**3. The aerodynamic of starting and energy gain by motoring**

**Figure 1.** Proposed grid connected HAWT system using backward VSMC.

158 Advances in Wind Power

**Figure 2.** Alternative implementation of the backward VSMC using BRB-IGBT devices.

Figure 3 shows the variation of *C* T form Equation (3) versus *λ* for a 5.6 kW wind turbine whose other parameters, taken to be typical of a wind turbines of that output, are given in the Appendix. Also shown is the measured starting performance of a 5.0 kW turbine whose blades were designed for rapid starting using the methods described by Wood [10]. In Fig‐ ure 3, a 5th order curve is fitted to the measured starting data, but more important, a linear approximation is also determined and used for simulation of motoring. It is important to

Figure 4 shows starting data of a 5.0 kW wind turbine, in terms of wind speed and tip speed ratio as a function of time. The 5 m diameter, two-bladed 5.0 kW turbine had fixed-pitch blades designed for good aerodynamic starting (without motoring). Even at a high wind speed of around 10 m/s the blades take about 13 s to reach the minimum angular velocity for power extraction.

Starting can be analyzed using standard blade element theory with no axial or azimuthal in‐ duction, Wood [10]. With all lengths normalized by the blade tip radius, *R*, and all velocities normalized by *U*, the aerodynamic torque, *Ta*, acting on the starting rotor, is given by

**Figure 3.** Measured starting torque for a 5 kW wind turbine and assumed power-extracting torque for a 5.6 kW wind turbine.

$$T\_a = N\rho \, U^2 R^3 \int\_{r\_k}^1 \left(1 + \lambda^2 r^2\right)^{1/2} r \sin \theta\_p \{\cos \theta\_p - \lambda r \sin \theta\_p\} dr\tag{4}$$

where *N* is the number of blades, *c* is the blade chord which depends on radius *r*, and *θ* <sup>p</sup> is the pitch. The integration is from the normalized hub radius, *r* h, to the tip. Equation (5) is derived in [10] where the assumptions behind it are justified in detail. In particular, it is as‐ sumed that the angular acceleration is small enough to allow a quasi-steady analysis and the lift and drag on any airfoil are given by the "flat plate" equations:

$$\mathbf{C}\_{\parallel} = \begin{array}{c} \mathfrak{Z}\sin\alpha\cos\alpha \quad \text{and} \quad \mathbf{C}\_{\perp} = \ \mathfrak{Z}\sin^{2}\alpha \end{array} \tag{5}$$

which are valid for angles of attack, *α* > °30 approximately. As no power is extracted the ro‐ tor torque *T* a acts only to accelerate the blades. Thus:

$$d\Omega \mid dt = \left(T\_a - T\_r\right) / \operatorname{I} \operatorname{ord} \lambda \mid dt = \left(T\_a - T\_r\right) / \left(\operatorname{II} I\right) \tag{6}$$

where *J* is the total rotational inertia and *T* r is the resistive torque due to cogging torque or resistance in the gearbox which may or may not depend on *Ω*. For the start shown in Figure 3 and 4, *T* r was negligible and the torque was inferred from Equation (6) and the turbine inertia. It is shown in [10] that for wind turbines of any size, *J NJ* b where *J* b is the inertia of each blade. In words, the turbine inertia is dominated by the blades as can be seen in The Appendix. When *T* <sup>r</sup> can be ignored, starting is independent of *N*. Equations (4) and (6) were solved by the Adams-Moulton method –a standard numerical technique for ordinary differ‐ ential equations - to obtain the solid line in Fig. 4, which accurately predicts the initial, 11 s period of slow, approximately constant acceleration. The calculations then become inaccu‐ rate because (5) is no longer valid. However, it is clear that starting is dominated by the long period of slow acceleration followed by a much shorter period of rapid acceleration during which the turbine reaches the rotor speed for power production. An important consequence of (4) and (6) which is independent of the form for blade lift and drag, comes from the scal‐ ing outside the integral: if *T* s is the time required to reach a particular *Ω* for power extrac‐ tion to commence, which is the most common strategy for small turbines, then *T* s ~ *U* -2. Alternatively, if power extraction starts at a fixed *λ*, *T* s ~ *U* -1. Thus the minimum starting time from Fig. 4 is approximately 40 s at the desirable cut-in wind speed of 3m/s. It is noted that this turbine is believed to be the first whose blades were designed for rapid starting

Knowing *T* s as a function of *U* allows a simple determination of *E* g(*U*), the energy gained by motor-starting when compared to aerodynamic starting, on the basis of the following as‐ sumptions:


