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

Computationally Efficient Trajectory Optimization for Linear Control Systems with Input and State Constraints

This paper presents a trajectory generation method that optimizes a quadratic cost functional with respect to linear system dynamics and to linear input and state constraints. The method is based on continuous-time flatness-based trajectory generation, and the outputs are parameterized using a polynomial basis. A method to parameterize the constraints is introduced using a result on polynomial nonpositivity. The resulting parameterized problem remains linear-quadratic and can be solved using quadratic programming. The problem can be further simplified to a linear programming problem by linearization around the unconstrained optimum. The method promises to be computationally efficient for constrained systems with a high optimization horizon. As application, a predictive torque controller for a permanent magnet synchronous motor which is based on real-time optimization is presented.Comment: Proceedings of the American Control Conference (ACC), pp. 1904-1909, San Francisco, USA, June 29 - July 1, 201

Robust nonlinear generalized predictive control of a permanent magnet synchronous motor with an anti-windup compensator

This paper presents a robust nonlinear generalized predictive control (RNGPC) strategy applied to a permanent magnet synchronous motor (PMSM) for speed trajectory tracking and disturbance rejection. The nonlinear predictive control law is derived by using a newly defined design cost function. The Taylor series expansion is used to carry out the prediction in a finite horizon. No information about the external perturbation and parameters uncertainties are needed to ensure the robustness of the proposed RNGPC. Moreover, to maintain the phase current within the limits using saturation blocks, a cascaded structure is adopted and an anti-windup compensator is proposed. The validity of the proposed control strategy is implemented on a dSPACE DS1104 board driving in real-time a 0.25 kW PMSM. Experimental results have demonstrated the stability, robustness and the effectiveness of the proposed control strategy regarding trajectory tracking and disturbance rejection

Current commutation and control of brushless direct current drives using back electromotive force samples

Brushless DC machines (BLDC) are widely used in home, automotive, aerospace and military applications. The reason of this interest in different industries in this type of machine is due to their significant advantages. Brushless DC machines have a high power density, simple construction and higher efficiency compared to conventional AC and DC machines and lower cost comparing to permanent magnet AC synchronous machines. The phase currents of a BLDC machine have to commutate properly which is realised by using power semiconductors. For a proper commutation the rotor position is often obtained by an auxiliary instrument, mostly an arrangement of three Hall-effect sensors with 120 spatial displacement. In modern and cost-effective BLDC drives the focus is on replacing the noise sensitive and less reliable mechanical sensors by numerical algorithms, often referred to as sensorless or self-sensing methods. The advantage of these methods is the use of current or voltage measurements which are usually available as these are required for the control of the drive or the protection of the semiconductor switches. Avoiding the mechanical position sensor yields remarkable savings in production, installation and maintenance costs. It also implies a higher power to volume ratio and improves the reliability of the drive system. Different self-sensing techniques have been developed for BLDC machines. Two algorithms are proposed in this thesis for self-sensing commutation of BLDC machines using the back-EMF samples of the BLDC machine. Simulations and experimental tests as well as mathematical analysis verify the improved performance of the proposed techniques compared to the conventional back-EMF based self-sensing commutation techniques. For a robust BLDC drive control algorithm with a wide variety of applications, load torque is as a disturbance within the control-loop. Coupling the load to the motor shaft may cause variations of the inertia and viscous friction coefficient besides the load variation. Even for a drive with known load torque characteristics there are always some unmodelled components that can affect the performance of the drive system. In self-sensing controlled drives, these disturbances are more critical due to the limitations of the self-sensing algorithms compared to drives equipped with position sensors. To compensate or reject torque disturbances, control algorithms need the information of those disturbances. Direct measurement of the load torque on the machine shaft would require another expensive and sensitive mechanical sensor to the drive system as well as introducing all of the sensor related problems to the drive. An estimation algorithm can be a good alternative. The estimated load torque information is introduced to the self-sensing BLDC drive control loop to increase the disturbance rejection properties of the speed controller. This technique is verified by running different experimental tests within different operation conditions. The electromagnetic torque in an electrical machine is determined by the stator current. When considering the dynamical behaviour, the response time of this torque on a stator voltage variation depends on the electric time constant, while the time response of the mechanical system depends on the mechanical time constant. In most cases, the time delays in the electric subsystem are negligible compared to the response time of the mechanical subsystem. For such a system a cascaded PI speed and current control loop is sufficient to have a high performance control. However, for a low inertia machine when the electrical and mechanical time constants are close to each other the cascaded control strategies fail to provide a high performance in the dynamic behavior. When two cascade controllers are used changes in the speed set-point should be applied slowly in order to avoid stability problems. To solve this, a model based predictive control algorithm is proposed in this thesis which is able to control the speed of a low inertia brushless DC machine with a high bandwidth and good disturbance rejection properties. The performance of the proposed algorithm is evaluated by simulation and verified by experimental results as well. Additionally, the improvement on the disturbance rejection properties of the proposed algorithm during the load torque variations is studied. In chapters 1 and 2 the basic operation principles of the BLDC machine drives will be introduced. A short introduction is also given about the state of the art in control of BLDC drives and self-sensing control techniques. In chapter 3, a model for BLDC machines is derived, which allows to test control algorithms and estimators using simulations. A further use of the model is in Model Based Predictive Control (MBPC) of BLDC machines where a discretised model of the BLDC machine is implemented on a computation platform such as Field Programmable Gate Arrays (FPGA) in order to predict the future states of the machine. Chapter 4 covers the theory behind the proposed self-sensing commutation methods where new methodologies to estimate the rotor speed and position from back-EMF measurements are explained. The results of the simulation and experimental tests verifies the performance of the proposed position and speed estimators. It will also be proved that using the proposed techniques improve the detection accuracy of the commutation instants. In chapter 5, the focus is on the estimation of load torque, in order to use it to improve the dynamic performance of the self-sensing BLDC machine drives. The load torque information is used within the control loop to improve the disturbance rejection properties of the speed control for the disturbances resulting from the applied load torque of the machine. Some of the machine parameters are used within speed and load torque estimators such as back-EMF constant Ke and rotor inertia J. The accuracy with which machine parameters are known is limited. Some of the machine parameters can change during operation. Therefore, the influence of parameter errors on the position, speed and load torque is examined in chapter 5. In Chapter 6 the fundamentals of Model based Predictive Control for a BLDC drive is explained, which are then applied to a BLDC drive to control the rotor speed. As the MPC algorithm is computationally demanding, some enhancements on the FPGA program is also introduced in order to reduce the required resources within the FPGA implementation. To keep the current bounded and a high speed response a specific cost function is designed to meet the requirements. later on, the proposed MPC method is combined with the proposed self-sensing algorithm and the advantages of the combined algorithms is also investigated. The effects of the MPC parameters on the speed and current control performance is also examined by simulations and experiments. Finally, in chapter 7 the main results of the research is summarized . In addition, the original contributions that is give by this work in the area of self-sensing control is highlighted. It is also shown how the presented work could be continued and expanded

