28

Power Electronics for Renewable Energy

Wei Qiao

University of Nebraska-Lincoln

28.1    Introduction

28.2    Power Electronics for Wind Power Systems

Basic Concepts of Wind Power Systems • Power Electronics for Control and Grid Integration of Wind Turbine Generators • Control of Power Electronic Converters for Variable-Speed Wind Turbine Generators • Power Electronics for Wind Power Plants

28.3    Power Electronics for PV Power Systems

Basic Concepts of PV Power Systems • Topologies of PV Power Systems • Topologies and Control for PV Inverters

References

28.1  Introduction

Power electronics plays an important role in wind and photovoltaic (PV) power systems. In these systems, power electronic converters are used to convert the electrical power from the form generated by wind turbine generators and PV cells to the form required by electric grids and loads in terms of frequency, voltage, power factor, harmonics, etc. This chapter reviews power electronics for control and grid integration of various wind and PV power systems.

28.2  Power Electronics for Wind Power Systems

28.2.1  Basic Concepts of Wind Power Systems

The main components of a wind power system are illustrated in Figure 28.1, which include a turbine rotor and blades, a yaw mechanism, a gearbox, a generator, a power electronic converter system, a transformer to connect the wind power system to a power grid, and a wind turbine generator control system. The wind turbine converts kinetic power in wind (i.e., aerodynamic power) to mechanical power by means of rotation of turbine rotor and blades. The mechanical power is transmitted from the turbine shaft directly or through a gearbox to the generator shaft, depending on the number of poles of the generator. If the generator has a low number of poles (e.g., four poles), a gearbox is commonly used to connect the low-speed turbine shaft and the high-speed generator shaft. If a generator with a high number of poles is used, the gearbox may not be necessary. The generator converts mechanical power to electrical power, which is fed into a power grid or used to supply local loads through optional power electronic converters and a power transformer with circuit breakers. The power transformer is normally located close to the wind turbine to avoid high currents flowing in long low-voltage cables. The use of power electronic converters enables the wind turbine generator to operate at variable speed to generate the maximum power and to have many other operational benefits, such as reactive power and power factor control, reduced mechanical stresses of the drive-train system, and enhanced grid fault ride through capability. The power transformer may be mounted in the nacelle to minimize electrical losses to the grid or at the base of the tower on the foundation. Grid connection is usually made at the foundation. The yaw mechanism rotates the rotor plane of the wind turbine to be perpendicular to the wind direction in order to extract the maximum power from wind.

FIGURE 28.1  Main components of a wind power system.

Wind power to electrical power conversion of the wind turbine generator is regulated by an electronic control system, which consists of the controllers for the generator and power converters, the turbine blades, and the yaw mechanism. The generator/power converter controller regulates the generator and power converters to generate a certain amount of electrical power with the voltage and frequency required by the power grid and loads. The turbine blade-angle controller optimizes the mechanical power output of the wind turbine and limits the mechanical power at the rated value during strong wind speed conditions. The power limitation may be done by stall, active stall, or pitch control (Akhmatov 2003). The yaw controller regulates the yaw mechanism to turn the rotor plane of the wind turbine to face the prevailing wind in order to generate the maximum power. If multiple wind turbine generators are connected to form a wind power plant, the control system of each wind turbine generator is usually coordinated by a wind plant central control system through a Supervisory Control and Data Acquisition (SCADA) System.

28.2.2  Power Electronics for Control and Grid Integration of Wind Turbine Generators

The voltage magnitude and frequency of the AC electrical power generated by a wind turbine generator are usually variable due to the variation of the wind sources. Therefore, power electronic converters are commonly employed to convert the electrical power from the form generated by the wind turbine generator into the form required by the power grid or load. Depending on the generator and the power electronics system, wind turbine generators can be divided into four types, including type 1: a fixed-speed wind turbine with a squirrel-cage induction generator (SCIG); type 2: a partial variable-speed wind turbine with a wound-rotor induction generator (WRIG), which has adjustable rotor resistances; type 3: a variable-speed wind turbine with a doubly fed induction generator (DFIG); and type 4: a variable-speed wind turbine generator with full-scale power electronic converters.

28.2.2.1  Power Electronics for Wind Turbine Type 1

Wind turbine type 1 represents one of the oldest wind power conversion technologies. It consists of an SCIG connected to the turbine rotor blades through a gearbox, as shown in Figure 28.2. The SCIG can only operate in a narrow speed range slightly higher (e.g., 0%–1% higher) than the synchronous speed. Consequently, wind turbine type 1 is commonly called a fixed-speed wind turbine. Many type 1 wind turbines use dual-speed induction generators where two sets of windings are used within the same stator frame. The first set is designed to operate in a low rotational speed (corresponding to low-wind speed operation); while the second set is designed to operate in a high rotational speed (corresponding to high-wind speed operation). The reactive power necessary to energize the magnetic circuits of the SCIG must be supplied from the power grid or a switched capacitor bank in parallel with each phase of the SCIG’s stator windings. The mechanical power generated by the wind turbine can be limited aerodynamically by stall control, active stall, or pitch control. The advantages of type 1 wind turbine are the simple and cheap construction and no need of synchronization device. Some disadvantages include (1) the wind turbine usually does not operate at optimal power points to generate the maximum power due to the fixed rotating speed; (2) the wind turbine often suffers from high mechanical stresses, since wind gusts may cause torque pulsations on the drive train; and (3) it requires a stiff power grid to enable stable operation, because the SCIG consumes reactive power during operation.

FIGURE 28.2  Configuration of wind turbine type 1.

