Complex-Based Controller for a Three-Phase Inverter With an <italic>LCL</italic> Filter Connected to Unbalanced Grids

Abstract

A new controller for a grid connected inverter with an LCL filter is proposed in this paper. The system is described by its complex representation and the controller is designed using the complex root locus method. The complex representation allows a considerable reduction in the order of the system, simplifying the design task and making it possible to use of advanced techniques such as the complex root locus. The new complex controller adds an extra degree of freedom that makes it possible to move the poles of the systems, and improve stability and speed of response compared to the conventional controls. The paper include a detailed discussion of the effect of the gains of the controller on the root locus. The proposal is validated with simulation and experimental results.

Sliding Modes in a Class of Complex-Valued Nonlinear Systems

“…Many examples refer to three-phase electrical systems [1], where this description allows order reduction and simplifies the analysis. Examples in the electrical systems field include electrical machines [2], and power converters [3] [4], while other applications deal with mechanical rotating systems [5], the study of mechanical vibrations [6], complex-valued neural networks [7], band-pass filters [8]... Control theory tools for complex-valued systems are not extensive and include, for example, the generalisation of the Routh-Hurwitz test for complex polynomials, proposed in [9] and extended in [10], [11]. More recently, complex extensions of other linear control techniques such as the root locus method [12] and frequency-domain analysis [13] have also been reported.…”

Unified Approach to Evaluation of Real and Complex Repetitive Controllers

“…Since these linear solutions incorporate the mathematical model of the reference signal in the closedloop control system, according to the internal model principle [5], they ensure zero steady-state error for tracking periodical reference signals whose all harmonic components are in the selected set. The control strategies based on the internal model principle that are used in three-phase inverters can still be classified into three categories [6]: real controllers, which are used to separately control each phase signal or each component of the space-vector that represents the three-phase signal in a stationary reference-frame, such as in [4]; complex controllers in stationary reference frame, which are used to control the space-vector formed by a three-phase signal in the αβ reference frame, such as in [7] [8]; and real controllers in synchronous reference frame, which are used to control d and q signals in a synchronous reference frame, such as in [9]- [11], and have frequency spectrum characteristics that are similar to those obtained for complex controllers in stationary reference frame.…”

“…FIGURE 8. Poles and zeros mapping of the generic nk + m RC whose transfer function is given by(9). The RC scheme was tuned with the following parameters: n = 6; m = 1; and sampling frequency of 1.8 kHz.…”

Model predictive flexible power control for grid‐connected inverter under unbalanced network

“…The steady performances and dynamic responses of these inverters have a significant influence on their power qualities [4, 5]. Commonly, the control algorithms, guaranteeing grid integrations friendly, include PI control [6, 7], proportional–integral–resonance (PIR) control [8], sliding mode control [9] and model predictive control (MPC) [5, 10].…”