*(b) AC Synchronous Generator Technologies*

Since the early time of developing wind turbines, considerable efforts have been made to utilize three-phase synchronous machines. AC synchronous WTGs can take constant or DC excitations from either permanent magnets or electromagnets and are thus termed PM syn‐ chronous generators (PMSGs) and electrically excited synchronous generators (EESGs), re‐ spectively. When the rotor is driven by the wind turbine, a three-phase power is generated in the stator windings which are connected to the grid through transformers and power con‐ verters. For fixed speed synchronous generators, the rotor speed must be kept at exactly the synchronous speed. Otherwise synchronism will be lost.

Synchronous generators are a proven machine technology since their performance for pow‐ er generation has been studied and widely accepted for a long time. A cutaway diagram of a conventional synchronous generator is shown in Fig. 7. In theory, the reactive power charac‐ teristics of synchronous WTGs can be easily controlled via the field circuit for electrical exci‐ tation. Nevertheless, when using fixed speed synchronous generators, random wind speed fluctuations and periodic disturbances caused by tower-shading effects and natural resonan‐ ces of components would be passed onto the power grid. Furthermore, synchronous WTGs tend to have low damping effect so that they do not allow drive train transients to be absor‐ bed electrically. As a consequence, they require an additional damping element (e.g. flexible coupling in the drive train), or the gearbox assembly mounted on springs and dampers. When they are integrated into the power grid, synchronizing their frequency to that of the grid calls for a delicate operation. In addition, they are generally more complex, costly and more prone to failure than induction generators. In the case of using electromagnets in syn‐ chronous machines, voltage control takes place in the synchronous machine while in perma‐ nent magnet excited machines, voltage control is achieved in the converter circuit.

**Figure 7.** Cutaway of a synchronous generator [22].

In recent decades, PM generators have been gradually used in wind turbine applications due to their high power density and low mass [39]. Often these machines are referred to as the permanent magnet synchronous generators (PMSGs) and are considered as the machine of choice in small wind turbine generators. The structure of the generator is relatively straightforward. As shown in Fig. 8. the rugged PMs are installed on the rotor to produce a constant magnetic field and the generated electricity is taken from the armature (stator) via the use of the commutator, sliprings or brushes. Sometimes the PMs can be integrated into a cylindrical cast aluminum rotor to reduce costs [35]. The principle of operation of PM gener‐ ators is similar to that of synchronous generators except that PM generators can be operated asynchronously. The advantages of PMSGs include the elimination of commutator, slip rings and brushes so that the machines are rugged, reliable and simple. The use of PMs re‐ moves the field winding (and its associated power losses) but makes the field control impos‐ sible and the cost of PMs can be prohibitively high for large machines.

Because the actual wind speeds are variable, the PMSGs can not generate electrical power with fixed frequency. As a result, they should be connected to the power grid through AC-DC-AC conversion by power converters. That is, the generated AC power (with variable fre‐ quency and magnitude) is first rectified into fixed DC and then converted back into AC power (with fixed frequency and magnitude). It is also very attractive to use these perma‐ nent magnet machines for direct drive application. Obviously, in this case, they can elimi‐ nate troublesome gearboxes which cause the majority of wind turbine failures. The machines should have large pole numbers and are physically large than a similarly rated geared machine.

**Figure 8.** Cutaway of a permanent magnet synchronous generator [18].

coupling in the drive train), or the gearbox assembly mounted on springs and dampers. When they are integrated into the power grid, synchronizing their frequency to that of the grid calls for a delicate operation. In addition, they are generally more complex, costly and more prone to failure than induction generators. In the case of using electromagnets in syn‐ chronous machines, voltage control takes place in the synchronous machine while in perma‐