Connecting an SCIG to a power grid produces transients that are short duration with high inrush currents, which cause severe voltage disturbances to the grid and high torque spikes in the drive train of the wind turbine. To mitigate such adverse effects, many type 1 wind turbines employ a phase-controlled soft starter to limit the rms values of the inrush currents to a level below two times of the SCIG rated current (Chen et al. 2009). The soft starter, as shown in Figure 28.2, consists of two antiparallel-connected thyristors in series with each phase of the SCIG to allow the phase current to follow in both directions. The firing angles of the thyristors are properly controlled to limit the stator currents of the SCIG by building up the magnetic flux slowly in the SCIG during the transient start-up period. The soft starter operates until the voltages at both sides of the soft starter are the same. Since the soft starter has a limited thermal capacity, at this moment, a contactor that electrically connects the wind turbine generator and the low-voltage terminals of the power transformer is energized, thus bypassing the soft starter. The contactor carries the full-load current when the connection to the grid has been completed. Finally, the capacitor banks are connected for reactive power compensation. To facilitate the excitation of the SCIG, it is desirable to connect the capacitor banks during the start-up period. However, the soft starter produces harmonic currents that can damage the capacitors, and, therefore, the connection of the capacitor banks will not be initialized until the grid connection process of the SCIG has finished.

28.2.2.2  Power Electronics for Wind Turbine Type 2

Wind turbine type 2 consists of a WRIG with an adjustable external rotor resistance connected to the turbine rotor blades through a gearbox, as shown in Figure 28.3. The adjustable external rotor resistance is implemented by a combination of external three-phase resistors connected in parallel with a power electronic circuit, which consists of a B6 diode bridge and an insulated gate bipolar transistor (IGBT) module. Both the resistors and the power electronic circuit are connected to the rotor windings via brushes and slip rings. The duty ratio of the IGBT module is controlled to dynamically adjust the effective value of the external rotor resistance of the WRIG. It is well known that the electrical power, P_e, generated by a WRIG depends on the rotor resistance and slip as follows:

FIGURE 28.3  Configuration of wind turbine type 2.

$P_e=n_p{I}_2^2\left(\frac{R_2}{s}\right)\approx n_p{V}_1^2\left(\frac{s}{R_2}\right)\left(\text{If}\left|s\right|\text{is}\text{small},\text{e}\text{.g}.,\left|s\right|\le 0.02\right)$

(28.1)

where

n_p and V₁ are the number of phases and per-phase terminal voltage of the stator windings, respectively

I₂ and R₂ are the per-phase rotor current and resistance referring to the stator side, respectively

s is the slip

The wind turbine generator starts to generate electrical power when the rotor speed is above the synchronous speed. As the wind speed increases, the input aerodynamic power increases, the rotor slip increases; as a consequence, the electrical output power increases. If the electrical output power is lower than the rated value, the external rotor resistors are short circuited by setting the duty ratio of the IGBT module to be unity. Once the electrical output power reaches its rated value, the external rotor resistance is adjusted to keep the output of the wind turbine generator constant. This is done by keeping the ratio of the total rotor resistance to the slip to be constant as follows:

$\frac{R_{2total}}{s}=\frac{R_2}{s_{rated}}$

(28.2)

where

s_rated is the rated slip when the rotor resistance is R₂

R_2total is the sum of R₂ and the effective external rotor resistance

Therefore, by adjusting the external rotor resistance using the power electronic circuit in Figure 28.3, the wind turbine generator can be operated in a wider speed range. Vestas uses this concept to achieve a speed variation of 0%–10% above the synchronous speed for their so-called OptiSlip wind turbine generators. To limit the rotor speed to its maximum value and to reduce the mechanical loads on the blades and the turbine structures, the aerodynamic power is also controlled by controlling the pitch angle of the blades in the high wind speed regions.

Figure 28.4 illustrates the detailed topology and control for the power electronic circuit to adjust the external rotor resistance of a WRIG. A surge arrester may be connected in parallel with the IGBT module to protect it against overvoltage that is created in the DC circuit due to current pulsing. The control system regulates the rotor currents flowing through the external rotor resistors. Therefore, the effect of varying rotor resistance on the rotor terminal of the WRIG is created. The control system consists of an inner-loop current controller and an outer-loop power controller. The inputs for the current controller are the measured rotor current and the rotor current reference value, which is received from the power controller. The output of the current controller is the duty ratio for switching the IGBT. When the wind turbine is connected to the grid, the power controller is activated. The inputs for the power controller are the measured electrical output power and the power reference obtained from the power-slip relationship of the WRIG. If the wind speed is not high enough to produce enough torque on the turbine for running on the rated power, the power is controlled to increase with the generator slip up to 2%. If the wind speed rises to a point where the rated power can be produced, the wind turbine will be controlled to output a constant rated power; while the slip will be controlled up to 4% by using the pitch control. Short time speed changes at rated power output are controlled by possible slip changes between the rated slip which is approximate 0.5% with no external resistance connected and the maximum allowable slip of 10%.

FIGURE 28.4  Typology and control of the power electronic circuit to adjust the external rotor resistance of a WRIG.

As illustrated in Figure 28.3, type 2 wind turbine generators still need a soft starter to limit the inrush currents during the start-up process and switched capacitor banks for reactive power compensation. Compared to wind turbine type 1, wind turbine type 2 has some advantages. It provides a partial variable-speed operation with a small power electronic converter, and, therefore, energy capture efficiency is increased; the mechanical loads to the turbine structures at high wind speeds are reduced; the flicker is mitigated and the quality of output power is improved; the action frequency of pitch control system is reduced; the noise emission is reduced in weak wind conditions because the turbine is rotating with lower speed; and the reliability of the wind turbine is improved and its life is extended. However, the connection of the external rotor resistances to the rotor terminal is usually done with brushes and slip rings, which is a drawback in comparison with SCIG due to the need of additional parts and increased maintenance requirements.

