Grid side inverter maintains the dc-link voltage constant and the power factor of the line side can be adjusted. Input current reference of DC/DC boost converter is decided for the MPPT of the turbine without any information on wind or generator speed. As the proposed control algorithm does not require any speed sensor for wind or generator speed, construction and installation are simple, cheap, and reliable. The main circuit and control block diagrams have appeared in Fig. 12. For a wide range of variable speed operations, a dc-dc boost converter is utilized between a 3-phase diode rectifier and PWM-VSC. The input dc current is regulated to follow the optimized current reference for MPP operation of the turbine system. Grid PWM-VSC supply currents into the utility line by regulating the dc-link voltage. The active power is controlled by q-axis current through regulating the dc-link voltage whereas the reactive power can be controlled by d-axis current via adjusting the power factor of the grid side converter. The phase angle of utility voltage is detected using Phase Locked Loop, PLL, in d-q synchronous reference frame [65].

Fig. 12
figure 12

Block diagram of system control [65]

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4.1 Co-Simulation (PSIM/MATLAB) Program for Interconnecting Wind Energy System with Electric Utility

In this study, the WECS is designed as PMSG connected to the grid via a back-to-back PWM-VSC as appeared in Fig. 13. MPPT control algorithm has been introduced using FLC to regulate the rotational speed to force the PMSG to work around its MPP in speeds below rated speeds and to produce the rated power in wind speed higher than the rated wind speed of the WT. An indirect vector-controlled PMSG system has been used for this purpose. The input to FLC is two real-time measurements which are the change of output power and rotational speed between two consequent iterations (ΔP, and Δωm). The output from FLC is the required change in the rotational speed Δωm-new*. The detailed logic behind the newly proposed technique is explained in detail in the following sections. Two effective computer simulation software packages (PSIM and SIMULINK) have been used to carry out the simulation effectively where PSIM contains the power circuit of the WECS and MATLAB/SIMULINK contains the control circuit of the system. The idea behind using these two different software packages is the effective tools provided with PSIM for power circuit and the effective tools in SIMULINK for control circuit and FLC.

Fig. 13
figure 13

Schematic diagram of the overall system [52, 55, 56]

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4.2 Wind Energy Conversion System Description

Figure 14 shows a co-simulation (PSIM/SIMULINK) program for interconnecting WECS to electric utility. The PSIM program contains the power circuit of the WECS and MATLAB/SIMULINK program contains the control of this system. The interconnection between PSIM and MATLAB/SIMULINK has been done via the SimCoupler block. The basic topology of the power circuit which has PMSG-driven WT connected to the utility grid through the ac-dc-ac conversion system has appeared in Fig. 13.

Fig. 14
figure 14

Co-simulation block of wind energy system interfaced with the electric utility

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The PMSG is connected to the grid through back-to-back bidirectional PWM voltage source converters VSC. The generator side converter is used as a rectifier, while the grid side converter is used as an inverter. The generator side converter is connected to the grid side converter through dc-link capacitor. The control of the overall system has been done through the generator side converter and the grid side converter. MPPT algorithm has been achieved by controlling the generator side converter using FLC. The grid side converter controller maintains the dc-link voltage at the desired value by exporting active power to the grid and it controls the reactive power exchange with the grid.

  1. 1.

    PMSG Model

The voltage equation of the three-phase PMSG type is defined as follows [73].

$$\left[\begin{array}{c}{v}_{as}\\ {v}_{bs}\\ {v}_{cs}\end{array}\right]=\left[\begin{array}{ccc}{R}_{s}+\frac{d}{dt}({l}_{as}+M)& \frac{-1}{2}\frac{d}{dt}M& \frac{-1}{2}\frac{d}{dt}M\\ \frac{-1}{2}\frac{d}{dt}M& {R}_{s}+\frac{d}{dt}({l}_{bs}+M)& \frac{-1}{2}\frac{d}{dt}M\\ \frac{-1}{2}\frac{d}{dt}M& \frac{-1}{2}\frac{d}{dt}M& {R}_{s}+\frac{d}{dt}({l}_{cs}+M)\end{array}\right]\left[\begin{array}{c}{i}_{as}\\ {i}_{bs}\\ {i}_{cs}\end{array}\right]+\left[\begin{array}{c}{e}_{as}\\ {e}_{bs}\\ {e}_{cs}\end{array}\right]$$
(7)

