Control, stability analysis and grid integration of wind turbines.

In Chapters 2 and 3 of the thesis we propose a self-scheduled control method for a doublyfed induction generator driven by a wind turbine (DFIGWT), whose rotor is connected to the power grid via two back-to-back PWM power converters. We design a controller for this system using the linear matrix inequality based approach to linear parameter varying (LPV) systems, which takes into account the nonlinear dynamics of the system. We propose a two-loop hierarchical control structure. The inner-loop current controller, which considers the synchronous speed and the generator rotor speed as a parameter vector, achieves robust tracking of the rotor current reference signals. The outer-loop electrical torque controller aims for wind energy capture maximization, grid frequency support and generates the reference rotor current. We perform a controller reduction for the inner-loop LPV controller, which is not doable by conventional model-reduction techniques, because the controller is parameter-dependent. In simulation, the reduced order controller has been tested on a nonlinear 4th order DFIG model with a two-mass model for the drive-train. Stability and high performances have been achieved over the entire operating range of the DFIGWT. More importantly, simulation results have demonstrated the capability and contribution of the proposed two-loop control systems to grid frequency support. In Chapter 4 we investigate the integral input-to-state stability (iISS) property for passive nonlinear systems. We show that under mild assumptions, a passive nonlinear system which is globally asymptotically stable is also iISS. Moreover, the integral term from the definition of the iISS property has a very simple form (like an L1 norm). These theoretical results will be useful for our stability analysis of wind turbine systems in Chapter 5. In Chapter 5 we investigate the stability of a variable-speed wind turbine operating under low to medium wind speed. The turbine is controlled to capture as much wind energy as possible. We concentrate on the mechanical level of the turbine system, more precisely on the drive-train with the standard quadratic generator torque controller. We consider both the one-mass and the two-mass models for the drive-train, with the inputs being the deviation of the active torque from an arbitrary positive nominal value and the tracking error of the generator torque. We show that the turbine system is input-to-state stable for the one-mass model and iISS for the two-mass model. Using our abstract results from Chapter 4, we identify the iISS gain of this system. We also propose an adaptive search algorithm for the optimal gain of the quadratic torque controller

Active sensor fault tolerant output feedback tracking control for wind turbine systems via T-S model

This paper presents a new approach to active sensor fault tolerant tracking control (FTTC) for offshore wind turbine (OWT) described via Takagi–Sugeno (T–S) multiple models. The FTTC strategy is designed in such way that aims to maintain nominal wind turbine controller without any change in both fault and fault-free cases. This is achieved by inserting T–S proportional state estimators augmented with proportional and integral feedback (PPI) fault estimators to be capable to estimate different generators and rotor speed sensors fault for compensation purposes. Due to the dependency of the FTTC strategy on the fault estimation the designed observer has the capability to estimate a wide range of time varying fault signals. Moreover, the robustness of the observer against the difference between the anemometer wind speed measurement and the immeasurable effective wind speed signal has been taken into account. The corrected measurements fed to a T–S fuzzy dynamic output feedback controller (TSDOFC) designed to track the desired trajectory. The stability proof with H∞ performance and D-stability constraints is formulated as a Linear Matrix Inequality (LMI) problem. The strategy is illustrated using a non-linear benchmark system model of a wind turbine offered within a competition led by the companies Mathworks and KK-Electronic

Small-Signal Modelling and Analysis of Doubly-Fed Induction Generators in Wind Power Applications

The worldwide demand for more diverse and greener energy supply has had a significant impact on the development of wind energy in the last decades. From 2 GW in 1990, the global installed capacity has now reached about 100 GW and is estimated to grow to 1000 GW by 2025. As wind power penetration increases, it is important to investigate its effect on the power system. Among the various technologies available for wind energy conversion, the doubly-fed induction generator (DFIG) is one of the preferred solutions because it offers the advantages of reduced mechanical stress and optimised power capture thanks to variable speed operation. This work presents the small-signal modelling and analysis of the DFIG for power system stability studies. This thesis starts by reviewing the mathematical models of wind turbines with DFIG convenient for power system studies. Different approaches proposed in the literature for the modelling of the turbine, drive-train, generator, rotor converter and external power system are discussed. It is shown that the flexibility of the drive train should be represented by a two-mass model in the presence of a gearbox. In the analysis part, the steady-state behaviour of the DFIG is examined. Comparison is made with the conventional synchronous generators (SG) and squirrel-cage induction generators to highlight the differences between the machines. The initialisation of the DFIG dynamic variables and other operating quantities is then discussed. Various methods are briefly reviewed and a step-by-step procedure is suggested to avoid the iterative computations in initial condition mentioned in the literature. The dynamical behaviour of the DFIG is studied with eigenvalue analysis. Modal analysis is performed for both open-loop and closed-loop situations. The effect of parameters and operating point variations on small signal stability is observed. For the open-loop DFIG, conditions on machine parameters are obtained to ensure stability of the system. For the closed-loop DFIG, it is shown that the generator electrical transients may be neglected once the converter controls are properly tuned. A tuning procedure is proposed and conditions on proportional gains are obtained for stable electrical dynamics. Finally, small-signal analysis of a multi-machine system with both SG and DFIG is performed. It is shown that there is no common mode to the two types of generators. The result confirms that the DFIG does not introduce negative damping to the system, however it is also shown that the overall effect of the DFIG on the power system stability depends on several structural factors and a general statement as to whether it improves or detriorates the oscillatory stability of a system can not be made

