*5.2. Model-Based Control*

The model-based control of a VSC-based STATCOM model consists basically of two control loops. The first one corresponds to the outer loop depending on the variable to be controlled, *Vac* or *Vdc*. The second one represents the inner loop based on the state-space model defined by expressions (17) and (18). Therefore, the conventional control uses a PI-controller, so that, the inner-control loop can be represented as:

$$
\boldsymbol{\upsilon}\_c^d = \boldsymbol{\omega}\_{\mathcal{S}} \boldsymbol{L}\_f \boldsymbol{i}\_f^q - \left(\boldsymbol{K}\_p - \frac{\boldsymbol{K}\_i}{\boldsymbol{s}}\right) \left(\boldsymbol{i}\_f^{d\*} - \boldsymbol{i}\_f^d\right) + \boldsymbol{\upsilon}\_{\mathcal{S}}^d \tag{2.3}
$$

$$\boldsymbol{\upsilon}\_{c}^{q} = -\omega\_{\mathcal{S}} L\_{f} \boldsymbol{i}\_{f}^{d} - \left(K\_{p} - \frac{K\_{i}}{s}\right) \left(\boldsymbol{i}\_{f}^{q\*} - \boldsymbol{i}\_{f}^{q}\right) + \boldsymbol{\upsilon}\_{\mathcal{S}}^{q}.\tag{24}$$

The complete details of the conventional model-based control can be found in [31].