where vas, vbs, and vcs are stator a, b, and c phase voltages, and ias, ibs, and ics are stator a, b, and c phase currents. The electromotive force induced in the stator windings of phases a, b, and c are eas, ebs, and ecs, Rs is the stator winding resistance, ls is the leakage inductance of the stator winding, and M is the mutual inductance between the stator windings. In a balanced 3-phase circuit, the sum of each phase current becomes 0, and when Ls = ls + (3/2)M (equivalent inductance (Ls)), the voltage equation is simplified as follows:

$$\left[\begin{array}{c}{v}_{as}\\ {v}_{bs}\\ {v}_{cs}\end{array}\right]=\left[\begin{array}{ccc}{R}_{s}+\frac{d}{dt}{L}_{s}& 0& 0\\ 0& {R}_{s}+\frac{d}{dt}{L}_{s}& 0\\ 0& 0& {R}_{s}+\frac{d}{dt}{L}_{s}\end{array}\right]\left[\begin{array}{c}{i}_{as}\\ {i}_{bs}\\ {i}_{cs}\end{array}\right]+\left[\begin{array}{c}{e}_{as}\\ {e}_{bs}\\ {e}_{cs}\end{array}\right]$$
(8)
$${v}_{as}={R}_{s}{i}_{as}+{L}_{s}\frac{d}{dt}{i}_{as}+{e}_{as}$$
(9)
$${v}_{bs}={R}_{s}{i}_{bs}+{L}_{s}\frac{d}{dt}{i}_{bs}+{e}_{bs}$$
(10)
$${v}_{cs}={R}_{s}{i}_{cs}+{L}_{s}\frac{d}{dt}{i}_{cs}+{e}_{cs}$$
(11)

Equations (9)–(11) can be integrated into a vector form as follows:

$${v}_{abcs}={R}_{s}{I}_{abcs}+{L}_{s}\frac{d{I}_{abcs}}{dt}+{E}_{abcs}$$
(12)

If the number of fluxes crossing the stator winding by the rotor of the PMSG is called epsa, epsb, and epsc, and the maximum value of the flux is epsf, the magnitude of the flux crossing the stator winding is as follows:

$${\Psi }_{a}={\Psi }_{f }\cos \theta$$
$${\Psi }_{b}={\Psi }_{f }\cos\left(\theta -\frac{2}{3}\pi \right)$$
$${\Psi }_{c}={\Psi }_{f }\cos\left(\theta +\frac{2}{3}\pi \right)$$
(13)

At this time, the synchronous phase angle θ was calculated as the rotational speed ωr. If θ = ∫ωr dt, the electromotive force induced in the three-phase stator winding is defined as follows:

$${e}_{as}={-{\omega }_{r}\Psi }_{f }sin \theta$$
$${e}_{bs}={-{\omega }_{r}\Psi }_{f }\sin\left(\theta -\frac{2}{3}\pi \right)$$
$${e}_{cs}={-{\omega }_{r}\Psi }_{f }\sin\left(\theta +\frac{2}{3}\pi \right)$$
(14)

To convert a 3-phase state equation to a d-q stationary reference frame (ω = 0), multiply the following transformation matrix:

$$T(0)= \left[\begin{array}{ccc}1& 0& 0\\ 0& \frac{1}{\surd 3}& \frac{-1}{\surd 3}\end{array}\right]$$
(15)

Multiplying Eq. (12) by Eq. (15):

$$T(0) {v}_{abcs}={R}_{s}T(0){I}_{abcs}+{L}_{s}\frac{d{I}_{abcs}}{dt}T(0)+T(0){E}_{abcs}$$
$${V}_{dqs}^{S}={R}_{s}{I}_{dqs}^{S}+{L}_{s}\frac{d}{dt}{I}_{dqs}^{S}+{E}_{dqs}^{S}$$
(16)