**6.** the turbine switches instantaneously from motoring to generating when *λ=λ* opt

The energy gain is the product of the difference between the motor-starting and aerodynam‐ ic-starting times and the power output at wind speed *U* minus the energy required to accel‐ erate the rotor. Thus

$$E\_{\mathcal{S}}(\mathcal{U}) = P(\mathcal{U}) \left[ T\_u(\mathcal{U}) - T\_m \right] - \frac{1}{2} f \, \Omega\_s^2 \tag{7}$$

where *T* m is independent of *U* from assumption 5. From 3 and 4:

$$P(\mathcal{U}\_r)T\_m = \frac{1}{2}f\,\Omega\_s^2\tag{8}$$

Therefore

where *N* is the number of blades, *c* is the blade chord which depends on radius *r*, and *θ* <sup>p</sup> is the pitch. The integration is from the normalized hub radius, *r* h, to the tip. Equation (5) is derived in [10] where the assumptions behind it are justified in detail. In particular, it is as‐ sumed that the angular acceleration is small enough to allow a quasi-steady analysis and the

which are valid for angles of attack, *α* > °30 approximately. As no power is extracted the ro‐

where *J* is the total rotational inertia and *T* r is the resistive torque due to cogging torque or resistance in the gearbox which may or may not depend on *Ω*. For the start shown in Figure 3 and 4, *T* r was negligible and the torque was inferred from Equation (6) and the turbine inertia. It is shown in [10] that for wind turbines of any size, *J NJ* b where *J* b is the inertia of each blade. In words, the turbine inertia is dominated by the blades as can be seen in The Appendix. When *T* <sup>r</sup> can be ignored, starting is independent of *N*. Equations (4) and (6) were solved by the Adams-Moulton method –a standard numerical technique for ordinary differ‐ ential equations - to obtain the solid line in Fig. 4, which accurately predicts the initial, 11 s period of slow, approximately constant acceleration. The calculations then become inaccu‐ rate because (5) is no longer valid. However, it is clear that starting is dominated by the long period of slow acceleration followed by a much shorter period of rapid acceleration during which the turbine reaches the rotor speed for power production. An important consequence of (4) and (6) which is independent of the form for blade lift and drag, comes from the scal‐ ing outside the integral: if *T* s is the time required to reach a particular *Ω* for power extrac‐ tion to commence, which is the most common strategy for small turbines, then *T* s ~ *U* -2. Alternatively, if power extraction starts at a fixed *λ*, *T* s ~ *U* -1. Thus the minimum starting time from Fig. 4 is approximately 40 s at the desirable cut-in wind speed of 3m/s. It is noted that this turbine is believed to be the first whose blades were designed for rapid starting

Knowing *T* s as a function of *U* allows a simple determination of *E* g(*U*), the energy gained by motor-starting when compared to aerodynamic starting, on the basis of the following as‐

**1.** there is no resistive or cogging torque in the drive train and generator

**5.** *T*a<< *T* m during motoring and can be ignored, where *T* m is the motoring torque

**4.** the motoring power is the turbine maximum (rated) power

a

*dΩ* / *dt* =(*Ta* −*Tr*)/ *J* or*dλ* / *dt* =(*Ta* −*Tr*) / (*JU* ) (6)

(5)

<sup>2</sup> *C C l d* = = 2 2 sin cos and sin

lift and drag on any airfoil are given by the "flat plate" equations:

tor torque *T* a acts only to accelerate the blades. Thus:

sumptions:

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**2.** motor/generator efficiency =100%

**3.** all grid power goes to accelerate the rotor

a a

$$E\_{\mathcal{g}}(\mathcal{U}) = P(\mathcal{U})T\_{\mathcal{g}}(\mathcal{U}) - \frac{1}{2}I\,\mathcal{Q}\_s^2 \mathbf{\hat{l}}^\mathsf{T} + P(\mathcal{U})/P(\mathcal{U}\_r)\mathbf{\hat{l}} \tag{9}$$

Assume *P*(*U*) = *k* <sup>1</sup> *U* <sup>3</sup> as in Equation (1) with *k* <sup>1</sup> = 5.6 to give 5.6 kW at *U* <sup>r</sup> = 10 m/s. Also *T* <sup>a</sup> = *k* 2/*U*, where *k* 2 = 132 to fit the starting data. If *Ω* s corresponds to *λ* opt, then

$$\frac{1}{2}\text{J}\,\Omega\_s^2 = \frac{J\,\lambda\_{opt}^2\,\text{U}^2}{2\,\text{R}^2} \tag{10}$$

and

$$E\_{\mathcal{S}}(\mathcal{U}) = \left[k\_1 k\_2 - \frac{J \lambda\_{opt}^2}{2R^2} \{1 + \langle \mathcal{U} \,/\mathcal{U}\_r \rangle^3\} \right] \mathcal{U}^2 \tag{11}$$