Modulated Model Predictive Control of Permanent Magnet Synchronous Motors with Improved Steady-State Performance

Finite Control Set Model Predictive Control (FCS-MPC) is an optimal control strategy that predicts the future trends of the control goals by assessing the discrete-time model of the system. FCS-MPC has many advantages, such as it has a fast dynamic response, and nonlinearities can be controlled by the customized cost function. Besides the featured benefits of the FCS-MPC strategy, the ripple in the output variable (in most cases, control variable) may be problematic due to the uncontrolled switching frequency. For that reason, the MPC-based closed-loop strategy offers a better regulation performance at high-sampling frequency. However, the selection of a low sampling rate causes an unpleasant distortion or poor power quality. A modulated model predictive control method is proposed in this work to suppress the unwanted distortion in the control variable. In the proposed method, a space vector modulator is integrated into the FCS-MPC-based control method to attain a fixed-switching frequency. By doing so, the distortions and unwanted harmonics are significantly decreased. In this paper, a modulated model predictive control (M2PC) method is proposed for controlling the permanent magnet synchronous motor. The proposed method calculates the dwell-time of the modulator stage by assessing the multi-objective cost function. The noticeable lower distortions in the stator currents are obtained by the proposed routine. All theoretical concepts are verified by extensive simulations. Based on the simulation results, the proposed method provides a better control performance for permanent magnet synchronous motors (PMSM). Furthermore, the proposed modulated MPC strategy offers superior steady-state performance compared to the conventional MPC method in all regards

Fault-tolerant Operation of Six-phase Energy Conversion Systems with Parallel Machine-side Converters

The fault tolerance provided by multiphase machines is one of the most attractive features for industry applications where a high degree of reliability is required. Aiming to take advantage of such postfault operating capability, some newly designed full-power energy conversion systems are selecting machines with more than three phases. Although the use of parallel converters is usual in high-power three-phase electrical drives, the fault tolerance of multiphase machines has been mainly considered with single supply from a multiphase converter. This study addresses the fault-tolerant capability of six-phase energy conversion systems supplied with parallel converters, deriving the current references and control strategy that need to be utilized to maximize torque/power production. Experimental results show that it is possible to increase the postfault rating of the system if some degree of imbalance in the current sharing between the two sets of threephase windings is permitted.Ministerio de Ciencia e Innovación ENE2014-52536-C2–1-R DPI2013-44278-RJunta de Andalucía P11-TEP-755

Application of Model Predictive Control in Modular Multilevel Converter for MTPA Operation and SOC Balancing

In this thesis, a one-step horizon model predictive control strategy (MPC) is implemented in a multilevel modular converter (MMC) to control the speed of an electric vehicle (EV) motor. Maximum torque per ampere (MTPA) and field weakening (FW) control strategies are used to generate reference signals for maximum torque output. The proposed control scheme aims to track the reference signal by independently regulating voltages from the MMC modules. To achieve this, the switches of the MMCs are directly controlled, eliminating the need for a pulse width modulator. A one-step horizon implementation of MPC ensures the robustness of the control system by making the real-time implementation possible. It leads to favorable performance under asymmetrical loads. The phase voltage is supplied to the motor through the MMC architecture which is composed of a large number of battery cells connected in series to supply the motor drive. Due to the non-identical characteristics of the battery, the state of charge (SOC) and the terminal voltage of the cells vary significantly at different operating conditions. The given control scheme is also incorporating a voltage balancing property that ensures the terminal voltages of all the battery cells in the MMC architecture are equalized. Finally, simulation results are presented to show the effectiveness of this control strategy and hardware is under development to validate the system performance