In recent decades, PM generators have been gradually used in wind turbine applications due to their high power density and low mass [39]. Often these machines are referred to as the permanent magnet synchronous generators (PMSGs) and are considered as the machine of choice in small wind turbine generators. The structure of the generator is relatively straightforward. As shown in Fig. 8. the rugged PMs are installed on the rotor to produce a constant magnetic field and the generated electricity is taken from the armature (stator) via the use of the commutator, sliprings or brushes. Sometimes the PMs can be integrated into a cylindrical cast aluminum rotor to reduce costs [35]. The principle of operation of PM gener‐ ators is similar to that of synchronous generators except that PM generators can be operated asynchronously. The advantages of PMSGs include the elimination of commutator, slip rings and brushes so that the machines are rugged, reliable and simple. The use of PMs re‐ moves the field winding (and its associated power losses) but makes the field control impos‐

Because the actual wind speeds are variable, the PMSGs can not generate electrical power with fixed frequency. As a result, they should be connected to the power grid through AC-DC-AC conversion by power converters. That is, the generated AC power (with variable fre‐ quency and magnitude) is first rectified into fixed DC and then converted back into AC power (with fixed frequency and magnitude). It is also very attractive to use these perma‐ nent magnet machines for direct drive application. Obviously, in this case, they can elimi‐

sible and the cost of PMs can be prohibitively high for large machines.

nent magnet excited machines, voltage control is achieved in the converter circuit.

**Figure 7.** Cutaway of a synchronous generator [22].

184 Advances in Wind Power

A potential variant of synchronous generators is the high-temperature superconducting generator [31; 27; 49; 55]. See Fig. 9 for a multi-MW, low-speed HTS synchronous generator system. The machine comprises the stator back iron, stator copper winding, HTS field coils, rotor core, rotor support structure, rotor cooling system, cryostat and external refrigerator, electromagnetic shield and damper, bearing, shaft and housing. In the machine design, the arrangements of the stator, rotor, cooling and gearbox may pose particular challenges in or‐ der to keep HTS coils in the low temperature operational conditions.

**Figure 9.** Schematic of a HTS synchronous generator system [11].

Superconducting coils may carry 10 times the current than conventional copper wires with negligible resistance and conductor losses. Without a doubt, the use of superconductors would eliminate all field circuit power loss and the ability of superconductivity to in‐ crease current density allows for high magnetic fields, leading to a significant reduction in mass and size for wind turbine generators. Therefore, superconducting generators pro‐ vide much promise in high capacity and weight reductions, perhaps suited better for wind turbines rated 10 MW or more. In 2005, Siemens successfully launched the world's first superconducting wind turbine generator, which was a 4MW synchronous generator. How‐ ever, there are many technical challenges to face especially for the long-life, low-mainte‐ nance wind turbine systems. For instance, there is always a necessity to maintain cryogenic systems so that the time to cool down and restore operation following a stoppage will be an additional issue.

#### *(c) AC Asynchronous Generators*

Whilst conventional power generation utilizes synchronous machines, modern wind pow‐ er systems use induction machines extensively in wind turbine applications. These induc‐ tion generators fall into two types: fixed speed induction generators (FSIGs) with squirrel cage rotors (sometimes called squirrel cage induction generators-SQIGs) [40; 1] and doublyfed induction generators (DFIGs) with wound rotors [9; 29; 19; 32, 43; 13; 34]. Cutaway diagrams of a squirrel-cage induction generator and a doubly-fed induction generator are presented in Fig. 10 and Fig. 11, respectively, and their system topologies are further illus‐ trated in Fig. 12.

When supplied with three-phase AC power to the stator, a rotating magnetic field is estab‐ lished across the airgap. If the rotor rotates at a speed different to synchronous speed, a slip is created and the rotor circuit is energized. Generally speaking, induction machines are simple, reliable, inexpensive and well developed. They have high degree of damping and are capable of absorbing rotor speed fluctuations and drive train transients (i.e. fault tolerant). However, induction machines draw reactive power from the grid and thus some form of reactive power compensation is needed such as the use of capacitors or power converters. For fixed-speed induction generators, the stator is connected to the grid via a transformer and the rotor is connected to the wind turbine through a gearbox. The rotor speed is considered to be fixed (in fact, varying within a narrow range). Up until 1998 most wind turbine manufacturers built fixed-speed induction generators of 1.5 MW and below. These generators normally operated at 1500 revolutions per minute (rpm) for the 50 Hz utility grid [37], with a three-stage gearbox.