For the 5.6 kW turbine documented in the Appendix, *J* = 18 kgm2 , *λ* opt = 7, and *R* = 2.5 m. Thus

$$E\_{\chi}(\mathcal{U}) = 70.56 \text{\textquotedblleft} 10.48 - \left[1 + (\mathcal{U}/\mathcal{U}\_r)^3\right] \mathcal{U}^2 \tag{12}$$

It will be shown below that (12) is a good approximation for *E* g(*U*). Since (*U*/*U* r) 3 ≤ 1, *E* g(*U*) is positive for all values of *U*. It is this result that makes motor-starting attractive provided the turbine power electronics allows bi-directional power flow.

**Figure 4.** Measured starting sequence of a 5.0 kW two bladed wind turbine which corresponds to the starting torque of Figure 2.

#### **4. Description of the generator and converter**

#### *4.1. Permanent magnet synchronous generator*

The PMSG model is developed in the *d-q* reference frame to eliminate the time varying in‐ ductances assuming a sinusoidal distribution of the permanent magnet flux in the stator and surface mounted round rotor [18]:

$$V\_q = -\left(\mathcal{R}\_s + pL\_{\
q}\right)I\_q - \mathcal{Q}L\_{\
q}I\_d + \mathcal{Q}\lambda\_m \tag{13}$$

$$dV\_d = -(R\_s + pL\_{\
u})I\_d - \Omega \, L\_{\
u} I\_q \tag{14}$$

$$T\_g = -1.5 P \lambda\_m I\_q \tag{15}$$

$$T\_{\mu} - T\_{\chi} = \text{J} \, d\Omega \, / \, dt \,\tag{16}$$

where Equation (16) is Equation (6) restated for completeness. *L* d and *L* q are the *d* and *q*-axis inductances, respectively; *R* s is the stator winding resistance; *I* <sup>d</sup> *, I* <sup>q</sup> *, V* d and *V* <sup>q</sup> are the *d* and *q* axis currents and voltage respectively; *λ* m is the amplitude of the flux induced by the permanent magnets of the rotor in the stator phases; *P* is the number of pole pairs; *T* <sup>e</sup> is the electromagnetic torque. Equation (16) is a basic representation of rotor dynamics which gov‐ erns the rotor acceleration, neglecting friction and other losses.

The PMSG operation mode depends on the direction of *T* <sup>g</sup>: positive for generating and neg‐ ative for motoring. *T* g is controlled through the backward VSMC. The parameters of the 5.6 kW PMSG used in simulation are shown in the Appendix. These parameters are close to those of the 5 kW PMSG in [19] with the exception of the rated speed which has been altered to be closer to the experimental turbine which used induction generator instead of PMSG.

## *4.2. Very Sparse Matrix Converter*

The VSMC has high efficiency, compact size, a long life span, low input current harmonics, and excellent input and output power quality control without commutation problems [20]. The VSMC provides a continuous transformation from AC-to-AC with adjustable voltage and frequency. The converter can operate in four quadrants and has the ability to shape cur‐ rent to be nearly sinusoidal at both the converter input and at the output using small AC filtering components. The displacement factor can be adjusted to unity by proper pulse width modulation (PWM) control [21]. The very sparse matrix converter is considered a high power density converter due to the lack of DC-link capacitors and has fewer bi-direc‐ tional switches than the conventional matrix converter which also reduces the system cost [22, 23]. Moreover, the rectifier stage is commutated at zero current providing increased effi‐ ciency of the converter by reducing switching losses [24]. Note that the sophisticated control algorithms that we propose for the backward connected VSMC can be implemented at low production cost due to the advances is digital signal processor technology in recent years. At the turn of the century industry preferred the use integer digital signal processors to reduce controller cost. Today (2012), floating point digital signal processors are now quite economi‐ cal and thus allow the use of sophisticated control in small wind power systems.