28.2.2.3  Power Electronics for Wind Turbine Type 3

Figure 28.5 illustrates the basic configuration of a type 3 wind turbine generator. It consists of a low-speed wind turbine driving a high-speed WRIG through a gearbox. The WRIG is connected to a power grid at both stator and rotor terminals. The stator is directly connected to the power grid, while the rotor is connected to the grid by a variable-frequency AC–DC–AC power electronic converter through slip rings. As a consequence, the generator in this configuration is commonly called a DFIG. In order to produce electrical power at constant voltage and frequency to the power grid over a wide operating range from subsynchronous to supersynchronous speeds, the power flow between the rotor circuit and the grid must be controlled both in magnitude and in direction. Therefore, the variable-frequency converter typically consists of two four-quadrant AC–DC voltage sources converters (VSCs), that is, a generator-side converter and a grid-side converter, connected back-to-back by a common DC link. The generator-side converter and grid-side converter usually have a rating of a fraction (typically 30%) of the generator nominal power to carry the slip power. As a consequence, the wind turbine generator can operate with the rotational speed in a range of ±30% around the synchronous speed. Below the synchronous speed, the rotor power flows from the grid to the rotor winding; above the synchronous speed, the rotor power flows from the rotor winding to the grid. In this configuration, the active and reactive power of the generator and power converter can be controlled independently. By controlling the active power of the converter, the rotational speed of the generator, and thus the speed of the rotor of the wind turbine, can be regulated. The acoustical noise from type 3 wind turbines can be effectively reduced, since the system can operate at a lower speed when the wind becomes weak. The dynamic response and controllability are excellent in comparison with type 1 and type 2 wind turbine systems. This type of wind turbines needs neither a soft-starter nor a reactive power compensator. They are typically equipped with a blade pitch control to limit the aerodynamic power during conditions of high wind speeds.

FIGURE 28.5  Configuration of wind turbine type 3.

Power electronic converters are constructed by power semiconductor devices, inductors, and capacitors with driving, protection, and control circuits to perform voltage magnitude and frequency conversion and control. There are two different types of power electronic converters: naturally commutated and forced-commutated converters. The naturally commutated converters are mainly thyristor converters, which use the line voltages of the power grid present at one side of the converters to facilitate the turn-off of the power semiconductor devices. A thyristor converter consumes inductive reactive power, and it is not able to control the reactive power. Thyristor converters are mainly used for high voltage and high power applications, such as conventional high-voltage direct-current (HVDC) systems and some flexible AC transmission system (FACTS) devices.

The forced-commutated converters are constructed by controllable power semiconductor devices, such as IGBTs, metal–oxide–semiconductor field-effect transistors (MOSFETs), integrated gate commutated thyristors (IGCTs), MOS-gate thyristors, and silicon carbide FETs, which are turned on and off at frequencies that are higher than the line frequency. Forced-commutated converters, such as IGBT-based pulsewidth modulated (PWM) VSCs, are normally used in type 3 wind turbine generators. As shown in Figure 28.6, the DFIG normally uses two bidirectional back-to-back PWM-VSCs sharing a common DC link. This type of converters has the ability to control both the active and reactive power delivered to the grid. The reactive power to the grid from the DFIG and converter can be controlled as zero or to a value required by the grid operator within the converter’s rating limit. These features offer potential for optimizing the grid integration with respect to active and reactive power control, power quality, and voltage and angular stability. The high-frequency switching of a PWM-VSC may produce harmonics and interharmonics, which are generally in the range of a few kHz. Due to the high switching frequencies, the harmonics are relatively easy to be removed by small-size filters.

FIGURE 28.6  Topology of back-to-back PWM-VSCs used in wind power systems.

In order to reduce the cost per megawatt and increase the efficiency of wind energy conversion, the nominal power of wind turbines has been continuously growing in the past years. As a consequence, there is an increasing interest in multilevel power converters especially for medium to high-power, high-voltage wind turbine applications (Carrasco et al. 2006; Portillo et al. 2006). The increase of voltage rating allows for connection of the converters of the wind turbine systems directly to the wind plant distribution grid, avoiding the use of a bulky transformer. The general idea behind the multilevel converter technology is to create a sinusoidal voltage from stepped voltage waveforms, typically obtained from an array of power semiconductors and capacitor voltage sources. The commonly used multilevel converter topologies can be classified in three categories (Rodríguez, et al. 2002), which are diode-clamped multilevel converters, capacitor-clamped multilevel converters, and cascaded multilevel converters. Figure 28.7 illustrates commonly used three-level converters using these topologies. Other topologies of multilevel converters can be found in (Hansen et al. 2002; Rodríguez, et al. 2002; Carrasco et al. 2006).

Initially, the motivation of using multilevel converters was to achieve a higher voltage and power capability. As the ratings of the components increase and the switching and conducting properties improve, other advantages of multilevel converters become more and more attractive. Multilevel converters can generate output voltages with lower distortion and lower dv/dt (Rodríguez, et al. 2002). Consequently, the size of the output filters is reduced. For the same harmonic performance, multilevel converters can be operated with a lower switching frequency when compared with two-level converters. Therefore, the switching losses of multilevel converters are reduced.

The most commonly reported disadvantage of multilevel converters with split DC link is the voltage imbalance between the DC-link capacitors. Nevertheless, for a three-level converter, this problem is not serious, and the problem in the three-level converter is mainly caused by differences in the real capacitance of each capacitor as well as the inaccuracy in the deadtime implementation or an unbalanced load (Shen and Butterworth 1997). By a proper modulation control of the switches, the imbalance problem can be solved (Lim et al. 1999).

The three-level diode-clamped multilevel converter and the three-level capacitor-clamped multilevel converter exhibit an unequal current stress on the semiconductors. It appears that the upper and lower switches in a converter leg might be derated compared to the switches in the middle. For an appropriate design of the converter, different devices are required (Rodríguez, et al. 2002). The unequal current stress and the unequal voltage stress might constitute a design problem for the multilevel converter with bidirectional switch interconnection (Hansen et al. 2002).

FIGURE 28.7  Multilevel converter topologies: (a) one leg of a diode-clamped three-level converter; (b) one leg of a capacitor-clamped three-level converter; and (c) one leg of an H-bridge cascaded three-level converter.

FIGURE 28.8  Topology of a matrix converter.

