State reference design and saturated control of doubly-fed induction generators under voltage dips

ABSTRACT

In this paper, the stator/rotor currents control problem of doubly-fed induction generator under faulty line voltage is carried out. Common grid faults cause a steep decline in the line voltage profile, commonly denoted as voltage dip. This point is critical for such kind of machines, having their stator windings directly connected to the grid. In this respect, solid methodological nonlinear control theory arguments are exploited and applied to design a novel controller, whose main goal is to improve the system behaviour during voltage dips, endowing it with low voltage ride through capability, a fundamental feature required by modern Grid Codes. The proposed solution exploits both feedforward and feedback actions. The feedforward part relies on suitable reference trajectories for the system internal dynamics, which are designed to prevent large oscillations in the rotor currents and command voltages, excited by line perturbations. The feedback part uses state measurements and is designed according to Linear Matrix Inequalities (LMI) based saturated control techniques to further reduce oscillations, while explicitly accounting for the system constraints. Numerical simulations verify the benefits of the internal dynamics trajectory planning, and the saturated state feedback action, in crucially improving the Doubly-Fed Induction Machine response under severe grid faults.

KEYWORDS:

• Doubly-fed induction machines
• saturated control
• low voltage ride through
• reference trajectory planning

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Standard Blondel-Clarke-Park amplitude-preserving transformations (Leonhard, 2001) have been applied to turn three-phase variables into two-phases vectors represented in a specific reference frame; in particular, in SVO (u − v) reference frame, u-axis is aligned to the stator voltage vector which corresponds to the line voltage one, owing to the typical connection of DFIG.

2. Also referred as non-resonance condition.

3. The case of ${\mathcal{C}}^{\infty }$ inputs with infinite non-null derivatives could be operatively managed only under some conditions guaranteeing convergence and explicit computability of the summation in (28(28) $$\begin{array}{c}\hfill \left[\begin{array}{c}{z}_{iu}^{*}\left(t\right)\\ z_{iu}^{*}\left(t\right)\end{array}\right]=-\sum _{k=0}^n{A}_i^{-(k+1)}{f}_i^{\left(k\right)}\left(t\right)\end{array}$$(28) ) as n tends to infinity;

4. Clearly, the considered smoothness properties for the current references are also consistent with the relative degree of the system, in order to enable the possibility to achieve perfect tracking.

5. These considerations are carried out assuming arbitrary and fixed changes in one of the derivatives of current references and line voltage; clearly, if some of such derivatives’ jumps can be adjusted, resetting or, at least, reduction of the jumps in the oscillation-free zero dynamics can be possible (in particular, for reduction purposes, shifting the changing to higher order derivatives can be profitable owing to the lower effect of such terms in (28(28) $$\begin{array}{c}\hfill \left[\begin{array}{c}{z}_{iu}^{*}\left(t\right)\\ z_{iu}^{*}\left(t\right)\end{array}\right]=-\sum _{k=0}^n{A}_i^{-(k+1)}{f}_i^{\left(k\right)}\left(t\right)\end{array}$$(28) ), as previously discussed).

6. Note that all the values are reported to stator-side both in Tab. A1 and in simulations

7. In simulations of Figure 5, no antiwindup mechanism was adopted for the PI used in (32(32) $$\begin{array}{ccc}\hfill v_{2u}& =& k_i{\tilde{i}}_d+\lambda {\tilde{i}}_q-y_{2u},{\dot{y}}_{2u}=-k_{ii}{\tilde{i}}_{2u}+\lambda \frac{R_1}{{\sigma }_1}{\tilde{i}}_{2v}\hfill \\ \hfill v_{2v}& =& k_i{\tilde{i}}_q-\lambda {\tilde{i}}_d-y_{2v},{\dot{y}}_{2v}=-k_{ii}{\tilde{i}}_{2v}-\lambda \frac{R_1}{{\sigma }_1}{\tilde{i}}_{2u}\hfill \end{array}$$(32) ), but this is not the cause of excessive rotor current spikes.

8. It is worth noting that, due to some conservatism in the feedback part saturation bounds (half of the control effort is constantly preserved for the feedforward terms), the available rotor voltage range is not fully exploited (see Figures 8 (a)-(b)). However, the system performance under the line faults are significantly improved, keeping all the variables within the nominal range.