**Figure 10.** Cutaway of a squirrel-cage induction generator [22].

Superconducting coils may carry 10 times the current than conventional copper wires with negligible resistance and conductor losses. Without a doubt, the use of superconductors would eliminate all field circuit power loss and the ability of superconductivity to in‐ crease current density allows for high magnetic fields, leading to a significant reduction in mass and size for wind turbine generators. Therefore, superconducting generators pro‐ vide much promise in high capacity and weight reductions, perhaps suited better for wind turbines rated 10 MW or more. In 2005, Siemens successfully launched the world's first superconducting wind turbine generator, which was a 4MW synchronous generator. How‐ ever, there are many technical challenges to face especially for the long-life, low-mainte‐ nance wind turbine systems. For instance, there is always a necessity to maintain cryogenic systems so that the time to cool down and restore operation following a stoppage will be

Whilst conventional power generation utilizes synchronous machines, modern wind pow‐ er systems use induction machines extensively in wind turbine applications. These induc‐ tion generators fall into two types: fixed speed induction generators (FSIGs) with squirrel cage rotors (sometimes called squirrel cage induction generators-SQIGs) [40; 1] and doublyfed induction generators (DFIGs) with wound rotors [9; 29; 19; 32, 43; 13; 34]. Cutaway diagrams of a squirrel-cage induction generator and a doubly-fed induction generator are presented in Fig. 10 and Fig. 11, respectively, and their system topologies are further illus‐

When supplied with three-phase AC power to the stator, a rotating magnetic field is estab‐ lished across the airgap. If the rotor rotates at a speed different to synchronous speed, a slip is created and the rotor circuit is energized. Generally speaking, induction machines are simple, reliable, inexpensive and well developed. They have high degree of damping and are capable of absorbing rotor speed fluctuations and drive train transients (i.e. fault tolerant). However, induction machines draw reactive power from the grid and thus some form of reactive power compensation is needed such as the use of capacitors or power converters. For fixed-speed induction generators, the stator is connected to the grid via a transformer and the rotor is connected to the wind turbine through a gearbox. The rotor speed is considered to be fixed (in fact, varying within a narrow range). Up until 1998 most wind turbine manufacturers built fixed-speed induction generators of 1.5 MW and below. These generators normally operated at 1500 revolutions per minute (rpm) for the

an additional issue.

186 Advances in Wind Power

trated in Fig. 12.

50 Hz utility grid [37], with a three-stage gearbox.

*(c) AC Asynchronous Generators*

**Figure 11.** Cutaway of a doubly-fed induction generator with a rotary transformer [43].

SCIGs can be utilized in variable speed wind turbines, as in controlling synchronous ma‐ chines. However, the output voltage can not be controlled and reactive power needs to be supplied externally. Clearly, fixed speed induction generators are limited to operate only within a very narrow range of discrete speeds. Other disadvantages of the machines are re‐ lated to the machine size, noise, low efficiency and reliability. These machines have proven to cause tremendous service failures and consequent maintenance.

**Figure 12.** Schematic of two induction generator systems.

SCIGs led the wind turbine market until the last millennium [16; 26], overtaken by the wide adoption of DFIGs. Nowadays, over 85% of the installed wind turbines utilize DFIGs [41] and the largest capacity for the commercial wind turbine product with DFIG has increased towards 5MW in industry. In the DFIG topology, the stator is directly connected to the grid through transformers and the rotor is connected to the grid through PWM power convert‐ ers. The converters can control the rotor circuit current, frequency and phase angle shifts. Such induction generators are capable of operating at a wide slip range (typically ±30% of synchronous speed). As a result, they offer many advantages such as high energy yield, re‐ duction in mechanical stresses and power fluctuations, and controllability of reactive power.