The cascaded H-bridge multilevel converter is heavy, bulky, and complex. Moreover, connecting separated DC sources between two converters in a back-to-back fashion is difficult, because a short circuit will occur when two back-to-back converters are not switching synchronously (Lai and Peng 1996).

Another type of circuit configuration is the matrix converter, as shown in Figure 28.8. A matrix converter is a one-stage AC–AC converter that is composed of an array of nine bidirectional semiconductor switches, connecting each phase of the input to each phase of the output. The basic idea behind the matrix converter is that a desired input current, a desired output voltage, and a desired output frequency can be obtained by properly operating the switches that connect the output terminals of the converter to its input terminals. In order to protect the converter, the following two control rules must be complied with. First, only one switch in an output leg is allowed to be on at any instant of time. Second, all of the three output phases must be connected to an input phase at any instant of time. The actual combination of the switches depends on the modulation strategy.

Grid faults, even far away from the location of a wind turbine, can cause voltage sags at the connection point of the wind turbine. Such voltage sags result in an imbalance between the turbine input power and the generator output power, which initiates the machine stator and rotor current transients, the converter current transient, the DC-link voltage fluctuations, and a change in speed. One of the major problems of the type 3 wind turbines operating during grid faults is that the voltage sags may cause overvoltage in the DC link and overcurrent in the DFIG rotor circuit and the generator-side converter, which in turn may destroy the generator-side converter. To protect the generator-side converter from overvoltage or overcurrent during grid faults, a crowbar circuit is usually connected between the rotor circuit of the DFIG and the generator-side converter to short-circuit the rotor windings. During this time, the generator-side converter is blocked from switching (Qiao et al. 2009), and its controllability is naturally lost. Consequently, there is no longer the independent control of active and reactive power in the DFIG. The DFIG becomes a conventional SCIG. It produces an amount of active power and starts to absorb an amount of reactive power. The grid-side converter can be operated to regulate the reactive power exchanged with the grid.

The crowbar circuit is connected between the rotor of the DFIG and the generator-side converter. The crowbar circuit may have various topologies. Figure 28.9a shows a passive crowbar (Petersson et al. 2005) consisting of a diode bridge that rectifies the rotor phase currents and a single thyristor in series with a resistor. The thyristor is turned on when the DC-link voltage reaches its limit value or the rotor current reaches its limit value. Simultaneously, the rotor circuit of the DFIG is disconnected from the generator-side converter and connected to the crowbar. When the grid fault is cleared, the generator-side converter is restarted, and after synchronization, the rotor circuit of the DFIG is connected back to the generator-side converter (Qiao et al. 2009).

FIGURE 28.9  Topologies of crowbar circuits: (a) passive crowbar; (b) active crowbar.

Figure 28.9b shows an active crowbar topology (Seman et al. 2006), which replaces the thyristor in the passive crowbar with a fully controllable semiconductor switch, such as an IGBT. This type of crowbar may be able to cut the short-circuit rotor current at anytime. If either the rotor current or the DC-link voltage exceeds the limit values, the IGBTs of the generator-side converter are blocked and the active crowbar is turned on. The crowbar resistor voltage and DC-link voltage are monitored during the operation of the crowbar. When both voltages reduce below certain values, the crowbar is turned off. After a short delay for the decay of the rotor currents, the generator-side converter is restarted and connected back to the rotor circuit of the DFIG. In both topologies, the value of the crowbar resistance has significant effects on the dynamic performance of the DFIG, such as the maximum short-circuit current of the DFIG and reactive power control capability.

28.2.2.4  Power Electronics for Wind Turbine Type 4

Wind turbine type 4 may have a variety of configurations, as illustrated in Figure 28.10. It could use an SCIG (Figure 28.10a) or a wound-rotor synchronous generator (SG) (Figure 28.10b) connected to the turbine shaft through a gearbox. It could use a wound-rotor SG (Figure 28.10c) or a permanent magnet SG (PMSG) (Figure 28.10d) connected directly to the turbine shaft without gearbox. The wound-rotor SGs in Figure 28.10b and c need an extra small AC–DC power converter, which feeds the excitation winding for field excitation. The generator is connected to the power grid through an AC–DC–AC power electronic converter, whose rating is the same as that of the electric generator used. Since the generator is decoupled from the grid, the generator can operate in a wide variable frequency range for optimal operation. The grid-side PWM converter can be used to control the active and reactive power delivered to the grid independently and to provide grid support features, such as power factor or voltage regulation. Therefore, compared to other types of wind turbines, the dynamic response of type 4 wind turbines is improved.

The AC–DC–AC converters in Figure 28.10 can be implemented by using the bidirectional back-to-back PWM-VSCs as shown in Figure 28.6 to achieve full control of the active and reactive power for the generator. A wound-rotor SG or a PMSG requires only a simple diode bridge rectifier for the generator-side converter, as shown in Figure 28.11. For a three-phase system, the diode rectifier consists of six diodes. The diode rectifier is simple and has a low cost. However, it can only be used in one quadrant. Therefore, it is not possible to control the active or reactive power of the generator by controlling the diode rectifier. In order to achieve variable-speed operation, the wind turbine equipped with a SG will require a boost DC–DC converter inserted between the diode rectifier and the DC-link, as shown in Figure 28.11.

The type 4 wind turbines with a PMSG are the most popular configuration of small wind turbines for residential and other nonutility applications, in which the grid-side converter may be a single-phase full-bridge instead of a three-phase PWM inverter. In this case, the AC terminals of the inverter may be connected between line and line or line and neutral of the power grid. Moreover, it is possible to use a matrix converter shown in Figure 28.8 to replace the AC–DC–AC converter for type 4 wind turbine systems.

