(b) V-F Control

In the islanded mode operation of PCS, it is controlled as the main power source to supply constant voltage and frequency (V-F Control). To obtain constant V-F Control, a closed loop voltage control structure was adopted. The closed loop voltage control equation using a PI controller is described below [22]:

$$\begin{cases} \nu\_{dr} = k\_p \left( 1 + \frac{1}{T\_i \ s} \right) \* \begin{pmatrix} \nu\_{drref} - \nu\_d \\ \nu\_{qref} + \begin{pmatrix} \nu\_{qref} - \nu\_d \end{pmatrix} \end{pmatrix} \tag{4}$$

where the proportional gain is represented by *kp* and the integral time constant of the voltage loop controller is represented by *Ti*, *vd* and *vq* are the voltages after the coordinate transform, from *abc* to *dq*, where these are the components of the *d* and *q* axes, respectively. While *vdre f* and *vqre f* are the voltages after the coordinate transform, also components of the *d* and *q* axes, but these represent the component of the reference voltage (*vare f* , *vbre f* and *vcre f*). Figure 6 illustrates the block diagram of the V-F Control which is equivalent to Equation (4).

**Figure 6.** Block diagram of the V-F Control structure [22]. Reprinted from [22] with permission (License 978-1-4799-7720-8/14) from U.S. Department of Energy Office of Scientific and Technical Information [22].