For induction generators, all the reactive power energizing the magnetic circuits must be supplied by the grid or local capacitors. Induction generators are prone to voltage instabili‐ ty. When capacitors are used to compensate power factor, there is a risk of causing self-exci‐ tation. Additionally, damping effect may give rise to power losses in the rotor. There is no direct control over the terminal voltage (thus reactive power), nor sustained fault currents.

As shown in Fig. 12(b), the rotor of the DFIG is mechanically connected to the wind turbine through a drive train system, which may contain high and low speed shafts, bearings and a gearbox. The rotor is fed by the bi-directional voltage-source converters. Thereby, the speed and torque of the DFIG can be regulated by controlling the rotor side converter (RSC). An‐ other feature is that DFIGs can operate both sub-synchronous and super-synchronous con‐ ditions. The stator always transfers power to the grid while the rotor can handle power in both directions. The latter is due to the fact that the PWM converters are capable of supply‐ ing voltage and current at different phase angles. In sub-synchronous operation, the rotorside converter acts as an inverter and the grid-side converter (GSC) as a rectifier. In this case, active power is flowing from the grid to the rotor. Under super-synchronous condition, the RSC operates as a rectifier and the GSC as an inverter. Consequently, active power is flow‐ ing from the stator as well as the rotor to the power grid.

**Figure 13.** Per-phase equivalent circuit of the DFIG.

**Figure 12.** Schematic of two induction generator systems.

188 Advances in Wind Power

SCIGs led the wind turbine market until the last millennium [16; 26], overtaken by the wide adoption of DFIGs. Nowadays, over 85% of the installed wind turbines utilize DFIGs [41] and the largest capacity for the commercial wind turbine product with DFIG has increased towards 5MW in industry. In the DFIG topology, the stator is directly connected to the grid through transformers and the rotor is connected to the grid through PWM power convert‐ ers. The converters can control the rotor circuit current, frequency and phase angle shifts. Such induction generators are capable of operating at a wide slip range (typically ±30% of synchronous speed). As a result, they offer many advantages such as high energy yield, re‐ duction in mechanical stresses and power fluctuations, and controllability of reactive power.

For induction generators, all the reactive power energizing the magnetic circuits must be supplied by the grid or local capacitors. Induction generators are prone to voltage instabili‐ ty. When capacitors are used to compensate power factor, there is a risk of causing self-exci‐ tation. Additionally, damping effect may give rise to power losses in the rotor. There is no direct control over the terminal voltage (thus reactive power), nor sustained fault currents.

As shown in Fig. 12(b), the rotor of the DFIG is mechanically connected to the wind turbine through a drive train system, which may contain high and low speed shafts, bearings and a gearbox. The rotor is fed by the bi-directional voltage-source converters. Thereby, the speed and torque of the DFIG can be regulated by controlling the rotor side converter (RSC). An‐ other feature is that DFIGs can operate both sub-synchronous and super-synchronous con‐ ditions. The stator always transfers power to the grid while the rotor can handle power in To analyze the DFIG's performance, it always needs to adopt its per-phase equivalent cir‐ cuit, as exampled in Fig. 13. From this figure, it can be seen that the DFIG differs from the conventional induction machine in the rotor circuit where a voltage source is added to inject voltage into the rotor circuit. The actual *d*-*q* control of the DFIG is similar to the magnitude and phase control of the injected voltage in the circuit.

The matrix form of the equation for this circuit is

$$
\begin{bmatrix} V\_s \\ V\_r/s \end{bmatrix} = \begin{bmatrix} R\_s + j(X\_s + X\_m) & -jX\_m \\ -jX\_m & R\_r/s + j(X\_r + X\_m) \end{bmatrix} \begin{bmatrix} I\_s \\ I\_r \end{bmatrix} \tag{1}
$$

The input power *P in* can be summarized from the output power *P out* and the total loss *P loss*. The latter includes stator conductor loss *P cu1*, rotor conductor loss *P cu2*, core loss *P core*, wind‐ age and friction losses *P wf* and stray load loss *P stray*. Among these losses, *P cu1* is assumed to vary with the square of the stator current *I <sup>s</sup>* while *P cu2* varies with the square of the rotor current *I <sup>r</sup>*. The stray load loss could be split into two parts: the fundamental component *P fun* occurring at the stator side and *P har* at the rotor side. Thus *P fun* is proportional to *I <sup>s</sup> 2* while *P har* is proportional to *I <sup>r</sup> 2* .

