**2. Small wind turbine system configuration with VSMC**

makes a step change from zero to a constant value, *U*, within the turbine operating range is considered, and any issues regarding the measuring of *U* is ignored. It is also assumed that power extraction takes over instantaneously from starting at a nominated rotor angular ve‐ locity. The justification is that if motor-starting for this case results in an energy gain, it is worth pursuing. If it does not, then it is to be discarded. We show that motor-starting is

The following sections present the electrical system in which motoring and generating modes are controlled by field oriented control (FOC) through a bi-directional very sparse matrix converter (VSMC) which is connected in a backward configuration (i.e. the "rectifier" portion of the VSMC is connected to the grid and the "inverter" portion is connected to the generator). This allows a sufficient DC-link voltage for grid connection at any wind speed while the system is in the generating mode, and also permits straightforward grid synchro‐ nization where power is regulated by current control, depending on grid voltage to avoid voltage flicker. In addition, by using a small filter, sinusoidal current can be injected into the grid at unity power factor (or slightly leading or lagging power factor as desired) to improve power quality [13]. An alternative to the VSMC is the well known back-to-back converter (where the rectifier is implemented with a conventional inverter structure). However, the back-to-back converter requires some form of DC-link storage such as a capacitor, which is

One particular recent power electronics development of interest for matrix converters is the emergence of the Reverse Blocking IGBT (RB-IGBT) which has become commercially availa‐ ble and tested for matrix converter implementations. It has been shown [14] that the conduc‐ tion losses, switching losses, and conduction voltage of RB-IGBTs are lower than the current generation IGBTs which should lead to higher converter efficiencies. Another recent power electronics development is the commercialization of the Bi-directional Reverse Blocking IGBT (BRB-IGBT) for use in high power converters which may one day be used in lower power converters. A prime candidate for such switching technology is the matrix converter and its derivatives. Matrix converters (having the ability for extremely flexible bi-directional control of power in three-phase systems) in their conventional (non-sparse) form have long been criticized because of the high cost and high power losses associated with a high transis‐ tor and diode count (e.g. 18 transistors and 18 diodes in one particular form). The use of bidirectional reverse blocking devices would remove the need for external reverse voltage blocking diodes, and reduce the control requirements of a full matrix converter (only nine devices to be controlled), as well as reduce power losses in the converter. Thus, BRB-IGBT devices may lead to economical matrix-based or other converter configurations with lower power losses and simplified gate drive requirements [15, 16]. The study discussed below, uses an established implementation of bi-directional power flow in a power switch, namely, a conventional IGBT transistor within a four-diode bridge as shown in Fig.1 (the diodes pro‐ vide both reverse voltage blocking capability and bi-directional power flow control). This configuration has the advantage of a simplified switch drive circuit (only one IGBT needs to be controlled regardless of power flow) but the disadvantage of increased conduction losses in two conducting diodes. An alternative bi-directional power switch configuration consists

worth pursuing

156 Advances in Wind Power

not the case for the a VSMC.

Figure 1 illustrates the proposed HAWT, including a PMSG connected to the grid through a backward very sparse matrix converter (where the rectifier side is connected to the grid and the inverter side is connected to the generator). Fig. 1 also shows the maximum power point tracking (MPPT) controller. The current flowing to or from the generator is controlled by field oriented control (FOC). The system operates as follows. Once blade rotation is detect‐ ed, the generator is operated as a motor with the rated electromagnetic torque in the same direction as the aerodynamic torque until it reaches the nominated speed for power extrac‐ tion where the MPPT unit takes control to keep the turbine operating at the optimal tip speed ratio (*λ* opt). The reference torque is converted to a reference generator current through the FOC unit and compared to the actual current to generate the appropriate generator volt‐ age. Then the reference voltage based on space vector modulation forms the switching sig‐ nals to the VSMC.

The turbine power output, *P* m, is expressed in conventional form as:

$$P\_m = 0.5 \rho A C\_p U^3 \tag{1}$$

where *ρ* is the air density, *A* is the rotor swept area, *U* is the wind speed and *C* <sup>P</sup> is the tur‐ bine power coefficient which is related to the torque coefficient, *C* T, by

$$\mathbf{C}\_{P} = \mathbf{C}\_{T}\boldsymbol{\lambda} \tag{2}$$

where *λ* is the tip speed ratio. *C* T is approximated by [17]:

$$C\_T = a\_6 \lambda^6 + a\_5 \lambda^5 + a\_4 \lambda^4 + a\_3 \lambda^3 + a\_2 \lambda^2 + a\_1 \lambda + a\_0 \tag{3}$$

where *a* 6 to *a* 0 are turbine coefficients defined in the Appendix.

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

**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 note that the *C* T from Equation (3) applies only when power is being extracted. The starting turbine does not extract power so the wind speed does not decrease through the rotor, and the blade aerodynamics is fundamentally different. The starting line and the curve from Equation (3), intersect close to *λ* ≈ 7 which is approximately the optimum tip speed ratio. This allows the controller to employ the linear plot for motoring and then switch to the steady aerodynamic curve from Equation (3) for power generation.