28.2.3  Control of Power Electronic Converters for Variable-Speed Wind Turbine Generators

The control system of a variable-speed wind turbine generator generally consists of two parts: the electrical control on the generator and power converters and the mechanical control on the wind turbine blade pitch angle and yaw mechanism. As shown in Figure 28.12 for a type 3 wind turbine generator, the control of power converters includes the control for the generator-side converter and the control for the grid-side converter. If multiple wind turbine generators are connected to form a wind power plant, the control system of each wind turbine generator is usually coordinated by a wind power plant supervisory controller, which can generate the active and reactive power references for each wind turbine generator.

FIGURE 28.10  Configurations of wind turbine type 4 equipped with: (a) SCIG and gearbox; (b) wound-rotor SG and gearbox; (c) wound-rotor SG with a high number of poles but no gearbox; (d) PMSG but no gearbox.

FIGURE 28.11  Topology of diode rectifier and boost DC-DC converter used in type 4 wind turbine systems.

FIGURE 28.12  Control of a type 3 wind turbine generator.

28.2.3.1  Control of Power Electronic Converters for Wind Turbine Type 3

28.2.3.1.1  Control of Generator-Side Converter

Two control schemes originated from motor drives applications, that is, field oriented control and direct torque control, are commonly used for controlling the generator-side converter. In the field-oriented control, the generator-side converter can be controlled to govern the stator active and reactive power independently. This is usually achieved by rotor current regulation in an orthogonal dq reference frame aligned to one of the fluxes in the generator. The most commonly used one is the stator-flux-oriented dq reference frame, where the d-axis is aligned with the stator flux linkage vector λ_s, namely, λ_ds = λ_s and λ_qs = 0 (Qiao et al. 2008). In the stator-flux-oriented dq reference frame, the q-axis and d-axis rotor currents are decoupled to control the stator active power (or rotor speed) and the reactive power, respectively. Consequently, the overall vector control scheme for the generator-side converter consists of two cascaded control loops, as shown in Figure 28.13. The inner current control loops regulate independently the q-axis and d-axis rotor current components according to the following dynamical model of the generator (Liang et al. 2010):

$\left[\begin{array}{c}{v}_{dr}\\ v_{qr}\end{array}\right]=\left[\begin{array}{cc}{R}_r+L_r^{\prime }p& -\left({\omega }_{\lambda s}-{\omega }_{\text{r}}\right)L_r^{\prime }\\ \left({\omega }_{\lambda s}-{\omega }_r\right)L_r^{\prime }& R_r+L_r^{\prime }p\end{array}\right]\cdot \left[\begin{array}{c}{i}_{dr}\\ i_{qr}\end{array}\right]+\frac{L_m}{L_s}\left[\begin{array}{c}{v}_{ds}\\ v_{qs}-{\omega }_r{\lambda }_{ds}\end{array}\right]$

(28.3)

where

ω_λs is the rotating speed of the stator flux space vector

ω_r is the rotor rotating speed of the generator

R_r is the rotor resistance

L_m is the mutual inductance

$L_r^{\prime }$ is the rotor transient inductance, $L_r^{\prime }=\text{σ}{L}_r$ with $\text{σ}=1-L_m^2/\left(L_s{L}_r\right)$

L_s and L_r are the stator and rotor inductances, respectively

p is the derivative operator

In steady states, ω_λs is equal to the synchronous speed ω_s; v_ds = 0 and v_qs = ω_s λ_ds with the stator resistance neglected.

FIGURE 28.13  Stator-flux-oriented vector control scheme for the generator-side converter, where $v_q^c=\left({\omega }_{\lambda s}-{\omega }_r\right)L_r^{\prime }{i}_{dr}+L_m\left(v_{qs}-{\omega }_r{\lambda }_{ds}\right)/L_s$ and $v_d^c=-\left({\omega }_{\lambda s}-{\omega }_r\right)L_r^{\prime }{i}_{qr}+L_m{v}_{ds}{L}_s$.

A similar control scheme is used for the DFIG systems, where the electromagnetic torque and the stator flux of the generator are controlled by using decoupled q-axis and d-axis rotor current regulation, respectively. The actual stator flux and torque as well as the stator flux angle are determined based on the generator equations using measured voltages and currents.

The direct torque control proposed by Depenbrock (1988) eliminates the inner current loops and the needs of transformations between different references frames. In the direct torque control, the stator flux is estimated by integrating the stator voltages, and the electromagnetic torque is estimated as a cross product of the estimated stator flux vector and the measured stator current vector. The magnitudes of the stator flux and the electromagnetic torque of the generator are then controlled directly by using hysteresis comparators, as shown in Figure 28.14. The outputs of the hysteresis comparators as well as the flux angle are used directly to determine the switching states of the converter. If either the estimated flux or torque deviates from the reference more than allowed tolerance, the power switches of the converter are turned off and on in such a way that the flux and torque will return in their tolerance bands as fast as possible.

28.2.3.1.2  Maximum Power Point Tracking

The aerodynamic model of a wind turbine can be characterized by the well-known C_P-λ-β curves. C_P is called the power coefficient, which is a function of both tip speed ratio (TSR) λ and the blade pitch angle β. The TSR is defined by

$\lambda =\frac{{\omega }_{t}R}{v_w}$

(28.4)

where

R is the blade length

ω_t is the wind turbine rotational speed

v_w is the wind speed

FIGURE 28.14  Direct torque control scheme for the generator-side converter.

Given the power coefficient C_P, the mechanical power extracted by the turbine from the wind is calculated by

$P_m=\frac{1}{2}\rho A_r{v}_w^3{C}_p\left(\lambda ,\beta \right)$

(28.5)

where

ρ is the air density

A_r = πR² is the area swept by the rotor blades

At a specific wind speed, there is a unique value of ω_t to achieve the maximum power coefficient C_P, as shown in Figure 28.15 and thereby extract the maximum mechanical (wind) power. Figure 28.16 illustrates a typical power-wind speed curve of a wind turbine. If the wind speed is between the cut-in and nominal values, the wind turbine is usually operated in variable speed mode, in which the rotational speed is adjusted (by means of speed or active power control in the DFIG shown in Figure 28.13), such that the maximum value of C_P is achieved. This is called the maximum power point tracking (MPPT). The wind turbine pitch control is deactivated, and the pitch angle β is fixed. If the wind speed is above the nominal value but below the cut-off value, the rotor speed can no longer be controlled within the limits by increasing the generated power, as this would lead to overloading of the generator and/or the converter. In such a situation, the pitch control is activated to increase the pitch angle to maintain nominal mechanical power extracted from the wind.

