Optimal power tracking of PMSG based wind energy conversion systems by constrained direct control with fast convergence rates

https://doi.org/10.1016/j.ijepes.2019.105807Get rights and content

Highlights

  • Simplicity: No aerodynamic torque, wind speed or current sensors required, reduced online computation by using deadbeat inputs.

  • Effectiveness: Optimal power tracking, fast dynamics, reduced switching frequency with more balanced among legs.

  • New Techinques: Sum-of-Square Observer Design, Stability for Direct Control.

Abstract

This paper proposes a simple direct control with fast convergence rates under constraints for tracking optimal power of permanent magnet synchronous generator (PMSG) based wind energy conversion system (WECS). The simplicity features are on neglecting the following: predicted control performances, measurement of aerodynamic torque/wind speed and stator currents. The superior features are on very fast and accurate tracking performances with asymptotic convergence and well-regulated stator currents. First, a nonlinear observer is designed to observe both aerodynamic torque and stator currents. The wind speed is then inferred from the estimated aerodynamic torque and consequently, the optimal speed reference is identified. Next, the conditions of asymptotic stability for the closed-loop dynamics are formulated. Finally, a simple direct control is proposed to maximize the convergence rates in transient states and reduce switching frequency in steady states. Comparative studies with finite set model predictive control are presented to validate the advantageous features of the proposed method. The comparative results show that the superiority of the proposed method is proved by better controlled outputs with lower ripples, smaller steady-state tracking errors, faster response in transient-states, good tracking performance even for fast-varying aerodynamic torque, and lower average switching-frequency.

Introduction

In modern wind energy conversion systems (WECS), variable-speed control by switch-mode converters is the key factor contributing to the recent development of wind turbine technologies [1]. In the variable-speed operation, the tip-speed ratio is kept at a constant for the maximum power coefficient and power extracted from wind energy while fluctuated power from wind is absorbed to reduce both mechanical stresses and acoustical noises [1], [2]. In addition, power converters used in modern variable-speed WECSs can be controlled to improve the quality of generated power as required by the grid codes [2].

Recently, due to the development of permanent magnet materials and power electronics, permanent magnet synchronous generators (PMSGs) based WECSs are popular with advantages of high power density and reliability without excitation systems and gearbox, lower rotor loss and high efficiency [2], [3]. Variable-speed WECSs with PMSG operated at full wind-speed range were developed since the 1990s with full-scale back-to-back power converters [2]. Fig. 1 illustrates the most popular type of WECS with high energy conversion efficiency where the main role of the generator-side converter control system is tracking the optimal power from wind-energy via regulating the rotor speed of the generator [4].

In the optimal power tracking problem, accurate wind speed is required to generate the optimal speed reference trajectory for generator rotor [5], [6]. With tip-speed-ratio (TSR) method, the reference speed is directly computed from wind-speed to ensure that maximum power point is achieved under different wind speed conditions [7], [8]. A mechanical anemometer and wind vane are often used to continuously monitor and collect speed data of the wind [2], [9]. Recently, ultrasonic sensors can provide more accurate and reliable wind-speed information that are promising for TSR method [2]. However, additional hardware for wind-speed measurement adds cost and complexity to the system. Hence, there are different methods introduced for wind-speed estimation without wind-speed sensor proposed in [6], [10]. Most of the methods are conservative with the assumption of a slowly varying aerodynamic torque [6], or a bounded constraint of a high-order derivative of the torque [10]. Other methods such as Kalman filters [11] and intelligent-based heuristic methods [12] were introduced. However, these methods account a heuristic approach with complicated computation for application.

In addition to wind-speed estimation, variety of advanced control methods including adaptive control [8], [13], variable-structure control [6], [14], [15], [16], T-S fuzzy logic control [17], [18] advanced PI based control [19], repetitive learning control [20], optimal control [21], feed-back linearization control [22] are recently applied for the speed-tracking control problem of WECS. The mentioned methods have advantages on a regulated switching behavior such as fixed switching frequency, evenly distributed switching among phases in addition to their original advantages of optimality and/or robustness, and stability [23], [24]. However, there are two main issues (i.e., known as two gaps on constraint inclusion and optimality of PWM methods) when these advanced control methods have been applied to the power-electronics based systems of WECS. The first issue is on constraint inclusion including limited control-inputs and state-variables where advanced control designs often offer the feedback control laws neglecting the constraints (e.g., optimal feedback control solution without input constraints) [25]. The second issue is on PWM methods which approximate the continuous control inputs by the discrete switching states using average applied time [26]. Such popular PWM method as space vector PWM is a time-average approximation algorithm, which becomes complicated in multi-level converters. It is the fact that a specific PWM method is neither unique nor optimized [27]. Hence, there is a chance to exploit the modulation stage for further benefits on better control performances, switching behaviors, and optimization.