The electromotive force induced to the stator is obtained as follows by substituting Eq. (13) into Eq. (16) as follows:

$${E}_{abcs}= \left[\begin{array}{c}{-{\omega }_{r}\Psi }_{f }\sin \theta \\ {{\omega }_{r}\Psi }_{f }\cos \theta \end{array}\right]$$
(17)

The flux linkage of the stationary system is as follows:

$$\left[\begin{array}{c}{\Psi }_{ds}^{s}\\ {\Psi }_{qs}^{s}\end{array}\right]= T(0)\left[\begin{array}{c}{\Psi }_{f }\cos \theta \\ {\Psi }_{f }\cos (\theta -\frac{2}{3}\pi )\\ {\Psi }_{f }\cos (\theta +\frac{2}{3}\pi )\end{array}\right]=\left[\begin{array}{c}{\Psi }_{f }\cos \theta \\ {\Psi }_{f }\sin \theta \end{array}\right]$$
(18)

To perform the control of a rotating device, the state equation of the stationary coordinate system must be converted into a synchronous coordinate system:

$${V}_{dqs}^{S}={R}_{s}{I}_{dqs}^{e}+{L}_{s}\frac{d}{dt}{I}_{dqs}^{e}+{{L}_{s}\left[\begin{array}{cc}0& -{\omega }_{r}\\ -{\omega }_{r}& 0\end{array}\right]+E}_{dqs}^{e}$$
(19)

If the 3-phase state equation is changed to the synchronous coordinate system d-q, it is as shown in Eq. (19), and rearranged as follows:

$$\left[\begin{array}{c}{v}_{ds}^{e}\\ {v}_{qs}^{e}\end{array}\right]=\left[\begin{array}{cc}{R}_{s}+\frac{d{L}_{s}}{dt}& {-{\omega }_{r}L}_{s}\\ {-{\omega }_{r}L}_{s}& {R}_{s}+\frac{d{L}_{s}}{dt}\end{array}\right]\left[\begin{array}{c}{i}_{ds}^{e}\\ {i}_{qs}^{e}\end{array}\right]+\left[\begin{array}{c}{e}_{ds}^{e}\\ {e}_{qs}^{e}\end{array}\right]$$
(20)

The stator induced EMF can be expressed as follows:

$$\left[\begin{array}{c}{e}_{ds}^{e}\\ {e}_{qs}^{e}\end{array}\right]=\left[\begin{array}{c}0\\ {{\omega }_{r}\Psi }_{f}\end{array}\right]$$
(21)

Finally, the PMSG’s synchronous coordinate system d-q voltage equation can be obtained.

$$\left[\begin{array}{c}{v}_{ds}^{e}\\ {v}_{qs}^{e}\end{array}\right]=\left[\begin{array}{cc}{R}_{s}+\frac{d{L}_{s}}{dt}& {-{\omega }_{r}L}_{s}\\ {-{\omega }_{r}L}_{s}& {R}_{s}+\frac{d{L}_{s}}{dt}\end{array}\right]\left[\begin{array}{c}{i}_{ds}^{e}\\ {i}_{qs}^{e}\end{array}\right]+\left[\begin{array}{c}0\\ {{\omega }_{r}\Psi }_{f}\end{array}\right]$$
(22)

Since the rotor of the PMSG has no energy input and output, it can be regarded as electromagnetic torque, which can be expressed as follows:

$${T}_{e}=\frac{3}{2}P{\psi }_{F}{i}_{qs}$$
(23)

where, P is the number of pole pairs.