FIGURE 28.15  Typical C_P-λ-β curves of a wind turbine.

FIGURE 28.16  A typical power-wind speed curve of a wind turbine.

There are some methods to perform MPPT control for wind turbines (Qiao et al. 2008).

1.  TSR control: The wind speed is measured by an anemometer. The controller regulates the rotating speed of the wind turbine to maintain an optimal TSR. However, the accurate wind speed may be difficult to obtain. In addition, the use of an external anemometer increases the complexity and cost of the system.

2.  Power signal feedback (PSF) control: This control requires the knowledge of the maximum power curves of the turbine, which may be obtained through simulations and practical tests. The measured speed and output power of the wind turbine generator are used to determine the target speed/power for the MPPT control by utilizing the power-wind turbine speed-wind speed characteristics of the wind turbine.

3.  Hill climbing searching (HCS) control: At a certain wind speed, when the wind turbine speed increases, the output power should normally increase as well; otherwise, the wind turbine speed should be decreased. In the HCS method, based on the comparison of the wind turbine output power at the present and previous time steps, the controller incrementally increases, decreases, or fixes the control variables to achieve the maximum power point of the system. However, this method could be ineffective for large wind turbines, since large turbines are difficult to adjust the speed fast.

In practice, MPPT controllers may use combinations of the three techniques.

28.2.3.1.3       Control of Grid-Side Converter

The objective of the grid-side converter control is to maintain a constant DC-link voltage regardless of the magnitude and direction of the rotor power. The grid-side converter can also be arranged to control the reactive power exchanged between the converter and the grid. This is usually achieved by current regulation in an orthogonal synchronously rotating dq reference frame aligned to the stator terminal voltage vector of the generator, that is, a synchronous voltage-oriented control. In this control scheme, the d-axis and q-axis components of the converter’s AC-terminal currents are decoupled to control the DC-link voltage and the reactive power, respectively. Similar to the generator-side converter control, the overall vector control scheme for the grid-side converter consists of two cascaded control loops, as shown in Figure 28.17. A phase-locked loop (PLL) is used for the transformation between the stationary αβ reference frame and the synchronously rotating dq reference frame.

FIGURE 28.17  Synchronous voltage-oriented vector control scheme for the grid-side converter.

28.2.3.2  Control of Power Electronic Converters for Wind Turbine Type 4

The control of the generator-side converter for type 4 wind turbines is achieved by stator current regulation in the rotor dq reference frame. The q-axis and d-axis stator currents are decoupled, where the q-axis stator current controls the stator active power (or rotor speed) and the d-axis stator current is controlled to be zero. Consequently, the overall vector control scheme for the generator-side converter consists of two cascaded control loops, as shown in Figure 28.18. The reference value of rotor speed or active power of the PMSG is generated by an MPPT algorithm, which is the same as that for type 3 wind turbines. In addition, the control of the grid-side converter for type 4 wind turbines is the same as that for type 3 wind turbines as well.

Figure 28.19 illustrates the control scheme for a type 4 wind turbine with a three-phase diode rectifier and a boost DC–DC converter. The input voltage and inductor current of the DC–DC converter are sensed to calculate the power delivered by the converter. The calculated power, the input voltage, and the inductor current are used by a MPPT algorithm to determine the optimal voltage reference of the DC–DC converter. The MPPT algorithm checks the power against the previous step to adjust the voltage reference of the DC–DC converter with a certain step that will cause the wind turbine to output a current and voltage so as to be operating at the maximum power under the particular conditions at that time. The reference voltage is compared to the measured voltage, and the error is passed through a voltage regulator to generate the current reference signal. The current reference is used by the inner-loop current regulator to generate a control signal, v_c, which is then used to generate the appropriate duty cycle for PWM switching of the semiconductor switch, S.

FIGURE 28.18  Vector control scheme for the generator-side converter of a type 4 wind turbine.

FIGURE 28.19  Control of boost DC/DC converter for a type 4 wind turbine.

28.2.4  Power Electronics for Wind Power Plants

A wind power plant typically consists of many individual wind turbine generators. The electrical powers generated by individual wind turbine generators are usually collected to a plant substation through three-phase AC power lines or cables and then delivered to the utility power grid through a voltage-step-up power transformer. With the increasing penetration of wind power into the electric power grids, the utilities in many countries have established grid codes for operation and grid connection of wind power plants. Many of these grid codes require wind power plants to provide frequency and voltage control, active and reactive power regulation, and quick responses under power grid transient and dynamic situations. The aim of these grid codes is to ensure that the continued growth of wind power does not compromise the power quality as well as the security and reliability of the electric power grids. The power electronic technology plays an important role in both system configurations and control of the wind power plant to fulfill the grid code requirements.

For example, the type 1 wind turbines consume reactive power during operation due to the use of SCIGs. To minimize the power losses of delivering the electrical power, mitigate the voltage fluctuations caused by wind power fluctuations, and increase voltage stability, dynamic reactive compensators, such as the thyristor-based static var compensator (SVC; Hingorani and Gyugyi 2000) or the VSC-based static synchronous compensator (STATCOM; Qiao and Harley 2007), may be used for the wind power plants consisting of type 1 wind turbines. Figure 28.20 illustrates such a system with a STATCOM. The STATCOM is a shunt-connected FACTS device. It uses a VSC to inject reactive power to or absorb reactive power from the power grid through an inductor. The VSC uses power electronic devices, such as IGBTs, IGCTs, or gate turn-OFF thyristors (GTOs) and can be configured as a multilevel bidirectional converter. Compared to the SVC, the STATCOM is able to provide faster and smoother dynamic reactive compensation and voltage control because of its rapid and continuous response characteristics. Therefore, the STATCOM is more suitable for voltage fluctuation mitigation at the PCC and grid fault ride through of the wind power plant.