The total loss is then given by

$$P\_{loss} = 3I\_s^{\ 2}(R\_s + R\_{fan}) + 3I\_r^{\ 2}(R\_r{}^{\ \prime} + R\_{har}) + P\_{conv} + P\_{uf} \tag{2}$$

The efficiency of the DFIG is

$$\eta = \frac{P\_{out}}{P\_{in}} = \frac{\Im V\_{out} \cos \phi\_r}{6I\_s (R\_s + R\_{fan} + R\_r \text{ '} + R\_{har}) + \Im V\_{out} \cos \phi\_r} \tag{3}$$

The efficiency can be expressed as a function of the load current *I <sup>s</sup>* and this function is con‐ tinuous and monotonic. Consequently, the maximum efficiency can be found when

$$\frac{\partial \eta}{\partial I\_s} = 0\tag{4}$$

That is, the condition of maximum efficiency for DFIGs is

$$P\_{conv} + P\_{wf} = P\_{cu1} + P\_{cu2} + P\_{stray} \tag{5}$$

In order to optimize the DFIG machine design, its losses and efficiency need to derive nu‐ merically or experimentally. An additional refinement parameter is the machine's operation‐ al point. The condition of the maximum efficiency occurrence indicates: when the loaddependent losses equalise the load-invariant losses, the machine efficiency peaks. In the design and operation of DFIGs, it is beneficial to match the generator's characteristics with the site-specific wind speed by moving this maximum efficiency point close to the rated or operational load.

For control purposes, the DFIG mathematical model is based on the synchronous reference frame as follows,

$$\begin{cases} \nu\_{sd} = r\_s i\_{sd} + \frac{d\nu\_{sd}}{dt} - \alpha\_s \nu\_{sq} \\\\ \nu\_{sq} = r\_s i\_{sq} + \frac{d\nu\_{sq}}{dt} + \alpha\_s \nu\_{sd} \end{cases} \tag{6}$$

$$\begin{cases} \nu\_{rd} = r\_r i\_{rd} + \frac{d\boldsymbol{\nu}\boldsymbol{\nu}\_{rd}}{dt} - (\boldsymbol{\alpha}\_s - \boldsymbol{\alpha}\_r)\boldsymbol{\nu}\_{rq} \\\\ \nu\_{rq} = r\_r i\_{rq} + \frac{d\boldsymbol{\nu}\boldsymbol{\nu}\_{rq}}{dt} + (\boldsymbol{\alpha}\_s - \boldsymbol{\alpha}\_r)\boldsymbol{\nu}\_{rd} \end{cases} \tag{7}$$

$$\begin{cases} \boldsymbol{\psi}\_{sd} = (L\_{ls} + L\_{m})\dot{\boldsymbol{t}}\_{sd} + L\_{m}\dot{\boldsymbol{t}}\_{rd} \\ \boldsymbol{\psi}\_{sq} = (L\_{ls} + L\_{m})\dot{\boldsymbol{t}}\_{sq} + L\_{m}\dot{\boldsymbol{t}}\_{rq} \end{cases} \tag{8}$$

$$\begin{cases} \boldsymbol{\psi}\_{rd} = (L\_{lr} + L\_m)\dot{\boldsymbol{t}}\_{rd} + L\_m \dot{\boldsymbol{t}}\_{sd} \\ \boldsymbol{\nu}\_{rq} = (L\_{lr} + L\_m)\dot{\boldsymbol{t}}\_{rq} + L\_m \dot{\boldsymbol{t}}\_{sq} \end{cases} \tag{9}$$

where*rs* and *rr* are the stator and rotor resistances in Ω, *L ls*and *L lr* are the stator and rotor leakage inductances in H, *L <sup>m</sup>*is the magnetizing inductance in H. *ωs*is the synchronous elec‐ trical speed in rad/sec. *ωr*is the rotor electrical speed of the DFIG and its relation with rotor mechanical speed *ωg* is*ω<sup>r</sup>* =*Pωg*, where *P* is pole pairs.