#### *4.2.1. Rectifier stage of the VSMC*

**Figure 4.** Measured starting sequence of a 5.0 kW two bladed wind turbine which corresponds to the starting torque

The PMSG model is developed in the *d-q* reference frame to eliminate the time varying in‐ ductances assuming a sinusoidal distribution of the permanent magnet flux in the stator and

where Equation (16) is Equation (6) restated for completeness. *L* d and *L* q are the *d* and *q*-axis inductances, respectively; *R* s is the stator winding resistance; *I* <sup>d</sup> *, I* <sup>q</sup> *, V* d and *V* <sup>q</sup> are the *d* and *q* axis currents and voltage respectively; *λ* m is the amplitude of the flux induced by the permanent magnets of the rotor in the stator phases; *P* is the number of pole pairs; *T* <sup>e</sup> is the electromagnetic torque. Equation (16) is a basic representation of rotor dynamics which gov‐

*Vq* = −(*Rs* + *pL <sup>q</sup>*)*Iq* −*ΩL <sup>d</sup> Id* + *Ωλ<sup>m</sup>* (13)

*Vd* = −(*Rs* + *pL <sup>d</sup>* )*Id* −*ΩL <sup>q</sup>Iq* (14)

*Tg* = −1.5*PλmIq* (15)

*Ta* −*Tg* = *J dΩ* / *dt* (16)

**4. Description of the generator and converter**

erns the rotor acceleration, neglecting friction and other losses.

*4.1. Permanent magnet synchronous generator*

surface mounted round rotor [18]:

of Figure 2.

162 Advances in Wind Power

Many aspects must be taken into consideration in synthesizing the rectifier switching signals [13]. Figure 5 shows the modulation strategy of the rectifier PWM switching signal genera‐ tion. Each grid cycle is divided to six sectors; in each sector, two of the grid side terminals are connected to either the positive or negative bus of the DC-link while the third terminal is connected to the opposite DC-link. In order to produce the maximum DC-link voltage, the maximum positive input voltage is connected to the positive bus of the DC-link for a com‐ plete 60o while the other phases are modulated to the negative DC-link bus and vice versa. So, the DC-link voltage is formed from the line to line voltage of the supply. Assuming a balanced symmetrical AC grid:

$$\begin{aligned} \mathsf{U}\_{a} &= \mathsf{U}\_{m}\cos(\omega\_{i}t) \\ \mathsf{U}\_{b} &= \mathsf{U}\_{m}\cos(\omega\_{i}t - 2\pi/3) \\ \mathsf{U}\_{c} &= \mathsf{U}\_{m}\cos(\omega\_{i}t - 4\pi/3) \end{aligned} \tag{17}$$

where *U* <sup>m</sup> is the maximum grid input voltage and *ω* <sup>i</sup> is the grid frequency in rad/s. The DClink voltage varies as the supply varies:

$$\mathcal{U}\mathcal{U}\_{dc} = \frac{\Im \mathcal{U}\_m}{2\cos(\omega\_l t)}\tag{18}$$

Figure 6 shows the space vector of the grid voltage and current. If the phase angle between the space vector of the voltage and current is set to zero, unity displacement factor is ach‐ ieved. The input current space vector *I* <sup>i</sup> is generated by the projection to the adjacent space vectors *I* <sup>α</sup> and *I* <sup>β</sup> following the grid sinusoidal voltages. The duty cycles of *I* <sup>α</sup> and *I* <sup>β</sup> are calculated as follows:

$$d\_{\alpha r} = m\_i \sin(\pi \,/\Im - \theta\_i) \tag{19}$$

and

$$d\_{\beta r} = m\_i \sin \Theta\_i \tag{20}$$

where *m* <sup>i</sup> is the current modulation index which is adjusted to unity to provide the maxi‐ mum injected current into the grid and maximize the DC-link voltage. In order to commu‐ tate the rectifier at zero current, the inverter space vector and switching pattern should be determined and matched with the rectifier space vector to ensure that the rectifier can be switched during the period of inverter zero voltage.

#### *4.2.2. Inverter stage of the VSMC*

Switching signals of the inverter stage are generated by FOC based space vector modulation which allows use of a zero voltage vector between the transitions from negative to positive bus. It also provides a chance to distribute the vectors symmetrically to reduce the current distortion and commutate the rectifier stage at zero current to reduce the switching losses [13, 24]. The error between the actual and reference current is compensated by a proportion‐ al plus integral (PI) controller to form the generator voltage and frequency to match the op‐ erating point which is considered the reference voltage. The reference voltage is transformed to a reference space vector. The amplitude of the vector and its angle determine the active vectors which are used to form the switching signal. The amplitude of the output voltage is proportional to the input voltage according to the transfer ratio of the matrix converter:

$$\mathcal{U}\_o \subset \sqrt{3} \Big|\_{2^{m\_c} \mathcal{U}\_m} \tag{21}$$

where *U* o is the output maximum voltage and mc is the VSMC conversion ratio (0≤ mc ≤1). Fig. 7-a presents the inverter space vectors which are used to form the generator or motor voltage. Fig. 7-b shows an example of the switching signals during one sampling period as‐ suming the reference voltage is in sector 1.