5 Control of the Generator Side Converter (PMSG)

The generator side controller controls the rotational speed to produce the maximum output power via controlling the electromagnetic torque according to Eq. (10), where the indirect vector control is used. The proposed control logic of the generator side converter appears in Fig. 15. The speed loop will generate the q-axis current component to control the generator torque and speed at different wind speed via estimating the reference value of iα, iβ as appeared in Fig. 15. The torque control can be achieved through the control of the isq current. Figure 16 shows the stator and rotor current space phasors and the excitation flux of the PMSG. The quadrature stator current isq can be controlled through the rotor reference frame (α, β axis) as appeared in Fig. 16. So, the reference value of iα, iβ can be estimated easily from the amplitude of isq* and the rotor angle, θr. Initially, to find the rotor angle, θr, the relationship between the electrical angular speed, ωr, and the rotor mechanical speed (rad/s), ωm may be expressed as:

$$\omega_{r} = \frac{P}{2}\omega_{m}$$
(24)
Fig. 15
figure 15

Control block diagram of PMSG

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Fig. 16
figure 16

The stator and rotor current space phasors and the excitation flux of the PMSG

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So, the rotor angle, θr, can be estimated by integrating the electrical angular speed, ωr. The input to the speed control is the actual and reference rotor mechanical speed (rad/s) and the output is the (α, β) reference current components. The actual values of the (α, β) current components are estimated using Clark’s transformation to the three-phase current of PMSG. The FLC can be used to find the reference speed along which tracks the MPP.

5.1 Fuzzy Logic Controller for MPPT

At a certain wind speed, the power is maximum at a certain ω called optimum rotational speed, ωopt. This speed corresponds to the optimum tip speed ratio, λopt [71]. So, to extract MP at variable wind speed, the turbine should always operate at λopt. This occurs by controlling the rotational speed of the turbine. Controlling the turbine to operate at optimum rotational speed can be done using the fuzzy logic controller. Each WT has one value of λopt at variable speed but ωopt changes from certain wind speed to another. From Eq. (6), the relation between ωopt and wind speed, u, for constant R and λopt can be deduced as appeared in (25):

$$\omega_{opt} = \frac{{\lambda_{opt} \,}}{R}u$$
(25)

From Eq. (25), the relation between the optimum rotational speed and wind speed is linear. At a certain wind speed, there is an optimum rotational speed which is different at another wind speed. The fuzzy logic control is used to search (observation and perturbation) the rotational speed reference which tracks the MPP at variable wind speeds. The fuzzy logic controller block diagram appears in Fig. 17. Two real-time measurements are used as input to fuzzy (ΔP, and Δωm*) and the output is (Δωm-new*). Membership functions appear in Fig. 18. Triangular symmetrical membership functions are suitable for the input and output, which give more sensitivity especially as variables approach zero value. The width of variation can be adjusted according to the system parameter. The input signals are first fuzzified and expressed in fuzzy set notation using linguistic labels which are characterized by membership functions before it is processed by the FLC. Using a set of rules and a fuzzy set theory, the output of the FLC is obtained. This output, expressed as a fuzzy set using linguistic labels characterized by membership functions, is defuzzified and then produces the controller output. The fuzzy logic controller doesn't require any detailed mathematical model of the system and its operation is governed simply by a set of rules. The principle of the fuzzy logic controller is to perturb the reference speed ωm* and to observe the corresponding change of power, ΔP. If the output power increases with the last increment, the searching process continues in the same direction. On the other hand, if the speed increment reduces the output power, the direction of the searching is reversed. The fuzzy logic controller is efficient to track the MPP, especially in case of frequently changing wind conditions.

Fig. 17
figure 17

Input and output of fuzzy controller

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Fig. 18
figure 18

Membership functions of the fuzzy logic controller

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Figure 18 shows the input and output membership functions and Table 1 lists the control rule for the input and output variable. The next fuzzy levels are chosen for controlling the inputs and output of the fuzzy logic controller. The variation step of the power and the reference speed may vary depending on the system. In Fig. 18, the variation step in the speed reference is from −0.15 to 0.15 rad/s for power variation ranging over from −30 to 30 W. The membership definitions are given as follows: N (negative), N++ (very big negative), NB (negative big), NM (negative medium), NS (negative small), ZE (zero), P (positive), PS (positive small), PM (positive medium), PB (positive big), and P++ (very big positive).