The electromagnetic torque is given by

The efficiency of the DFIG is

190 Advances in Wind Power

operational load.

frame as follows,

h

3 cos 6 ( ' ) 3 cos

The efficiency can be expressed as a function of the load current *I <sup>s</sup>* and this function is con‐

0 *s I* ¶h

In order to optimize the DFIG machine design, its losses and efficiency need to derive nu‐ merically or experimentally. An additional refinement parameter is the machine's operation‐ al point. The condition of the maximum efficiency occurrence indicates: when the loaddependent losses equalise the load-invariant losses, the machine efficiency peaks. In the design and operation of DFIGs, it is beneficial to match the generator's characteristics with the site-specific wind speed by moving this maximum efficiency point close to the rated or

For control purposes, the DFIG mathematical model is based on the synchronous reference

*sd sd s sd s sq*

w y

w y

( )

w wy

w wy

*L L i Li L L i Li*

( )

*dt d*

y

*dt*

*rd rd r rd s r rq*

*dt d*

y

<sup>ì</sup> = + -- <sup>ï</sup>

<sup>ï</sup> = + +- ïî

*dt*

( ) ( ) *sd ls m sd m rd sq ls m sq m rq*

ìï =+ +

ï =+ + î

y

*rq rq r rq s r rd*

y

*<sup>d</sup> v ri*

<sup>ì</sup> =+ - <sup>ï</sup>

<sup>ï</sup> =+ + ïî

*v ri*

*<sup>d</sup> v ri*

*v ri*

y

y

í

ï í ï í

> *sq sq s sq s sd*

j

= = + ++ + (3)

j

<sup>=</sup> ¶ (4)

(6)

(7)

(8)

*P PPPP core wf cu cu stray* +=+ + 1 2 (5)

*in s s fun r har out r*

*out out r*

*P IR R R R V*

tinuous and monotonic. Consequently, the maximum efficiency can be found when

*P V*

That is, the condition of maximum efficiency for DFIGs is

$$T\_c = \frac{3}{2} P L\_m (i\_{sq} i\_{rd} - i\_{sd} i\_{rq}) \tag{10}$$

In DFIGs, active power is used to evaluate the power output and reactive power is responsi‐ ble for its electrical behavior in the power network. The DFIG requires some amounts of reactive power to establish its magnetic field. In case of grid-connected systems, the generator ob‐ tains the reactive power from the grid itself [48]. In case of isolated system operation, the reactive power needs to be provided by external sources such as capacitors [4] or batteries [9].

#### *(d) Switched Reluctance Generator Technologies*

Switched reluctance WTGs are characterized with salient rotors and stator. As the rotor ro‐ tates, the reluctance of the magnetic circuit linking the stator and rotor changes, and in turn, induces currents in the winding on the armature (stator). See Fig. 14 for a schematic of the switched reluctance generator system.

**Figure 14.** Schematic of a switched reluctance generator system [12].

The reluctance rotor is constructed from laminated steel sheets and has no electrical field windings or permanent magnets. As a result, the reluctance machine is simple, easy to man‐ ufacture and assembly. An obvious feature is their high reliability because they can work in harsh or high-temperature environments. Because the reluctance torque is only a fraction of electrical torque, the rotor of switched reluctance is generally large than other with electrical excitations for a given rated torque. If reluctance machines are combined with direct drive features, the machine would be extremely large and heavy, making them less favorable in wind power applications.