**Figure 5.** Modulation strategy of the rectifier stage.

*Udc* <sup>=</sup> <sup>3</sup>*Um* 2cos(*ω<sup>i</sup>*

*dα<sup>r</sup>* =*mi*

*dβ<sup>r</sup>* =*mi*

ieved. The input current space vector *I* <sup>i</sup>

switched during the period of inverter zero voltage.

*4.2.2. Inverter stage of the VSMC*

suming the reference voltage is in sector 1.

calculated as follows:

164 Advances in Wind Power

and

where *m* <sup>i</sup>

Figure 6 shows the space vector of the grid voltage and current. If the phase angle between the space vector of the voltage and current is set to zero, unity displacement factor is ach‐

vectors *I* <sup>α</sup> and *I* <sup>β</sup> following the grid sinusoidal voltages. The duty cycles of *I* <sup>α</sup> and *I* <sup>β</sup> are

sin(*π* / 3−*θ<sup>i</sup>*

mum injected current into the grid and maximize the DC-link voltage. In order to commu‐ tate the rectifier at zero current, the inverter space vector and switching pattern should be determined and matched with the rectifier space vector to ensure that the rectifier can be

Switching signals of the inverter stage are generated by FOC based space vector modulation which allows use of a zero voltage vector between the transitions from negative to positive bus. It also provides a chance to distribute the vectors symmetrically to reduce the current distortion and commutate the rectifier stage at zero current to reduce the switching losses [13, 24]. The error between the actual and reference current is compensated by a proportion‐ al plus integral (PI) controller to form the generator voltage and frequency to match the op‐ erating point which is considered the reference voltage. The reference voltage is transformed to a reference space vector. The amplitude of the vector and its angle determine the active vectors which are used to form the switching signal. The amplitude of the output voltage is proportional to the input voltage according to the transfer ratio of the matrix converter:

> *Uo* <sup>≤</sup> <sup>3</sup> 2

where *U* o is the output maximum voltage and mc is the VSMC conversion ratio (0≤ mc ≤1). Fig. 7-a presents the inverter space vectors which are used to form the generator or motor voltage. Fig. 7-b shows an example of the switching signals during one sampling period as‐

is the current modulation index which is adjusted to unity to provide the maxi‐

*<sup>t</sup>*) (18)

) (19)

sin*θ<sup>i</sup>* (20)

*mcUm* (21)

is generated by the projection to the adjacent space

**Figure 6.** Rectifier stage space vector diagram

Duty cycles of the working vectors are calculated as follows depending on the space vector angle and magnitude.

$$d\_{\alpha i} = m\_v \sin \{\pi / \Im - \theta\_o\} \tag{22}$$

$$d\_{\beta i} = m\_v \sin \{\Theta\_o\} \tag{23}$$

and

$$d\_0 = 1 - d\_{\alpha i} - d\_{\beta i} \tag{24}$$

where *d* αi and *d* βi represent the duty cycle of the active vectors while d0 represents the duty cycle of the zero vector.

#### *4.2.3. Backward VSMC*

In order to guarantee the transformation of power from the generator to the grid, the DClink voltage must be held at a fairly constant and sufficiently high average value. Given a variable wind speed and MPPT, the generator operates at variable frequency and variable voltage amplitude which is often less than the corresponding grid voltage. Due to the lack of the DC-link capacitor, the VSMC cannot operate as a boost converter to keep the DC-link voltage at the required minimum value. If employed in its forward configuration, the VSMC can be considered a step down converter according to equation (21) -. So, if the generator is connected in the conventional manner to the rectifier stage and the grid is connected to the inverter stage, (i.e. forward VSMC operation), the converter will operate only when the gen‐ erator operates at its rated condition, i.e. with the wind speed at or above its rated value (to solve this problem, for a forward configuration of the VSMC, a transformer with a very large step-up ratio would be required for the grid interface) To overcome this problem (i.e. with a lower ratio step-up transformer at the grid interface) a backward connected VSMC system is proposed in [13] where the rectifier stage is connected to the grid and the inverter stage is connected to the generator as shown in Figure 1. In backward operation of the VSMC, the rectifier stage converts the grid AC voltage to a near-constant average DC volt‐ age at the DC-link (variations in the average voltage correspond to variations in the grid voltage) while the inverter steps down the DC-link voltage to variable AC voltage with vari‐ able frequency depending on the generator and turbine operating point. In other words, the backward VSMC can be considered a step up converter from the generator side to the grid side. Such operation can be achieved by controlling the modulation index of the inverter stage to boost the generator voltage to the grid voltage depending on the operating speed. This configuration has the merits that control of the DC voltage is not needed, nor is syn‐ chronization with the grid required. Voltage flicker is not an issue due to the small filter on the mains side of the converter. The generator voltage and the grid current are synthesized using a space vector PWM technique with the guarantee of injecting current into the grid with or without reactive power to meet the grid power quality requirements as explained in next subsections.

