The global energy consumption is rising and an increasing attention is being paid to alternative methods of electricity generation. The very low environmental impact of the renewable energies makes them a very attractive solution for a growing demand. In this trend towards the diversification of the energy market, wind power is probably the most promising sustainable energy source. The progress of wind power in recent years has exceeded all expectations, with Europe leading the global market . Recent progress in wind technology has led to cost reduction to levels comparable, in many cases, with conventional methods of electricity generation.
In addition, power electronics is undergoing a fast evolution, mainly due to two factors. The first factor is the development of fast semiconductor devices, which are capable of switching fast and handling high powers. The second factor is the control area, where the introduction of computer as a real-time controller has made it possible to adapt advanced and complex control algorithms. These factors together make it possible to have cost-effective and grid-friendly converters connected to the grid.
2. Wind Energy Background
The use of wind energy goes back far in history. Wind power plants have, for instance, been used as water pumps and as mills. One major difference between the earliest windmills and the new generation of wind turbines is that the mechanical transmission of power has been replaced by an electrical transmission. The oil crisis in the mid 1970s resulted in a new interest in wind energy. This attention has continued to grow as the demand for reduced polluting emissions has increased.
The amount of power captured from a wind turbine is specific to each turbine and is governed by
(1) where is the turbine power, is the air density, A is the swept turbine area, is the coefficient of performance and is the wind speed. The coefficient of performance of a wind turbine is influenced by the tip-speed to wind speed ratio or TSR given by
(2) where is the turbine rotational speed and r is the turbine radius .
3. Permanent magnet synchronous generator
Synchronous machines are ac rotating machines that rotate at a speed proportional to the armature current frequency. In this type of machine the magnetic field created by the armature currents rotate at the same speed as that created by the field current on the rotor. Synchronous machines have been used for many years as generators of large power plants such as turbine generators and hydroelectric generators. These synchronous generators are normally used at constant speed and are connected directly to the electric grid.
For variable speed applications permanent magnet synchronous machine (PMSM) are used and are quickly becoming the next-generation variable speed ac motor drives due to the availability of high-energy permanent magnet materials. The PMSM has widely found its application as a high performance machine drive because of the ripple free torque characteristics and simple control strategies. Compared to induction machine drives, the PMSM has less rotor losses hence, it is potentially more efficient. In addition, the PMSM can achieve higher torque densities than its wound rotor counterpart.
PMSMs have lower reactance values than their equivalent rotor wound machines. In addition, PMSMs are more power dense than their rotor wounded counter parts and they can provide full rotor flux at all times. Due to these characteristics, permanent magnet synchronous generators (PMSG) have high peak torque capabilities that would be beneficial to a wind turbine system during wind gust. These machines can also resist repetitive torque pulsations of up to 20% of the rated torque .
3. Power converters in grid connected applications
In this part the commonly used converters topologies are presented. The analyzed topologies are two-level, three-level and multi-level converters.
3.1. two-level converter
The two-level inverter is a very commonly used topology. The layout is shown on Fig.2.13, and it shows, that a three phase inverter consists of six switches. The capacitor models a ripple-free DC-link voltage.
By controlling the switches, for instance by Space Vector Modulation (SVM) and Pulse With Modulation (PWM), and filtering the output, a quasi-sinusoidal waveform is obtained. However without the filter, the output voltage would be a square wave. To ensure, that short circuits do not occur, dead time is normally incorporated, meaning that two switches in one leg of the inverter are never turned on at the same time.
3.2. three-level converter
The three-level inverter is an alternative to the two-level inverter, and have some advantages, that makes it better suited for a medium voltage application. But a trade off is, that it consist of twice as many transistors as its two level counterpart. Fig.2.14 shows the schematic of a three-level three phase inverter.
One of the advantages of the three-level inverter is, that the transistors always turn on and off in pairs. This means, that the full DC-link voltage will always be shared by two switches, where the two level inverter switches has to be able to block the full DC-link voltage. The switching scheme of a three-level inverter has three states; first one where switch 1 and 2 are turned on, second state where the middle switches 2 and 3 are on, and the last one where switch 3 and 4 are turned on.
3.3. Multi-level converter
Currently there is an increasing interest in multilevel power converters especially for medium to high-power, high voltage wind turbine applications. Multilevel inverters consist of six or more switches pair leg, and the main idea is to create an even higher number of output sinusoidal voltage levels, than the three-level inverter, further decreasing the harmonic content. Since the development of the neutral-point clamped (NPC) three-level converter, several alternative multilevel converter topologies have been reported in the literature. According with  the different proposed multilevel converter topologies can be classified in the following five categories and these are represented in Fig.2.15:
multilevel configurations with diode clamps (a)
configurations with bi-directional switch interconnection (b)
multilevel configurations with flying capacitors (c)
multilevel configurations with multiple three-phase inverters (d)
multilevel configurations with cascaded single phase H-bridge inverters (e)
Because the multilevel inverter consists of many switches, the control of the inverter is more complex. Also, the NPC voltage becomes harder to control, because the number of neutral points increase.