Table 1 Rules of fuzzy logic controller
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5.2 Control of the Grid Side Converter

The power flow of the grid side converter is controlled in order to maintain the dc-link voltage at reference value, 600 V. Since increasing the output power than the input power to dc-link capacitor causes a decrease of the dc-link voltage and vice versa, the output power will be regulated to keep dc-link voltage approximately constant. To maintain the dc-link voltage constant and to ensure the reactive power flowing into the grid, the grid side converter currents are controlled using the d-q vector control approach. The dc-link voltage is controlled to the desired value by using a PI-controller and the change in the dc-link voltage represents a change in the q-axis (iqs) current component. Figure 19 shows a control block diagram of the grid side converter. The active power can be defined as appeared in the following equation:

$$P_{s} = \frac{3}{2}\left( {v_{ds} i_{ds} + v_{qs} i_{qs} } \right)$$
(26)
Fig. 19
figure 19

Control block diagram of grid side converter [55, 56]

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The reactive power can be defined as:

$$Q_{s} = \frac{3}{2}\left( {v_{qs} i_{ds} - v_{ds} i_{qs} } \right)$$
(27)

By aligning the q-axis of the reference frame along with the grid voltage position vds = 0 and vqs = constant because the grid voltage is assumed to be constant. Then the active and reactive power can be obtained from the following equations:

$$P_{s} = \frac{3}{2}v_{qs} i_{qs}$$
(28)
$$Q_{s} = \frac{3}{2}v_{qs} i_{ds}$$
(29)

6 Simulation Results and Discussion

A co-simulation (PSIM/SIMULINK) program has been used where PSIM contains the power circuit of the WECS and MATLAB/SIMULINK has the whole control system as described before. The model of WECS in PSIM contains the WT connected to the utility grid through a back-to-back bidirectional PWM converter. The control of the whole system in SIMULINK contains the generator side controller and the grid side controller. The generator can be directly controlled by the generator side controller to track the MP available from the WT. The wind speed is variable and changes from 7 to 13 m/s as input to WT. To extract MP at variable wind speed, the turbine should always operate at λopt. This occurs by controlling the rotational speed of the WT. So, it always operates at the optimum rotational speed. ωopt changes from certain wind speed to another. The fuzzy logic controller is used to search the optimum rotational speed which tracks the MPP at variable wind speeds. Figure 20a shows the variation of the wind speed which varies randomly from 7 to13 m/s. On the other hand, Fig. 20b shows the variation of the actual and reference rotational speed as a result of the wind speed variation. At a certain wind speed, the actual and reference rotational speed has been estimated and this agreement with the power characteristic of the WT appeared later in Fig. 14. i.e. the WT always operates at the optimum rotational speed which is found using FLC; hence, the power extraction from wind is maximum at variable wind speed. It is seen that according to the wind speed variation the generator speed varies and that its output power is produced corresponding to the wind speed variation. The fuzzy logic controller works well and it gives a good tracking performance for the MPP. The fuzzy logic controller makes WT always operates at the optimum rotational speed. On the other hand, the grid side controller maintains the dc-link voltage at the desired value, 600v, as appeared in Fig. 20c. The dc-link voltage is regulated by exporting active power to the grid as appeared in Fig. 20d. The reactive power transmitted to the grid appears in Fig. 20e.

Fig. 20
figure 20figure 20

Different simulation waveforms: a wind speed variation (7–13) m/s. b actual and reference rotational speed (rad/s). c dc-link voltage (V). d Active power (W). e Reactive power (Var)

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7 Conclusion

Variable speed operation and direct drive wind turbines (WTs) have been considered as the modern aspects of wind energy conversion systems (WECS). In this chapter, a fuzzy logic controller (FLC)-based MPPT strategy for (WECS) is proposed. The generator side controller has been used to track the maximum power generated from WTs through controlling the rotational speed of the WT using FLC. The performance of the proposed MPPT strategy is analyzed mathematically and verified by simulation using MATLAB/PSIM/Simulink software. The PMSG has been controlled in an indirect vector field-oriented control technique and its speed reference has been obtained from FLC. The simulation outcomes have been conducted to approve the performance of the proposed MPPT strategy, and all results have confirmed the adequacy of the proposed MPPT strategy.