3. Open-loop control of PMSG-based WECS with SVM

In order to achieve variable speed operation in PMSG with the maximum power efficiency, the inverter voltage should be regulated. SVM-based grid-side inverter has been implemented to maintain the inverter voltage constant irrespective of the wind speed variations. Space-vector modulation is used to enhance the inverter voltage by selecting a revolving voltage reference vector. Eight voltage vectors in a complex αβ plane, among them six active nonzero vectors (V1–V6) and two zero vectors (V0 and V7), form the look up table such as to vary the switching time of the inverter.

The main idea of this control is to transfer all the active power generated by the wind turbine to the grid and to produce no reactive power such that unity power factor is obtained. The expression for active power in d-q reference frame is given in Eq. (3) as

$$P\_{d\eta} = \frac{3}{2} \left( \upsilon\_{ds} i\_{ds} + \upsilon\_{qs} i\_{qs} \right) \tag{3}$$

The active power is the power which is transformed to electromechanical power by the machine and expressed in Eq. (4) as

$$P\_{cm} = \frac{3}{2} \left( e\_d i\_{ds} + e\_q i\_{qs} \right) \tag{4}$$

$$
\sigma\_d = -\omega\_\epsilon L\_q \dot{\imath}\_{q\text{s}} - \omega\_\epsilon \psi\_{q\text{s}} \tag{5}
$$

$$\mathbf{e}\_q = \omega\_\epsilon \mathbf{L}\_d \mathbf{i}\_{ds} + \omega\_\epsilon \boldsymbol{\psi} = \omega\_\epsilon \boldsymbol{\psi}\_{ds} \tag{6}$$

Also, the active power is found by Eq. (7) given as

$$P\_{em} = \frac{3}{2} \omega\_e \left(\psi\_d \mathbf{i}\_{qs} - \psi\_q \mathbf{i}\_{ds}\right) \tag{7}$$

Figure 3. Simulated outputs for open loop control of PMSG based WECS. (a) Rotor speed ω<sup>m</sup> in rad/s, (b) stator voltage Vabc in volts, (c) stator current Iabc in amps, (d) stator current Idq in amps, (e) electromagnetic torque in N-m, (f) DC bus voltage at various stages in volts, and (g) real and reactive powers in stator terminals and load bus.

The relationship between ω<sup>r</sup> and ω<sup>m</sup> is expressed as in Eq. (8)

$$
\omega\_r = \frac{p}{2} \omega\_m \tag{8}
$$

### where

vds, vqs: voltages in d-q axis reference frame w.r.t stator ids, iqs: currents in d-q axis reference frame w.r.t stator ϕds, ϕqs: flux linkages in d-q axis reference frame w.r.t stator ωe: electrical angular speed of stator flux in rad/s ωr: electrical speed of rotor in rad/s ωm: mechanical speed of rotor in rad/s

P: number of poles in the machine

Further, the generator torque is controlled by quadrature current component directly. Active and reactive power control is achieved by controlling direct and quadrature current components at the stator terminals, respectively. The operation and control of grid-side inverter is quite similar to that of controlling the rotor-side converter at the generator end. Two control loops are used to control the active and reactive power, respectively. An outer DC voltage control loop is used to set the d-axis current as reference for active power control. This assures that all the power coming from the rectifier is instantaneously transferred to the grid by an inverter.

The simulated results of PMSG-based WECS for the open-loop control mode have been depicted in Figure 3 from (a–f).

From the simulated outputs, it is observed that the electromagnetic torque dips to a negative value of 100 N-m with the rotor speed at 200 rad/s. The negative sign implies that the machine was operated as a generator. The stator current gradually builds up, and, after 0.9 s, it settles down, while the stator d-q axis current peaks and gradually attains its steady state value of �100 A when time elapses.

The electromagnetic torque rises and maintains at a constant value. The idea of inserting boost converter stages in between the DC link is to effectively increase the generated AC output voltage. The generated voltage gets rectified, doubled up in first converter and raises triple-fold in the second converter and reaches to 600 V. In Figure 3g, it is clear that the magnitude of real and reactive power at the stator terminals and load bus almost reaches their nominal value within the stipulated time interval of 1 s.