Full- & Reduced-Order State-Space Modeling of Wind Turbine Systems with Permanent-Magnet Synchronous Generator

Wind energy is an integral part of nowadays energy supply and one of the fastest growing sources of electricity in the world today. Accurate models for wind energy conversion systems (WECSs) are of key interest for the analysis and control design of present and future energy systems. Existing control-oriented WECSs models are subject to unstructured simplifications, which have not been discussed in literature so far. Thus, this technical note presents are thorough derivation of a physical state-space model for permanent magnet synchronous generator WECSs. The physical model considers all dynamic effects that significantly influence the system's power output, including the switching of the power electronics. Alternatively, the model is formulated in the $(a,b,c)$- and $(d,q)$-reference frame. Secondly, a complete control and operation management system for the wind regimes II and III and the transition between the regimes is presented. The control takes practical effects such as input saturation and integral windup into account. Thirdly, by a structured model reduction procedure, two state-space models of WECS with reduced complexity are derived: a non-switching model and a non-switching reduced-order model. The validity of the models is illustrated and compared through a numerical simulation study.Comment: 23 pages, 11 figure

Issues in the design of switched linear systems : a benchmark study

In this paper we present a tutorial overview of some of the issues that arise in the design of switched linear control systems. Particular emphasis is given to issues relating to stability and control system realisation. A benchmark regulation problem is then presented. This problem is most naturally solved by means of a switched control design. The challenge to the community is to design a control system that meets the required performance specifications and permits the application of rigorous analysis techniques. A simple design solution is presented and the limitations of currently available analysis techniques are illustrated with reference to this example

Wind turbine control using PI pitch angle controller

This paper suggests two methods to calculate the gains of a proportional-Integral pitch angle controller for a 5 MW wind turbine. The first method is analytical and the second one is based on simulation. Firstly, the power coefficient characteristics for different pitch angles are calculated. Secondly, the output powers vs. rotor speed curves from cut-in to cut-out wind speeds are simulated. The results from first and second analyses used to find the control gains at different wind speeds. Finally, the results are compared using a wind turbine model to determinate turbine’s tracking characteristic

General review of the MOSTAS computer code for wind turbines

The MOSTAS computer code for wind turbine analysis is reviewed, and techniques and methods used in its analyses are described. Impressions of its strengths and weakness, and recommendations for its application, modification, and further development are made. Basic techniques used in wind turbine stability and response analyses for systems with constant and periodic coefficients are reviewed

Variable gain for a wind turbine pitch control

The gain variation is made in the software logic of the pitch angle controller. The gain level is changed depending upon the level of power error. The control uses low gain for low pitch activity the majority of the time. If the power exceeds ten percent offset above rated, the gain is increased to a higher gain to more effectively limit power. A variable gain control functioned well in tests on the Mod-0 wind turbine

An active fault tolerant control approach to an offshore wind turbine model

The paper proposes an observer based active fault tolerant control (AFTC) approach to a non-linear large rotor wind turbine benchmark model. A sensor fault hiding and actuator fault compensation strategy is adopted in the design. The adapted observer based AFTC system retains the well-accepted industrial controller as the baseline controller, while an extended state observer (ESO) is designed to provide estimates of system states and fault signals within a linear parameter varying (LPV) descriptor system context using linear matrix inequality (LMI). In the design, pole-placement is used as a time-domain performance specification while H∞ optimization is used to improve the closed-loop system robustness to exogenous disturbances or modelling uncertainty. Simulation results show that the proposed scheme can easily be viewed as an extension of currently used control technology, with the AFTC proving clear “added value” as a fault tolerant system, to enhance the sustainability of the wind turbine in the offshore environment

MOD-0A 200 kW wind turbine generator design and analysis report

The design, analysis, and initial performance of the MOD-OA 200 kW wind turbine generator at Clayton, NM is documented. The MOD-OA was designed and built to obtain operation and performance data and experience in utility environments. The project requirements, approach, system description, design requirements, design, analysis, system tests, installation, safety considerations, failure modes and effects analysis, data acquisition, and initial performance for the wind turbine are discussed. The design and analysis of the rotor, drive train, nacelle equipment, yaw drive mechanism and brake, tower, foundation, electricl system, and control systems are presented. The rotor includes the blades, hub, and pitch change mechanism. The drive train includes the low speed shaft, speed increaser, high speed shaft, and rotor brake. The electrical system includes the generator, switchgear, transformer, and utility connection. The control systems are the blade pitch, yaw, and generator control, and the safety system. Manual, automatic, and remote control are discussed. Systems analyses on dynamic loads and fatigue are presented