4. Power converters topologies for wind turbines
Basically two power converter topologies with full controllability of the generated voltage on the grid side are used currently in the wind turbine systems .
4.1. Bidirectional back-to-back two-level power converter
This topology is state-of-the-art especially in large wind turbines. The back-to-back PWM-VSI is a bi-directional power converter consisting of two conventional PWM-VSCs. The topology is shown in Fig.2.16.
To achieve full control of the grid current, the DC-link voltage must be boosted to a level higher than the amplitude of the grid line-line voltage. The power flow of the grid side converter is controlled in order to keep the DC-link voltage constant, while the control of the generator side is set to suit the magnetization demand and the reference speed .
An advantage of the PWM-VSC is the capacitor decoupling between the grid inverter and the generator inverter. Besides affording some protection, this decoupling offers also separate control of the two inverters, allowing compensation of asymmetry both on the generator side and on the grid side, independently. The inclusion of a boost inductance in the DC-link circuit increases the component count, but a positive effect is that the boost inductance reduces the demands on the performance of the grid side harmonic filter, and offers some protection of the converter against abnormal conditions on the grid , .
On the other hand, in several papers concerning adjustable speed drives, the presence of the DC-link capacitor is mentioned as a drawback, since it is heavy and bulky, it increases the costs and maybe of most importance, it reduces the overall lifetime of the system . Another important drawback of the back-to-back PWM-VSI is the switching losses. Every commutation in both the grid inverter and the generator inverter between the upper and lower DC link branch is associated with a hard switching and a natural commutation. Since the back-to-back PWM-VSI consists of two inverters, the switching losses might be even more pronounced. The high switching speed to the grid may also require extra EMI-filters.
In order to achieve variable speed operation the wind turbines equipped with a PMSG will required a boost DC-DC converter inserted in the DC-link.
4.2. Unidirectional power converter
A wound rotor synchronous generator requires a simple diode bridge rectifier for the generator side converter as shown in Fig.2.17. The diode rectifier is the most common used topology in power electronic applications. For a three-phase system it consists of six diodes. The diode rectifier can only be used in one quadrant, it is simple and it is not possible to control it. It could be used in some applications with a dc-bus.
The variable speed operation of the wind turbine is achieved by using an extra power converter which fed the excitation winding.
The grid side converter will offer a decoupled control of the active and reactive power delivered to the grid and also all the grid support features. These wind turbines can have a gearbox or can be direct-driven.
4.3. Modular power converters
However, at low wind speeds and hence low level of the produced power, the full scale power converter concept exhibits low utilization of the power switches and thus increased power losses. Therefore, a new concept in which several power converters are running in parallel is used as show in Fig.2.18 .
By introducing power electronics many of the wind turbine systems get similar performances with the conventional power plants. Modern wind turbines have a fast response in respect with the grid operator demands however the produced real power depends on the available wind speed.
The reactive power can in some solutions, e.g. full scale power converter based wind turbines, be delivered without having any wind producing active power. These wind turbines can also be active when a fault appears on the grid and where it is necessary to build the grid voltage up again; having the possibility to lower the power production even though more power is available in the wind and thereby act as a rolling capacity for the power system. Finally, some systems are able to work in island operation in the case of a grid collapse , .
5. Control strategies for grid side converter
According with the pervious description the system considered for modelling and implementation can be represented in Fig.2.19.
As it can be seen the system consists in:
an LC filter
The generator and the generator side converter are not included in this model and a variable power source P (t) is fed into the DC-link of the grid side converter.
The optimum control strategy for the grid inverter control must be chosen based on the characteristics of known control methods. The control methods to be investigated should be as a minimum Voltage Oriented Control (VOC), Virtual Flux Oriented Control (VFOC) and Direct Power Control (DPC).
First a short description of the synchronization methods will be presented followed by the description of the control strategies for grid side converter.
4.1. Phase Locked Loop (PLL)
Phase, amplitude and frequency of the utility voltage are critical information for the operation of the grid-connected inverter systems. In such applications, an accurate and fast detection of the phase angle, amplitude and frequency of the utility voltage is essential to assure the correct generation of the reference signals and to cope with the standard requirements for the grid-connected converters. Grid-connected operations are controlled to work close to the unity power factor in order to reach the standards. It requires the use of a synchronizing algorithm which is able to synchronize the reference current of the H-bridge VSI inverter with the grid voltage. 