FIGURE 28.20  The use of STATCOM to assist with grid connection of type 1 wind turbines.

FIGURE 28.21  VSC-based HVDC system for grid connection of off-shore wind power plants.

HVDC is an interesting alternative for long distance power transmission from an offshore wind power plant. In an HVDC transmission system, the low or medium AC voltage at the wind power plant is converted into a high DC voltage on the transmission side, and the DC power is transferred to the onshore system where the DC voltage is converted back into AC voltage, as shown in Figure 28.21. For certain power levels, an HVDC system based on the VSC technology may be used instead of the conventional thyristor-based HVDC technology. Another possible DC transmission system configuration is shown in Figure 28.22 for a wind power plant consisting of type 4 wind turbines. In this configuration, individual wind turbines are connected through a common DC grid in the off-shore wind power plant, while a grid-side power converter terminal realizes the on-shore grid connection.

FIGURE 28.22  An alternative HVDC system for grid connection of off-shore wind power plants.

FIGURE 28.23  Low-frequency HVAC transmission for off-shore wind power plants.

Because of the physical limitation of submarine cables and associated power loss and transmission capabilities, 50/60 Hz high-voltage AC (HAVC) may not be efficient or economically beneficial for long distance (e.g., ≥50 km) power transmission from an offshore wind power plant. HVDC is capable of extending the power transmission capability and distance. However, it can also increase the capital costs (i.e., equipment and installation costs) as well as operation and maintenance costs in certain perspectives. First, HVDC requires an offshore power conversion substation. Unlike HVAC where the platform mainly accommodates transformers and switchgears, a HVDC offshore platform will include more equipment and apparatus, such as high-voltage power converters. It requires a larger and heavier foundation and platform structure that leads to more expensive installations. Second, HVDC faces more challenges for fault mitigation and protection. A HVDC system needs to rely on solid-state devices, or upstream/downstream AC breakers to clear a fault. Contributions of DC link to fault currents, shutdown sequences, and limited valve short-circuit current capability can all complicate the protection and control requirements. Finally, semiconductor devices operating at a very high voltage level can raise more reliability issues than conventional AC equipment. Maintenance and repair of HVDC power converters requires special skills compared to conventional AC transformers and switchgears. These issues, together with installations at offshore sites, make the system reliability and availability performance more challenging and maintenance more expensive.

Another interesting option for long distance power transmission from an offshore wind power plant is to transmit power at a low frequency, such as 16.7 or 20 Hz. Submarine cables have strong capacitance that causes high reactive current through the cable. The reactive current is proportional to voltage and frequency. In other words, reduction of the frequency will lower the reactive current and, therefore, increase the cable capacity to allow it carrying more real power. For example, by reducing the frequency to 16.7 Hz, reactive current will decrease by 67%–72% compared to 50/60 Hz. Therefore, it enables the cable to transmit more real power over longer distance. Figure 28.23 illustrates the use of low-frequency HVAC to transmit offshore wind plant. The low-frequency AC output from individual wind turbines is stepped up to high voltage by a power transformer at the offshore substation and then sent to the shore. At the onshore frequency conversion substation, the low-frequency output is finally converted to 50/60 Hz utility voltage. Such a frequency conversion substation can use thyristor converters, which is more reliable and less expensive than IGBT-based HVDC substations.

28.3  Power Electronics for PV Power Systems

28.3.1  Basic Concepts of PV Power Systems

A PV cell uses the photoelectric effect to produce DC electrical power when exposed to sunlight and connected to a suitable load. A typical PV module (or panel) consists of multiple (e.g., 36 or 72) cells connected in series, encapsulated in a structure made of, for example, aluminum and tedlar. The series connection of cells produces a high voltage (around 25–45 V) across the terminals of the module, but the weakest cell determines the current seen at the terminals. This causes reduction in the available power, which, to some extent, can be mitigated by the use of bypass diodes, in parallel with the cells. The parallel connection of the bypass diodes with the cells solves the weakest-link problem, but the voltage seen at the terminals is reduced. Without any moving parts inside the PV module, the tear-and-wear is very low. Therefore, lifetimes of more than 25 years are easily reached for PV modules. However, the power generation capability may be reduced to 75%–80% of the nominal value due to aging. Figure 28.24 shows typical curves of the current-voltage and power-voltage characteristics of a PV cell, with insolation as a parameter. It should be pointed out that the characteristic curves also depend on cell temperature. These curves reveal that the captured power is determined by loading conditions (terminal voltage and current). At a certain temperature and insolation condition, there exists a unique terminal voltage at which the PV cell captures the maximum power from sunlight.

FIGURE 28.24  Typical current-voltage and power-voltage characteristic curves of a PV cell. (Courtesy of Ecowave, Aspendale, VIC, Australia.)

FIGURE 28.25  Main components of a grid-connected PV power system.

Figure 28.25 illustrates the main components of a grid-connected PV power system, which consists of a PV array, a PV inverter, and a control system connected to the power grid. The PV array can be a single module, a string of PV modules, or multiple parallel strings of PV modules. The PV inverter converts the DC electrical power generated by the PV array into AC electrical power with the frequency and the voltage level required by the power grid. Moreover, the use of the PV inverter enables the PV array to operate at the optimal voltage or current level to extract the maximum power from sunlight and to have other operational benefits, such as reactive power and power factor control. The control system regulates the PV inverter to perform these functions by using the information acquired from the PV array and the power grid.

28.3.2  Topologies of PV Power Systems

Three PV power system topologies are commonly used, which are the centralized inverter topology, string inverter topology, and module-integrated inverter topology (Kjaer et al. 2005; Blaabjerg et al. 2006; Carrasco et al. 2006).