Direct control method in form of FCS-MPC is simple and promising due to the combination of discrete switching-states, optimization, and modulation into one single decision problem [24]. In the literature, FCS-MPC is considered as a nonlinear direct control method, which mitigates the two mentioned issues of indirect control methods in power electronics [28]. Numerous research papers on FCS-MPC for WECSs are published. These research works focus on various issues of predictive control for WECS such as proven stability [29], predictive controller tuning [30], [31] reducing online computation burden [32], [33], improving robustness and constraint inclusion [34], [35], improving dynamic response and reducing ripples [36]. From the reviewed research works, the advantageous properties of FCS-MPC are summarized as a straight-forward concept, flexible to design, fast control dynamics, multiple constraints inclusion, and customized cost functions. However, the cost of FCS-MPC is still on computational burden, which limits FCS-MPC on only single-step prediction. Even the advantage of horizon-one prediction is simple and robust due to short prediction; the current drawback of FCS-MPC is the extreme dependence on the single-step predicted performance. The consequences of this drawback are on variable ripples, non-smooth controlled outputs, variable switching frequencies, vulnerable to noises [25], and heuristic approach for cost function selection and stability guaranty [28], [37]. Therefore, there is a need of a new direct control method which is simple with less prediction work, reliable with stability and low switching frequency, and flexible on optimizing control performances/switching behaviors.

To achieve the abovementioned targets, this paper presents an innovative method with simplicity for the optimal power-tracking problem of variable-speed PMSG-based WECS using stability conditions, deadbeat control (DBC) inputs for faster convergence rates instead of complicated prediction. The major contributions of this paper are on a simple but effective approach without complicated prediction by utilizing the deadbeat control inputs, a stability condition to improve switching behavior, and a nonlinear observer for aerodynamic torque. This method belongs to a class of direct control methods and can be considered as an alternative of the well-known finite control set (FCS) model predictive control (MPC). Unlike other control methods, a nonlinear observer is designed to estimate both stator currents and aerodynamic torque disturbance from only rotor speed information to neglect the measurement of aerodynamic torque/wind speed and the stator currents associated with the complicated d-q frame conversion. Unlike FCS-MPC, this method does not require the predicted controlled-outputs to reduce computational burden. Generally, deadbeat control inputs are derived to neglect conventional computation on predicted control-performances. Then, the direct control can directly maximize the convergence rates in transient states and reduce switching frequency in steady states via a simple exhausted search algorithm with stability conditions. Comparative studies with FCS-MPC are also presented to prove the advantageous features of the proposed method. The comparative results show that the superiority of the proposed method comes from excellent controlled outputs with less ripples, zero steady-state tracking errors, very fast response under asymptotic stability in transient-states, good tracking performance even for fast-varying aerodynamic torque, and low average switching frequency.

Section snippets

WECS based on 2L-VSC PMSG and control problem formulation

This section formulates the control problem for tracking optimal power in variable-speed WECS. The energy conversion from aerodynamic wind power to electric power is modeled for the control system design. The control problem is then stated.

Nonlinear observer design for aerodynamic torque without Wind-Speed measurement

The sum of squares (SOS) technique is a new methodology in the literature of observer and controller design, which are attracting more researchers in control areas. In this paper, details on applying SOS technique to design an observer for WECS are introduced. The SOS technique is useful for synthesizing an observer for WECS because the powerful methodologies of Linear System can be directly applied to the nonlinear model of WECSs without any linearization stage. Hence, employing SOS technique

Simple direct control with maximum convergence rates

This section proposes a simple direct control with online-computed deadbeat inputs. First, the stability conditions for closed-loop dynamics are derived for both speed and currents. Then, a simple direct control is proposed to achieve the fast convergence rates in transient states and low switching frequency in steady-states.

Comparative studies and performance validation

This section uses comparative studies to validate the performance and prove the superiority of the proposed direct control method in comparison with the FCS-MPC. First, the advantages of the nonlinear observer are validated. Then, the superiority of the proposed direct control compared to the conventional control method such as feedback control and FCS-MPC is also exhibited under comprehensive scenarios. The conventional FCS-MPC is selected as a competitive method for the proposed method

Conclusion

In this paper, a new direct control method is proposed with fast convergence rates and a nonlinear observer for tracking optimal power of PMSG based WECS. The key simplicity feature is on using convergence rates for stability checking and deadbeat control inputs instead of predicted performances in optimization as well as using observers to neglect wind-speed and stator current measurements. Fast-dynamic response, asymptotic stability, and low switching-frequency are still achieved. This method

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This work was supported by Khalifa University, Abu Dhabi, United Arab Emirates under Award No. FSU-2018-25. This work was also supported by Nazarbayev University, Kazakhstan under the NU-ORAU Program, award no. SST2017030.

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