There are two basic synchronization methods:
Filtered Zero Cross Detection (ZCD);
Phase Locked Loop (PLL).
The first method is based on the detection of the zero crossing of the grid voltage while the second one, PLL, is a feedback control system that automatically adjusts the phase of a logical generated signal to match the phase of an input signal. The PLL is used to synchronize the inverter current angle,, with the angle of the grid voltage, , to obtain a power factor as close to 1 as possible. The angle is used to calculate the reference current that is compared to the actual output current of the inverter.
PLL requires two orthogonal voltages which can easily get for three phase systems representing the voltage space vector in a rotating reference frame (dq). For single phase systems the classical solution was the filtered ZCD. Now the trend is to use the PLL creating virtual orthogonal components. The main idea in the PLL is that it changes the inverter current frequency,, if the inverter current and the grid voltage are out of phase. If the current lags the grid voltage the PLL will decrease until the inverter current is in phase with the grid voltage, but if the inverter current leads the grid voltage is increased until they are in phase.
4.2 Synchronous Voltage Oriented Control -PI with PLL
This control strategy is well-proven being used for a long time in applications like active rectifiers, active filters or grid converters. The grid converter structure to be simulated is depicted in Fig.2.22.
In this strategy the current is oriented along the active voltage and normally and this is also the reason why this strategy is called voltage oriented control. A conventional PLL is used to detect the phase grid angle Ï', grid frequency and grid voltage. The frequency and the voltage are needed in order to monitor the grid conditions and to comply with the control requirements while the grid angle is required for transformations to the synchronous frame. The currents are transformed from stationary (abc) to synchronous frame (dq) and conventional PI controllers are used. Decoupling of the cross-coupled d and q axis is performed as it is shown in Fig.2.23. To decouple the grid voltage from the output of the current controllers a voltage feed forward is used.
A standard PI controller is used also for the DC voltage and its output is feed-forwarded to the output of the P controller to obtain the reference for the active current and another PI controller is used to obtain the reference for the reactive current.
The biggest disadvantage is the low performance in case of unbalanced or faulty grid where the grid angle is difficult to define.
This strategy can be also implemented in the stationary frame replacing PI controllers with the resonant controllers like in Fig.2.24. In this situation can be reach the advantage of less complexity due to the less need of transformations and no need of decoupling and voltage feed-forward.
4.3. Synchronous VFOC-PI without PLL
VFOC proposes the use of a virtual flux by integrating the grid voltage. The angle of this flux will be in quadrature with the grid angle but will be less sensitive to grid disturbances due to the low-pass filter effect of the integrator. The performances of the grid angle estimator are limited and the dynamic is difficult to tune. More flexibility can be obtained with PLL where the dynamic can be adjusted by tuning the PI controller. VFOC will exhibit the same performances as VOC with PLL except for the much distorted grid case (THD=8%) where it produces grid angle error. VFOC is more robust for disturbed grid but cannot outperform the PLL. 
4.4 Adaptive Band Hysteresis (ABH) control with PLL
This control strategy is base on indirect PQ power control with adaptive band hysteresis (ABH). The diagram of the ABH control is similar with the diagram of the VOC-PI control strategy from Fig.2.22 and the control structure is presented in Fig.2.27.
Hysteresis control is known to exhibit high dynamic response as the concept is to minimize the error in one sample. As the typically sampling frequencies are in the range of 50-100 kHz, this means a very high bandwidth. A constant band for the hysteresis comparator leads to variable switching frequency. An on-line adaptation of the band can be done in order to keep the switching frequency quasi-constant. The PLL is used in order to orientate the output of the P and Q controller with grid angle and for grid monitoring. 
Even if this strategy is using a PLL for orientation of the reference currents, it will exhibit improved performances under grid voltage variations due to the higher bandwidth of the current controller that help in order to keep the currents under the trip limits.
4.5 Direct Power Control (DPC) with SVM and PLL
The control structure for this strategy is presented in Fig.2.28 while the diagram of this control method is similar with the one from Fig.2.25.
This control method is a simplified VOC strategy. The difference between this two control strategies is that the current controllers are eliminated. The power controllers produce directly the voltage references for the space vector modulator (SVM) and this can be also the reason why this method is called direct power control. A conventional PLL is used also in this strategy in order to detect the grid phase angle Ï', grid frequency f and grid voltage V from the grid voltages.
The power used to balance the DC voltage is estimated using the DC voltage controller output and other PI controllers are used for active and reactive power controllers.
DPC can be also implemented using hysteretic control yielding in more robustness over for distorted grid conditions but with the price of very high computation intensity, difficult to implement in low-cost DSP technology . The control structure for VFDPC-SVM with PLL is represented in Fig.2.29.