Recent Advances in Converters and Control Systems for Grid-Connected Small Wind Turbines http://dx.doi.org/10.5772/51148 167

**Figure 7.** a) Inverter space vector diagram (b) Inverter switching signal for sector 1.

#### **4.3. Motoring-generating mode**

*dβ<sup>i</sup>* =*mv*sin(*θo*) (23)

*d*<sup>0</sup> =1−*dα<sup>i</sup>* −*dβ<sup>i</sup>* (24)

where *d* αi and *d* βi represent the duty cycle of the active vectors while d0 represents the duty

In order to guarantee the transformation of power from the generator to the grid, the DClink voltage must be held at a fairly constant and sufficiently high average value. Given a variable wind speed and MPPT, the generator operates at variable frequency and variable voltage amplitude which is often less than the corresponding grid voltage. Due to the lack of the DC-link capacitor, the VSMC cannot operate as a boost converter to keep the DC-link voltage at the required minimum value. If employed in its forward configuration, the VSMC can be considered a step down converter according to equation (21) -. So, if the generator is connected in the conventional manner to the rectifier stage and the grid is connected to the inverter stage, (i.e. forward VSMC operation), the converter will operate only when the gen‐ erator operates at its rated condition, i.e. with the wind speed at or above its rated value (to solve this problem, for a forward configuration of the VSMC, a transformer with a very large step-up ratio would be required for the grid interface) To overcome this problem (i.e. with a lower ratio step-up transformer at the grid interface) a backward connected VSMC system is proposed in [13] where the rectifier stage is connected to the grid and the inverter stage is connected to the generator as shown in Figure 1. In backward operation of the VSMC, the rectifier stage converts the grid AC voltage to a near-constant average DC volt‐ age at the DC-link (variations in the average voltage correspond to variations in the grid voltage) while the inverter steps down the DC-link voltage to variable AC voltage with vari‐ able frequency depending on the generator and turbine operating point. In other words, the backward VSMC can be considered a step up converter from the generator side to the grid side. Such operation can be achieved by controlling the modulation index of the inverter stage to boost the generator voltage to the grid voltage depending on the operating speed. This configuration has the merits that control of the DC voltage is not needed, nor is syn‐ chronization with the grid required. Voltage flicker is not an issue due to the small filter on the mains side of the converter. The generator voltage and the grid current are synthesized using a space vector PWM technique with the guarantee of injecting current into the grid with or without reactive power to meet the grid power quality requirements as explained in

and

166 Advances in Wind Power

cycle of the zero vector.

*4.2.3. Backward VSMC*

next subsections.

Equation (15) shows that the torque direction and hence the generator mode can only be controlled by the quadrature current component direction. In addition the torque is also controlled by the magnitude of Iq to match the wind power at different wind speeds. The amplitude and the direction of the generator quadrature current Iq can be controlled through the inverter stage of the VSMC.

The VSMC can operate the generator as a motor using FOC by controlling the current com‐ ponent which corresponds to the torque limited only by the generator torque rating. Figure 8 shows the flow chart of the starting strategy. The controller produces the reference genera‐ tor current depending on the mode of operation, either motor starting or generator mode (MPPT control). If in motor starting mode, the actual and reference motor currents are com‐ pared to generate the proper machine voltage vector which results in rated torque operation of the machine. Once the turbine reaches the nominated speed, Ωref, corresponding to λopt, motoring ceases and generating with MPPT control is enabled. Figure9 shows the proposed control technique for motor starting.

**Figure 8.** Starting strategy flow chart.

**Figure 9.** Block diagram of the generator-motor FOC technique.