FIGURE 28.26  PV grid integration using a central inverter.

28.3.2.1  Centralized Inverter Topology

In this topology, the PV power system (typical >10 kW) consists of many parallel strings that are connected to a single central inverter on the DC-side, as shown in Figure 28.26. This inverter system is characterized by high efficiency and low cost per kilowatt. However, the energy produced by the PV array cannot be maximized due to module mismatching and potential partial shading conditions. Moreover, a failure of the central inverter will result in the out of operation of the whole PV power system. Therefore, the reliability of the PV power system is limited due to the dependence of power conversion on a single inverter.

28.3.2.2  String Inverter topology

Similar to the central inverter, the PV array in this topology is divided into several parallel strings. Each PV string is connected to a designated inverter, the so-called string inverter, as shown in Figure 28.27. String inverters have the capability of separate MPPT for each PV string. This increases the energy production by reducing module mismatching and partial shading losses as well as the reliability of the PV power system. String inverters have been a standard in PV system technology for grid-connected PV power systems.

An evolution of the string inverter topology applicable for higher power levels is the multistring inverter topology, as shown in Figure 28.28. It allows the connection of multiple PV strings with separate MPPT control via DC/DC converters to a common DC/AC inverter. Consequently, a compact and cost-effective solution, which combines the advantages of central and string topologies, is achieved. This multistring topology allows the integration of PV strings of different technologies and of various orientations. These characteristics allow time-shifted solar power, which optimizes the operation efficiencies of each string separately.

FIGURE 28.27  PV grid integration using string inverters.

FIGURE 28.28  PV grid integration using a multistring inverter.

FIGURE 28.29  PV grid integration using a module-integrated inverter.

28.3.2.3  Module-Integrated Inverter Topology

This system uses one inverter (also called a microinverter) for each module, as shown in Figure 28.29. This topology optimizes the energy production of each module by adapting the inverter to the PV module characteristics using the so-called MPPT control. Although the module-integrated inverter optimizes the energy production of each module, it has a lower efficiency than the string inverter-based PV system. Module-integrated inverters are characterized by a more extended AC-side cabling, since each module of the PV system has to be connected to the available AC grid (e.g., 120 V/60 Hz). Moreover, the maintenance processes are quite complicated, especially for facade-integrated PV systems. This concept is suitable for PV systems of 50–400 W peak.

28.3.3  Topologies and Control for PV Inverters

The topologies of PV inverters are categorized on the basis of the number of power processing stages, whether an isolation is used or not, and location of the isolation. Based on the number of power processing stages, PV inverters can be classified into two major categories: single-stage inverters without DC–DC converter and dual-stage inverters with a DC–DC converter. Whether a DC–DC converter is used or not depends on PV string configuration and the voltage level of the power grid. Having more modules in series and a lower grid voltage, such as in the United States and Japan, it is possible to avoid using a DC–DC converter to boost the terminal voltage of the PV string. Thus, a single-stage PV inverter can be used, leading to a higher efficiency. The single-stage inverter must handle all tasks, such as MPPT control, grid-current control, and voltage amplification. This is the typical configuration for a centralized inverter, which must be designed to handle a peak power of twice the nominal power. In a dual-stage inverter, the DC–DC converter performs the MPPT (and perhaps voltage amplification). Depending on the control of the DC–AC inverter, the output of the DC–DC converter is either a pure DC voltage (and the DC–DC converter is only designed to handle the nominal power), or the output current of the DC–DC converter is modulated to follow a rectified sine wave (the DC–DC converter should now handle a peak power of twice the nominal power). The DC–AC inverter in the former solution is used to control the grid current by means of PWM or bang-bang operation. In the latter solution, the DC–AC inverter is switched at line frequency, unfolding the rectified current to a full-wave sine, while the DC–DC converter takes care of the current control. A high efficiency can be reached for the latter solution if the nominal power is low. On the other hand, it is advised to operate the DC–AC inverter in PWM mode if the nominal power is high.

The issue of isolation is mainly related to safety standards. Isolation is typically acquired by using a transformer (a requirement in the United States). In a single-stage inverter, a line-frequency transformer is placed between the AC terminals of the inverter and the power grid. In a dual-stage inverter, the transformer can be placed on either the grid or low-frequency side or on the high-frequency side in the DC–DC converter. The high-frequency transformer is more compact, but special attention must be paid in design to reduce losses. Modern inverters tend to use a high-frequency transformer. Commonly used high-frequency DC–DC converter topologies with isolation include full-bridge, single-inductor push–pull, double-inductor push–pull, and flyback. A full-bridge converter is usually used at power levels above 750 W due to its good transformer utilization. The main disadvantages of full-bridge topology in comparison with push–pull topology are the higher active part count and the higher transformer ratio needed for boosting the DC voltage to the grid level. In some countries where grid isolation is not mandatory, PV inverters with a DC–DC converter without isolation are usually used to simplify the PV inverter design. In this case, simple DC–DC boost, buck, buck–boost converters can be used.

A common DC–AC inverter topology is the half-bridge two-level voltage source inverter (VSI), which can create two different voltage levels and requires double DC-link voltage and double switching frequency in order to obtain the same performance as the full bridge. A variant of this topology is the standard full-bridge three-level VSI, which can create a sinusoidal grid current by applying the positive or negative DC-link or zero voltage to the grid. The semiconductor devices of the VSI can be switched at the line frequency or using PWM control.

Another interesting PV inverter topology without boost and isolation can be achieved by using multilevel concepts. This is beneficial for the power grid and results in an improvement in the total harmonic distortion (THD) performance of the output voltages and current. However, other problems such as commutation and conduction losses appear.

An MPPT control is usually implemented either in the DC–DC converter or in the DC–AC converter of a PV power system to capture the maximum power. Several algorithms can be used to implement the MPPT, for example, perturb and observe method, incremental conductance method, parasitic capacitance method, and constant voltage method (Blaabjerg et al. 2006).

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